PB81-218349
Water Temperature Dynamics in Experimental
Field Channels: Analysis and Modeling
Minnesota  Univ., Minneapolis
 Prepared  for

 Environmental  Research  Lab
 Duluth, MN
 Feb  81

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Page Intentionally Blank

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                                                 EPA 600/3-81-008
                                                 February 1981

                                                 PB31-213349
              WATER TEMPERATURE DYNAMICS

IN EXPERIMENTAL FIELD CHANNELS:  ANALYSIS AND MODELING
                           by

                   Heinz G.  Stefan,
                    John Gulliver,
                   Michael G. Hahn,
                          and
                      Alec Y. Fu

                University of Minnesota
        St.  Anthony Falls Hydraulic  Laboratory
          Mississippi River at 3rd Ave.  S.  E.
             Minneapolis, Minnesota  55414
         Grant Nos.  R 80368601 and R 80473601
                    Project Officer

                Kenneth E.  F.  Hokanson
        Monticello Ecological  Research Station
         Box 500,  Monticello,  Minnesota 55362
      ENVIRONMENTAL RESEARCH LABORATORY - DULUTH
           OFFICE OF RESEARCH AND DEVELOPMENT
         U.  S.  ENVIRONMENTAL PROTECTION AGENCY
                DULUTH,  MINNESOTA 55362

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                 NOTICE






THIS DOCUMENT  HAS BEEN REPRODUCED



FROM THE BEST  COPY FURNISHED  US BY



THE  SPONSORING AGENCY.  ALTHOUGH IT



IS RECOGNIZED THAT CERTAIN PORTIONS



ARE  ILLEGIBLE,  IT IS BEING RELEASED



IN THE  INTEREST OF  MAKING AVAILABLE



AS MUCH  INFORMATION  AS POSSIBLE.

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                                   TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing)
1 REPORT NO
  EPA-600/3-81-008
             3 REfiJfJgNT S ACCESSION NO
                       21834 9
4,TITLE AND SUBTITLE
 Water Temperature Dynamics  in Experimental Field
 Channels:  Analysis and Modeling
             5 REPORT DATE
              FEBRUARY 1981 ISSUING DATE.
             6 PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
 Heinz G. Stefan, John Gulliver,  Alex Y. Fu, and
 Michael G. Hahn
                                                           8 PERFORMING ORGANIZATION REPORT NO
9 PERFORMING ORGANIZATION NAME AND ADDRESS
 University of Minnesota
 St.  Anthony FalTs Hydraulic Laboratory-
 Mississippi-River _at-3rd  Ave._.S.E.	
 Minneapolis, Minnesota55414
                                                           10 PROGRAM ELEMENT NO
             11 CONTRACT/GRANT NO
             "R8036360-1 and" R8047 3601-
12 SPONSORING AGENCY NAME AND ADDRESS
 U.S. Environmental Protection Agency
 Environmental Research  Laboratory-Duluth
 6201 Congdon Boulevard
 Duluth, Minnesota  55804
              13 TYPE OF REPORT AND PERIOD COVERED
              14 SPONSORING AGENCY CODE

                EPA-600/03
15 SUPPLEMENTARY NOTES
16 ABSTRACT
 This study is on water  temperature dynamics in  the  shallow field channels of  the
 USEPA Monticello Ecological Research Station  (MERS).   The hydraulic and temperature
 environment in  the MERS channels was measured and simulated to provide some back-
 ground for several biological studies at the Research Station, including one  of  the
 effects of artificially high water temperatures on  fish and invertebrate populations.
 An analysis of  the temperature measurement problem,  the channel temperature regime,
 tnicrohabitat conditions, and temporal and spatial water temperature dynamics  was
 essential for the investigation.  The results of this study are also applicable
 to the study of temperature dynamics in thermally polluted shallow streams, to the
 design of canals for cooling water disposal, and to the study of natural water
 temperature regimes  of  small streams.

 A computer simulation program, TSOIL, to predict the unsteady water temperature
 distribution in the  three-layered system was  also developed.
17
                                KEY WORDS AND DOCUMENT ANALYSIS  _
                  DESCRIPTORS
                                              b IDENTIFIERS/OPEN ENDED TERMS
                                                                         c  COSATI Field/Croup
18 DISTRIBUTION STATEMENT
 RELEASE TO  PUBLIC
                                              19 SECURITY CLASS jThts Report)
                                                UNCLASSIFIED
                                                                         21 NO OF PAGES
20 SECURITY CLASS (Thispage)
  UNCLASSIFIED
                                                                         22 PRICE
EPA Form 2220-1 (Rev  4-77)   PREVIOUS EDITION is OBSOLETE  ,'

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                                 DISCLAIMER

     This report has been reviewed by the Environmental Research Laboratory-
Duluth, U. S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views
and policies of the U. S. Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement or recommenda-
tion for use.
                                      11

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                                   PREFACE

     Shortly after the Monticello Ecological Research Station  (MERS), a field
laboratory of the USEPA Environmental Research Laboratory - Duluth, went into
operation in August 1973 a research program on the effects of elevated water
temperatures, resulting from waste heat discharges on fish and other aquatic
organisms, was initiated by the USEPA staff.  The purpose of these studies was
(a) to validate water quality criteria data produced in the laboratory under
semi-natural field (mesoscale) conditions and (b) to identify significant
response by aquatic organisms under field monitoring conditions.  The field
channels in which the experimental studies were conducted were supplied with
water, heated artificially by waste heat, from Northern States Power Company's
Monticello Generating Plant.
     To provide assistance in these ecological studies, it was necessary to
document, analyze, and predict water temperature characteristics in the field
channels.  The study described herein fulfilled that purpose.  The study of
water temperature characteristics in the 520 m (1700 ft) long field channels
required investigation of several components such as surface heat exchange
processes , longitudinal dispersion, stratification, and heat transfer to the
cnannel bed.  A summary of these studies is provided in this report.  Additional
details on the substudies can be found in the following memoranda and theses.
     1.  Physical Characteristics of the Experimental Field Channels
         at the USEPA Ecological Research Station in Monticello,
         iMinnesota, by Michael G. Hahn, John S.  Gulliver, and H- Stefan,
         Memorandum No. 156. St.-Anthony Falls Hydraulic Laboratory,
         University of Minnesota, April, 1978.
     2.  Operational Water Temperature Characteristics in Channel No. 1
         of the USEPA Monticello Ecological Research Station, by Michael
         Hahn, John Gulliver, and H. Stefan, Memorandum No. 151,
         St. Antnony Falls Hydraulic Laboratory, University of Minnesota,
         January, 1978.
     3.  User's Manual for Operational Water Temperature Statistics
         Computer Programs WTEMP1 and WTEMP2, by Alec Y. Fu and H. Stefan,
         Memorandum No. 162, St. Anthony Falls Hydraulic Laboratory,
         University of Minnesota, July, 1979.

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      4.  Water Temperature Data Processing for the Experimental Field
          Channels at the USEPA Ecological Research Station in Monticello,
          Minnesota, by Alec Y. Fu and H. Stefan, Memorandum No. 167,
          St. Anthony Falls Hydraulic Laboratory, University of Minnesota,
          April, 1979.

      5.  Soil Thermal Conductivity and Temperature Prediction in the
          Bed of the Experimental Field Channels at the USEPA Ecological
          Research Station in Monticello, Minnesota, by J. S. Gulliver
          and H. Stefan, Memorandum No. 165, St. Anthony Falls Hydraulic
          Laboratory, University of Minnesota, January, 1980.

      6. - Pore Water Temperatures and Heat Transfer in a Riffle  (Rock)
          Section of the Experimental Field Channels at the USEPA
          Ecological Research Station at Monticello, Minnesota, by H. Stefan
          and J. S. Gulliver, Memorandum No. 166, St. Anthony Falls Hydraulic
          Laboratory, University of Minnesota, April, 1980.

      7.  Analysis of Surface Heat Exchange and Longitudinal Dispersion
          in a Narrow Open Field Channel with Application to Water Tempera-
          ture Prediction, by John S. Gulliver, M.S. thesis, University
          of Minnesota,  August, 1977.

      8.  Experimental Studies of Vertical Mixing in Temperature Stratified
          Waters, by Michael G. Hahn, M.S. thesis, University of Minnesota,
          March, 1978.

      9.  Stochastic Water Temperature Characteristics in an Outdoor
          Experimental Channel, by Alexander C. Demetracopoulos,  Plan B
          paper for M.S. degree, University of Minnesota, November, 1976.

      The overall geometrical, hydraulic, and soil thermal characteristics of
 the Monticello field channels have been described in Item No. 1 above.  A
 first summary of operational water temperature characteristics in the field
 channels was given in Item 2.  The surface heat exchange and the longitudinal

 dispersion in the artificially heated channels subjected to real (unsteady)
 weather conditions were described in Item 7.   The water temperature stratifi-

"catrrorr~rn'the"-llpoo±su--of--the--£teld-channel3--w-a3--described--and- analyzed- in- -  -  -
 Item &. - A-computer progrant was developed for the statistical analysis of 3-
"hour water temperatures recorded at several stations in-four-of the-eight

 field channels.  A user's manual was prepared and made available to the MERS
 staff (Item 3).  Water  temperature data processing was described in Item 4.
 Water temperature statistics were computed for the four channels equipped with
 water temperature instrumentation for the periods from December 1975 to
 September 1977.  The tabular computer printout covers many pages and copies
                                       IV

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are available for purchase.  Earlier statistical analysis of some partial
records led to an unpublished, but fairly extensive, progress report by H.
Stefan, C. Gutschik, A. Demetracopoulos and J. Gulliver entitled "Water
Temperature Data Retrieval and Statistical Analysis for the Experimental
Channels at the USEPA Monticello Field Station," September, 1976, 53 pp.
A spectral analysis of some water temperature records is given in Item 9.
Finally, the heating and cooling of the channel bed by the water above has
been analyzed and a computer program for soil temperature prediction was
described in Item 5.  Pore water temperatures in_ .the.riffles.are_described_ in
Item 6.
     The work performed for the USEPA Monticello Ecological Research Station
 (MERS) under this grant had two basically different purposes.  One was to
provide background material and general information in support of the biological
work conducted by the MERS field station staff.  The second purpose was to
investigate surface heat transfer, longitudinal dispersion, and water tempera-
ture predictions in streams under field conditions.  The second purpose is
basic and includes verification of the applicability of relationships developed
for larger water bodies to smaller streams.
     This report has been divided into sections which address the two above
purposes separately.  Section 4 - Hydraulic and Thermal Characteristics of the  -
MERS Field Channels provide  general background information, Section 5, Longi-
tudinal Dispersion, Section 6 - Heat Budget, and Section 7 - Water Temperature
Prediction, give results of basic experimental and analytical studies.

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       fc                           ABSTRACT

      This report summarizes some of the morphological, hydraulic, thermal
and meteorological characteristics"of the experimental field channels at the
USEPA Monticello Ecological Research Station.  It contains an overview of
measurements and parameters which characterized the physical operation condi-
tions of the channels from December 1975 through December 1977.
      Reported herein are measured values of hydraulic channel roughness,
permeability and porosity of rock sections, and thermal diffusivity of bed
materials.  Recorded water temperatures have been statistically analyzed to
give local diel, longitudinal,and vertical water temperature variations.  A
data bank of 3-hour water temperature data was established.  Mean, standard
deviation, skewness, and water temperature values at 5 per cent and 95 per cent
probability of occurrence have been calculated on sliding, weekly samples of
these 3-hour data.
      Various aspects of the water temperature regime of the experimental
field channels of the USEPA Monticello Ecological Research Station (MERS)
were studied theoretically.  Longitudinal dispersion and heat transfer
relationships which were included in a dynamic water temperature model had
to be established.  Water temperatures at various channel locations and
Tieteorological  parameters were continuously recorded.  A convective water
surface heat transfer relationship (wind function)  was determined from the
recorded longitudinal temperature-proflie and meteorological parameters during
quasi-steady state periods.  Progressive'-heat fronts were-used with tracer
theory to determine longitudinal dispersion coefficients for the field "
channels.
      The wind function and the longitudinal dispersion coefficient were
incorporated in an implicit finite difference computer model, MNSTREM, for
the highly dynamic water temperature prediction in the very shallow field
channels.  The water temperature model results were verified against
3-hour water temperature measurements over four time periods of up to one
month.

                                      VI

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      Development of a model for diel water temperature variations at a
one to three hour time scale goes beyond conventional stream water tempera-
ture modeling.  The value and necessity of 3-hour to 6-hour weather data in
making accurate predictions has been demonstrated.  A standard error of
0.24 C between predictions and measurements could be achieved.
                                       VII

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                              TABLE OF CONTENTS
 Preface 	   m
 Abstract 	    vi
 List of Figures-	.~.     x
 List of Tables T.	  xm
-Abbreviations arid-Symbols -sn-n. '.~~l 7	—.-. .%-7.-»-» .-.:. .^»-*777.	    xv
 Acknowledgements 	xviii

      1.  INTRODUCTION 	     1

      2.  CONCLUSIONS 	     5

      3.  RECOMMENDATIONS 	   9

      4.  HYDRAULIC AND THERMAL CHARACTERISTICS OF THE MERS  FIELD
          CHANNELS 	  10
          4.1.  Channel Geometry 	  10
          4.2.  Channel Hydraulics  	  14
                    Flow Rates and Residence Times  	  14
                    Roughness and Water Surface Slope	  14
                    Flow Velocities 	  17
          4.3.  Soil and Rock Characteristics  	  21
                    Grain Size Distribution 	  21
                    Permeability of Riffle Rock Sections  	  23
                    Soil Thermal Diffusivity and Soil Temperature in
                        Pool Sections 	  23
                    Rock/Water Thermal Diffusivity and Temperatures
                        in Riffle Sections  	  28
          4.4.  Observed Operational Water Temperature Regime  	  31
                    Water Temperature Instrumentation  	  31
                    Water Temperature Data Processing  	  31
                    Water Temperature Data Analysis and Results  	  37

      5.  A S-TTO*- OF-LONGITODINAL DISPERSION IN THE MERS-FIELD CHANNELS..  57
    ":- "".5.1.  Background '..." — .-	'.-..".";...."... .\ .. .v;-; _.:.'. rr."T7;~T '"5 Tv
    ----   5.2. -~Methbd-of Longitudinal Dispersion-Coefficient  -	     -  .'.
                Determination from Transient Water Temperatures  	  60
          5.3.  Formulation of Dimensionless Longitudinal  Dispersion
                Numbers 	  64
          5.4.  Results of Temperature Routing Tests  	  66
          5.5.  Effects of Variable Cross Sectional Area  on  Longitudinal
                Dispersion 	  67
          5.6.  Comparison with Other Longitudinal Dispersion  Measure-
                ments 	  69
          5.7.  Effect of Roughness (Mannings  'n') on Longitudinal
                Dispersion in the MERS Channels 	  70

                                      viii

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     6.   HEAT TRANSFER ACROSS THE WATER SURFACE IN THE MERS FIELD
         CHANNELS	  71
         6.1.  Background 	  71
         6.2.  Net Shortwave (Solar)  Radiation 	  72
         6.3.  Net Longwave Radiation 	  75
         6.4.  Net Evaporative and Convective Heat Transfer 	  76
         6.5.  Determination of Wind  Related Heat Transfer Coefficient
               from Measured Steady-State Longitudinal Temperature
               Profiles 	  78
                   General Procedure  	  78
                   Errors in Computed Heat Transfer Coefficients	  79
                   Determination of Wind Function Coefficients 	  81

     7.   DYNAMIC WATER TEMPERATURE PREDICTION IN OPEN CHANNELS 	  91
         7.1.  General Objective	  91
         7.2.  Formulation of One-Dimensional Finite Difference Equa-
               tions for Water Temperature Prediction 	  91
         7.3.  Description of Numerical Finite Difference Computer
               Program for Water Temperature Prediction 	  96
         7.4.  Examples of Water Temperature Predictions in the MERS
               Field Channels 	  97

References 	 115

Appendices

     A.   Temperature Front Data for Determination of Longitudinal
         Dispersion Coefficient 	 119
     B.   Data and Computations of Bulk Surface Heat Transfer Coefficient
         and Wind Function Parameters from Steady-State Longitudinal
         Water Temperature Profiles 	 126
     C.   User's Guide to the Minnesota Stream Water Temperature
         Prediction Model (MNSTREM)  	 133
     D.   Program Listing for the Minnesota Stream Water Temperature
         Model MNSTREM 	"... 137
     S.   Sample Input Data for MNSTREM 	 148
     F.   Partial Sample Output from MNSTREM 	 153
     G.   MERS Weather Station 	 157
     H.   Sample Output from Program WTEMP1 Water Temperature Statistics. 162

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                               LIST OF FIGURES


Number                                                                     Page

 1.1    Aerial photograph of the Monticello Station experimental channels,
    *"   Northern States Power Company Monticello Power plant, and
        Mississippi River 	     2

 4.1    MERS channels showing the transition from pool to riffle to pool.    H

 4.2    Channel cross sections 	    12

 4.3    Cross sections of riffle 5, channel 1 on April 6, 1977 	    13

 4.4    Velocity profiles in Channel 1, riffle 5, looking downstream.
        Measured October 30, 1976 	    18

 4.5    Velocity profiles in Channel 4, riffle 11, looking downstream,
        with bottom free of weed.  Measured May 9, 1977	     19

 4.6    Velocity profile in Channel 5, Pool 14, looking downstream.
        Measured October 30, 1976 	     20

 4.7    Size distribution for material in Channel 1 at MERS  	     22

 4.8    Soil profile below pool and location of thermistor probes  	     25

 4.9    Schematic cross section of one channel pair drawn to approximate
        scale	     25

 4.10   Measured soil temperature profiles in pool 6 during heat wave
        test:  warming period	     26

 4.11   Comparison of measured and predicted soil temperatures in  Pool 12
...... _ during- heat- wave test	,	V	     27

 4.12   Vertical temperature profiles in Riffle 17 during period of
        rock temperature study	     30

 4.13   Thermal probe placement in MERS experimental channels	     32

 4.14   Seasonal water temperature plots of Channel 1  	     39

 4.15   Seasonal water temperature plots of Channel 5	     41

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Number                                                                     Page

 4.16   Diurnal water temperature plots of Channel 1  	  44

 4.17   Diurnal water temperature plots of Channel 5  	  48

 4.18   Vertical temperature stratification in Channel 1, pool 6.
        Measured August 11, 1976 	  54

 4.19   Per cent days with stratification  AT > 1.0°C  and  AT >  2.0°C
        in Channel 1, pool 6 and pool 12 	  55

 4.20   Per cent hours with stratification  AT > 1.0°C—and  AT >-l.O^C   	~
        in Channel 1, pool 6 and pool 12 	-	  56

 5.1    Schematic streamlines at transition from riffle to pool in
        Monticello experimental channels without and with transverse
        winds 	  61

 5.2    Schematic outflow concentration curve for ;jet mixing in experi-
        mental pool 	  61

 5.3    Temperature fronts in MERS channel 1 on November 17, 1976	  63

 5.4    Computed temperature fronts  (normalized) which occur at location
        17 in Channel 1 with and without heat transfer 	  65

 6.1    Comparison of Eq. 6-46 and 6-47 with computed values of the
        wind function, F 	  84
                        w
 6.2    Comparison of Eq. 6-48 with computed values of the wind function
        minus natural convection term 	  85

 6.3    Comparison of Eq. 6-49 with computed values of the wind function,
        F , minus natural convection term	  36
         w
 6.4    Comparison of Eq. 6-50 with computed values of the wind function,
        F , minus natural convection term	  87
         w
 7.1    Control volume in time-distance coordinates for formulation of
        finite differences 	  53
    > ,__ .Gejieral__flo_w__chart _for_ MNSTEH,^ _tHe_ Minnesota Stre.am Water
      .".Temperature "Prediction Model ......................... .....
 7.3    Run A.   Hourly water temperatures at three stations in channel 1
        from January 31 through February 4, 1976 ........................

