EPA-660/3-75-038
JUNE 1975
                                Ecological Research Series
 valuation  of Mathematical  Models
for  Temperature Prediction  in
Deep Reservoirs
                                  Office of Research and Development
                                 U.S. Environmental Protection Agency
                                        Corvailis, Oregon 9



-------
                      RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development,
U.S. Environmental Protection Agency, have been grouped into
five series.  These five broad categories were established to
facilitate further development and application of environmental
technology.  Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in
related fields.  The five series are:

          1.   Environmental Health Effects Research
          2.   Environmental Protection Technology
          3.   Ecological Research
          4.   Environmental Monitoring
          5.   Socioeconomic Environmental Studies

This report has been assigned to the ECOLOGICAL RESEARCH STUDIES
series.  This series describes research on the effects of pollution
on humans, plant and animal species, and materials.  Problems are
assessed for their long- and short-term influences.  Investigations
include formation, transport, and pathway studies to determine the
fate of pollutants and their effects.  This work provides the technical
basis for setting standards to minimize undesirable changes in living
organisms in the aquatic, terrestrial and atmospheric environments.

                         EPA REVIEW NOTICE

This report has been reviewed by the Office of Research and
Development, EPA, and approved for publication.  Approval does
not signify that the contents necessarily reflect the views and
policies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement or
recommendation for use.

-------
                                          EPA-660/3-75-038
                                          JUNE 1975
         EVALUATION OF MATHEMATICAL MODELS FOR

       TEMPERATURE PREDICTION IN DEEP RESERVOIRS

                            By

                    Frank L.  Parker
                   Barry  A. Benedict
                     Chii-ell Tsai

                Vanderbilt University

                Nashville, Tennessee
                   Grant No.  R-800613
                Program Element 1BA032
                   ROAP 21AJH/Task 12
                    Project Officer


                     Bruce Tichenor
Pacific Northwest Environmental Research Laboratory
         National Environmental Research Center
                Corvallis,  Oregon  97330
         NATIONAL ENVIRONMENTAL RESEARCH CENTER
           OFFICE OF RESEARCH AND DEVELOPMENT
          U. S. ENVIRONMENTAL PROTECTION AGENCY
                 CORVALLIS, OREGON  97330

             For *ale by the Superintendent of Document*, U.S. Government
                   Printing Office, Washington, D.C. 20402

-------
                               ABSTRACT






    The deep reservoir model with one-dimensional assumptions can be




applied to a reservoir or lake where the principal variation of flow




characteristics is in the vertical direction.  Among the models evaluated,




the MIT deep reservoir model appears to be most easily used and to give




results most compatible with the measured temperatures.  The temperature




predicted is strongly dependent upon the magnitude of the absorption co-




efficient of water, and the diffusion coefficient.  However, our sensi-




tivity analysis shows that an absorption coefficient of about 0075m




and a diffusion coefficient of 15 to 20 times molecular diffusion are




appropriate choices for the seven TVA reservoirs studied.  The determina-




tion of whether or not a reservoir model depends on the Densimetric Froude




number.  However, the representativeness of the result is not solely depen-




dent upon the Densimetric Froude number.  By the use of a fitted curve to




the measured temperatures, it was possible to determine the maximum standard




error of estimate for the predicted outlet level temperature, 1.6°C.  Temper-




atures on individual days may exceed those values and they surely are ex-




ceeded at other depths in the reservoir.  These limits are suggested as the




limit of accuracy of these types of models.




    This report was submitted in fulfillment of Grant R-800613 by Vanderbilt




University, Nashville, Tennessee, under the sponsorship of the Environmental




Protection Agency.  Work was completed as of June, 1975.
                                     ii

-------
                            TABLE OF CONTENTS


                                                                         Page
List of Figures  ............................   v
List of Tables ............................

Section I
   Conclusions .............................   1

Section II
   Recommendations ...........................   3

Section III
   Introduction .............................   4

Section IV
   Analysis of Deep Reservoir Models ..................   8
   General Description of Deep Reservoir Models .............   9
   Water Resources Engineers' Model ...................  24
      Principal Assumptions .......................  25
      Factors Considered and the Basic Equations ............  25
     ' Direct Absorption of Solar Radiation ...............  25
      Selective Withdrawal .......................  26
      Depth and Velocity Distribution of Inflow .............  27
      Internal Mixing ..........................  28
      Governing Equation ........................  29
      Verification ...........................  33
      Results of Test Run ..................  ......  33
   MIT Model ..............................  39
      Principal Assumptions .......................  39
      Factors Considered and the Basic Equations ............  43
      Varification ........ . ..................  48
      Sensitivity Analysis .......................  48
   Cornell Model ............................  48
      Assumptions ............................  48
      Basic Equations ..........................  49
      Verification ...........................  52
      Results of Test Run ........................  53
   Problems with Deep Reservoirs Models .................  58

Section V
   Sensitivity Analysis .........................  64
   Fontana Reservoir ..........................  69
   Douglas Reservoir ..........................  91
   Cherokee Reservoir ..........................  109
   Norris Reservoir ...........................  126
   South Holston Reservoir .......................  140

                                     iii

-------
   Hiwasee Reservoir 	  158
   Fort Loudon Reservoir 	  176

Section VI
   Analysis of Data	197

References	204
                                       iv

-------
                                  LIST OF FIGURES


                                                                          Page


Figure 1            Reservoir Representation                              11

Figure 2            WRE Model -- Effect of Thickness of
                    Horizontal Layer (July 6, 1966)                       35

Figure 3            WRE Model -- Effect of Thickness of
                    Horizontal Layer (Sept. 1, 1966)                      36

Figure 4            WRE Model -- Effect of Thickness of
                    Horizontal Layer (Dec. 1, 1966)                       37

Figure 5            WRE Model -- Effects of Diffusion Coefficient
                    (July 6, 1966)                                        40

Figure 6            WRE Model -- Effects of Diffusion Coefficient
                    (Sept. 1, 1966)                                       41

Figure 7            WRE Model -- Effects of Diffusion Coefficient
                    (Dec. 1, 1966)                                        42

Figure 8            Cornell Model Test Run Results
                    July 6, 1966                                          55

Figure 9            Cornell Model Test Run Results
                    Septemper 1, 1966                                     56

Figure 10           Cornell Model Test Run Results
                    December 1, 1966                                      57

Figure 11           Surface Layer Schematic                               61

Figure 12           Fontana Reservoif   Measured Temperature
                    Profile                                               72

Figure 13           Fontana Reservoir   Computed Temperature
                    Profile                                               72

Figure 14           Fontana Reservoir - Computed Outflow Temperature      76

Figure 15           Fontana Reservoir   Layer Thickness Sensitivity       76
                    Day 75

Figure 16           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 132                                               77

-------
Figure 17           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 187                                               77

Figure 18           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 215                                               78

Figure 19           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 244                                               78

Figure 20           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 285                                               79

Figure 21           Fontana Reservoir   Layer Thickness Sensitivity
                    Day 335                                               79

Figure 22           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 75                                   80

Figure 23           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 132                                  80

Figure 24           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 187                                  81

Figure 25           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 215                                  81

Figure 26           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 244                                  82

Figure 27           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 285                                  82

Figure 28           Fontana Reservoir   Absorption Coefficient
                    Sensitivity, Day 335                                  83

Figure 29           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 75                                   83

Figure 30           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 132                                  84

Figure 31           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 187                                  84

Figure 32           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 215                                  85

Figure 33           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 244                                  85
                                           vi

-------
Figure 34           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 285                                  86

Figure 35           Fontana Reservoir   Extinction Coefficient
                    Sensitivity, Day 335                                  86

Figure 36           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 75                                   87

Figure 37           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 132                                  87

Figure 38           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 187                                  88

Figure 39           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 215                                  88

Figure 40           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 244                                  89

Figure 41           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 285                                  89

Figure 42           Fontana Reservoir   Diffusion Coefficient
                    Sensitivity, Day 335                                  90

Figure 43           Douglas Reservoir   Computed Temperature
                    Profile                                               93

Figure 44           Douglas Reservoir   Computed Outflow
                    Temperature                                           96

Figure 45           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 69                                   96

Figure 46           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 121                                  97

Figure 47           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 186                                  97

Figure 48           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 218                                  98

Figure 49           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 250                                  98

Figure 50           Douglas Reservoir   Layer Thickness
                    Sensitivity, Day 276                                  99
                                          vii

-------
Figure 51           Douglas Reservoir - Absorption Coefficient
                    Sensitivity, Day 69                                   99

Figure 52           Douglas Reservoir   Absorption Coefficient
                    Sensitivity, Day 121                                  100

Figure 53           Douglas Reservoir   Absorption Coefficient
                    Sensitivity, Day 186                                  100

Figure 54           Douglas Reservoir   Absorption Coefficient
                    Sensitivity, Day 218                                  101

Figure 55           Douglas Reservoir   Absorption Coefficient
                    Sensitivity, Day 250                                  101

Figure 56           Douglas Reservoir - Absorption Coefficient
                    Sensitivity, Day 276                                  102

Figure 57           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 69                                   102

Figure 58           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 121                                  103

Figure 59           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 186                                  103

Figure 60           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 218                                  104

Figure 61           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 250                                  104

Figure 62           Douglas Reservoir   Extinction Coefficient
                    Sensitivity, Day 276                                  105

Figure 63           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 69                                   105

Figure 64           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 121                                  106
                                                                           i
Figure 65           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 186                                  106

Figure 66           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 218                                  107

Figure 67           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 250                                  107
                                          viii

-------
Figure 68           Douglas Reservoir   Diffusion Coefficient
                    Sensitivity, Day 276                                  108

Figure 69           Cherokee Reservoir   Computed Temperature
                    Profile                                               112

Figure 70           Cherokee Reservoir   Computed Outflow
                    Temperature                                           113

Figure 71           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 66                                   113

Figure 72           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 123                                  114

Figure 73           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 186                                  114

Figure 74           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 213                                  115

Figure 75           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 248                                  115

Figure 76           Cherokee Reservoir   Layer Thickness
                    Sensitivity, Day 277                                  116

Figure 77           Cherokee Reservoir   Absorption Coefficient
                    Sensitivity, Day 66                                   116

Figure 78           Cherokee Reservoir   Absorption Coefficient
                    Sensitivity, Day 123                                  117

Figure 79           Cherokee Reservoir   Absorption Coefficient
                    Sensitivity, Day 186                                  117

Figure 80           Cherokee Reservoir   Absorption Coefficient
                    Sensitivity, Day 213                                  118

Figure 81           Cherokee Reservoir   Absorption Coefficient
                    Sensitivity, Day 248                                  118

Figure 82           Cherokee Reservoir - Absorption Coefficient
                    Sensitivity, Day 277                                  119

Figure 83           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 66                                   119

Figure 84           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 123                                  120
                                            ix

-------
Figure 85           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 186                                  120

Figure 86           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 213                                  121

Figure 87           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 248                                  121

Figure 88           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 277                                  122

Figure 89           Cherokee Reservoir   Extinction Coefficient
                    Sensitivity, Day 66                                   122

Figure 90           Cherokee Reservoir - Diffusion Coefficient
                    Sensitivity, Day 123                                  123

Figure 91           Cherokee Reservoir - Diffusion Coefficient
                    Sensitivity, Day 186                                  123

Figure 92           Cherokee Reservoir   Diffusion Coefficient
                    Sensitivity, Day 213                                  124

Figure 93           Cherokee Reservoir   Diffusion Coefficient
                    Sensitivity, Day 248                                  124

Figure 94           Cherokee Reservoir   Diffusion Coefficient
                    Sensitivity, Day 277                                  125

Figure 95           Norris Reservoir   Computed Temperature
                    Profile                                               127

Figure 96           Norris Reservoir   Computed Outflow
                    Temperature                                           129

Figure 97           Norris Reservoir   Layer Thickness
                    Sensitivity, Day 106                                  129

Figure 98           Norris Reservoir   Layer Thickness
                    Sensitivity, Day 139                                  130

Figure 99           Norris Reservoir   Layer Thickness
                    Sensitivity, Day 183                                  130

Figure 100          Norris Reservoir   Layer thickness
                    Sensitivity, Day 225                                  131

Figure 101          Norris Reservoir   Layer Thickness
                    Sensitivity, Day 252                                  131

-------
Figure 102          Norris Reservoir   Absorption Coefficient
                    Sensitivity, Day 106                                  132

Figure 103          Norris Reservoir   Absorption Coefficient
                    Sensitivity, Day 106                                  132

Figure 104          Norris Reservoir   Absorption Coefficient
                    Sensitivity, Day 183                                  133

Figure 105          Norris Reservoir   Absorption Coefficient
                    Sensitivity, Day 225                                  133

Figure 106          Norris Reservoir   Absorption Coefficient
                    Sensitivity, Day 252                                  134

Figure 107          Norris Reservoir   Extinction Coefficient
                    Sensitivity, Day 106                                  134

Figure 108          Norris Reservoir   Extinction Coefficient
                    Sensitivity, Day 139                                  135

Figure 109          Norris Reservoir   Extinction Coefficient
                    Sensitivity, Day 183                                  135

Figure 110          Norris Reservoir   Extinction Coefficient
                    Sensitivity, Day 225                                  136

Figure 111          Norris Reservoir   Extinction Coefficient
                    Sensitivity, Day 252                                  136

Figure 112          Norris Reservoir   Diffusion Coefficient
                    Sensitivity, Day 106                                  137

Figure 113          Norris Reservoir   Diffusion Coefficient
                    Sensitivity, Day 139                                  137

Figure 114          Norris Reservoir - Diffusion Coefficient
                    Sensitivity, Day 183                                  138

Figure 115          Norris Reservoir   Diffusion Coefficient
                    Sensitivity, Day 225                                  138

Figure 116          Norris Reservoir   Diffusion Coefficient
                    Sensitivity, Day 252                                  139

Figure 117          South Holston Reservoir   Measured Temperature
                    Profile                                               142

Figure 118          South Holston Reservoir   Computed Temperature
                    Profile                                               145
                                           XI

-------
Figure 119          South Holston Reservoir   Computed Outflow
                    Temperature                                           145

Figure 120          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 78                                   146

Figure 121          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 142                                  146

Figure 122          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 203                                  147

Figure 123          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 245                                  147

Figure 124          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 299                                  148

Figure 125          South Holston Reservoir   Layer Thickness
                    Sensitivity, Day 362                                  148

Figure 126          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 78                       149

Figure 127          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 142                      149

Figure 128          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 203                      150

Figure 129          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 245                      150

Figure 130          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 299                      151

Figure 131          South Holston Reservoir   Absorption
                    Coefficient Sensitivity, Day 362                      151

Figure 132          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 78                       152

Figure 133          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 142                      152

Figure 134          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 203                      153

Figure 135          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 245                      153

Figure 136          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 299                      154
                                           xii

-------
Figure 137          South Holston Reservoir   Extinction
                    Coefficient Sensitivity, Day 362                      154

Figure 138          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 78                       155

Figure 139          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 142                      155

Figure 140          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 203                      156

Figure 141          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 245                      156

Figure 142          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 299                      157

Figure 143          South Holston Reservoir   Diffusion
                    Coefficient Sensitivity, Day 362                      157

Figure 144          Hiwassee Reservoir   Measured Temperature
                    Profile                                               162

Figure 145          Hiwassee Reservoir   Computed Temperature
                    Profile                                               162

Figure 146          Hiwassee Reservoir   Computed Outflow
                    Temperature                                           163

Figure 147          Hiwassee Reservoir   Layer Thickness
                    Sensitivity, Day 80                                   163

Figure 148          Hiwassee Reservoir   Layer Thickness
                    Sensitivity, Day 148                                  164

Figure 149          Hiwassee Reservoir - Layer Thickness
                    Sensitivity, Day 209                                  164

Figure 150          Hiwassee Reservoir   Layer Thickness
                    Sensitivity, Day 267                                  165

Figure 151          Hiwassee Reservoir   Layer Thickness
                    Sensitivity, Day 302                                  165

Figure 152          Hiwassee Reservoir   Layer Thickness
                    Sensitivity, Day 364                                  166

Figure 153          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 80                       166
                                          xiii

-------
Figure 154          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 148                      167

Figure 155          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 209                      167

Figure 156          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 267                      168

Figure 157          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 302                      168

Figure 158          Hiwassee Reservoir   Absorption
                    Coefficient Sensitivity, Day 364                      169

Figure 159          Hiwassee Reservoir   Extinction
                    Coefficient Sensitivity, Day 80                       169

Figure 160          Hiwassee Reservoir - Extinction
                    Coefficient Sensitivity, Day 148                      170

Figure 161          Hiwassee Reservoir   Extinction
                    Coefficient Sensitivity, Day 209                      170

Figure 162          Hiwassee Reservoir   Extinction
                    Coefficient Sensitivity, Day 267                      171

Figure 163          Hiwassee Reservoir   Extinction
                    Coefficient Sensitivity, Day 302                      171

Figure 164          Hiwassee Reservoir   Extinction
                    Coefficient Sensitivity, Day 364                      172

Figure 165          Hiwassee Reservoir   Diffusion
                    Coefficient Sensitivity, Day 80                       172

Figure 166          Hiwassee Reservoir   Diffusion
                    Coefficient Sensitivity, Day 148                      173

Figure 167          Hiwassee Reservoir   Diffusion
                    Coefficient Sensitivity, Day 209                      173

Figure 168          Hiwassee Reservoir   Diffusion
                    Coefficient Sensitivity, Day 267                      174

Figure 169          Hiwassee Reservoir   Diffusion
                    Coefficient Sensitivity, Day 302                      174

Figure 170          Hiwassee Reservoir - Diffusion
                    Coefficient Sensitivity, Day 364                      175
                                           xiv

-------
Figure 171


Figure 172


Figure 173


Figure 174


Figure 175


Figure 176


Figure 177


Figure 178


Figure 179


Figure 180


Figure 181


Figure 182


Figure 183


Figure 184


Figure 185


Figure 186


Figure 187
Fort Loudon Reservoir
Profile

Fort Loudon Reservoir
Profile

Fort Loudon Reservoir
Temperature

Fort Loudon Reservoir
Sensitivity, Day 76

Fort Loudon Reservoir
Sensitivity, Day 132
Measured Temperature


Computed Temperature


Computed Outflow


Layer Thickness


Layer Thickness
Fort Loudon Reservoir - Layer Thickness
Sensitivity, Day 204
Fort Loudon Reservoir
Sensitivity, Day 226

Fort Loudon Reservoir
Sensitivity, Day 253

Fort Loudon Reservoir
Sensitivity, Day 280

Fort Loudon Reservoir
Sensitivity, Day 343
Layer Thickness


Layer Thickness


Layer Thickness


Layer Thickness
Fort Loudon Reservoir   Absorption
Coefficient Sensitivity, Day 76

Fort Loudon Reservoir   Absorption
Coefficient Sensitivity, Day 132

Fort Loudon Reservoir   Absorption
Coefficient Sensitivity, Day 204

Fort Loudon Reservoir - Absorption
Coefficient Sensitivity, Day 226

Fort Loudon Reservoir   Absorption
Coefficient Sensitivity, Day 253

Fort Loudon Reservoir   Absorption
Coefficient Sensitivity, Day 280

Fort Loudon Reservoir - Absorption
Coefficient Sensitivity, Day 343
178


181


181


182


182


183


183


184


184


185


185


186


186


187


187


188


188
                                           xv

-------
Figure 188          Fort Loudon Reservoir   Extinction                    189
                    Coefficient Sensitivity, Day 76

Figure 189          Fort Loudon Reservoir   Extinction                    189
                    Coefficient Sensitivity, Day 132

Figure 190          Fort Loudon Reservoir   Extinction                    190
                    Coefficient Sensitivity, Day 204

Figure 191          Fort Loudon Reservoir   Extinction                    190
                    Coefficient Sensitivity, Day 226

Figure 192          Fort Loudon Reservoir   Extinction                    191
                    Coefficient Sensitivity, Day 253

Figure 193          Fort Loudon Reservoir   Extinction                    191
                    Coefficient Sensitivity, Day 280

Figure 194          Fort Loudon Reservoir   Extinction                    192
                    Coefficient Sensitivity, Day 343

Figure 195          Fort Loudon Reservoir   Diffusion                     192
                    Coefficient Sensitivity, Day 76

Figure 196          Fort Loudon Reservoir   Diffusion                     193
                    Coefficient Sensitivity, Day 132

Figure 197          Fort Loudon Reservoir   Diffusion                     193
                    Coefficient Sensitivity, Day 204

Figure 198          Fort Loudon Reservoir   Diffusion                     194
                    Coefficient Sensitivity, Day 226

Figure 199          Fort Loudon Reservoir - Diffusion                     194
                    Coefficient Sensitivity, Day 253

Figure 200          Fort Loudon Reservoir   Diffusion                     195
                    Coefficient Sensitivity, Day 280

Figure 201          Fort Loudon Reservoir   Diffusion                     195
                    Coefficient Sensitivity, Day 343
                                           xvi

-------
                                 LIST OF TABLES
Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8



Table 9



Table 10



Table 11



Table 12



Table 13



Table 14



Table 15



Table 16
Assumptions

Input Parameters

Factors Involved in Analysis

Model Construction

Parameters Varied in Sensitivity Analysis

Frequency Analysis of the Wind Speed

Legend for Figures 12-201

Statistical Analysis for the Predicted
Water Temperature at Outlet Level
Fontana Reservoir, 1966

Statistical Analysis for 'the Predicted
Surface Water Temperature   Fontana
Reservoir, 1966

Statistical Analysis for the Predicted
Water Temperature at Outlet Level
Douglas Reservoir, 1969

Statistical Analysis for the Predicted
Surface Water Temperature   Douglas
Reservoir, 1969

Statistical Analysis for the Predicted
Water Temperature at Outlet Level
Cherokee Reservoir, 1967

Statistical Analysis for the Predicted
Surface Water Temperature   Cherokee
Reservoir, 1967

Statistical Analysis for the Predicted
Surface Water Temperature   Morris
Reservoir, 1972

Statistical Analysis for the Predicted
Water Temperature at Outlet Level
South Holston Reservoir, 1953

Statistical Analysis for the Predicted
Surface Water Temperature   South Holston
Reservoir, 1953
                       xvii
Page

 14, 15

 16, 17, 18, 19

 20, 21

 22, 23

 66

 70

 71



 73



 74



 94



 95



 110



 111



 128



 143



 144

-------
Table 17



Table 18



Table 19



Table 20



Table 21


Table 22


Table 23
Statistical Analysis for the Predicted
Water Temperature at Outlet Level -
Hiwassee Reservoir, 1947

Statistical Analysis for the Predicted
Surface Water Temperature   Hiwassee
Reservoir, 1947

Statistical Analysis for the Predicted
Water Temperature at Outlet Level
Fort Loudon Reservoir, 1971

Statistical Analysis for the Predicted
Surface Water Temperature - Fort Loudon
Reservoir, 1971

Least Squares Curve Fit for Measured
Surface Water Temperature

Least Squares Curve Fit for Measured
Water Temperature at Outlet Level

Densiraetrie Froude Numbers for Some
TVA Reservoirs
160



161



179



180


198


199


203
                                          xviii

-------
                                SECTION I

                               CONCLUSIONS

1.  This study losing field data indicates that the deep reservoir model
    with one-dimensional assumptions can be applied to a reservoir or
    lake where the principal variation of flow characteristics is in
    the vertical direction.  The factors considered in the heat trans-
    port equation must include the heat gained or lost through the
    water surface, heat transported by inflow, outflow and vertical
    advection, and the mixing mechanism due to diffusion and convection.

2.  Among the models evaluated, the MIT deep reservoir model appears to
    be most easily used and to give results most compatible with the
    measured temperatures.

3.  The temperature predicted is strongly dependent upon the magnitude
    of the absorption coefficient of water, and the diffusion coefficient.
    However, our sensitivity analysis shows that the value of   about
    0.75m"  and a diffusion coefficient of 15 to 20 times molecular
    diffusion are appropriate choices for the seven TVA reservoirs
    studied.

4.  The Densimetric Froude number is an important parameter to indicate
    the degree of stratification of a body of water.  The determination
    of whether or not a reservoir or lake is suitable for the application
    of a deep reservoir model depends on the Densimetric Froude number.

-------
    However, the representativeness of the result is  not solely dependent



    upon the Densimetric Froude number.





5.  Perhaps, the most important water temperatures are those at the



    surface and in the withdrawal layer.   By the use  of a fitted



    curve to the measured temperatures at these elevations,  it was



    possible to determine the maximum standard error  of estimate for



    the predicted surface temperature, 1.2 C,  and of  the predicted



    outlet level temperature, 1.6°C.   Temperature variations on



    individual days may exceed these values and they  surely  are exceeded



    at other depths in the reservoir.  These limits are suggested as



    the limit of accuracy of these types  of models.





6.  In a reservoir where the temperature  goes below 4°C, the density



    instead of temperature, should be used for the determination of the



    entrance level of inflow, the thickness of withdrawal layer and the



    condition for the convection to occur.  The models evaluated, MIT,



    WRE and Cornell must be modified before they can  be applied to  such



    conditions.

-------
                            SECTION II
                          RECOMMENDATIONS

1.  Though it is possible to further refine the mathematical models
    used in temperature predictions for deep reservoirs, it appears
    that at this time it would be advisable for operational purposes
    to utilize the existing models, such as the MIT model, which
    have been most thoroughly verified.
2.  Though an analysis of the reservoir temperatures has been made
    for a series of the TVA reservoirs, no analysis has yet been
    made for the temperature distribution of a single reservoir over
    a period of years to determine the proper coefficients to be
    used in the model.  This should be done.
3.  An intensive thermal analysis of reservoirs in the southeast
    section of the United States has been made.  Such an analysis
    needs to be. made for other sections of the country to determine
    if the coefficients most suitable for the southeastern section
    of the United States are also most suitable for the other sections.
4.  For a better theoretical and emperical understanding of thermal
    regimes in reservoirs, further detailed laboratory and field
    studies on the effects of multiple inflows on the assumption of
    horizontal homogeneity need to be carried out.  In addition,
    further field studies on withdrawals is required to determine
    the layers affected and the internal currents induced by the
    intermittent releases.

-------
                               SECTION III




                              INTRODUCTION




    Water quality is one of the major considerations in water resources


planning, and water temperature is a key factor in determining water


quality.  Due to the influence of temperature on the physical and chemi-


cal properties of water and on the aquatic life within a water body, a


reasonable prediction of the temporal and spatial variation of the


thermal structure within the reservoir is essential for successful


management.  This has become even more evident with passage of PL 92-500,


Federal Water Pollution Control Act Amendments of 1972, where thermal


water quality standards are specifically included in the term "water


quality standards" (Section 303-h).


    Relief from these standards may be obtained under Section 316 if the


petitioner can show that the effluent limitations are "more stringent


than necessary to assure the projection and propagation of a balanced,


indigenous population of shellfish, fish and wildlife in and on the


body of water into which the discharge is to be made ...".


    With the increase in the size of power production units and plants and


the trend to nuclear power, the prediction of the thermal structure in


receiving waters is even more so a necessity.  Consequently, a large
                                                                     i

number of mathematical models have been constructed but most have had only


very limited field verification.  All of the models have certain


features in common and it has, therefore, become more important to


verify the models' field results and obtain the range and mean of the
                               4

-------
necessary coefficients than to further elaborate on the details of the


models themselves.  For practical field applications, this is especially


true.  For research purposes some of the phenomena should be disaggre-


gated and be more intensively studied but for purposes of meeting the


legal requirements of Section 316, determination with greater confidence


of the coefficients of the aggregated phenomena is more important.


     Therefore, a series of comparative studies of mathematical models


of typical thermal systems have been commissioned by EPA.  These include


a comparative study of the local thermal structure of submerged discharges


into large bodies of water , of the local thermal structure of surface

                                     2
discharges into large bodies of water , and this work on the thermal


structure of large, deep bodies of water (i.e., reservoirs or lakes).


     The distinction between a deep reservoir or lake and a shallow, run


of the river reservoir is the maintenance of horizontal isotherms and a


strong stratification during summer.  Also deep reservoirs usually have


a low annual through-flow to volume ratio.


     Though there are many mathematical models available today for


calculation of temperature rises in reservoirs, few of them have been so


thoroughly explicated that they can be used easily except by a specialist


in the field.  Though many of the models have been developed under EPA


contracts, there is no detailed evaluation and comparison of the various


models.  Therefore, it is not possible to know beforehand what informa-


tion is required for the computer program evaluation, which factors are


considered in the models, the sensitivity of the models to changes in the


variables nor how the results would differ from one another if the


various models were used.

-------
    Therefore, the most widely known and used models, Water Resources


Engineers (Orlob) , MIT (Harleman-Huber-Ryan) , Cornell Aeronautical

                     ^                 f\                               7
Laboratory (Sundaram) , Colheat (Jaske)  and Corps of Engineers (Beard)


have been collected and evaluated.  After preliminary analysis only


three models, WRE, MIT and Cornell were further evaluated.  The Colheat


Model was developed primarily to simulate the thermal properties of a


flowing water body where the vertical stratification is very weak or non-


existent.  The assumption that convection is restricted only to the longi-


tudinal direction makes it unsuitable for use for deep reservoir analysis.


The Corps of Engineers' model simulates thermal properties within a


reservoir on a monthly basis.  This time span is too large for the detail


required in this study.


The purposes of this study are:


    1.  To review each model, including analysis of available documenta-


        tion and computer codes, tabulation of assumptions and factors


        involved in analysis, listing of input parameters required and


        the criteria for application to prototype in an explicit form.


    2.  To analyze the major differences between models.


    3.  To verify each model using numerous reservoirs' field data.


    4.  To perform sensitivity analysis of the most important input


        parameters.


    5.  To recommend criteria for choosing suitable input parameters re-


        quired to run the predictive models based on the field data


        verification and sensitivity analysis.


    It was anticipated that this study would provide clues in choosing


a suitable model, provide the necessary information about the proper use

-------
of each model and lessen the difficulties one may encounter in running



such programs, to the extent that a new investigator in the field will



not be tempted to build his own program, but would further detail and



verify the existing programs.

-------
                                SECTION IV


                    ANALYSIS OF DEEP RESERVOIR MODELS


    In temperate zones, the spring heat.ing, primarily by the absorption

of the solar and atmospheric radiation, tends to warm up the waters

closest to the surface.  However, surface cooling, due to back radiation,

evaporation and conduction, and wind-induced turbulence will cause mixing

whenever the density gradient is too shallow and too weak to maintain a

stable condition.  During this period the temperature distribution is

only weakly stratified.  The heat in the surface layers is transported

slowly down to the deep water primarily by advection.  As solar heating

continues, the temperature of the upper region, epilimnion, increases,

while the lower region, hypolimnion, remains cool and relatively undis-

turbed.  A zone in between the two regions in which the temperature

gradient is the largest is called the thermocline.  This steep density

gradient tends to inhibit the transfer of heat and momentum between the

warm upper layer, and the underlying cooler waters.  The tributary

inflows, which tend to be warmer than the lower reservoir waters during

the summer season, mix and enter the reservoir water column at the eleva-

tion where its density is equal to that in the water column.

    Thermal stratification affects not only the extent of dilution 'and,
                                                                   !    i
mixing of the inflow waters, but also the quality of the water in

hypolimnion.  The development of deficits in the hypolimnetic dissolved

oxygen concentration usually follows the establishment of thermal

stratification.  After its formation, the thermocline moves downward as


                              8

-------
the stratification increases.  When the surface water attains its
maximum temperature and then begins to cool, the epilimnion tends to
become more dense and unstable with respect to the lower, less dense
waters.  The thermocline sinks rapidly as the epilimnion cools further
until the whole reservoir mixes or overturns and is isothermal.  In
climates where the temperature falls below 4°C, two overturns may occur
per year.  The reservoir then is isothermal in the early spring as well.
     The cycle of stratification is very complicated.  The solution of
this problem must consider all the influences from the meteorologic,
hydraulic and hydrodynamic factors and the thermal and density properties
of the water.

GENERAL DESCRIPTION OF DEEP RESERVOIR MODELS
     The basic equation, 1 , relating all the energy inputs to a body of
water can be solved for reservoirs, rivers and estuaries and coastal
regions.
     Q    Q  + Q  ~ Q
Where:
     Qr
shortwave radiation incident to the water surface;
reflected shortwave radiation;
incoming longwave radiation from the atmosphere;
reflected longwave radiation;
longwave radiation emitted by the body of water;
net energy brought into the body of water in inflow,
including precipitation, and accounting for outflow;
energy utilized by evaporation;

-------
     Q,      =     energy conducted from the body of water as sensible
                  heat;
     0      =     energy carried away by the evaporated water;
     Q      =     increase in energy stored in the body of water.
     A three-dimensional analysis is so complicated that it is usually
not justified by the increased accuracy of the results.  In most practi-
cal problems, one or two dimensional analyses will describe adequately
all the principal factors.  The existence of horizontal isotherms, although
sometimes tilted slightly by the wind action and/or the effect of lag
time of inflow, and the much faster dispersion in the horizontal direc-
tion than in the vertical direction, ensure that the assumption of hori-
zontal homogeniety of physical properties in the model is compatible with
the prototype.  Most mathematical models are based on the one-dimensional
vertical motion assumption and can predict the thermal structure of
reservoirs that are in good agreement with the measured values.
     In a stratified reservoir, the body of water must be segmented into
a series of discrete horizontal elements to compute the vertical variation
of temperature.  Therefore, heat flux due to vertical advection, and
diffusion between elements is added to Eq. 1 and applied to each element.
A schematic of the reservoir model considered is shown in Figure 1.  For
simplicity, the elements except for the top and bottom are usually of
equal thickness.  The basic heat transport equation and the continuity
equation are written for an element.  At the beginning of the calculation,
the surface elevation is determined either from a measured surface eleva-
tion or calculated from measured inflow and outflow rates.  The inflow
and outflow distribution in each layer is evaluated according to certain
                               10

-------
OUTFLOW'
                 ATMOSPHERIC
                  EXCHANGE
INFLOW'

Qln »TIn
          ABSORBED SOLAR RADIATION

                           DIFFUSION
            VERTICAL
            ADVECTION
SCHEMATIC   OF   RESERVOIR  PROBLEM
 TYPICAL  HORIZONTAL  SLICE
       FROM    RESERVOIR
       Figure 1. Reservoir representation

                 11

-------
formula or criteria.  Applying the continuity equation to each control
volume, beginning with the bottom element, the vertical advection
across the bounding surfaces can easily be found.
     For a chosen period of time', At, the net change of heat content, or
the rate of heat change, in the control volume is evaluated.  The heat
fluxes considered include that from inflow, outflow, vertical advection,
diffusion, and absorption of radiation energy for an internal element.
In addition to these, surface absorbed energy and surface heat losses,
due to evaporation, conduction, and longwave back radiation must also
be included in the surface layer heat balance.  From the rate of heat
change, the final temperatures are obtained.
     Each of the models is essentially an accounting procedure of the
energy budget over a period of time.  The procedure iterates until
balance is achieved and stability criteria are satisfied, and proceeds
to the next time step.
     The differences in solution method relate primarily to: a) the
handling of Qy, the net energy brought into the body of water in inflow,
including precipitation, and accounting for outflow;  b) the use of
directly measured or internally calculated meteorologic data, to account
for solar radiation, back radiation, conduction and evaporation (the
latter parameter includes the selection of the formula, and coefficients
from relevant meteorologic input); and c) the mathematical scheme for
numerical calculation.
     The models differ in how they handle the inflow to and the outflow
from the reservoir  (whether it entered or discharged at one or more
levels, how it is distributed over the vertical cross-sectional area,

                               12

-------
and the entrance mixing); and in determining whether or not there should

be a time delay in the water inflow input to take into account time of

flow in the reservoir; in determining whether the horizontal segments

should not also be divided into fast flowing and slower flowing sectors.

     The physical aspects of solar radiation, back radiation, conduction

and evaporation, etc. do not, of course, change.  However, not all of the

measured meteorologic data are available or even feasible or economic to

measure on a daily basis.  Some of them must be evaluated from relevant

input data (for example, the evaporation calculated from wind speed, rela-

tive humidity or dew point temperature etc.).  The models may differ in

the formulas used; in the coefficients chosen; in the mechanism of

testing for stability in the horizontal slices and thereby initiating the

thermocline; and in the mechanisms determining the heat transfer in the

vertical directions.

     The models also differ in the thickness of the top and bottom layers,

and the time increments iterated.

     Tables 1-4 illustrate the major differences between models as

determined by reading the documentation and the computer program listings
                                  i
and test runs on the data furnished with the model and/or test runs on

data prepared from Fontana Reservoir if original model test data is not

available.  The assumptions made are shown in Table 1; the input parame-

ters in Table 2; the factors involved in the analysis in Table 3; and the

model construction in Table 4.  Some difficulty (due to program mistakes

or inadequate information provided in the model) was experienced in getting

some of the programs to run and  in obtaining full documentation on each

model.
                              13

-------
                           Table 1.   ASSUMPTIONS
 Assumptions
       Cornell
        Model
        MIT
       Model
 Water Respurces
Engineering Model
Horizontal
homogenei ty
Yes—one dimensional
stratification in
vertical direction only
Yes—one .dimensional
stratification, in
vertical direction only
                     1
Yes—one dimensional
stratification in
vertical direction only
Primary
mechanism
for the
formation of
thermocline
 Nonlinear interaction
between wind induced
turbulence and buoyancy
gradient2
Differential  absorption
of incoming solar
radiation
Differential absorption
of incoming solar
radiation
Surface
boundary
conditions
one of the three is
specified in a sinusoidal
form3
1) water surface tempera-
ture Ts
ii) heat flux at surface
O.S. %
lii) equilibrium temper-
ature If
usually TV  is,specified
Meteorologic Input
Water surface temper-
ature calculated
Meteorologic Input

Water surface temper-
ature calculated
Bottom
boundary
condition
(no flux)
Yes
Yes
Yes
Water budget
(water losses
due to evap-
or-tion and
gains to
rainfall)
Advective
heat  (add
or subtracted)
No
No
No (the reservoir sur-
face -levation 1« cal-
culated as a function
of initial surface
level and the cumulative
inflow and outflow; the
input measured pool ele-
vations has never been
used)


Yes
Not directly; however
the measured daily sur-
face elevations are
used as pool level for
each simulation day.
The water budget impltes
evaporation, rainfall
and possible leakage
                                                     Yes
                                   14

-------
                   Table  1  (continued).  ASSUMPTIONS

1.  The reservoir system can be represented  by more  than one segment, with
    thermal  simulation carried downstream  segment by segment, to achieve a
    quasi two dimensional  solution from a  series of  one dimensional solutions.
2.  The assumption that the  bulk of incoming solar radiation is absorbed with-
    in a small layer near the surface is implicit in the governing equations.
3.  A + B sin (||g-t + $)
    where A - mean value
          B - amplitude
          t - time in day, t = o corresponding  to the  time when reservoir
              temperature profile is isothermal
           - phase angle
                                 15

-------
Table 2.  INPUT PARAMETERS
Input
Parameters
Unit
Short wave
Solar radi-
ation
Net Long-
wave
atmosphere
radiation
Wind
speed
Air
Temperature
Cloud
Cover
Atmospheric
Pressure
Relative
Humidity
Wet BUI b
Temperature
Dew Point
Temperature
Equilibrium
Temperature
Cornel 1
Model
Input data in
specified units
only
No3
No
No3'10
No3
No3
No3
No3
No
No
Yes12
(in terms of mean
value, amplitude
and phase angle
in a sinusoidal
form)°c
MIT
Model
Input data in
specified units
only
Yes
(net flux)
kcal/m2 day
Yes1 '2;7
kcal/m2 - day
Yes
m/sec
Yes
°c
Yes2'6
decimal
No
Yes
decimal
No
No
No
Water Resources
Engineering Model
can be in any units
user supplies conversion
factors, standard units
as indicated
Yes1'2'4'8
(gross flux
i.e. no reflection)
kcal/m2 - sec
No ;
(calculated)
Yes8
m/sec
Yes8
°c
Yes8
decimal
Yes1'2'8
mb
Yes2'5'8
decimal
Yes2'5'8
°c
Yes2'5'8
°c
No
         16

-------
Table 2 (Continued).  INPUT PARAMETERS
Input
Parameters
Evaporation
Precipitation
Outlet elevation
Inflow rate
Inflow
Temperature
Initial
Reservoir
(i) temperature
(ii) rate of
temperature
change
Reservoir
surface
elevation
Reservoir
Geometry
.(i) Length v s.
elevation
(ii) Horizontal
cross-section
area v s. elev.
Fraction of
solar radiation
absorbed at the
water surface
Outflow rate
Cornell
Model
No
No
Yes (depth
of intake for
power plant)
ft
No9
No9
(i) Yes
(isothermal)
ac
(ii) (isor
thermal )
Yes
(constant
reservoir
depth) ft
(i) No
(ii) No11
No
No9
MIT
Model
No (Input constant
for built-in formula
to calculate heat loss)
No
Yes
m
Yes
m3/day
Yes
°c
(i) Yes (isothermal
only)
°c
(ii) (isothermal)
Yes (used for compari-
son only, the actual
value is evaluated
from continuity) m
(i) Yes
m m
(11) Yes
m^ m
Yes
(0.4 * 0.5
recommended)
Yes m3/day
Water Resources
Engineering Model
No (input evaporation
coefficient to calcu-
late heat loss)
No
Yes
m
Yes (daily avg.)
rrr/sec
Yesi (daily avg.)
°c
(i) Yes (either iso-
thermal or variable)
°c
(ii) Yes (By default use
1 x 10'9 °c/sec)
Yes (daily avg.)
m
(i) No
(11) Yes
m^ m
No
(Assume equal to
0.4 internally
for the top 0.3m
layer)
Yes (daily avg.)m /sec
              17

-------
              Table  2 (Continued).   INPUT PARAMETERS
Input
Parameters
Friction velocity
Short wave radia-
tion extinction
coefficient
Diffusion coeffi-
cient



Heat exchange
coefficient
Cornel 1
Model
Yes (in terms of
mean, amplitude and
phase angle in a
sinusoidal formld)
ft/sec
No
Yes [in terms of
(C] + C2 Z) w*]
(upper and lower
bound of the coeffi-
cient are also inputed)
ft2/day



Yes 9
Btu/fr-day-°c
MIT
Model
No
Yes
1/m
Yes
2
m /day



No
Water Resources
Engineering Model
No
Yes
in terms of extinction
depth (m)
coefficient = 6.908/
extinction depth
Yes, empirical deter-
mined constants A, ,
A2, and A3 (i) DC A]
for E< EC A
(ii) Dc A2E 3 for
*~ c
E = -— 4^- stability
of the water column
2
m /sec
No
1.  May be calculated internally by program
2.  May or may not  have to be inputed
3.  Wind speed, air temperature, vapor pressure,  humidity, short-wave solar
    radiation and cloud cover are necessary data  for external calculation of
    of the equilibrium temperature
4.  Calculated internally both with and without reflection.  If data are in
    input, the net  flux . Input flux x "                          • 'f «*
    in input, the net flux   cal. flux (with reflection)

-------
               Table  2 (Continued) .   INPUT PARAMETERS
 5.  Only one of the three parameters is used.   If more than one are presented
     the last read in  has  the priority.   But  at  least one of them should be
     presented in input data
 6.  To be read in only when atmospheric radiation is to be calculated intern-
     ally by program
 7.  If calculated by  program cloud cover should be  known
 8.  Meteorologic data provide at least one observation per day, constant
     values such as average monthly meteorologic  conditions should be avoided.
 9.  Taking account of the power plant cooling water only and in terms of heat,
     q , per unit area per unit time added by power  plant
10.  Also used for friction velocity calculation externally
11.  A constant surface area is needed for calculating q  (see 9)
                                                                   2
12.  Either surface temperature (°c) or heat  flux at surface (Btu/ft -day) can
     be used to replace equilibrium temperature
13.  A + B sin (-1?F t + )
                              19

-------
Table 3.  FACTORS INVOLVED IN ANALYSIS
Factors

Diffusivity






Stability mixing
process










Heat transfer in
control volume
(horizontal layer)
1. Direct
absorption
2. Diffusion
3. Vertical
advection
4. Horizontal
advection
Cornel 1
Model
Eddy diffusivity
Eddy diffusivity
» molecular
diffusivity




Free convection
if stratification
is unstable












1. No

2. Yes
3. No

4. No

MIT
Model
Molecular
diffusion
(constant)
neglects
turbulent
diffusion




Convective
mixing 1f
negative
temperature
gradient
occurs

^— - < n
ay
(T - tempera-
tare, y - ele-
vation, posi-
tive upward)



1. Yes

2. Yes
3. Yes

4. Yes

Water Resources
Engineering Model
So called "effective
diffusion" accounts for
turbulent diffusion and
convective mixing cal-
culated from temperature
jrofile
D = A, for E < Er
C 1 C
*here E = ~-ff stability
of the water column, E =
some critical value of
stability
Convective mixing if
legative temperature
gradient occurs
OT
ty <0
W J
(T - temperature,
y - elevation,
positive upward)






I. Yes

2. Yes
3. Yes

*. Yes


-------
Table 3 (Continued).  FACTORS INVOLVED IN ANALYSIS
Factors

Heat transfer
across water sur-
face
1 . short wave
solar radiation
2. Net long-wave
radiation
3. Evaporation
4. Conductions

Inflow consider-
ation
1. enter at the
level of equal
temperature

2. distribution in
vertical direc-
tion

Withdrawal
consideration
1. level
2. distribution
in vertical
direction
3. limit on with-
draw zone












Cornel 1
Model
In terms of heat
flux
qs = K(TE-TJ
o t. o
K - heat exchange
coefficient
TE- equilibrium
temperature
T - water surface
temperature


1. Yes

2. No
(spread instan-
taneously into
a thin horizontal
sheet)



1. single level
outlet
2. No
(uniformly dis-
tributed at the
level of withdraw]
3. No











MIT
Model



1. Yes
2. Yes
3. Yes
4. Yes



1. Yes

2. Gaussian vel-
ocity distribu-
tion either with
or without en-
trance mixing



1. selective
withdrawal
2. withdrawal layer
thickness &
, Gaussian
' velocity dis-
tribution in
withdrawal layer
3. Yes
(withdrawal
layer never
extended over
the region with
temperature
gradient equal
or greater than
cut-off gradient)
of |£= 0.05
Water Resources
Engineering Model



1. Yes
2. Yes
3. Yes
4. Yes



1. Yes

2. uniform velocity
distribution over
the interflow
thickness deter-
mined by Debler's
critera


1. selective with-
drawal
2. withdrawal layer
thickness and
uniform velocity
distribution
over withdrawal
layer determined
by Debler's
criteria
3. Yes
withdrawal zone
always on top
or underneath
the thermocline



                  21

-------
Table 4.  MDDEL CONSTRUCTION
Parameters
Mathematical
scheme of
approximation
Stability
criteria for
use

Applicability
criteria
Time step
(At)
Depth Interval
(Ay)
Test Case
Cornel 1
Model
Explicit finite
difference scheme



deep, stratified
turbid lake
Variable
AVrct{^ax
0< Ct < .5
KH - diffusivity
Constant
(i) maximum
100 intervals
Cayuga Lake
400 days
MIT
Model
Explicit finite
difference scheme
n At ^ , /•• \
(Ay)2 - * U;
u At «, -i /?\
V Ay ~ ] U;
stratified2
FD < 1 = 0.32
Constant
(1) Determine At
max. from Efil)
(ii) guided by time
step of input data
(iii) must satisfy-
stability criteria
Constant
(i) 50 intervals
or less is recom-
mended
(11) min. 20
intervals
Fontana Reservoir
3/1/66 to 12/31/66
Water Resources
Engineering Model
mplicit finite
ifference scheme
p Q (element) -At q
V V(element) '°
recommended
R < 1 always
a
2
strongly stratified
FD «0.1
Constant
(i) 1 hr..
-------
            Table 4  (Continued).  MODEL  CONSTRUCTION
Parameters
Running
time for test
case




Cornell
Model
(400 days) 13 min.
for Ay = 5 ft.