 7.4    Run B.   Three" hour water temperatures at three stations at

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                                                                         Page

          Run C.  Three hour water temperatures at Station 3  (upstream)
          and Station 17 (downstream) in Channel 8 	    106

7.5b      Run C.  Three hour water temperatures at Station 3  (upstream)
          and Station 17 (downstream) in Channel 8 	   107

7.5c      Run C.  Three hour water temperatures at Station 3  (upstream)
          and Station 17 (downstream) in Channel 8	   108

7.6a      Run D.  Three hour water temperatures at Station 3  (upstream)
          and Station 17 (downstream) in Channel 1 	   110

7.6b      Run D.  Three hour water temperatures at Station 3  (upstream)
          and Station 17 (downstream) in Channel 1 	   Ill

B-l       Steady state water temperature profile and "best fit" curve
          for November 19,  1976	   130

G-l       Sample strip charts for wind velocity, wind direction, and
          solar radiation 	   158

G-2       Sample hygrothermograph strip chart for degrees Celcius air
          temperature and percent relative humidity 	   159

G-3       Weather station with hygrothermograph and shelter, pyrano-
          meter, wind vane,  and anemometer 	   160

G-4       One-year cycle of air temperatures.  February 1976
          through January 1977 	   161

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                                LIST OF TABLES
Number                                                                    Page

 4.1    Water Surface Slopes, Cross Sectional Areas, Wetted Perimeters,
        Manning's Roughness Coefficients, Shear Velocities, and Shear
        Stresses on the Bottom of Channel 1 on April 18, 197-7 ...........   ^5
 4.2    Water Surface Slopes, Cross Sectional Areas, Wetted Perimeters,
        Manning's Roughness Coefficients, Shear Velocities, and Shear
        Stresses on the Bottom of Channel 1 on June 15, 1977 ............   16

 4.3    Summary of Water Temperature Information Stored on Magnetic Tape.  35

 4.4    Monthly Mean and Standard Deviation of Daily Minimum and Daily
        Maximum Longitudinal (Spatial) Temperature Difference, and of
        Diurnal (Temporal) Temperature Difference at the Outflow for
        Channel 1, December 1975 - November 1976 ........................   53

 4.5    Frequency Analysis of Temperature Stratification in Channel 1
        (January 1 - Decemoer 31, 1976) .................................   53

 5.1    Longitudinal Dispersion in MERS-Channels from Temperature
        Front Data [[[   68

 5.2    Average Pool and Riffle.D  from Temperature Front Routing Tests.   68
                                 L
 5.1    Wind Function Formulas Determined by Various Investigators ......   88

 7.1    Standard Error of Water Temperature Predictions when Weather
        Parameters are Averaged Over 1, 3, 6, and 12 Hr Periods ........  112

 7.2    Standard Error of Water Temperature Predictions with Instan-
        taneous Readings of Weather Data Taken at 3 , 6, and 1 Hr
        Increments ....... ...... ........................................  114

 A-l    Channel 1 Cross-Sectional Areas and Surface Widths for
        Temperature Front Experiments ..................................  120

 A-2    Residence Times to Each Station in Temperature Front
        Experiments [[[  120

 A-3    Measured 0 Values for 11/17/76, 11/18/76, 11/22/76, 12/6/76,

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Number                                                                 Page

 B-l      Data and Computational Results for Determination of Bulk
          Surface Heat Transfer Coefficient and Wind Function
          Parameters from Steady State Longitudinal Water Temperature
          Profiles 	   127

 B-2      Maximum and Minimum Values of  K , F , and F -5.52{A6 )
                                          S   W       W        v
          in sample computation due to maximum possible errors in data  132
                                      xiv

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                       ABBREVIATIONS AND;SYMBOLS
    A = cross sectional area  (L )
    A = mean cross sectional area over entire reach
    B = surface width (L)
    B = mean channel width over entire reach
    C = concentration (ML  )
   C  = fraction cloud cover  (-)
    c
   C  = cloudiness ratio
    r                             _X o -1
   c  = specific heat of water  (EM    C  )
    P
a,b,c = coefficients
    D = thermal diffusivity  (L T  )
    D = 2D /U
          L  -T
   D* = D  BQ ~
         L	_L  _]_
  D*  = D_ A B Q   A
                                              2-1
   D  = longitudinal dispersion coefficient  (L  T  )
    Ij
   e  = actual air pressure  (mb)
    a
  e   = saturation vapor pressure at dewpoint  (mb)
   a2
  e   = saturated vapor pressure (mb)
   sw
   f  = bottom friction factor
    h = mean channel depth  (L)
    n = mean channel depth over entire reach
                               -2  -1
   H  = convective heat loss(EL   T  )
                                 _9   -i
   H,  = evaporative heat_loss ^EL ~__T!  )
   H  = net long wave radiation (EL   T  )
                                          -2  -1
   H  = net short wave solar radiation (EL   T  )
  H   = incoming solar radiation (EL~  T~ )
  H   = reflected solar radiation (EL~  T"1)
   S L
    i = distance node
   3  = time node
    k = Darcy permeability coefficient (LT~ )
    EC = 2m/U = 2 K  p"1 c ~1 h'1 U~l
                                      XV

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     K  = bulk surface heat transfer coefficient
      S -                                -1
      L = latent heat of vaporization  (EM  )
      ra = K  p"1 c ~1 h'1
           s *    p
      M = mass of tracer injection  (M)
      n = Mannings roughness coefficient
     NS = 3T/3t
      P = wetted perimeter (L)
     p  = atmospheric pressure (mb)
      Q = flow rate (L3 T*1)
      r = reflectivity or albedo of water surface
      R = hydraulic radius (L)
     RH = relative humidity (-)
      S = rate of surface heat input (EL   T  )
     S  = slope of energy grade  line (-)
     SS = Q B"1 h"1 3T/3x
      t = time (T)
      T = water temperature (  C)
                           o      o
     T  = air  temperature ( C  or   K)
      a
     T  = dew  point temperature  (°C)
     T  = equilibrium temperature (°C)
      E
     TQ = T(x=0)
     T  = surface water temcerature (  C or   K)
      3                    "             _!
      U = mean channel flow velocity (LT  )
      U =  mean  channel  flow velocity over entire reach
     u^ =  shear velocity  (LT~ )
(Wftu)   =  wind  speed  function
      z
     W  =  wind  velocity at  elevation z  above  ground (L
      z
      x =  distance  along channel  (L)

      a =  solar angle  (degrees)
    A8  =  virtual temperature difference  (°C)

        - porosity of bed material  (-)
                                      o  -4   -2
     e   = emissivity of atmosphere  (E  K   L  )
                                 -2 o -4
     £   = emissivity of water  (EL     K   )
                                    xvi

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 Q = dimensionless water temperature = [T(t)-T(0)/ T(°o)-T(0)]


 9 = dimensionless temperature = [T(x)-T ]/(T -T )
                       _                E    O  E

 p = water density (ML  )


 a = Stefan-Boltzman constant


T  = bed shear stress (FL  )
 o
                               xvi i

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                               ACKNOWLEDGEMENTS

      The very understanding cooperation and planning by the Project Officer,
Dr. Kenneth E. Hokanson is gratefully acknowledged.  The planning and per-
formance of many of the.field, experiments, required some^involvement and. help
from the permanent staff of the field station (MERS), expecially Mr. Thomas P.
Henry and Mr. Jack Arthur, Acting Chief of MERS.  The cooperation of
Mr. Charles F. Kleiner in providing and maintaining some of the required
instrumentation deserved particular recognition and gratitude.
      Funding for this study was provided through grants from the U. S.
Environmental Protection Agency, Environmental Research Laboratory - Duluth,
Minnesota 55362.
      Reviews of a draft copy of the report by Professor John A. Hoopes,
University of Wisconsin, Madison, Wisconsin, and Professor Frank H. Verhoff,
West Virginia University, Morgantown, West Virginia, are gratefully acknow-
ledged.
                                     XV 111

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                                  SECTION 1
                                INTRODUCTION

     The Monticello Ecological Research Station (MERS) is a Branch of the U.S.
Environmental Protection Agency's Environmental Research Laboratory in Duluth,
Minnesota.  The MERS is located approximately 40 miles northwest of Minneapolis,
near Monticello, Minnesota, on 34 acres adjacent to a Nuclear Power Generating
Plant owned and operated by Northern States Power Company.  An aerial photo-
graph of the Monticello Field Station is given in Fig. 1.1.  The MERS has eight
soil bottom experimental open channels of approximately 520 m (1700 ft) length
each.  The Mississippi River serves as the main source of water for the channels
which operate in a once-through mode.  Heat exchangers using waste heat from
the power plant can be used to artificially heat the water in any of the chan-
nels.  The channels are in an elevated area above the Mississippi River and
not normally subjected to flooding.
     Flow rates in each of the channels as well as water stages can be con-
trolled.  The discharge from the channels is returned to the Mississippi River
without any provision for treatment.
     Heated cooling water effluents from power facilities create artificially
high temperatures in natural waters.  These thermal additions also intensify
the dynamic character of natural water temperatures.  Analysis of the higher,
more variable water temperatures is needed to aid in determining effects upon
the ecology of natural water's.  Such studies are "conducted at the MERS.
     Artificially heated water in "a river, lake, pond, estuary, or coastal"
area  is cooled primarily through heat transfer with the air.  Such heat trans-
fer has been thoroughly studied for large water surface areas but the relation-
ships developed may not apply well to shallow and narrow open channels.  The
quantitative effect of wind velocity, which enhances heat transfer, is different
for narrow channels and wide surface areas.

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Fig. 1.1.  Aerial photograph of the Monticello Station
           experimental channels- (center);   Right - Northern
           States Power Company Monticello Power Plant.
           Bottom - Mississippi River.

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      Water temperatures in small open channels are highly dynamic due to the
 time dependent character of the controlling processes:  advective transport,
 wind and flow induced mixing, and heat exchange with the air and the channel
 bed.  In the MERS field channels the unsteady character of water temperature
 is especially acute  since neither the mixing characteristics nor the effect
 of advective transport are negligible in the channels.  The channels are ex-
 posed to a wide range of air temperatures, humidities, wind velocities, and
 solar radiation.   The corresponding heat transfer with the environment is
-signif icarvtt— a differ.ence_in_ temperature between the upper and lower end as
 high as 15°C has  been recorded  and diurnal variations above 5 C have been
 observed at the downstream end.  The experimental channels provide an excellent
 medium for the study of unsteady water temperatures in open channel flow and
 their relationship to meteorological parameters.
      The energy transport equation applied to an open channel of constant
 cross section takes the following form:

                                                      h
                                                     p
 D  is a dispersion coefficient in the direction of flow (x-direction) ,  S is
  L
 a source or sink  term  which  includes heat transfer with the surrounding
 environment,  t is time,  U is mean channel velocity, h is mean depth, p  is the
 density of water, and  c  is the heat capacity of water.   The potential im-
 portance of the dispersion mechanism and of heat exchange with the air  is
 evident in Eq.  1-1.

      Continuous water temperature records and meteorological  data were
 gathered^  and usedMio^jiietermine longitudinal dispersion  and  adapt known  air-
 wa'tef " heat transfer rela-ti-cnships to narrow open channels with well defined
 non-uniform cross sections  (crenelataons) .  The effect  of wind upon longitudinal
 dispersion in the cnannels was studied.  This information was needed to develop
 a dynamic model of channel water temperatures.  It was  intended that the model
 should be able to predict the diurnal water temperature variations -on a time-
 scale of  1 to 3 hours, as well as the longitudinal gradients.  The  longitu-
 dinal gradients were induced by adding artificially  heated  water to the
 channels  and oy the diurnal  heating and cooling cycle at the  channel surface.

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A time scale of 3 hours was found adequate to simulate the observed diurnal
variations.
     The model simulation had to pay attention to several factors not usually
considered in stream temperature modeling:  (a) the particularly complex
geometry of the channels caused by the alternation of riffles and pools,(b)
the presence of weeds and intermittent stratification and (c) the unusually
short time scale required.   This led to a water temperature  model  which
is more dynamic than any other model known to the authors.
     This study of the physical environment in the MERS field channels was
intended to provide some background for several biological studies at the
Research Station, including one on the effects of artificially high water
temperatures on fish and invertebrate populations.  An analysis of the
temperature measurement problem, channel temperature regime, microhabitat
conditions, and temporal and spatial dynamics was essential for such investi-
gations.  The planning of future channel experiments may be facilitated  by
the results of this study.  In a broader sense, this study also contains
material applicable to the study of temperature dynamics in thermally polluted
streams, to the design of irrigation canals for cooling water disposal, and to
the natural water temperature regime of small streams.

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                                    SECTION 2
                                   CONCLUSIONS

1.   The field channels at the Monticello Ecological Research Station represent
    a meso-scale ecosystem whose temperature regime and hydraulic charac-
    teristics have been measured.   The water temperature regime has also been
    simulated in a dynamic numerical model using channel morphological and
    hydraulic parameters as an input and air/water heat exchange as a water
    temperature forcing function.
2.   Development and operation of instrumentation for continuous monitoring
    of flow rates and water temperatures in the channels from 1975 to 1977
    was in the hands of MERS staff, in particular Charles F. Kleiner.  The
    investigators participated in the selection of the temperature sampling
    sites shown in Fig. 4.13.  The investigators also collected intermittently
    data on flow velocity profiles, water temperature stratification, surface
    water  surface  slope  and  flow cross  sections.   These  data  have  been  used  to
    describe the temperature regime of the channels, derive a number of
    relevant physical parameters, and verify techniques  for the analysis
    of temperature dynamics as described below.
3.   The nydraulic characteristics include:

             Mannings roughness:    n = 0.06 in the clear channels
                                    n = 0.3 with weed growth
             Mean flow velocities:  U = 0.1 m/s in riffles
                                    U = 0.02 m/s in pools
    depending on flow rate and downstream channel control.  Velocity profiles
    are strongly affected by growth of filamentous algae in the rock sections
    and macrophytes in the pools.
             Darcy permeability coefficient of rock  k = 0.18 m/s
             Rock ,porosity        e = 0.4-2.

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 4.  The soil profile below pool bends is composed  of  four  layers:  a highly
    organic surface layer, water saturated sandy loam,  water  saturated
    bentonite clay layer, and a dry sandy loam, in order,  from  surface
    downward.  The depth of the highly organic surface  layer  is variable and
    increases with time.  The thermal diffusivity  of  each  layer was determined
    by fitting soil temperature prediction to temperature  measurements.
            D = 0.0017 cm /s in the organic  surface layer
            D = 0.013  cm /sTn'fche wet sandy. loam_.helow.-
            D.3_-5-.0013^ cm./s in the dry sandy loam below J:he_benton,ite- seal
    The thermal diffusivity of the riffle was estimated to be  D = 0.0031 cm /s
    in the rock/water system without natural convection.
 5,  Vertical stratification of the pool sections was  studied  in the artificially
    heated channel 1 and was found to occur  most frequently in  August.  The
    temperature gradient was found to occur  primarily in the  lowermost 20 cm
    of the pool below a 60 cm isothermal layer; the temperature difference
    was up to 5°C strong.  Analysis of some  1975/76 data in pools 6 and 12
    showed that a temperature differential of more than 1  C developed during
    33 per cent of all hours in August and less frequently during other
    months.  The more downstream pool showed a stronger tendency toward strati-
    fication, presumably because the cumulative effect  of  atmospheric heating
    of the water in it is stronger.
 5.  A dynamic soil temperature model for the pool  sections was  developed,
    primarily to assist in invertebrate studies.   The model solves the
    unsteady heat conduction equation and predicts the  soil temperature
    profile for a specified time variation of the  water temperature at the
 _  _gpil/wateJL interface^.. It was_verified  (Fig. 4.11}  that spil_temp_er_atures _.	
 __,„	jnay..be accurately, predicted with this "model.
'7.  Three-hour "water temperature measurements in four of "eight  fieia channels
    have been recorded, processed and statistically analyzed  for a period
    from December 1975 through September 1977.  A  computer program and
    User's Manual were provided to EPA.
 8,  Longitudinal dispersion in the MERS field channels  was studied separately
    using temperature fronts.  The longitudinal dispersion coefficient was
    found to be best approximated by

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                                    DL = 7.47 * f ,

     where  Q  is flow rate and  B  is mean surface width.   The
     effects of pool/riffle interaction appeared to be minor and longitudinal
     dispersion was similar to that in a channel of uniform cross section.
     In the range of very low mean flow velocities investigated (0.04 m /s
     discharge and U = 0.02 m/s yi pool to 0.1 m/s in riffle), the typical
     wind and vegetation effects could not be distinguished separately.  A
     typical value of  D   was 0.1 m~/s, with more detail provided in Tables
                        LJ
     5.1 and 5.2.
     Evaporative and convective surface heat exchange were found to be
     dependent on wind speeds and natural convection potential.  A wind speed
     function
                              Wftn = 0.0096 (A6 )     + 0.0083 W2

     was found to fit the experimental field data well.  A9   represents a
     virtual temperature differential defined by Eq. 6-30 and W  is the wind
     speed at 2 meters above the ground in m/s.  The windspeed function is
     used to calculate evaporative surface heat transfer in accordance with
     Eq. 6-22 and convective surface heat transfer according to Eq. 6-26.
10.  The water temperature regime was found to be highly dynamic for several
     reasons:
     (a)  the shallow mean depth of the channels (< 1 m)
     (b)  the residence time of several hours in the channels
     (c)  the open cycle mode of operation whereby water from the Mississippi
          River is fed (heated or unheated through the MERS channels in a
          once-through mode)
     Since the nydraulic conditions on thermal responses in the Mississippi
     River and in the MERS field channels are very different, channel water
     temperatures are usually in transient conditions with ooth strong
     longitudinal gradients (several degrees C) and significant diurnal
     variations (several degrees C) at the downstream end.  Taole 4.4 provides
     specific figures.  Upstream conditions were more stable because the
     inlet water came from the Mississipi River, a deeper water oody than
     the channels.

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11.  A finite difference,  implicit computer model MNSTREM for the simulation
     of the very dynamic channel water temperature regime was developed.   It
     was shown capable of  simulating 1 hr,  3 hr or 6 hr water temperatures
     over periods up to one month with standard errors of 0.2 to 0.3°C
     between measurements  and predictions.   Weather data, specifically solar
     radiation, air temperature, dewpoint and wind velocity are required  as
     input at least every  six hours.  Three hour input data are standard  for
     the model.  If intervals of more than  six hours are used, the accuracy
     of the prediction suffers (Table 7.1).  MNSTREM has unusually high time
     resolution meaning that it can predict rapid water temperature changes
     in very shallow water.

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                                   SECTION 3
                                 RECOMMENDATIONS

      Water temperature variations "in time ancT~space"are a characteristic of
"any aquatic environment-and especially the MERS field channels.. Standard
 methods for the characterization of water temperature dynamics  and incorpora-
 tion of these characterizations into water temperature criteria for pollution
 control are needed.   The  MERS field channels lend themselves to studies of
 dynamics very well.   They should be used for continued studies of fate
 and effect of various pollutants in an ecosystem at the meso-scale.
      The focus of this study was on water temperature as a water quality
 parameter.  For the  model formulation, a dispersion parameter and surface
 exchange relationship adequate for water temperature modeling were derived.
      Studies of pollutant (mass) transportiin the MERS channels require more
 refined and detailed information on the flow and dispersion in  a bed of
 macrophytes since uptake  and precipitation are added factors (not present
 in the temperature model).
      If further ecosystem studies in the MERS channels are conducted,
 detailed investigations of  the hydrodynamics and transport dynamics of a
 pool and of a riffle, including the effects of vegetation must  be conducted.
 For example, tne effect of  vegetation on longitudinal dispersion needs
-investigation.- -Slow. af_f ec.ts_must fee ._ss.r_t.ed._pu.t.Jr.om. the. f ield_ observations	
 to derive-the crue biological and chemical kinetics of the s_ystem.
      The 3-hour water temperature~data base derived from continuous recordings
 snould be analyzed further  by time series (spectral, correlation) analysis.
 In addition, weather data and flow data snould be digitized.
      Continuously recording flow metering and channel stage recording
 devices at each end  of a  channel should be installed in the MERS channels.
 Flow rates were recorded  manually once a day and stages only intermittently.

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                                   SECTION 4
         HYDRAULIC AND THERMAL CHARACTERISTICS OF THE MERS FIELD CHANNELS

 4.1.   CHANNEL GEOMETRY
      Each  of the eight  experimental  channels at the MERS is approximately
 520 m (1700  ft) long, with  alternating "pool" and "riffle" sections of
 approximately 30.5 m(100  ft)  length  each and one 90 degree bend from an
 east-west  to north-south  alignment.   There are nine pools and eight riffles
 in each  channel.  The approximate geometry of the pool sections is 3.5 m
 (12 ft)  surface width and 0.8 m (3 ft)  maximum depth.  The pool cross section
 is approximately parabolic.   The  riffle sections are contracted areas to
 increase flow velocity.   They are trapezoidal in shape and formed by 38 mm
 (1.5  inch) gravel placed  in  the channel.  The riffle width at the water
 surface  is approximately  2.5  m (8 ft).   Riffles are very shallow, e.g. 0.3 m
 (12 inches).  As the water  stage  can be controlled by a bulkhead at the end
 of each  channel, the exact water  depths and surface widths can also be changed.
      The channels are arranged in pairs, separated by a high berm.  There is
 a gravel road between channel pairs.  Figure 4.1 shows one pair of channels.
      Locations in the channels are numbered, with the number 1 assigned to
 the inlet, numoer 2 to  the  first  pool,  number 3 to the first riffle, etc.r
 up to the  outlet which  is numbered 19.   In addition, each channel was given a
 number from  1 to 3.  Figure  4.2 gives measured average riffle and pool cross
.sections in_Channel 1 .(northernmost  channel).  Cross sections, are not uniform
 in all cases.  One example of a non-uniform- riffle cross section is given in
 Fig.  4.3.
                                     10

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Fig. 4.1.  MERS channels showing the transition from pool
           (foreground) to riffle to pool.  The channel on
           the left is flowing full, while the channel..on
           the right is partially drained, exposing the gravel
           sides and bottom of the riffle section.
                          11

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        F
305
        I*-30 5
                    185.9
                              208
                                    "T
                                     193
               |<	 62.*
                           62
.5  —*|
  Average riffle cross section  for Channel  1 on April  6,  1977.
         457 —»j
                                          457
                             216 4
 Average riffle cross section  for Channel  1 on June  15,  1977«
                              341 4
   Average pool cross section for Channel 1 calculated  from
   measurments made from July 13, 1977  through July  19,  1977.


Fig. 4.2. Channel cross sections,   (dimensions in centimeters)
                            12

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I-1
LJ
                                                                                               Upstreom
                                                                                               Section
                                                                                                    Middle
                                                                                                    Section
                                                                                                      Downstreom
                                                                                                      Section
                                '00m
                            Scolei  '	
05m
                             Fig.  4.3. Cross  sections of  riffle 5,  channel  1 on April  A, 1977.

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4.2.  CHANNEL HYDRAULICS
Flow Rates < and Residence Times
     Flow rates in each channel are controlled  and metered  in  the  control room
of the office building.  V-notch weirs are  installed  at  the head  (inlet)  of
each channel and are available for installation at the end  of  each channel.
Maximum design flow for a channel is on the order of  37.9 i/s  (600 gpm) .
Actual flow rates have been as high as 39.1 £/s (620  gpm).  In its first  year
of operation the flow rate in Channel 1 was approximately 18.9 H/s (300 gpm),
and" the total hydraulic residence time of the water in the  channel on  the
order of 12 hours. In the second year, beginning in August 1976, the flow  rate
was approximately 28.4 2,/s (450 gpm) to 37.9 H/s  (600 gpm) , with  residence
time on the order of 4 hours.  A lower stage was used with  the higher  flow.
Roughness and Water Surface Slope
     The hydraulic roughness was determined in  Channel 1 on three  different
occasions.  Water surface slopes were measured  in Channel 1, enabling calcula-
tion of roughness coefficients, wall shear stresses on the wetted  perimeter,
and shear velocities.   Two sets of values are presented in Tables 4.1 and  4.2
where the station numbers refer to pool and riffle locations.    (Counting  in a
downstream direction,  the odd-numbered stations are riffles and the even-
numbered stations are  pools.)   Computations were made for three different  flow
rates and for clear and weed choked conditions  in the channel.
     On April 18,  1977 the channel was relatively free from weeds and obstruc-
tions.   On June 15, 1977 heavy macrophyte  growth in both the riffles and pools
had raised the water surface  level substantially from the April level.
     Manning's roughness coefficient  'n' is  defined by the Manning equation
(see  e.g.  Olson,  1973  or-Barnes,  19"67  or Limerinos,  1970).
                                                                          ,4-1,
 where  Q = flow rate  in m  /s,
        A = cross sectional area of  the  channel  in m ,
        R = hydraulic  radius (m) of  the  channel  cross  section,  defined as
            the  cross  section area   A  divided by the  wetted  perimeter  P,  and
       SE = slope  of'-energy grade line
                                       14                                   -  -

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   TABLE 4.1.  WATER SURFACE SLOPES  (S), CROSS SECTIONAL  AREAS  (A), WETTED
               PERIMETERS  (P), MANNING'S ROUGHNESS COEFFICIENTS  (n),  SHEAR
               VELOCITIES  (Uj, and SHEAR STRESSES ON  THE BOTTOM OF
               CHANNEL 1, T  ,  ON APRIL  18, 1977.  (Flow rate  = 0.0320  m  /s)*
Section
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
S
0.000537
0
0.000263
0.000104
0.000208
0.000116
0.000436
0.000053
0.000312
0
0.000573
0
0.000260
0.000104
0.000210
A P n
(m ) (m)
.316 2.13 0.064

.372 2.04 0.061

.372 2.16 0.052

.307 2.04 0.057

.297 1.92 0.047

.279 1.S9 0.058

.297 1.92 0.043

.214 1.71 0.024
U T
° 2
(m/s) (N/iri )
0.028 0.78

0.022 0.48
.
0.019 0.36

0.025 0.63

0.022 0.48

0.029 0.84

0.020 0.40

0.016 0.26
* After Hahn et al,  1978b.
                                      15

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  TABLE 4.2.   WATER SURFACE SLOPES (S),  CROSS SECTIONAL AREAS (A), WETTED
              PERIMETERS (P) ,  MANNING'S  ROUGHNESS COEFFICIENTS (n), SHEAR
              VELOCITIES (u^), AND SHEAR STRESSES ON THE BOTTOM OF
              CHANNEL 1,  T ,  ON JUNE 15, 1977.  (Flow rate = 0.0379 m /s)*
Section
- 3- -
4
5
6
7
8
9
10
11
12
13
14
15
16
17
S
•^— 6^000773
0.001020
0.000505
0.000333
0.000250
0.000185
0.000908
0
0.000467
0.000330
0.001417
0.000168


0.001010
A
(m2)
0.5-76
1.77
0.520
1.81
0.548
1.79
0.465
1.64
0.465
1.70
0.353
1.65
0.399
1.56
0.242
P
(m)

3.93
2.50
3.96
2.62
4.02
2.19
3.81
2.26
3.87
2.10
3.93
2.19
3.69
1.71
n
- .148
.881
.109
.518
.081
.376
.131
0
.093
.472
.107
.318


.055
u*
(m/s)
.0396 —
.0671
.0320
.0387
.0226
.0283
.0433
0
.0308
.0378
.0485
.0262


.0375
To
(N/m }
. 1.57
4.50
1.02
1.50
0.51
0.80
1.87
0
0.95
1.43
2,35
0.69


1.41
*After Hahn et al,  1978b.
                                     16

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     The transitions between pools and riffles appeared to produce an insigni-
ficant loss compared to the roughness of the riffle sections.
     It is noteworthy that in the clear channels  (without growth) the hydraulic
headless occurs predominantly in the riffle sections.  With heavy weed growth
the contributions of pools and riffles may, however, be equal.
     The average values of Manning's roughness coefficient were  n = 0.056  on
April 18, 1977, and  n = 0.29  on June 15, 1977.  The associated measured head-
losses along the channel were 0.097 m (3.8 in.) on April 18, 1977, and 0.21 m
(8.3 in.) on June 15, 1977.  The measurements excluded the first and the last
pool.
     It should be noted that the roughness coefficients calculated for the
channel with heavy weed growth account not only for the additional resistance
to flow caused by the weeds, but also implicitly  include the effects of the
weeds in altering the channel cross section and length of flow.  The overall
pool and riffle cross sections with no area reduction were used in computing
the  'n' values.  In parts of the weedy sections the flow may have been appor-
tioned between several subsections, thus producing a divided flow with several
cross sections and hydraulic radii.
Flow Velocities
     Mean flow velocities in riffles and pools vary, of course, with flow rate
and stage.  Mean values applicable to conditions  observed on April 18, 1977
with a flow of .033 m /s (508 gpm) were:
                          Riffles:  .108 m/s  (.335 ft/s)
                            Pools:  .019 m/s  (.062 ft/s)
Velocity distributions as a function of depth were measured on several occasions
with the aid of a micro currentmeter.   Sample results are shown in. Figs. 4.4
through 4.6.  The effect of the attached filamentous algae growth on the
velocity distribution is very apparent.
                                       17

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                                          178cm

                                            B
algae
growjh
               0     10    20     30
             0 -
         E  10
         8  '5
            20
            25L
algae
growth
                       Velocity (cm/sec)
                   0     10    20    30
                0  -
                    Location A
                10
                15
               20
               25
         10    20    30
                                                                       0 -
                         Location B
10


15


20


25
                                                                                    growth
          Location C
      .Fig. 4.4. Velocity profiles in Channel  1,  riffle 5,  looking downstream.
                 Measured October  30, 1976.

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             10     20
-  5
e
f  '0

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                                                           320cm
10
o
                      Velocities
                      too  small
                      to measure
algae-
growl h
                                                                         7"
Velocity (cm/sec)

  0    25    50
                                                           0 -
                                                          20
                                                        £
                                                        u
                                                        a.
                                                        
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4.3.  SOIL AND ROCK CHARACTERISTICS
Grain Size Distribution
     Size distributions of the pool and riffle bed materials and of the sedi-
ment deposited within the first riffle section of Channel 1 were measured.
     The rock size distribution for the riffles was made on a random 325 N (73  Ib)
sample of the gravel collected from the sides of all riffles in Channel 1.
Two in. (50.8 mm), 1.5 in. (38.1 mm), 1.0 in. (25.4 mm), and 0.75 in.  (19.0 mm)
sieves were used.  The results are plotted in Fig. 4.7.
     A visual inspection of the rock material in the first (farthest upstream)
riffle of Channel 1 indicated that it contained a considerable amount of fine
sediment in the form of a mud or slurry.  No such sediment was observed in the
last (farthest downstream) riffle of Channel 1.  Permeability measurements
made in the two riffles indicated a lower permeability of the first riffle
compared to the last, as would be expected if there were sediment deposition
upstream.  The origin of the sediment accumulation is presumably the Mississippi
River water.  The first pool of each channel acts as a settling basin for
suspended sediment carried by the river.  The sediment removal in the first
pool is, however, not complete and some sediment is apparently deposited in
the rock of the first riffle.
     A sample of the sediment in the first riffle was obtained by digging a
hole into the gravel cross section and collecting samples of the gravel and
the slurry from througnout the vertical cross section.  The sediment adhering
to the rocks was later collected by washing the rocks.
     The mechanical analysis of the sediment was performed according to the
standard method (AASHO Designation:  T88-57) described in the Soils Manual
for Design of Asphalt Pavement Structures published oy the Asphalt Institute.
The resulting sediment size distribution is shown in Fig. 4.7.
     The size distribution data for the pool bottoms in Channel 1 obtained in
1975 and available at MERS were also plotted in Fig. 4.7.  The bed material
was previously sampled in each pool and a size distribution was determined
for each individual sample.  The per cents finer than  in each category were
averaged for the nine pools and the resulting size distribution curve was
plotted.  Also, the per cent finer than in each category was determined for

                                      21

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                          U S  Stondord Sieve  Numbers
                                         25  18     10
                                  O Sediment in grovel of first riffle
                                  O Upper bound for soil in pool bottoms
                                  A Average  pool soil  size distribution
                                  O Lower bound for  soil  in pool  'bottoms
                                  O Gravel from riffles
                                   I   i I I 11 ll
I   I I I
...I
           02      05    .1      2       512
                          Sediment Size  in Millimeters
          10    20
                50
Fig.  4.7.   Size distributions  for material  in Channel  1  in MBRS.