MIT
Model
(300 days)
1.4 min. for Ay
= 2.0m
At 1 day
2.0 min. for Ay
= l.O"1
At 1 day
Water Resources
Engineering Model
(300 days)
2. 6 min. for Ay 2.0m
At - 1 day
3.1 min. for Ay 1.0m
At = 1 day


1.
2.
the program compiling  time  is not included
the densimetric Fronde number in defined as
        -LQ  /5T
          m  / ge
    where L - reservoir length
          Q - volumetric discharge through the reservoir
          D - mean  reservoir depth
          V - reservoir volume
      p - reference density
      g - average density gradient
      g - gravitational  acceleration
                                        •£
3.
Check by stability criteria, Equation (2),  internally and the input At
is subdivided  if necessary in that particular  time step.
                         23

-------
     A brief description of each model evaluated is given in the fol-
lowing sections.

WATER RESOURCES ENGINEERS' MODEL
     The WRE model has been developed by Water Resources Engineers, Inc.,
through a series of studies for various agencies 3> .     It was the
first comprehensive model proposed for predicting the thermal structure
in reservoirs.  The computer program of WRE model used for this study is
the modified EPA version.  Although this model has many versions and is
widely used, most users indicate that an intensive effort is needed to
have this model run properly.  This is partially due to the difficulty
of acquiring full documentation and partially to some computer coding
problems.  Several errors were detected during this study.  The most
serious one is the concept of 'effective' diffusion, based on the numeri-
cal evaluation of the eddy conductivity coefficient from the measured
temperature profile in a reservoir.  By comparing the rederived heat
transport equation, as shown later in this section, with the WRE's
computer program, a mistake in the computer code related to the diffusion
term was discovered.  The density of water, p, appears to have been
omitted from the diffusion term.  Since the MKS system is used, the actual
diffusion is approximately one thousandth (1/1000) of the 'effective1
diffusion, as defined by WRE.  After correction of this error,  the magnitude
of the 'effective1 diffusion coefficient is then of the same order of
magnitude as the molecular diffusion coefficient.
     Other difficulties in using the WRE model were related to  the numerical
scheme for evaluation of the heat flow term at the top layer.  This
                              24

-------
general problem will be discussed in detail in a separate section.
     We were unable to acquire the original WRE test run data.  There-
fore, Fontana Reservoir data used in the evaluation were prepared from
TVA measured field data.

Principal Assumptions
    (a) There is horizontal homogeneity, i.e., stratification is in
        the vertical direction only.
    (b) Effective diffusion accounts for the heat transfer due to
        wind mixing turbulent motion and reservoir instability.
    (c) There is differential absorption of incoming solar radiation.
    (d) There is no flux, of volume or heat, through the reservoir
        bottom or sides except that due to inflow and outflow.

Factors Considered and the Basic Equations
         Since the heat transport equations used in the computer program
    are different than those indicated in WRE report, the heat transport
    equations were rederived.   The set of implicit equations were solved
    by the Thomas Alogrithm, and are shown below.
Direct absorption of solar radiation —
        * (z)  = o (1-6)  e -n(zs-0.3-z)                              (2)
        where  (z)   =    short wave  radiation at elevation z
               z      =    elevation of water surface
               3      =    fraction  of solar  radiation  absorbed at the
                        water surface (g=0.4  is assumed)
               n      =    radiation extinction  coefficient, m
                            25

-------
                                            .(10)
Selective withdrawal—


        (i)     Up to five outlets  are  allowed



        (ii)    Based on Debler's experimental results^UJ  the critical



               Froude number,  FC,  is 0.24,  therefore:
               0.24 =
                                                             (3)
       The withdrawal  depth in meters,  then is:
       d =  2.0
                       \%
                       Sp
                                    = 2.0
                                           feef
(4)
      where q = ^,  one half of the discharge per unit width,
                Vi



      and w is the reservoir width



      e = —  -5^-, normalized density gradient
          P0  dz



(iii)  The velocity is uniform within the withdrawal zone



(iv)   The principle  of superposition is applied for the  regions



      in which withdrawal layers overlap



(v)    Withdrawal  layers never extend through the thermocline,  or



      physical boundaries.



(vi)   At the onset of fall cooling, when the epilimnetic region



       is well-mixed and isothermal Dabler's criteria do  not hold



       for withdrawals from the epilimnion  and  Craya's approach^  ^



       is used.  The flow is withdrawn from epilimnion until the



       discharge is larger than Craya's critical flow given by:
                     26

-------
               qc = 1.52  /gli  HE,       2h 

-------
Internal mixing —
        (i)     Free convection occurs if stratification is  unstable.
        (ii)   The heat transport, H, due to diffusion can  be written as:
               H = pc •  D(z,t) .  rcg'fl                             (8)

               The general properties of diffusion coefficient  D are  as
               follows :
               (a) It is usually  greatest near the surface  but  declines
                   rapidly with depth and attains  the minimum at thermo-
                   cline.
               (b) In the hypolimnion, it increases with depth  in an
                   erratic manner, reaching a maximum at about  mid- depth,
                   thereafter decreases as the bottom is approached.
        (iii)  The form of the diffusion coefficient  used is:
               D  =  Ai  (constant),   E < EC                         (9)

               D  =  A2EA3,           E>Ec                        (10)

               where E = stability of the water column
               E = critical stability parameter

               The following values are suggested:
               Ai = 2.5 x 10" 4 m2/sec
               A2 = 1.5 x 10"8 n/'Vsec
               A3 = -0.7
               Ec = 1.0 x 10"6 m"1
                             28

-------
Governing equation —




        The time rate of change of thermal energy H in a control volume



        of thickness Az, is:



        3H.
        where subscript j indicates the increment of depth; j = 1 at



              bottom surface



        H  = The heat energy stored in the control volume (kcal)



        hj = Heat flow associated with inflowing water (kcal/sec)




        h  = Heat flow associated with outflowing water (kcal/sec)




        h  = Heat flow by advection (kcal/sec)




        h^ = Heat flow by diffusion (kcal/sec)




        h  = Heat flow by short wave solar radiation (kcal/sec)
         Sri



        In terms of temperature T, Eq. 12 can be written as:



                   3T. ,

        p.  CA. Az _l±i = p. c (TI) .  (qlD . -p.c CT0) .  (q^ + h. Aj




                                                    9T
        A       .Al

        *J*1 -                                                      (13)
         or




         Pj
                                             p CD.A-

                                              J  J  J     Az
                                                                    C14)
                             29

-------
                D.A.               D.A.
+ P-;
           /I
where
Pj    =   PjcCWqI}J    Pj'CVj  Cq^+hft                C16)
T     =   vater temperature (°c)



T,.    =   inflow  temperature (  c)




q.,    =   inflow  rate  (m3/sec)  into control volume




T     =   outflow temperature (°c)




a     =   outflow rate (m /sec) from control volume




h'    =   net  insolation heat flux per unit area (kcal/m2-sec)



D     =   diffusion coefficient (m2/sec)



v     =   vertical advection velocity (m/sec)



Az    =   thickness of control volume (m)



p     =   average density of water (kg/m3)



p     =   density of water (kg/m3)



AV.J   =   A-'Az volume of jth control volume (m3)




z     =   vertical axis, positive upward  (m)



A-    =   cross -section area at depth step j Cm2)
                                                                (18)




 f     =   mean water temperature of jth control volume (°c)



 c     =   specific heat of water (= 1 kcal/kg-°c)
                      30

-------
 since




       TJ-% = TJ-1                                           (19)




                                                             (20)





                                                             (21)




 Equation 15 becomes:
where

              D.A.
Kj,2
T  ftl - lim TCt+At)  - T(t)

1  ttj "      - At   ^"
Taylor series  o£ 2nd order





T(t+At) = T(t)  + T(t)At + T (t)  Q-                         (26)
                                  Zi




and by definition of derivative
for small At




T(t+At) = T(t) + T(t)-| + T(t+At) ^                        (28)




or use superscript k to indicate time step



       = T(k) + t(k) At + j(fcfl) At  = a(k) + ^.(k+1) At       (29)

                       2          ^                   Z
where  a    = T    +                                         (30)
                     31

-------
By Equations 22 and 29



f         (35)




Then Equation 31 becomes




                                        "                     (36)
The system is a set of implicit equations and can be solved by the


Thomas algorithm and transforms into an upper bidiagonal form.  The


coefficients of this new system designated by Si ,, Si 7, Si _ and
                                              J j-1-   3 >*•   3 >*>


F! are as follows:



Sj,l = °'  j=2'3 " N



Sj>2 = 1,  j=l,2,3 -- N                                      (38)



Sl,3 = S1,3/S1,2; Fl = F1/S1,2                               (39)
                     32

-------
                                                                      C40)
                   ,         ,'Sj,3                                  C41)


        then TN = F^                                                   (42)


        and


                          '  * = N'lj N"2>  "'  2'1                     C43)

                         .(k+1) -At  f  j=1>2>  .„  N                    (44)
                  j       J         &


      This  is an implicit method of combining  an  explicit  finite difference

 and an implicit finite difference scheme.   It has advantage of unconditional

 stability  at the cost of complexity of computation and longer computa-

 tion time.



Verification

      The model was verified on Fontana Reservoir for the  period from
                                   !
 February 20,  1966 to  December 31,  1966.


Results of test run ---

      Since the WRE model did not furnish the  test run data,  a set of  input

 data for Fontana Reservoir  was prepared in  this  study according to the

WRE program.   Based on the  sensitivity analysis  of Fontana Reservoir  for

 the period from March 1, 1966 to December,  1966,  the  following effects

 on  temperature stratification were observed.
                             33

-------
 Ci) With Variation in Thickness of Horizontal Layer, Az, Only ---
WRE's report states that calculation with a constant thickness of
one meter most closely matches the measured values of temperature.
However, no details of the test runs are given.  The results of
our study show that the thickness of horizontal layer affects the
thermal simulation greatly.  This is undesirable.  In general, our
results indicate that in the wanning period, Spring and early Summer,
the larger the horizontal layer thickness the higher the temperature
profile.  A typical example can be seen in Figure 2.  The temperature
profile of Az = 2m is 2°C to 3°C higher than that of Az = 1m and the
profile for Az = 1.5m falls in between.
     In the early fall, as the water body loses heat, the temperature
profile predicted with the larger horizontal element followed the
trend but at a more rapid rate at the water surface than at inter-
mediate depths.  Calculation with the larger   vertical increments
predicts a higher temperature than with the smaller   vertical incre-
ments as indicated in Figure 3.  During the period that the reservoir
is isothermal, the profiles predicted are very similar for all thick-
nesses as shown in Figure 4.
     The use of Az = 0.6m probably violates the criterion that within
the time period simulated the through flow must be less than the volume
 in that element.  The temperature profile became isothermal in Fall as
 shown in Figure 3.  Since no remedy is provided within the model and
no warning is given if the situation exists, all simulation results should
 be examined very carefully.
                               34

-------
   500
   480
Q)
   460
O
i
UJ
   440
   420
 FONTANA RESERVOIR,  1966
 DAY'- 187  (JULY 6)
                                                                    MEASURED
O  O  o  O  A z = 0.6m

•  •  •  •  Az = I.Om
Q  Q  Q  Q  Az = 1.5 m

o  o  o  •  A z = 2.0m
                            8    10   12    14    16    18    20   22    24   26   28   30
                                      TEMPERATURE (°C)
                    Figure 2.  WRE model -- Effect of Thickness of Horizontal Layer (July 6)

-------
   500
   480
 tt)
 0)
 E
-" 460
i
UJ
UJ
  440
   420
   FONTANA RESERVOIR, 1966
   DAY: 244 (SEPT.n
           MEASURED
O  O  o  O Az = 0.6 m
•  •  •  • Az = 1.0 m
o  o  D  a Az = 1.5m
o  o  o  o Az = 2.0m
                           8     10    12    14   16    18
                                      TEMPERATURE (°C)
                                                  20   22   24   26   28   30
                 Figure 3.   WE model -- Effect of Thickness of Horizontal Layer (Sept. 1)

-------
   500
  480
o>
E
— 460
§
UJ


UJ44Q
  420
                         •o
FONTANA RE
DAY: 335 (
• • • •
D D a a
o o o o
ISERVOIR, 1966
DEC. 1)
MEASURED
Az = I.Om
Az
Az
= 1.5m
= 2.0m
8    10   12    14    16    18   20

          TEMPERATURE (°C)
22
                                                                     24   26   28   30
               Figure 4.  WRE model -- Effect of Thickness of Horizontal Layer (Dec. 1)

-------
     The use of a horizontal thickness of one meter in the Fontana



Reservoir did simulate thermal profiles compatible with the measured



field values.  However, the extrapolation of this conclusion to



other reservoirs may not be true.  It is very likely that in some



reservoirs a layer thickness other than one meter is necessary in



order to satisfy the criterion mentioned above.  In addition to the



oncertainty of simulated results, the use of one meter instead of



two meters or a larger thickness always means longer computation



time.



     The Fontana Reservoir is probably the best example for verification,



since it is very deep, 100 meters, and has useful storage of more



than one million acre-ft.  It is concluded that large variations in



temperature with changes in horizontal element thickness is a serious



drawback of the WRE model.



(ii) With Variation in Diffusion Coefficient Only —  After the



coding error in the diffusion term was corrected, the 'effective'



diffusivity recommended by WRE is equivalent to:



DC = 2.5 x 10"7 m2/sec,   EEC                              (46)




where



E = the stability of water, = —  |£                                 (47)
                               (J  (3 £*


                                                -6  1                  '
E  = the critical stability parameter = 1.0 x 10  m




which is of the same order as molecular diffusivity, 1.4 x 10"7 m2/sec.



Test runs using a diffusion coefficient one thousandth (1/1000) of the
                               38

-------
 'effective' diffusivity give almost identical results as runs using
the 'effective' diffusivity (Equations 45 and 46).  The comparison
of the measured temperature profiles with those calculated with the
diffusion coefficients listed in Equations 45 and 46, marked STAND,
and diffusion coefficients 10 times as large are shown in Figures 5
through 7.  For the early summer, Figure 5; late summer, Figure 6; and
winter, isothermal, Figure 7; both diffusion coefficients give similar
results and closely approximate the measured values.

MIT MODEL
     The details of the development and testing of the thermal strati-
fication model are shown in Reference 12.  The current version has some
modifications in the numerical scheme,  selective withdrawal, etc., as
pointed out in the "Foreward" of Reference 4.  Most of the assumptions,
factors considered in analysis and input data are similar to WRE's.  The
major differences between these two models are in the numerical scheme
and the handling of inflows and outflows.  The computer program is clear
and easily followed.  The inclusion of the test data on Fontana Reservoir
in the report provided useful guidance to new users.
Principal Assumptions —
     (a) Thermal gradients exist in the vertical direction only, i.e.,
         horizontal isotherms.
     (b) The diffusion coefficient (molecular) is constant at all
         depths and at all times; mixing due to unstable density
         profile accounts for convection in the epilimnion.
                              39

-------
   500
   480
vt
w
V

^5
E

r  460
UJ
_l
UJ
  440
  420
                                                        FONTANA RESERVOIR, 1966

                                                        DAY •• 187 ( JULY 6)
_  MEASURED


•  • •  •  STAND


O  O O  O  Dc = 10-STAND
      0    2    4    6     8    10   12    14    16   18   20    22   24   26    28  30

                                     TEMPERATURE (°C)
                     Figure 5.  WRE model -- Effects of Diffusion Coefficient (July 6)

-------
   500
  480
M
w
0>

0>
   460
§
UJ
_i
UJ
  440
   420
                                                         FONTANA  RESERVOIR, 1966
                                                         DAY : 244 ( SEPT. I)
                                                                    MEASURED


                                                                    STAND
                                                         O O  O  O  Dc = 10 • STAND
                           8     10    12   14    16    18    20   22   24   26   28   30

                                      TEMPERATURE  (°C)
                       Figure 6.  WRE model -- Effects  of Diffusion Coefficient (Sept.  1)

-------
   500
   480
 (A
 k.
 0)
 *-
 0>


 ~ 460



O



i
LM
^440
   420
FONTANA  RESERVOIR, 1966

DAY: 335( DEC.i)


__^   MEASURED


• • • •   STAND


O OO O   Dc = 10-STAND
                            8    10   12    14    16    18    20   22

                                     TEMPERATURE (°C)
          24    26   28   30
                      Figure 7.  WRE model -- Effects of Diffusion Coefficient (Dec. 1)

-------
          (c)  Solar radiation is transmitted in the vertical direction



              only and there is differential absorption of the  incoming



              solar radiation below the water surface.



          (d)  The sides and bottom of the reservoir are insulated.



          (e)  The density and specific heat of water  are  constant.



Factors Considered and Basic Equations ---



          (a)  Variable area with depth



          (b)  Direct absorption



              Transmission of radiation at elevation, y,  is given by




                    0(l-3) e"n frs'tf                        (48)




              where:



                     <|>  = net incident solar radiation




                     B  = fraction of  absorbed at the surface




                     n  = light extinction coefficient



                     y  = water surface elevation
                      o



          Cc)  Inflow               '



              (i)  Inflow enters at the level at which its temperature,



              or the mixed inflow temperature if entrance mixing is



              allowed, matches the temperature in the reservoir.



              (ii)  An option to account for the travel  or lag time of



              inflows within the reservoir is provided.



              (iii) Entrance mixing could be included by  providing an



              entrance mixing ratio;  100% is recommended  for Fontana.
                             43

-------
(iv)  Inflow velocity profile is approximated by a
Gaussian distribution, at elevation y
                             *i2
      U. (y) = U,   me                               (49)
       1        ^-maxW
where:
       i    (t) = maximum value of the inflow velocity at
        IftcLX
                 time t,
is determined from:
             rYe
             (S
       lift) =)  B(y) Ujl
             '
                          ^Y)  dy                          (50)

   where:
         Qi(t)   =  total  inflow
         y      =  surface elevation
         y,      =  bottom elevation
         B(y)    =  width  of the reservoir at elevation y
         y.  (t)  =  elevation of inflow
         a.      =  inflow standard deviation
(d) Outflow
    (i)  multiple outlets
    (ii) outflows are centered at the outlet with a Gaussian
         velocity distribution:
                44

-------
     u°Cy) =
where:
     U     = maximum velocity or velocity at y=y
       max


     y  t  = elevation of centerline o£ outlet



     a0    = the outflow  standard deviation calculated on


             the basis that  95% of the outflow comes from


             the calculated  withdrawal layer or:


           - 
-------
                 e      =  normalized density gradient = —  -£       (55)
                 g      =  gravitational acceleration
If the temperature gradient at the outlet is smaller than the value
specified above, the withdrawal layer is restricted by the thermocline.
The built-in cut-off gradient is set at 0.05 °c/m.
             (iv) The velocities from each outlet are superimposed on
             one another.
         (e) Variable water surface elevation
             The surface level is calculated from the initial surface
             level and the cumulative inflow and outflow.  The measured
             elevations are used as reference only.  The reservoir is
             schematized into a series of horizontal elements with con-
             stant thickness, Ay, except the bottom element, which is
             half as thick, and the surface element, which varies
             between 0.25Ay and 1.25Ay to account for the variation in
             the surface elevation.
         (f) Governing Equations
             The heat transport equation applied to each horizontal layer
             has the following form:
                                                                     (56)
                     CV60Atjr)T(jr)) + ^j (Ui(y)B(y)Ti-U0(y)B(y)T(y))
             where :
                 T(y)   = temperature at elevation y
                 V(y)   = vertical velocity at elevation y
                             46

-------
                 l^Cy)  = inflow velocity at elevation y
                 UQ(y)  = outflow velocity at elevation y
                 T.     = inflow temperature
                 A(y)   = area at elevation y
                 t      = time
                 a      = molecular diffusivity
                 (j>(y)   = transmission of radiation at elevation y
             and the continuity equation can be written as
             -£ (V(y)A(y)) = B(y) (Ui(y)-Uo(y))                       (57)
     The isothermal profile at the beginning of the Spring provided the
initial condition and the two boundary conditions are given by the no
heat flux through the reservoir bottom and the balance of heat input
at the water surface.
     The mathematical model used is an explicit finite difference scheme.
The selection of layer thickness, Ay, is restricted by the stability
criteria:

                        %
                                                                     (59)
             where :
                 D      = diffusion coefficient
                 At     = time increment
                 V      = vertical advection velocity
                 Ay     = depth increment
                              47

-------
A routine check on the second criterion was built into the program to
subdivide the time interval  if  the vertical velocity should become too
large.

Verification
     The model was verified  on  Fontana Reservoir for the same nine month
period as the WRE  model.

Sensitivity Analysis
     The MIT model has been  found to be the most satisfactory and has
been most thoroughly evaluated.  The evaluation results are shown in
the  Section II, Sensitivity  Analyses.
CORNELL MODEL
     The model was developed through an extension of a study on the
                                                      f!41
physical effects of thermal  discharge into Cayuga Lake*-  '.  It is a one-
dimensional model  designed for  deep stratified lakes.  The surface ele-
vation of the lake is assumed to be constant throughout the simulation
period and the  reservoir  is  divided into a number of horizontal layers
of equal thickness.  The  geometry of the reservoir is not considered.
     Heat flow  from inflow,  outflow, and vertical advection through each
horizontal layer are not  considered, nor is the differential adsorption
of incoming solar  radiation. Eddy diffusivity, which is related to wind
 induced turbulence and the buoyancy gradient is the primary factor of
heat transfer within the  reservoir.
 Assumptions
      (a) Horizontal homogeneity and constant cross-section area.
                              48

-------
      (b) Lake is deep and isothermal during the springtime.
      (c) The lake is turbid and the incoming solar radiation is ab-
sorbed within a small layer near the surface.
      (d) Eddy diffusivity accounts for all heat transfer within the
lake  except for the heat added by the power plant and pumping.
      (e) The annual equilibrium temperature and wind speed over the
lake  can be expressed in a sinusoidal form.
Basic Equations
      (a) Governing equations
      The change in temperature with depth when the plant discharge
      surfaces is:

                               J   "
                                                or
where:
    T
    t
    z
    KJJ
    w
    z.,z,
    zm
    S(z)
                        =  temperature  (°C)
                        =  time (day)
                        =  depth below  the water surface (ft)
                                  1                2
                        =  thermal diffusivity (ft /day)
                        =  the  specified pumping velocity (ft/day)
                        =  the  specified intake and discharge  depths  (ft)
                        =  the  depth of the  lake (ft)
                        =  the  explicit thermal discharge or heat input
                           term (°C/day)
                              49

-------
     S  •           + ATp   Tsl   -CZ-Z                              (62)
                      -"       e
             where:

                 ATp    = temperature rise across condenser


                 T      = surface temperature


                 w      = pumping velocity


                 z      = length scale

When the discharge temperature is less than the surface temperature, the

effluent will remain submerged and S(z) is zero.  The pumping speed is

related to CL , the heat per unit area per unit time added by the power

plant by the equation:


                 WP = W'0? 'ATP                                 (63)

             where:


                 p-Cp   = heat capacity per cubic foot of water

                          (112.32 BTU/°C-ft3)

                 AT     = temperature difference produced by power

                          plant

                 ATp = T(zd)   T(Z;L) (°C)                           (64)


The thermal eddy diffusivity, K., has the form given by Rossby and

Montgomery1-  ':

                 KJJ = K^0(l + CTR^"1                                (65)


             where:


                        = (C-j^ + C2z)w* = the eddy diffusivity of

                          neutral stratification (ft /day)
                              50

-------
                 a      = a dimensionless  constant  (=0.1  for preliminary


                          study)



                 W*     = T<5                 ?TT
                          -=•  = B,  + B?  sin G£r t + ₯), friction
                          P      i     L       ttb
                          velocity


The empirical relation of Munk and Anderson is suggested for determining


wind speeds over lakes.

                         cz     N-1     3T
                 R. =    (  STT)     a z TT~ ' Richa-rdson Number       (68)



                 ay = A1 + A2  (T  4°) + A3 (T   4)2, Coefficient


                  of volumetric expansion for water


             where:


                 N      = a  dimensionless constant (N=2)


                 T      = wind shear stress
                  o


    \.9,A,,B, ,B2,C, ,C2   = constants



     (b) Initial condition


                 T(z,tQ) = TQ                                        (70)



     (c) Boundary conditions



                 (S___   = 0    i
                                     ?TT
                 T,, = TQ  +  5TQ  sin (2£r t + <}>),  the equilibrium
                  i;     e      e       juj                             r73")

                 temperature


             where:


                 T      = temperature at water surface
                              51

-------
                 t      = time
                       = phase angle
                 T      = average value of equilibrium temperature
                          over one annual cycle
                 STe    = one half the annual variation
                 K      = the heat transfer coefficient at the lake
                          surface (BTU/ft3-day-°C)
An explicit finite difference scheme is used for numerical evaluation.
At each time step, the thermal diffusivity is evaluated from the known
temperature profile and its value is restricted to the range between
the input maximum and minimum thermal diffusivities.  The variable time
increment, At, is then determined from the maximum value of the thermal
diffusivity at this step by the following equation:
                                '2                                   (74)
             where:
                 C.     = a nondimensional constant, 0 <(L < 0.5
                 AZ     = spatial mesh size

Verification
     The model has not been verified explicitly in any lake.  The exter-
nal parameters were chosen to correspond loosely with Cayuga Lake.  The
results of the model were in qualitative agreement with the measured
values of the thermal profiles in Cayuga Lake.
                              52

-------
Results of Test Run



     A set of test  data was prepared from Fontana Reservoir field data



 to  evaluate  the model.  Several  runs were made for different input



 conditions.   Problems about the  selection of input parameters were



 evident  during the  preparation of the  data and during the running of



 the program.   It became obvious  that long computer times were required.



     In  the  numerical example  given by Cornell,  the  friction velocity,



 w*, is taken to be  the  surface current velocity  at 0.1  ft/sec.  However,



 calculations according  to Munk and Anderson's empirical relationship



 yield  w* at  about one tenth of the value given in the example.  The


                                             3   2
 resultant eddy diffusivity, IC.Q, is 4.96 x 10  ft /day  compared to 7.98


    2    2
 x 10   ft /day used  by the Cornell Aeronautical Laboratory.  The eddy



 diffusivity  affects both the thermal diffusivity and time step, and



 therefore the simulated thermal  structure in reservoir.  The current



 velocity at  the surface in Fontana Reservoir is  not  available.  If the



 suggested relation  is used, the  eddy diffusivity is  of  order of 5.0 x



 10  ft2/day  and the computer time for  a 300 day  run  will be about 90



 minutes.  Therefore, a  maximum time limit of 15  minutes was set for all



 runs.  Other parameters defined  loosely are the  dimensionless constant



 a.in Equation 651the length scale,'a1,in Equation 62,and the maximum



 and minimum  thermal diffusivities.



     In  a lake of variable cross-sectional area  with depth, the assump-



 tions  used in this  model, constant cross-sectional area and horizontal



 homogeneity,  imply  a distortion  of the  vertical  scale.  Hence, the



 computed temperature profile has to be  converted in  some way before



 it  can be compared  with the measured value.  Due to  the nonlinearity
                              53

-------
of the diffusion coefficient with respect to depth and temperature



gradient, the conversion will be very complicated.  Since the model has



not provided any method to account for vertical distortion and no



available scheme is applicable to this situation, the values directly



calculated are used for evaluation.



     The profiles for typical times of the year are shown in Figures 8



through 10 for runs without inflow/outflow and with inflow/outflow con-



verted to that corresponding to power plant cooling water.  Both runs


                                         2   2
used a diffusion coefficient of 7.98 x 10  ft /day as in the Cornell



example.  As shown in Figure 8 for July 6th, the predicted values for



both conditions are reasonable approximations of the measured values



except at the surface where the difference is 6°C.  In Figure 9, for



September 1st, the predicted values vary greatly from the measured



values, in some instances as much as 6°C.  In Figure 10, December 1st,



the predicted values are in better agreement with the measured values



though differences as great as 4°C are noted.  The predicted values for



the inflow/outflow case are in much better agreement with the measured



results than is the case without inflow/outflow.  When higher diffusion



coefficients were used, the time limit of 15 minutes was exceeded.



The differences between computed and measured temperatures may be due



to:



     (i) distortion of the vertical scale of reservoir caused by use of



         a constant surface elevation and cross-section area.



     (ii) neglect of inflow and outflow other than cooling water.  Since



         in most of the reservoirs suitable for analysis of these models,
                              54

-------
             500
en
01
                                                                   FONTANA  RESERVOIR , 1966
                                                                   DAY:  is? (JULY 6)
                                                                              MEASURED

                                                                              WITHOUT INFLOW/OUTFLOW
                                                                              WITH INFLOW/OUTFLOW
                                                                              COUNTED AS POWER
                                                                              PLANT COOLING WATER
                                            10    12    14    16    18   20
                                                   TEMPERATURE (°C)
                                   Figure 8.  Cornell model test run results, July 6,  1966

-------
en
ON
              500
FONTANA  RESERVOIR, 1966

DAY : 244  ( SEPT. I.)
             480
           0)

           E
             460
          UJ
          _l
          UJ
             440
             420
   —   MEASURED


   O    O   WITHOUT INFLOW/OUTFLOW


   •    •   WITH INFLOW / OUTFLOW

           COUNTED AS POWER

           PLANT COOLING WATER
                                      O •
                                       8     10    12    14    16    18    20   22   24    26   28   30

                                                   TEMPERATURE(°C)
                                Figure 9.  Cornell model test run results, September 1, 1966

-------
en
            500
            480
         0)
         E
            460
         UJ
         _l
         UJ
            440
            420
FONTANA  RESERVOIR, 1966
DAY: 335 ( DEC. i.)

  ——^  MEASURED

  000  WITHOUT INFLOW/OUTFLOW

  •  •  •  WITH INFLOW / OUTFLOW
           COUNTED  AS POWER
           PLANT COOLING WATER
0    2     4    6    8     10
                                                 12    14     16    18   20
                                                 TEMPERATURE  (°C)
           22   24    26   28  30
                              Figure 10.  Cornell model test run results, December 1, 1966

-------
     average yearly flow is considerably greater than the volume of the
     reservoir, the inflow would bring in an amount of thermal energy which
     would not be negligible.  The same, of course, would be true for
     the energy loss due to outflow.  In addition, the inflow and
     withdrawal from hypolimnion would provide mixing which is not
     accounted for by eddy diffusion.
     (iii) The eddy diffusivity depends too strongly on the wind condi-
     tions above the reservoir.

PROBLEMS WITH DEEP RESERVOIRS M3DELS
     All of the three models evaluated use temperature for the deter-
mination of the entrance level of inflow and for evaluation of whether
an unstable condition prevails to enhance convection.  Temperature is
also used for the calculation of withdrawal thickness in the MIT model.
However, the density of water is greatest at 4°C.  Therefore, the
models without modification, cannot be applied to a reservoir where
the water temperature goes below 4°C.  This oversight is probably due
to the fact that the temperature of the Fontana Reservoir is higher than
4°C the year round.  However, water of 4°C floating on the top of the
colder water was discovered in the results from the test data supplied
with Cornell model.
     The calculation of water temperature at the surface layer is an
important problem.  With variable surface level, the volume of the
surface layer also changes with time.  The heat transport equation des-
cribed earlier is derived for a fixed control volume with respect to
time.  Therefore, directly applying the heat transport equation to the
                               58

-------
surface layer, whose volume varies with time, will cause serious



errors.  To approximately account for the heat balance in the surface



layer, one should calculate the total heat content of the surface layer



at each time step.  Suppose y , y-^, y  and y, are the surface elevations



at the beginning of each day tp t2, t^, t4, etc., as shown in Figure



11.  A linear variation of water surface is assumed.  The mean eleva-



tion, y, , y^, and y,, should be used at each time step, t, , t-, t, for




calculating the thickness of the surface layer water surface area and



the absorption of the solar radiation at different levels below the



water surface.  The heat balance equation of the surface layer can then



be written as:
                                                                        (75)
     with Vs = VSQ + |]:At                                               (76)




             where:



                 V      = volume in the element corresponding to the



                          present surface



                 V      = volume of surface layer at the end of the



                          current time step



                 k      = time step



                 p      = density of water



                 q.     = inflow rate
                 ^m



                 a      = outflow rate




                 Q,     = heat transport due to diffusion
                              59

-------
                  Q,      =  heat transport due to absorption of radiation


                  Q      =  heat transport due to vertical advection


     Another approximate method could also be derived.  The surface ele-

vations are assumed to be discrete, instead of continuous, as indicated

by the solid line in the Figure 11.  At each step the surface

elevation is held constant and equal to its mean value y,, y^, y,.

The heat transport and continuity equations for internal elements are

the same as usual.  However, the same heat transport equation can be

applied to the surface layer only by modifying the continuity equation.

The assumption of a constant surface elevation at each time interval

implies that a volume of water with a temperature equal to that of

the surface layer has been added to that layer if the surface eleva-

tion is rising, or is subtracted from the surface layer if the surface

elevation is falling.  The volume of water added or subtracted is equal

to the vertical advection through the interface of the surface layer and

is the most immediate underlying layer.  The continuity equation for

the surface layer is then written in the MIT model notation as:

     utBAy + VjjjA = uQBAy                                            (77)

     The V!  is different from V-  which when multiplied by the area be-

tween the surface layer and the immediate underlying layer is the sum of

the inflow and outflow for all elements below the surface layer, or

         _1  J«-l
      jm   A  i = ^          o

     These two terms are related to AV  as shown in Equation 79:
               _ AVs    1
               ~        A
                              60

-------
 (ft

I
 
co
                     TIME.days
             Figure 11.  Surface layer schematic
                        61

-------
     The heat transport terms die to inflow, outflow and vertical advec-



tion are:




«  Vjm>0



     AT • Vs » Vjm • A . T.m_± At + AV£ (Tja_.   T.J               (80)




     + u- BAyT. • At -u  • B • Ay • T.- At
        i   ' i        o        '    jm



Substituting Equations 77 and 79:




     AT ' Vs - Vjm ' A • (Tjm-i - V At * ui B^ (Ti 'VAt       ™



(ii)  Vjm<0




     AT • Vs = V.jm - A • Tjm At + Ui BAy - T. - At -u^AyT^At   (82)




By Equation 77:



     AT • Vs = uiBAy(Ti -T^) At                                    (83)




     The MIT model uses the second approximate method.  The final results,



Equations 3.20 and 3.22 in Reference 4 are correct, although the con-



tinuity equation for surface layer, Equation 3.14 appears to be wrong.



Equation 3.14 implies that total inflow and outflow are always equal,



which is not always the case.  The approximation has proved to be satis-



factory as determined by verification on seven TVA reservoirs when com-



pared to the results from the first approximate method which was



incorporated into the MIT model in TVA's study *•  '  '.



     The WRE model also uses an approximate method in which the same heat



transport and continuity equations used for internal elements are applied



to the surface layer.  It is modified only when the vertical advection,



qav, is positive.  The quantity  (
-------
is negative.  The WRE model for the surface layer appears to be



incorrect.  It may have contributed to the wide variation in predicted



temperatures when the layer thickness was varied.



     In the Cornell model, a constant surface elevation is assumed.
                             63

-------
                             SECTION V


                       SENSITIVITY ANALYSIS



     Based on results from the test runs on Fontana Reservoir, the three


models were evaluated.  Only the MIT model was chosen for further


sensitivity analysis of input parameters on seven TVA reservoirs.  The


Cornell model, though it has some attractive theoretical features,


lacks means of inputing inflow, outflow, and the variation of surface


elevation.  The model, therefore, does not approximate the most typical


cases.  The running time for the model is considerably greater than


for the other two models.  In addition, the test run results are poor


compared to the measured field data.


     The Water Resources Engineers' Model has also been found to be


inappropirate due to the complex structure of the program, the longer


computer run times for the program and because of inadequate documenta-


tion of the model.  In addition, a drastic change in the predicted


temperature in response to variation in the layer thickness was observed.


     The MIT model is, in our opinion, the most easily used.  We have


applied the model to seven TVA reservoirs, having widely different flow


through times, volumes and depths.  We have varied the height of the


vertical increments, Ay, the fraction of radiation absorbed in the top


meter of water in the reservoir, 3, and the average absorption coeffi-


cient of water, n, and the vertical diffusion coefficient.  Transmission


of the radiation below the water surface is related to $ and n as shown


in Equation 48.          /     ,   ,..   0^&~^
                             rf0  (1   3)                              (48)
                               64

-------
          where:


             o     = total  incoming radiation in kilocalories



             TI      = the average absorption  coefficient of the water


                      (meter ), and


             Y      = depth  below the water surface in meters


The degree of variation of the parameters  is  shown in Table 5.  We have


tried to cover the range of  values to be expected: from average flow


through times of 0.01 to 0.85 years; absorption coefficients suitable to


distilled water and to highly turbid water; diffusion coefficients from


molecular diffusion to 1000  times molecular diffusion; depth increments


from 1 to 3 meters; and fraction of radiation absorbed in the top meter


of water from 0.2 to 0.5.


     Parameters not included in the sensitivity analysis were held con-
                                i

stant throughout the study.  The original  time step input of one day


was used, since all the meteorological  and hydrological inputs were


daily averages measured on a daily basis.  Inflow travel time within


reservoirs is neglected and  a mixing ratio of 1.0 and four grid spaces


are used for entrance mixing.  Entrance mixing is simply a way to repre-


sent the mechanisms not accounted for by the mathematical model and is


considered unsatisfactory as pointed out by the authors of the model.
                             65

-------
                                                       Table 5.
                                       PARAMETERS  VARIED IN  SENSITIVITY ANALYSIS
                                      Units
                                  Average
                                  Values
 Low
Values
 High
Values
ON
ON
Vertical Increments, m

Fraction of Radiation Absorbed
         in Top Meter of Water

Average Absorption Coefficient
                 of Water, m~l

Vertical Diffusion Coefficient
                                                           0.50
                                                           0.75

                                                           Molecular
                                                           Diffusion
0.20
p.05

30 Times
Molecular
Diffusion
0.40*
1.40

1000
Times
Molecular
Diffusion
                       *Not the high value

-------
Atmospheric radiation was calculated by the model.  If measured solar
radiation is not available, the routine described in TVA Report 14
was used for computation.
     We used the original program unless we found programming or logic
errors.  For this study several modifications were made:
 (i) In Function  'FLXOUT(N)' the statement:
    RAD = 1.13587 E   6* (  (TS + 273.16)** 4   0.937 E   5* (TAIR + 273.16)**
          6* (1.0 + 0.017* CC**2)
    was replaced by the following two statements
    AR = 0.937 E   5* 1.13587 E   6* (TAIR + 273.16)**6* (1.0 + 0.17*
          CC**2)
    RAD = 1.13587 E   6* (TS + 273.16)** 4   AR
    This is done in order to correct the error in the coefficient and
    make a proper transfer of the parameter back to the main program.
    (ii) In SUBROUTINE'SPEED(N)' the statement:
    IF (EPSIL.LT.0.0) EPSIL =   EPSIL was inserted into the program.after
    statement No. 15.
    This is necessary only in Douglas Reservoir where a negative tempera-
    ture gradient was formed.     i
    (iii) In SUBROUTINE  ' SPEED (N)' the cut-off gradient was put into the
    routine for calculating withdrawal layer thickness when using Kao's
    or Koh's formulae.  The original program applied the cut-off gradient
    only when the temperature gradient at the outlet was less than 0.01
    and Kao's and Koh's formulae are not used in that case.   This
    results in withdrawal of a large amount of surface water such as
    occurred in Norris Reservoir.
                             67

-------
     (iv) In addition, the program was modified to call a subroutine TPI£T to



     plot the simulated temperature profiles for chosen dates and to store



     the results in the computer disc.  A routine was also written to



     read and plot the results of the sensitivity analysis.
     One of the important parameters is the amount of evaporation.  There



are a number of empirical formulas available.  The MIT model uses two



different evaporation formulas.
Kohler's        E     = 0.000180 Wp  (ec   YeJ
                 in                     o     9.



and Rohwer's    ^    = (0.000 308 + 0.000185W)




             where:
(84)




(85)
                E_    = mass flux in kg/day-m



                 p    = density of water in kg/m



                 W    = windspeed in m/sec



                e     = saturation vapor pressure of the air at the



                        temperature of water surface in mm Hg



                e0    = saturation vapor pressure of the air at tempera-
                 cL


                        ture Ta (air temperature) in mm Hg



                 Y    = relative humidity expressed as a fraction



     The major difference in the two formulations is that Kohler's shows



no evaporation at zero windspeed while Rohwer's does indicate evapora-



tion at zero windspeed.  We have found no  apriori means  of deciding



which is most appropriate.  However, the test runs indicate Rohwer's



equation yields better results only in Fontana Reservoir; both give



about equal results in South Holston Reservoir and Kohler's shows more
                              68

-------
favorable results in the rest of the reservoirs tested.  Whichever



evaporation formula more nearly predicted the measured values was sub-



sequently used in all of the sensitivity analyses for that particular



reservoir.  The frequency analysis of wind speeds shown in Table 6, seems



to indicate that Kohler's formula yields better results in the reservoir



where the wind speeds are mostly higher than 2 mph.



    The results of the sensitivity analysis are shown in Figures 12-201.



The legend for these figures is shown in Table 7.






FONTANA. RESERVOIR



    Figure 12 shows the measured Fontana Reservoir Temperature data



with depth for selected days.  Figure 13 shows the computed temperature



data for the same days using the corrected MIT model.  As can be seen



from the figures and from Tables 8 and 9, the predicted and measured



values for the outlet water temperature and the surface water tempera-



ture have standard errors of estimate of 1.2 and 1.7 degrees C respec-



tively.  Such good agreement might have been expected, since the model



coefficients were adjusted to fit the measured values of this reservoir
                                 I


for this year.  We were interested in how well the model would fit the



measured temperatures for other reservoirs and other years.



    The closeness of the estimate of the outflow temperature using the



Rohwer evaporation formula to the measured outflow temperature is shown



on Figure 14.  The effects of the variation of the layer thickness,



fraction of solar radiation absorption at the water surface, radiation



absorption coefficient, and the diffusion coefficient for selected days



are shown on Figures 15-21, 22-28, 29-35 and 36-42 respectively.  It
                             69

-------
Table 6.

Wind Speed
(MPH)
Fontana
Douglas
Cherokee
Norris
South
Holston
Hiwassee
Fort
Loudoxm
No
%
No
%
'No
%
No
%
No
%
No
%
No
%
1
OvO
2.0
18.0
5.9
4.0
1.1
3.0
0.8
0.0
0.0
22.0
7.2
1.0
0.3
0.0
^~0.0
2
2.0
4.0
117.0
38.2
162.0
44.4
49.0
13.4
31.0
8.5
91.0
29.7
20.0
5.5
31.0
8.5
3
4.0
6.0
100.0
32.7
128.0
35.1
112.0
30.7
128.0
35.1
94.0
30.7
128.0
35.1
128.0
35.1
4
6.0
8.0
39.0
12.7
46.0
12.6
103.0
28.2
87.0
23.8
48.0
15.7
91.0
24.9
87.0
23.8
5
8.0
10.0
18 '.0
5.9
20.0
5.5
48.0
13.2
58.0
15.9
33.0
10.8
71.0
19.5
58.0
15.9
6
10.0
12.0
10.0
3.3
3.0
0.8
31.0
8.5
31.0
8.5
12.0
3.9
33.0
9.0
31.0
8.5
7
12.0
14.0
3.0
1.0
2.0
0.5
13.0
3.6
16.0
4.4
2.0
0.7
8.0
2.2
16.0
4.4
8
16.0
16.0
1.0
0.3
0.0
0.0
2.0
0.5
9.0
2.5
4.0
1.3
7.0
1.9
9.0
2.5
9
16.0
18.0
0.0
0.0
0.0
0.0
3.0
0.8
2.0
0.5
0.0
0.0
2.0
0.5
2.0
0.5
10
18.0
20.0
0.0
0.0
0.0
0.0
1.0
0.3
3.0
0.8
0.0
0.0
3.0
0.8
3.0
0.8
11
•> nr\ r\
? zu . u
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0
0.3
0.0
0.0

-------
                                   Table 7.
                          LEGEND FOR FIGURES 12-201



STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3


Layer
Thickness
AY(m)
2.0
1.0
3.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Fraction of
Solar Radiation
Absorbed at
The Water Surface
3
0.50
0.50
0.50
0.40
0.20
0.50
0.50
0.50
0.50
0.50

Radiation
Absorption
Coefficient
0.75
0.75
0.75
0.75
0.75
0.05
1.40
0.40
0.75
0.75


Diffusion
Coefficient
D(m2/day)
Dm*
Dm
Dm
Dm
Dm
Dm
Dm
Dm
30 Dm
100 Dm
*Dm «= molecular diffusion

-------
     543,0 *-
1
!
1
1
1
1
1
1
1
1
1
1
1
1
i
i
i
i
1
1
i
i
i
i
i
i
i
i
i
1
1
1
1
1
t
1
1
1
1
1
1 0
1
01
1
1 1
1
1
1 1
1
1
1
1
0 1 2
21
1 3 *
*l * *
* 516
4 1
5 1
6 1
1
1
1
1
1
1 1
1
1 1
1 1
1 1
1 I
1 1
1 1
1 1
I 1
i 1
161)2
1112
H 1
11 2 3
1 1 3
12 1
7 1 3
•> 131 4
1 1
13 1
1 1 4
1 1
1 4
•\ 1 1
16 4 1
4 4 15 5 55
• 5 15 1
1
1
1
1
1
1
1
1


Z
3
3
4
4

5

0 BA>
OA1

OA>
OA1
oyf
< oyl


•> ?
3
4
4



l\ T3
1 I32
1 1'7
'1 215
J ?44 	
'1 285
'1 3*9
LET


2 2
4
4







2
1



"

.
	






1
1
1
J
1
\
	
~,
1
1
2,9 4,5 7.0 9,5 12.0 14.5 17.0 19.5 22.0 24.5 27.0 29,3
              Figure 12   HJT HQnf-L  *
          TFMPE°ATJPE  1-1 DEGREES c

F1.IA KFiFRVUM  1966—1F4SUKEO TE"PEKATUKE
g
I
f
y
A
T

0
N


N

H
g
I
E
*
1
1
X

I.
1
1

1
1
1
1
49.1 »a +BT— r,..-j
1
1
1
1
I
1
1
1
4$S,« **,—.,-.-
1
J
1
1
*sne f,— — —
1
1
1<
1
439,8 *c........
1
1
1
1

1
1
1
1
1
1
1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 ! 1
1 1 1
• ••«••• •••+»H—W^««nwV<»*^0«VI«+0*B»«» I •
101 1*1
00 | 11*1'
01 I 116
00 1 11 1 1 *
U 1 11 1 1 • 22
0111 1 «
0 111 | 2 2 *
0 11 1 216
__,0— -11— 	 .*__._2-2--*— - • 	 -J
Oil 12 1*3
0 11 1 |22 1 * 33
Oil 21 1 63
0* 1 22 | 1 S »
p-»0 l-»*-+«—-2H»«+«»»«— -••*3. «»-6— — —
• 1 1 22 I 3 J 66
* 12 I 3 16
• 22 1 » 06
* 21 1 » * 1
...*-22p-*~ — — 3-3*-— — 66-*— 4— -- 4-
*2 13 1 641
•23 31 4 46* 15
*3 4 1 51 * 1
»* 51 66 1
61 6 1 I
61 | 1
61 | 1
1 1 1
! 1 1
1 1 1
1 1 1
1 1 1
1
|
i '
1
j
|
1
J.
|
1 j
1 1 1
1 1

1 2
2 21 *
2 I A j
2 1 3*3
33 *
1 1 5
33 1 *
3 1 i
3........* — .-_+<)_4
1 *
1 64 f
1 4 5
44 *
-..-..-*.+ 	 — J.._
44 1 13
4 1 5
4 4 US
!
-M~-. -•••*•-..•«.»_
5 1
» 1
1
1










2
2
..-— -_3
1 4
1 1*
4
44
44
4
*
•





.........




._.._-««




1 0 f>AY| 75
1 1 OAYI 132
1 2 9«Y| 187
1 3 "AVI 213
1 ' HAYI 285
1 » DAYI 335
i • OVERLAP
1 < OUTLET








2
2
•
4 3
.*«......








•-_«-.__




.........

















1 1
1 I
i 4.
1 1
i 1
1 1
1 1
-1 J.
1 1
L
1 1
1 1

1 1
i 1
J. 4.
1 1
i 1
1 1
1 1
1 1

1 1
I 1
1 1
1 |

. _| ,*
1 1
1 1
1 I

1 1
1 1
1 1
1 1
1 |
1 1

1 1
1 1
1 1
1 1
1 1
ZtO 4,3 7.0 ».» 12.0 14.5 17.0 19,5 22.0 ?4.5 27.0 29,9
             Figure  13   M|T Hur>El *     FONTANA KFJFK'AJIR 1966—CnHPOTfcn  TEMPERATURE PR1F1LE--
                                                     72

-------
                          Table 8.
          STATISTICAL ANALYSIS FOR THE PREDICTED
            WATER TEMPERATURE AT OUTLET LEVEL

Reservoir/Year: Fontana/1966
Time Period Covered: 120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate ( C)
1.19
1.25
1.16
1.19
1.22
2.88
1.21
1.27
1.15
1.25
\
Correlation
Coefficient
0.96
0.96
0.97
0.96
0.96
0.77
0.96
0.96
0.97
0.96
                            73

-------
                         Table 9.
          STATISTICAL ANALYSIS FOR THE PREDICTED
                SURFACE WATER TEMPERATURE

Reservoir/Year:  Fontana/1966
Time Period Covered: 60th - 360th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate ( G)
1'.74
1.75
1.70
1.74
1.70
2.20
1.74
1.75
1.76
1.81
Correlation
Coefficient
0.95
0.95
0.96
0.95
0.96
0.92
0.95
0.95
0.95
0.95
                              74

-------
can be seen in Figures 15-21, that the variation in the thickness of the



horizontal layers from 1 meter to 3 meters had virtually no effect on



the predicted temperatures.  The standard errors of estimate for the



temperature when varying the depth confirm this.



     It can be seen in Figures 22-28 that the variation from 0.2 to 0.5



in the fraction of the solar radiation absorbed at the surface made



little difference in the predicted temperature.  This is also confirmed



in Tables 8 and 9.



     It can be seen in Figures 29-35 that the variation of the radiation



absorption coefficient from 0.05 to 1.40 made a great difference but



the variation from 1.40 to 0-75 made little difference.  The use of



a coefficient of 0.05, however, made a large difference between the



predicted and measured temperatures.  This is also confirmed in Tables 8



and 9.



     It can be seen in Figures 30-42 that a variation in the diffusion



coefficient from molecular diffusion to 100 times molecular diffusion



resulted in a great difference between the predicted temperature and



the measured temperature for the greater diffusion coefficient.  This



difference was most pronounced during the warmer part of the year as



shown in Figures 38-40 and as indicated in Tables 8 and 9.
                             75

-------
iT,9
J5.0
ZZ,5
Z0,0
IT, 3
15.0
It. 9
10,0
T,S
5,0
t.3 •






• ..•r»...'
0 0
iniiiiii









0
0
1U1111U









0
0
1
1 IIUU








u
0
11111
1111







0
r>
U
U
111






1
• 1
1
1
01







111
1
10
1
1


0 . HE
1 - ftO
• - Oy




0
0
11 11
10
0



SUREO
HER
HUP





0
1
1*1* 0
1









0
1
1*
UO
110



Figure 14   HjT
                 "»V4
      INA KFSFK"dlK  t<>66--C
.0 4


43.0


90.0



2



<






.0 4

l




...



,i
•0
*
J




.....



7
2<
*0





.........



.0 9










.3 U
....









.0 U










3 IT








o ME
1 ST
2 Of
3 »t
< ou
.0 19
	





»...*....*

ISURID .
IND
S -
TL6T
.
.9 Z2
....
. -.1




.



.0 U




	

....



i IT
	
1

"
1


.

	 1

0 J9.J
 Figure 15 H,T MQDEL  ,
          TFMPERATUKE IN DECREES  C
FONTANA RESERVOIR 1966—OAVI T3   .-SURFACE ELEVl   300,1 N
                                     76

-------

19.0
»0.0
49.0
60.0
73.0
90.0
109.0
120.0
119.0
190.0 .
2.


*- 	 	 	
<
_
•-••-?-»*



i
i
i
i
i
i *
1 0
1 «3
21
21 3
•1
21
213
01





1
i
i
i
... i
i
i

1
. !

21
0
*9
P .








*
01 0







-
*
21 J

















0 MI
1 JT
2 DE
> OE
.;.« ov
< ou








sumo
NO
n
12
RLA» — «
LIT


- ..











.
••^— » • • ••<



	
0 4.3 7.0 9*.5 12.0 14.3 17.0 19.3 12.0 24.3 17









*•*«•£••*
0 2t.
 Figure 16  HIT MOOEL *
          TIM»E«ATU«E IN DEGREES C
FONTANA RESERVOIR 1966—OAyll32  —SUHF1CE ELEVI  901.
.0
19.0
10.0
49.0
D
I 60.0
P
T
H
I 73.0
N
H
E
T 90.0
E
R
109.0
120.0
139.0
190.0
2


.-._»-.-
<
	






21
Zl 1
1






*
*
» 0
1
9
0







0
21
-*l-»---
3







. ° 12
0 *
1
1







0 1
*
3







0
.0* 1

	
_

_

2
010
1

_




o - MEASURED
1 - STAND
2 - OELll
3 - OEIZ2
< - OUTLET
1
1
0 0

"






)^.0™^
)




.
•••-•••••
-^
"""" "\
...;.,..
---i-i-i.






>. -». -*^ ^ i2.^ ^ I7i() WiJ J2_0 M;5 Ht0 Mj,
                                  TEHpE>ATUHE IN OESREES C
Figure 17 M,T HOOEl; *    FONTAXA RESSRVOIR 1956.-DAYJH7  —SURFACE ELEVI  309.9 N

                                         77

-------
.0
15.0
30.0
45.0
40.0
75.0
90.0
105.0
120.0
135.0
150.0
2



<


0 4.





.
.—.—..
5 7



0
* 3
0



.

0
213
1 3

"
-1,1.1.1-
'
0 *
0 *
• 3



-1.1.1...
0
a 2
*
•3
1


-
.11......

.1— .1.0.
0
213




.
-—-.—,
0 HE
1 ST
2 OE
3 DE
»--* ov
< ou
21
0*0
.3.1.-11.<



.
.
SURIO
NO
21
22
RLA»
LET
tl 1
0 (
0





..—....
. .
0

. . ....
.


~
"
1
1
	 ..1
1
1
i
|

T
I
1
1
1
. . . 1
" "l
	 1
0 9'.5 12.0 14'.5 17.0 19.5 22.0 24.5 S7.0 2*. 3
       Figure 18 H,T HOOElI •
           TEH'ERATUIE IN DEGKEES C
 FDNTAMt RESERVOIR 19»6--0tf1215  ^-SURFACE ELIVl  505.9 H



15.0




30.0



45.0



D
E 60.0
t
T
H
I 75.0
N
M
E
T 90.0
E
R
105.0
120.0




.0

14A-A j



... -_!---




«—.-..-



f
•*«•-•*«••









































21


_


.






_








— ._— .



— .. 	 -.






3 *
0
















...1.111.




.....1.1.







. .

0
0
. .









. .






-1.1.1...




.-..H..—



-1-1.1...




0 2»


_ . .


_


-1........



_


.











0
-1-0— —2
21
21 3

2*






.













.-.-.1-1-



0
•-01.1.1.
*2
21
213
31 	 1.1.













i— .1.1.4

*2
12
„,»— 1.
0
•12
12
*




—I— 11-














o > MEASURED •
1 - STAND
2 - OELZl
. 3 . OELZ2
— * - OVERLAP --!-<
< - OUTLET
1
1
! •
0
0





..



"








"


.—...»..,

.........
__




~"™"™™'"™™


1


....




.....







. - . .



.....
.—,....


I....^..—.

.. . .




——,...-





.111.1.1^








.-.1-1.11








'

.



'



..-.,-...


2.0       4.5       7.0
      Fljur. 19
               H,T
9.5      12.0      1».5   "  17.0      19^5      22^0      24^5
          TEMPERATURE IN DEGREES C
FONTANA RESERVOIR 1966--DAYI244  --SURFACE ELEVI  501.9 N
                                                                                                   17.0     29,3
                                              78

-------
13.0

45(o



90.0

tzo.o


_












0
*J
*

... .....

.........





2 01
0 2 1



— *— ...





0









3








0 **








0
1 0




0 Mi
1 JT
i oe
. 3 w
< ou








SURiD
NO
Zl
12
LIT






.........<


1 . .-




—m^~+mmmm


....^..*.












                                             14.5      1T.O      19'. 3       21.0       2«'.5
                                    TEMPE«»TURJ IN DECREES C
 Figure 20  HIT HOieC *    FONTAXA  RfSERVDIR If »6.'OAylZ65  .'SURFACE eiEVI   *»*.3  N
                                                                                                1T.O     2».»
.0
15.0
JO.O
45.0
D
E 60.0
P
T
H
I 75.0
N
H
E
T »0.0
e
R
105.0
120.0
135.0
ISO. A 4
»«....«...

<
«.....-..
t»-...^.-.
.


.....^.^..
_

0
— «.».-
*
0
*
*
.-.«.».-
*
*
.........
.
'
_




0 0
_
...^.....


..........


*
•
•3 0
-_.«lM.


.-.^.»»4
»...*o....
*
•
*
•
«
•
. *
*
*
*
0
!
.........
_







_





.
0 - ME
1 - ST
2 - OE
3 - OE
< - DU

.........
...-.-«.
SUREO -
NO
S .
LET



.....IM*
.





— i,:ii-

—,-,-...

.
	
-....•••-«
	 I
	 	 J
...*^...».




^.^^ ' 1 B^
..-•*•••«•
                                   TEMl>E
-------








75.0
to.o
105.0

1*0,0




IM.H.J






<





•^••^•••.




fe«r--s- 	 •


*3
ft*






*






.





_„—__.-

* .








'

__*»___«•














	

<•_«••*.*»•

































.. — ._—..

— •^•_K_-




— _ —























• «•••••_ + ••••—« —
0 • MEASURIO
1 - STAND
2 - BETAl
3 i BETA2
... * . OVERLAP 	
< - OUTLET







....




_•—«_•___





...











»••_•«•«•





. 	









1
!






	 i
2.0 4.5 7.0 9 '.5 12.0 14.5 17,0 19.9 12.0 24.5 27,0 *t.l
                                               IN DECREES C
Ftjure 22 M,T mnfL «     FC1NTAHA  RESERVOIR 1966--OAYI 75  i-SURFACE ELEVl  500.3 M




15.0



30.0


45.0



D
E 60.0
P
T
H
I 75.0
N
H
E
T 90.0 <
E
105.0
120,0



135.0


150.0



^^-».B...
-


- .
,w— »._..

V....4__.





^







,»-.-..._.



.-_— -i___





_
>•._•«»•.






*
*
*
*











0






. ,






.






«—•__•—



*
0
*3
_












.












1*
0
I*
0 ...




















.•_•_»»•





*3

0 0























_



•
*


— .0 	






»• — K—MK<







.









•~*~K— B— •










.


	 ;;







. .





~~«~1- M,







.

















0 . MEASURED
1 - STAND
2 - BETAl
3 - BETA2
---* - OVERLAP — ~
< i OUTLET
1
1


















. . .









	 -_-_






"



. . . , . . -
••«•»«•••

-iiiiiii;



. ...
'


. . .....
















. , ..
*






.;.:,:.-.







	





,:.;,„„
,



.1.;,:-:.,


. ..
2.0 4.5 7.0 9.5 12.0 14.5 17.0 19.5 22.0 24.5 XT.O 29,!
Figure 23 H,T HOBEI;
                                  TEMpEI>ATURE IX DEGREES C
                        FnNTANA RFSERVOIR 1966— DAyl 132  —SURFACE  ELEVI   50«,4 M
                                          80

-------

.0
• 0
.0
• 0
.0
.0
.a
.0




<

,.—.„--






l*
»
*
•
*
*
*
*
I*HA
-------
.0
30.0
45,0
60.0
73.0
90.0
105.0
120.0
135.0
150.0 •
2.



<




















0
0









0
0









0 «







0
•3
*3
*







0
12
»3
1*





•3
0
0*
•3
*3


«_•.-.«


0 - MEASURED
1 - STAND
2 - BETA1
3 . BETA2
< - OUTLET
> — ..:.;.
•3
0
0 . .









1


. 	 	





1
. ... 1
1
1
. . 1
1
	 ..1
1
1
"l
1
1
	 1
1
1
	 1
0 4.5 7.0 »'.3 12.0 14.5 17.0 19.3 IZ'.O Z4.3 17.0 29.5
                                             TEHpE»ATURE IN DEGREES C
           Figure 26  H,T HQnEL ,    FnNTAIA RESERVOIR l«66—DAyl244  "SURFACE ELEVI  901.9  N





D
P
T
H

I 75.0
N
N
E
E
R
120.0



135.0





<











*— •• — -



..___„.. 	




.

.

0
»3
*










-••___•«







0*
0 *



















_
0



m««H~


. -






	 _;_;.__


.



_







_

_




• «~-«~w-






0 1*




•~»__-_«-














0
0
.




_«~«»_





— •»«.
















0 MEASURED
1 STAND
2 BETA1
3 BETA2
— - * OVERLAP 	
< OUTLET
1





.






_ .






_






	




«_«»..«


	






»«»«£<•


. . ...



_














_i— ...;


130.0
               4.5
                         7.0
                                   9'. 5
                                                                          19.5
                                                                                    22.0
                                            12.0      14.5      17.0
                                             TEM'ERATURE IN DECREES C
           Figure 27  M,T HDOE,_ »    FPNTANA RESERVOIR 1966—DAyl2S5  —SURFACE ELEVI  494.3  M
                                                                                               24.5
                                                                                                         27.0     29,5
                                                     82

-------
19.0
10.0
49.0

60.0
79.0
90,0
105,0
i20,0
139.0
190,0 •
2.





<















.0
*
0
*
*











0 0
.


.








•

• 0






*
•
. « .
*
*
*
*
. •
*
0




























— — — '..




0 - HE
I - ST
2 « IE
3 . IE
-— • 1 0V
< - OU











ISURID
INO
fAl
'A2
fLET
1
0 4.3 T.O 9 '.3 12.0 1*.9 17.0 19.5 22






,.-.-«.«







0 24





..— _:™.,












-i-,;,^





	
.9 (7,0 2*.
                                  T«MpE«ATU« IN DECREES C
Figure 28 MT MODEL *    FONTANA RESERVOIR 1966—OAyUJJ  —SURFACE ELEVI  4«».« H
.0 t
15.0
30.0
45.0
D
E 60.0
P
T
H
I 75.0
N
H
E
T 90.0 4
E
R
'105.0
120.0 4
139.0
190.0 4

,i 	




	
*
•0
—
— -.



•4 2
4 2
2
2
2
2
2
2
2
2





2 4
• 0 4
4








i






.




1
.

	
























0 MEASURED
1 STAND
2 ETAl
3 ETA2
—4 ETA3 --— «
* OVERLAP
< OUTLET



.














1
	 1
1
1
1
1
	 "l
1
. 1
1
..... 1
1
1
1
..... 1
1
1
. . . 1
1
1
I
*^*.*^»^*
    4.5
              7.0
                        9.9
                                                               14.9
                                                                         22.0
      29  MIT HO»EL «
         12.0      14.9      17.0
          TEH'ERATURE IN DEGREES  C
FONTAMA RESERVOIR 1966—DAY I  75  —SURFACE ELEVl   500.3 H
                                                                                   24. S
                                                                                             J7.0
                                                                                                      29,5
                                         83

-------






















»O.Q

110. 0


_



















<




.........


















3
»
*
31
»4






— .

4 0
2
I
2
2
2
2-i—




•










31
4 0
*

2
2
2
2






- — ......












31
*
• 2
n 2

2
2










.........








2 *
3 * 4
14
» 2
024 0






. . -



,










.




























.















.




























—.-.-...

0 MEASURED
1 STAND
2 !Til
3 ETA2
» OVIRLAF
< OUTLET
	 1



. .











, . ,

- . .



— — .....



















. .



. . .













. . . .



. .



. . .
1


.
I


. .....
1
- * -



_-.......«
--— ----...
. ....



. 1
-. ,t

. i _ .
2.0 ».5 7.0 9.3 12.0 14.3 17.0 19.5 22.0 2*. 3 17.0 2».5
Figure 30
                         TfHPEHATUHE  IN DECRIES  C
HIT MODEL *    FONTANA RESERVOIR 19&6-.D4Y1132   -.SURFACE  ELEVl   501.4 M
.0
15.0
30.0
45.0
60.0
75,0
90.0
120.0
135.0
150,0 i
2
.
.
<




.
0 4
.....1^._


*
*4
2
2
2
2
2
2
* 2
* 2

5 7


31
0
31 *
* 4
0
2




.0 1
-__;.—.—
0 3
3 14
1 4
2
2
2




_
5 12
3l
.0*1.*
03 1 4
4
3
2
2




_
0 14
— ..i-j,*
0
114
> 4
..
2
2






J 17
*
301 4
,,4.. 	
2
2
2






3 2
0 0
1 *
2
2 	





,
o MEASURIO
1 STAND
2 ETA1
3 ETA2
>-.— 4 ETAS ----
* OVERLAP
< OUTLET
1
-J.
0 19.5 22
E — —»«-..
0 40





__
0 24
.-—.._;_




.
>.«.«.n
5 27
>...^.«MI
.. .
. . . . 1

'
>»..*«M<
1
	 ;-J
.0 2*. 9
Ptgur. 31 H,T HonEL
                         TeHl>E«ATU«E  IN  DEGREES  C
               FONTANA RESERVOIR  19&6--D4yl197   ..SURFACE  ELCV   509.9 M
                                                    84

-------
19.0
90.0
45.0
60.0
73.0 ',
los.o
tio.o
130.0 .
i.



<
...



.




*
z
t
?..
2
2
2
2






0
• 4
0
_
_






0
-o-,i;U-
1 4






0
0 I
. . » 1
0 31 4
111 *
0 11 4
1
01 I 4
1 4
2
2





2
.2.







0
3 1 4
4
2
2




.™ — ,;_, 	 j— ;»«
1)214
1 0 C
> 110 4 2
•1041 2
21
2
2 1
2





0 MIASURID
1 STAND
2 BTil
» ETA2
T— 4 8TAI -•-•
* OVERLAP
< OUTLIT
1
. 1 	






»...-..;
6












1
	

. . 	
»»- «*«-«l

. . ....
A 4,3 T'.O 9'.5 12.0 14,3 1T.O 19'.S 12'. 0 J4.J JT.O at.!
                                   TEMPSHATURE  IN DECRIES c
      32 H,T HonEL .     FHNT4N4 MSIRvOIR  H66—OAVI213   i-SUXFACC CLIVI   303.9 H
^>
13.0
10.0
45^0
75. 0
90.0
105.0
120.0
1)5.0
150.0 <
^



<.





>»--—— 4
0 4




*
__.»-i,20
2
2
2
.— — ^-_
2
2
2


5 7.




03
20 .



_
0*9
.



0
40




5 12'




03 14 '
2




0 14.


0
t 1
) 1 4
3 1.4







.. . 9»
) l
) 1
» 1 4
4
2



I 1 *4
11 41 2 0
»» * - JO* •- --
0 1
• 14 2
> 1 4 21
» ». * 1 .. ..
4 2
t 2
2
t
2
*- .




0 » NIAJURIO
1 > 57AND
2 '- ETAl
> - CTA2
.1.4 1 ETA) -•--
• • OVIRLA*
< i 01171(7
1
_ 1








1








1
. . ...
1






	
j" " 17.0 * 19.5 12.0 24'.3 27.0 29.1
                                  7fM»E*A7UIIE IN DECREES C
Figure 33 HJT MDOE|; »    poNTANA RESERVOIR 1966—OAVI244  i-SURFACE ELIVI  501.9
                                                 85

-------
.0
15.0
10.0
45.0
60.0
75.0
iOJ.O
120.0
I3J.O
150.0
2'.


<

«.^.-»-»
«.we«*ffW'
•....*...
0 4.

.-...«..
— --.;.;-
0
*4
* 2
2
2
2
2..
•-» «i*~
2
2
.-...—•-
.-• f*^*.9.
5 " 7.



*1
0 31




•™ 1»«-».
. ;
— -..— ...1
o 9;

-,i~.;.

40
4






.;..„...

o..,o<— —
2
2


.........

»«*..-.
1

0 •«





114 21
314 21
114 21
-»14.2I
114 2
114 2
114 2
114.2
,-..»l*.2
114 2
11402
114 2
114 2
1* 2
20
1
i. . ..





.





0 • HlAsuMO
I STAND
2 CTA1
. 1 ITA2
•..4 . ITAl ...»
* . OVERLAP
< . OUTLET
1
1
1
1
.. . 1 	
*v*
1
1
1
i
i
i
i
.1 ...
j
	 j 	
i
i
. ..i 	
i
i
i
	 i 	


. 	 i



~


— — -.«-*
5 "l2'.0 14.5 17.0 *19'.J ' '*2.0 I*".5 " ' It.O MJ
Figure 34 H,T HOO|I;
          T(H»E»*TUH6  IN  DECRIES  C



FONTANA RESIRVOIH 1966.-Otyi2S5   i-SURFACE ELIVI  4*4.1 M
                                   +«*••$« ^ K • A ~>>v*—<*
15.0
10.0
45.0
60.0
75.0
90.0
105.0
£20.0
135.0
150.0
2

V»»*»«..-<*4
««-*i»i~
<-
.
«*v~*v*~^<
«-•*•••_•!



i-»e^««»-
...^.l.»
0
* 4
04
* 2
* 2
,_.,«_;2"
4
* 2
* 2
4 ...

.




0 0
4
2
.
«••____•
•
_





•
4
..,i.*.(.
* 2
** 0
4
2





•2
•2
4
..»z.
-,,«J.— .
*2
4
•2
*2
4
*2
*2
*2
4*2
2
0
v^«K«^«_«



~H~~W~~«


••«*•(•• — *


••^•••~*~




^•^-•••«*










•— ^*«v«-«
-«-»--•--
««v~~«~~*

a HEISUMD
1 S7AND
2 ITtl
. J ETAZ
>»— » (TAl -«--
* OVERlAf
< OUTLET
1
.. . . .1. . .
1
1
	 1 	
. ,^_ , .....
. ..1 	
1
1
	
1
1
1
. 1 ..
.-.•.*--.•».-.-...«.<
1
1
1
. .
..-- ---..*--^— ..^.
. .. ..
1
1
1
..1 	
1
1
1
. ..1 	 	
1
, ... ..
	 	 	

'••••••*W«^
J
i
j
	 i
i
	 	 mf

——,—..
..

0 4.5 7.0 9'.5 12.0 'l»,5 17.0 19'.5 22'. 0 24.3 J7.0 29.9
Fl,ur« 35
          TtH'EAATURE IN DECREES  C



FONTANA RESERVOIR 1966«>OAyll35   (-.SURFACE  Iklyi  49*.S M
                                                86

-------
13.0'
10,0
43 iO
60,0
T9.0
!09.0
ito.o
iuuo_
130.0
2



t



.


1*

...
».

:


..•!..
•<>^f>*
...



3









i






-





. . .


. .






. ..



. .


















0 MEASURED .
1 STAND
t DIFFl
ii-» OVIRLAF -•--
< OUTLIT
1
. ..











I*-—*- «»v

	



	
.-.; • "i
i


i
]



0 4.3 T'.O »'.3 12'.0 l»'.9 1T.O 1»'.9 12.0 14.J tT.O 29. 1
Figure 36 M,T
                                   TEMPERATURE IN OECME5 C
                        FONT4MA  MSERVOIR 1*»«~.04YT TS  i^SURFACI EllVl  JOOtJ
.a <
19.0
10.0
43.0
60.0
73. 0
90.0
105.0
120.0
139.0
150.0 •
2.

*"*
<
'
.
"
.........4
.
0 4
>....»».
	 __._!*
l"t"
* l
0
>— .12)—
* 1
• 3
•3.
>... »^._
*
*
*
*
...»..^.

0
1 21
2 1
3


.
'

.
It"
0
1 t 3


'

>.-.^«».
*
0 0


_

.........

1 •
*
...0— .-


1
.
"
.........
.

.



.........

.........4
0 ME/
1 STA
2 DIP
3 OIF
--.« QVI
< OU1
1
1
. 1
1
.. .1
1
1
1
i 	
!

1 1
1
1 1
.. .. 1 	 	 	 	
1
1
1
1
1
i

>_-„-.-.„<
	

1 1
1
SURID 1
ND 1
Fl 1
M .. I
LET
1
.


	 i
1
1





1

3 T.O 9.9 12'.0 1».S 1T.O 19".3 22.0 24.3 tT.O 2».3
Figure 37 M,T HDnE|; t
                                  TEHFERATURE IN gEGREES C
                        FONTANA RESERVOIR 1966.-04YIU2 '^.SURFACE EllVl  90*.4 M
                                                  87

-------


)0.0

60,0
75.0
10. Q
105,0
120.0
-
150.0 4
z




<


-

	
0 4.




1
12)
*)
*)
*
»
»
*
*


5 7'.
1
1
1
1
1
1
1 0
1 "
I 2 )
12 1
0 1
i • i » .
12 ) 1
2 0) 1
3 . ] . ...
1
1
1
j
1
1
1
	 1 . . . .
1
— j 	
0 »'.5 12'.

0 If
.........
0 • )
2 )
)



.........



0 14,

0
t 2 )
2 >

	


.........



5 17.
1 )
0 0
0 112)
. on I.I 	
1
1
1
1
1
	 1 	
1
.. . . 1 	

"
1
1
	 ! 	
1 • STAND
2 i DJM1
) ' DIM)
...» . OVERLAP ••— <
< « OUTLET
1
	 1 	
0 19'. 5 22'
10 0

.........
i.........
. .
	

.........
	


0 «4
j
	 1 . . ...
!
j
"T"
	 i 	
i
	 i 	
i
	 i 	 i
i
i
™TH
5 If. a 29.1
Figure 38 HIT
                         TlH'EKATUU IN DESRIES C



               fONTANA RIJIKV01R l*»6-.........
i....^....

0
0
... .» «
...-...«.
1 2 >
12 )
)
--»--.»«.

• ~ • • •"»•* »
..v.....
...-...».

0
1 2
2 )
.1 ;
,— ^,..-.


1
0 12« .
^•«...«.«
_
— •»w»^e**
	
..p«.««.«
.««...f|.v
....-.•-«

o HEASUMO
I STAND
2 OIFfl
* OIFM
a-.* OVlKLAf -.--
< OUTIIT
. . . \ ... .
.....:^n
o* !
"


**•**«?•••*'

	
...WB^.^*I
	
• «• "»e™ "•* '
*""*"
!»»«.**.««o
0

«•**••*«•
w-»«W«»M

i..«.».^«».
m«-

•1
1
I»W-W*9»W»<

M«*W^«*V«<
•***»F»*»i
•^•wev*Bi
»**p«-«ir«4
•••*•»»»»•<
i
•— •••»—^i-^
i
(••••^^•••^^
i
0 4.5 7.0 9'.5 IZ'.O 14.5 17.0 1»'.5 22.0 24'.} 2T.O 2».l
Figure 39
                         TBH'E«ATg«E IN oESREES C



MIT MODEL *    FONTANA RESEKVOIR l*66—DAVi215  ^'SURFACE ELEVI  505.9 M
                                                      88

-------
    .0
 19.0
 30.0
 4S.O
 60.0
 TS.O


*.-. .

.



*»?5?«»«.«
.




; .1.
.-.1--2'0
«I
• 1
.* » .
•»
•1
. *
.-.«.-...

».e-"~a..
1
1
. ! 	
1
1
1
1
1
... 1 	
1
1
1
1 0
0 I * 1
•...»!...
--.3.-...*.- .......
. . I 	
1
1
1
.... 1 	
1
!
... 1
1
1
1
1
1
1
.... 1 . . ...




0 • »
..-.,....
.



...
.
0
i!
1 1 »

......•.,



•«...«..

. 0
».g......
i
> it
j >
i

.........

,-..-....
......•..•.«*....«<
1 • 1
i z Jl o
HJ 10
.«..*.. ..•....<
0 1
0*1
*1 1
I*
1

••••^••••91

1
1
•••»•*••«<
— *4*-**-«.
... .

^* »•»• « ••<



kv»•«»«..*«
««-»«W«i»w*
1
•*•>••*• »«*
i
»«••»•»«»»«•
1
	
	 1
1
	 1
«•*«!«« «^*<
• ••«*«^W*i
. .-..„!
,...,-^..«
"1
Io3.o
I2o.o
I3A.O


190.0
     Z.O       4.3        T.O
                                                                                     ii.9
                        »'.S      12'. 0       14'.3       1T.O      I9'.l
                                  TSH'EAATURE  IN  OEOREES  C
Figure 40 HIT MODEL' *    FONTANA RESERVOIR  19t6..0Ayi244  V.SURFACE EllVl"  301.9 M
                                                                                                U.3
                                                                                                          IT.O      19,3
.0
13.0
30.0
43.0
60.0
73.0
90.0
103.0
120.0
133.0
130.0
Z

»»OT«.....

<
.
.
,.-.-«.»!
0 4
i


.........
0
...».2»i-
1 2
12
12 3
• 3
...•M?...
* 3
• 3
'
5 7'.


" 01
0 I
2
3
3*

0 " 9'.
i. ........



0 2
2
1
.........
....
— ;.™,
f " «.
t.........



o...o»«*
3
3

_
"
0 14,



0. *0
1
.........

3 17.
•3
•3
•3
•3
.—.-•]..
•3
•3
•3
•3__
«3
•JO
•3
•3
*
0
.
»--..---.
.

>.........
.........


.........


0 m HEASURID
1 • STAND
2 . DIFFl
3 . OIFF3
.-.» ; OVIRLA> -—
< i OUTIET
1
0 19'.

—"^-

.........




.........<
,..^.....~



	
*





1
	 	 1
I.........*
J
1
. 	 I
1
1
1
».--.-..*»
1
. . 1
...1
1
1
1
i
i
i
3 tZ.O Z4.3 17.0 19,3
           ««ur« 41 H]T
                                  TEMPERATURE IN OeORKS C
                        FONTANA RtSERVOIR 1966--OAYI2U  i-SUKFACE tLEVI  494.3 N
                                                              89

-------
.0 ««
19.0
30.0
49.0
60.0
TS.O
*0.0
los.o
120,0
133.0


<
v........
.
^•••••••«»l
•....«...<
• »..««.,


.
.0
i
0
i i
12
*
• • i
......9..
"


	 »___-_
0 0
2
, ?


	 •«->•-



1*
--»»-12>>
121
* 1 0
2 3
1






*
1
0




	 	




... .



....







.. . .


-•-•^^fl—


.
. .
o NIASUMO
STAND
oim
DIM!
«— OVIRkA* -•-•
OUTLIT
	



"
..





.........
	



.-».^.«^»



	
..».»..».
	
..^.«..«.

	 ]

. . .


.
i
i
. 	
2.0 ».3 T.O »'.S 12.0 H.3 IT.O !»'.» M.O 2V.J ST.O 2*.>
       Figure 42 H|T MaoE|; »
          TIMPEIATURE IN OECKIES C



FnNTAMA RtSIRvalR l«66"0tnl>!  ^SURFACE ELIVI  »»».« H
                                                 90

-------
Douglas Reservoir



  Figures 43 and 44 show the computed temperature data for Douglas



Reservoir for 1969 at various depths and the confuted outflow



temperature.  These can be compared with the measured data as shown



in Figures 45 through 50.  It can be seen from the Figures and



as shown in Tables 10 and 11 that the predicted results, standard errors



of estimate of 2.1° and 2.0° for outlet water temperatures and



surface water temperature, respectively, are not as good as they were



for Fontana Reservoir.  In Figures 45 to 50 it can also be seen that,



the variation in the horizontal increments from 1 to 3 meters



makes a random difference in the predicted results, with 3 meters



giving better results on day 121 and 1 meter giving better results



on day 186.  Overall, as shown in the statistical analysis in



Tables 10 and 11, the change in thickness in the horizontal



segments makes little difference.  In Figures 51 to 56 the effect of



a change in 3, the fraction of solar radiation absorbed at the water



surface, from 0.20 to 0.5 has a negligible effect on the predicted



temperature.  As shown in the discussion on the variation of the



horizontal segments, the predicted values vary randomly both greater



and less than the measured values.'  Over the whole year, however,



the variation in the predicted values do not differ markedly from



the standard errors of estimate as shown in Tables 10 and 11.



  In Figures 57 to 62, the effect of a variation inn, the radia-



tion absorption coefficient from 0.05 to 1.40 is shown.  While there



are slight differences from each other in the predicted temperatures



when n of 0.75 and 1.40 are used, there is a very large difference



from the other predicted temperature and the measured temperature when
                              91

-------
an n of 0.05 is used.  This is also verified by the statistical



analysis reported in Tables 10 and 11, where the standard error of



estimate for an n of 0.05 is twice the standard error of estimate



for the water temperature at the outlet level for the other eta



values.



  In Figures 63 to 68 the effects of a variation in the diffusion



coefficient from molecular diffusion to 100 times molecular diffusion



is shown.  It can be seen that 100 times molecular diffusion generally



gives poor results and only on day 121 does 30 times molecular



diffusion give predicted temperature results closer to the measured



values than does molecular diffusion.  It can be seen from Table 10



and 11 that overall 30 times molecular diffusion predicts similar



temperatures to those predicted using molecular diffusion and that



using 100 times molecular diffusion gives measurably worse results.
                              92

-------

' .
103,3








2*9,3 <
"




0
0
0
0
0
< 0
0
0
0
0 4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
61
61 1
61 I
61
1
1
1 61
1 6 1
I 6 I
1
o 1
1
iS 7,0 9






1



.» 1Z




1
1
1




.0 \<<




1



2
2
2
.3 17



1
1



Z
n DA
2 1 DA
DA
DA
DA
DA
flv
< au
,0 19






2
2
3
H 69
fl 121
VI 1B6
n zie
VI 2T6
ri 339
ERUP
.5 22




3
S
32
2 3
3
J
i
1
3
» 4
13 4
1
.0 24
1 1
1 1
4 1
1 1
1 1
1 1
1 1
1 1
i I
1 1
1 .... 1
1 1
1 1
t IX
Z 1411
1 1
L -L a. l
.1 i
41 1 1
1 1
1 1
* 1 1
1 i
* 1 .1
34 I I
341 1
1 1 I
1 1 1
» I I
1 1
» . 1 . '
1 1 1
1 1
1 1 1-
1 1
.3 2T.O -Z9.J
Figure 43
           M,T
TfMPE«»TuBE ]N DECREES C



        t«6»—Cdl'MTtD T6«PE*»TURe KlOFUE—
                                          93

-------
                              TABLE 10

             STATISTICAL ANALYSIS FOR THE PREDICTED
               WATER TEMPERATURE AT OUTLET LEVEL

Reservoir/Year:  Douglas/1969
Time period covered:  120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°c)
2.11
2.23
2.07
2.11
2.15
5.73
2.28
2.12
2.09
4.97
Correlation
coefficient
0.95
0.94
0.95
0.94
0.95
0.28
0.94
0.94
0.94
0.63
                                 94

-------
                          TABLE 11
             STATISTICAL ANALYSIS FOR THE PREDICTED



                    SURFACE WATER TEMPERATURE





Reservoir/Year:  Douglas/1969



Time Period Covered:  60th   360 Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate ( C)
2.03
2.05
2.07
1.97
1.88
2.26
2.22
2.13
1.98
blows up
Correlation
Coefficient
0.98
0.98
0.98
0.98
0.98
0.97
0.97
0.98
0.98

                              95

-------
	2T,'l «..—-,.—«——
1
1
_ 1
1
I
1
1
_ 1
1
!
i
i
i
i
i
19,0 *««--«-—
1
1
}1 .1 *••-»*•»•
J_
1
1
1
1
1
1
1
i i
i * •
1 00
I 0
?*»,»
1
'AO,Q »r>








l_ .

u

.

	 . J
00
0 00
10.-0- . J
\
L l__l_ J
1 I 1
I
L . .. ..

a -Uo,
i
i
i
i
i
i
I
i

i
i
	 l
i
I
1 Oi
1 i
._ _J_..0. . -
. . ai o 11
0 10 1
0 1
o in
a. . _ . . i
n 11
L . ..11
1 1
1 !
-^ . -1 . . -.
1 1
- - 1.
1
1
1
1
1
0 IJO'.O ISO



1
0
100
•0
1
01
10
0












0 210

1111
1*0000
1
100
0















0 2*0


1 0 10
**0
0
1












0 . H|
1 - KD)
• . 0V


0 2TO



*
•0
10
10
110
1
•
M








s 	 . ,-
sumo
LU
RU>
_


0 200




L J

1
0

10
1
>..j 	
0
00
1 0
0
10

*




0 JIOj











_

.

1
0
»
00
1 0
1 90
.™iii2.
i
i
.
0 J60


















)
L
0
           Figure 44
                       M,T
               n»YS
Dnur.(,»S R«S(RVUIR  l9
                                                                        OUTFl.0"
-»fl-J
1,0
	
- —
10,0
.._-
19.0
JO.O
J'.o
JO.O
J5.0
40,0
*9,0
90.0
*j 0
21
*l
21
	 *
*
2
*
«-**•»!*
*
	 1
*
2
i— -— *-
I
t
*
*
*
2
•
•«"-B-*»



0
0
0
0
0





























































n - MEASURED
J - STAN"
2 - Bfclll
3 - nttzz
< - OUTLET
1
1
1



















1
1
. ...i.
1
	 ]_
1
1
	 L.
1
1
. i-
1
-J_.
. 	 L
1
f~
1
1
1
L
1.
. L
1
1
1 '
1
       2.0
                 1,9
                            T.O
                                      1,i
                                                12.0
            Figure 45
                       HJT
                    14.9      17.0      19.9
                        « DEBRtES C
                   1069—04 Y I <•«  — SU»fACE ELEVI
                                                                                         22.0
                                                                                                              27.0
                                                                                                                       2«.5
                                                       96

-------
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 I
	 1 — ..
1
1
... — 1- —
1
. ... . 	 j. 	 .
1
1
1
„ . -.1 —




t
2 I
21 J
1
3
1
_





) o
n
0
0





• 9
1
J 9







2*
3
2 0
1







i
21
21
0
0







n o
'















o MEASURED
1 STAND
t DElZl
3 OEU2
< QUTLIT
1
1
1





.........








_








	

_ ._ 	



	 	
2.0 4,9 7,0 9,9 12.0 14,3 17.0 19. i 22.0 24.9 27.0 19,
T!HPE'ATUȣ |N DEGREES C
Flgure-46 H,T MUPEL • UOU6LA5 «SER"l)IR 1969--1)A»I121 — Su«f*CB HEVI J9y.« M


—
	
	

	
L
1
>
1°
s,o
"io.o"
i?,o .
. .. ...
2»,o
29,0"
.
}0,0
J5.0
*0,0
4J.O
>0.0 ,
• z
!••.»••...
••-•»•••.
.._ .

	
.
•B-"e»—
<



B..»9..-J
0 4








,..—..-..<
» 7.


























0
0








n z
0 2 1
1 3
1






I)
0
I 1
3
2 1
I 9




921
21
3
^




o MEASURED
1 STiMtl
2 OELZl
3 °EU2
< OUTLET
i
i

*
0
3
21







0 1
a n I
1 .. i__
0 121 1
92 1


.





1
1
1
1
1
1
~~[
" 1
1
..._j_
1
1
1
1
. 1_
1
J
1
1
1
1
1
0 ».S 12.0 14. » 17.0 19.J Zi.O 24. » ZT.O 2», J
Plgure 47
                          ttnu'!t«»
                                             l«»9--0/lYll«ft   --SURFACE
                                                                             2»9,»
                                            97

-------
.»
9,0
10,0
20,0
29,0
4fl.0_
'.
»o,o
»V>.j
SO.O 4




n
^
L
•••••»—•






._.
















_






















tl








0


«E'
STi
DEI
DEI
™ OVE
< ngi





0
0


SURID
NC
21
12
LtT



0
2
2 IJ
2 1
1
2 1





J
*
*
21
*1
3





0
0 *
3
21


. . ..
"
.


	 	 .J

.
-_
__
.
>
2.0       ».J       7.0
Figure 48   H)T MUOEl  »
                              t'.i      12.0      1». S      17.0      19.5      22.0       2*. 9       27,0      2*,S
                                        TEM'E>ATutE (N DECREES c
                              OnuBL*5 RFSERVUIR l»M— 0»» 1210  --SURF*CE ElEVI  29T.7  M
'.0
..
lo.e"
19,0
20,0
29,0
10,0
»9,0
40,0
49,0
SO.O

L
••-•si—

<

„,..,„...

























































0







0 0


o MEASURED
1 STAND
2 OEL21
' DEL22
< OUTLET
i



A
a
21
•>




i
f
*
0
12
3
12
•12
12
1
*
'





1
•
1*









2.0       4.5       7,0
Figure 45   HjT HOPEL •
                              •>.»       12.0       14.9       17.0       19.5
                                        TEHPE°ATURE  IN  DEGREES C
                              ODUPHS RESERVUIR  I960— OAYI250  —SURfACE ELEVI   2»9.«  H
                                                                                22.0       24.5      27.0     Z'.J
                                                98

-------


5,0

10.0




20,0



25,0


|0,0
19,0
40, 0~
49,0



















_


1-
1
















"-T---B-





















-i— »«»












































.,...,...




,
















-— —





















	 	






*
12
*
2
2
12
3 2
12
3 1«
0 2
12

o MEASURED
1 S7AND
2 OEIZ1
I OELZ2
< OUTI.I7
1
1
1
2
2
I
2
2
*












~



















.-,....;-












_




.








.
2.fl 4,5 7.0 9.5 12,0 14.5 17.0 19. J 22.0 24.5 27.0 21*3
Flgur. 50
            H,T
                            Onuf.|.A4
                                                              —SURFiCf  CI.EVI  243,3 H
1 »
i r


i •
I
	 J... *3
i *
i •
i
i *
i •
80,0 *e!i-"H«—
| *
1
1
1
1
1
1
39,0 «„-.-,..—
1 .
1
1
1
1
1
1
1
1
1
1
1
0
.
0
0
0
o
0
.
""
....,..;.


















































o - HE<
1 - ST«
2 - BET
3 - BET
< - OU1
1
1








SUREO
ND
Al
A2
RUAP — -
H7
1
1
1
1
1
1
1 -
1
I
1
1
1
|
1
|
1
1
1
1
1
1
1
r
i
i
i
i
i
i
i
i
i
i
i •
i
i
i
i
i
i
i
. .T-^-L
1
|
1
1
1
1
i
1
i
1
1
1
1
1
1
1
1
1
1
1
1
. — -J_
1
1
1
r
' 2.0 4,» 7.0 9.J 12.0 14.9 17,0 1».S 22.0 24.5 27.0 2».J
PlgUM 51    H,T BQOEL •
                                      7EnPt«ATu»E.JN  DEGREES c
                                     ESERVQIH 1969--UATI  6«  '-SURFACE  ELEVI

-------
•«
9,0
J5,n
20,0
ts,o
--W.4-
	
»'.«
»0,0
^5,0 4

»0.0 <





<
....









I*
1«
«»


.




129
2}
0
0
n
0





12*
i'3
n
0







1
23 n
0







12
173
n
a







0 o
*2 3
t
t















o HMJUMD
1 STAND
2 IETA1
» SETA2
... • OVERU' — -<
< OUTLIT
1
1




_




— . .
..