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each pool, and the highest and lowest per cents among all the pools in each
size category were plotted as upper and lower bounds for the sediment sizes.
Permeability of Riffle Rock Sections
     The hydraulic (Darcy) permeability of the rock was determined by separate
experiments for the downstream part of the last riffle in Channel 1 and for
both the upstream and the downstream part of the first riffle in Channel 1.
     In the case of the last riffle, the water level in the pool immediately—
downstream was lowered so that all flow was only- through the-rocks- and-piezo--	
metric elevations were measured to determine the water table profile along the
riffle section as a function of location and of time.  Experiments were con-
tinued for several hours.  For the downstream riffle a quasi-steady state
condition was reached.  The Darcy permeability coefficient of the rock was
found to be 18 cm/s.   With a channel flow on the order of 0.0315 m /s  (500 gpm),
the mean flow velocity through the pores of the rock was calculated to be
approximately 0.02 cm/sec with a rock porosity on the order of 0.42.
     Porosity of the rock was found by measuring void space in a container
of 19.6 liters total volume.  Average porosity from several samples was 0.44.
Soil Thermal Diffusivity and Soil Temperature in Pool Sections
     A study of soil thermal diffusivity and temperatures below the bed of the
pools was made for two reasons.  One reason was to determine if the heat
exchange between the pool water and the bed had an important influence on the
water temperature regime in the channels.  The influence was found to be
negligible.  The second reason was that aquatic biologists studying benthic
organisms desired to know something about the temperature regime in the mud.
The soil temperature regime was studied oy heat transfer analysis  (unsteady
and one-dimensional).,                 -  -              ' .-         "  •
   -  The soil - temperature profile as a function of depth and time was  predicted-
for known water temperature in the pool above the soil/water interface.  A
numerical finite difference model of the unsteady, one-dimensional heat con-
duction equation was developed  (Gulliver  and Stefan,  1980).  Measurements of
soil temperature profiles were obtained from thermistor arrays placed  in the
bed of pools 6 and 12 in Channel 1.
                                        23

-------
     Analysis of soil composition and of measured soil temperature profiles
led to the conclusion that a four-layered system had to be used:  the first
layer of the pool bed was a highly organic layer of variable depth  (0-15 cm).
It appeared that this layer had developed since the channels went into
operation and that the organic material was the residue of several growth
seasons.  The second layer (below) was a water saturated sandy loam of 38 cm
(15 in.) thickness.  This second layer was backfill material which rested
on a 5 cm (2 in.) bentonite layer which had been installed to prevent the
channels from leaking.  The fourth layer below was a dry sandy loam.  Figures
4.8 and 4.9 give cross sections.
     Several heat wave experiments were performed.  The soil surface was
suddenly exposed to heated water, after a cold period, and the penetration of
the warm front into the soil with time was recorded by the thermistor arrays.
An example of a record is given in Pig. 4.10.  Analysis of several such fronts
made it possible to refine initial estimates of soil thermal diffusivities.
     Although there were three thermal diffusivities and one layer depth to
be determined, the heat wave experiment encompassed two unsteady and two
quasi-steady periods and the problems of fitting four parameters could be
solved.  The  surface  layer thermal diffusivity and  surface layer depth
were highly interacting, but the use of unsteady periods helped resolve the
problem to a reasonable degree of accuracy.  The following soil properties
were determined by fitting predictions of the numerical finite difference
model to soil temperature measurements:
          Highly organic (surface)  layer depth = 12.5 cm (5 in.)
          Thermal diffusivities:
               Highly organic  surface layer    D = 1.7 x 10   cm /sec
               Water saturated sandy loam"   •   D "= 1.3 x 10~  cm /sec"
                and bentonite layer
               Dry sandy loam                   D = 1.3 x 10   cm /sec
               (lowest layer)
     The above thermal diffusivities were used to predict soil temperatures
in pool 12 during other heat wave tests.  A set of predicted soil temperatures
is compared with thermistor soil temperature measurements in Fig. 4.11.  A
                                      24

-------
                   Woter
                                      ^Bottom of Pool
                       \\\\\\\\\\\\\\\\\\
           Highly organic surface layer
           of variable depth               " 2.5 cm
\
/
water
sandy
f
i
saturated
loam
38 cm

O- /ft
0 	
n —
*
-5'm I0*cm f '
T >y 1
23cm
	 JT
i


                                                                36 cm
                  5cm _be_ntomte_ _  _ _ ^V^


        dry sandy loam  to end  of domain
Thermisfor  Probes
Fig.  4.8.   Soil profile below pool and location  of thermistor probes.
            Channel  2
              Channel  1
                         Dry sandy loam
          Sentonife layer
  Fig.  4.9.   Schematic cross  section of one channel pair
              drawn  to approximate scale.
                                      25

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                      Temperature (°C)
 Fig.  4.10.  Measured soil  temperature  profiles in
    ...  ,  . p^ol_fi_duxing_nea±_wave_test:.  .warming.,- ...
_„_  - -„,  . period.          -  -  ,
                          26

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                                                       Measured  Soil Temperature
                                                              O  6 cm depth
                                  24  j  25  |  26
                                  December 1977
   I   2   I  3
Jonuory 1978
Fig. 4.11. Con,parison  of  measured and predicted  (solid  lines)  soil temperatures in Pool  12  during
           heat wave test.   Notation for depth of predicted  soil temperatures:  (1)   soil  surface,
           (2)  2.5 cm,  (3)   6 cm, (4)   16 cm, (5) 28 cm,  (6)  41 cm,  (7)  60 cm, (8)  1 m.

-------
surface organic layer of 6.25 cm  (2.5 in.) was assumed.   The  standard  error  of
the predicted soil temperatures in the example is 0.48 C.
     More information on the soil temperature investigations  conducted at  the
MERS is given in Gulliver and Stefan, 1980.
Rock/Water Thermal Diffusivity and Temperatures  in Riffle Sections
     Water temperatures in the voids of the rocks forming the riffle section
were studied for the same reasons as the soil temperature profile in the pool.
It,may be recalled that the rocks are of 30 mm average size and  form a system
of high hydraulic permeability.
     The transfer of heat from the water flowing over the riffle into  the
water and rock below is potentially by the following processes.
     (a)  Horizontal flow of water through the pores of  the rock.  The
          hydraulic permeability was determined previously to be 18 cm/sec
                                                                        —4
          and the effective pore flow velocity on the order of 0.4 * 10
          to 2.5 * 10   cm/sec, assuming a porosity of 0.44.
     (b)  Vertical conduction through the water and the  rock  mass.
          Estimates of thermal diffusivity of the water  and the  rock
          as found in the literature are 5.9 x 10~  cm /sec for  dry
          gravel and 1.4 x 10   cm /sec for water.
     (c)  Vertical forced convection through the voids of the rock
          system.  This could also be looked at as a downward hydro-
          dynamic diffusion process.
     (d)  Vertical natural convection through the voids  of the rock
          system, when unstable water temperature stratification
--        occurs-
"  " "The penetration of a heat wave from the bed surface into the rock of
riffle 17 was studied experimentally from December 19, 1977,  through
January 2, 1978  (Stefan and Gulliver, 1980).
     A vertical array of six thermocouples at 2.5, 7.6,  15, 25,  38, and 51 cm
below the rock surface was installed in the center of riffle  section 17 in
Channel 1.  The location is approximately 15 m from the  upstream end of the
riffle.  The lowermost thermocouple is in the sandy loam below the rock.
                                       28

-------
 Temperatures at the six sensor locations were read once  daily during  each work-
 ing day following an artificially imposed surface water  temperature  rise.  The
 rock temperature profiles indicated by the sensors are shown  in  Fig.  4.12.
      The temperature response in the upper 15 cm  (6  in.)  appears to  be with a
 time lag on the order of only a few hours.  This rapid response  as well as the
 shape of the temperature distributions with depth suggests  that  a very effec-
 tive vertical mixing mechanism in the upper 15 cm-of _the rock exis-ta.  This.  —
 mechanism could be a hydrodynamic diffusion or forced convection process induced
 by the bed shear stress of the free surface flow "in  the  riffle section.   ~  -
      Below 15 cm depth the temperature response is delayed  but still  quite
 rapid.  It is noteworthy that between December 20 and 22 and  over a  48 hour
 period the temperatures in the rock rose by the same amount as the surface
 water temperature, namely 2 C per 24 hours.  This observation would  suggest
 that the rate of downward heat flow during that time period was  constant and
 that the sandy loam (below the rock) was the main heat sink.
      The observed rapid changes in rock temperature  profiles  cannot  be explained
 by horizontal flow through the rock.  The horizontal advance  of  a temperature
 front based on uniform horizontal flow and measured  permeability would be
 about 5 m/day in  terms of real pore flow velocity.
       Density stratification  of the  water  in  the rock iiass  is associated  with
  vertical  temperature  gradients.   Stratification may be responsible for
  the steeper  temperature  gradient  below 15  cm than above.   It reflects  a
  smaller  vertical thermal diffusivity  than  above 15 cm depth.
       During  the cooling  phase the vertical temperature profiles are more
--un-i-feem  than-during, the  heating.   This_reflects _the effect of natural  vertical
---eoRvecfcipn ,induced,bit__d,e_n.5j-.ty_.instability.   _                     -
       An  analysis of"the  data described" by  Stefan and Gulliver -(1980),  gave
                                 -3   2
  a thermal diffusivity of 3.1*10    cm  /s for  the rock/water system at depths
  between  15 cm and 38  cm  below the riffle  bed.   This value  is applicable  when
  the water temperature in the rock section  provides a stable density  strati-
  fication  (channel water  lighter  than  pore  water in  the rocks).

-------
                    Temperature, °C

                       6       8
Fig. 4.12. Vertical temperature profiles  in
           Riffle 17 during period of  rock
           temperature study.
                       30

-------
     In the upper 15 cm of the riffle  bed  a mixed  layer  appears to exist.
Water temperature in that layer is very  nearly  the same  as the channel water
temperature.
     Under unstable conditions (pore water lighter than  channel water) natural
convection takes place and thermal diffusivity  is  much increased.

4.4.  OBSERVED OPERATIONAL WATER TEMPERATURE REGIME
Water Temperature Instrumentation
     Temperature sensors (thermocouples) were installed  at the upstream and
downstream ends and in the center pools  and  riffles of each of experimental
channels 1, 4, 5, and 8.  The sensors provided continuous  water temperature
information which was recorded on four strip charts for  the four channels.
Three stations per channel were not sufficient, however,  for the analysis of
stratification, surface heat transfer and mixing.  Channel  1 was selected for
in-depth study of temperature regimes, and 21 continuous recording sensors were
installed in Channel 1 (schematic in Fig. 4.13).  Ten of the sensors measured
water temperature 12.5 cm (5 in.)  to 25 cm  (10 in.) below  the  water surface.
There were two vertical arrays of four sensors each installed  in Pools  6 and 12
which provided information on water temperature stratification  and soil tempera-
ture.  Three sensors were within  12.5 cm (5  in.) from the bottom of pools 4,
10, and 18, and one sensor 2 to 5 cm (1 to 2 in.) in the  rocks  of riffle 17.
All temperature sensors were connected to Leads-Northrup multi-channel color-
coded temperature chart recorders.   Temperatures were recorded  from November
1975 through December 1977.

Water Temperature Data Processing
    Elements
     The water temperature data processing described herein is  for"water
temperatures measured at several stations in channels 1,  4, 5,  and 8 of the
MERS.  The data processing had the following elements.
         ••  Extraction from strip charts
          •  Review and estimation of missing or faulty data
          •  Calibration
          •  Storage
                                      31

-------
      Inflow from
   Heot  Exchonger
   Channel  Nos
87654321
                                                 Legend
                                                                                                           i
 V =  vertical array of 3 probes placed at 5 and 10 in fronj channel
      bottom and IS in. from water surface             |

 M =  additional probe placed 1 and 2 in. in mud.

 K =  additional probe placed 1 to 2 in  in riffle gravel.    , ,
                                                    f
S  =  additional probes at 1,2, 3, 5, 10. and 15-20 in. in sojil(below
      pool for non-continuous soil temperature profile

R  =  addtional probes at 1, 3, 6, 10, 15, and 20 in. in gravel below
      riffle for non-continuous riffle gravel temperature  profile.  >

 n  =  probe placed at 10 in  from the gravel bottom rather than S
                                                     t
 Placement of all  other probes noted is 5 in. from bottom in both
 riffles and pools
                                                                                                                  Outflow  to
                                                                                                                  Mississippi
                                                                                                                  River
                                                                                                               19
                     Fig. 4.13.'  Thermal probe  placement in MERS experimental  channels  (four  channel pairs)

-------
These elements will be described in sequence.
    Extraction of data
     Water temperature data were extracted for four channels  including  two
hot channels, with up to 15 C above the Mississippi River temperature,  one
warm channel, with up to 8 C above river temperature, and one ambient channel
which has no heat addition above river temperature.
     For the statistical analysis, stations 2, 3, 9, 10, 17,  and 18 of  channels
4, 5, and 8, as well as stations 3, 4, 6, 12, 17, and 18 of Channel 1 were
selected.  For each station, 3-hour water temperatures beginning at midnight
of each day were read off the strip charts and hand recorded  on data sheets
(eight values per day).
    Estimation of data
     For periods during which no temperatures were recorded,  estimation of
water temperature became necessary.  This was done by one of  the four follow-
ing procedures.
     (a)  Linear interpolation between water temperatures at  upstream   .
          and downstream stations.
     (b)  When the period of missing data was only a few hours, and
          when no water temperatures were recorded for all stations,
          linear interpolation between the last water temperature
          before the gap and the first water temperature after the
          gap was used.
     (c)  When a temperature record was not available for the first
          station (or the last station),  linear extrapolation using
          temperatures from the two immediate downstream (or upstream)
         ' stations'was used.       	         •   '      "          "
     (d)  When no temperature record was  available for all stations and
          for a long duration, temperatures from another channel mul-
          tiplied by a coefficient were substituted (linear intra-
          channel transfer) .
Details on the periods of missing data, their causes,  and the procedures used
in estimating the data were documented by Fu and Stefan  (1979b) .
                                       33

-------
     Erroneous data were also found in the records.  Some water temperatures
recorded^on the strip charts were not representative for several reasons:
(a) sensor might be in the air due to low flow, (b) sensor might be buried in
the sediment, and (c)  sensor might not be recording the true water temperature
values.  Owing to these reasons, estimation of corrected water temperature data
was also necessary.  The procedure is explained in Fu and Stefan (1979b).  Periods
during which estimates had to be made are also identified by Fu and Stefan (I979b)
    Calibration
     From January 1976 through June 1976, one complete calibration and numerous
spot checks of the recorded temperatures in Channel 1 were made.  After July
1976, temperature calibrations were made approximately every month.  Channels
4, 5, and 8 were included.
     The corrections obtained from these calibrations were tabulated by Fu and
Stefan  (1979b).  Between the dates when calibrations were made, strip charts were
examined to identify discontinuities in the records.  Calibrations were considered
valid only up to these points.  Operational records and abbreviated remarks on
the strip charts were also consulted for this purpose.
     Corrections of less than + 0.2 C were ignored.  Corrections  >|0.2| were
added to the hand recorded water temperatures.  The entire water temperature
records for Channels 1, 4, 5, and 8 were stored on a magnetic tape.  No cali-
brations were applied to the estimated water temperatures.
    Water temperature data storage
     All calibrated water temperatures were stored on a nine track magnetic
tape.  The length of the temperature record of each station is listed in Table
4.3.  The magnetic tape is divided into four files (multi-file tape).  Each
file contains a temperature record of a single channel.  Within each file,
temperature records are stored in the order listed in Table 4.3.  The first
file contains temperature records of Channel 1, the second file those of
Channel 4, the third file those of Channel 5, and the fourth file those of
Channel 8.  A computer program was used to read the raw data (without calibra-
tion) , to apply the calibration and to write the calibrated water temperatures
on the magnetic tape.   More detailed information on the data tape can be
found in Fu and Stefan,  (1979a).
                                       34

-------
Ul
tn
1
1
TABLE 4.3. SUMMARY OF WATER TEMPERATURE INFORMATION
i
File , | Station
Sequence Set | Set No. in
No. Identifier Identifier Channel Order of
QN SI FI No. Storage
1 PFILED | CHANNEL 113
! 4
1 6
i 12
! 17
i 18
1
t
I
!
i
2 PFILED i CHANNEL 442
! 3
11
; ' 9
10
1 17
18
t 1 }
I •
3 PFILED CHANNEL 552
3
' 1 ' 11
9
10
17
18



i
i
' 1
i
STORED ON MAGNETIC TAPE (Cont'd)
i



Period
12/4/75
12/4/75
12/4/75
12/4/75
12/4/75
12/4/75



10/20/76
11/26/75
11/26/75
10/19/76
10/10/76
11/26/75
10/20/76

10/19/76
11/24/75
11/24/75
10/18/76
10/19/76
11/24/75
10/19/76
- 9/19/77
- 9/19/77
- 9/19/77
- 9/19/77
- 9/19/77
- 9/19/77


TOTAL
- 9/19/77
- 9/19/77
- 10/18/76
- 9/19/77
- 9/19/77
- 9/19/77
- 9/19/77
TOTAL
- 9/14/77
- 9/14/77
- 10/17/76
- 9/14/77
- 9/14/77
- 9/14/77
- 9/14/77
•
No.
of
Days
656
656
656
656
656
656


3,936
335
664
328
336
335
, 664
335
2,997
331
661
329
332
331
661
331

No. of
3 -hour
Temperatures
5,248
5,248
5,248
5,248
5,248
5,248


31,488
2,680
5,312
2,624
2,688
2,680
5,312
2,680
23,976
2,648
5,288
2,632
2,656
2,648
5,288
2,648
                                                                                TOTAL
2,976
23,808

-------
               TABLE 4.3  (Cont'd).  SUMMARY OF WATER TEMPERATURE INFORMATION STORED ON MAGNETIC TAPE
          File
        Sequence
          No.
          QN
   Set!         Set
Identifier   Identifier
    SI '          FI
         Station
          No. in
Channel  Order of
  Mo.    Storage
Period
No.        No.  of
 of        3-hour
Days    Temperatures
U)

-------
Water Temperature Data Analysis and Results
    Elements
     The water temperature data analysis as described herein included
           •  Development of a statistical analysis package
           •  Computation of a number of statistical parameters from 3-hour
              data
           •  Determination of the seasonal cycle
           •  Determination of the diurnal cycle
           •  Analysis of longitudinal gradients
           •  Analysis of water temperature stratification in the pools
These elements will be described in sequence.
    Development of a statistical analysis package
     A computer program WTEMP1, described in detail by Fu and Stefan  (1979a),
 to extract from the 3-hour water temperature data statistical information
was developed including:
           •  Water temperatures at three probabilities of occurrence
              specified by the user
           •  Maximum and minimum water temperatures in the period
              analyzed
           •  Mean, standard deviation and dimensionless skewness
              coefficient of the water temperature
WTEMP1 can handle a series containing .up to 19,200 individual water tempera-
tures, equivalent to 400 days of data from six stations in a single channel.
WTEMP1 can also nandle sliding statistic  calculations for- sample periods of
up to 7 days.  The-output is in tabular- form.
     A second interactive program WTEMP2 for computing statistics on specified
data time intervals, composite station locations etc. from daily statistics was
also developed (Fu and Stefan, 1979a).

    Computations
     Computations have been carried out for individual stations and channel
composite using weekly sliding samples.  The tabular output format from WTEMP1
is shown in Appendix H.  The complete output comprises 151 pages for Channel 1
and 126 pages each for Channels 4,  5, and 8.
                                      37

-------
    Seasonal water temperature cycle
     A graphical presentation of the statistical computer output  is  shown  in
Figs. 4.14 and 4.15.  The weekly mean, maximum and minimum water  temperatures
have been plotted for two channels and several stations.  Channel 1  was
artificially heated, and Channel 5 was not.  The seasonal water temperature
cycle can be easily seen.  The seasonal amplitude is on the order of + 15°C.
The annual mean differed by channel and station depending on the  artificial
heating.
     Water temperature fluctuations superimposed on the seasonal cycle are  either
due to irregularities in the artificial heating of the inflowing  water or  due
to weather.  Those due to heating are smoothed out along the channel.
    Diurnal water temperature cycles
     Diurnal water temperature cycles are shown in Figs. 4.16 and 4.17.  Because
the inflowing water is taken from the Mississippi River, upstream stations in
the field channels reflect conditions found in the river, modified (or not) by
artificial heating.  Because the field channels are shallower than the river,
diurnal water temperature amplitudes at the downstream end of the channels
are larger than upstream .  Amplitudes of diurnal water temperature cycles
also vary strongly with season as seen in Fig. 4.16.  Winter values  have been
on the order of 1°C upstream and 2 to 3 C downstream.  In the summer 2°C
diurnal amplitude upstream and 5 C amplitude downstream are not uncommon.

    Longitudinal water temperature gradients
     Water temperature differentials between the upstream and the downstream
ends of a channel are of interest for fish studies in the field channels.  Such
longitudinal water temperature gradients are dependent on several other hydro-
thermal parameters as will be shown by theoretical analysiVin a  later section.
It may; suffice^.here. to indicate that the- longitudinal_  AT  can be expected to
rise with the addition of artificial heat.  A greater flow rate will decrease
the longitudinal  AT.  Since the geometry of the MERS channels is fixed in
terms of length and width, the two most important controllable parameters  are
flow rate and heat  input.  Actual values of longitudinal  AT's will  then depend
 on  the amount of heat rejected to the atmosphere, which is a weather depen-
dent process.
    The daily minimum and maximum temperature difference between  the inflow
and outflow of the artificially heated Channel 1 was recorded over a one-year

                                      38

-------
   uj a-

   o
   UJ
      8-
                                      YERR(S)
              STflTION 4
      s-
      = 750
      8-1
      9
8-
Si
           itn
    n
    in
   LU-
   a
      8-
                                  i TSO      i.aa
                                YEHR(S)
              STRTION S
                               i MO      i ru
                                     rEfirHS!
Fig.  4.14. Seasonal water temperature  plots of Channel 1.   (Cont'd)
                                       39

-------
  tfl
  UJ
  o
    8-
                                            CHflNNEL 1
            STflTION 12
                                                       t sa
            —i	—r-
             I DOC      I.SO
    8-1
  in
  in

  UJ g.
  C3
  UJ
  a
     8-
  1.73)      2 000


YEflR(S)
             STflTION 17   •. Y'/W*


IM75 - a
	 1 	 * 	 1 	
°7SC 1. 000 1.250
8-,
*

' * ,"» '..• «"«••
1 	 1 	 [ ~ 1
1 SOD l.TSO 2 ODD 2 ZSO
YEflR(S)

	 1 i
2 SOD 2 TSO

  !3
  CO
  UJ
  a
     s-
            STflTION 18
                                    YEflR(S)


Fig. 4.14. (Cont'd).   Seasonal  water temperature plots of Channel 1.
                                       40

-------
                                CHRNNEL 5
  3-
  8
3
in

Bg-
   UJ
   Q
     8-
                                   YEflRtS)
              STflTION 9
                                   YERHt S)
Fig. 4.15. Seasonal  water  temperature plots of  Channel 5.
                                                           (Cont'd)
                                    41

-------
     B-i
     ;
     8-

     R
   3

   IT)
  e
  a
     8-
                                    CHflNNEL 5
             STflTION 10
             —T~
             i oao
                   —r-
                   1 23)
     8-1
   a
   Si


^

tn
_j
LU  g.

u  9

O
UJ
Q


   8-
                                    1 7S)      J 000

                                  YEflR(S)
              STflTION  11


°TSQ I 000 1.291 I 500 l.TSO
8-
9
YEflR(S)
1
2 000


2.250

I
2.500

1
Z.7SO

                                      I 750      I 000

                                    YERR(S)
Fig.  4.15.  Seasonal water  temperature  plots of Channel  5.   (Cont'd)
                                      42

-------
  in
  ^>

  to
  C

  UJ

  Q
     8-
                                 CHflNNEL 5
             STRTION  18
                                                             —r~
                                                             2 UO
	1

 2 73
—r~
 1.2SO
                                     I.TSD

                                   YERR(S!
Fig. 4.15.  (Cont'd).   Seasonal  water temperature plots of Channel 5.
                                     43

-------
SIllllQll 3
                                                     STHIIUN 12
    ClintltlEL I

1/13/76 fO l/2b/76
                                              -Leu
                                                                  • Ol     • Ol
                                                                    onus i
                                                     S1RIION 17
                                                                  tOt     too
                                                                    OflTIS)
                                                     SlflllUII IU
                utmsi
                                                                    OHMSI
        Fig. 4.16.  Diurnal  water  temperature  plots of Channel l.(Cont'd)
                       1/13/76  to  1/26/76

-------
                                                    OHYISI
Fig'. 4.16.  Diurnal water  temperature plots of Channel 1.
            4/25/76 to  5/8/76
(Cont'd)

-------
.£>.
a\
                                                                                               CIIHtllllL I


                                                                                            II/U//6 10 11/22/76
                                   unrisi
                           Fig.  4.16.   Diurnal water temperature plots of Channel 1.  (Cont'd)
                                         11/9/76 to  11/22/76

-------
binilUII 3
               ofmsi
SIMIOH S
                                                    SlflllUN
                                                    I •>     4 flu
                                                    SlflHON 17
   CHHNNLL  I

6/17/V/ TO b/JO/77
                                                                        • oo     ti to
                                                                   oim si
               DHYI5I
                                                                 tta     »»
                                                                   onrisi
        Fig.  4.16  (Cont'd).   Diurnal water temperature plots of Channel  1.
                                6/17/77  to 6/30/77

-------
                                                                                 ClUUltttL S

                                                                              1/19/77 10 2/1/77
tf a
                                                                       DfiTIS)
                                                         smnmj is
                      oiirisi
                                                   <*ai     *,o>
              Fig. 4.17.   Diurnal water temperature plots of Channel 5.   (Cont'd)
                           1/19/77 to 2/1/77

-------
51 fill UN 2
       40)     ta
               OHYISI
SiniiON 3
               onris i
                onrisi
                                                     sinnuii ID
                                                     STfHION 17
   CIIIIMKEL S

1/19/77 TO S/2/7/
                                                     JOU     <0u     t OO     tOO
                                                                    onnsi
                                                                         • OU     !• U
                                                                     DfiYI SI
                                                     SUII ION 10
                                                                     onrisi
        Fig. 4.17.   Diurnal water temperature plots of Channel  5.   (Cont'd)
                      4/19/77 to  5/2/77

-------
LH
O
                                                                •la,
                                                                8
                                                                      bIHIIUII 10
                                                                       siniioii
   ClllVMIH  5


11/9/Vb 10 II/2.WO
                                                                                      DI1TISI
                                                                           sL^/v
                                                                                                       u OJ
                                                                                      onrisi
                                                                       SIIIIIUII 18
                                  UHllbl
                                                                                                  I-1
                        Fig.  4.17.   Diurnal water temperature  plots of Channel  5.   (Cont'd)

                                      11/9/76 to  11/22/76                                    ,   '

-------
5IIII1UN 2
      • 04     «0
bullion 3
bullion U
               OHTISI
                                             P. a-
                                             H 8
                                             y n
                                                      SUIT HIM  10
                                                   CIIIINIIlL 5



                                                //I3/7V 10 7/2b/7/
                                                oj     i at
                                                                      oiirisi
                                                      simian i/
                                                                      omrisi
                                                      SIH1IUII 18
                                                                                      \_.
                                                                      iiirrisi
    Fig.  4.17  (Cont'd)
Diurnal  water  temperature  plots  of Channel 5,

7/13/77  to  7/26/77

-------
period.  Complete results are given in Hahn et al, 1978a.  Table 4.4 summarizes
the monthly mean and standard deviation of the longitudinal temperature differ-
ences.
     Daily diurnal water temperature variations at the outflow of Channel 1
were also recorded over a one-year period  (Hahn et al, 1978a).  The monthly
mean and standard deviation of these values are also given in Table 4.4.  It
should be emphasized that Table 4.4 gives the characteristics of a heated
channel, meaning that inflow temperatures were increased up to 15 C above the
temperature of the Mississippi River water.  Longitudinal temperature gradients
and diurnal variations are not as large in a channel with ambient unheated
inflow.

    Water temperature stratification in pools
     It was found that the pool sections would frequently become thermally
stratified.  Spot measurements of vertical water temperature stratification
in Channels 1, 5, and 8 were made using six thermistors attached vertically to
a point gauge and connected to a telethermometer.  The point gauge was attached
to a cross bar which spanned the width of the channel.  Vertical adjustment of
the point gauge enabled measurement of a complete temperature profile.  An
example of the vertical stratification measurements is shown in Fig. 4.18.
Typically a thermocline would form at about 60 to 70 cm from the surface.  The
lowermost 15 to 20 cm would have strong temperature gradients.  Additional
measured water temperature profiles can be found in Appendix B of Hahn, 1978.
     A frequency analysis of temperature stratification in pools 6 and 12 of
Channel 1 was made for the calendar year 1976.  The continuous temperature
records of a vertical array of thermocouples were analyzed on a day by day
basis.  Daily tabulations of the number of hours of stratification in the
ranges'0.5°C < AT < 1.0°C, 1.0° < AT < 2.0°C,.and  AT > 2.0°C were made.  AT
is the vertical temperature differential.   The magnitude of  AT  was determined
from the temperatures measured by the top and bottom thermocouples in each
pool.  If stratification occurred for one hour or more in a given pool, the
day was classified as a day with stratification.  If the total number of hours
of stratification in a particular range was less than one, zero hours were
recorded.  Stratification was observed somewhat more frequently in the down-
stream pools than the upstream ones.  Water reaching the downstream pools has
had a longer exposure to solar radiation than water in the upstream ones.  An
annual summary frequency analysis of the stratification data is given in
Table 4.5.   A breakdown by months is shown in Figs. 4.19 and 4.20.
                                     52

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    TABLE 4.4.   MONTHLY MEAN AND STANDARD DEVIATION (a) OF DAILY MINIMUM
                AND DAILY MAXIMUM LONGITUDINAL (SPATIAL) TEMPERATURE DIFFERENCE,
                AND OF DIURNAL (TEMPORAL)  TEMPERATURE DIFFERENCE AT THE
                OUTFLOW FOR A HEATED CHANNEL 1, DECEMBER 1975 - NOVEMBER 1976
Month
— -
December (1975)
January (1976)
February
March
April
May
June
July
August
September
October
November (1976)
Minimum
Longitudinal AT
' -Mean
5?f -
6.0
4.6
3.2
1.9
1.8
2.7
1.7
0.9
1.7
0.9
1.0
"- <°c)
" 2.0
1.5
1.3
2.7
1.8
1.3
1.5
0.9
1.1
0.7
1.0
1.0
Maximum
Longitudinal AT
Mean
" 8.0
9.5
7.7
6.9
5.6
5.7
4.3
4.0
4.5
3.5
3.4
5.7
oa
2.5
1.8
1.7
3.1
1.6
1.4
1.6
0.9
2.0
0.9
2.6
3.9
Diurnal
AT at Outflow
Mean
1.9
2.3
2.5
3.4
5.3
4.4
4.0
3.5
3.7
2.9
2.9
2.5
a
0.9
1.0
1.3
1.6
1.9
2.2
0.0
0.8
1.5
1.2
1.2
2.4
TABLE 4.5.  FREQUENCY ANALYSIS OF TEMPERATURE STRATIFICATION IN CHANNEL 1
            (January 1 - December 31, 1976)

Pool

NO.
- % days with stratification. ._ _6__.
12
"-" %- hours' with- stratification- - 6" -
12
\

o
> 0.5 C
48
34
-13 - -
11
/ertical AT

o
> 1.0 C
. 29- __
26
6 -
8


o
> 2.0 C
9
16
_ 2 ' ,., "...
3
                                    53

-------
     25
   20
£
o

-------
   100
   80
   60
   40
   20
o
o
     0
5  ioo
   80
   60
   40
 Pool 6
Pool 12
       D   J
      1975
              M   J    J
                  1976
  Fig.  4.19.   Per cent days with stratification  AT > 1.0 CO
              and  AT > 2.0°C A in Channel 1, pool 6 (top)
              and pool 12 (bottom).  Average channel flow
              rate was 0.0175 m3/s until August 1976 and
              0.0317 m3/s afterwards.
                          55

-------
o

    50 n
    40
    30
    20
     10
     0
£   50
    40
    30
    20
     10
        I    I
Pool 6
               Pool  12
        D   J
    •"-  1975 -
    M
M
 J   J
197-6
0-
     Fig.  4.20.   Per cent hours with  stratification    T  >  1.0  C O
                 and   T > 2.0°C  A in  Channel  1,  pool 6 (top)
                 and pool 12  (bottom) .   Average channel flow
                 rate was 0,175 m3/sec  until August 1976 and
                 0.0317 m3/sec afterwards.
                           56

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                                   SECTION 5
          A STUDY OF LONGITUDINAL DISPERSION IN THE MERS FIELD CHANNELS

5.1.  BACKGROUND                   ~.        -       -      .             .   _  _
     The flow field in the MERS" channels-is vecy non-unS-form and" mean flew^—--"•
velocities are very small.  Water moves through the MERS channels  in a way
far different from the movement of a piston in a cylinder (plug  flow). Water
may move faster in the center of a riffle or a pool than at its  edges.  Trans-
verse and/or vertical mixing takes place between the faster and  the slower
water masses.  Vegetation is present in pools and riffles in the summer.
There is a weak jet effect at the transition from the riffles to the pools.
In the pools water masses may be entrapped near the banks.  There  can be
wind and there is intermittent stratification in the pool.  As a result of
all these interacting processes, heat or material contained in the water will
spread out longitudinally along the channel.  It was believed that the effect
of longitudinal spreading had to be incorporated in the water temperature
model.
     Since a detailed study of the very complex low velocity channel nydro-
dynamics was not part of the research objective, the water temperature simula-
tion could be based on two conceptually different models.
      (a)  a tanks in series model with an adjustable residence time
          parameter
      (b)  a.uniform .channel flow model._with-a longitudinal dispersion    .
          term                      -                  -         -         - -
     The latter approach was chosen arbitrarily because it was believed and
later verified by the model results that the ooserved channel water tempera-
ture dynamics could be well predicted by a diffusion equation.   The term
longitudinal dispersion coefficient is used herein to describe a bulk coeffi-
cient which lumps the effects of all the processes mentioned above.  It
might also have been termed a bulk or hydrodynamic longitudinal  diffusion
                                     57

-------
coefficient.  To use separate coefficients for riffles and pools was
con-sadered but the frequent transitions and short lengths of  these
elements made it advisable not to use this approach.
     The use of a diffusion equation to describe longitudinal mass  trans-
port in a channel is only justified after the initial convective period
as shown by Fischer (1967). The MERS channels begin with a pool into
which water is discharged from a weir producing a very well mixed up-
stream condition.
     The mean residence time of the water is anywhere from 10 to 30
minutes depending on flow rate.  The convective length estimated from
the relationship
     with   i   1.8 m for a pool
            h   0.8 m for a pool
            n   0.1 (0.06 to 0.3}
            g   9.8 m/sec

gives a value of approximately 5 m or far less than the length of the
first pool (30 m).  It can therefore be considered that the convective
length does not reach beyond the length of the first pool.
     A study of longitudinal dispersion in the MERS field channels was
made for two reasons.   (1)  A longitudinal dispersion coefficient was
needed in the unsteady channel water temperature model to be discussed
in Section 7, and (2)  the size of the MERS channels is intermediate
between laboratory flumes and full-size canals; size,is an important
factor for longitudinal'dispersion and no"studies had ever been made on
a system of that intermediate size.
     Longitudinal dispersion was first studied analytically in pipe flow
by Taylor (1954) and was later applied to open channel flow by Elder  (1959)
For a straight, two-dimensional channel Elder obtained

                            Dr = 5.93 h u.                        (5-1)
                             Lj           *
                                   58

-------
where  h  is channel depth and  u^  the shear velocity.  Experimental verifi-
cation of Eq. 5-1 by Elder (1959), Fischer (1968), Thackston and Krenkel  (1967),
and Sayre and Chang (1968) has indicated values of the constant from 5.3 to
15.7 for various flow and straight channel conditions.
     Elder's equation, however, is not generally applicable to natural streams
and larger channels in which dispersion coefficients are much larger than
those predicted by Eq. 5-1.  Fischer proposed that in natural streams velocity
profiles and transverse mix-ing are dominant in determining longitudinal
dispersion.  Thus, the longitudinal dispersion coefficient depends upon
shoreline configuration, bends, and bed formation, as well as the stream
velocity  (see e.g. Day, 1975).
     A considerable amount of research on longitudinal dispersion in laboratory
flumes and in natural streams has been reported since the above cited early
studies.  A recent summary of Fischer et al (1979) lists some of the investi-
gators who have contributed analytical or experimental information.  Prior
reviews were given by Ditmars (1974) and Fischer  (1973), El-Hadi and Davar
(1976).
     The prediction of longitudinal dispersion for a stream of given geometry
without some form of field measurements of velocity profile or dye dispersion
is still a difficult problem.  Relationships based on geometrical and hydrologic
stream characteristics were proposed, among others, oy Bansal (1971), McQuivey and
Keefer  (1974), Jain (1976), Fischer et al (1979), and Liu and Chen (1980).
These relationships are of a semiempincal nature, e.g.,

     Liu and Chen:         D. = (0.27 to 1.25) u_ B2/h
                            LJ                   *

  -- Fischer: • —  	O -- 0.011 U 2 ~B2/hu.   -  -~  —"
               --            ]_, -                 *

where"  D  = longitudinal dispersion coefficient,     "" '      ~   ~
         L
         U = mean velocity,
         B = stream width,
         h = mean stream depth,  and
        u^ = shear velocity.
                                       59

-------
      The channels investigated in this study do not have the accentuated lon-
 gitudinal mixing characteristics of natural streams caused by meanders and
 large widths.   They are  also very different from laboratory channels.  Abrupt
 changes in cross sectional  areas from "riffle"  to "pool" sections occur every
 30 meters (100 ft).  The parabolically shaped pool sections are 4 m wide and
 approximately  1 m deep.   The repeated expansions and contractions in flow
 would be expected to affect  longitudinal dispersion.
   --  At elevated velocities longitudinal mixing is enhanced by ]et effects of
 the-flow-from-the raffle sections into the. pool sections.  Flow streamlines
 which could be expected from such }et mixing are-sketched  in  Fig.  5.1.   Lomax
 and Orsborn (1971)  studied the effects of jet mixing in a small, experimental
 pool of circular shape  and constant depth.   A schematic of a measured outflow
 concentration curve is  shown in Fig. 5,2.  Inflow started at  t = 0  with a
 concentration  C   in the  pool.  Concentration of the inflow was  C = 0.
      The pools at the Monticello Field Station have a length of nine times
 the width and very low  flow velocity.  This confines ;jet mixing effects to
 the upstream portion of each pool and reduced its significance.  Jet mixing
 was therefore evaluated as part of the longitudinal dispersion coefficient.
      Dispersion in the  MERS channels can also be affected by wind mixing,
 plant growth,  stratification and/or natural convection in the pools because
 the mean flow velocities in the pools are only on the order of 1 cm/sec.  The
 measurements and the analysis integrated all those effects.