	





1
1
1
1
1
1
1
1
1
i
1
1
1
!
1
	 I _
1
4~
1
1
	 1 	
1
1
1
1
.... 1
1
1
1
. . 1 . .1
          *.J
                    T.O
    figure 32   H[T
r.i      12.0       14.J       17.0      If.9      12.0
          TEn»e«ATU«E IN  DEfiREEJ C
Onu 1
_a_ .U.JLJ 	 i_
23 I I
1 ... 1
- 	 J 	 J 	
1 1
1 1
1 1
1 1
1 1
1 1
1 - _J_
1 1
1 . 1
1 1
1 " ~ f ~
1 .... ..J....
1 1
1 1
i r~"
1 1
1 1
! i
2.0       
-------
,0 »B?— S> 	 <
1
1
1
1
1
1
1
1
1
I
1
1
1
1
	 1
1
1
1
1 	
1
— »0,0 *•..-»»•—
1
1
	 1 	
1
1
1
1
1
1
1
1
1
1
1
»0,0 *<.---7 	 <








__.





































0








0
1

o HE
1 ST
2 BE
3 BE
< GU





0
0


tSURCD
'NO
rAi
tAZ
ERLAP 	
TLET
l o' T"
1 | 0 <3 |
1 1 1
1 * 1
1 1 *} 1-
1 121 1
1 1
1 1
1 »2» 1 	 . __i_
1 1
1 1* I
i •» n
i i
123 1 1 |
12 3 ! ----[--- \-
1 1
21 ..! 	 ^ 	 |_
\ \ \
i i
i i
r i
i i
      4.5
                 7.0
Figure 54
            M)T
12,0      14,9       17.B       19.5      22.Q
 Te«i>E«ATuRe IM DECREES e
          »69—UArl21B  —SURFACE SLFVI  297.7 H
                                                                                                  87.0
                                                                                                           29.5
tO
5,0
10,0
-H.O-
20,0
29,6
10,0
?>.o
»o,o
49,0
90,0
2
>•»••*•-•-
	
O9«ea™



<
•;— 19-—


























































0







0 0


0 . HEiSURiO
1 - STANO
2 - BETAl
3 - »ETAJ
	 * - OVERLAP 	
< - OUTLET
1
1
1 1 1
1 0*1
1 1
1
1 _l_
1
1 *1
1 0
1
1 It
1 *
1 01*
1
0 1. «. 	
ll»
0 1
1*
l»
1
1*1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
•1 1
1
1
1
1
	 	 l_
1
1
l~~
1
1
1__
1
1
-L-.
1
	 x_
, 1
-_l--
1
1
1 ..
1
0 .,.5 7,0 y,9 12, U 14,9 17. b 19.5 22.0 Z4.5 27.0 25U9
Figure 55
                                                 I'l BtRMES  C
                           Onur-LA4 KFJEKVUIK l«69—UAYI290   —SgRFACE ELEVI  295,8 M

-------
.0
	 1
	


JO, 8.

J'«Q
fOT0
.... _
$9,0
	
»0,0
49.0

90.0 <
1

.*-•*«,—








.





.

kei— si— "
O A
>-«T--r5-»?;--r-5-s»---^r™=1!
1 1
1 1
1 1
1 1
1 1
1 1
1 1
\ \
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
J- 1
1 1
1 . 1
J 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1




	
-*-•-*-—








...
_










o MM
l tit
t IE1
» IE1
< OKI
i «
i i
i » i
1 *3 1
i i
i • i
i i
i • i
l i
i* . i .
• 0 1
0 1
« 1 1
1 1
1
•> 1
1 1
•I.I . 1 .
»» 1
0 1
«> 1
.1 - ' .
1 1
1
1 1
1
1 1
.1 . 1 .,.
SUMO 1 1
NO 1 1
Al 1 1
At 1 1
l«T j [
L 1
1 • 1 •
J_ .. ..I»fl. JS'.S 12.0 14.1 17,0 If,} 22.0 . . «4.9
1
1
1
1
1 1
1
1
	 1
1
1
1 1
| ' ' "" T
	 1
t
1 1
1
-4:
i i
,: .:.: .:~r
!
. 	 L
17.0 29.9
        Figure 56
                    HJT
                      II U66REES C

UOUr'l»i KFSfRVuIR 1«69-«I)AVI276  --S1JRF4CF ELEVI  293.1 H
 9,0  >
	4—.
10,0
zo.o
}0,0  .i—
29,0  •---
«o,o
»l 0
1
1 0
•21 o
1
•21
_e_. ^ J 	
1
•21
1 0
•21
• 2 0
I
• Z 0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

























•






























0 "E4SURSD
1 STAnn
2 ET'l
J 8TAZ
< "WuM
1

















	 ™r-_
1
1
1
1
1
_L
1
1
1
1
	 J.
1
.. 	 1
1
. ... . .1
	 L
1
1
1
L
_L
1.
1
1
1
1
1
1
1
>0,0 *ei— i™ *.
    2.0
              4,«
                        7.0
                                  l.i
         Flgun 57
                                            12.U       I4.J

                                             TfH'E«ATu«E  I"
                                                                17.0
                                                                          19.
                                                                                   22.0
                                                                                                       27.0
                                                                                                                29.;
                                             102

-------
.0
9,0
JO.O
19,0
20,0
»~9,F
30,0
|9,0
	 1
"
4,5,0
»0,B
it
IM---S--T


<"
...
•*•»•«*••*•
i
>
"! :

.
*«r— -3— t
0 4





3
It
31
lr-=s«s->


i ~1



3
1 1
0
0
0
0





3
t 1
1
n
n

p
-


1
1 Z
1
1 321
3 1 2
3 11 2"
1
1 0
0 1 2
I 2
12
1
2
1
1
2 1
1
2 1
2 1
2 1
1
1
2
1
1 2
1
1
1
1
1
1
1
1
1
1
1
1
0 P
3 •







o HE
1 ST
2 ET
3 ET
---• QV
< ou








tJURID
ItlO
U
12
riBT

















- .


1
1
1
1
I
1
1
4
1
1
1
1
1
1
J
1
1
1
1
1
1
1
L 	 1_
1
1
J
1
|~
1
1
1
" \~
0 9,9 12.0 14,9 17.0 19.9 22.0 24, i 27.0 29.9
Figure 58   NJT HuneL  ,
                                      TEMPERATURE  1" DEGREES  C
                                    RfSEKVuIR I«»«~p*m21   — SuRMCE  FLEVI   299, «  H
,n
3,0
	 	 I
t».o"
	
H,o
20,0
J'.o
JO.O
?'.o
40,0
»5,0
50.0
2
- - 1
1
	
	

'e«*ra""™
<
,,-...-..-

ke?— "5— '
0 4















•

















1

e
0 3







>
*
09 1
1
1






3 0
0
3 1
1
1
2



3
3 « 1
1
1




0 . HfcASUREP
1 - STArc"
2 •. 6T41
3 . ET»2
< - PUT1.ET
1
1
9 "7.0 9.J 12.0 14.9 17.0 19.S 22.

1
3 n
0
1






U 74.
1 0 1
0*3 1
1 	 l_
10 1 12 1
0 1 1_2 	 1_
1 2 |
J 	 _L.
1 1
Oi 	 U
1 1
12 1
2 1
1 1
2 	 L
1 1
1 . -J_
21 1
1 1
21 	 L
21 1
2 "" 1
1 1
1 1
1 1
1 _L
1 1
1 l_
I I
! L
1 1
I 1
1 1
1 1
r-»j j
1 1
i i
S 27.0 27, >
Figure 39   HJT HU«H.  -
                                    TFM"taATl">l:  1"  nfcGRCES  C
                                              51—i>*Yil»o   — SURFACE
                                          103

-------
».o

1S«0
90*0
.
21.0
	
__Jfl,0,j
M.o
__J
	
*0.0

41 0
30.0 t
- -a*




K


_
	


—
-a *.












3 T.












a 9;












3 12,












0 1*.






0





3 IT.





0



a ME'
1 IT'
i JT'
3 ETJ
< nu1
0 19,





o
0
3
3


SURfO
W
I
2
HT
3 22.



•
3
3 1
1
I






0 2*.

2
3
3 *
3 I
1
1
Z
2
2
2





3 2T.
0 1
03 * 1
3 12 1
1 2. .1.
2 1
1
..2. L.
1
2 1
2 1
1
1
- . 	 U
1
	 J
1
1
1
1
. 	 	 L
1
I
1
1
. ... 	 L
1
|
1
1
1
0 29,3-
       60
           H(T
                           DOu-,1.45 HFSERVuIK l969--i)i»IZU  ..SURFACE  ELEVI   297.T H

— »"-*


3,0 4



10,0
	 1

-M«0


20,0


23,fl


»o.o


33,0













•3--M—



.........


""





B- .a


™..s 	









* — --






















— ...™













i


















-S— .i-«









~































~






'
































'















.. 	 i-































0
— 0 	






















0 0








1 STAND
2 ETAi
3 ETA2

1
1













0

0

1
\

.-.3...1-













1 1
0 »1 |
3 * 1
1 11 2 1

i i
P ..

»l - -
31
0*

« I .
13 2

1 2
1 2
32

-.2 	 ...









r

1
Z 1

1
-•* 	 \~
2 1

1
	 l_
	 Ll_
1
•, 	 — I—
1
- -H-
1

i
i"

i
i
i
i
i
i
i
i
1 1
1
' 2.0 ~ 4<9 7iO 9«* 12.0 ".& 17.0 19,5 22.0 24*5 27.0 -ZSU5.
                                     TErt'ECATURE I'1 Oer.REfS c



Figure 61   MJT MOPEL -    unu6L»i RE46PO/JIR 1149.-tfAyl25u  —SO"f»CE ELEVI  2'3.d h
                                           104

-------
i»
5,0
10,0
i',0
10,0
J
29,0
"~
IO.Q
11,0
40,0
4»,o
}0,0 .
.2

•*"-C-»*

- .
>eir«=a«-


>««- -i--- '
0 4





.











.








































0 HE
I ST
Z 6T
3 ET
< Du


'
*
* 2
•2
•Z
•*
0
• J


WIRED
kftD
u
12
ERUP 	
•I.BT
1«
J»
*Z
•2
912
1 2
2









«- — ..*.




1
1
1
1
1
1
1
1-
1
f
1
1
1
J -
1
_ L-
1
1
1
1
l_
1
1
1
1
	 L_
1
1
1.
1
1
1
1
1
1
1 _
1
9 7,0 9,5 U.O 14,5 17.0 19,9 22.0 74,9 27.0 29.3
Figure 62   KJT HuptL •
                               Tth'1e'AT()»6 JH nfCREES C



                             KES6K9«J»r I2T«>  — SURFACE plfVI  2">3,3 n
5,0
10,0 '•
. J
19,0
iO,0
29,0
>o,o
39,0
40,0
49,0
50,0
Z
*
9
..
*
•j
*
*
*
*
*
•




>BS"S^— <
0 4
0
0
0
0
0
n






























'






























n MEASURED
1 STAfi"
2 OIFFl
3 BIFFS
< HUTUBT
i
1
I





















. „_.
.







5 7,0 9,J U.O 14, i 17.0 19.3 22.0 >4.» 27.0 29.5
S3   HjT MUOEL ,
                              TF«»6«»TU»E  I" TEORtES C



                             EJfKVUlK l^M— i)»YI <•»  --SURFACE  FLEyi
                                     105

-------
10,0
19,0
20,0
29,0
40, fl
JS,6 j





<








1
1
1 2
29
2






1
I
ft
i
0
0
0





1 2
I 2
0
2
ft

3




1
2 0
o

1

3


1
1
1
*
12
n
0
3
3
3
3






3
3
3














o MEASURED
1 STAND
2 OlFFl
3 DIFF3
< OUTLET
1
1
1



























. . . _
.
- - - 1
1
>o,e »«
    2.0~  ~   4.5       7.0       9'.9       12.0       14,9      17,0      19,9      22.0      24,5       27,0     24,5
                                                    Tu»e I" OEC.KEES C
        Figure 64   H(T MDP6L *    i)njr.l.»4  nFSFKVutu 1<>49«U*YI121  «5u«F»CF FLEVt  299,» K
5,e
'
10, 6
13,0
20,0
29,0
}0.0
»5,0
*o.o
49,0




<







































3
1
0








n
0 1
1
1






0
n
1
1
1 2
2
2
2



C
1 1
1 2
1 2
2



0 - MEAS'JHED
1 - STAND
2 - CIFF1
3 - OIFF3
< - nuTLCT
1

ft
0
1 2
2


3




(
0
1 1 2
2
3
3
3
3
3
3





0 1
9 3
12 3 1
i. 	 1
	








    2.0       4,9       7,0        9.>       U.U      l«. S      17.0      19.9      22.0
                                             Un"eIIATb°e IN PeCKEtS C
        Figure 65   H)T HUngL »     OnW'U»i  KFS^ijVuU l«69«u»r 1 1»6  --SURFACE FlEVI  249,9 K
                                                                                                         27.0     24.5
                                                    106

-------
,0 .
>|0
10, 0
I'.o
20,0
29,0
|0,0 4
19,0
40,0
«9,0

















































































0












0










0
n


o . MEASURED
1 - STJnn
2 - OJFF1
3 - D[FF3
< - %ntT
1
1





a

I
1
1 2
2







• 2
1 2
1 2
1 2
2 3
2 3
3
3
3




0 *3
2«
* 3
2 3
3
3
J









J0,0
    2iO       ">t5       7,0       9,5       12. u      14.J      17,0      19.3      22.0       24.5      27,0     29.5
                                            TFri'1e»4Tu»e 1" r>EC.R6eS C
        Figure 66   HjT  MQIEL  .     jojc^i  KF»FK''U'« i«6«—iXvizit  --SU»FKE F.UF.VI   Z97.7  H
>o
3,0
1°. o
13,0
20,0
25,0
JO.O
J9,0
»0,0
i'(o
90,0 '
2

BS---S—

<







































'




















0







0 0


0 . HEJSHREO
1 - STAH^
2 - niFfl
3 . niFpi
< - OUTLET
I
I
I
1
1
1
1
1 1
1
1 12
1 !>
1
1 123
|
1 * 3
1 "12 3
1
01 « 1
1
1
112 3
0 1
1 » 3
112 3
|
1 2 3
1
1
1
I
1
1
I
1
1
1
1
1
1
1
1
1
1
1 •
*1
2 3
3








0 " >,.i ~7.0 V.» U.U 1».J 17. B 19, > S2.0 '«.> 27. ) J9.3
        Figure 67
                   HJT
                                                                            F.I.F.VI
                                                    107

-------
 5.0
10, e
19,0
20,0
29,0  ii
35,0
»0,0

™~
\»~TB™™~


.



























































8 . ME;
1 „ ST/
2 . on
3 • on
==-» - UVE
< - nui



* 4
e
* 3
I*
1*
1*
0
1*


SUMO
NO
n
F3
UET
*
*
•3
*
I*

















1
1
1
1
1
1
i...
4
1
1
1
-1—
. .__
1
I...
1
1
1
1
1
'l~
	 _L_
1
1
1
l~
1
1
1
_ . 4.-
1
.0 *.S 7,0 9.5 12.0 1*,S 17. 0 19.5 22.0 2*. 5 27.0 29.3
Figure 68
                                            TEhl'e0ATu1ie  I'! BE^MES  C
                       Huneu .    unyni.44 RFSFRVylK  1949— u**l276   --SgRFACF
                                                                                     293,3 H
                                                    108

-------
CHEROKEE RESERVOIR
     Figures 69 and 70 show the computed reservoir temperatures and the
computed outflow temperature at Cherokee Reservoir respectively, for
1967.  These can be compared with the measured data as shown in Figures
71 to 76.  It can be seen from the Figures and as shown in Table 12 and
13 that the predicted temperatures at the outlet and at the surface
have larger standard errors of estimate, 2.7° and 2.1° respectively,
than the results for Fontana Reservoir.  It can also be seen from
Figures 71 to 76 that the variation in thickness of the horizontal
segments from 1 to 3 meters makes minor differences in the predicted
results with the measured temperature than does the 2 meter thickness.
This is also evident in Tables 12 and 13.
     It can be seen from Figures 77 to 82 that a variation in 3, the
fraction of solar radiation absorbed at the water surface, from 0.2 to
0.5 makes little difference in the predicted temperatures.  This is also
evident from Tables 12 and 13.
             *
     In Figures 83 to 88 the effect of a change in n, the radiation
absorption coefficient, from 0.05 to 1.40 is shown.  It is also shown
that the use of a sorption coefficient of 0.05 predicts the temperature
very poorly and that in general the value of 0.4 gives the best predic-
tions.  This is verified in Tables 12 and 13 where the standard error
of estimate is 2.3° and 1.9°C for the outlet temperature and the surface
water temperature, respectively.
     In Figures 89 to 94, the effects of varying the diffusion coefficient
from molecular to 100 times molecular diffusion are shown.
                                  109

-------
                             Table 12
             STATISTICAL ANALYSIS FOR THE PREDICTED
               WATER TEMPERATURE AT OUTLET LEVEL

Reservoir/Year: Cherokee/1967
Time Period Covered:  120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
2.70
2.99
2.22
2.62
2.54
5.52
2.97
2.29
1.80
2.08
Correlation
Coefficient
0.83
0.80
0.88
0.85
0.86
0.00
0.78
0.89 .
0.92
0.88
                               110

-------
                            Table i-3
             STATISTICAL ANALYSIS FOR THE PREDICTED
                   SURFACE WATER TEMPERATURE

Reservoir/Year: Cherokee/1967
Time Period Covered: 60th   300th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
2.07
2.09
2.11
2.06
2.01
1.49
2.25
1.88
1.90
1.72
Correlation
Coefficient
0.95
0.92
0.95
0.95
0.96
0.98
0.95
0.96
0.96
0.97
                               111

-------
•1*1 1
191,1

i
i
L**™**"""
""?""
-. ..
BB~:_
....
IB «r«
• i - - «
"'"""I
1
I
0
*•**"-"
0
-.-
0
0
e
e l
o I
0 J
01
|
1
... J - .___,_
9
e"""'"o
B
1
BBS-sSt-B
1
I

.........
	 «"
t 1
.
•. .-»
-«L.
i
rfB?B-:ii
t
1 •
*. ! .
i
l ' '
i""* "" '"
i
E5-*-I-. t
t »
1 >
» 1
)

r 'i
1
r
''""r"
t
.-.»—».»
i *

»
»
4'
'
'
. .
i
^....^Ji.^.;?!
M' V '. I
t M
LJ1I
r T"
» i »
4 I
• J
e - DAY] t
l B DAY] i i
i - BAY] { {
» ATUItE JN eiBMII

                                          MSHtVOIR t*tT»CDll>UTiO
                                                    112

-------
?'|5 <
J»,0
?*•*
20.0

TJ-*-;





- -tO,

«*•?*••-







1
I .1

a. »9






.4.4.4.4.

,,H
u
^1.4,4.4.

9 1^0






9
"'*"*"
.4...4»^

l U
I
_
"
9 PO





0
0
0 0
g
-£.Sei;£?
)l
1



9 l«0

1
1
1
1
1
1
1
1
r
i
1 9
190 0 •
004 I
.. . . . e . . I .
' o T l
I I
1 i
.4.4.4.4 »J.»- 4.4.
---. j?..?* .
,^J......
1
1
1
	 1
1
•9 J10.0 J»0

1 1 " "
1 1
1 1
1 1
00091 |
19 1
111 000 I
0 i 1190 |
. 1 III .11? 1 . ...
01 or
oo i i i
1 I 10
J» . . 1 . .11
1* 9
1 B
1) 0
1
1 1 1 09
I 11
1 ... 1 ....
„. .,......T.?»?..7.?.,|,,
! »
i . . i ....
| 1
i 	 ..) ........
i • eoMpuTJo i
1
i
I --,--—
l i
1 i
iO J'0.0 }00,0 ' }IO

	 1
1
1
1
1
1
. . . 1
1
,-^.J • - - -

1
1 1 	
"i«l~J?r
00
1 00 1
III • 4T "
1 0
urn 	
*
i
l
1
i .... i
.-- ! .. -
!••• ••.-•! —
iO 1*6*0
       Plgure 70
                   H|T KQDiC
                                 CMtROKel  KISERVglK  l»6T--COHPUT|B OUTFtflK
 1,0
10,0 *«s-f
     I
20,0 .*BSS*r=T=
»s,o !**--= '
10,0 tac.444.4.,

     I
to,e
    ZiB
'












• 4.



---'
TT-
-*"'



•*^'



--V








S"



.
"




s



3
3
"







..
*



-
l

*.£.4.4.
t

*
^
m-\mtm»o
*
.





••*_••

'***•''



1.4.4.$.



.4.4.4.




I
11 '
X
! . l

i

i
.4...:.4.*.4.4.-.4,
|
j
1
1


1
.4...*j.,i.S.leS,S.

1 I -

1
1 .
.:... ;...*. i.;.i.i,
1

1

* 1
1
j









-»•£_•«•








I
.4.1.4.4T
"'



'



.4.4.4. .it




1 |
1
1 1
. 1 . . 1 . .
1 1
1 1
1 1
1 1
.......£-*£.•---•.•••.• e— ss?
1 1
1 1
1 1
	 ..i., 	 „_.._„;...;.
1
t 1
1 I
1

1
,,„_.
•~"""f

\ . . 1 .

1 0 • M|A(IJK(Q
l i « IT»NO
i t i OKI!
i i « BUJI
.4'.4...4.4.49* • OyCKkAV *s%-
i < « OUTUT
i t
i

'



~



«— s^,^^



_ .


... • • .





.




•»•»•••*




... -



— „„,„



--»^w-*«?




""'"""*'

• • • • * *










•«™"T*"»«







• ' i. '
"'""""



w»a«^».-



• i."."


,4,—^.i
* - • -» *

»J3*^™»»'


.



.
~*?™T"T"



•
«S--«i
.„.*;....   .^._
                                                                                  t»t»
                                                                                                     *7.0
       Figure 71
                       «QD|C •    CHIMKEi
                                                       I" OIOMIJ C
                                                       ^D*Y( »»  ?ilUM»Ci
                                                                                                               J
                                                  113

-------
                                                              a
     i         i          i         i          i                  n
     1  . 4 . . I  .  . .  .  '  .     .i  .,..'.   .   i  .  ..  . i . . . .  I.,  .  . ..I..   ...
     t

I0,fl  »iir*;«™*:{™i:™*ris-Ti8T3»«™s%3
                                                    If1
(0,0
|0,B *fey*-=-TT*r
|i,6 »c:»;e-?9 sit
|0,0 «n--;i-r? «
     I



  '  l'
     I


fO,6 *(z.i;«»-i£-

    tii       *ll
      Figure 72
                                            »>
                                       II   1
                                                  0|
                   .....+...—..,i».i.f....»...8....,«...,.r,....-

                                                    I
                                                    I
                          "
                    •",!         '
                     '
                  LJ-^uJ-iM-iM--

                                 I
                                    -*lrT*y»;t-ili-«T*lirt~~-*«j»« •   . . ..
                                          I    '     r       ' r   «»oguiT

                                                                 a • HfUUMO
                                                                 1 V ITiHO
                                                                 »

                                                                                                    I         1


                                                                                                  .1	.....J
                                                                                  r-»s-»»» •^•»I»«Tt(?»JT


                                                                                I                   I

                                     p;i^rs*H^T£tB-««*ei*r?-rr»*B^*»T-»-«*B«s-»«eii*si*-«5«i»*-»
                                        u;o      1^1      tTiO      it.i      ti.g     tv.i
^5i*r5?-Ti:-s*B;
  no      »;»

                     TIN'IUTUH {N Bf»RI|f C

 igoiC  *   CHIROKCI ReSIRVgiR i»»Te-P*VllH
                                                                         11,1V!  ItO.Q H
                                                                                                          ttrf
*»|B
JO.e
      e       4,9


      Flgurt 73     H)r
                       T;O
                                »;»
                               CHIRDKCI
                                         u',9
                                                    I
                                                 'n*r
                                                     |M  DIIMM
                                       RtHRVOJR l*tT;-.D»rlll»
                                                                 SURM(t
                                                                                IH.l N
                                                 114

-------
le
1
1 ....
1
1
1
• • j?- ' -
1
1

1
t».o *,£.;.;.£-
' "'- -
10, P icT;ir>?T?
1
1 "'^ '""'
1
f8|8 *cTT*;ir--
!
i
i.. ...
1
»0.» *e«tB=?T-
}••» 4



.>.!.*...


5™*-=?
-£.:**.{.
i T"
1
1
i
1
i
1 '
!
.: - i .---
... - J~™
1
... ._-». r., ,..
1
1
- .. {.....
3 ~|*'"~
1
^.H..u^.*-.
1 V
1 I
1 )
	 * 11 ~l r"r
t i
1 1
t 1)
T!t1"*"?""""
1
B ' r.i it





t
i
£
e
>«-ii5~i
0 14
i
1
1
1
1
1
1
.. 1 . J
• I11
1
l
1 I 1
f....^.!^--:,..
»
0
. . 1 . . .
'"l " VH|
1 r IT
1 -HI
1 i 01
•--•-•!"!i-*~f * 8V
• OU
1

., .»
i »
0
e
.


>|ilMO ";
tND
11
I»U» «r»
'HT '

i
i
1 «





.
I*






•-S-t»5BB
ii iT,6 i»,i tt.o i4;i I?
1

. 1
* "1
,:?-,i-:J
., . .
' 1
"«y-*-"«>»«
J
V* "JiTi
Figure 74
            H|T I4QOIC •
TiH'HtTuM IN eioRiii e
        i»5T«-e»»m>  »IURP*CI ILIVI  >i6f* M
Flgur. 75     MIT «QI>EC •
                                              IN CCBMfl t
                                                        B«IU»f»«l  II.IVI
                                           115

-------
               i
l»,e  E™-riT"*ii«r.*
JO.O
}0,0
jj,6  r;^:B-«.-»«t»-
      <
»0,0
JI.O
»0,0 •si--i5-i-*ST-i;1-B;»eiB»
    2.0       4(J       r.e
       Figure 76    H|T
                          «-"r.« ™«"5s
                               'S-3 ?™li---

 »'.}      mo      i»

           TlN'i't

CHEKHKci  RCSERVOIR
 1,0
•o,e

               ':4??;*-x?*FB:r-:|>*(B
                        I         I
                        e        «l

                           -  ..  !

,o,e






      <



10,0  BE-i-i.;.

                                   .£.s.£.s.*.£.£.£.^. ..»...£.
                                                      ......... .;,
                                                       e   »
                                                                                 .»s
                                      ..,:...-
                                         ii
                                        't
                                BS-T--W

                                   fl   • |

                                       1 I

                                      I  I
                                                                     •• STAND
                                                                     • ?««?
                                                             ITiO
                                         I

                                      "i?*r
                                                                                    •-•«BFB». ""B1

                                                                                              —-t^w*-*.
                                                                                                      !         I
                                                                                                      Lis-ri".. •
«.0



 Jlt.l
                                                                                          t».i
                  -F-t-tr-i'
                   IT^O
:.J.
 l»,l

                                                       |«~«"""~"**i*i™™p»» «»»»••«'
                                                   «•» -«-«»5-*-r-——*r
                                                                   0
                                                         ^****p?-»
                                                                                   «T»"BTB!»9*""B^»»B

                                       WHO
                                       •ITU
                                   1  •I|TAI   ,
                                 --'   DVIIH»» iB?.
                                       ogtiiT

                                         i
                                       . i
                                                                                    -».*B.«F* ..B"»BFF. Bl
                                                                                                                I
                       r.o
                                                      ,»      17. s      ir.i      «».«

                                                       |N EJOMM C

      Figure 77    MJT M(|DEC •   eHCKOKff mffRVplK  l*tTB»,»  M
                                                                                                     f*
                                                                                                    tT.O

-------
0 *c«,.».;-•.»»?.;.«.;...:...
1 -


5,0



to.o


)9,0



J0,0


39,0


>o,o

lf.fi
f'f u


|0,0




*»,0


(- -..r...--




e:.»;.i.l.i.£.i.£.




1
1
1


«--•.«



	


,-i.i..;.;.


c«V*-"







.i.;.;.}.
"



...i™.


.*.«.«.
.--

•1
»-«"«


t*

•
ea-»*9-««p«»±*l»±<>
' " I" "


. ._!_._..,_._



	



1 1 II*
1 1 1 I
1 1 1 1.
... ' - - - t ' 1 .. 1 1.
-•-••-,--•' '-,-- -- : • :»» I'*'"— ?«•»•••*"«"•
1 1 1 11 » 1
1 1 1 1


1 1 1001
1 11)1 0 |
• .-.'-«• i ' ..'.... 1
..., r|e. ? T-?)r-- r-"r ««*•?»•«»•-'"-«*?•«•??*?
t» e
.s...i!!Jei.1.S.iJ *....-•-

i i

')••••••»*»*•«•»•* ••»*•••£ ••*
'"»»'" V "r •-V""*" :r " ""I T -]-•"'•-••
i i
!L ..L^^U.:..,
rsr-T$-s»E-!-9--«»-!-.7="?

1 1
1
1 1
10 ' ~ \~ ' ~ ' '
\

\ !
i i
|
1




1 ...

|
i....i....i....i.. j

T'""T " I ,T "I 	 r"o nu|ukig ":

1 i
1 ITAND
1 IHAl
_. J , . . 1 	 J Mt»t

•-T -(« .-, r-T(-- T-
1 1
!f
* OUTLET

1 i
• 1 ~ •**'


* • • •
^•••9.*»r


,».B;,«


.^,..1.1,



*•••• i* '


.


(i..t:,^.

.



•••«eiip?




ev*"?**^*





. • . •
-•e»»«*»r





^' ; •_•



•••• ".""
'




..,i(i^





_




•~?"T*~IP*



TTTT?


» «
*"*"*"""*


-*P--^-P^


-• -™i.
. T ...


^»^<_-*_^
"c"" -T~*

-r*J


,J?..4.i,,

. . . 1
r


^•^.^^ftj
'



-Tt-r--^^'
.. ... ,

. ..:.;
2iO       «il       T'iO       »'•!   '   lt',0      !*;>      ITiO
                                        TlH'i«*TU*l I" OIBMI3 C
   Figure 78     H|T "gO|[ •   CHIROKd RCilKVDU )*»Te*OAvU*)  >
                                                                                          I*, I
                                                                          ILIVl  ItO.B
l»

»«
l"



lOgO


13,0


?°|0



^9|0











JO,B



JS,B



»o,e
?
.


Bir»;5---






-
"


ei-5r5«-



....
....


_
'



<
E--S-5—


ei-*-*-~



TT— rS-i-



^s?-«r»"**'
0 ^






.



ie..S«S-»*


.i.i.i.i.
	




..


»««»*




s"r"=""a*


• •••~v»?l


_




»5«™S-S-<
9 T










__
...


_
""




.


_




...


...
1*

*
mZmmmmmmm



.»..i...<
o »•
1
1
1
1
1

1
1

1
.,..'.

1
1
ei_. 	 s.i.J.t.i..,
""l"
1
1
.'...»

... .. (
1
1 '*'
••••••••9*sl29g«**
" 	 1
HI
1 0

'"•»""p~ ""*
»• l
1
.........0..-..-— i
1
1

riri.i.;-»---T«---
1
1
... 1 ....
--•-•-•r?*-?-S*s--"<
i u;o t*'










..•-.-_e~
t

-«•-§«-
•
in
1 .

1

e
^m^mmummm
e
e


..„„„..


""'"'"


_



_
••••••••£•'
» IT,
..






U *
0
• »

>"
0
r^...-,.,
'







•••»•••••




.-

_
"fl . MEi
i i IT'
t • l|1
1 >• 111
• * - f1ij|
PT** P" ^*V


.
£•••^•••••4
0 IV.


.
rwrs"««a"

•gy




C*?*~afF»


,,,;-.ri.







• •»**p-«



_
'"""""""


I"MB
NO
tl
»I
I'T


m
••~r~*~r~
» *>


• • _Z'
1*90






••.•r^_^-


.;...»..,







rl.**M»*



• •
.





_




o i»;



'






««-r-^ffr
'


— e-»i-s-







.i.^t..l.






.-
. !• «•


_




9 ITi
i
i



i
* «* *•
^»T -*^p*1


FTf"--i««


•M--i-i»


........:



i
'"T2™™"™™^
'



. . -
I

_ -
~ r

l
. ..I
'r


_._...!
r5 «t,i
                                                   . |N PiBljllEI  C
   Figure 79     H|T MQOIC »   CHEnDKEi REitRVOIR l«»TE»fi«Yll*»   «j!U«F»Ct ILEVI
                                                                                IW.l n
                                                                117

-------

>, a
.0,0
.0,0
)o.o
to.o
J«,0

es— «--i-
BT--SB"-
- i i -
5.
'
.
"








»•

I
._r_,.-^.,-rv-..-,.,
I
	

,^.»,^e»,..— -,
1
1
•**L* -•-•*
•'" "1
i
i
i 	
	 "i — • •
i
i
t
                                                                                                           ;
(0,0 *ei-i-
    i,e    '
       4,1   '    no       r.i      i»;o      iv.i      IT.O
                                    TlH'iMTUKf |» PISRIil e
Figure 80     K[T KBDIC •   CHIKOKCi KEilRVOIR  ;»6T?-0*TIH»  f
                                                                            «.o

                                                                             }!»,*
                                                                                      t».j
i»
*,»
10 0
»wt "

19. a <
t*f v *


20 fi
»u,°
29 0
f *tw






)9,0



jo.e



49,0
"



pe__»____v_T_?_w_s?
'
	
"

1
1
1

\~
1
1
1

1
_
1
1
1


< 1
1
hef*prs---*e-*-*-.5.
1


hE?BBr£~*~*?*a?*^?£*
.



— — -».*««-;.«
"
j


P..-._.C_?
_



_













•>••>•..••••
"



_
-.




"



'Tr^?3-^r?«
»i"5-*B9




'.- -.. -.-





.........






.



^••••••••«
"



....—..




'S=— BC3.-V1
M-9S9-- »




"




_i_i_-— • _
!?S"T?S"™"






-«-ri-«-



....
-








•r~~^r~rc^
_
"



_





— — _* _.L_i_
•*"™?""^Sy






	 r 	 ri

•
* »
««"•-•-"-
Jtj

I*
.•»» •




pr~2>*>P»--.BiVi
^ —




*r




1
r---»-lf»
i* '
• 1
u»

• ^y
>
«|fr 	

i

'!-r-~ T— -•
0 Hf
•IT/
l[1
ii
fc-i« QU
BU



»r~~y^~r2t"
_
"



_
'
u»

It » .
;zj a"
1°
.
— 9—-P-






• •.^.•-B..



,«..£•«.—
iJUMO
ND

AI
• I A* •»_••
riiT



»p""™™»»yf«™i
.;..,..„-.,
.
• i


T— '

0 P
_


'*""""L?'"






p-*-*.«..



_
'









-.,;,.-i_



.






•>•••<• B»BI*M*






— r-r—r?



•.. •••••••



- . .
"


...iT._^.

"

"

_

1

. !
.„ ,

"" "'

.
"' '



.
'



_«-••«•,<
-r



. .
''


.
2.0
                   T.O       »'.?      u;o      is?      ino      i».j      w.o
                                      TlM'IKATUM |N DEEMfS  C.
   Figure 61    M|T HQPEC *   CHEROKEi  RESERVOIR i«^Tr«Oiy li*»  nHIKfUl «t(VI  ?2>,1 H
                                               118

-------




,0


,ft


,0
,0

,n














,o



,9 ,







1








<

*e E»-






-:.








... --i.i.







































.























. .














_



























e
. . .


-T-i-j 	


























0 0




— i — .-




















,



•
0 *

•8
.
0
* e

I*
•i
•i


•t
•i
•i
•
•?
»t "

•t
.
e



,0. ...


_
e MUiuneo
i STAND
2 BETAl
> • KTA2
< Byt^lT

1
















'•""S^*""



.— r-l-r


• - .


.....^...
















•



w
•--•r--?-


....
....,„_.„


• . -•-


-^-1.^--



h. ........
1
1
1
1

1
1

1
. 1
"r !
1
1
•~ — 1
1
1
. 1
	 '1
1
1
. . . 1
1

1
. . ...J
1

t_5 	 ;_;^
I
1
1
^s_-^4
Ji«
   Figure 82     M]T HOHSt •   CHIROKEi
           1T.O
    (N OESMEI C
l»»T?.|)»yiZTT  -i
                                                                                            '.3      IT.O     2»,l
                                                                          EI.EVI  Jl».l M
,«
>,0
;o,o
l',o
«o,e
*»,»
JO.O
i'|0
»o,o
JS.O
>0,0
2
kBB-»-»-—
ES-r-s—


*es-^s="""
<


c....j...
'•»-- si---
0 *

'-"««™
Jl*
»• I
** i
• {
* £
• t
* 2
• 2
* 2
• 2
* 2
* 2
• 2
.....i-i-
» 2 •
'i*
-i---iB-3






.:...i.-.
1
I
1
1
1
1
1
1
!
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
_i_ir—i-».i.i--— .
1
1
1








_
••••••r««>








0 M[
I *T
< IT
» «T
~«» «T
* 0V
< ou





•

SUR!0
ND
i
1 -ri-
«!.*»
l«T
"1"
1
-•«»•-•««*•»•«•»"•"
1
1
|
. 1 ...
' 1 	
,
1
!
i
.i...:.,.!.,.,,..^
'I
i
I
. . i ...
.•••••••v*«-~vj*-a«
r
i
i
i
7.1
'?«?-?— ^

...:
	 i



?i..,i.i.
^"""-f.S """«;» "il;5 " »*.> ".o i».J «.« «*.» *T-« *••'
   PlBure 83     KJT H01EC
                                                                      119

-------
,"



'

10,6




(1,0




|O,B


.1,8




90,0



11,0



tO, 8

ji.e


1
l
1
. . 1 ...
«r— -B— ^ -------r-
1
1
1
"™ *"" ™ "~r"



gr^..j.»*..H.»«
T ' "r 	


1 ....

1

•E-KSB=-T*-?-=B%-B»

•

< 	 ; 4

~"T| »4*~"

*»

1 •»

1 *

"•"-"P*"*
. . 1 .
1





. .
"~"""**5


•y""^?B*l



•S-B?SE*9

>l

»»

» *
Jl •
,»e.,ie-3
"




.....£•«.



»...±..j>



»...!...

.



1 t l*>
1 1
i n i*
i i
i i
> ; » 1
™...i.*.:..i.i.iri.-'i.A
r""l"l """ 4 l" '"" 1"
1 i e e
» 1 1 4 0| 1
] l
}»l^EB4rB*rs*Oe*«*4**"*2v*.
''1 )'
48 |I
j
0 | t
*»^«0p±9 •••••••••a*>T**?>«<>V*
1 i
1
It

" ( '
i 1
1
. t ! i

"p" ' " "'i' |
e l
t |
1
" • V '
1
	 } 1

• • T
1
1
,:---.-.;. .i-i-i-i-I...!...!.,
r
i
j
••BKKBBWV









^••••••••l


.1.......








_._->_i 	

1
1

1

|
.-L
r
i
i
... i
••>«»•»••»*••».»»••*»
"|
i
i
. i . . .

f. ,...,„ ^. .......
i
. . ..i 	
'" i ' ' "
i
|
i

i"
i


!
1 1
J
• • t i1" * * *'i"" *•-•
l if ITINO |
i • IT«J i
» • IT»| i
«i»4 «• Itil .-T-*.....i...
• i- CVIIU» ' 1
t •• OUTLIT i



. . •


	
r - T.



.V.^B".C.
.



.«lfMl.


i;™,;.ii
-












•"«•» i

™?iTir«



1
.. . . 1


. . . . |
«. „



.l...iplf,,
. .

1
. . 1
,;......„
-H
i
ilil^lilij

1

• J

»__..-•-» ^


•£...£^£?



..^«£M«d
:-.-=, •


! ! I 	 \- \

J.o 4,j ' T'.C »;j ' it«6 i$,| 17,0 if',1 ti.o "»4,i " $7,0 "' *»,i
TIH'I'ATUM |N DI8RIM C
Figure M B|T MgDfC * CHMCKft RIJHVOU }f 6.»DAyilt) ielU*MCI IL«YI 1*0 1 6 M
1,0

jo,o




11,0



{0,0






}o,o




)i,e




4,0,8



45 8
" '


an M
,...B«JE~~E,

. 4ij ^.
»»-^B.-^E--.-..E-

1

BB*E"B...*.*~.a"£~
1
j

f^T*.g7H«..H»«.
r
i




•i»»5S«**S"~SrTSCT



<. . 1 ....

r 	 "

i

.

i

j
r
i
i
i







SS"*BrB..



»...££.«
-.






-ii-«t--




££...£...


t

-IB-BlBl-

11 4

*-.! •




i t
t i
i i
x I . . . . '
~~-"^-9,5B*aM"- ,*"-•*****
i i
i i
._. 	 -ji.-.j..^ i 	 ., 	 ..
e...- --B ..B— * i-.----

1 1
1 1
....'....' . . .»

- r-? B.?^-;--- • r -»»j •«
1 1
1 111
1 1
••••••••••••»«B9«»V*i»»lv»*4*
, -,-- -. -,
1 1 It 4
1 1
I 1 11 4
"""-"" i""i""i"'ir* """""
1 1
II i 4 e
| |
»»«*»«iit» I •e**9«4 **»••••»•»•»£•
r -"' ' ]' ' ' i e -
> ll 4 lo
i PI
.?.»•> . 1

s'l 4l" "" |' "
1 1
i » 1 1


"l" " 1
1 1
1 1
1 '
.............................

1 1
1 1
1 1
.

.?T".| —

1 I
8
1 4
rM.«...
4
8
4
r^_..^.._

.lr......




...~T.T..









i n
1 »14I
i "i
I > .!>*'.. . . .
	 »"'"l"i*e?*Ib»i " "'"'
r
BBB-.""
0 "1
• 1 4 } 1 1
, .... .,»._. r. ».» . .w_? „,

4 1 |l
1 1


. . 1 . .1. 1 	 .1 . _. .
.,.,..?..«r—..?.....?-I.-t.............

1 1
^-J^J^^L-^

i • | • "i i
_UiL— «— J
i i • " • M • • •
i i i
t i
.1 .. i.. ... i .... l
r-«?*«l*rT«««*r»T»TTT?»T??TT»TT;<

t 1 1 1 1
1 1 1
. 1. 1 ... 1 	 .1 . . .

~*~V"i * '" *r * *""?"i •"* "
1 1
ll i l
1 1 . . - 1 . _ .

"e Hi»|UKIO '" 1 1 '"l
i STAND i i i
t ITU 1 1 1
. » -*T*i .1 . i . . . i . . .
*'*• OVIKtif *"l ' "l " T---|- -«
< OUTFIT i l
I l l l
1 . 1 . . l .... l ....
»o,e t,i—~.--t..-~
    2.9       *.?
                 7.0
                                    1210
                                                                           2Z.O
                                                                                     «V,f
Figure 85
            HJT
                                                       IN

                                 CHERHKCf «t»IRwOI« P6TT-04TI184  nplU«F»Cf
                                                                            JM.J H
                                                                120

-------
|0
1,0
10,0
13,0
(0,0
29.O
lo,o
»o,o
ts,o
tO.fi 4
2*



er— -5—

BB-P-B---
•i-^3---^
r=-J==«-

0 4



-----
,.-..:.
,».».£«.
'pl-i«-«
'•"iea-es
fc-i-i-i.g.

? r



-™«B--

!*5S"-^;-»
-™-?«s-3
1
»l
Ti»lr»=-T

o »•



~^-~-

.
C--5S-H-5
1 1
1 1
e--i=i5*T
I t

i It



SI-*T5"»

I
. ! . i
«-s»r«-
» i
> »
4 0
0
•S-^TS--*
-ST«ri"»

0 1»

i ' i
i i
. . i . . i
i i
i i ' i
i t i
1 0
1 » 11 0 4
•••?— ;-«}ijl-i-o-»^i-i-..r.
> 11 «
.» 11 .»" .
» t » 1
1*1 1
,„> ^.L- • i - - •
4 !" T " •
i i
» i i
•«p-0«-5-*-«-"T»— •--^-««-
* 1 1
! !
8 i i .
i i
i i
i. , 1...
-•»-»a-*₯ff-"-9B-r*1»«---*-
1 0 ;• N|i|UMD
1 > • IT4ND
i t . IT»I
1 . ' • '«?
...^. ....«.i,» i i^tj »,i.
1 • •• 0»IRL*>
I < > ouriir
1 1
J lf.0 !«.$ 2*

• J , . •
II ft
1
1 1*1
0 1
. . t 1 «...
* • • 1 I
1
1 1
1
*--«TT-a«i|BT»i-Ji
1 t
1
... II ...
r
	 !' 	
t
1
. ...»l . . . ..
••™?^r"T*T'"F'T«
i !
. .,.!.....
1 1
?™^"S-T«-*-»--T--»s
....uL.^.
1
1
.0 M.l 11



1
??«-»-*
.
.,,..
-..-—„»
*•""
fB2«4--»

e «»,»
Figure 86     Hjy


5,0
10,0

J»,0

29,0
i°,o
JS,0
'





ns— *B5— •"
HB— ES—

B--- -B--^

fce-^rs-B-T

"

"
-
_
"






"
.a...^...
....
..





>«•*«---

,.i.i-— i.





.
	
	
^
- --• .
1 1
!
i i
i i
!. . 1. '
i i
i 11 i
i i
...,„.,.:.; 	 f.i.-ii.-.i.
1 > 11 o 4
ri •""•• *'* o t
1*1 14
1 1
' . l *
"ll'l'e 4 i"
1 1
> 11 41
0 . 1 ...
1 1
» 1 1 4 |
1 1
1 • 14 1
I i | " 0 MltJUKIO
1 1 STtNO
1 4 | i ITA)
1 . S IT*»
1 < 1 OUTUT
1 1
1 1 . .
• L» i- ",i B
.11** . ..
F— ---•-*—•-»•-•-
1 4 2
.'.'....
4 2
0 0 |
2
1
1
1
1
1
....T.?.,,r_.r..T.
1
2
1
2
I
21
2 1
1 1
.........'...-...i.
1
1

,;.--;-;„



«•>•*•_•_«


                                                    OiSMEI C
Ptgure 87    HJT NQnEL •   CHBROKeE RCSiKVQlR i»6TB-0»YI?»»  -?SU«f*Ct 'IIVI   114.J  N
                                                                121

-------

10,0  e»-*ra
90,0
{0,0  n~ ri—
}l,0  e,..r
}0,0  «{
J>,0  eB-»y§«










«




v«



.




••



--








••




1
1
1
1
1
1
1
1
1
1
1
I
- - , -
1
I
1
5™~TS~™?"*™~5"2?™"?
|
I

I .
I
i
i
i
s-^rs»BB-*-ir--ij-i
1

1
...j.i.;.,.i...i.i.
	 1
1
1
1
-«•""£>•••" BT5-»
1
1
1
1

1
1
1
t















Bi~B-B-»








E«B«~?9












=™-e-BBS







,






....



.
•B"S5B™"—








"



.


0

--



-B-B-B«T


















^
•""••••••








.........



•-«--"•

o e


...;...£.



m—^lmm—ym







.



__a^v_**_


,
B~B*?"^*B




B»e"-»«








-r. ......

t
HA
,,,....0,


314

---«---»'
0 M|l
IT<
ITJ
ITi
T*« ITJ
oyi
< oui

..