 5.2.  METHOD OF LONGITUDINAL DISPERSION COEFFICIENT DETERMINATION FROM
       TRANSIENT WATER TEMPERATURES
      The contribution of longitudinal dispersion to longitudinal water tempera-
..ture profilss.-increases with the transient  character of water temperature.
 The effect of longitudinal dispersion "is'most evident "when" a tempeFature pulse""
 or  a front of  elevated  or  depressed temperature moves downstream.   In this
 section,  temperature fronts will be related to longitudinal dispersion theory
 and used to estimate longitudinal dispersion  coefficients  in  the MERS experi-
 mental channels.
      The longitudinal dispersion coefficient for natural streams is often
 determined from an instantaneous infection  of a conservative tracer.  The
 one-dimensional mass transport equation for the tracer is
                                       60

-------
                                        Pool
            Riffle
Fig. 5.1.  Schematic  streamlines at transition  from riffle to pool  in
           Monticello experimental channels  without (above) and with
            (below)  transverse winds.
                                 Ideal  longitudinal dispersion curve
                                         Observed jet mixing in pool
     Fig.  5.2.   Scnematic outflow concencration curve for  net mixing
                in experimental  pool  (after Lomax and Orsoorne,  1971)
                                 61

-------
 with solution for an instantaneous injection
 where   C =• tracer concentration (M/L ),
         M = mass of tracer injection  (M),
         A = channel cross-sectional area (L ),
         U = cross sectional mean flow velocity (L/T),
         x = distance from point of injection (L),
         t = time from moment of injection (T), and
        D. = longitudinal dispersion coefficient (L /T).
         L
      The use of Eq. 5-2 assumes that the shape of the tracer cloud will be
 Gaussian.  By the method of moments, or by a routing method, the longitudinal
 dispersion coefficient between two points may be found.  More comprehensive
 details of  D   determination from tracer pulses in natural streams are given
 by Godfrey and Frederick (1970), among others.
      In the MERS experimental channels water temperature was used as a tracer
 to estimate longitudinal dispersion coefficients.  The most readily obtainable
 trace, however, was not a heat impulse but a temperature front.  Such fronts
 could be obtained  by  turning  on or  shutting  off the  heat  exchanger  in  the  feed
 line to Channel 1.  (See  Fig.  5.3 for examples.)
      A longitudinal dispersion coefficient can be- accurately determined  by
"-routing the temperature front downstream and adjusting  D   to minimize the
                                                          L
 error in measured and predicted water temperatures.   The analytical solution
 for a temperature front assuming no sources or sinks is
                         9=| Erfc  (x-Ut)/(4DTt)"'"|                   (5-4)
                                      62

-------
                  10
O1
uf
               _  6
              0°
               OJ
               ex
                                                  I
I
I
                             50       100       150       200       250

                                                     Distance Downstream (m)
                  300
                  350
400
                       Fig.  5.3.   Temperature fronts in MERS channel 1 on November 17, 1976.   Front

                              !    inception is at t=0.

-------
where   0 = „}_[ _ *}„(  and                                             (5-5)

                                                  .2
                                      v^T  f
                                    '  ~  J
                        Erfc(g) = 1 -  rr   I   d"Q   dQ
Erfc is the complementary error function.  Measured values of  9(x,t) were
compared to values computed by Eq, 5-4.,  The D  value which minimizes the
error between computed and observed  Q  is the "measured"  D   for the test.
     Heat transfer may also affect the longitudinal dispersion coefficient
calculated from a temperature front.  The order of magnitude of this error was
estimated by computing a temperature front with and without heat transfer using
typical values of channel depth and width, flow rate, and longitudinal disper-
sion coefficient, with upper limiting values for the bulk surface heat transfer
coefficient, and the upstream temperature front (Gulliver, 1977).  The computed
results indicate that surface heat transfer has no appreciable effect upon the
longitudinal dispersion coefficient determined by the routing method.  Fig, 5.4
illustrates why this should be expected.  Longitudinal dispersion can be di-
rectly visualized as the spread between the 0.16 and 0.84 values of dimension-
less concentration  Q.  Surface heat transfer reduces the values of  0  but not
appeciably the longitudinal spread.

5.3.  FORMULATION OF DIMENSIONLESS LONGITUDINAL DISPERSION NUMBERS
     Many investigators have expressed longitudinal dispersion by a dimension-
less number, D /u^ h , where  u^  is bottom shear velocity.  For the MERS
channels flow rate, rather than water surface slope, is more accurately mea-
sured.  With
and
where   f.  = bottom friction factor for entire channel,
         b
         h = mean depth of channel, and
         n = Manning's coefficient for the channel,
                                      64

-------
                        084 —
                      Q
en
ui
                                                                            with surface
                                                                            heoi tronsfer
                                                 without surface
                                                 heot  trorisfer
LM 04 m/sec
        2
                                                                                D(_- 28m /sec
                                                                                 x= 427m
                                                                                           -2    -10 -I
                                                                                Ks=45 col cm  doy  C
                                                                         T(CO)-T(o) = 20°C(at x=0)
                                                                                                                      8
                                                                                                                    CD
                        016 -
                                                       234
                                                       Time from  Pulse Instigation  (hr)
                            Fig.  5.4.  Computed temperature fronts  (normalized)  which  occur at
                                        location 17 in  Channel 1 with and without heat  transfer.

-------
one derives for the dimensionless expression


                                           \g  n /

where  Q = flow rate and   B = mean surface width.  For constant mean channel
depth  h  and constant Mannings  'n'

                                   Dt, B     DL
                              D^=_L_  « -_£-.    	  _           (5_7)

     For  a  stream or  channel of  variable  cross  section,  Bansal (1971)  proposed
 a dimensionless local dispersion coefficient

                              V = I  ITI -   An L"                       (5-8,
                               B    o  h U     AQ

 where    U = local cross sectionally averaged flow velocity,
         U = average flow velocity, U,  over stream reach,
         h = average depth over stream reach,
         B = average width over stream reach,
         A = average cross sectional area over stream reach,
         A = local cross sectional area,  and
         Q = flow rate.

     D* and  D *  represent different expressions of the dimensionless
               5
 longitudinal dispersion coefficient for  a channel of variable morphology.

 5.4.   RESULTS OF TEMPERATURE ROUTING TESTS
      Five  recorded  temperature  fronts  were"routed through the MERS" channels
 to determine  the  longitudinal dispersion  coefficient   DT.   These five events
                                                        L
 were  selected by  three criteria:   1)   the temperature  drop or increase had to
 be strong  enough  to be accurately  traced  as it moved downstream, 2)  external
 conditions such as  stratification,  ice cover,  or  algal mats on the water  sur-
 face  which would  alter the computed dispersion coefficient had to be absent,
 and 3)  large  diurnal variations or  other  transient water  temperatures except
 for the temperature front had to be absent.  The  data  for   0, channel morphology,
                                       66

-------
and travel times are given in Appendix A.  Temperature records from 5, 6, or
7 stations were available.  Values of  0 computed from Eq. 5.4 were compared
to measured 0  values (for  0 > 0.05 only).  Values of  D.  were chosen
                              —                          Li
successively until the error between computed and measured  0's  was minimized.
Below this range estimates of  0(x,t)  were considered to be more charac-
teristic of entrapment rather than longitudinal dispersion.
     A dispersion coefficient, representative of the entire channel, was
calculated for each experiment using the temperature front data from all sta-
tions and the corresponding equation 5-4.
     Each set of data was reduced for four  D   formulations:  (1) D. = constant,
                                  — —        "           _          "
(2) Dr = D* Q/B, (3) D.  = D*  QA/(A B), and (4) D  = D*Q/B .  Results are given
     L                Ll     D                    Ll
in Table 5-1.
     The D  formulation which is most applicable may be selected by computing
          LI
and comparing ratios of the standard deviation of the fitted coefficients to
the mean of the five tests.  These ratios represent the relative spread in
fitted coefficients.  Numerical values are shown in Table 5-1, last line.  The
dimensionless coefficients  D*  and  D*   represent about equally well the
                                       a
longitudinal dispersion for variable geometry and both are better than the
constant  DT.  The choice between  D*  and  D*   remains purely arbitrary.  The
           L                                  o
reason for both coefficients giving equally good results will be examined in
the next section.
     Finally, the small standard errors and the consistency of the results
indicate that the temperature front approach to determining longitudinal
dispersion coefficient is valid and practical.

5.5.  EFFECTS OF VARIABLE CROSS SECTIONAL AREA ON LONGITUDINAL DISPERSION
     The subdivision of a channel into a series of-pools of long residence
time connected by riffles of short residence time makes the longitudinal
dispersion almost entirely dependent upon the mixing processes in each pool
and the number of pools.  The processes are complicated and include:
      «  jet-like mixing at the transition from riffle to pool
      »  flow through the pool guided by vegetation and wind
      «  stratification effects.
It was not part of this project to analyze the motions in a pool in detail.
                                     67

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                 TABLE 5-1.   LONGITUDINAL DISPERSION IN MERS-CHANNELS FROM TEMPERATURE FRONT DATA
o>
co


Date
of
Experiment
11-17-76
11-18-76
11-22-76
12-06-76
12-14-76
Mean
S.D.
S.D.

Mean
*Standard error



Date
of
Experiment


11-17-76
11-18-76
11-22-76
12-06-76
12-14-76
Mean

r\
Flow L

3 2
(m /sec) (m /sec)
.0349 0.100 (.0142)*
.0382 0.095 (.0084)
.0373 0.100 (.0152)
.0394 0.124 (.0172)
.0428 0.128 (.0106)
0.109 (.0131)
0.015

0.140

•
TABLE 5-2. AVERAGE POOL AND RIFFLE


D. (l)=Const DT (2) =
L Li
DL (pools)
2 2
m /sec m /sec
0.100 0.099
0.095 0.093
0.100 0.100
0.124 0.124
0.128 0.124
.109 .100
D B
L
Q


9.3 (.0143)*
8.0 (.0082)
8.7 (.0153)
10.3 (.0168)
9.6 (.0108)
9.2 (.0131)
0.88

0.095


D FROM TEMPERATURE
L

D* Q/B
5 (riffles) D
L
2
m /sec
0.174
0.164
0.176
0.219
0.217
.190
D A B D
~ * L
B fiA


4.8 (.0136)* 7
4.4 (.0095) 6
4.9 (.0153) 7
5.6 (.0182) 8
5.3 (.0103) 7
5.0 (.0134) 7
0.46 0

0.093 0


FRONT ROUTING TESTS

JL
DL(3) = DB QA/(A B)
v (pools) Dr (riffles)
Ll Li
2 2
m /sec m /sec
0.102 0.026
0.102 0.026
0.114 0.029
0.135 0.034
0.139 0.035
.118 .030
B
L
Q


.55
.56
.07
.30
.88
.47
.68

.091
















-------
      The measured longitudinal dispersion coefficients  D* (Table 5.1) are
 of the same order as  those  reported by Fischer (1973)  for laboratory channels.
 This suggests that the  combined effects of pool mixing and pool number were
 comparable to the effects of advective motion and transverse mixing in a
 straight channel.
      That the pools dominate the effective longitudinal dispersion can be
 seen from an expression for the flux T of material in an open channel.
                                             3C
                                T = 0° - ^L i^                           <5^9)

 The advective flux QC in riffles and pools are comparable since Q and C are
 the same.  The dispersive flux is, however, a function of cross sectional
 area A and D .  The cross sectional areas of the pools are three to four
             L
 times those of the riffles  (Table 4.2).  The dispersive transport in the
 pools is therefore dominant over the dispersive transport in the riffles.
 It is for this reason that  in Table 5.2 for all five experiments, the disper-
 sion coefficients in  the pools are comparable, whereas the riffle values are
 not.  (The values in  Table  5.2 are computed from  D*  and  D*   values in
                                                              B
 Table 5.1 using riffle  or pool values of B and A.)

 5.6.  COMPARISON WITH OTHER LONGITUDINAL DISPERSION MEASUREMENTS
      If the mean flow velocity  U = Q/A in  D*  is replaced by the shear
 velocity   u^ , a comparison of these results with the dimensionless longitudinal
 dispersion coefficients, D/(u.h), cited by Fischer (1973) is possible.  Field
                            L   *
 measurements on the MERS experimental channels have indicated that  u*/u=0.55
 for these channels.  The hjgh value of  u^ /U  is misleading, however, when
 compared to the longitudinal dispersion coefficient.  In the MERS channels
~ffio'st~of the «ater~surface-"drop-oecurs- in the r if fie-sections.--In fact,  - - -•
 water surface slope in  the  pools is so-smalt that it-cannot- be- measured.--- - -   -  .
      As shown in the previous section,  longitudinal dispersion occurs predomi-
 nently in the pool sections.   Thus the  dimensionless coefficient,  D /u^h ,
 compares  u   representing  surface slope in the riffle sections' and  D
            *                                                          L
 representing longitudinal dispersion in pool sections.  One would expect
 this value to oe smaller  than for most  natural channels.   For the mean value
 of  D* = 9.2,
                                      69

-------

This value can be compared with others cited by Fischer  (1973) .   It  is  found
that the value given here is in the range of rectangular laboratory  channels
with smooth sides, in which longitudinal dispersion  is much  less  than  that
found in natural channels.  This is noteworthy since the geometry of the MERS
channels is very different from a laboratory flume.

5.7.  EFFECT-- OF ROUGHNESS- (MANNING-1 S 'n-J-)- ON- LONGITUDINAL DISPERSION- IN   _   __
      THE MERS CHANNELS                               ..... ~
     The mixing processes in the pools of the MERS channels  are not  very de-
pendent on Mannings 'n1 values.  Vegetation may be a factor, but  it  is  doubtful
that the relationship for shear flow in channels have much significance. Changes
in Mannings 'n1 caused by seasonal variations in vegetation  are therefore not
expected to have much significance on the longitudinal dispersion coefficients.
     The longitudinal dispersion coefficients reported in Table 5.1  are for
late fall/early winter conditions when vegetation was still  present, although
not as extensive as in mid-summer.  Mannings 'n1 values in November/December,
when the measurements were made, are probably close to a seasonal average.
                                      70

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                                  SECTION 6
      HEAT TRANSFER ACROSS THE WATER SURFACE  IN THE MERS  FIELD CHANNELS

6.1.  BACKGROUND
     Net heat transfer across an air-water interface is the sum of several
components.   The source term in Eq. 1-1 may'be written as

                             S = H  - H. - H  -H                       (6-1)
                                  S    I    e    c
where  S = net heat flux per unit surface area,
                                                                         — 2 —1
      H  = net shortwave  solar radiation entering the water surface  (EL  T  ),
      H5 = net long wave radiation leaving the water surface,
      H  = energy leaving the water surface due to evaooration, and
       e
      H  = energy convection from the water to the air.
       c
Many different empirical, semi-empirical, and deterministic relationships to
determine the terms of Eq. 6-1 have been developed.  Paily, Macagno, and
Kennedy (1974a)provided a detailed summary.  Only the equations to be used in
this application will be given here.  The parameters required to compute the
net heat transfer are temperatures (water, air, and dew point), barometric
pressure,  solar radiation, cloud cover, and wind velocity.  In this study
the effect of wind direction on heat transfer in the MERS channels was also
investigated.

     A  separate analysis of each term  in  Eq.  6-1 results  in. a  net  heat  flux
with nonlinear dependence on water temperature.  In order to reduce complexity
in  analytical derivations and numerical computations, methods  of computing heat
flux as a linear function of water temperature have been  proposed  by  Edinger,
Duttweiller, and Geyer  (1968), Brady,  Graves  and Geyer  (1969), Dingman  and Assur
 (1967), TVA  (1968), Yotsukura, Jackman, and Faust  (1973), Paily, Macagno, and
Kennedy (1974b), Jobson and Yotsukura  (1972)  and others.   The  main drawback

                                    -   71        "

-------
 to the.linear models is that they are only valid over a limited water tempera-
 ture range.  Each of these methods may be expressed in a formulation first
 proposed by Edinger, Duttweiler, and Geyer (1968).  Edinger, et al introduced
 a hypotehtical equilibrium temperature, T  ,  and proposed that the net heat
 flux across an air-water interface may then be expressed as

                               S = -Ks  (Ts - TE)                         (6-2)

where.  T   is water surface temperature and  K   is a bulk heat transfer
        S                                     S
coefficient at the watex surface.  Equation 6-2 indicates that net heat
transfer will be small if (a) water surface temperature is close to equilibrium
temperature and/or (b)  K  is small (calm wind, high relative humidity, etc.).
                         S
T  and  K   are indicative of water temperature response to weather conditions.
 D       S
     The MERS experimental channels are typical of many small streams and
canals in that large diurnal variations in temperature occur.  These diurnal
variations are of interest for three reasons.
     (a)   The diurnal temperature maxima and minima affect the channel eco-
          system studied by other investigators.
     (b)   Currently available water temperature prediction models use
          coefficients and time scales appropriate for deeper waters
          (typically one day).  Water temperature analysis at much
          shorter time scales (3 hour) has not been much explored.
     (c)   Wind sheltering of the water surface in the MERS channels
          by the banks is a strong possibility and needs to be
          explored.
Thus, predicted temperature on less than daily time scales are required, and
the heat transfer equations and"tlme scale- of. daia input are chosen accordingly„
6.2.  NET SHORTWAVE (SOLAR)  RADIATION
     Essentially all shortwave radiation is from the sun to the water body
(either direct or diffuse).   In this study solar radiation is continually
measured as a weather parameter and net shortwave radiation is expressed as
the difference between (measured)  incoming and (estimated) reflected radiation,
                                       72

-------
or
                                 H  = H   - H                            (6-3a)
                                  s    si    sr                          v     '
                                 H  = H  (1-r)                           (6-3b)
                                  O    O J.
where  H   = incoming  solar  radiation (EL   T  ),



       H   = reflected solar radiation,  and



         r = total  reflectivity o£ the water surface.
Anderson  (1954) proposed  an  often used equation for total reflectivity  of  a


water surface,



                                   r = A a8                               (6-4)




where   a = solar angle in degrees, and


  A and B = constants  depending upon cloud cover.