I 1^

»» »
M *

S}4
• 91&
- «»•
M*
•»*
B^BB*"B?^
IU

n*

-, ,.
-*-*)-)»-

» i* i

:.i!i.i.
*"»»»*"

•>* 2

_
-" T'"
i
i

l"

t

SUMO
NO
a
ti
k} ••TO
Kit*
l«T


9
»

t
e

i
	 i.i.
"
i
.. .
!

!
• ..
'•^•^••••91
'
1


.



>-•*-.--• H



.



. ...
kB»-»--««-^








    ZlO
              SJ
                       7,6
                                 »;»
                                      ij;o
       Figure 88    H|T Mgnjc •   CHtRIKCE
                                                         17.0

                                                    J DIBIIIE9 I


                                               J»6T?,B»yiJT7  BB
                                                                       i»,i
                                                                                 «.o
                                                                                       M.J
                                                                                                             .J.
                                                                           IlIVI   III,I M
 >,0  CB
JO.O  e»..9.B,,
*»,e
                      12
{0,0
j3(0  e5""rBr~~*?"~?S""5*
10,0
                    * >
                       !• VBB'S^S^B B?B7?*BB9
>0,t>
                          i


                      !  *?
                      rSB
                      1
                                !-- B--BB-B5-

                                             -B-?-B-i- T-T—-B- -?--'
                                                                       HfttUREO
                                                                       JT*NO


                                                                       BIFF*
2,0       «,»       7.0




   figure 89     BJT Mur>EL
                                          UiO
                                                    l*.J      IT,B


                                                       N DESRfiS C


                                                   l»6Tr-01YI »»
                                                                   OUTKT

                                                                     i

                                                                   it;*""''

                                                                                                      i


                                                                                                      i  ...
                                                                                                     ?***»"*•••»•


                                                                                 Z2.0
                                                                                           IV.I
                                                                                                    IT,0     2*,f
                                                                                  >16,9 M
                                                                         122

-------
,0 <
9,0
10,0
19,0
20,0
29,0
}0,0
J9,8
30.0 4







<
*
"








t
1
1
1 1
"
1 t
1 I
"

; 7

i
i
i
i
i
i
i
i i
11 2
lit o
1 21 9
1
2 1)
1
2 9
9 1 9
1 8
I 1
• '|
1 1
1
1
1
1
1
1
0 »'.» 12


I
1 2
I 0»
)


-«-»-*-«

0 1*

•
•
2 > .
1
o o



"
_
"

• 9 17

I
1





""o . MI
1 • 17
1.0
__ 9 . oj
< . Ou
0 1*

1





":-.«-Tr^
iMi5~e~*
AND
'I>1
riiT
.» «2







' '
""
- - • • -
.0 I*

	 .;.;.«-;.— i— .
I

.
'

1
"I"' " '
,) "7.0 2«,9
       Figure 90
                   M|T
                                          REJERVgtR p6TeiP.«•••
*


<









"





>•••••••••
.-




!•••••••••(
-.




.


_
-







>..».-.£.




!_•««•••••
















*•»•»••••*•
"




_
tmmymmlmmm
















'••••••^^v




.»..^...





1
1









i«»a««a«»9





"















,T;-i— ;,

1

I
----•-•s*
1

I


2
I





1 1 1 1
1 1 1 11*
1 1
1 1
?H««H»*a*«*«B£«4«S»~«BBa
| |
1 1
| |
1 1
•••f •••••^••»*a«v*+^pw*»«~~* —
I 1
1 1 1
1 1 9
1 1 1 1
1 11 2
1 1 "
lit 9
1 1
1 0
11 « 1 »
j |
U Z 19
lit 9
1 1
t U 0 II
'1 1
_l»_ga*2****">B3«*"~"*""v~
10 1
2109 I
» \ \
2191.
.;.f).3..^+»»--»«-3-+--»*— —
2 | 9 I
1 1
2 1 9 1
1 - 1 .
1
. . 1 .»*
-«--— ---*-•-•*-•-*
1 i a • o
0
• t 9
1 .
~O~^J™"«I~*IT— "a»~"^
1
9 1
1
9 1
) 1
1
\
1
1
1
1

1
1
1
1
••••••^••••««>«»^
|
1
1
1
••••••-••^••••v~«*»
1
1
1
1 . .
1 10. HftsURID 1
1) 11' 'T*NO (
I II. OIFfl 1
1} 1 _ 9 . OJFF9 |

I 1 < • OUTII7 1
1 1 1
1 1 1
1 1
~B™T*"-*"-"~™~"

1

>»BHf •»•+ 0«~*»*^ 4




•— — 4?™™4"*~— ~~~^~"^*

1

. . . * * .
i


	






i
• . .
._H*^W«_t«aH*BMW.I
'

1
1 »•
>•••--••••*•••— r~«^'
1
1

. . 1 . . .
mmmm ^» • fatmm»mmmmm*i
1 "' 1
1
1
. . 1 . . . 1

1 1
1
1 !

.0 " *iJ 7.0 " »i> >*'•• **•' *T>0 l*l} 'll0 *4tJ "*° ***'
>o,o *,..-«-.
                                                       |N BEGUM* C
       Figure 91     MJT H01EC  •    CHiK"KB6
                                                                  123

-------




9,0

10,0


IB •
4?,O


20,0

23,0





)3|0

»o,o



»>.«







C»««3V»B








V-—-S---



••»*—••».

f,...^.^.

i - -
"



nr— r»--'
*







h«« •.»••»






.

"


...
••™?5^™C"

»«-»;_

-™-»-



r--TS?-i-





""~"B™

••••••••V



.. -




_



-

-i?-~S-^



1

«~l«S"™





-*-,=,

-»-*•••««






e*^5?"Tr»

...



"""

«i'"-»5»
i
i
. -a- .-



Fi,;e..i.







•«£»M«






"" """"




1
" V
.

I?.,.;..:
20

t"
i

z«»«««
"





"~™







1
1 "

1

Z
Z
Z
2
0
•--»—«-

... i
i
j

......I?.





"""""

.£...-..-


1
,.-
1 2
. • .
i"



»
»
" »
>

lf«-'— ~




,..i_. .;.*.-.— ;..j
1 2 1
...•...•ii.!,e,!,i.

...p..,.»..,^,.,..
a a
82 l>

»
i
i

.
*<••>•••••••
"





...^..,|.

..,Z...I.
"a NI.SURIO
t OIPH
* OJPPJ
»•• oylRLAP *v~*
< OUT.I7

1
.- -

. .
- . •

~-.~;,


.
"

—•'•'-•


• "I '

"""""
--.-..

"""'""

mmym^m^mm^mmmm^ymmmt
||



•(••••

• •"«* " 4,
j

.-,_--
I

	 | - r . - . . (
.
....


^
	 	 .;;.-••]



1 I
. ^--,. ^
i


1

••••9MB9«M*M»MV**HMM*««4
I " '' " •'••••-•
1



' ZiB  '""  *iS   "   VtO
     Figure 92     HJT
                        "*"       " " "               '*              JZ.O
                          CH!R"KEt
                                                 |» DiOKICI C
                                             t*6TeiQ»YIZl3  ?
                                                                             JJ6.4  H



'•0


(0,0



,3,0



ZO,B




*',»




|0,0




29,0





"



*»,o




2
• KK~— ^ E — — •





iC5.«sv...



- ...i.^.



I£M«~».




'X?B*SS'~B





"

<







-



*.---?--.




. " *
.....





.







-••••••g*




r-~s--r-















-








S 7
' " " "


.


•=5'?-C*?




"


. -




••••••»••
'





-



_
~




""""""'



.1-..--.-




0 9
5~S™^~T57^


.
"

.



-.•£«•«



•£••»••••




••••?•»?










"




.



_




» 12






...
-







••«•••••
"




.



















_




0 1*
>_.._••._..


.


«•-••-•••£•



••.••BVB«



•»»«..-2*




.......i.











1

•

1 "

i

..«..-%-




» 17
1
1
1
1 .-.
1
I
• . ' . •
V "
1


P7l
i
i i_

ii a'i*
i
11 a z
I

a I "
l 1 2
I
i I i

10 z
i
I 21 »
1

1 "
z 1 >
1
z 1 s

Z 8 HiiSURiOJ
1 STAND
2 t 01PF1
' OlFpl
-~,» OVERLAP — --
< OUHET
i
i
i
0 19. J Z2
*

•

•

^••^•••*
1 *

1 21

2 *
a a
i
•••••••••r
l"

1

_

1

3






""'








_
"



_
0 2*
- T T


• . . •


••9*****?7



. - *



«~HH*^




...iTi.i-









_



.

I-" «



_
^



.
,J 27
: ' 'i
1

-l-iAjJ


•!•••. .t.1^4
1


- ,



•»~*»«.«^4
i



•••••••Z**4



1

•




'3
1



' " " |
1
I
|

' 1

1

0 2t,9
                                                 I" DEOREEJ C
Figure 93     «JT HQOEC •   CMEK"KEE RfS'RVgiR 1967—O.yIZ*«  -
                                                                 124

-------
  1°
9,0





_
	







<



















_





















0









0 0








12
0 «J
»«
0 Mi
1 ST
t BI
1 0|
< OU
(
l«
I*
I*

*t
;•_
I*
o
i i
i
'
i
tJURIO
1NO
•ft
aiT
I . .


'











.


. _.




"


.....
—

—
—
30.0

                                                                                        I
                                                                                       j-
                                                                                        I
                                                                                       . I
                                                                                   •••••^4

                                                                                   —4-
                                                                                    -i-~*
     Figure
    r.o      »-.j


«1|T M01EC •   CHEK^KFE
                                           ?     n.o
                                           |N BEORBiJ C
                                       125

-------
NORRIS RESERVOIR
     Figures 95 and 96 show the computed reservoir temperatures and the
computed outflow temperatures respectively, at Morris Reservoir for 1971.
These can be compared with the measured temperatures as shown in Figures
97 to 101.  It can be seen from the Figures and in Table 14 that the
predicted temperatures have larger standard errors of estimate than do
the predicted temperatues for Fontana Reservoir.
     In Figures 97 to 102 it can be seen that the variation in thickness
of the horizontal segments from 1 to 3 meters makes minor differences
though the use of the 3 meter segment does lead to a larger error as
shown in Table 14.
     It can also be seen from Figures 102 to 106 that a variation from
0.2 to 0.5 in g, the fraction of solar radiation absorbed at the water
surface, makes little difference in the predicted temperatures.  This is
varified in Table 14, where the standard errors of estimate of tempera-
ture are essentially the same for all three 3s tested.
     It can be seen from Figures 107 to 111 that a change from 0.05 to
1.40 per meter in n, the radiation absorption coefficient, predicts the
temperature poorly when the absorption coefficient of 0.05 is used.  The
error is as great as 12°C in some instances.  This is verified in
Table 14, where the standard error of estimate of the temperature is
1°C greater with the use of the lowest absorption coefficient.
     In Figures 112 to 116, the effect of varying the diffusion coefficient
from molecular to 100 times molecular diffusion is shown.  It can be seen
that in general the use of 30 times molecular diffusion yields the best
prediction of temperature with the use of 100 times molecular yielding
the worst.
                                 126

-------
3*tO,3 •<
330.3








1 i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i i
i >
i
i
i
i
i
i
i
< i
i
i
i
,J ».5
1 1 I
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 I 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 lu
1 " 1
•> 1)1
01 1 | 1
"11 1 1
"11 1 1 ?
>\ 1 | 7 1
a i u i
1 i\ 1 3
' •> | 31
12 1 '1
12 1*1
' 131
21 13 1
21 31 1 4
21 3| l 1 3 1 * 1
'13 1 t 1
31 K 1
31 « | 1
7.0 1,3 "i.U
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
111:
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
191 1 1
1 " 1 1 1 1 2
1 1 1 21
I 1 1 2 13
1 ? 1 13 1 4
12 1 31 1*.
21 13 1*1
131 14 1
31 14 1 1
3 1 <>l 1 1
1 * 1 1 1
141 1 1
AY| 183 1
1 1 3 - PAYI 22> 1
| | * . nyFKLAC 1
1 1 < - fuKFT 1
1 1 1 1
1 |l 1 1
14,1 17. u 19,5 22.0 '4




**
3 *
4
4





.5 27
1
. J
1
1
'
.
._-
, ,-,-J


.


,0 29,.
Figure 95
            ''IT
 1*1 "t-a'j'E I-



''c'V ir  l»7i —
                                                127

-------
                          Table 14
           STATISTICAL ANALYSIS FOR THE PREDICTED
                 SURFACE WATER TEMPERATURE

Reserveir/Year:  Norris/1972
Time Period Covered: 60th - 360th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
2.31
2.29
3.16
2.32
2.28
3.21
2.36
2.39
2.46
2.64
Correlation
Coefficient
0.94
0.94
0.92
0.94
0.94
0.89
0.93
0.94
0.93
0.92
                              128

-------

1 1 1 1
1 1 1 1
I'll
1 1 1 1
1 1 1 1
1 1 .1 1
1 1 1 1
1 1 1 1
1 1 1 1
till
till
I 1 1 1
1 1 1 1
1 1 1 1
- L i 1 I
III!
1 I 1 1
i i i i
i i i i
	 L_ 	 1 , . i . . I
i i i 1
	 J___. ! i I
i i i i
i i i I
I i i i
i i i i
i i i i
i.i i i
1 t 1 10
101 1 no
1 1 0 10 0 0 1
1 10 0 1 !
1 1 1 11
0 1 1 1 ). 111
u i mi ui u mm uummi
i i i i
i i i i
i i i i
iiii
i i i i






U

1 1U
11






0





1
0 1
1
0 1
« 10 I
111
0 1
11
1
1
11
1
0 . HE
1 , KO
• « 0V




•
1
1
11
1 0
0


SURED
I.ER
RLAP

1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1 ' "' '
1 1
1 1 ' '
0 0 0 1 |
1 1 1
1 1 1
1 1
1 0 16 1
mi i i
n i
i i
1 0 1
i i
1 0 0
1 1 1
1 1 1
1 1 11 I
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
*60,9 9Q.O 120.0 i'0',0 IBOtO 213.0 240.0 270.0 300.0 310.0 3*0.0
Figure 96
             "IT
                                    Dtst«vn1B 1V71 — i
1
1
1
1
1
1
1
1
1
1
-
1
1 	
1
	 J
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
t
1
1
1
1 2
1 2 13
•3 1 0
i* 1
21 10




o
1
01
1
1
0 1
\
0 1
0 1
1
1
1
1
1
1
1
1
1
1
1
c
i
1
1
1
I
1
1
1
1
1










2
I









I 3

























i - STAND
2 - PtLZl
3 - PEIJ2
< - OUTLET
i

T


_






1
. 	
_

	
	



1
\
1
1
1
1
1
1
	 1 	
I
1
	 1
1
1
1
1
1
1 _
1
1
1
1
1
1
1
1
1
1U ! i*a 	 " "**b~~ 7 <"3 '«•« »*•* 17>u "•* 2Zt° ***5 *7|° **'5
Figure 97
                  "!  I1'  PERM6S  C




"j'Ktj «.F»I=HUL!K I'M— uAfUOfc   — SU1FACE
                                                                               308,1 M
                                                                129

-------
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1 21
1 1 23
i 1 2*
1 1 2'
1 1
1 1
1 t
1 1
... ! _ 1
1 I
1 1
. L$_. ... 1.
l i
i l
" 1 " i
i i



i i t
1 1 3
1 1
1 1

l !
i i
	 J 	 1
1 l
i l
1 1
i 1
i l
l i
' l
! 1
„




?l 3
n
0







i.
31
" n








23
»








1 2"3
10 2"3
2 * 0 1 0
n 01
n















n







o MEASURED
1 *T»NP
Z DELZl
3 DEUZ
< OUTLET
l-SJ— —



"
— -. ,.- J
'




_

. -
"
"
	
	 . . _

. ,
--- 	

„






1
1
"I
..1 	
1
1
1
L 1_
1
1
1
I
l
1
1
1
I
1
1
1
1
1
1
1
. 	 1
1
1
	 . J
2.0 *.» 7.0 ».» 12. Q !<>.» 1T.O 19.9 22.0 24.5 17.0 2*. 9
Figure 98
               jw rEf'KEES  e
rFjFh-'ufK  I"71--J*yil39   --.Sl/KMCE FLEVI   312,2 H


10, P

J0,0
JC.P
»c'ln
~ >o","'>
*c,o
7P.n
ec.o
*ri0
l
1
1
1
1
l
._.. .. .!
1
l
l
1 2
!
1 2
1 3
1 Z13
< |23
! 1?
1 2«
1 t
1 2*
1 23
1 3
1
1
1
1
1
1
1
1
1
1
1
1
1


7
2 \ 3
1 S
3
3 0
3 n
0







2 3
1 3
9
"
0







21 03
3 0









* 3
* 3
















o . ME
i - ST
2 - BE
3 - >SE
< - nu
3
t *







is'JReu
inn
LZl
L22
EKLAP — i-
TtST
1
1
1
1 *0 1
•11 e
e l i I
1 1 . . 1
l I

'







1
l
I
1
1
i 1
I
1 "
1
	 _J_ 	 	
	 I 	 	 	
1
1
1
... 1 - . . 1
1 I
, T -
1 1
I ' T —
1 1
! ' i /
1 ' -T"
1
r "
i
i i
i i
                   7.0
                                                  11,5
                                                     J"
                                                             17.0
                                                                       19.5
Figure 99
                                                                                  22.0
                                                                                   110,3
                                                                           2J>,5
                                                                         130

-------
,0 4r 	 	 	 «. 	 --*--— ..-_-, 	 ...i.4 	 „ 	 _ ... ........
1
1
1
1
1
1
1
1
ao^o +.- — -.—
i
i
i
i
i
i<
i
...
i
i
i
	 r
i
i
i
i
i
i
i
i
i
i




:
2
•'»
2

'



H
1
1
1
j
|
I
1
1 i
1 i 1
1 2 I
12 3
* 1 3
1 \
Z 13
2 1 1
2 31
... .1. » 1
1 3 1
3 1
1
1
1
1
|
1
1
1
1
1
1
1
1
1
1
1
1


2
2 1 JO
3 o
n
0







2
2 3
3








2
2 n
* *
n






e ME
i ST
2 DE
» DE
...» oy
< OU

"IS
0






ISURBO
1MB
.11
.It
•HI
22
1 o



	








21 8 0 |
2 31 0 0 |
0_ 0 . . J_.
0 1 1

.. __






- , ,



.
	 l_
1
1
,-!--
1
I
1
1
1
" " .1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
. 1
1
1
1
, . . .1
	 iiil 	 _4.S 7,0 V.S 1*,0 U,5 17.0 IV.5 22.0 24.8 27.0 2f.3
Figure 100
                             'Kti
                                                                          310,1

1
1
1
1
1
1
I
I
1
1
r< "
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i















2
2
2 '
i 3




1
1
1
1
1
1
I
1
1
1
1
1 2
1 2 1
1210
2 1 S
2 1 3
2 I ' *
2 1 1
1 * '
1 I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1


2
• I
1 3
JO t 3
3







2
20 1







2
2 1 3
•3






1 . STAND
3 m OEL£2
< - OUTLET
i
i
I
1 2* 0 |
1 3* 1
12 1 0 I
2*00 |
1 0 1
1
1 1
1 1
1 1 1
1
1
1 .... 1
II '1
1 1
1 	 1 	
1 1 1
1 1 1
1 1 _..__!
1 1 1
1 1 1
1 1
1 1
1 1 T~
1 1 1
1 1 "1 —
1 1
1 1
1 1
1 1
1 T
1 1
1 ' 1
1 1 1
1 1
1 1 1
100.1 +, 	 * 	 ..*„ 	 ... * 	 --» 	 	 - - -- -
Figure 101    MJT
                                               -- u«»i252
                                                           -SURMCF
                                                                          io7<9 n
                                                                13X

-------
 10,e *«•'
 20,0 +
_in*P.
 o,n ~+,
 oo.o
 70,0
 «o,~b
loo,n +-




<








1





*
*
0
0
0
n





123
0


















^
I? 3









1 »

























o MEASURED
i STAND
z BETAI
3 S6TA2
1
1






"
1 1
1 1
1 "~ 1
.-J 	 ]_-
1 1
1 1
. , ,.L .,...__,.. ,_J_
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 . 1
1 1 1
- i- 	 -i — i-
	
. 	 J
1 1
1 1
1 1
1 1 1
1 1 1
1 1 1
- 1 • i ' •• • i
1 1 1
1 1 1
1 1 1
1 1 . ..1
               4.5        7.0       9.»       12.0
                                                                   17.0
                                                                             19.
                                                                                       22.0
        Figure 102    ..JT  Hul'tL »
.0 <
0,0
p,6
r o
0,0
"
0,0
0,0


.



<







*
*
*
*
*
*
*





*3
n
r
0







* * r
n r
n n









c
r








0 C
10 «
* 3 010
0 01
n















1 2 3







0 "EiS'JREK
1 STANP
Z BETAl
< n^T^PT
1
1
1
1
. _ _r..^ . _n
|
1
1
1
1.. 	
1
"1 	 1
1
J 	 	
1 " -— -
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

_
1
1
1
- —(
	 1
.... 1
1
• 1
1
1
1
r_
1
1
1 _
1:
1
1
1
1
1
1
1
                          7.0
                                              1Z. ,9
                                                                   17.0
                                                                             19,}
                                                                                       22,0
                                                                                                  24.9
                                                                                                            27.0
        Figure 103
                                                                       —SURFACE >E|.EV|   J12.Z n
                                                                               132

-------


10,0
20.0

30.0

JO, 6





70,0
~- -
|0,0


"100,0
2
1 ' I
..._.!. ' I
l i 1

1 ' 1
i l l
.. „..! ....!. 1 .
l l 1
1 1 U23 '
1 1 1
1 1 123 | o
1 1 12S JO
1 1 t
1 » o j
1 I n |
1 I0|
1*1 1
< ! - 1 1
L, 	 . I . • L.. ..I...
! * l 1
1 1 l
1*1 1
1 I 1
l 1 l
1 I 1
i 1 1
1 1 1
1 l 1
1 1 l
1 I 1
1 .... 1 — .-'-. ..—U . --,
1 l 1
1 1 1
I l 1
1 1 1
1 l 1
1 1 1


12*
o










n j
n

















230









o MEASURED
1 STANO
2 BETAI
» B£TA2
< OUTLET
i

1 0
112 S 0
0













"~


• » -
1
1







""

L_

-






-- - - 	 ,_ -



'
'




'















L 	
>
1
.. ._ _.



— . 	 - — »_
.0 4.3 7.0 9".» 12.0 1*.5 17.0 19.5 22.0 M.S 27.0 2».
L 	
          Figure 104
                       "IT  KU"fcl
wt**r\ni IK DEGREES  c
        1971—U/IYI 183  —SURFACE
                                                                                       310,

1 1
1 j
1 1
t 1
1 1
1 1
1 ™ 1 "
1 1
1 1
1 1
! 1
1 1
1 1
•o n i - ' • i
r i
i i
K i
i i

i i i
i i
i i
I i
.... |
"i " i
i i
i-..-.. l 1
i i
i i
i i
i i
l
i
i
i



"
""•a
123
i




"
1
•3







'
1 230
3 o
0
p
i






.•23.....








8
8






041 1
0
_
"
•" 1
"




o - MEASURED
i r STAN"
Z - "ETAl
3 - BETA2
1
1

^••••••o^
)











_-

100 |
in e o ~ n
08 1
01. . . i



.





....

«»««^M«««

	
1
1
1
1
1
j
1
j


1
1
' T
1
l
.... 1
1
1
1
1
1

1 1
.... ' - ... 1

-.-   -ilA
                  *iS
                            7.0
                                      ».5
                                               u.o
          Figure 105
         1".,5       17,0
            «  PEOREES C
            -UAVI2ZS  —

-------

1 1
1 1
1 1
t 1
L 1
I 1
1 1
1 I
1 1
1 1
1 1
1 |
1 1
1 1
1 1
l< 1
1 1
1 1
1 1
1 1
I 1
1 1
	 ._!__. !
	 ! I
1 1
1 t
1 1
""I" I 1
1 1
! !
i i
. .. j .. i
i i
i i
i i
	 i 	 i
1
1
1
1
1 ...
1
1
1
1
1
1
1
1
|
1
1 '2
. L .. .m.
i i*?
±1*
•ji
*S 1
1
1
J.
1
L _ ..1 ....
1
1
I
L 1
1
1
1
1
1 	 . . 1.
1



12
U»
123
* 3
12?
3
_ ...

~





o 12 )
123
l» 3








0 12
3





0 Hit
i at
i IEI
3 BEI
— * oyj
< BUI
1
1 	
1
oi» e
123 0
* 3 1
. 1 	 ...
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
SURSD 1
NO I
Al 1
•AZ I
LIT 1
1
1
1
• o 1
1* 1 1
«3 0 1
• 10 0
^•••0«»««»+*«e-if »»••»*


- ... 1 , .-,-1
1 1


! 1
i i
i

'-•^•^i-i«»i»5ff»-4*-«*
._ 1 	 _L 	
. . L 	 1 	
-•^•••••-»ti«»i««»»
1
...^.U-i-^-a-
1 1
! !
___!_ _.__l .._
2.0 4.5 7.0 ».» 12.0 14.9 17.0 1«.S 22.0 14.5 M.O Z».5
Figure 106
                      Jfl  DE6M6J C



       KFSFKVUth  1971--1>AYIZS2  --SURFACE ELEVI  J07.9 M

	
l°.o

20,0 4
JO.O

»0,0


60.0

70,0
(0,0
99,0
10C.O
... - ! I
i i
l 1*1
1 1 3 1 41
1 M 4 ')
2 '
f ?
**
.. ...., ..
2
1 * 4 1 0 12
j * 1 ?
1 3« 10^ Z)
1 <
1
1
!
1
1
l
1
1
< I
1
)
J
i
14 0 21
[ 2 1
01 2
1 ?
1 2
0 1 I
1 I
g i z
n 1 2
\ t '"
1 2
1 2
i 2
1 2
1 2
1 ?
l l
l i
l i
i i
1 l
j i
i i
l i
i i
i i
i i
i i
l 1
1 !
1 !
1 1








4 *
1 * 1
1


"























o . HE
i - ST
2 - ET
3 - ET
• - ov
< - Oy
-
- • —






ItS'-lKCU
l«0
M
»2
A3
ERU»
rter
i
l
i
i

l i
i
l l
i
i i
l 1
1
i
i - . . , -
1 l 1
!
1 1
1 1
1 1
1 1
\ \ -
1 1 1
- i - - - i - - • !'
i i 1 1
i i i
i i i
i i i
• i i i
i 	 i 	
i i
	 I 	 i ' T '" T~
I 1 1
l 1 	 	 	
                                                                    19.5
                                                                              t-Z,0
Figure 107
'.»       12.t,       1*. S      17.0



          Tf|,Pfc»ATo»e JN nfcCKEES C



•IO°RI»  KF»PK''yIK 1971—il'YIlOO  --SURFACE  ELEVI   SflB.l M
                                                                                                   27.0
                                                                                                            29.8
                                                                  134

-------
|0 H
19, n
iO,0
39^0
'»Tg1>6  P'  nEGRfES  C
Figure 108
             "JT


;o,o

20,0 i


40, P

50,0
_60,0 «
10,0
«o,n
»o,n
lon.n
i









<





. ..


3
"
31*
*4
*
3«
.




1 1
1 1
1 '
1 1
1 !
1 I
| 1310
1 ' . . "
1 1
3 11 * c
1 1
31 |4 " '
1 4 I n 1
I 1
4 P j 1
0 | I
0 1 1
1 1
1 1
I 1
1 '
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 '
1 1
1 '
1 1
1 '
1 '

3 *
o
4


2
2
2




3
»

z




a

2





0 - ''EASl'REB
l - STANO
2 - FT»I
3 - ETA2
* - nvERlAP
< - OUTLET
i
0 1
3 112 4 0 |
01 1 1
21 . . 1 . 1
.2_..
2

.
-


-

_
1
1 1
1 1
1 1
1 1
1 1
1
1
1
1
1
1
1
1
1 1
1 1
1 1
1 	 1
1 1
1
1 1
1
1 1
1 1
1 1
i r~
' -i i
i
i i
i
y <,,S 7,0 »,> 1^.0 !».» '?.« '»•» ?Z>0 ?*'S *7'° ?.»15—
Figure 109
                             "u'Kti HF»Fh'/w'K  497X--wArlX»3   "SURFACE  FlEVI   310.3 H
                                                                     135

-------
1 1 1 •
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
I 1 1
1 1 1
1 1 1
1 1 1
1 I 1
I 1 1
1 1 1
1 1 1
1 1 1
1 1 131
l< 1 1
1 1 131
1 1 914
1 1 1
1 1 »ll »
1 1 1
1 1 1
! 1 1
1 1 1
1 1 1
1 1 1
1 1 1
I 1 1
1 1 1
1 1 1
1 1 . 1
_...._]. . 1 1
1 1 1
T ' 1 " 1 - 1
1 1 1
1 1 1
!,_._! '
1
1
1
1
1
1
1
1
1910
1
s 11 »
5 1 1*0
1 4 T 1
1
1
4 I
1
1
1
1
1
1
1
1
1
1
1
.,.,-.' -
1
1
1
1
I
1
i

3
4

.






3
0
* A
0



z


o HEJ
X .STJ
z en
3 «T*
1 100
1 1 * 4 0 0
1 1 0 0
3 1 9 I* 2 0 1
01 04
n |
4 1
. . ..J..._ J
1
1
I
1 . *
1 1
1
1 2
1
J_
1 1
1
21
2 1
|
1
1
1
1
1
I
1
1
. . ...1 	 . 	 J
ISUREO 1
INO 1
1 1
2 1 J
* OVERLAP i
< OUTLET i
i i

. 1 . . .-
2
2
t
	






.




.....


'




I - - r-




-
„ .

i
•









i
1

i - , L -


2.0 4,S 7.0 9-.S 12.0 14. S 17.0 19. J 22.0 24.3 17.0 29.!

>
"
Figure 110
             "IT
                      J"
"J'RTS KFiEK''u'K  l°71--llAr IZ25  ••
                                                                        ELEVI  310,1 H

.
10,0
20,0
30.0

S°in


oo.o .
70,0
00,0
»0,0
100,"
2
J ' 1
! I I
l i 1
1 l 1
1 1 1
i 1 - 1
l t 1
1 ' i
1 1 1
1 1 1
1 1 l
! ' l
1 l 1
1 1 l
1 1 i
l i 1 :
t \ \ •>
< 1 1 1 3
1 1 |31
1 1 131
t 1 31*
i i 3 11 *
i i jii4
1 I314|
1 1 1
1 1 1
1 1 1
r i i
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1


3
3 I
3 10
3 I
I 1
1 4*
4
4







3
• I
I"
4
4
4







3
301
4
4
4







3
3 1
•
4

'

-


o MEASURED
l STAMD
2 ETAl
3 ETA2
» OVERLAP
< OUTLET
i
i
1 2*0
1 -J-VVT 	 1 	
»! 1 * i - - , - •
1 1 0 * 0 ,|
104 2
4 2
1 2
1 2
t
t
2
- * --
1 t
S
1 2
1 2



. T "~
l
. . . - !
1 2 1 ' "
1 Z
t
I
12
21
2
2
r
i
I
.
' ' 	 "
1
,mZmmmqmm*l i
\
\
1
(. i .": i _ ..n
i 	 i 	 ,
i i
i i
•i
T"
1
•"••••"•••*""'7'"^-
i 	

'T-rH-
,J <.,S 7.0 9.5 12.0 Kt.S 17. U 19. » 22.0 24,! 27,0 29,3
Figure 111
                   " ft. *
                             My"KTi
                                               1971— .U/SYUS2  —
                                                                         EL*VI   307,9 «
                                                                      136

-------


;o,o
20,6

>n,n

JL

T
H

•H
1
T »0.0

	 B 	
70,0
	 _
JO,C
yb.o

100,0
2
I '
! I
1 112
- .. 1-. I Z »
1 12 31
1 * 3 10
I l« "
— _. .1 « L .
1 »3 VI
1 »3 1
„..»....*. 	 ,»?.0-* 	 ...
1 *5 1
I «J 0 1
1 1
1 0 1
1 n i
< 1 1
1 I
1 1
1 1
1 1
1 1
1 1
1 1
1 I
1 1
I 1
1 f
! I
1 1
I I
1 1
1 t
1 I
1 I
1 1
1 1
I I
r
I 3"


.





- .
"



3 2
*









I








i






	
....
""
.







—
1

1
. . t ._. .
1
I
o MEASURED
i STAND
2 OJfFl
3 DJPF3
< OUTL»T
i. i -.-;-
^

... ..








_

_





1








"


	

.


••^•{•••••l
_ _ - _

. 	 	 _-
1

1
1

. . . r ~
i


1

• » •
-h—

1
}-
..........
^r ~-

	 . 	 , 	
.0 ' £ I* Cer.KEES C
               'n 1«71--U»YI106  —
                                                                                 308.1 M

	 '_
10,0

20,0 ^


B
e *o,0
T
H
I ?°in
H
^
R
70,0
00,0
yc,n
ICP.n




>•«-•-»•..




s
_

- .





L

1
' 12'
1? »
i? »
» 3-
»3
»1
• 3




_. .- -

__i 	 ?
2
3 n
0
0
.





.
"l •>
0
cos
k







"
•\


}





1 0 f
10 0
123 919
0 01
0















>*
	







i STAND
2 DJFFl
3 PJFF3
i
I
i












-

_
...

.



. - *





...^v«.w.


_J




_










-
^••••••••4





,

1
	






—




-. -

»





                  7.P
Figure 113    PJT t"u"tl.
                             v.s
                             17.0
         TFnl>t'!ATu''E !•» pEftKEES C
f.jBRI» ^FS'V'U'R  I'M—1)AYI139  — SyKFACE  ELEVl
                                          137

-------

	 1 1 1 1
II ' !
1 1 1 1
1 I 1 1
1 1 1 1
1 1 1 1
' . ' . ' . 1 , . .
1 1 1 1
1 1 L 11 2
1 1 1 1
I 1 1 1 1 2 <"
1 1 1 1 12"
1 1 1 1
1 1 1 • 1 3
D 1 1 I0|
P 1 1 I0|
T 1 -1 I 1 Z 1 »
H l< 1 I I
1 1 1 >2 IS
N 1 1 1 21 3
1 1 1 1
* 1 1 U 1 ) 1
si, ., » I 1 1 1
1 1 I 1 1
R 1 1 1 1
1 ! 1 1
.- i'. - . . 1 , 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
1 .1 1 1
till
1 1 1 1
1 1 1 1

1 0
0
3
'
3
3




.:.!«..-


1 |l 1 1

*
0
2






'


Z
3




"

1 1 0 |
1 132 0 |
1 P 1 1
10 3 1 __ |
1 1 1
1 1 1
1 1 1
1 1 1
1 I 1
1 1 1
1 1 1
1 1 1 1
1 1 1 1
1 1
. ' - --' 	 1
1 1 ' " 	 T~
1 I 1
1 1 1
1 1 1
1 1 " 1 "'~\'
1 1 1 1
1 1 1
1 . . 1 	 1
l l
1 1 ~T
1 I T ~ "
. . l - - . ' 	 . ..1
II 1
l l i i
i r r " i
i ~i r
o MEASURED i i I
1 STAND 1 1 1 1
i op
3 0(1
< Oul
.
Fl 1 , 1 1
F3 1 1 1 1
KLA' .-i.*«— —..*—«——*--—.—»
Mr 1 1 1
1 1 1
1 1 1
1 1 1
100,0
                                            12" 9.
    ?      l?iO
    I" DEGREES C
                                                                          19.5
                                                                                    22.0
                                                                                                        27.0
        Figure 114    M|T
1971«UAy|183  —SUBP»CF EkEVI  310.3 A




10,0

20,0 <
30,0 4

"~ ~l~ 40,b ,
p
J
N
H
i
E
70,0
»c.o
»o,n
100,0
	 i
i |
i :
i i
i i
i i
i i
i i

i l

i i
< 1 i

1 11 Z
1 i
l l
i i •
i i
i i
i i
i i
i i
i i
i i
i I
1
1
_ 	 1.
1 . _ .
1
1
1
1
1 l.o
1
11 02
1 1 0 Z
1
I I *
1
1
2 i
i
Z 1 3
2 1 3
1
J 3
1
T
1
1
1
1
1
1
1
i
l
i
i
i
i


Z
3
3






0
* 0
0
3
3







91. _~l-
0
3







o - MEASURED
i - STAN"
Z - DIFFl
3 . BJFF3
< - QU
•L«T



3










».....*».


100 1
* 0 0 1
0 0
0



.

. -










1
b •
1
1 .
. . L .

= :r.:_:_fr~
i
_,. 	 i 	
- — % — -
i

•
._!. 	
- i* t
'•tit.
11-
j •' \
• .1 .-

. , ,.J . - ..
,a 4,5 7,(, 9,5 12. if 14, S \7.0 19,3 22,0 24.,$ 27,0 2*. 3
        Figure 115    HJT H(j"EL »
                                                                                     310.1 M
                                           138

-------
.0 *,— r-—+— — — -+.........*.i.. 	 i_4 	 , 	 . „ , . . . -.-„.-- - ^
1
1
	 L
i
i
i
1
l
i
l
l
1
Q 1
P l
T K
M 1
1
1
: H i
_..: J 1
T 60.0 *«r-irp-«
r
1
1
1
1
1
1
1
1
1
1
t
1
t
1
1
1
1
1
1
1
1
1
1
1
1
1
r i
i i
i
i
i
l~ i

i
i
i
i
1 1 1
1 1
1
1
1
2.0 *
i
i
i
"" 	 " i




1
1
1 l
2
2







1
1 0
1
I
2
2






0 1
1
10
2
2
2
2
2
3
3





" I
2
2
2
'
3
3
3



o HE
1 ST
2 rij
•> 01
1
1
1
1
OJ Z 0 3
I 02 3
* 213
2 1 3
31
3 1
t 1
3 1
3 1
I

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
ASURED 1
MO 1
FF1 1
FM 1
< OUTtET 1
1
1 1

1 1
3* ^ 1
3* 1 1
*1 1 1
» 6 o |









...

...



_ _ __



1
1
i
1
1
1

1
1


1

1

1
1

1
1
1
.5 7.0 »'.» IZ'.U 1*,J 17.0 19. S 22.0 24". 5 "~ »7.0 * Z».S
•STOP*
                 Figure 116    MJT
                                             "U»Kt» hFiBKVJlK 19H--Otr1252  —SyRF»CF  fLEVI  3«7i9
                                                139

-------
SOUTH HOLSTON RESERVOIR

     Figures 117 and 118 show the computed and measured temperature

profiles for South Holston Reservoir for 1953.  It can be seen that the

computed temperatures do compare, in general, reasonably well with the

measured temperatures.  However, some of the predicted temperatures are

quite different from the measured values and account for the fairly

large standard errors of estimate for outlet level and surface water

temperatures, as shown in Tables 15 and 16, 2.4° and 2.9° respectively.

The computed outflow temperature using the Kohler evaporation formula is

shown in Figure 119.  In Figures 120 and 125 it is shown that the effect

of the variation in thickness of the horizontal segments from 1 to 3

meters makes only minor differences in the predicted temperatures.  This

is verified in Tables 15 and 16 where the standard errors of estimate

are similar to those predicted by using the standard thickness of 2

meters.

     In Figures 126 to 131 the effect of the variation of 8, the fraction

of solar radiation abosrbed at the water surface, from 0.2 to 0.5 on the

predicted temperature is shown to be negligible.  This is verified in

Tables 15 and 16 where the standard errors of estimate are shown to

be similar to those obtained for the standard B of 0.5.

     In Figures 132 to 137 is shown the effect of variation in n, the

radiation absorption coefficient, from 0.05 to 1.40.  It can be seen

that the use of the 0.05 coefficient predicts temperatures quite different

from the measured values and quite different from the predicted values   '
                                                                         ;
using other absorption coefficients.  This is verified in Tables 15 and

16, where the standard errors of estimate are one half and twice those

predicted with the standard absorption coefficient, 0.75.
                                 140

-------
     In Figures 138 to 143 are shown the effects of varying the
diffusion coefficient from molecular to 100 times molecular diffusion on the
temperatures.  It can be seen that, in general, the use of the molecular
diffusion coefficient predicts the temperatures most closely and that
the use of 100 times molecular diffusion predicts the temperature
most poorly as indicated in Tables 15 and 16.
                                 141

-------

	 - 1 1
1 1
1 1
1 1
• ' 1 " 1
_ 1 1
1 1
1 1
f 1
-I- I
1 . 1
L I I
i 1 I
V ' 1
A 1 1
I ' ! 0
0 1 1
N 1 10
I | «
N 1 1
1 I
H 1 1
£ 1 1 0
t 1 1
R l< 1 n 1
1 1 01
1 1 !
1 1 121
I I •
I I 0 <
. 	 1 	 -I t 2
I I 0 «
I I 10
1 1 •
1 1 *2



0
0
i
1
S 1
1

4
*
s
3*
1 1 103 »
1 1 12 3*
	 J 	 1 1 12*
1 1 13




1
1
2
3






1
I

2
4







2









2

*

0 OA>
1 OA>
2 DA>
3 DAI
5 041
* Oy!
< - Ob


... -
-
I
4
3


1 78
1 1*2
11 203
'1 24$
ri 299—--
ri 362
RLAP
LET

...


2
3
3




1
1
1
1
I
1
1
1
1
|
1
1
1
1
1
11
1
S 1
I
1
- 1
1
1
1
1
1
1
1
1
1
1
1
1
, [
\
1
I
1
2tU *•? TiO «.> 12.0 !»•? I7if !«.? ?2.0 **i« *7»o -24^.





1 	






i
1
                                                             I" PEBRFES C
                Figure 117
ITOP*
                                               142

-------
                         Table  15
          STATISTICAL ANALYSIS FOR THE PREDICTED
           WATER TEMPERATURE AT OUTLET LEVEL
Reservoir/Year: South Holston/1953
Time Period Covered: 120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
2.88
2.72
3.02
2.95
3.08
7.07
2.49
	
3.21
4.19
Correlation
Coefficient
0.87
0.89
0.86
0.87
0.86
0.00
0.90
	
0.83
0.66
                             143

-------
                         Table 16
          STATISTICAL ANALYSIS FOR THE PREDICTED
                SURFACE WATER TEMPERATURE

Reservoir/Year: South Holston/1953
Time Period Covered: 60th - 360th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
2.44
2.53
3.09
2.32
2.29
1.05
2.82
	
2.18
1.75
Correlation
Coefficient
0.96
0.96
0.94
0.96
0.96
0.99
0.95
	
0.97
0.98
                            144

-------
1 1 1 1
1 1 1 1
1 1 1 1
	 1 	 1 	 4 |
1 1 1 1
1 1 1 1
| j I |

1 1 1 1
	 1 	 1 	 ..-.. 1 I
1)||
1 1 1 1
L 1 1 1 1
it 1 1 10
VI 1 1 01
A 1 1 1 0 |

I ! 1 01 1 i
0 ! 101 11
N I 1 0 1 i |
! .1 0 1 1 * |
N 	 1 - - - 1 0 H 1
i | o 1 1 I
ft 1 ! 81 1 |
1 ! . . . 1 °i 1 1 *
E 1 1*1 12
-It 	 W 	 1*1 Z
1 1 • I '2 1
t 1 • t » | 3
i r ** if * |
1 | * •! |
1 1 *AS 1 !
1 1 ** 1 1
t 1 •» 1 1
I 1 * t 1
1 1*1 1
1 |*| |
1 I »• " 1
1 1 >• 1 1
i i ft j j
__ . ..._4_ 1 5* 1 I
2.0 4.3 T.O 9.3 12







0




2
t












.0 It
1 1 1
1 1 1
1 1 1
1 1 1
t - 1 - 1
1 1 1
1 1 1

1 1 1
| j |

1 1 1
1 1 1
111 1
11 1 1
Ul i i


1 4- J 2-
1 121
1 21 1
1 J 4 1
Z 1 4 1
1 * 1 3
1 * 13
1 * i 1

IS* 1
1 1 1
1 1 1
1 1 1
1 1 I

1 0 OAY| Tl 1
I i DAYI 1*2 i
1 2 OAVI 203 I
1 3 DAVI 249 1
1 5 OAYI 142 1
I * OVERLAP i
j e ruiT^FT i
1 1 1
•5 T7.0 \9.5 ?2.0 74


	 1



1

	
2

1














i* TT


	 „








i
i











. . . -•

i
. ft JO.

























1
1
              Figure 118
r*
                                          Sul'T"
 HMPE°ATu»E JN



U41V! l»53   .-C
                                                                                       PROFILE-

_ _l . 1 1
1 1 1
1 i 1
1 1 1
1 1 1
	 1 	 1 1
— I--.. 1 1
I 1 1
i i i

Till
fill
pill
t - - --I 1 1
R ' II
A 1 1 1
Till
V I 1 1
£111
1 1 1 1
N 1 1 1
C 1. 1 1
1 1 1
1 i 1

1 1 1
1 1 1
- . .1 	 1 1
1 1 1
1 0 1111 111 1 lllllll
1 1 1
1 1 1
1 1 1








•111
11111





'


01
11
11


1 1 1
1 1 1
1 .. . - 1 	 1 .
1 1 1
1 1 1
1 1 1
1 1 1
1 ----- .1 	 L _-
1 1 1
^ u 	 *. 4 - -
i 11 11 i
i ill
i l I
ill I
J .i. 4. - - 1 	
1 1 01
11 I
1 1
1 1
11 0 1 .
1 1 1
1 1
1 10 1
11 1 .
1 1 1
1 1 1
1 I 1
1 1 1 .
1 1
1 1
1 1
1 1
i o . MEASURED
1 1 e KQHLER
i * - OVERLAP
i i
i i
i I
I I
i I
V
.
0




I
I
1
I

1
I
1
j
i
I
I
I
I
i
I
I
i
i
1
I
i i . -
1
1 I
i i
I
11
i 	
i
I
I
I
I
2>LT"""o!o Hot" "lSO*0 1«C.O 213.3 240. 0 270.0 300.0 330.0 360.0
              Figure 119
                          HJT
                                          SU''T« "ULSTu1  1*'J
                                                                          OuTFLuK TEMPERATURE"
                                                                           145

-------

1
1
1
1
1
1
1
1
1
:<
D 1
P 1
T 1
H 1
|
	 1- SO^O *.«-«---
1
H 1
I 1
1
.„ . 1 t .
70,fl *,...n...
|
1

|o,e *»-*»--„
i
1
i
yo,o ».».«*i— •
l
l

210
1
•0
*
*
*
1
•
*
•0
1
«™**0»-
*
*0
... , *
* 0
• 0
l
*
*
mmmmmt^fm


L

0
0
0 * 1

_
. ... . ..
e=e-?i=-^

0
0
L i_ J

'
- -I
. ..

1 1
2 > 1
1
1
1
1
1
L.
1
1
t
I
1
1 .

1
1
1
1
1
1
1
1
1
1
L 1
1
1
1
I
1
1
1
1
1




-*

' "
» . m




.

L
	
	






^





.
_
	

	
,




0 . MIASURID
j ... ITAMD
2 . DELZl
* » DELI*
hp»«* .» OyFBI AB ----
< •• DU1
L J

rLiT
L ...


.
. . _. J
.

	 _J

__
- 	 1



" *

J
1
1
|
. . 1 ....
|
1
1
1
1
1
1 . 	
1
1
1
1
1
1
1
i
4- 	
l
1
...iii.i.i,;.i.;.;.
l
- 1 v . .
*+a. .«»i- ^
1

|
1
1
	 1
1
1
1
1 ,
?,p 4,J T,0 9-.S 12.0 l*,J 17,0 l«.l *2.0 I4t! M,0 »^














•


•
1
Figure 120   MJT MO«EL  •
      TEMPERATURE (N DEBRfES C
SOUTH HQLSTnN 1»5S—04 YI T«  ^.SURFACE HIV I  920.9 M
• 0 ^^•^^—••^•^••••••^••••'••••^j
1
1
1
-----:.\
10,0 *•»- 'C9—
1
1
jo.e *.-—-.—
I
1
1C
B 1
p i
T 1
H 1
_ .& - 1
H 1
i 1
T 60.0 *»»— ^i—
E 1
R 1
_. .. ' l"" *" "
1
1
1
1
1
1
1
1
1
i
i l
t 1 2 '
21
2is a
i
•S 1 0
i l
2» 01
• 01
1
» 1
1 I
• 0 1
*0 1
* 1
1 1
•0 1
* V|- 	 ~"
* 01
* 1
1 °
S 1
1
1
1
1
1
1
1
1
I
1
"" "*
0».
30
n


'




. . .J
.
1
_ 	 J
"
'


-B~-»—



1 9 1
1 0 1 *l
1 I - 1 . .
J
1
1
«•«« mmm .-»-i-.-— ..
1
1
1
1
1
	 ..1 ... .
1
1
i
i
i
i
i
i
l
i
l

"


"
l o . MEASURED
l i « STAND
1 2 . CELZ.1
1 3 • DELZ2
1 < - OUTLET
1 1
1
1 1
1
1 "

1


1
1 1
1 "~ T
1 1
I ..!....
1 1
1 1
1

i " •
l
i
i i J
\
\
	 ^..i,..;.;.;.^;...;.-.
1
.... . . . 4
" 	 — -p—r
_...j 	 },„_/._,
i
i
i
i r 	 "
i i
i i .
2,9 4,» 7,0 9.9 12,0 U,9 17,0 19.9 22.0 2V,9 2?,0 	 2»j

:


l
i -'
J.
.- .
l
'
i
1 	
Figure 121  MJT
      TBHPE5ATUHE JN. DECREES t
              1993—0*^11*2  w-SURFACE ELfVI' 92*.2 M
                                                            146

-------

10,0
{6,0

JO.O
i 10.0
t
H
	 a
H
T 4°i*

	 a 	
70,0

l°t°
?o,e




<





'•••»e6«-<


*«*»-a«-»-<

I
1
1
1
1
1
1
1
1
1
1
1 2
2 J
*
2 31
1
* 1
* 01
1 I
* 1
1 	 . _JJI
* 1
* n
• 10
* 1 0
_. . 1
1 1
1
1
1
	 1
1
1
1
1
'-•=SSr"S"*?B"~BSB"B
1
1
I
1


0
2
1 1 J
*



"




0
0! S
i
3



.




0 2





...




0
2
*



L



_ _ .
o . HE
1 • IT
2 - PI
S . DE

1
1






kSURlD
IND
.:i
.12
FOI AD ....
< • OUTLET
1
0
I









(
1
t
. -I














)
13 2 1

	
	





_
•«»•»•«« *





>
..
._










>
                TiO
Figure 122  MjT HUOEL •
9.9      12,0      1»,9      17.0      It,9      22.0
          TEMPERATURE IN DEGREES C
    SOUTH MfLSTHN 19J3--B»Y1203  i—5U»pACE  ELEVI   918.8  H
                                                                                     2*. 5
                                                                                               Z7.Q

!
10,0 »«..»ea—
	 I
j
1
20,0 ««B«S»«-
1
	 . |
1
j
j
Jl

T 1
H 1
1
N 1
H 1
S 1
ft 1
	 I
1
1
1
1
1
1
1
1
1
1
1
1
L 	 	 ! 	
1
1
l
1
II 1
1} 0
0
1
0
1
0
10
1 0
1 o
1 0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1


.........
* 1









2









0
?









2
I 2






a t
2 t




_

o . MEASURED
1 « STAND
2 - OELZl
S - OELZ2
< - OUTLET
i

9 1
1 1

_


_.



0 Z 1
o ;• 1
o i h i

i i
i 1
i l
i i
i l
l
i
i
.... i
i
i
i i
i i
i i
i i
l
l
i
i
i
.1 i
, ii
i
i i



Figure 123   MJT
                                                 "  DEGREES  c
                              SOUTH nnLSrnM t9S3«-OAVl2»S   —SURFACE  ELEVI  SU.» H
                                                          147

-------
.0
10,0
jo,o
20,0
V
t 40,0
T
H
I 10,0
H
•
T 90,0
I
70,0
_. . ._
|0,0
90.0

100 0

v




.



1 	 ' J







•





...
....




0
0 2
•i
0
0
0
0
. .





>
1 2


._..
'




C
2




.







'
	 	 . _ 1
. J

. . J

. J


0*
0*
*
0*
*
0 *
*


_ -. -


.... . .._..

. _
...
o . HE/
1 .• ST/
I » DEI
» • OEl
«*«* « OVL


L



L . .... .
IJUMO
IHD
.11
.Z*
< • OUTlIT






_
..
L.. „._._!
.

1 1
1 1
1 	 I 	
1 1
1 1
1 1
.. -...I.,-— .. -.. I 	
1 1
J-. 1 	
1 1
[ . 1
1 1
1 1
1 1

1 1
1 1
1 1
1 1
1 . .'
1 1
1 1
I 1
1 1
1 1
I 1
1 1
1 1
1 1
1 1
1 1
1 1
1 . .1
	 „*.(! 4,» 7,0 9".J 12,0 14.9 17.0 19.9 22.0 14,9 «,fi Z9.J 	
Figure 124   «JT HQIEL  *
                              S1UTH
    JN DECRieS C
19S3--04YI299  --SURFACE BLEVI   J03.1


10,0 '
—
20,0
JO.O <

p
6 40,6
H
N
H
f
f
R
70,0
•0,0
vo,o
100,0 .
i


L
<





..




1
1
10
10
1
1
L ,....!.. . .
10*)
*
•3
* 1
•a e
• 10
* I
21 1 o
* 1
* 1 0
* 1 0
* 1
1
1
1
1
1
1
1
r
i
I
I
i
i
I
i
i
i
i



"






"



.





.









_
L, . ...


.











o MEASURED
i STAND
2 OELZI
3 OELIZ.
---* OVERLAP ----
< BUTL«7
I
.
	



_


••«<*»•••••

i
"
	
I i

I


1 ^ , , I
i
I
""]' ' I "
--•-r--- -~i, 	 —
i ' 1 1
\ 	
1
	 .1 	 !. .' 	
1
1
9 4,9 7,0 9,9 IZ.O 14,9 17,0 19,9 22.0 24,9 Z7,0 .29,S__ ._
                                                JN  DE8REES  C
Figure 125   M|T HQPEL »        SnuTH hOLST^N 1993--OAYI362  —SURFACE  ELEVI   902,2  M
                                  148

-------
,0 <
1^,0
~~ 	 20,0
|0,0 4
~~ 0
1 90,9
H
N
H
4
	 _R
TO.O
~



100,0















. 	 	


0
*
0
*
*
0
0
*
*
•0
0
• 0
• 0
•
_. •



0
0
0 12





0
0
0













•I























—





i







o MIAJURIO
. ..1 1T4NB
I BETA1
i BETAI
< DUTUIT














- -l
j






	




.. .-

.






	

.1
0 *,5 7,0 ».5 12.0 1*,J 17.0 19,3 22.0 H.S 27.0 -24,
»

	






	

1
>
9
Figure 126   H|T MODEL  •
      TEH'E'ATUIIE IN DEARIES  c
SOUTH HC^'TIN I953r-04yl  T8   —SURFACE  SLEVI  5Z0.9 M









2o,o



«0.0 <


9
p
T
H
N

H
I
	 T 6°§o
R

70,0







yo,o

100,0
2




L








<
'
..

















0 " *
I
1
1

1
1
1 *

1
*l 0
1
* 1 0
* 1
01
* 01
1
1
* 1
0 1
• 1
•0 1
1
* 1
0 1
0 1
* 01
1
* 0
1
1
1
1
1


1
1
1
1
1
3 7,0 »•




012

( e
n
>
























_
T U


9

s


f




























12)


















,










0
0 1 2 |3





«























. . - .


.
















o MEASURED
t STAND
2 BtTAl
3 KETA2
< OUTUET
i
I













.






















.









- - ,
_..
	














.


1


. .


i
" i
1
i
I



. . _ -. 1
I

	 .

1


h~


	 I 	
l


.
'-•»<







_



...




>



t


1 . ....
kg"""""j»." " 17,0 19, J 22,0 24,5 *T,0 »»»'
TEMPERATURE 1^ DECREES C
Figure 127 M(T MgnEL » SOUTH HOUSTON l»S3»-OAYIl»2 --SURFACE EUEVI SZ*,2 M
  149

-------


10,0
20,0
ID 0

0
6 »0,0
p
T
H
J jo,e
.N
H
I
T 60tO 4
____*_
70,0
	
•0,0 <
?°te '

100,0 i
2.



<
-.-


"






•« «««..-<


1
1
J
1
1
1
1
1
1
1
1
1
1
•1
1
• 1
01
* 1
• 1
L ai
• i
. o
10
* 1 0
L 1
1
1
1
1
L . 1
1
1
1
1
1
1
1
1


0
123
I)




.


0
0
123






.»..». .j


0


. ..
j

j

_ .. .j



0
1 t 1


. - - .J
L- 	


	 	
. J


1 2


.
.
L.
_

_


a . MEASURED
i eiima
t • BETAl
1 • BETA!
... • . DVE»I»» — — <
< • OUTLIT
i
i
i
0

_


.. .J
.

	 1
(••••SB--S.
(
I? '
.-.-, J


J
.



.

.........I
L. ... .

.


> 1
i 121
1 "
L
1
1
1
1
1
1
j


!
i
i
.... i
i
i
i
i
i
i
i . . . . i -
i
i
i
i
^••••••••••*
i
i
0 4.9 7.0 9.9 12.0 1*.S 17.0 19. i 12.0 I*. 5 17. fl 	 29. J_-
Figure 128   ^JT MCf>El  *
                                   TEMPERATURE ]N DECRIES C
                             S1UTH MPL5T1N 1933—QAyiZO}  --JURF»CE
,t> 4
10,0
	 -
20,0
30.0

U
6 *0|8
p
T
H
i »°.o~
N
H
.... T 60,0
R
70,0
80,0
90,0
100,0
2
*.-«•».— *—5.—i.*.i...;B-».
I
i
! 1
1 1
I 1
! !
U , -I--.- !-
1 1
X_. i 1
1 1
1
1 * i
1 o
1 • o
1 I
L o
• i
0
• 10
* 1 0
1 i o
1 * 1
1 0
1
1
1
1 1
1
T
1
1
1
1 1
1
1 1


0 l»
'










'







0







-—•-—<

12 t






"
0

'




o MEASURED
i STAND
2 BETAl
3 BETA2
< DUTLBT
i
i

0
U 1


_





0
0 •
0 1
. . ..»» . .
2 i 1

J 1
1
1
J j

1
1
1
i 1
1 	 f
1 1
..." . . .;. r~
1 ;
i
	 1 	 „.
i
i
1 ' i
i
	 i
i9 <>,t 7,0 9,» 12,0 10.9 17,0 19,9 12,0 2*,5 27<0 29,1
Figure 129   M|T  HQOEL  «
                                    TEMPERATURE I" DECREES C
                              SOUTH HOUSTON 1999—DAY 12*3  —SURFACE ELEVI . 311, t M
                                       150

-------

10.0
J
20iO
?°f° •
0
i »o,o <
»
T
H
N
H
T 60*0 <
.1.
R
70,0

J0,0 '
90.0 <

1
1
1
1
1
< 1
1 	 	 1
1
1
1
1 *
1

1
1
I

1
1
I

1
I


|


0
l»
1
3
0
0
0
0





1
1
1
1

123







0










>

-






0*
0»
*
*
0*
*
0 »
*













0 MEAJURID
1 3T4NO
1 BETAl
» BETAl
< OUTLIT
1










1
1
"l"
1. J
1
1
- 1. 	 J
1
"l "
1
1
I
1
|
1
1
1
1
|
1
1
1
1
. . . 1 . . ,
1
1
1
1
1
1
1
1
1
" " 1
•
1 	






>

t
	
h
2.0
          1,3
                    7,0
    Figure 130  HJT
     12.0      l*.S      17.0      19.9      22.0
      TEMPERATURE I" DECREES C
              1955—OAYI299  ...SURFACE EUVI  903,1 H
                                                                                          **. i
                                                                                                   27.0

-
10,0

20,0


Q
E *0,0
H
I ?°|0
N
H
I
T S°tO *
E
R
70,0
go.o
90,8
100,0 .
2


L
<
•»«»ei»w-
....






.,.-»-..-.
0 •>
\
\
19
10
1
1
-. . . 1
10*
»*
«3
» 1
* 1
•I 0
* 10
* 1
•
*
*
*
*



t 7,
0
0
0




0 9'









T 12.









0 1*.









S 17,
















0 PE'SURED
1 JTANB
Z BfTAl
a RETA2
< nurte7
1
0 19,$ 22.









...•••••~4
0 »*.
1 1
1 1
1
1 . . 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 ..... 1
1 1
1 1
_J_- . _l.
. . 1 .... 1
1 1
1 1
.,.._! . 4-
\ i
i i
i i
.1 .1
T"T~
V — ' T 	
1 !
t i
1 1
. ... ,.l ..- ...A. -
1 1
1 1
1 I
1 . 1
, 1 " 1
I 1
1 1
. . 1 . 1
S «7.0 »».». .
    Figure 131  MJT
      TFnpERATURE P DECREES C
jnuTH H"LSrnN 1»>3--OAYI362  -.SURFACE
                                                                                J02.2 M
                                                  151

-------
•ft tas-

10, 0
20,0


D

7
H
	 (L ...
N
... _S.
70,0
	
{0,0 4
.0 4

100 0 4
2.
1
1 o
1 *
1 0
- - 1 •
1 «
1 *
1 0
< * 2
t 0
. ^ « 2
•W""9>B^^.P#"—*S?*QiB~
' rm * 2
-«•
•02
1 0
1 • *
* *
• t
L_ 1 .2

•• n ^ „
1
"_' .!
1
!
i
•g--BS*"***~-^~*-e*1
Jl .. 4.5 7,
0
- 0
0 921
2
2



..
_
0
0
0
_
.
...
o '" ?;
2







._. ..

1
I 3







"






L 	 -
.
L J









. ... .



.... )





.
—•• *— •-<
'

0 MEASURED
. .i STAND
2 1TA1
* ETA2
< OUTFIT
I
.1
i

.



.mmmm • «- .


.
_
'














.


J
... ....




k


-
* . -

.
'


. 1 ....
9 12.0 14.9 17.0 19.9 22.0 24.9 27.0 . .24.1

i
k
t

i









1
      Figure 132   MjT
      TKii'£"ATuRE IN OEORJES e
snurn Hni,sTON i«»s>-oAyi 76  --SURFACE EI.EVI   920.9
-- * • * • **" ~ * * "*""' A *** A A 2 " A t 'a ' ^ ^ " " * j

.0,0 .
.. .. . .
20,o 4
90*0 4

B
.. -E *0.» H
P
T
H
I ?°«e <
N
H
I
	 J_ ,.ftO,0
R
70.8
60. 0
90,0
100,0
2

. • . 1
1
« a

•*"»»B"»"»d

i.
^»-"S5— <
	
.. -
	


1
1 > 1
_ . , !.
* ,
111 0
1
.*. ' 9
• I
01
« 01
1
• i 2
0 1
* 1 2
•0 1 2
1
• 1 2
0 1
0 1
* 01 ' 2
1
1
1
1
1
1
1
1
1
1
1
1

101
0
0
2
Z
2
_





0
i
I
2
2
..





1
1 t
. .

'





9
20 1






.0 HE
i ST
2 ET
3 ET
— * DV
< DU







ISURBD
W>
M
12
ruET


_
_
.-—-.--<





	
J



b
1

"! ~\
	 ..i 	 i -
i
i
j j
;. :T:..



.



	 i 	

i
i
i
9 4,9 7.0 9.S 12.0 14,9 17,0 19,9 22.0 24,9 27iO 1.9,
; -
p
i
•
      Figure 133   MJT MQ"EL •
                  IN DECREES  e
SOUTH HnLSTnM 19S3»pAyil42   —SURFACE  ELEVI   924,2 M
                                                                     152

-------
	 ... •O <
10,0
ib,6 t
30.0

0
i »o,o <
•
H
N
N
f 6ote
	 E
	 R
70,0

	 	
I0!8
jo,o

	 -


. .

<












1
1
1
1
1
1
1
1
1
1
I a
I
•
I
I
» I
01
• i
• i
	 	 01
* 1
a
10
• 1 0
I
1
I
I
... .. I _
I
I
I
I
i
I
i
i
i
i
i
i o
10
0 » 1
3 t 1
1
1
1
1
L
Z 1
1
I 1
1
	 1...
1
1
1
2 1
. 1
1
1
1
1
J
1
1
1
1
1
1
1
1

a 3

2









0
1

2
.







i
2

.



e MEAJURID
1 STAND
z Bin
3 ETA2
< ounir
1 C
1 •
0 1
> 11 I
1 2.
1
21
1 .. .
1
1
1
1
1
1
I
1
1
J . 	 1
1
1
1
1
1
1 ...
1
1
1
I
1
1
1
1 '
1
1
J 1 1
_ .._ 1
1
1
1
1
1 	
1
"l
1
1
1
1

1
1
1
1
1
1
1
1
1

1
I
•••*^**««+
1
1
I
!
1 . 1
.. .-ZtS- 4,9 7,0 9'. 5 1Z.O 1*.3 17,0 19.3 22.0 M.J 27*0 .2S*S.
Figure 134  HjT
jnuTH
                  IN DECRIES e
              l
"
...
.
i
i i
i i
.1 . . i
i •
M. J
S- *,s 7,0 9,» 12,0 1».S ".O 19,3 22.0 t*,5 27,0 *.,!

Figure 135  HJT
                                                |N PERRIES C
                              SOUTH HHLST1N l»»St-0»VI2*S  p-SURFACE ELSVI  511,6 N
                                                          1S3

-------
1°
lo, e
""*o«o
"~ D
i *0,0
(>
T
H
N
H
T 60. 0
E
R
70,0

10,6
*°le

100,0
	 	 Zi

<



.



_




I 	 1
1
|-
1
1
1
1
1
1
1 o
10
1 SI
»l»
1
0
10
1
1 0
1
1 0
1 0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1


1








0
s
2
2
2
2
2
2
2
2
2
'





2




.. .


*12
• 12
312
312
»12
312
0 312
312
2
2


_

..
9 ME/
I ITJ
t Itl
3 ETi
< OU1
2





ISURJD
MO
U
12
SRUP — r-'
rut















._ . . J


.





. . .
1
1
1
1
1
1
. , ,1
1
1
1
1
1
1
4- .--
1
1 .
1
1
	 1 __
1
1
. . 1
1
1
|
... 1
I
1
|
1
1
1
.1
Q 4«9 7.0 9.5 12.0 14.9 17.0 19.9 22.0 2*. 9 27.0 29.5
Ptgure 136
           MJT
                              S1UTH
                  IN DECREES e
              19S3--OAVI299  --SURFACE
                                                                            303,1 M


iO,D

20,0
10,0
_
1 ,°
f
H
I S°T°
N
H
i
R
70,0
»o,o
90,0
100,0
2



<


_..
_





1 21
1 21
10 2|
1 21
10 21
1 2|
1 21
•••.'- - I' -. -.-.-
10* 21
• 21
*i 21
» 1 2|
* 1 2
* P 2
* 102
* 2
31 2 1 0
* 2 1
• I 1 0
* 2 1 0
* 2 1
1
1
1
1
1
1
1
1
1
1
"






.



































o MEASURED-
i STAND
2 ETAI
3 ETAZ
< HUTLBT
I
I
I
.


.






"I I\_

_! 	 L 	
1 1
1 1
I I
1 1
I [
	 T. :;;.r
* i
i i
.. +...-. t
! I
i I
i i
i i
i i
i i
T 	 	 1 —
1 .1
1 1
! !
i ; , r—
1 - /I
i i '
	 i . .......i ,
i i
i i
i i
i i
'i ' "i
i i
i i
i i
9 <>,? 7.0 9,9 12.0 ft,? 17.0 19,$ 22,0 24,9 27,0 29,9
Figure 137  HJT M.or>EL •
                   " DECREES e
SnUTM HOI.5TPN 19»3»DAyl362  —SURFACE ELEVI  502,2 H
                                                               154

-------

1
1 ~
	 1
1
1
1
1
.' 1
|0,o *....,;..-
l<
i
0 I
P 1
j i
-h I
i
H 1
i 1
~ . K 1
1
1
1
1
	 1
1
1
1
1
. _.. 1 -
1
1
	 1

0
UJ
0
•»
*
0
•
0
*
- *
•0
0
1- *-0
* 0
»
L . *



- 0
0
0 12


"


0
0
0



1
1









2 1










..


-













- - -








i. -
o NIASURID
i S7AMD
2 DJFFI
s OJFF»
< OUTFIT








•

i i
I i
I J -
I I
I 1
I I
1 I
I i
-4_- 	 1---
1 1
1 1
1 1
1 1
1 	 1 	
1 1

1 1
1 1
| 1
1 1
j
1 1
1 1
1 1
1 i
1 . 1
1 i
1 1
1 1
| j
! 1
i i
. i . i
i i
..1 	 i...
.1 ... i
2iO *|J 7.0 •>;> 12.0 14.$ 17.0 19.3 12. 0 24.3 17.0 2»J
Figure 138  MJT
            IN PEOREES e
HOUSTON 1953--0»YI  78  --SURFACF  ELEVI  320.9 H
Figure 139   MJT
                              SOUTH
                                                N PE8REES C
                                            i9S3--o*yii»2  —SURFACE EUF.VI  sz».2 H


J0,0
	 ..
20,0


0
p
H
I JO.O
N
H
E
E
R
70,0
S",o
-
?0,0
100,0 .
	 2,
1 1
i !

i i

•*••»•»•-<
.

....
_ . .




i
i i
L_ . .1
1
1! 2 0 3
1 2 0 J
121 1
01
11 93
1
1
0 t
*3 1
«0 1
* 1
0 1
0 1
* 01
i
» n
I
I
I
I
I
I
1
1
I
I
I

01
20 3
0








9
2 *


1





1 2 3









0
0 1 *
'
• -I - . - -






o ME*
1 STi
2 D|F
3 OIF
...» PVE
< oui
1








SURED
NO
Fl
F3
LET

* - - '








1
1
L 	 J.
I 1
I I
1 I
1 I....
1
1 I
1
i 	
(
I I
... ...1 	 I
.1. :.f
i ..-•••
i
i
i i
. ..i 	 	
i i
i .1
t i
«...„...*. _.*o ^ Ui8 Utj iTi0 19>S Mi0 MtJ I7i0 Mt,
                                                         155

-------
                                                              ---+-
10.0
D
E ^0,0
H

M
	 l_
70,0
	 	 	
10,0
90.0 4

	



__

.


•W"»JB»«"I

'






i
12
0
*
• 3
0
(
*}

. .
*





2
1
3
)
kO>!"!>*-9—
0
0





0
1
2
3

,

•— i^*»»B*



0
0
1
2
J





'
.... ..



0
Z
3


...

_
"




0
1
1


J

__
'
0 . HE'
. .._!.«_ 1TJ
I . DJ
3 . PJ
— -« . nyi
< - aui

i
2



...
.. .
	
ISURIO
mo
'Fl
=F3
ERLA* ••»— 4
n.r
0
z a
_


'
.
...
i
-
I Z3


..
' j









)
) 3 *
_


L 	 . .
_








.
'
. 1 ....
	 Z*fl 4.9 7.0 9;S 12.0 14,9 17.0 19,3 ZZ.O Z4.5 27,0 2**!







•

K


>
1
Figure wo   M;T  MDOEL •
                                      SOOTH
                                                        IN DEGREES  e
                                                    i«5s«D»Yizo3   —SURFACE  ELBVI  SIB.S M
100,0
0*' - A '"*• " *" "A* * A "A" A "A ""A "*"A "at '
—
.0,0
—
20,0
JO.O

D
p
T
H
N
H
1
i
R
70,0
10,0
90,0
i



••*•>>—<,
<

_..







....... 3.
'
i
12
*
*
•







2
3
0 3
*
0
3
0





. . -.,.
'
0 1
3







....
~
2
3








	
0










1






0
Z 3

.



o MEASURED
1 STAND
z DIFFI
I
"
9
1 I
. . .-.-


_
_
•


01
01 *1
0 1
. . U.I .
*•*••»•••*••**»«*
Z 3 1
1


1
1
- ..".!.. .

	 .!. .
i
i
i



-;•*
i
.— , i

— •*
i
i
...I

i


-! -
i
«»«4> ' i
'[/

i
     2,0       4,»       7,0       9-.3      12,0      14,9      17,0      19,9       ZZ.O      24,9      27,0     Z»,S
                                            TEH'E<1ATU>E |N DECREES C
         Figure 141   HJT  MongL >        SOUTH HBLSTDrf 1953«BA»I2*»  —SURFACE ELEVI   511,6 M
                                                               156

-------


10,0
JO,T"
10,0

0
f 40,0
H
N
M
T 60.0 1
I
._.-»--
70,0


•0,0 <

~ JOT0 4

.. - -
1
1
1
1
!
1
< l
1 — _ I
1
	 1
1
1 1
1 1
1 t
	 1 1
1 1
1 1 Z
1 12
12
L_ ..J. 12
1 12
1 *
1
1
I
1
I
1
1
1
1
1 	 1
1
1
1
...J
1


0
1
2
) 2
02
'
0
0
0



. .-.




1

3
3
1
3
_.J
'
..
!


0
2
9
}






1 **
1 *»
1 2*
1 2*
1 ** '
1 2»
1 o 2*
- I .2*
12 1
2 J 3
1 1
3
9 1
3 1
J
1
1
	 L.
1
	 	 ...J. . 	
1
1
1
1
L

I
1
1
1 0 . HI
I 1 «-4l
1 2 « DI
1 » • 01
1 < - OU
1
1



L

L

J.

ISUKID
IND
FFl
FF»
UlAf -----
TUT
i
i





j
_
.. _


i i
i i
— .1 	 i ...
i i
_j_ . a 	
i i
i i
l i
l l
i i
l i
l i
\ i
i i
i i
i i
l i
l l
i i
i i
l l
l i
l i
l i
i |
l . l
i i
l i
l i
j i
l i
l i
l l
l i
l l
. i i
	 g.Q- *-•» TiO 9,J IZ.O l*iS 17iO 19, S 22.0 24.3 ZT.O JStS 	
                Figure 142   HJT
                  IN DECRIES  C
SOUTH HPlSTUN 19S3—0*ri299  --SURFACE  BUBVI  S03.1 M


	 1
_ 	 _ 1

1
. 	 l<
1
1

I
1
C 1
t 	 1 	
J JO.O *«,—„
M
i
E 1
R 1
1
1
1
1
1
1
1 2 3
1 I t
10 2 1
1 1 3



ID 2 31
' 1 2 31
1 2 31
	 ...L. J 2. .11. ,.,„.....
101 2 31
* 2 II
11 2 31
112 3|
i 1 2 9
1 02 t
I 203
1 2 13
129 1 0
12 9 |
12 9 | 0
1* » ' . 9
123 1
i
1
r
i
i
i
i
i
i
i -
i
i
i
i
i











i


























'
.



o MEASURED
i STAND
3 PJFF3
— * OVERLAP — -

••»•»»••«




.





i i
1
1 " l
l
l
	 1 	 ..
l l

l l
l 1
l l
1
1
1 .
l
i
"
i
l
l
1 l
l l
1
•op«  o
                Figure 143   MJT
                                                   TEH'EtATURE (H OE8RKS C
                                                           i953--o*ri3»z  —SURFACE ELEVI   $02.2 H
                                                                         157

-------
HIWASSEE RESERVOIR
     Figures 144 and 145 show the computed and measured temperature
profiles for Hiwassee Reservoir for 1947.  It can be seen that the
computed temperatures do compare, in general, reasonably well with the
measured temperatures.  This can also be seen in Tables 17 and 18 where
the standard errors of estimate are quite small, 1.0° and 1.4° for the
outlet and surface water temperatures, respectively.  The computed
outflow temperature is compared with the measured outflow temperature in
Figure 146 and is found to predict the temperatures very closely as is
shown in Table 17.  In Figures 147 to 152, is shown the effect of the
variation in the thickness of the horizontal segments from 1 to 3 meters.
The change causes only minor differences in the predicted temperature.
This is verified in Tables 17 and 18 where the standard errors of
estimate are only slightly different from those calculated using a
2 meter segment.
     In Figures 153 to 158 the effect of the variation of 3, the fraction
of the solar radiation absorbed at the water surface, from 0.2 to 0.5
on the predicted temperature is shown to be negligible.  This is verified
in Tables 17 and 18, where the standard errors of estimate are shown
to be similar to those obtained with the standard 3 of 0.5.
     In Figures 159 to 164 is shown the effect of variation in n, the
radiation absorption coefficient, from 0.05 to 1.40 per meter.  It can
be seen that the use of an absorption coefficient as low as 0.05 per
meter gives very different results on day 209 in Figure 161 and similar
results during most of the rest of the year.  This is verified in Tables
                                 158

-------
17 and 18 where the standard error of estimate of temperature at the



outlet level is almost 4 times the error for the standard case.



     In Figures 165 to 170 are shown the effects in predicting temperatures



of varying the diffusion coefficient from molecular to 100 times



molecular diffusion.  It can be seen that, in general, the use of



molecular and 30 times molecular diffusion coefficients predicts the



temperatures more closely to the measured values than does the use of



the 100 times molecular diffusion coefficient.  This is also indicated



in Tables 17 and 18.
                                  159

-------
                         Table 17
          STATISTICAL ANALYSIS FOR THE PREDICTED
            WATER TEMPERATURE AT OUTLET LEVEL

Reservoir/Year: Hiwassee/1947
Time Period Covered: 120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
1.01
0.96
1.03
1.03
1.06
3.95
1.08
	
1.06
1.44
Correlation
Coefficient
0.98
0.98
0.98
0.98
0.98
0.79
0.98
	
0.98
0.97
                            160

-------
                         Table 18
          STATISTICAL ANALYSIS FOR THE PREDICTED
                SURFACE WATER TEMPERATURE

Reservoir/Year: Hiwassee/1947
Time Period Covered: 120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
1.38
1.53
1.34
1.38
1.37
1.44
1.40
	
1.30
' 1.26
Correlation
Coefficient
0.99
0.98
0.99
0.99
0.99
0.98
0.99
	
0.99
0.99
                            161

-------
490,6
*7°i*
*9°t'
\
y
A
T 450.6
0
N
J *«,»
N
N
1
T **.°i*
f
R
4(0,6

410,6



._.
1

_._ ._ J 	 ..
I
	 . L
1




1 10
I i
1 01
01
1 0
1 0
-i— - « 5 -
e
0
0
1 o
1
1 0
1
0 2
i V- «-,
02
1 	 1 «
0


19
3
1 9
3 S
,. * 7
» •
94
94





1
9
9
9
1

3





1
1
1
1
1
i
2
4




1
1

Z
2
2



1
1
1
1
.

1
1
1 2
12
2 1
2
1
1
4
1 4 :
4
0 DAVI tO
1 DAVI 148
DAVI 209
OAVl 267
OAVI 364
OVERLAP
OUTLET
i


. i ...
2
4
4
4
4
4
4
4 1
4
1
'
3


1 1
! I
. . i .... i
i i
i i
. .1. ..\-
\ --- f-
	 ii'_ _._ L
2 1 1
11 	 l_
11 1
1 1
» 1 1
1 1
. ..'-1. v-h
s i i
1 1
> I i
i 1 I
I i
i i
I i
. I .... 1
	 r ~ — \"~
i i
i i
. . t .... i '
i i
i i
	 i 	 i
i i
i i
1 " T
1 1
2.0 4,9 7.0 9,9 12.0 U,9 17.0 19.3 22.6 24,9 17.0 29,9
TEMPERATURE IN DEGREES t,
Figure 144
«|T HOOEL « HIWASSES RESERVOIR i947--HEASu*Ei> TEMPERATURE PROFILE—
490,6 4
410.6
470,4
7"*M|»
y
A
I
0
	 H.
I 440,6
_M
H
T »»0,6
ft
420,6
410,6
400,6
3V.0.6
2



»»--«»**^













0
0
0
10
0
01 9
01
0 1
0 1
0 1
0 1
0 1 9 i
0 19 1
0 I"
0 1 91
101 9 1 Z 3
1* 2 * 1 4
* • 49 I
•34 1
» 1
« 1
* 1
» 1 .




i
1
1
1
1
1
1
1
I
1
I
>





1
-i-i.-..



2
2
4




1
1


2
2
2
Z
S




I

2
2
Z
2
2
2

4
4
4
4



2
Z
2 4
4
*
4
4
4
4
4
4
4
3
9
0 DAV) SO
i OAVI 148
2 DAVI 209
» DAVI 267
1 OAV| 164
* OVERLAP
< OUTLET
I


1
2
2


}
3
a
3
3




-..». .





(

1
1
1
1
1
1
1
... 1
. -1-
1
2 1
.... 1
.1.
1
1
;i
!
. . ....i.
i
. .1 . i
i !
i
i
i
. i
i
i
.0 4,9 7.0 9.9 12,0 14.9 17,0 19.9 22.0 24,9 2T,0 29,9
Figure 145
                                     N DECREES C
H(T HQI>EL •   HIUASSEE  KFSERVUIR  1947—COMPUTED TEMPERATURE PROFILER-
                                  162

-------
J'.o
**,»
j-pr,.

1 1
1 1
1
J 	 _..J .. ... ..
1
1 1
11 i
A 1
U
i
1
1 1
1
u
C
1
10
1

1 1
1 1111 1
i i 11111
10 1 1
1
1 1
1 1
1 1
60
W
10. D

20,0


p
a
H
"
I *°I°
_a 	
H
i
R
Y°»e .
»o,o
yo,o
iooto
2







o 1
U








0 1
Ull11
11







1
1
1
I
1


1
1



1
U 0
H
1
1






•
1 1
1
10
U







1
I





o . MEASURED
i « epHpuTio
* • OVERLAP
. 1 .
l
l


I. . .
1
1
1
1
1










1
1
1 I..
1
1
11



• 0 '0.0 110. 0 l»0',0 1*0.0 210.9 2*0.0 270,0 300.0 330.0 360
OAVS
Figure 146
H(T HQQEL 1 HIHASSEE RESERVOIR 19*7— 'COMPUTED OUTFLOW TEMPERATURE—
1 01 2 i\
\ 01 *1
1 01 21
i 1*1
1 0 *
i *i
i **i

J **
1 *
< 1 *
, 	 J *:
1 210
12*
21 0
* 0
• 0
L 	 • 00
* 0
*
1
1
1
' 1
1
. . 1
1
1























































n . MEASURED
i . STAND
2 - DELZl
3 . OELZ2
1
1
1










.







_
••»••«•<

— —


.
.0
1
1
	 1
1
1
T
1
1
1
1
1
'
	 1.. -

'{
1
1
1
1
1
1
1
T"""""*ts To 9*5 12.0 l-.S 17.0 19. S 22.0 2*.S 27.0 29.3
TFM'E«ATU»E »N PEP-KEtS C
Figure 147^ ^^ ^ H,WASSEfc RESEK-'ulK 19*7--OAYI 80 -SURFACE ELEVI 4*6,0 H
163

-------
	 1_ 	 1
1 1
1 1
1
1
— 	 — -f- !
r r
i i
1 !
1 1
0 1
P 1
T K 1
H 1
1
N 1 9
H I 23
E 1 »
1 1 •
R 3
#
T •
1 Z
1 1
1 1
r i
i i
i i
i i
i i
i i
i i
i i




2
0
0
0

'




*
2
3«
3
32
*
2
*
12 0
23
u






2
21 3
3
2 0
0
0
0
0
0






2 1
2 3
0
0








3
0







illl1*- Uf U» 3
X noocc
til 1 1 >l 1
c -*N m •• v
. ! i
2







kSURED
IND
.Zl
.Z2
HBT
0 >1
0











-

. .. _.
_





1
1 	
1
r ~
i
i
	 i
i
i
i
i
"~" r
i
. .- _ T
i
i
j
i
	 ~T"
i
.. j
i
2,0 4|5 T.O 9'.5 12.0 14,5 17,0 19.5 22. 0 24.5 27.0 ~ i9,f
            figure 148
                     MIT  MODEL
           TEMPERATURE IN DEOREES C
MIWASSEE RESPRVDIR i9»T«oArii*e  —SURFACE ELEVI  463,9 H
«EJ .0 *



20,0

30,0
D
E 40.0
P
( »0,0
	 N 	
H
T bffnr
i "
R
'
70,0 .
'
'
80,0
"
yo,o
"
100,0
2
1
1
I
1
1
1
|
!
I
1
u 1
1
1
1
< 1
1
1
1
1
1
1 2 3
2 0
» 0
3
* oo
3
i
i





3
1 2
t

'







12 3
0








2 0
01 3








0 Z
0 1
2
3
I
3







02 3
0 13
2
021 3
3





130
2
* *
*






o - MEASURED
i - STAND
2 - DELZl
3 « DELZZ
-;.» - OVERLAP — '•-
< - OUTLET
I
21
3
12

.

_____ -_-_




0
3 0
0








2 1
1
1
1
1
• f
1
T
1
1
1
1
r
i
i
. .1..
i
i
j.
i
/ f
i
l
li.-;--!
1
.0 4,5 7,0 9,5 12,0 14, » 17.0 19.5 22.0 24.5 27.0 ' 29,5
TeMPE"ATU"£ IN PE6REES C
Figure 149
                     HIT MQIEL  «   HIWA3SEE RSSFRVOIK 1947«D»YIZ09  —SURFACE ELEVf  463,4 n
                                         164

-------
\
\
10.0 *w«*pis
1
2Q|0 +«ff-"ffS

1
1
1
K
B 1
r .!
H ~

H
1
M _i_
1 1
R 1
1

	




1
1 1
1 '
1
1
1
*
1
t
1
1
1
1
1
1 1
1
1
1 1
13 1 0
2 1 0
• 1
3 1 0
* 1
S 1
1 1
i 1
1
1
1
1
1
1
1
- - - - - ,
1
1
1




2 0









3









Z 1





1
1
1
1
I 	
-i - -
---•] -
. 	 i . ,. __.
i
i
r
i
T- t - -
3 1
0 1
I 	 1
1
1
1
1
1
1
T""
1
1 	
1
-1
I "
o MEASURED
i STAND "
Z OELZl
5 DELZZ
< OUTIIT
i
i
-- — --I-*


	 ii-o
*
3 0
•6
2 }



" '
1


Ot 1
o i i
~r
i i
or 	 r
i i
9 1 . 	 I
o I r
0 1 1
° - t — r
i i
1 i
i i
i i
i i
i i
i i

i i
i i
i i
i i
i i
i i
i i
i i
i i
i i
i i
i i
i i
i i
i r
...^.U..-.!
1 2,0 *,} 7.0 »'.s u.o i+.» 17,0 n.s 22.0 z»,s ZT.O 29,5
TEMPERATURE IN DECREES c
Figure 150
             MODEL  *    HJHASSKE  RESERVOIR  19*7--OAyiz67  I—SURFACE ELEVI  494.1 H
3-F»*

1 1
1 1
1 1

20,0
1
1
1

1_ 1
l< 1
1 1
1
1
D
1 40tO •
T
H
I 90,0
n
H
i
T 6<>to 4
•*"-""
	 TO to,
	 -
dO,0 4
	
V'0,0 i
1
100,0 .
2.
1
1
1
1 213
1*1
*
*
*
•
i •
>•»••«»•••*•••£••»;»•
1
1
..-. .
	 r •
i
'!
. .... I . . .
i
i
i




2 I
a
0
0
0


















5
'








2
2 1'








2
•1
*13
Z31
I




0 H£A
i STA
Z DEL
3 DEL
< OUT
1
1 «
*
*
*
»
*
*
*
1*
Z 1
3
0
0




SURED
NO
Zl
zz
RLAP 	
IET
0
0
0
0
0
0
0
0







0 - n,j 7.0 9.J 12.0 1*,S 17.0 1».5 ZZ.O Z*.







1
i
i
i
i
i
i
i
- 1
i
i
T
1
1
	 h
1
... __T_
1
1
. 7"T"
1 -
1
1
1
1
5 ZTiO Z9k5
Figure 151
         HJT
                       JN  TESREES C




HJHASSEE RESERVOIR 1»*T--OAVI302  r-SURFACE ELEVI  **6t3
                                    165

-------
'
~Pi*


tul°

|0,0

--fo.o



•^_-
SS? * -:



aai ''"•"-"- ;


MB*--- •& -*WR?
*a£U -Wi»
'•SfifeL-'1'^


e -1.-
*••-'-.
»0,0 i

i? . . .
*
•••""*••

1
-,








.ijjLI-±-~
U:?!?'"" "



1








.
*•*»•»*•
0 4
1 0 1
110 I
110 1
	 . 1 . . 1 	 1 .
10 1
1 Z* 1
Z 11 1 0 1 1
12 I 0 I I
2* 6 1 1
ii o i
• 1 1
•101 1
•; i

• 0 i
* 1 1
• I ! '
• 1 1 1
1 1 1

	 1
1 1 1
1 1
i • • i
'-"." " 1 " 1 1
1

II II
II II
1 1 1
1 1
1 ||0
1 111
1 lit
II 1 »
1 1 <

, 	 1 ... 1 ...
1 T',0 «'.9 12.0 14. J 17.0
1 1
1

1
.1 _ ......

1
1 1 '

. .1 ... . 	 	



I . - ^ - . • ^ ' ' 'ii 	 ]
1 ...
1 1 1

1 . . '
1 1
1
_ 	 ! 	 . 	 1 .. 1
1 I
„...!..... ,. 	 	 1 ..... 1
. MEASURED I
••• STAND i i
- 05LI1 1
• OEljI 1
. OUTLET

l ... . . . . , .....
19.9 22,0 14,9 27. 0 29,3
Figure 152
                         TEMPERATURE  |N DEOREES C
MIT MODEL *   HIWASSEE  RESERVOIR  l»4T.-DAyiJ6*  =-»u*F»CE ELEVI
K*'\ ••




	 !_1


40.fi K


"

M .
fO,0 4


|B,0 •


70,0 i




°t° *

100,0 1
i




	 x

*



1

. ... . •



kV'V'Wl


••T*E»*»1<






*«i-»si-««
0 *
Figure
' ' 0
0
0

O •
»:
? "
0*
•
*
*0
*
•0
*
• 0
1
0
0
00
0



"
-•**?!•*«-






fc— "S--B-
rr" "r
153
•i r • -
• i
* i i
~«~ .. . ... .j
i i
i
i . . ..'... '
r i
i ' " i " "i
i
i t
\ r
i i
	 i . , . i . .

i
i i
. . I . . . . i . . . . I . .. .
i i
i r •
i i i
i
i i
i i i
i -- T |
i
— BW^«Tr***W*5«»*^5»*PB-»-S"-«t*— •-•-&•
i r
i i
r / / T\ . . i 	 	

i t
i i
J j
'1-9--WB--»*--5*"-i-*-e-«-3— »— .»— -B-
o »;» itiO • 14;» 17
TEMPERATURE (N DEBREE
!

i
i
..!,..
» . W . WP .
1
j ,
" 1 	 ' 1
1
1
1

. . 1 .
1
1
1
H," ' ' ' - •--
1
1
1
|
^••••••^••^•••^••.•.
I I
1 . . . 1 . . ,~1

l STAND
1 liTAl
1 1 BITAt
< BUTklT
1 1
1 . '

,0 i9;s -ft
i e
v-; "'


1
1
. 1 _« fc. .. _.! .*_•-- -r- -

1
1 . . 	
1 1
1 1
, ... 1 	 1 :. . . ...

1
1
. . . !... 	 1 . . ....
•». ??*•*? •*: ft*???..*???4
1
1 1 	

1
. . i 	 ";: . . 4 -

i ' /
! i <
i
. , 	 	 	 	 i . . / 	
'|- *"- "-j*V-^--"£
i i '
1 '
1 	
! ,T- ^
. . i 	 	

0 24, S 17. 0 2»t!

•



--

r~~





'•

—


1

1
L-
r~




1
         M|T
                       REIERVQIR 19«T.«OAYI  BO  ..SURFACE  ELEVl  446,0 H
                                            166

-------



19,0 *.i.*H-"'

10,8
'I'iBiB



fcjfejfe] 	 	
	
SHSp
-FTT
*f%
ID,O
10. 0




••-•«•--•



y^i
v^F—

<£>':;V "
— ' • — i






ii^.i.;.




,



-
	 • —
-» i
i-

1
i -4
T TZTI "~ T ~ 	 1
1
i — i
i* ~u
I i»i e
r 10
* i
19
1 I* t 0
... 1 • 1°
I» 0 |
1 t . . "o — i 	
— o 	
	
0
.....
i
i
i
i
r i
l i 	
i i





r
i
L^-.--.L.-^.
" 	 ! 	 T 	
1
r * — i -i 	 1
i i
9 | 1
i — • 	 r 	 1 	 1
i i
~"T I ~
r- L. . l . . . .
l i
l i
.... 1 . 1
l i
l l
1 l
l i
.. l 1
	 [_ _ i
i i
. • ^ - * • ' •
i !
i i
.-]- — | 	
1 9 .. HIAfURRD
11 »• VTANB
I •• IITAi
1 < i OUTIIT
9 S*|
0
1
1
1
1
1 	 1 	 1
. .
•
r~





1 I I
1 1 t
1
1 	 1 	 1
t
' - 1
	 _....-
'
r


- -
	 :
- -- i
......
t.
—
-
t—
1-
r



i
-'.• .

l

r~

r i i
i i
T ..!... .T 	 ! . . L . . ..! 	 	
~ — ''HE! — * — »;i ' — 773 	 v
! 	
-
.j u.o IM iT.o i»,» h'.o n'.s 	 mo *»,»
Figure 154
                                  TIH'ERATURi ]N BIOREII C
MJT M08|l •   HJWASIII
                                                                   ILIVI  *6J,» H
K*


»0,B t
- -

|D,0 t

— 	
fj0f 0



IMfl


7°i°

18,0

?°t°
	
109, 0
z
P'""J


.... ......