If time increments of  one day or greater are of interest, the  relations of


Koberg  (1964)  for  H    are  more appropriate.  Brady, Graves,  and Geyer (1969)


calculated A and B as


                               Q  *

                   A = 2.20  + -7—	(C °'7 - 0.4)2/0.16                (6-5)
                                4 • U       C





                                C °'7

                   B = -1.02 +  !; ,   • + (C °'7 - 0.4)2/0.64               (6-6)
                                 lo .0     r




where  C  = 1  - H  /H   = "Cloudiness ratio/" and
        r        si  sm


      H   = solar radiation  which would occur with clear skies.
       sm


Ttie-se- ate-obv-iously -empirical-equations.— The -solar-angle- may-be .-determined	


from,  the.,following equations .as-J-is.ted,~in-PaiLy-_et..al.-il_^74^._._-._ ..—	
                   sin a  =  sin  $  sin fi  + cos   cos fi  cos(h)           (6-7)




where   $ = geographic latitude (radians)


        iS = declination  of the sun (radians)



            23.45 TT      \2 IT   ,,__   1                                   ,.  Bi
                     cos  TTT   (172-D)                                   (6-8)
              180          365
                                      73

-------
          D = day of  the year  (Jan.  1=1), and
         ,h = hour angle of  the  sun  (radians)
            = n  (day  hour -  12)/12                                       (6-9)
For this particular application,  however,  the  average value of sin a over a
time increment is desired, rather than an  instantaneous value.  Thus, the
solar angle which will be used is

                             ct(rad)  = sin    (sin a)                      (6-10a)
where                                       /. h2
                          sin a   = .   .    / sin a dh
                                   Vhl
                ...         .       . f sin h.   sin h, }
         = sin  $ sin fi  + cos  $   cos 6 \      2 -      1'                 ,,,„,_,
                                        -- - - - -                 (6-lOb)
     The value, of  H    may be estimated from the equations which are listed
                    Sfu
in Paily et al  (I974a) .

                     H   = H   (1-C  )   [a"  + 0;5(l-a')l                 "   (6-11)
                      sm    so    s   '-
where   C  = a constant equal to  the  approximate value  of some less significant
             parameters (such as  dust depletion)  which  are difficult to
             determine,
           = 0.01,
       H   = solar radiation incident on the atmosphere,
           = I  sin ct/R ,
              °                        2                2
        I  = solar constant = 2 cal/cm /min=2880 cal/cm /day,  and
         R = ratio of the actual  to the mean distance from the sun to
             the- earth.      .          - .                  .
                           1 + 0.017  cos|-^| (18.6-D)J
                                                                         (6-13)
                                         L •><•>-'         J
a1 and a" are coefficients.

     a1 = exp J  m  [- (0.465+0.130w)]  [o.179+0.421 e~°*721jn] J          (6-14)

     a" = exp |  m  [- (0.465+0.134w)]  [o.129+0.171 e~°'88m ]}          (6-15)
                                      74

-------
where   m = optical air mass
                      P  .P
            	a/ o
            sin ct  + 0.15 (a  + 3.885)
        a =  solar  angle  in degrees ,
    P /P  = ratio of air pressure at location altitude  to  sea  level air
     3  O
            pressure,
              288 - 0.0065 Alt \5'256
              	288	j                                         15'17)
      Alt = altitude in meters.
        w = atmospheric moisture content  (cm)
          = 0.85 exp 0.110 + 0.0614 T  ,  and                             (6-18)
                                  o
       T, = dewpoint temperature ( C) .
        d
     Although Eq. 6-4 through 6-18 are a rather long list  to compute a simple
parameter, r, to input a typical value of reflectivity  can create large errors
when time increments of less than oae day are used.  For the MERS experimental
channels, r values from .04 to  .2 have been computed over  a day, and when
the importance of the  H   term is considered, these variations are too
large to be approximated accurately by "typical" or "average"  values.

6.3.  NET LONGWAVE RADIATION
     Net longwave radiation is expressed as

                           H4 -°ew (Ts"- eaTa '                        (6'19)

where   T  = water surface temperature ( K),
        T  = air temperature ( K),
         cl
        e  = long-wave emissivity of the water surfaca  (assumed equal
             to water surface long-wave reflectivity),
           = 0.970
        e  = emissivity of the atmosphere, and
         3
         a = Stefan-Soltzman constant.
                                     75

-------
      For  atmospheric emissivity without cloud cover, £   ,  the Idso and Jackson
                                                      clC

      (1969) formula will give accurate  results  for  air temperatures above and


     below freezing point.



                          = 1 - 0.261 exp   -0.74xlO~4 T (°C)2 ]                (6-20)
                                          L             Si     J
                  ac



The Bolz formula is then used  to  find  e <•
                                         a




            - .	.         ~*F~ = e  " (KK. C-2)      -                     (6-21)
                               «v~.   ac—     G-



wfieFe   C" "= 'fraction cloud cover',  and       — ---    .-"—---
         c

         K = a coefficient  which  depends upon cloud height.



The coefficient   K  varies  between  0.04 and 0.25.   A TVA  (1968) study


recommends an average value of K = 0.17,
     6.4.  NET EVAPORATIVE AND CONVECTIVE HEAT TRANSFER



          Evaporative heat transfer from a water  surface may be expressed by the


     relation,



                              HQ = pL(Wftn)z  (esw -  e^)                      (6-22)





     where   e   = vapor pressure of the air  at height z,
              32


             e   = saturated vapor pressure at water surface temperature,
              sw


           Wftn  = a wind function using wind velocity at height z,



               L = latent heat of vaporization for water (E/M), and



               p = density of water (M/L ).



   ...Saturation vapor pressure a_t. any air temperature.  3L(_JC)__may;Jpe:.comp_uted_pyer- _


	water.. by_t_he .Magn.us-Tetons formula, (see. _Murray,  1967).
                         <*,  - ..1.7, «XP ["•26r!£.;62"-16>]
     Atmospheric vapor pressure is computed from relative  humidity, RH





                                     ea = IbT  esa                            (6'24>






                                          76

-------
The latent heat of vaporization is
                      L = 597.31 - 0.5631 T                              (6-25)
with  L  in cal/g and  T   in  C.
     The convective heat transfer from an air-water interface, when evaluated
according to Bowen  (1926) may  be expressed  as
                               P (mb)
                     Hc = °'61 "WOT  pL Wftnz  (Ts  - **>              (6-26>
where  T    is air temperature at a height  z  above the water surface,  p    is
in mb and Wftn  is the same as that for evaporative heat transfer.
              Z
     A number of empirical wind function formulas(Wftn)   have been developed
                                                       z
for various conditions.  A formula used by many  investigators, e.g. Marciano
and Harbeck (1954), for natural water bodies is
                              (Wftn)  = a + b W                           (6-27)
                                   Z          Z
where   W  = wind velocity at elevation  z  above the water surface, and
   a and b = empirical constants.
Brady, Graves, and Geyer (1969) used the formula,

                              (Wftn)  = a + b W 2                          (6-28)

for heat loss from power plant cooling ponds.  Shulyakovskyi  (1969) incor-
porated a natural convection term in Eq. 6-27 to describe accentuated heat
loss from thermally loaded water bodies.

                        (Wftn)z = a + b Wz + C(A6 )1/3   ,                (6-29)

where   8  = virtual temperature or the temperature of dry air at the
             same density as under tne given conditions, and
       A8  = the difference in a virtual temperature between air at the
             water surface and at 2 m height.
The difference in virtual temperature is, in effect, a theoretical tempera-
ture difference which represents differences in density.  The relation for
A8  is
  v
                                    77                         .

-------
             A9  = T (1 + 0.378 e /p ) - T  (1 + 0.378 e /p )             (6-30)
               v    s            s  3     a            a  a

Ryan and Hacleraan (1973) excluded the constant term in Eq. 6-29 because of
the large number of studies at natural water temperatures which found  a = 0.
They fitted laboratory natural convection and cooling pond data to the formula

                         (Wftn)  = b W  + c(A6 )1/3                      (6-31)
                               Z      Z       V

     Constants for the above equations have been determined for large water
bodies.  For smaller water bodies like the  MERS  channels,  the forced
convection constants (a and b) need to be evaluated separately.  In  the next
section the constants in Eq. 6-27, 6-28, 6-29, and 6-31 will be determined
from water temperature and weather data at the MERS and  compared to results
for water bodies with large surface areas.

6.5.  DETERMINATION OF WIND RELATED HEAT TRANSFER COEFFICIENT FROM MEASURED
      STEADY-6TATE LONGITUDINAL TEMPERATURE PROFILES
General Procedure
     With constant inflow rate and inflow temperature and quasi-steady
weather conditions,  the longitudinal temperature profile in the channels
will approach steady state.  Conversely, when water temperature records
indicate steady-state and weather conditions are nearly constant, the
longitudinal water temperature profile in the channels may be used to deter-
mine coefficients in the steady-state equation of the longitudinal water
temperature profile.  If longitudinal temperature gradients are not  large,
and if Eq. 6-2 is used for the source term, water temperature is predicted
by the solution to Eq.  1-1 for zero dispersion.
                                   f - - f  -    .       -      -
          8    T(x) ~ TE
where    — = —	—
         9o     o ' TE
         T  = equilibrium temperature,
          £•
         Io = T(x=0)  ,
          U = bulk channel flow velocity,

                                     78

-------
             m = Ks/Pcp h '



            K  = bulk surface heat transfer coefficient,
             S


             h = channel depth, and




            c  = specific heat of water.




 From a measured longitudinal temperature profile and a computed equilibrium



 temperature, the value of  K   may be determined by Eq. 6-32 as
                             Q


       - -   -- -     -     -    - 	c~ Ti U ~  ~   ~~
 -   -       .               KS = -P-^T-  lnf                         (
                                               o


                                   S Q      e
 or                        K  = -p -^—  In f-                           (6-34)
                            s       IT       y
                                    Bx       o



 where  Q = channel flow rate, and



        B = mean channel surface width.




 Errors in Computed Heat Transfer Coefficients



      For a large measured longitudinal temperature gradient the contribution


 of longitudinal dispersion,  D  , to water temperature gradients may be
                               u

 significant.   For this case the following solution to Eq. 1-1 with  D   >  0
                                                                      Lj

 must be applied.
                                                                         (6-35)
 The error  Y(%)  in determining  K   from Eq. 6-34 by assuming  D =0 is
                                   S                              L



                          In 9/9  (D =0) - In 9/9_ (D  > 0)
                                                                            *'
. For-the calculations-it is convenient to-rewrite Eq. 6—35 as,
                 In p2 (DT > 0)  - - - I (1 + K D)*' - - 1 I                 (6-37)
                    V    Ll          """ '                  *
                     O              D
 where  D = 2 D/U
               L



        K = 2 m/U .
                                      79

-------
     For a given per cent error  Y, equations 6-34, 6-36, and 6-37  may be
combined to give

                          pL\l JL . O _ o                          ,6 3g
                          UOO/  100    4                               (   JB
Eq. 6-38 may be solved for  Y.   Typical input parameters for  K  and  D  at
the MERS channels are

                              0 < D  < 1.0 m/sec
                                   Lt
                       9 x 10~5 < m < 2 x 10~4 sec"1
                              .05 < U < .2 m/sec
It is found that  Y  does not exceed 2 per cent.  Longitudinal dispersion
therefore will not significantly affect the surface heat transfer coefficients
computed from steady-state longitudinal water temperature profiles, while
ignoring longitudinal dispersion.
     Equation 6-34 also implies  that the longitudinal temperature profile has
achieved steady-state.  True steady-state can be approached but is rarely,
if ever, achieved precisely.  Therefore an estimate of the unsteady character
of the longitudinal temperature profile and its effect on computations of  K
                                                                            s
is also needed.  With  D  =0, Eq. 1-1 may be written as,
                        L

                        If ^BbS-
or
                               NS + ss
                                         - m f-                         (6-40)
                                             9o
where  NS = 3T/3t  is the unsteady contribution and
       SS = (Q/Bh)  3T/3x  is_ the steady-state contribution.
The per cent error  Z  in  9/9   created by assuming  NS = 0  is
                      __ _  ,
                      100 ~ \     SS+NS
                                      80

-------
If, for each assumed steady-state  Q/Q  , the location with  the maximum 3T/3t
is used to compute  NS, and  SS  is taken as the average over channel length,
Eq. 6-41 will give an estimate of the largest possible error in  K   computa-
tions.

Determination of Wind Function Coefficients
     The bulk surface heat transfer coefficient  K  (cal  cm"   day"  °C~  )   is
given by Edinger and Geyer (1965) as

                          KS = 9.256 + pL(Wftn){& + 0:61).  .             (6-42)

where  Wftn = wind function (cm mb   day" ),  L = latent heat of
vaporization  (cal/g) , and  g (mb/  C) -• mean slope of the saturated
vapor pressure versus temperature curve between water surface and dew point
temperatures.  Brady, Graves, and Geyer  (1969) suggested the formula

                           3  = .4604 +  .0197 T + .001585 T2            (6-43)

where      T =  (T  + T )/2  (°C)
           T = water surface temperature (°C),  and
          T, = dew point temperature (°C) .

Equations 6-37 and 6-29 may be combined to give the wind function for a steady-
state longitudinal temperature profile.
      =  pL(Wftn)  = — - ~     -   cal cm~2  day"1                (6~44)
Equation 6-44 is not dependent upon channel depth, indicating pool stratifi-
cation does not affect computations of  F  .  This is so because stratifica-
tion decreases' not only the effective channel depth, but also residence time
as long as the flow rate is constant.
     Using Eqs. 6-34 and 6-44,  K   and  F   were computed for 47 cases of
near steady-state longitudinal temperature profiles.  The parameter  NS/SS
and the maximum per cent error in  K_  due to unsteady water temperatures
were also computed for each ease. The data and computational- results of all
cases is given in Appendix B,  Table B-l.  A sample calculation is also given
in Appendix B.
                                     81

-------
     A least-squares fit to determine the coefficients  in  Eqs.  6-27,  6-28,
6-29, and 6-31 was undertaken with all 47 cases.  In addition,  the  data
were also fitted to the equation
                          F   = nl,(Wftn)  = b W  +  5.52(Ae )            (6-45)
                           w            z      z           v
                            z
where  c = 5.52  was found by Ryan and Harleman  (1973) .   Equation  6-45  was
included because natural convection should not depend  strongly on  water
surface area, and Ryan and Harleman's  (1973)  results may be applicable to
the MERS channels.
     The following five equations result from a least  squares  fit  on  computed
F   values from the MERS field channels:

     1.  F (cal cm"2 day'1 mb'1) = a + b W  (m/sec)                      (6-46)
          w                               y
              with a = 17.5
                   b =• 2.40
              and a standard error = 3.79
     2.  F  = a + b Wn2                                                 (6-47)
          w          9
              with a = 21.18
                   b = .316
              and a standard error = 3.74
     3.  F  = a + b W. + c(A8 )1/3                                      (6-48)
          w          y       v
              with a = 9.17
    ......     7  ." b ~= 2768 "~"  ".""'_";• ----  •• ----- -------
                   c = 2.78 '     ' ------ '  -      ----   •  -
              and a standard error = 3.72  " ""      .........    "
     4.  Fw = b W9 + c(A8v)1/3                                          (6-49)
              with  b = 3.10
                    c = 5.68
              and a standard error = 3.81
                                      82

-------
     5.  FW = b Wg + 5.52 (A9V)1/3                                      (6-50)
              with  b = 3.21
              and a standard error =3.77

     Equations 6-46 and 6-47 are compared to experimental  (field) values of
F   in Figure 6-1.  Three ranges of the parameter  NS/SS are indicated  by
different symbols.  The scatter in Fig. 6-1 is not uncommon, as indicated
e.g. by similar plots by Brady, Graves, and Geyer  (1969).  Equations 6-48,
                      	-                                      1" /O
6^49, and 6-50 are compared_to computed values of  F  - 2.78(A9 ) _ ,
FW - 5.68(A9V)1/3 , and  FW - 5.52(A9v)1/3  in Figs. 6-2,  6-3, and" 6-4,
respectively.   Comparison of the standard errors of Eqs.  6-46 through  6-50
and comparison of the individual curves with  F   data indicates  that all
five equations give a remarkably similar fit to the data.  This indicates
that for a given type of water body, in this case narrow open channels  with
constant thermal loading, any of the five equations may be applied  as a wind
function.
     Paily, Macagno, and Kennedy (1974a)compiled a list of wind function
formulas given by various authors for different water bodies.  Some of  the
wind function formulas which compare with those used here  are given in  Table
6-1.  Table 6-1 gives (Wftn), = F  /(pL) as a function of  wind velocity at
                            /    W2
2 m above the water surface.  Equations 6-46 through 6-50  were converted
to the form of Table 4 and added on the bottom.
     Wind velocities at 9 m above the water surface were related  to wind
velocities at 2 m, W , by the formula

                                 W2 = Wg(2/9)'3                         (6-51)

as suggested by Paily,--Ma'eagno,~ and"Kennedy (1974a)for wind over  land.
Because of the- small size of. jbhe Monticello channels',, the  ve.rtical  wind
velocity profile is essentially that over land.   A comparison of the relation-
ships found in the MERS-channels and from previous investigations as shown in
Table 6-1 can now be made.
     A number of the investigators  (Kohler, Marciano and Harbeck, Harbeck,
Hughes, Turner, and Ficke).listed in Table 6-1 used a wind function formula
                                       83

-------
           Q.