, —
* . . .
1 ••* V VV9V«V '
r 	 • '
^

'


U " "

	
_-
»••-«••••<
• 0 4

— 1 1 1 1 l» ^ 1 	
i i ! ""
	 1 1 10 ,
| 11.191 1
, . J ,.,,
| 19 \li 1 . .
• * 1 1 12 1 1 1
oil r-
	 1 	 r r — T- u ~«r 	 j j
i . . i i i
fi i« i i
	 1 	 1 	 ~{ on " ~ r i 	 . i 	

1 	 r o 	 i "i r j 	 .
!,. j 	
l l ° i - - 	 i ..!..-. --i— ;r5= ^si^s=»
' 9° ! 	 I j - -. ! | --I 	 1 	
1 	 1— - — 	
09 1 ..'...'-•-• - - ^ — _^.— »-^
1 1 '
	 -r- -- 1 . .- 	 	 ..
,..,**.«••**.—*-?-** »,.^-,*P*-»f9— *— - -- ^ HEASURBO 	 	 	 I
_ ITAMD
. BETAl •
J | . »TA1 I
i - " i*i < * OUTLET
i i '

t»-»i.|— BT»1-B^»«-»«*^-f-»"yB^*!-e-»7B"-J* . • tiiO 14,5 *7
-j-- 7,9 »;j 12.0 i»t» »'«w
... ...


	


-
m^i^e.
1. 	 ...1

	




'*fT~ •--»'

.

n4»i.i~».
0 X*].

"~







r~

...








r
1

Figure 1SS
         MJT
                                     M DEOREES C
             HIVASSEE  RESERVOIR  1»»T..DAYIZ9»

                                 167
                                                                  «LEVI  »»!.» M

-------


.
	 ID. B A-i— i«-

"|uj»n

|0,0


B«~WBB-^^


l<
1
Afl A i-i-iA- "







'



B»SB***B*



-

... -..!,...
n*«mn*9B»4
]" 	 r»-
1
1 *
1
"
.•"•|- :"--,—
1
TOfO <
ito - 1 •. .- .
luiX'-i...

*•»••«••'•»'



. ~-v:



WO.B -

*i»*ri»«i
'••»e^«^»*'





i i
"i i i
i i i
i i
i i i
i i i
i i i
i i i
! 1
r -• -j ----- i
t i i
i i .
. ! !
i i i
. 	 i .... i .... i ....
i i i
1 1 1 IIS
I 1 1
. ; i ....«'.... i .
>»BB«B»B—«»«*»SB**»B*PBI»»*B«W«**"W»-"*B«
e i 'I
D 1 1
1 1
e [ i
1 I
I i
' . 1
1 1 1
1 i
...... 1 .....'..... '
1 I 1
1 1
. 1 . l . 1
i r i
i i
1 1 1 0
1 1*1 0
1 1 10
i _ i r • i .
1 1 • 1 o
1 1 i
1 1 * 1 0
1 1 . I . o >





1 1 10
1 1 • 1 0
1 1 1
. 1 1 . . • 0 	
L ' '• • ' • '
1 1 Ml 	
1 .1 01
1 l *»• 1 I
. . . 1 . . 1 . .... 1 	 	
1 0 |
1 1 I
o i i r
1
-. -. . .. j
. . 1 - . . 1 . . 1 . . . .1 . . ..»-!
»ij«»««»w"»«f»*»w»B— ".Jr »*•«•»•»*»"«*•*« *9*»—B*»««]
i ii
>»B9«»»«r««
i i i
iii i
i i _ i . . i . .
i i i
i i i

• i i i
i .1 . i , 	 	 i
i r 	 -i 	 1
i i i
l ' '

0 MEASURED 1 I
1 • IUNB 1 1
S IITA1 1 . 1
. S IITAS . 1 ..... 1 	
< DUTLIT i i
i i i



• •^' • '•,

'1
1 1 1 1 1 1 1 1 1
1 1 1 . 1 .... 1 	 	 1
>f»«*«**fsiw*re»««W»»»*P"»S»»»i«*f-«"^B9-« •+»•»*— -»•"* *«ai»«W-»«W+-" -S»"»1-«* *»*••»§»• *»,»4>ir»B»*««»*-«>9»»«»WWW»*

Figure 156
         HIT  MOBIL  •
           TEH'fRATUU !N DEBREfS C
HJWASSEi RESERVOIR ;»4T.«OAYIZ»T  ..SURFACE EkEVI   454,1 H


1

1
JOyll tmi-'ri-
I*'
19,0 *»»—B»-
~ "T
1
40,0 *«»w»»ii
1
fO,0 •••••ci<
1
1
|0,0 *rm-w*v


\
' fD,0 ii^i-iS
	 l_
100,0 »••"••»
ITT
'1 1
1 1
1 1
1 1
_ 	 	 j 	 ,
! ! .

i i
- r " 	
i
»»»«••«••••»*•« W«S»»"S*^-T4»"*5«
II
1 1
1 1
- . . ' . . 1 ....
1 * 0
1» 1 1
1 • 1 01
. . . ' . I
••••e»*fl*vve9*w«"vf'9"ff*»"«9*H»ea
"• 1 0 I
••- 	 T 0 	 T
* 1 1
1 1 .
1 1
1
- T r i
...'.-. i . . .
--j • i i
i i
1 i i
: i . . . T . i . .
~ i i i
1 i i
i i
.1 .... t . . i . 	
•••iw"-r*»"jc"**r"w~-«"+i'-*«""«»
1 ' 1
1 1 1
1 1 1
.1 . . . 1 . . 1 . . .
Sr*"**-"**


r •" ; " '
-£•••£-»*
-•l»0i"7
-S-^59--»
~ ~


-£••-•••••
1
I
(r**Mr>»v-4

•1
^•wi-iffB-
»••«•••*•
'


»t— -••-»---»-»«»^*»-"Sw-»»"*»"B"»""»"««»'>"«I'T»«)l
1 10 I 1
1 101 1
r~
i !° --1 	 \ 	 -r-
•
*3
*
*
«£•••-•••
_
^9W«B*»*


«e
ST
M
SI
-;- DV
ou
10 1 1
1 1 1
10 1 I

1 ? 1 .... l ......
••»—£—« v» +*•*•**••"••+**•••••••*•••+ v*^v" *••*••+
10 | I 	 F
* 10 1 1
1 1 1
0 1 1 .
1 1 1
01 1 1 "
01 1 1
. ..1 ..... 1 	 1 . . . .
P •»- B -w«W****t»*«*?-»W*»W0 •?!»•»•»•*•>» 9»+m*m9+t


>•
i i ^-^
. ._ 	 . 	 1 	 jj —
••••2-B«t««««*w««w«*>«w*""'*"V«*««i^«**0**i***«
i l l
>•
i i i
i i T — 	 r~
i i • • i J.^.i.i.*
i i it
i i ii
. . i . . ! .-. . .:\I . J'.T;
i i i • ,
i i i '
i i i
.1 i 	 i 	 ' 	
HURiO 1 ' 1 	 	 1 	 	 	
kND 1 1 T
rAi i i '
fAS 1 1 . 1 . . . .
f
! .
l
BRUAP —»-*»—•!•- 	 *r-B— --*-*-- --->^--.»
nil i i " I 	
1 1 	 1 	 1
1 .1 . 1 .. . '. 1 . . . .
4,S T'iO 9-,f IZ.O 14. J ITtO 19.5 IZ.O Z4.S ZTiO Z*>9
Figure 157
         NIT MODEL -
           TEH'gRATURE I" DECREES G
HIWASSIE RESERVOIR i»47«.o*yi»oi  ^.SURFACE ELEVI  444.»
                                           168

-------

1
1
-jr>70-isi«ii-"


I
i
in, B l,;-»Bi,.;,
T-- '"
»o,o *••<•••••*
1
1
^.^ 1 	 —
#*» *•.«••*.«
	
" '(B|V 'Wiw***"""'

TO 8 '
; 4-.
\
r___
loo.o !...;».;.

• i •
i •
i -- •
1 •
1 T~
1 *

il S
* 1
• 1 0
••-Y»"»»»»»s»5ii»-*
" • 1
* 1 0
••!••' «o •
•j~V ^n
- — ; — j 	

!

|

i - -
i
i
.... i . . i
T 1
1
I

I 0 |
r~o- I !

IT r I
o : i
*•- : -T- - r
r ] !
i i
, 	 ]-....- 	 !
r.... !....! "..'."
! r
i 	 *

j f


f i
r 	 - t i
rr, i . i
---t -I
1 . , -i 1.. .... _ ^ 1 . . ..
1 1
1 1
1 1



\
1 	
1

1
1
--- , 1 , 	 	
1
I
]•• —
...{..
r 	 T 	 '
1
1 	 ' " "1 	 	 1
1
1 •" —1
1
!
1
1
1. — -1
1
1
I
o MEASURED
I MTAl
> IITAI
»•«• • OylltLAI* ••••»
< OUTLE7
1
1




1 	 i




1 1
1 1





1 	 1
	 1
	 1
-i— .I.i.
''I




1 	 1





1 1





	

'„ .
..----.-,




- 	






.,,-.,.;.

^W,i-™,


<*y*»*«^4*4
- r

. i
T
r 1
t
. . . i
figure 1S8
     nv

MJT NUPIC •
 izTO"     »,»•     i7.o      inr
  TIMP£*ATUM  IN DEARIES C
RESERVOIR i*«T..OAYI)64  »,IU»f»CE  EllVl  *J*,l H
B.,?/'

— iP"B~i

•T5»-

	 ( 01 t • i rr"
oia 11 i i



ii~*i~
<
J?.i? «•-•?• -
....

BIZli 1 1
r i*i i . ' .
8*2 1 1
*ii i i
o*ia i i
..?"• '*. . r~; . . .' T .
" * 0* t I 1
• * t\ i i
• i i i i
•Oil I . _ 1 	
k" -• z " i * I
• I 1 1 1
•'l^ . 1 - „ - ..i,;,;,,,;,!.; 	 j,...
r 	 r*~* — v " "i '
izi i '
* i5 i i i
|0,0 *••»»*«<
...

40,0 ,
	 1


70,0
18 . . ' . » '-• - - -„•.
I'lor*""*"""""" *r "* j
ri-o 1 I 1
» a i i
1 1 1 ....'..-
II 1 I
h - j j i
1 	 r 	 I 1 I
1 i i
fO,0 tii—im—
	 I. .
1
100,0 *••-»&*•»*
III
1 1 1
,J 7,0 9.J 1*.0 l»

,
'
_



• » 17
I |
1 I

....
" 	


1 »T1
1 (TJ
. ' ITl
'""< OU'
.
0 1»
1
1
r~ i
i
i
. '
i
[
i
i
i
.,.i-..;.i».— »i—
I
i
>,i,j— ;.I— ^;-,
I
i
I
i"
i
i
1
NO 1
L i • -
""' "T" "
i
. i
9 IZ.O nr

1

1
1
1
1
r
1
*"="~~"*~*"""""""*
1 1
1 I
1 	 1 	 TT —

1
1 . .
1
1 k
1 1

1
1
1
' 1
..... 1 . .-1
lmmmmmmmmm+ W* ••
'* *TtU ***'
Figure 159
         MIT
                                    JN DEBRIES C
                      RESERVOIR i9»T«-OAn «0  «»UR?ACI IUIVI  »**,0 H
                                              169

-------
1
1
1 -•-•
1
! T
	 T 	 ~ 1
1 1
1 1
|
!. . i
1 1
l<

|
1 *
[
1 •
1 " •
1 1
1 }
1
1
r
i
•i — 	
i i
i !
I
I
1
I
T
I
1 3
1 *
1
1 >1
1
1
1 *
T
i 3i
1 1 II" (T
1
»l 0
r,«. .-T^i,;,,. ,
0 1
" ff" r~r
1
• 1
t 1
I
z"" ~r
M—^Us-.*,
-\
i
1 ....
i
i
i
i
i

31
0
0
0
I
0
0 2
0
2
I





1 I
0
I
0
I
I





...

n







2







0 MEASURID
1 STAND
I ITA1
. * IT»J.
< OUTLET
i
4.-.-.,-.--Or--------
1 0 11
0 1





" ~i





-






. . .
	 ,













"\ n
1
1
I
i
, ,
. i

1

. . i



-
i


i
i
i
i
i
i
i
2,0 M 7.0 9-.S 12VO - 14,5 17.0 19,9 tZ.O 24,5 17.0 Z»,J
TEMPERATURE IN DECRIES C
Figure 160
MIT MOBIL • HJWASSEE RESERVOIR i»47.-OAYU4» ..SURFACE ELEVI 4*3,9 H
1
1
'*"*""*"
J 	 1
" i
i
i
	

i 1
i

!. . i..
i
i
i .


„

i
i
1 o
1 • o
1
	 -• r
i
i
i
i
i
i
i
i
z;o *
' 00

1
1
. -
. - -|




•
2




"
	



*
0
2





'


3
0
.*!
t







1
0
Oil
1






3
0
30 I
0 1





o HE
1 ST
t BT
» BT
< ou
1
sio
1 0
0 , .


2



tSUREO
INO
n
42
ERtAP •---
JL.T
1 01 1
3 1 12 01 1
ie . i " . i . . i
2

2 ~
2
2
2

.
...

-



1 	 |—
1
1
. '
1
....



. . .



„
	 —


I
1
1
.... 1
1
1

1
1
. . 1
'I
1

	 /_• 1
. . 1
1
i 	 ' - T-
1
,9 7.0 r.S 12,0 1«.S 17,0 19. » 22.0 24.J Z7VO 	 tr&—
figure 161
                       N DECREES C
HJHASSBE RESERVUIR  19«T.-DAYI209  -nSURFACE ELEVI   463,4  M
                                      170

-------

1
!

1
1
1
1
r" i '
i
i
	 1 	 1 !
K.I 1 !' •
r ' i
< 1 j

- i j i
„ 1 , . . 1 . . . 1 . J>
r • T 11 i o
	 1 i
1 1 8
10,0 *....»..,
1
•" l .
78,0 *«i-»si«-i

HT'B
' | 	
1
i
i
1
**-»»9-^B»+*«-— B«*
- - r -
l
i 	 i
.-.-'.
L '
T
i
i
! 1 1
1 1



•'
	 	 	
0
1
i


,






'









Jl
I









0











0 MEASURED
i STAND
t mi
» ITA2
< OUTUT
i i
...~,I.J>4
1 1
j l
n
i i_
si
1 1
} 1
0
J 10











01
2 01
S~T 	
2 1
2 0
* 0
^
0
^J 	
2
2
2










....


	






' -


_ L 	 .


—










~


. ...1
	 ZiO *,» 7,0 »',» 1Z.O !»,» 17, 0 l».J 22. 0 24.9 2T.O 	 29, S
  Figure 162
                         TlH"E«ATU«E I* DEBRCH 6
MIT MODEL •   HJWAISBE RESERVOIR i9»T«-oAYt2»T  •,•>
                                                                     nevi   *s*,i

	 , 	
1
1


< 1.
1 1
I
40.0 »..~.i.-,*.-«.«B-
1
*
	 1 	 i —

1 •
1

	 T '

1
1

"

~T
1
T .-
l
., ... 1 .....
r??T-j-?
a
- 8 ---
0
e




--
' ~
2
2
2





. ... . .

.
2 .








11
2
t







11
* 2
11 2
1 2



lit
. »»
iff
112
HZ
Iff
t
2
0
0
_
,


i STAND
2 ETA1
1 iTA*
„!,• OVERLAP
< OUTLET
i
l
l
0 1
0 1
o 1
1
0 1
1
0 1
0 . 1 ...
0 1
0 !
1
1
1
t
1 ...
T

1
1
1
1
1
1 ...
1
1
t _
J ._,
1
1
1
, - - -t-
j
1
	 r
i
i
. i
i
i
i
-:i;.i-;,i
1

l
l
. . . l
l
1
. . l
l
i
l
	 l
l
l
l
	 l
l
.««!.» *••?•••"?*;•- '••••:J:9"li-=~* *-' Jj.o n.s 17.0 19,5 22.0 **.S tT.U M.S
Figure 163
         HIT MODEL
                                   JN 06«R*E»
                     MStRVQIR 19»T«-OAYI102
                                                                  fLtVI  *46.» H
                                          171

-------
1 I 'I • 1 0
1 I 1 • 1 0
	 1 	 -[ | * ! 0
1 	 1 . . • 1 .
l<
J0,0 *«i-«i»«-
1
T
1
I 1 * I 0
1 • 1
1 * I I 0
1*20
• t 0 |
*I2 o 1
* I 1
•il 8 1
II '1* I 1
1 *2 1 0 |
1 1 * i o |
1 - - • . 1 . 1
1
1
!
	 » — 1 	 1 	 -
• 1 1
1 1
1 . 1 ' 1
1 1 1 1
|
i
1 1
1 1
-_ _.' 	 ..1 ._ ._
",'
1 1 1
	 r ii
i
i
i
r ....
i
i
r ~~T 	 i" '
1 1
1 I
1 1
r i i
1 1
1 - 1 . ,
1 1
... . . 1 I
i i i
180 0 i ' ' ' • ' ' - ' ' - - - -




























e HE*
1 IT'
* IT'
» 8T«
i
i
i
i
( . . _
.1 T"
i
i
i
i
i 	
•
i
i
i
. i
i
i
i
i _
i
i
i
i
"i - ~i
i
i
• i
SUMO i
NO I 1
l i
2 1
< OUTFIT i
I
i
1
. . 1 . . .
1

1
	 	










'

'

»««--•-"»
1
.... 1
	 l_
1
_T _


1
1
1

1
i
1
1
1


... 1
1

ZiO *il T.O V.S IZ.O U.J 17,0 19,5 12,0 Z*.J 17,0 2».J
Figure 164
         HIT  MODEL
           TEMPERATURE ]N DEOREES C
H|WASm RBSERVOIR 1**T..OAVI3A*  *«IU*FACE BLEYI   414.1 n

1
1
1
1

l<
1
1
1
1
01
0!
01
I
•1
!•
*l
»
0 *
«J
- p»l
| 0*1 1
L- 2;
•
*
*
•0
•J
40.0 *•»-»-=— »l»OB"-s-
1 l»»0
1 »>
	 1 «2_P
_L • 90
j- • o
1 •
- 1 •-• i
- *ilj*=**3=*~rr
\
	 i
!
i
i ....
..i
























'



I


























o . MEASURED
1 - STAND
2 - DIFF1
3 m BlffS
...» . OVERLAP —
< - OUTLET
i
i
i
I









i r"
. i .... i
j |
| 	 ^_
. . i- T^-
i
i
i— — T-
| .._4__
i I
1 	 !-
• r-~"rr
! - fl-
l/t
1 1
• ! !
1 1
100,0^--,.---.- 	 =-- 	 =»- 	 --*- — - l?-0 „,, MiQ „-., 27l0 29fS
 Figure 165
          H|T MODEL »
            TBhPERATURE JN DECREES C
 HjHASSEt RESfRVOIR 194T*-OAYI "0  —SURFACE ELEVI  446,0 M
                                           172

-------


lo,e «.;-..*..-

20,0 *»r—ri—






_ _ !<


— j.:-_:__..
1
	 L _.
70,0 *.?—.-;--.
1
1





2|0 4

1 1
L 1 1
I l
1 1
! !
L 1 1

1 1 l
i
1 1 *
1 . , 1 , . .
1 I
1 1 123
1 1
1 1 »3
| , U30
1 123 0
1 0
1 0 |
[ 1 Z 1 30 j
1
1 2 21 0 1
11) 1
1 1
U J 1 I
,...,.....:.,...,...! 	 ,.
i
i
i
i _ i
i
i
i
i
i
i i
i i
i
t 1,0 9,9 12



I t
iso
3 0

0

0
0







.




0 I*


1
0
)
c



















S 17


230 |
1
"1
1
1


|
1
. . _ J

|
~ 1 1
1
1
1
1
|
" 1 '
1
1
1
1
1
"••"I 	 '•
1
1

0 MEASURED
1 STAND
z BIFFI
3 DIMS
< OUTIET
1
1
1
,0 19.5 22

JO 2 1





















.0 Z*


I
1




" '




" " '










,t ZT

i
-+
•~~~r
1
1
T


I
1

1
1
1
1

1
1
1
1
1
1
I

I
1
1
1
1
T
o - ^«TJ
Figure 166
         HJT HOCEL •
           TEMPERATURE  |N  DECREES C
HIWASSEE RESERVOIR 19*7--OAVII*B  ..-SURFACE euvi

1
1 1

1
j
I 1
„ 1 . 1 . -
l« 1
1
! i
i i
i i
1 1 o
I i 02
_ j. j
1 I
1 I
	 1 	 i
1 1
I 1
- 	 i — i





1 2
3








•
0
3








a
01 2
3




•


0
0 I
» 2
3







0
0 1 2
0 1 2
I
2 S
3



o HE/
1 STJ
z DIP
3 DIP
< DUI

1 02
1 0 2
0
3
3
i




SURED
NO
Fl
FS
RIAP -"-
l«T
u
12 J.
3
l








>..... ..].!*........*
01 1
13 01 1
0 1 1
1 1
1 1
1 1
1
1 1
1
1 . 1
1 I
1 1
.'--..'
	 1 .
T
i
T~
1
i 	 r~
i
J ... i
i
i i
i i
i i
i i
i
i i

  Flgur.
            TEMPERATURE IN OERREES C
                    19VT*«OAYI209  —SURFACE  ELEVI  »»3.* H

                     173

-------
1 1 1 1
1 1 1 1

1 1
1 |
* ' 1 u 1 1
1 1 1
1 1 1


.. . i . . .
, .-..-i-U-,-—!---;.--,,
I I
1 I
I I
< J 1 1
1 1
1 ... 1 . 1 ....
- -•- 1 	
_ _ T
(0,0 »«iT-«Bi—
1
I
1
! !
i i
1 1 1 0
1 1 0 f
It 1
r 10 i
i i
i i
1 1
~~~~ ~~ 1 - - - . [ - - 1 ....

v
! !
i i
i i
' 1 1 '\
1
1
i i
i i
i i
?0,0 *•«---!«-*— -»•- r-»--*-- .s--«-.--— -«
' ""' 	 J 1 1
1 1 I
1 - .'..!...




z
3




1 1 1 01
1 1 123 01
1
1
1
1

I
1
1
1
1 1 01
1 tzs
	 1 	 12» o I'- ' '
1 1
1 121 0 I
r i a --j -
1 10 I
1 US 0 |
1 1 1
1 It* 1
1 I 1 1 J
1 1 1 0 I
II I 1*1 T
1 1 1 .1 	
1 1 o I i
it I) I 1
101 1 I I
l» 1 . . 1 . 1 ....
t 1 II
I
1
1
1
1
1
1
1 ' ~l
1
1
1
! 1
1 1
1 1
1 1
1 1 1
1 • |
. .1 . 1 ... . . .
II 1
1 1
1 1
.' ' 1
1 o MEASURED ill
i 1 STAND I 1 1
I z OIFFI i "I I
i 3 BIFFS i i i
i < OUTUT i i i
i ill
I I I i I
i . i " . . . I
k
k













	 IAO_ . *i» 7.0 9-.S 12.0 !*,» 17,0 19. S 12.0 14,5 ZT.O Z»,5
Figure 168
         M(T HQOiL •
           TEM'ERATURE  |N  DECRIES



HINASSEE RESERVOIR l»*T--OAY 1267
                                                                  UiVl   «9«,t  M
•* 	 ~K"Z — - — STI 	 * 	 * ----- -..- ---, - . . f
i i


	 i , .... i

i
i
i
i r i
i i
i i 10
I 1 0
i i 20"
1 12 0
1 I 2
( 1
1
' '
1 1
1 1
1 1
1 1
_L 1 1
1 1 1
.^ i___J... .!. .
i i
1 i.. i
i i



Z
"








2







— ii...
3
3
3






. . •
12 3
3"
3
}
3



»s
*3
•3
•3
»3
•t
*3
Z J
1 	 .
0
0
_
_



o HE.AJUREO
i STAND
* DIFFI
3 BIFFS
< OUTLET
I
I e
1 e
10
0
0
6
0
0










1
!.._!_
ft
t 	 f-

. i ....




' " " ; 1 : l(.

	 I '.... .'. .
- f
*«» «i» T,0 9,9 12.0 1*,S 17,0 19,5 22.0 H.t 27,0 j»-,!T
,. „„ ... TEMPERATURE »N DEBREES C
       HIT MODEL •   HIHASSEE RESERVOIR
                                              o«rii°2  ^-SURFACE ELEVI
                                          174

-------

J

J 	
1
1
1
1

1
_ 1 	

1


1


1 1
,

1
1 1



1 1*1 0
1 l*J 0
1 1*1 0
1*1
1*1 0
1 *JI
! izs i o
I I Z» o
1ZS 0 |
in o T
• » i
• 0 1
*; i o i
o 1
1
1 1
1 1
1
1 1
1 1
1
1
j
1
1 "i
— -•;•'. . ' . .
- | |
t 1
1 1
1 1
1 1






















_










.





... . r
8 . ME
i - JT
t m DJ
3 « Dl
1SUREO
1ND
FFl
FPl
I < • OUTLET
! i -•- -




..


1 	 "
._ 	

I •-
1
1
1 1
1 ' - " ^1
1
1

r ~ T"
i
i i
j
i
i
i i
i i
i
i i
i i
i i
i
i
i
i i
i i
i i
i i
l i
i i
i i
i i
i i
i i
i . .1
J 7,0 »'.S 12.0 !»,» 17,0 19. i 12. 0 2»,S 17,0 29, J
Figure 170
        MIT
          TenM«*TU»E |N DECRIES C
HJHASSEE K§«*VOU  i»«T--o»ri»M  *
                                                              ELEVI  «»,i H
                                   175

-------
FORT LOUDON RESERVOIR

     Figures 171 and 172 show the computed and measured temperature

profiles for Fort Loudon Reservoir for 1971.  It can be seen that the

computed temperatures predict the water temperature at the outlet

reasonably satisfactorily.  The good fit of the predicted outlet water

temperature is shown in Figure 173.  These results are statistically

verified in Tables 19 and 20 which show standard errors of estimate of

1.5°C and 3.0°C for the outlet and surface waters, respectively.

     Figures 174 to 180 show the effect of the variation in the

thickness of the horizontal segments from 1 to 3 meters.  The change

causes only minor differences in the predicted temperatures.  This is

verified in Tables 19 and 20 where the standard errors of estimate

are only slightly different from those calculated using a 2 meter

segment.

     In Figures 181 to 187 the effect of the variation of 3, the fraction

of the solar radiation absorbed at the water surface, from 0.2 to 0.5

is shown to be negligible.  This is verified in Tables 19 and 20 where

the standard errors of estimate are shown to be similar to those obtained

with the standard $ of 0.5.

     In Figures 188 to 194 is shown the effect of variation in ri, the

radiation absorption coefficient, from 0.05 to 1.40 per meter.  It can

be seen that the use of an absorption coefficient as low at 0.05 predicts

the temperature poorly on day 132.  On the other days the differences

between the temperatures predicted using 0.05 and the other coefficients
                                                                   i
are relatively small.  This is also verified in Tables 19 and 20 where/

the differences in the standard errors of estimate of temperatures are
                                 176

-------
somewhat larger at the outlet than with the standard absorption
coefficient of 0.75 per meter.
     In Figures 195 to 201 are shown the effects in predicting temperature
of varying the diffusion coefficient from molecular to 100 times
molecular diffusion.  It can be seen that the variation of the diffusion
coefficient makes little difference in the predicted temperatures.   This
is verified in Tables 19 and  20 where the standard errors of estimate
are all similar.
                                  177

-------
•T4.O t




.




.
-» «0

IJ'lO








2
* * *

^


- . -






	





' -«

.

0 4


.
1

.






.









S 7















0

e



0
0 9


....


.









6
6
6

6

6
» 12











• .





_



1
0 14



















1
1
1
> 17










_

. .

-
I 1
1



0 DA
1 DA1
t DA
3 t»A
s BA
» DA
• 0V
< nu
0 19



L ... _






_

.. . ..,..

i





l\ T6
n 112
n 2
-------
                         Table 19
          STATISTICAL ANALYSIS FOR THE PREDICTED
           WATER TEMPERATURE AT OUTLET LEVEL

Reservoir/Year: Fort Loudon/1971
Time Period Covered: 120th - 330th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std. error
of estimate (°C)
1.53
1.56
1.37
1.54
1.58
2.05
1.43
	
1.59
1.69
Correlation
Coefficient
0.92
0.92
0.94
0.92
0.92
0.86
0.93
	
0.92
0.90
                            179

-------
                         Table  20
          STATISTICAL ANALYSIS FOR THE PREDICTED
               SURFACE WATER TEMPERATURE

Reservoir/Year: Fort Loudon/1971
Time Period Covered: 60th - 360th Julian Day
File Name
STAND
DELZ 1
DELZ 2
BETA 1
BETA 2
ETA 1
ETA 2
ETA 3
DIFF 1
DIFF 3
Std . error
of estimate (°C)
2.98
2.78
3.09
2.86
2.88
2.81
3.38
	
2.95
2.92
Correlation
Coefficient
0.86
0.89
0.85
0.88
0.88
0.89
0.81
	
0.86
0.87
                           180

-------
'"ft ^•••^•••••••^••••-•••^••••••••^
1 1
1
	 l_ _-


3£?,!:^

L.: -- - ' --

if»,i *Bi.. j.-.—d
i • j

•»!>» '

ffe^K^i






i
i
3*»Ki^
^WM.i.c
.






—





•1..-T .-.






:.g5i|r:.3

|
S5^flr«
\-tr±.; - -.



.





0
0
0
0
n
| |
i n
R4 •
10
in
•••^•--^ttcr — -KB-*"*-*-* »R»+ " ' * ' ' * ' A ' ' ' * * " " A
• 1 1 1
1 1
1 1 . _ I
1 |
I [
1 	 -L 	 	 U
1 1
1 1
1 1
1 1
I 	 1 |
1 1
1 I 4
1 1
1 1
1 1
1 I
1 1
* : :
..*.'. i
61 11
1 1
61 11
1 1
1 1
t | | 1
1 1
& 1 11
t 1 11
1 1
& 1 1

	









1



--










_


0 .• t>AY| T»
l . nivj ]»
1 . DAYI ZO*
3 -* OAY I iZ6
i . BAYI 210
t .. DAY) 3*3
l * •. nuni A*
1
l
i. - 	 I
1
l
I
I
1
I
I
1
l
1
1

I
1
I
i
1
52 14
• 3 »
21 14
1
23 Ul
1
11 I 41
1
t I 3 4|
* 11 M

1

"*•"*"*"
1
1



•••""**— •"
....._
"-"""""".
. . .





i i i i i < • OUTLIT i i ....
20 ^9 TiO 0* ? 12iO 1^*9 17*0 l?i" ?2tO ?4i? 17 §0 J*i
 Figure 172
                 M(JnEL .
                            FDRT
      TEMl>E«ATu>E I" PEOKCES C
           1971     r-cn«(PUT60 TEHRtRATURE

II11
1 | 1 I
1 ! ' 1
-I | 1 1
1 1 i >
(III

j-jj.-- 1 ' I _ 1 1 I
1 i i i 11
,.| | .. 1 1 11
*0'BT" •"• * • i n
. + ||0
1, 1 11 0

1 I 10 0 ._!_..
1 1 111
i- - 1 1 1 I I 0 1
?-- .1 , .;-« i | i o i
1 1 - H 1
1 . . .•! ! - - ! -.- .,
i" ' "b o>i i j
l i " i . .
1 B 11 1 1
, *« -« ( )
1 | 1 1
1 ... i 1 1
. 1 - ' J 1 1
!'•"• i i i
».jB^-'-fr'=Tf:!r"^^r5~i:;<

0
- . 1111U
11
0 . .. -
..





'1 "zia.
i l l
l l i
1 ! 1
. 1 . 1 ... .1
1111 101 1* 1 1
10 | 1 111 I
1 | 111 i i
01 1 1
1 ' !
1 1 11* 1 0
1 1 HI
1 1 1
1 1 11
1 ' ' -
1 1 - - '
_.L -.. --1- . - J- -1—
1 1 111
1 1 1
4. .. 1 	 -.0- - -
1 1 1
1 1 1 . 1
1 1 1
1 1 1
1 . ... 1. 1
1 I.'.
1 1 1
1 1 1
1 1 . '
i o * MEASURED i
1 1 • KQHli» 1
1 * . OVERLAP 1
1 I.I.
i I j
i 	 j ...... j - 	
S 2*0.o" 270.0 . 300.0 ' 3JO,
1
1
.;.- '.i.


. ... . .


..Bi.i-i,


0. .
jys^**^*j^
1 0
11
i * ;i
i


	 L
1
0 360.
Figure 173  MJT
                           FORT
          PAYS
LU"ur>U"  1«71    .-COMPUTED OUTFLUW TiHpfRATUHE.

         181

-------
1
J
1
l.fi 4


	 1
|
10,0 »
1
1

1
1
-*0*fl-J
1
1
1
1

1
t
1

1

J0,0 *
1
1
1

1
1
70,0 *
1
1
1
m* c* . . r
j
1

1
I-
1
|
|
I


L
1
1
|
1
I
... 1 . . '.

	 1_
1.
	 1.

	 |_
1
1
- 1
1 2
•
I *
1 *
1 0*

1 t
1 f . . _J
1 2
• ?
1 2
t . .
*
12 0
l*
12- - J
o
0








- -J
.- ..J




— 1
1
1
1
1
1
1
1
1- 	 1
1
1
I I

\
1
1

1
1
1
1
1
1
1
1
J
T
1
1
1
„ 	 I
1
1
1

1
1

™ .- -
i


1
!
i

i
i
i


i

i
i
i
i

_i
i
,
1
-1.
1
1
L -
1
1
1
I
1
I

1
,
•
1
J...
1
I
.1 . .
1
1
J
_. I ..

1
1

i
1
1
I
I
_ L
1
|r
1
1

1 o
1 1
1 Z
l i
1 <
1
— j^.. _.
l
j

I
4
4
J
_. 1
1
1
4.
1
1
|
.1
1
1
|
|
1
1
4
|
1
1
1 *
1
1 -
~. -J---.
• MEASURED
• tyANR
. ftfl Z1
n OELZZ
- OUTUT
l
...4-
i i - . . i 	
i l l
i i |
I . 1 ...J....
1 1 1
1 1 1
1 1 1 	
1 1 I
i II
i i i
1 | |
1 1 I • '
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 | |
1 1 1
III
1 | |

i 1 1
1 1 1
i i l - - •
-J 	 _l 	 1 	 J
1 1 1
1 1 1
1 1 1
i | j
1 1 1
1 1 1
1 1 1
! ! 1 , •
i i i
i 	
...




—







i —







__

>




                7.0
                                                                  -19*3-
                        —S»i	li»0	   -U*J-	17 *0-
                                     T!HI>EI>ATUIIE |N DECREES  C
Figure 174  MJT ,4UnEL  ,  fnRT  LUi|[)nuM H7J       —l)Af| 76   --SURFACE ELEVI
                                                                              2*6,1 h
1 1
1 1

, . ' 	 . i 	 i.
1 1
1 1
.- - 1 1
1 1
1 1
1 1
1 1
- . U 1
i ;
i i
i i
-20«D *•»— OBP-^+— =™ --
. - .4_. 1
1 1
1 1
1 1
- 1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 I
1 1
1 1
1.0 4,J 7


•
..

J




_l


.J
J


•










,0 9
1 1
L L 1

1 1
1 1 2
1 1 *
1 1 1 3 *
U- .-.L. - - — 1- - -J-*
1 1 311
4 • 1 12
.._... .1 1 312..
1 1 12
1 13* 2
1 1 12
1 .12

...... 1 * 10
1 Z 1 1
1 01
1 D 1
1 1
... 1 1
1 1
1 1
1 |
1 1
1 1
1 1
1 I
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
I I

.3 U.U 1*, S 17
21
*11 J
i*0 I
z; i
i
i
i
j - — i
i
i
i
i
i
i

i
i
i
l
i .
i
i
i
i
j
i
i
i
o - MEASURED '
1 - STAND
2 - DELI1
3 - OELZ?
< - OUTLET
i
l
l
,0 19.5 22
1
1
1
1
1
1

1 4 .
1
|
1 ...
1
1


1
1
1
1
1
1
1
1 ....
J.
1
1
1
1
. L 	
L
1
... 1. 	
. -1- .-.,:-.-
1
1
1
_l
.0 24.! IT
_L
1
|
1
l
1

1
1
1
l
1
1
1

1
1
1
1

....!

i
i

i
i
i
i
	 u
1
1
1

.0 2(,f
Figure 175  HJT «Un£L .  fPKT  LQnUnjr  197*
                                                IN DECREES C
                                                — BAril32  —SURFACE  ElEVI   2*7,7 M
                                           182

-------
	 fcfi *•--•-*.» •»-!
1
I
1
1
I
1
. . 1

1
1
1

20,0 *»-----..-<
1
1
. |
1
1
1

1
. _ . . 1 .
1
1
	 U
L
1
1
1
	 L


'


..J




.






	









1 1 ' - - -
t |
1 i
1 |
1 |
1 |

- - • 1 1
1 l
1 1
1 1
— •;-- 1 J
...... - j J . ... .

-} j
i i

i i


. 	




. .. .


1 3*2 10 1
1 23 2 10 	 l_
1 1221.. .J__J 	 U
1 1 22 1 I 1
	 * 	 .22 	 ».-0— — i-.-i— i-.-«
'i i u i "~7 i"~ 	 u
1 3 22 1 I 1
1 s;« i | |
1 • 1 ! 1
1 SI* L ... . -I 	 1_
1 ».* 1 1 1
13 * 1 1 1
031 • 1 1 I
1*1 1 I
3-1 • 1 | 1
01122 1 | |
01 2 1 | |
01 1 1 |
1 ' i i
i i i i
i i i ~ i
..™..-.i.™.- i 	 i 	 J
j.. ... j_ i i
i i i i
i i i i
i i i i
i i i i
i i i .i
o MEASURED 1 1 1 1
1 ST1MR 1 1 | |
2 DEUi 1 ..1... 	 I 	 |_
3 °FIZ} 1 1 1 1
< OUTLET l l l l
ill
i i i i i
-1 	 1 1 . 1 . . 1. _ . ..1. -, . _— 1- ... 1
2.0 + iJ 7,0 9.5 12,0 \7iO Z«,S
Figure 176  H,T Murfcl .  fc,RT
                                      ,9Tt
j" RESREES c
—3*1 UP*,  ..SURFACE ELEVI  2*7,6 M

1
	 1
1
1
	 1.
. - .. J
1
1
1<
I
\s,a +»—»-..--.
1
1
1
1
I
1
1
I
1
1
1
1
1
l
l
*o,o «. 	 	 —
1
1
1
»'.o *»— -- —
1
1
1
1
?o,n +.—--—
2.J 4









,S 7
.. ..




. ..





.0 »
.. .


"
_








T i*
\
i
L
1
1
1
1
1
j
I
1
1
1
J
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
|
1
1
1
k. 	 	 	 *- 	 <
u It. 5 17

. _

[_ j

L




0 - »tl
1 - STi
2 - DEI
3 - DEI
< - OU1
0 19.
1 1 1 It 1 1
1 1 2 | 1
1 1* 1° 1
112 1 1
1 » o 1 1
1 2121 1 1
1 21 0 1 1
1 }2I 0 1 I
1 120 1 1
1 01 1 L 1
1 IJl 1 1 1
'! * ' ! '
1 12 1 1 1
1 012 1 1 1
191 1 I
13*1 1 1
0 • . 1 1 1
III!
Oil
11 1 , ' '
'1 1 1 1
| 1 1 1
1 1 1 1
1 1 I.I
i i ~r ~ i
ii11
i ! • i .1
I i i .- i
| 1 L 	 --{-
kSUREO 1 1 1 1
UdJ I II 1
.11 1 1 1 	 f-
Z2 1 1 . . 1 	 ^-.--1-
rii? 1 I 1 1
1 1 1 1
1111
1 1 . . 1 . . .J-
5 2Z*0 24»3 27 »Q 2*i*

                                                    OEC.KEES c
Figure  177
            ,JT
                         r:iKT
                                                                      6LEVI.  2*7.»fl
                                           183

-------
,0 +•
1
1
1
1
5,0 +«
1
1
1
1
1
|<
1
1
1
1
i
20, n <...
1
1
i
_ _ .1. .
1
1
m.e *.-

1
1
1
1
. 1
1
1 ...
1

;_._a 	 t 	 i___


1
--- -4 	
1
i -i ..
i
|»,0 ««
i
i
»o,o *«-
1
— L-
1
1
J
50,0 *E-
2.0

1 "
1.
.1
1
. . . . 1 _
	 1
1
1
1 |
.-_..! 1
I
1
1
1
J~ _~ ~~."
1
1
1
I
1
1-
1
1
-•-' r-

1
1
1 .
1
|
...J.." . .
1

I
4. -
. . _ L. _.„_





1
1
1
.. I
1
1
1
|
1
i
1
1
I
1
1
1
1
1
1
1
	 _ 1
I
._4...
1

1
1
1
I
1
1
1
1
. ,J_ J 	
I 1
1 1
1
1
	 1
4. .
1
1
1
1
1
1
E.""H •• T ™ "•=*«"=»•
1 .
1
1
1
1
1
1
1
L .
1

1
1
1. - -
o - MEASURED
1 - STAND
2 , DEU1.
3 j,_41EU2-
< - OUTLET
1
-_ -- 1 4 I .
.... -4J. 7.0 9i5. . _ .12,0... 14*3 U*tt 14*S

1
1
1
1
j
. . . j. .
1
.1
1
1
t-
1
1
0.
.1
""TV"
1
1
1
1
1
1
I

1
1
1
......I
1
.4
1
1
. _1. 	
22.0
*
'
1 S -124 -0
1 .. .2. 1__*_4_0-
1 *. 2-. 0-J- _
S2* 1
• n
a*
-3*-
**
t.
**
-— -•«»-—
*l*
-31* 	

12
1
1 	
1
1
1

1
1
I
1
1 ....
1
|
4
|
1
I

**.*

I
... 1
|
1
j

I
1
1
-.-^-1--
|
1

|
1
1
|
|
|
. 1
|
1 .-
j
|
1
|
1
1
1
j

*7i°
. .
	








, _ 1


' 	 ™*

1
i

.
.". "*



j


	 U
"if
Plgure 178
           HJT
                             luuUpyr,
                                                 JN r>£!!REES C
                                                 — UAVI233  —SURFACE
                                                                              247.6  H
.. _... .-..-
1
	 L
,.oi
.- 1
1
10,0 i
	 1
	 1
	

21.0
35,0
40,0
?0 o 0
2
1
1
1

1
1
	 ._ 1
I
X 1
1
1
1
1
1
1
- 1 .-
i
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.. .




... J









-"i— -

	



J














-=— -S~-
















- _ ___^



«.--«--
. -






o - HE
1 r.ST
2 - QE
3 - DE

1 3* 1 L - I
121 1
| * n i I

i t a i 1
.1.3* ... _L 	 1
1 2 .. ..1. I
__ . 	 1 — A 	 B_4 	 1 i. t , . .
*-. „ ,«. * 	
1 n I 1
111 1
1 1 1
131 1
1 01 I
131 1
13 1 .1 -. . . . 1
1 * n I 1
I I 1
101 I
101 I

1 i (
1 1 1
1 1 1
1 .1 t
1 J 1
i 1 '
" i ... i .. .i
ii1'
1 .1 . ...1 	 U
i i i
'i .. _LL ,._,., ...i „..,.!
ASUREO 1 1 1
AJIO i 	 L '
LZl 1 1 J — ' 	 -1
LZ2 1 1 -.^J.,-. 	 1
< - OUTLET 1 1 ' 1
1 1 1 1
i i 1 1

1 1 1 . • . 1 . . .--
.5 ' 1,1 "7.0 9.» 12.0 !*.,» 17.0 19.5 22.0 .2«U3 	 2J*0 	 29*.
Figure 179
           MJT
                                                 IN  r>E<-,RFES  e
                                                 --OAYI2SU   —SURFACE ELEVI  2*7.s
                                         184

-------

1
1
1
1
1
1
1
l<
_-. . 1
1
1
1
	 I-
--to, a *•=-»-:

i
l
L

i . .
i
i

i


1
i
i

i
— \ -


i
i
i
i
i
i
i

.1
i
i
.. -i
i
i
i
i
i
i
t
i
-. i
. j.
•
i
j

— 1._
|
I
.i
i
. 4.


i
i
i
i
i
i
i
i
i
i
i
i
i
i .
i
i
i
i
i
i
i
i
i
i
i
i
i
i


i
i
i
i _
i
i
i
i . .
7.0 S

? 1
• 1
a * i
* i
0 3« 1
i 1
12 1
a* i
2 i
M 1
2 I
* 1
« 1
* 1
.1 1 .

. fl .. 1
1
0 1
1
1
1 .
1
1
L - - L ...
1- .. _. _.l
1 1
1 1
1 [
!„ _ .. 	 L
!„ 	 -_ .1 	
1 1
1 l
I i

1 1
1 1
1 I
i _ ..I....
.i- . . L2*a L4.




.







...










,S. -11

1
1
1
1
1
1
1
1
I
1
1
1
1
j
1
1
1
1
1
1
1
1
1.
... . u
1
1

1
-1. - -.
o - MGASUMO
2 . OELZ1
» • BiLZZ
< - OUTLBT
l
i
.. -l 	
.0 If. 9

1
1
1
1
1
1
1
1
1
1
1
1
j
.1
I
1
1
. L. _
1
1
4
J. ..
1
I

1
l
1
i
I
1
1
I

i2«0_

1
1
I
I
1
1
1
1
	 L - . -
1
1
t .

1
1
... — »,„.„.,
. 4_
1
1
--L.
1
1
1


1
1
|
1
1
1
1
a
III 3

1
1
4 	 	
1
..4 	
1.
1
1 	

-J 	
—•———.
1
1
1

1
1

I
1
1
1
1



1 . . 	
1
i
1
1
1
1
fTiQ

1
4
••»*
	 L
4
1
	 1

	 1
1


1
I


1


|




|
I


;f .3
                                     T!H»E»»TU«£ IN ne«R6ES c

Figure 180  H|T MQflgL  •   FPRT IQMD'V: l»Tl       —0»YI3*3  --SUKFACf  EUVI   246,1  M
. n . . t . . 4 f—t-~ 	 — »™i.«.i-*
,0 *——»•-—•
1
1
	 J
1
	 1 ""
... . 1
10,0 *«p-"9»"~
	 L< 	 -
1
..15,0 .4«i="ss?«"
1
1
I
1
|
1
1
1
1
1
. 1
1
1
1
I
1
»».o •-—-*—
1
1
I
•te.o «.—.--—
2.0 1
..—••"».«







	
1
tJ T
1
n
i
•3
1*
* fl. 	 	
*
0
*
0
0




to" 9
• •*••••••!







+_. „.---«
.} "



















*- 	 ^










.





1 STAND
2 BETA1
7 BETA2
1
1
— — .1... *-^.i— -—•.—- — •*•
i a 	 L_
i i i
i i '
1 ... -.1 .... '

1 1 1
1 1 '



' ' !
1 .-!.... '••
j 	 [ 	 \~
1 1 1
1 1 . _-_^'
1 -L 1

1 | j
t II
1 I
I 1 1
1- 	 	 -1—. 	 ^-L-
1 1 1
j 1 I
r-^;:r-s:r=a
 Figure 181
                               IU"IU"J|1
iv DEGREES e
..uAyi 76  —SURFACE
185
                                                                               2*6.1 n

-------
1
1
1
1
J
1
1
1
1
J
1
K
1
1
1
1
1
1
1
23g8 *e— ••«!••
1
1
1
I

1
1

1
1
	 1 ..
1
1
1
1
I
. . 1 .











_ . _ . J
™— ™— ?— ™5"*














S 7i
1
1
1
1
1
1
1
1
1
,J .
1
1
1
1
_l
1
I
1
. .. . ..L.
1
I
1
1
1
1
1
1
-I- .
1
I
1 . .
1
J
1
1
1
1
I

o 9. a
i
i
i
i
.1 ..
i
i
i
i
i
i
i
i
i
i

1 12!
1 Ul
1 9
1 8
1
1 J
1
1
]
1
1
1
_!-. J
1
1
1 .
1
I
!
1
1
J_
. . I
12.0 14.
1
1
1 »JO

*.
* 1
* i
** 1
. . .i* .1...
1* 1
If I
* i
»• I
l_l» _J 	
129 1
19 1
1 1
1
1
1
1
1
1
1
I
1
1
L
1
1
1 . .
1 0 .
j 	 IB.
1 1 -
1 3 -
1 < •
1
J_
I
S 17.0
*
i *
1

J_
1
1
1 . .
J.
1
1
1
1
I
1
1
1
1
I
1
1
1
1
1
J
1
I
1
1
. 1 	
MEASURED
&ETA1
1ETA1 -
OUTLBT
1
1

.19.5.
1
1
1
1
i
1
1
. 1 •
1
1
1
1 .. .
1
1
1
1
-L..... .
1
1
1
1
.1 ...
1
1
1
J
1
1
1
I

1
1
1

1
1
1
. 1 -. ,
22.0
1
1
1 _ ..
1
1
J
1
1
1
J . ...

1
1
	 J — , — ,
*
1
1
1

1
1
1. ..
1
1
1
1
1
1
1
1
1
1 •
1
1
1
1
74.5
1
L 	
1
1 .
1
1 . .. _
1
1
1
I
1
1
1
1

1

1
1
1
I
t
1
. 1 ....
1
l
1
1
|
L 1 U , . .
1
1
1 .
t-i.a ;g..
'
...


__







'







_






i
                                    TFn»E»ATu!»E  1" PE6REES C
Figure 182   HjT yBr-g|_ >
                             (.uii|)no,  197;
                                                 --04TI132  --SURFACE ELFVI  2*7,7 M
1
1
	 1
1
. . 1
1
_ 1
1
It
1
1
1
-.. - J-
I
1
1
1
. 1
2J.O *e~--a—
1
1
1
1
1
1
1
1
1
1
1
1
1
•---B--BB+





















-




























..










0
0
8



e - MEASURED
1 - STAND
2 - BETAl
J - 8ETAZ
< - OUTLET
1
1
1 » IQ 	 L-
izi i cT^r ~ i
i i i

• L 1 1
1 1 . . 	 l_
»» 0 1 1 , 1
* 1 1 1
Q_ 1 1 1

1
*3 1
I
* 1 - J
1« .1
L
1 J
I .
1
1
I
1
1 ...
1
1
1
1
1
1
1
1
1
L
1
1
.. 	 a_
_.. 	 i._
i
i
	 u
. ... .j_
i
i
. ..— 1_
... :.._JL
_4_
• i
"~"._j^..
	 i_
i
_L_
. -L
* ' 2.0 4.5 7.0 V.i iz.6 l*j» 17.0 1».5 Z2.0 24.3 2T.tt J3.J-
 Figure 183   (,JT
                                                    PEGKEES C
                                                            —SURFACE  ELEVI   2*7.6 n
                                                 186-

-------
.0 -
5,0
10. n
15,n
iO."
2S,6
*°*P
»»,0
*o,o
49,0
JP.O H
2



<





























































.







	 a



o MEASURED
1 STAJlO
2 BETAl
3 BETA*
< OUTLfT
1
1
	 «— ......«--—0. — „
i • i i
i i i
121 10 I
1 1 1
1 0 _L 	 1
* 1 1 1
1 0 1 1
. « 1 0. 1 . __..]_..
* 0 1 1
01 1 1
*3 1 1 i
1 1 	 U.
1 1 I
0* 1 1 I
1 1 1
* 1 .... 1 - -,..,_l
•3 11 |
1 1 1
1 1 1
1 1 1
! 	 1-"-=+
1 1 !
1 1 	 L
1 .1 	 L_
L 1 1
1 1 . 1
. *, « »
1 1 J._.
1 I _ ..L-
__ J..._ 1 1
! i !
i i .._j_
i i i
i i i
! 1 1
1 1 1
« »•» T.O ».» 1Z.1) !»,> 17.0 19. J 22. 0 Z4.5 87.0 29.8
Figure 184   H(T
                                     TFftl>El'ATO»t P DECREES t




                        f"KT I.U'"U' «••  1971        — uATl22e  — SjUFKE  fLEVI   2*7. S M
.9 4
s.o
0,0
5,0
0,0
5.0
f>,0
».n
( ,C
ii,r
2



<






.u 4









*" 1









*__«—•••









h-. ------



















.» '7








1 ST
Z BE
3 BE
— .* ny
< ny








kS'JREb
knO
fAl
FA2
rLET
1
1
.
.1 22
1 «
1 *
1 123 a
1 123
*
1* 0
*l
*l -
• I
• 1
• 1
0*1
0*1
*i
0*
*




.0 24

...;.;.;.


.» 27
0 J
0 -J.-
._ 1
1
... -L
1
— L
. - .- i -
1
1
j
1
- . 1
J
.... 1
1
1
..1
1
1
1
1
1
1
I.
.0 2*. 3
                                                  Iv
Figure 185
                         r-KT . U--
                                                                               2*7.6 R
                                                        187

-------
 10.0
 20.0
JO.O
1
1

<





-

























..








"
	








"





1











-





..
o MEASURED
J -1IANJ1 .
2 BETAl
3 BETA2
< nuTLIT
1
1
1

*
* 0
*
* 0
*
... ._ ..a
*
* 0
3
. - •
*.0_. .
0
0













. . 	
	 _



_.


	 ^--J

--—----*
1
...I
1
.1
,..,— J.
i
	 L
-, 	 , 	 1..
1
1
1
l
1
1
	 L
1
1
-L=±
1
i
J 	 1
l
. . 1 	 L
• . 	 L. L
1 1
1 1
1 . 1 ,. 	 ,_j.
•° *•* 7,0 t.f 12. U 1*.5 17.0 1»,5 22,0 24.5 »"!o 29,9
*».o
    2

        Figure 186
                       ,,gntL
                                        y-v'  ivi
IN t>Efi(tBES C
— o»vi2Bo  — SURHCF  EIEVI   2*7,5
  .0
 5.0
 10,0

1
1
1
1
1
1
1
1
J V
1
1
1
1
1
1

1
1
I
1
1
p
1
1
1
1
1
1

1
1
1
1
1























































*3
0
•3
0 *
1*
0

*
*
*
0
*
0
0












































































































1 - STAMP
'. - »ETA1
•» - 9ETA*
< - OUTLET
l
















_














-


.













. . .


-
/


	 l _ _
" -l —
_- .. — — i —
1
1 	
l

l
	 1
— U -
..i-
1
1
-I
1
	 1- —
1
	 	 \ —
..j"
1
J.
1...
1
" 'l ~
1
1
!
i
i
i
i
i
L,j i,.s 7,u 9.5 i«.0 1*,S 17,0 19.5 22.0 2*. 5 27,0 29,3
 U.O *-
 20.0
 #0.0  +.
 35.0
 HO *
         Figure 187
                        Mj-hl  ,
                                                        — il4fl3*3  — 5U1FACF ELEvl  2*6,1 M
                                                       188

-------
- -4.0 ^
5,0
10,0
	
1?.°
20,0

»0,0
»5,0
40,0 4
	 1
_ . ..
*5.0 '
ftO,0 i
" . .2i
>e— i? 	 * 	 rT--i-*-i".iO»l*.i.i 	 »_; 	 .„


< 	 .
K--ZS-—





..











.


"U 1
•11 l
nz
31 ?
-.31—2-
• 0 Z
31 Z
» 2
0
* _2
0
0





V
i
i
i
i
i
i
i
i
	 1 	 .
i
i
i
i
i
i
i
i
i
i
i
i
i
j^
i
, - 1 -
i
	 _ L ..
1
l
1
1
" 	 i
1
1
1
1
1
1
1
1
1
L ._
1
1
1
1
J- 	
1
1
1
— 	 1 . . .
1
1
!
i
i
	 1
1
i
i
i i l i
i i l i
1111
i i i i
L _ . . . 1 1 1
1 1 1 1
1 1 1 1
i - i 	 a. ^_ ,.._.!_
i i i i
. _i i i i
ii i i
i _i i i
i i i i
till
.__ . _i i i i
i i i i
i i i i
i i i i
i i i i
i i i i
i i i i
i .__ i i i
i i i i
i i i i
i i i~ i
i i i i
i i i i
i i i i
. ... i i i i
i o MEASURED i i i i
.. J . J STAMP 1 1 1 1
1 l !TA1 1 J J 	 L
1 3 ETAZ 1 1 1 1
i < OUTLET i i i i
i i i i i
l i i i i

0 *iS 7.0 »'.5 12.0 1*,5 17.0 19.5 2Z.O .Zi.4 	 ZTafl 	 29.?
                                      TSn»ti> Atone IN HEBREW  c
Figure 188  MIT  Mgr-EU »  F"KT
                                       1971
                                                  — Oi/l  T&   — SU«F»CF 5|.E»I  2«6.l n
.0 <



s.o
-


lo.o



i»,0



20,0



25,0



30,0



39,0



40,0



*'.P

Sff.O












<




=*••-- 	



	 — r 	






































































































































,»--•.»•

i
1

1 3
1 3 1
1 3 1
1 3 10
' 1 31
1 3*
1 31
1 31
1 1 1
3 *
3 1
3 1
3 1 13
3 1 I
01
" 1
1
1
1
1
1
1
1
1
1
1
1
1
I
I
1
1
1
1
I
1
• /. < 17
Z *
20*
3 I 02
3 1 Z
2
2
2
2

2
2
2
2
2
2
2

2













































1 - STAn"
2 - FTM
3 - ETAZ

1
1
,._„--— ._*..———<











-


























»__.._•_«•—




































'

.- 	 .-
1
I
	 1
1



I

	 L
. - 1
L


	 	








.1.......














~- — -;;;
Figure 189
                          F"KT Uu IK".-'
                                      i«,."t"ATu»e  i"  re'K^t?  c
                                       ,,71.        —OMU'i  —M'F'CF 5LEVI

-------
1
1
1
1
1
1
1
1-
1
1
1 .
1
1
1
1
1
1
1
1
	 I
1

1
1
1
1
1
1









....

1
1
1
1
. . - 1 -
1
1
1
i
i
i
i
.. . .j- ...
i
i
i .

1
. a
i
i
i
i
-i.
i
i
i
.1 .
i
i
i
i
. i _.
i
. . i_.
i
i
i
i
i
i
i

i _
i. ...
i
i
i
... i ......
i
i
i
— .. J _ . .
i
i
i
...
i
i
i
L 	 J
1
1
1
1
I J
1
1
1
1
1

^
\
\
1
1
.1
1
1
J_
.1
L -
1
1
1
. ... I
1
1
1

1
i
. i ..
i
... J_
i
i
i
. ... ..L.
1
U.B It. 5 17.0




-



. ...;__"
1
1 _3
1

2 *
. J. 	
1 2
1
0
1 11 2J .
1 1 ..
in 02 I
1 31
1 0
..J Sl_
031
1
	 131..
-031
01
0 1
i - -
. . .. _L
1
.1
1
. 1.

1

_ 	 ._ 1 _
o . MEASURED i
1 . STAND 1
z - ETJ
» - tu
u a
12 . - 1 	
< . OUTLET I
i i
i i
i 	 i..
19. 5 22.0
2 1
2 |

1
Z 1
1
2 1
2 1
1
1
1
	 | 	
1
1 . .
1
1

1
1
— . |

1
1 .
I
1- . .
1
1
1

2»f3
10
LQ_
Q 1
1
1
	 1
a
i
i
|
i
i
i
. i
i
i
i
i
i
i
i
. i
i
i
i

i
f~
i
i
I
. i
i
i
i
27. 0
^L
1
1
1
	 1_
1
1
1
, . 1
1
l
i
l
1
1
1
1
1
. . 1
i
i
1
1
l
i
l
1
i
i
i
1
1
l
l
29,!
Figure 190  M{T Mur>£L .  f0KT  llK'O'V 19TI
                                                IN DERREE; c
                                                — 6Ayl2









.5 7
1
1








+ _ 	 ._









	









.•j \i









. > 11
1
1











0



n - MEASURED
1 - STA.tD
2 - ETA1
3 - ETA2
1
1
1
,0 19. » 22

1
J
J_l-
1
2» - -U

31 1 2
0
.31 12.0,
31 0
0..1
31 2
1
*1 2
1
31 Z
31 I
.




.0 24
2
-







.5 27
1 ..
1
_i:izi:
i
i
i
- - ~'^r
i
.. . _i_
i
	 ..L-
- . L_
1
1
1 L-
1
1 .
1
1
	 U
1
                                                  I"
Figure 191  MJT "o'El.  *   F"*T '.J 'i>"u'.
                                                                               i*7,6 h
                                               190

-------

1 1
1 1
1 1
1 1
' 1 1
. 1 1
1 1
... _ ..!„, 	 1
1 1
I I
K 1
. . . 1. 	 1. .
! I
_ ..... i 	 i .,...

i i
i i
i i
i i
i i
i i
	 i i
... i i

i i

	 i i
^o-oi <---!• —
i i
i i
_ .i- 	 i .
i i
i i
t i
1
1
1
J_
1
1
.i.~ i..,:.:^-i.
i
i . ...
— 1_
i
i
i. r. 	
,.._ L
1
1
1
1
	 	 ..1 	 ...
1
1
.L ...
I
. .. J.
1
1
1
1
_l-
l
1
1 .
1
1
1 I
1 	 1 	 ^ '
1 1
1 1
1 1
1 J
1 1
1 1
--,.., I 	 U . ..
1 1
-I J
. . -1 	 _I 	 ..
1 1
1 1
— . - --J-- ..J.-.. 	
.... . 1 - •-]_--• - J
1 1
1 1
1 1
1 1
1 1
1 1
1 _. 1
1 . I
. - 1 .... 1 . - _
1 1
, 1
1 1
1 1
	 	 L 	 J. ...
1 12*
1 1 2. •
1 3120
1 » I 2
	 ...» 	 , 	 *..,.i0— .
1 • o»
1 .11... 2
1 M 2
. 1- *l •
1 *l I
I »l t
1 »l 2
1 *l 2
1 *l I
1 *1I2
1 *1I2
1 B1I2
1 *1I2
1 1112
1 1
1 1
9 1
fl . J


______







1 1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 J
1 1
I I o MEASURED 1 1
1 1 1 IT1ND 1 • 1
I I i- it
.1 ... 1 1 IT
41 1 1
12 .. J ... . . ,.I -. ...
i i < OUTFIT i i
ii ii
i i i i i i
- . ... 1 1 1 1 1 1 1 . 1 : 1 -.-:-.







.____ 	



— I 	 . 	 1 	


















__






"* 2.0 4.9 T.O r.i J2.0 1*.} 17,0 19.5 22,0 24.5 Z7.0 It.!
Figure 192  H,T
                        F"RT
                                                JM P6GREES e
                                                --0»YU53  --1U1FACC
                                                                            2*7.6

IP *
3,0
18,0
15.8
20.0
29,0
?o,o
35,0
»0,0
<,3,f
90,0
.....i...»

7



BB— 55 —


+.........
.0 *i









,. .. ^









to" " «




.




*i~ ''









.3 i"









t> IT








1 S.
2 ET
3 ET
...* PV
< nu
to 19








AitD
41
42
EKLAC —
TLET
l
1
t» 22

112
312 0
112
312 0
312
fl J
212
312 0
0
*2
0
0




tft 2*
1 -b
i 1
1 I
1 L-
1
I

! i
i _ -i-.
! !
t........U^^-
i.--"±
l. +
i
i
i
	 ^,.|-_ — «—
1 	 	 U
1 1
ti "" 2T.O M»3
                                                p
Figure 193  HJT HG"EL •  rn*T lU-'
                                     '.»Ti
                                                                     ELEVI
                                             191

-------
1
1
I
1
1
1
K
1
1
1
1
1
1
1
._ . J -.
1
1
_L
1
l
1
1
.. 1
1
1
	 1. .
._. - . 1
$»,fl *»»— i—
1
1










1 •
1 0
1 *
1 0 2*.
1
1 • *
\ 0
1
1 *2 _
I
1. «
1 *Z
1 0
. J...M 	 1
I
i a .
l
1 8
1
1
[ 	 	
1
- . 1
1
1
i . . ..
|
1
1
1. - - -J
I
1
|
1
1
1
1
1 	 I
1
1
1
1
1
1.
1
1
1
1
	 L .
1
1
1
1
.. 	 _J . ...
. . 1
1
1
1
1
I
.1.
1
1
.. 1
1
... 1
1
1
!
----- 1
_.l 	
1
... 1.
I
1
1
1
... ._ 1
1
2.Q 4,9 7.0 9.J 12.0 1*.J
1
1
1
1 ... . .
!
1
1
. . . .1. _ .
!
1
1
1
_ .. .1 	 .
1
1
1
1
1
1
. 1
1
1
1
I
1 .
_L ..
1
. . .. J
1 o .
l l .
1 I .
1 J •
1 < •
1
.. -J
1
17.0
1
1
1
_ -1 	
1
1
1
1
1 .
1
.i
1
1
1
1
1.
1
1
1
1
1
1
J
1
r
i
i
i
i . _
HEASURIO
STAND
ETAi
ETA2
.BVEKUP --
CUTLET
1
_l_
1
19.3
1
1
1
.1
1
1
1 .
1
J_
I
1
1
1
_I
1 .
J .
1
1
l.._
1
1
1
J
1
1
1
L
. l_
1
. 1
1
1
1
-J -
Z2.fi
1
1 .
1
1
1
>-.-!-.,...._
i
i
i. .. -
i
i
i
. . .1 	 	
i
i
i
i
.... . i . 	
i
i
i
... i. _
i
i

i * *
i

i
i
i
i
. -_i 	 	 ,_i
i
i
i
1
	 1 	 J__
. 1

- -. L_
._ L
1
1
l
l"
1
1
l
1
l
1
1
1
	 J 	
1
.... 1
~ l ~~
1
1

|
I

1
i
	 1
1
1
1
. . j 	 .„. 	 L , 	 . i
2*. S tt.O J«.S
Figure 194   MJT HO:,EL  .  fnRT i j
                                   TEn'E'ATU'E  IN  DEGREES  C



                                  s  1971        — 0»rl3*3   --
                                                                     6LEVI   4*6.1  H

«° 1
9,0
10,0
15,0
go,o
»0,0
35, P
31.0
»rT7:r-«*

<







— -S—B-









1
•3
012 2
123
I* 0
*
*3
0
*
0
0























































o - MEASURED
z - "IFFI
3 - DIFF3
< - OUTLET
1




- ,:.-j








1 _L
.. _ __ (

...l-rr-.ri-

1 1
. ,.,.1 .... 1
1 1
. , . . - . 1-.-^-. — J_
1 1
1 1
1 1
1 1
1" 1
1 . 1
1 . 	 1_
" 1 '~~~~ I
1 ,1
1 1-
	 1 	 __L-
1 / 1
1 . . '-".. I1-
1 1
                                   12. u
                                                       17,0
Figure 195   MJT  "u^El  •
                                                                     ELEVI  2*6.1
                                               192

-------
,0 *„:-..„.
1
I
... . . I
J,0 +«*..„£.

1
(OfO *•--•*»•
1
1
- 1
l<
1
1
1
10,0 >er-T3"
I
1
1
L
|
1
1
• |0,e *•«••*•
i
i
1
1

l
i
1
i
I

1
1
i
	 4 .
.. .2.0

. 1
1
L
1
1
1
-J. ... .
1
I
1
1
1
1.
-1
I
l
i
l
i
.!
•«•*»•*«••
.1
i
. 1. _ .
i
i
.1
j
,]- ,
I
. i
-i
!
i
*,s
«**«-
1
1
«-*-«
1
1
1
_. .1.
1
1
1
1
. ...L- „
1 - -
-i-+^=!
U
I
t
1
.1 .
1
1
••••*•**
1 . -
1
1
1
..!....
\
_L
.. 1
1
... _L.
1
1
1
1
J
1
7.0

1
1
1
1
1
1
.. .4 ._ 	
1
U
1
1
-- 1
.- -1.
1
1
I
-w-.*-------
	 	 I . ...
1
1
|
4- -

1

I
.. . _l . _. _
	 1... ._.
1
1
. J.
- - i. 	
1
1
1
. ..1 ...
».S

1
1
1
1
_L .
1
. 1
...J. ...
1
1
1
4_
_!.—
- J ... .
1
1
1
[
.._!.
1
1
. 1-
L .
._L. _
1
1
!
. .1
1
1
1
...i
\
1
1
12,0

1
1
1
1
1 	
1
1
- 1 -. U
1 1H
1 *fi
I 123
1 123
1 *
1 «2»
	 l-i21 	
	 i.2.3
-^---l-l-t---
-. .-1-U-J... .
I IZ J
01
o 1
1
L ..
1
1
L
1
. L. .
1
. J.
|
. 1
1 .
1
I
1
. 1 .
1
1
J_
1
11.9

1
1
1 1 »3
1 1 23
»2~3_. .
» 13
» 13
a. l .
l
l
l
. i. .
1
— L
I ..
4- - -
1
1
	 1 	
1
1
1
1

4
4
1 ,
1
I
1
.. . J
1 o
i i
1 2.
.j. . J
i <
i
, 4
17.0

3 f
* *
1
1
|
1
1
1. ._
1
|
1
. I. _
I
1
-L . _
I
- -I ... .
1
1
I
L
1
1
|
1
L
1
1
|
1
1
MEASURED
ITiNH
M?E1_
_B1E£1- _
DUTLIT
1
1
1 . _
19.5

1
1
I
1
.L~ ..
4
J
1
I
1
1
|
1 	
. 4—
1
1
|
4
1
1
x
_L

1
1
|
1
1 -.••
1
1
4
1
1
1
. 1.-.
22 ..Q

1
J. . _
4
1
1
1
4
-.-. 1--
!
i<*
i
i
i
i
i
i

i
1
i
i
i
. ' -
i
i
.L 	
|
1
1
1
1
1
1
- »-, -1 --,-:•
2V, 9

_ -1
..-.I —
. 1 .
1
— j —
1
1
1
1
1
1
1
1

1
- i_I •
L

I
1

|
	 L_
,-.-W
1
1
1
1
1
1
h
— =r-X^-
IT, a

1
1

~ 1
1
1
1
1
1
— \-
— — "!*
|
•.l,.-il

i
i
l
i
l
l
l
i
l
i
1
i
^^J-
3«,S
     Figure 196
                MJT
                            pnKT
                                                    — BA»I132  ~SuRF^CE ELEVl   2*7.7

	 tB-t
SA

10,0
__
2Q.9
W.O
.JOj.0
33,0
»0,0
i'.o
SO.ft


<


















	






















•


























	
.
U
0



1 - STAND
? - P1FF1
3 - PIFF3
< - OUTLET
l
1 • ID 	 L-.
1 _ 	 16. 	 1—
12? 1 o ' '
1 1 1
" ! ~hz._4:
1» ,0 1 .... I . ... . '
»3 1 1 1
B 1 1 1
« ;[-— 1 	 — h
1 ! !
123-1 1 j
123 , J ..... 	 s-l 	 = 	 i-
'" i " 1 — r
1. 	 1. - -L-
!. -!-- -i
J -> "1-^t
1 t::r^t
i i i
i . ..\.',". ~..-i
\ t i
i r. "".. r

2,0       *,S       7,0

                                                   193

-------

1
1
.-_ 1.

1
1
. I-.

- - Li
1
1
1
1
1
.J
1
1
J_

1
1
1
1
j^
1
1 '
	 -L_.. .
1
1
I
i
I
1
	 	 1 . _
2,0

1
1
1
1
I
1
1
1
!
i
i
i
i
i
i
1
1
1
1
1 .
1
1
1
1
L . .
I

1
1
_L

1
1
I
1
*iJ

1
1
1
1
I
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
|
1
1

...L .
1
1
1 .
1
!
! .
1
1
. 1
1
T.e

I
I
I
I
i
I
I
1
i
I .
1
I
i
	 I
4
1
1
1
1
1
i
- 1

1
1
1
L
-I -
1
L -
i_
1
.1
?;s

!
1
1
1
I
1
1
1
1
1
1
1
1
L
L
1
1
I
1
1 .
1
1
|
1
1
1
" .
1
I
1 -
1
I
1
	 J ... . ._.
1
1
1
.1
12tO l*i

1
1
1
1
1
1
1
1 . .
1
1
1
1
I
I
- . . - -J- .„
1
1
I
L
1
1
1
I
L
1
1
1
j
. . .. 1 	
1 o
i i
1 2
	 a. ..J
i <
i
i
J 17.. 0

1
1
1
1
|
1
1
1
1
I
1
1
1
1
J
	 1 ...
1
1
I

1
1
J.
I
1

_j
1
1
1
MEASURED
STAND
QJEF1
Oi££l 	
DUTI.IT
i
i
i
19. S .

1
1
1
1
_l
1
I
1...
1
1
1
1
1
1
. i_
. 0. .
1
0
01
I
a
i
. '
_i
i
i
t
,
i
i
-i ,-
i
i
j

i
i
i
i
tz.o

1 «
-I
12J
1
| Q
«31_ 	
1 0
•31 0
* 0
a i
1* I
j^
1
0121 1
1
*J 1
1" 1
1
1
-J_

I
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
2*. 3 21

	 J _
J 	
10. 	 I 	
1
|

1
|
|
1
1
j

|
1


1
1
1



1

1
1


1
1
I
0 ?Q.?
Figure 198  HJT p.unEl .  pnRT  LUl'ii' «••  )»71
           I': DECREES c
           --utflZZt  — SuPF*CE ELEVI   2*7. S n
- .
5,0
;;o,6
I'.Q
20.0
29,0
JO.O
**.'
so.o
2




<




































««==?-




























1
... .-l
. ...





o - MEASURED
l - STAN?
< - OUUET
« 1 o _.i
...» -l-tt 	 l_
1 12* 1 1

. . 1. 	 L_
1 	 X
»s 1 1
»* i i
•? i i
•3. ... . 1 . 1
•3 1 1
0*3 1 1
«*» 1 1

0*1 1 '
*[ 1 1
1 1 1
1 1
I 1 1
..'.-.-:$^,
* i ' '

t i . i
\ - . \ . .-/...r.
i.i i
i i i
,„ i,.> 7,0 *.? 12.0 l».J 17.0 19.5 22.0 Z*.5 21.0 .i£JL_
Figure 199  MJT
I»7i
           i1- rEf»Kees c
           ~-i'Yl2!3  —SuRrACF EtFVI  2*7.6 n
     194

-------

1 1
1
- . - .. 1
1
	 1 1
1 1 .
1
1
l~s,o *,-..-*..-*.. 	
1 1
1 1
-.1 -. 1
1
1 1
1 1
	 1
1
1 1
	 {
' * • •

	 l__- _ 1
1 1
1 1
1 1
1 1
1
1
\
1
1
L. -
1
I
I
1
I
1
1
l-
. .... 1 . 	
1
|
1
. .. . I.. _.
1
.1 ..
.. L ..
1
i
.1
1
T
...1 	
1
1
1
1 1 I 1
2.0 4.1 7.0 9.3
1
1
1
1
J
1
1
1
1
1
1
1
1
1
-I
1
"l
1
1
1
L

. 1.
_ 1
1
I
1
.L.
_ J. .
1
1
.1.
1
1
1
J
12.0.
1
1
1
1
I..
1
1
1
L
I
1
1
1
.. 	 1.
1
.. . -1-
1
1
1
... —1 .
1
-J
1
. J.... .
\
\
1
I
. .1
1
1
.. -J . . .
1
1





._.


... .....


1
1
1
1
• 1 1 1
• O.I 	 Z_"j 	 1 —
1 1 1
1 B 1 1 1
1
I
1
I
1
1
1
1
|
1 .
I
1
1
1
• 1
1
* 01 .__ ... 4
* 1
A 1

1
* 0 1
5 1
* J - _l
* fl 1
1
0 1
0 1
1 1 	 1
[
1
1
. ' '.. — L
1
1
1
1
...... ..L.
1
1
. 1 - .... .
I
I
1

1
1
0 HEiSURIQ 1 1
1 ITiND 1 1
L i at
-.-!_ ..Oil
FF1 1
Tft . .1
< OUTlIT 1
1 1
.1 . 1 -. 	 1
1ft. 5. 17^fl 1.1.9 22. L
I
1
1
1
1
I
1
I
	 1_
1
1

1
1
1
	 L_
1
1
1
1
1
1
1
1
L
"i". . . 1
1
1
1
1
I
! l l

                                      TEh*E«ATu«E IV DECREES C
Figure 200   HJT  MITEL •  F"RT lO'HTijr' 1S71       "i»ri2"0  "SJKfACE  EUEVI

_-:L
5,0 •

10,0 4
-15^0. j
aoao
~»*.o
20.fi
93,0
40,0
^£jA 4
£Oj fl .
2
u .
_
	
Li. ....

















T~ " 7

j



.




0 *
*
.0
*
L fl * J
I*
«S
'
*
*
0
!.
0
n




9 1 2









'J ^^



"






T 17










.

-----
... .




1 STAND
2 D1FF1
3 niFF?
1
1
0 1».5 22
1 1 L
" " ~ 1 " i .1
1 I 1
1 _L _ _1_
1 I 	 L
i l 1
1 1 1
l l 1
[ ! 	 1-
i i i

i i i i
i i i

! i i
1 J 	 — -L-
L 	 " 1
1 1 1
. L .1 	 1
1 1 .1 .
1 1 . 	 L-
I 1 1
1 '
1 L -1.
1 1 . _ , .-J .
Ill 1
1 1 	 -1
                                     fififfATgHE  l'<
Figure 201  HJT MU"EL  »  Fn"

-------
                                SECTION VI
                             ANALYSIS OF DATA

     The surface temperature, being related to the equilibrium tempera-
ture, can be well represented by a simple sinusoidal relationship.   A
sinusoidal type function was least square fitted to the measured
surface water temperatures as shown in Table 21.   The water temperature
at the outlet level cannot be fitted as easily, because it is dependent
upon several variables, e.g. time (day of the year), depth of outlet,
outflow rate and variation of thermocline depth, etc.  However, if the
time period considered was shortened, such as using only the data between
early summer and winter instead of the full year, a least square fit of
a third degree polynomial can be fitted reasonably well.  The results
of a third degree polynomial fitted to the measured water temperatures
at the outlet level are shown in Table 22.  The average standard error
of estimate for the curves fitted are 1.2°C for the measured surface
temperature and 1.6°C for the measured water temperature at outlet
level, respectively for seven TVA reservoirs.  The predicted temperatures
were then evaluated for the standard error of estimate with respect to
the aforementioned fitted least square curves.
     In general, the sensitivity analysis of the input parameters has
shown that for:
1) Vertical Increments or Horizontal Layer Thickness, AY
     The effects of variation of layer thickness on the temperature profile
are different from one reservoir to another.  The general trend is that the
use of a smaller AY, 1 meter, yields temperature profiles a little lower in
                                  196

-------
                                                     Table 21
                              LEAST SQUARES CURVE* FIT FOR MEASURED SURFACE WATER
                                                  TEMPERATURE
ID
Reservoir/Year
Fontana/1966
Douglas/1969
Cherokee/1967
Norris/1971
South Holston/1953
Hiwassee/1947
Fort Loudoun/1971
No. of Data
Points
27
31
37
48
12
12
12
Std. Error
of estimate( C)
1.
2.
1.
1.
1.
1.
1.
22
23
53
30
79
70
50
Correlation A
Coefficient (°C)
0.
0.
0.
0.
0.
0.
0.
98
97
97
97
98
98
99
16.
17.
16.
17.
17.
19.
17.
96
60
70
46
01
07
88
B
- 9.
-12.
-10.
-11.
-11.
-10.
-12.
:)
72
82
08
54
63
43
32
»
0.
1.
1.
1.
0.
0.
0.

927
180
006
065
970
850
992
      *Curve Type: A + B sin (J^, t + T)

-------
                                Table  22
         LEAST SQUARES CURVE* FIT FOR MEASURED WATER TEMPERATURE

                            AT OUTLET LEVEL
                                     Std.                        Time Period
                       No. of-Data   Error of       Correlation  of Fitted Curve
 Reservoir/Year           Points     Estimate (°C)  Coefficient  (Julian Days)
Fontana/1966
Douglas/1969
Cherokee/1967
22
27
32
0.96
1.10
1.06
0.97
0.98
0.96
103
69
117
341
352
332
Morris/

South Holston/1953

Hiwassee/1947

Fort Loudoun/1971
 9

10

10
1.09

1.50

1.56
0.96      113   362

0.96       80   364

0.92       76   343
* Third Degree Polynomial
                                198

-------
the middle or deep portion of the reservoir than the use of a larger
increment.  Because there is little difference in the predicted temperatures
using either 1 or 2 meters, the use of 2 meters per layer is recommended
since this reduces computing time considerably.
     The MIT model recommends a minimum of twenty layers.  From the results
of this study, it is recommended that AY=2m be used unless this causes
the number of layers to be much less than twenty.  In a reservoir of one
hundred meters or more, a thickness of 3 meters appears to be satisfactory.
2) Fraction of Solar Radiation Absorbed at the Water Surface, 3
     The value of the surface absorption ratio, 3, is generally assumed to
be about 0.4.  Recent TVA field data suggests a value of 0.24 in Big Ridge
Lake and Fontana Reservoir.  The higher the value of 3, the lower the tempera-
ture profile is likely to be, since a larger portion of the solar energy
absorbed at the water surface means less energy geing transmitted downward
into the body of water.
3) Radiation Absorption Coefficient,!!
     The value of n may vary with the time of year, being a function of
turbidity of the water.  The values selected for analyses ranged from 0.05
for clear water, 0.40 and 0.75 for intermediate waters to 1.4 for highly
turbid water.  Results on all reservoirs using 0.05 show that too much
solar energy was transmitted to too great a depth.  All reservoirs tested
contained more turbidity than distilled water.  Temperature profiles fol-
lowed a general pattern, being lower for higher nvalues.  Because of the
temperature sensitivity to a change in n, a carefully measured value is
important to thermal simulation.  For prediction of temperatures in unbuilt
reservoirs, n , between 0.75 and 1.40 can be used for the preliminary study.

                                 199

-------
 4)  Diffusion Coefficient,  D
     The MIT model authors recommend, based on their verification using
Fontana Reservoir, the use of molecular diffusion for all depths at all times,
which neglects turbulent diffusion.  Other field data indicates diffusion
 coefficients higher than molecular diffusion.   Diffusion coefficients
 are a function of density, gradient,  depth,  and time.   Due to the approxi-
 mate nature of the mathematical model and the  complex interaction in
 diffusion,  we are unable to assign a specific  diffusion coefficient.
      In this study molecular diffusion coefficients  30 times, 100 times,
 and 1000 times molecular diffusion were tested.   The use of a coefficient
 1000 times  molecular diffusion always caused the model to malfunction.
 This was not unexpected since the stability  criteria,  Equation 58, is
 violated when AY = 2m and  AY = 1  day are used  with this diffusion
 coefficient.   The use of 100 times molecular diffusion also results in
 most cases, in predicted temperatures different from measured tempera-
 tures.   The temperatures predicted with the  use of 30 times molecular
 diffusion and with molecular diffusion are similar.   It appears that an
 appropriate choice would be 15 to 20 times molecular diffusion.
 5)  Reservoir Classification
      The criterion which is widely used for  classification of a strati-
 fied reservoir, is that due to Or lob *• ' who  introduced a densimetric
 Froude number in the form

              Uv.  =  =£   I —                                       (86)
          where:
              L    =  length of reservoir in  meters

                                 200

-------
              Q    - volumetric discharge  through the reservoir in. ra3/sec
              D    = mean reservoir depth  in meters
              V    = reservoir volume in cubic meters
              e    = average normalized density  gradient in reservoir
                     (1(T6 m'1)
              g    = gravitational constant  (=9.8 m/sec2)
     substituting the average values,  we  have

           IFD  '   320I5   $                                        (87)
     For IFD   <   ^ , the reservoir is considered strongly stratified.
     The densimetric Froude numbers for the seven reservoirs tested are
listed  in Table 23.  Except for Fort Loudoun Reservoir, the densimetric
Froude  numbers are much smaller than 1/n.   Based on the Froude number
criterion,  all but one are considered to  be strongly stratified.
     When we compare the computed temperatures  with measured temperatures,
we note that an adequate simulation by the  deep reservoir model for a
particular reservoir does not solely depend on  its  densimetric Froude
number.
     The densimetric Froude numbers of the  seven reservoirs do not
extend  over the whole range of interest.  Therefore, no critical value
can be  established with regard to the applicability of the model.
However,  it appears that for a reservoir with large depth, low densimetric
Froude number and small variation in surface elevation, such as Fontana
Reservoir,  small  differences in predicted and measured temperatures
result  from the application of the MIT deep reservoir model.  The greater
the deviation from deep reservoir conditions, the less accurate the
calculated  temperatures will be.
                                201

-------
                       TABLE 23  DENSIMETRIC FROUDE NUMBERS FOR SOME TVA RESERVOIRS
                                     Mean Annual    Normal Maximum               Reservoir   Densimetric
Fontana
Douglas
Cherokee
Norris
South Holston
Hiwassee
Fort Loudoun
Length of
Lake Miles
29.0
43.1
59.0
72.0**
24.3
22.0
55.0
Runoff at Dam,
10^ acft/year
2,667.7
4,830.7
3,316.6
2,956.1
735.4
1,369.9
9,949.8
Depth,
Feet
432
129
150
196
240
252
74
Storage* ,
103 acft
1444.3
1514.1
1565.4
2567.0
744.0
438.0
386.5
Surface
Area, Acres
10,670
30,600
30,200
34,200
7,580
6,080
14,600
Froude
Number
.006
.06
.05
.02
.005
.01
1.02
*  At maximum controlled elevation
** Clinch River Arm Only

-------
                               REFERENCES

1,  Shirazi, Mostafa A. and Davis, Lorin R.  Workbook of Thermal Plume
      Prediction, Volume 1: Submerged Discharge.  National Environmental
      Research Center, Corvallis, Oregon.  U.S. Environmental Protection
      Agency Technology Series EPA-R2-72-005a.August, 1972.

2.  Shirazi, Mostafa A. and Davis, Lorin R.  Workbook of Thermal Plume
      Prediction, Volume 2;  Surface Discharge.  National Environmental
      Research Center, Corvallis, Oregon.  U.S. Environmental Protection
      Agency Technology Series  EPA-R2-72-005b. 1974.

3.  Water Resources Engineers, Inc.  Mathematical Models for the Predic-
      tion of Thermal Energy Changes in Impoundments.  Federal Water
      Quality Administration, Washington, D.C.  Water Pollution Control
      Research Series  16130EXT12/69. December, 1969.

4.  Ryan, Patrick J. and Harleman, Donald R.F.  Prediction of the Annual
      Cycle of Temperature Changes in a Stratified Lake or Reservoir:
      Massachusetts Institute of Technology, Cambridge, Mass.
      Mathematical Model and User's Manual, MIT Hydrodynamics Laboratory
      Report No, 137.April, 1971.
5,  Sundaram, T.R.  Rehm, R.G,, Rudinger, G. and Merritt, G.E.  A Study
      of Some Problems on the Physical Aspects of Thermal Pollution
      Report VT-2790-A-I.Cornell Aeronautical Laboratory, Buffalo, New
      York.June, 1970.
                                203

-------
 6.  Hanford Engineering Development Laboratory  The Colheat River
       Simulation Model.  HEDL-TME 72-103*August, 1972.

 7.  Beard, Leo R. and Willey, R,G,   An Approach to Reservoir Temperature
       Analysis.  Water Resources Research  6(5): October,  1970.

 8.  World Meteorological Organization, Measurement and Estimation of
       Evaporation and Evapotranspiration.   Geneva, Switzerland  Techni-
       cal Note 83. 1966,

 9.  Water Resources Engineers, Inc.  Prediction of Thermal Energy
       Distribution in Streams and Reservoirs.  Prepared for the Department
       of Fish and Game, State of California. Walnut Creek, California.
       June, 1967.

10,  Debler, W.R.  Stratified Flow into a Line  Sink* Journal of
       Engineering Mechanics (ASCE)85(EM3):  July, 1959.

11.  Craya, A.  Theoretical Research on the Flow of Non-Homogeneous
       Fluids, LaHouille Blanche 4(1):56-64 January-February, 1949.

12.  Huber, W.C. and Harleman, D.R.F.  Laboratory and Analytical Studies
       of Thermal Stratification of Reservoirs. Massachusetts Institute
       of Technology, Cambridge, Massachusetts   Hydrodynamics Laboratory
       Technical Report No. 112  October, 1968.

13.  Kao, T.W.  The Phenomenon of Block in Stratified Flow. Journal .of
       Geophysical Research 70(4); February, 1965.
                                 204

-------
14.  Sundaram, T.R.  Easterbrook, C.C., Piech, K.R.  and Rudinger,  G.
      An Investigation of the Physical Effects of Thermal Discharges
      into Cayuga Lake. Cornell Aeronautical Laboratory. Buffalo,  New
      York  Report VT-2616-0-2. November, 1969.

15.  Rossey, C.C. and Montgomery, B.R.  The Layer of Frictional
      Influence in Wind and Ocean Currents» Physical Oceanography
      3C3):101.  1935.

16.  Munk, W.H. and Anderson, E.R.  Notes on the Theory of the
      Thermocline. Journal of Marine Research  1:276. 1948.

17.  Tennessee Valley Authority  Water Temperature Prediction Model for
      Deep Reservoirs.   Water Resource Management Methods Staff,
      Technical Report No. A-2, October, 1973.

18.  Tennessee Valley Authority. Temperature Predictions for TVA Reser-
      voirs Graphical Presentations. Water Resources Management Methods
      Staff, Report A-6  December, 1973.

19.  Tennessee Valley Authority, Heat and Mass Transfer Between a Water
      Surface and the Atmosphere.  Water Resources Research Laboratory
      Report No. 14.  April, 1972.
                                205

-------
                                   TECHNICAL REPORT DATA
                            II lease read Instructions on the reverse before completing)
1. REPORT NO.
   EPA-660/3-75-038
2.
                             3. RECIPIENT'S ACCESSIONING.
4. TITLE AND SUBTITLE
 Evaluation of Mathematical Models for Temperature
  Prediction in Deep Reservoirs
                                                           5. REPORT DATE
                             6. PERFORMING ORGANIZATION CODE
                                         1Q7CJ
7.'AUTHOR(S)

  Frank L.  Parker, Barry A.  Benedict, Chii-ell Tsai
                             8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORG \NIZATION NAME AND ADDRESS
 Vanderbilt University
 Nashville, Tennessee   37235
                              10. PROGRAM ELEMENT NO.

                                   1BA032
                              11. CONTRACT/GRANT NO.

                                    R-800613
12. SPONSORING AGENCY NAME AND ADDRESS
                                                           13. TYPE OF REPORT AND PERIOD COVERED
 Pacific Northwest Environmental Research Laboratory
 National Environmental Research Center
 Corvallis, Oregon   97330
                              14. SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
16. ABSTRACT
      The deep reservoir model with one-dimensional assumptions  can be applied to a
      reservoir or lake where the principal variation of flow characteristics
      is in  the vertical direction.   Among the models evaluated,  the MET deep
      reservoir model appears to  be most easily used and to give results most
      compatible with the measured temperatures.  The temperature predicted is
      strongly dependent upon the magnitude of the absorption coefficient of
      water,  and the diffusion coefficient.  However, our sensitivity  analysis
      shows  that an absorption coefficient of about 0.75m~l and  a diffusion
      coefficient of 15 to 20 times molecular diffusion are appropriate choices
      for the seven TVA reservoirs studied.  The determination of whether or not
      a reservoir model depends on the Densimetric Froude number.   However, the
      representativeness of the result is not solely dependent upon the Densimetric
      Froude number.  By the use  of a fitted curve to the measured  temperatures, it
      was possible to determine the maximum standard error of estimate for the predicte
      outlet  level temperature, 1.6°C.   Temperatures on individual  days may exceed thes
      values  and they surely are  exceeded at other depths in the  reservoir.  These
      limits  are suggested as the limit of accuracy of these types  of  models.	
17.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
  Thermal pollution,  reservoirs, mathema-
  tical models,  sensitivity analysis,
  Tennessee Valley Authority Projects
                                              b.lDENTIFIERS/OPEN ENDED TERMS
                 Deep  reservoir models,
                 Massachusetts Insittute
                 of Technology, Water
                 Resources Engineers,
                 Cornell Aeronautical
                 Laboratory
                                           :.  COSATI Field/Group
18. DISTRIBUTION STATEMENT
                                              19. SECURITY CLASS (This Report)
                                              20. SECURITY CLASS (Thispage)
                                                                         22. PRICE
EPA Form 2220-1 (9-73)
 U.S. GOVERNMENT PRINTING OFFICE: 1975-699-073 I\S REGION 10

-------