           O  0
-------
oo
U1
                 30
             o
             T3
             E
             o
             8   20
            CD
             
             c\j
             i
             5
                 10
p   NS/SS=0
O   0
-------
    2P
    24
-t
CO
.  '   0
                                                          ""TT
              n  NS/SS=O

              O  0
-------
CD

-J
                        o
                        XI
                        o
                        u
                           28
                           24
                           20
                           '6
                        CD

                        <

                        OJ
                        m

                        IT)
                            0
D   NS/SS=0


O   0
-------
           TABLE 6-1.  WIND FUNCTION FORMULAS DETERMINED BY VARIOUS
                       INVESTIGATORS*
Investigator
Kohler (1954)
Marciano and
  Harbeck (1954)

Harbeck (1958)

Rymsha  and
 Doschenko (1958)

Hughes (1964)
Turner (1966)
                            Wind Function Formula (Wftn)

                                (cm/day-mb)

                        0.005175+4.995x10   W_
                        0.01134
                        0.01309 W.
                        0,0209+9.107x10  (T-Ta2)+0.01018 W
                        0.008864
                        0.02045
Water Body
Lake Hefner,
barge and
midlake
stations

Lake Hefner
Lake Mead

Winter Time
Rivers

Salton Sea,
California

Lake Michie,
No. Carolina
Brady, Graves,
  and Geyer (1969)

Shulyyakovskyi (1969)

Ficke (1972)
Ryan and Harleman
  (1973)
                        0.0239+0.00147
                                          1/3
                        0.015+0.0094 (A0v)+0.0112

                        0.0125 W,
                        0.00934 (A6v)1/3+ 0.01107
Power Plant
Cooling Ponds
Pretty Lakes,
Indiana

Cooling Ponds
and Laboratory
Data
Stefan,  Gulliver
  Hahn & Fu
                        0.0296+0.00637

                        0.0358+0.00132
                                          1/3
                        0. 0155+0. 0047(A9v)+0. 00711

                        0.0096 (A9v)1/3+0. 00832 W2
                        0.00934
                                          . 00852
MERS channels

   6-46

   6-47

   6-48

   6-49

   6-50
*Listed by Paily,  Macagno,  and Kennedy (1974a).
                                       88

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like Eq. 6-46 for lakes with natural water surface temperatures. These  inves-
tigators found a very small or zero constant term.  The large constant  term
in Eq. 6-46 is believed to reflect natural convection due to the artificially
elevated water surface temperatures in the Monticello Field channels studied
herein.
     Brady, Graves, and Geyer (1969) used a wind function similar to Eq. 6-47
forT^at loss- from power plant cooling" ponds, given in Table 6-1.  Their
      ~v~    _ ^	      —                              — -          ..               _ .
constant term is smaller than, that of Eq.-6-47.-  The explanation for this  is
similar to that for^tfie higher constant term in Eq. 6-46.  The-virtual
temperature difference (A6 )   in the cooling ponds studied by Brady et  al
varied from 5 to 12°C.  The range of  A6   in the open channel studied  here
was 7 to 35 C,  resulting in stronger natural convection effects.

     Equation 6-48b has the same form as that used by Shulyakovskyi (1969) .
The constant terms in the two equations are strikingly similar.  However,  the
natural convection term in Eq. 6-48 is approximately half that of Shulyakovskyi's.
With three fitted constants,  this equation should give the best fit, but the
standard error is only slightly smaller than with two fitted constants.
     The natural convection constant in Eq. 6-49 is very similar to that
proposed by Ryan and Harleman (1973), which was found to be satisfactory in
a numoer of evaporation experiments at the laboratory scale and the field
scale.  The Monticello data essentially confirm Ryan and Harleman's natural
convection term.  In fact, the results are so close that a least-squares
fit using Ryan and Harleman's (1973) natural convection constant, Eq. 3-50,
gave a smaller standard error than Eq. 6-49.
     As expected, Eqs. 6-46 through 6-50 have smaller forced convection terms
than- the corresponding equations in Table 6-1.  One possible cause is that
the Monticello channels experience a land surface rather than a water surface
wind boundary layer.  More important yet is the observation that, except for
a narrow range of wind directions, the relatively high channel sides at
Monticello create a separated wind ooundary layer over the channel water
surface.  The reduced wind velocities near the water surface in a separated
boundary layer would cause less forced convection than in an unseparated
boundary layer.
                                     89

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     Since any of the equations 6-46 through 6-50 will give similar accuracy
in determining a wind function for the channel studied, criteria for selec-
tion of a wind function equation will be based upon how well the equation
describes physically real processes and whether the equation may be used
for channels which do not have heat additions.  Equation 6-49 fits both of
these criteria.  Equations 6-46, 6-47, and 6-48 are not as good as Eqs.
6-49 or 6-50 because they contain an unexplained constant rather than a
natural convection term.  In addition, for natural water"surface temperatures
where  A6   is small, Eq. 6-49 will reduce to a form similar to wind functions
determined from lake evaporation in Table 6-1.  Finally, the natural convec-
tion term determined by least-squares fit from the MERS field channel
data is very close to the one derived from laboratory data by Ryan and
Harleman  (1973).  This gives further credibility to the wind function in
Eq. 6-49 , which is selected as the most appropriate relationship.
                                     90

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                                  SECTION 7
            DYNAMIC WATER TEMPERATURE PREDICTION IN OPEN CHANNELS

7.1.  GENERAL OBJECTIVE
     To describe water  temperature  dynamics  in an  open  channel under all
types of weather conditions, a numerical solution of Eq. 1-1 is necessary.
The most important terms to be described numerically are the source  terms
which incorporate heat transfer across the air-water interface and longitudinal
dispersion.  The source terms are highly non-linear and require an iterative
scheme to accurately predict air-water heat transfer.  Linearized source terms
may be used to solve Eq.l-r analytically for temperature distribution but the
solutions with linearized equilibrium temperature relationships are  limited
to specific upstream water temperature and steady-state weather conditions.  A
one-dimensional unsteady finite difference model for stream temperature
prediction titled MNSTREM for Minnesota Stream Water Temperature Prediction
Model has been developed.  MNSTREM will be described herein and applied  to
water temperature prediction in the MERS field channels.  MNSTREM has unusually
high time resolution, meaning that it can predict rapid water  temperature
changes in very shallow water.

7.2.  FORMULATION OF ONE-DIMENSIONAL FINITE DIFFERENCE EQUATIONS FOR WATER
      TEMPERATURE PREDICTION
     The finite difference equation for water  temperature with convection,
longitudinal dispersion, and air-water heat exchange will be formulated_in a
Crank-Nicholson implicit scheme.  The basic transport equation is

where   T = temperature (  C) ,
        t = time (T) ,
        x = distance (L) ,
                                   2
        A = cross-sectional area  (L ) ,
        Q = flow rate (L3/T) ,
       D  = longitudinal dispersion coefficient  (L /T) ,
                                       91

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         B = channel surface width  (L) ,
         p = density of water  (M/L  ),
        c  = specific heat  (E M~  °C~1) , and
         P                                                              2
         S = net rate of heat transfer  through  air-water  interface  (E/L )

The equations will be formulated in the control volume , shown  in  Fig.  7.1
about the i»]+J5 location.  Then
                         A    - A
                         A    ~
                                         At .
and
                     BS   BiSi,-j+%    VSi.
                     pCp      PCP            2 pCp
 since Crank-Nicholson implicit differences are being used.   Formulation of  the
 x-differences depends upon- the grid Peclet number.
                              Pe -                                       (7.2)
                                      L
If  Pe  is large/ an upstream difference scheme  is appropriate  (as  in QUAL  I) ,
and if  Pe is small a central difference scheme  is appropriate.  For many open
channel conditions where  D   is significant, Pe  is  in  an  intermediate  region.
                           ij
For the MERS experimental channels,

                   Q = .05 m /sec
                   A = 1.5 m3
                  D  =: .1m /sec
                   Lt
                  AX = 3 •+ 8 m, and
                  Pe a 1 ->• 3
which is in-the range where neither the upstream nor central difference  formu-
lations' are accurate (the-greatest error occurs- at-Pe=2).-  The exact  solution
to the steady-state transport equation without  a  source  term gives  (Chien,  1977)

                .      31
              3x VL ax
                                                    - T
         i+l
   exp(Pei+1) -
                                               1  ^ *P         T
                                               jxp(Pei_1 )  -  1J
       	 .            (7-3)
exp(Pe.
                                      92

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                 •Ax
  j-H
                             i.j-M/2
     ]   o
       i-l
                                                                At
 O
i-H
  i= distance , node
  j.— time node
  x= distance
  t= time
Ax= distance increment
At=time  increment
      Fig. 7.1.  Control volume  in  time-distance coordinates for  fornjulation
                 of finite differences.

-------
At large values of Pe, however, the exponential terms are expensive to compute.


A power 'law approximation to Eq. 7-3 which has been developed by Patankar and


Baliga  (1978) is
       «s
                 3x \   L 3x
                    Ax
Ti *
                           5 1
                                                                  5 -,
                                                                        (7-4)
In Eq. 7-4 the terms in brackets -signify the largest of the individual terms.


Because one temperature is assumed to be valid over a whole control volume,


the Peclet numbers between matrix locations use the hormonic mean of D .
                                                                      L
                               Pe
                                                                        (7-Sa)
                                                                        (7-Sb)
     Because the finite  difference equation is to be Crank-Nickolson implicit


(rather than fully implicit)  the convective-dispersive term in Eq. 7-4 should


be:

                                          r                     1

                                      - S   22
                                      ~ 2   3x
           JL
           ax
                   3x
                  3x
                                                                        (7-6)
Combining Eq.  7-1,  7-4,  and 7-6  gives the finite difference equation:
               a T  .    ,-bT    ,+cT
                  1-1,3+1
                                                  +Z     =0
                                                     1,3
                                                          (7-7)
where     a =
 Q At

2 A  Ax
                        1  +
                                 t1-0-1!^
                                     94

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              .At
         b = 1 + a + c ,  and
                                                 At B.  S.    .
      Z. .  = (l-a-c)T.  .  + a T.  ,    + c T.  ,  .  + - - — *fj *
             l                 -
       .  .            .  .       .  ,         .  ,  .
       1,3            i,:       i-l,D       i+l, J       pcpAi


     To solve for the longitudinal temperature  profile at  t=j+l,  Eq.  7-7 is

first rewritten as


                         Ti,3+l  +  Wi Vl,      =                          -

were at all locations except the boundaries.
                                W
                                 i     b + a W.
and                                  a G    + Z
At  1=1, T        is known and
          1 ,
                                       Z   + a T
                    = -c/b  and   G  = -3 -                           (7-11)
At the lower end of the channel reach to be studied (i=I), a constant gradient

of temperature will be assumed, or


                      T         = 2 T      - T
                       1+1,  3+1      I,j+l    1-1,  3+1
Then,
and finally
                          	W-  =-0   - -  -

                                (a-c)  S-l + ZI
                            I ~ b-2c+(a-c)W
                                        = GI  '

-------
The longitudinal temperature profile is then found through back substitu-
tion from  i=I-l  to  i=2  through a rearranged form of Eg. 7-8.

                         T       = G  - W  T
                          i, 3+1    i    i  i+1, j+1
Eq. 7-8 through 7-12 comprise a tri-diagonal matrix algorithm  (TDMA) ,
     The implicit method of solution is always stable and convergent  (Mickley
et al, 1957).  However, because a Crank-Nicholson implicit scheme, rather
than" fully implicit, is used oscillation matrices in the solution for tempera-
Lures can develop.- "A Crank-Nicholson-scheme- is used because it is more- •-
accurate when the transition to the final steady values of the dependent
variable are of interest.  For finite difference procedures which are both
convergent and stable, a reduction of increment step size gives a good  indica-
tion of result reliability (Mickley et al, 1957).  To assure that no oscilla-
tion occurs in the matrix, and to test the significance of numerical damping,
the numerical solution is computed with half the original time step.  If no
significant difference exists between the three runs, then no oscillation or
numerical damping problems are assumed to exist.
     The source term in Eq. 7-1 is nonlinear ly dependent upon water temperature.
Therefore, the term  S.      cannot be included in the TDMA' scheme and  is
included through iteration.  First, it is assumed that  S,  .   = S.   .  Then
                                                         i ,3+1    i r 3
S       is computed from  T.      determined from the TDMA.  Finally, S.
 1,3+1                     1,3+1                                        1,3+1
is used to solve new  T.       values.  These two steps are repeated until
                       i , 3+-I-
there is no significant change in the  T.  .     values.  For open channels,
                                        i , 3+-1-
such as the MERS field channels, where heat exchange is important this type
of iteration can significantly reduce errors in the prediction of water tem-
perature.
7_.3Y  DESCRIPTION OF NUMERICA^FINITE" DIFFERENCE" COMPUTER" PROGRAM~FOR WATER-'" "
 -"---"TEMPERATURE PREDICTION--       ../•..  ..-		    -   .  .
     The water temperature prediction program MNSTREM begins with a channel
reach of specified length, distance increment, time increment, and initial
water temperature in each segment.  The channel reach is divided  into a
number of segments.   Each segment is assumed to have a constant surface
width and cross sectional area and may consist of one or more distance increments.
                                     96

-------
     MNSTREM reads cross sectional area and surface width for each segment
as well as dimensionless longitudinal dispersion coefficient for the channel
and latitude and longitude of the study site.  Upstream water temperatures,
flow rates, and the required weather parameters are read by MNSTREM to con-
tinuously compute water temperatures.  Measured water temperatures may be
input to MNSTREM for comparison with computed water temperatures.  Individual
residuals, the residual sum of squares, and the RMS residual are then computed.
A more detailed description of all required input parameters is given in
Appendix C (User's guide).  A general flow chart for MNSTREM is given in
Fig. 7.2.  The program listing, given in Appendix D, provides a more detailed
description of the required computations.  A sample input is given in Appendix
E.  Appendix F gives a partial sample output which includes a comparison with
measured water temperatures and computed residuals.
     The most important input parameters for accurate water temperature pre-
diction with MNSTREM are:
     a.  Flow rate and cross sectional areas since water temperature
         prediction is very sensitive to residence time,
     b.  Solar radiation, relative humidity, air temperature, and
         wind velocity measurements for accurate air-water heat
         transfer prediction, and
     d.  If temperature fronts or pulses are being routed  D ,
         At, and  Ax must be chosen carefully to match real
         longitudinal dispersion with the combination of  D
                                                           I*
         and numerical dispersion in the model.
                            1  \
7.4.   EXAMPLES OF WATER TEMPERATURE PREDICTIONS IN THE MERS FIELD CHANNELS
                             \                       •
     The wind function (Eq.  6A49 in Table 6-1)  and the dimensionless longi-
                             A
tudinal dispersion  coefficient.-1  D*  =  D  B/Q  =  7. 47  (Section 5.4)  are used
                              I
in MNSTREM to predict water  temperatures in  the MERS field channels.  MNSTREM
is applied to water temperature  prediction over four different time periods
and compared to recorded  water temperatures.
     a.  January 31 through  February  4,  1976,  with  weather data averaged over
         1 hour time increments  (Run  A) .
                                     97

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            Program  MNSTREM
'Read  input data  describing channel
 reach,  initial water  temperatures,
 flow  rates,  and  measured  temperatures
                                                         1
                                                  SUBROUTINE TEMP
             CALL  PRNOUT
                                                 SUBROUTINE PRNOUT
                                          Prints intermediate  statistics,
                                          water temperature data,  final
                                          water temperature predictions,
                                          measured water  temperatures, and
                                          residuals
         Test  increment size
            if desired
      Fig. 7.2.  General flow chart for MNSTREM, the Minnesota  Stream
                 Water Temperature Prediction Model.   (Cont'd)
                                     98

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        SUBROUTINE TEMP
                                              SUBROUTINE ITEMP
                                        Sets up the initial water
                                        temperature profile at each
                                        i node from input data for
                                        each segment..    _  -
          Main Loop
   One loop for each input
       of weather data
         CALL HFLUX
     assuming T    ,=T.
                      13
1
                                             SUBROUTINE HFLUX
                                    Computes heat flux source,  S,  and
                                    longitudinal dispersion coefficient
                                    for each channel segment
        Second Loop
  One loop for each hour
                                                    2.
                                              SUBROUTINE QRATE
                                     Computes flow rate for  each  hour
 Tri-diagonal matrix algorithm
 solution to determine"water
.~temg_epa.-tur-e£L at—time, step
        Fig. 1.2.  General flow chart for MNSTREM,  the Minnesota Stream
                   Water Temperature Prediction Model.   (Cont'd)
                                   99

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          I
Are further iterations \
on source term needed?  f~
                               No
           Yes
     CALL HPLUX
  Using new values
     of T   .  ,
         if D+l
                              SUBROUTINE HFLUX
 Compute Residuals
Fig.
  7.2 (Cont'd) .
General flow chart for MNSTREM, the Minnesota
Stream Water Temperature Prediction Model.
                             100

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     b.  April  3  through April  12,  1976, with weather data  averaged over
         3 hour time  increments (Run B).
     c.  June 20  through July 19, 1977, with weather data averaged over
         3 hour time  increments (Run C).
     d.  November  16  through December  6, 1976, with weather data averaged
         over 3 hour  time  increments  (Run D).
Finally, the accuracy of using  instantaneous rather than time-averaged readings
of weather data is evaluated by comparison of water temperature predictions
with the two types of data input to the model.   In addition,  the predictive
capabilities of time-averaged weather  data over  various averaging time periods
is analyzed.
     In order to predict water  temperatures the input data  listed in Section
7.3 and Appendix C must be obtained.  The water data acquisition system has
been described in  Section 4.4.  The MERS weather station is described in
Appendix G.  Hourly inflow water temperatures and channel water temperatures
were read on water temperature  strip charts and adjusted according to calibra-
tion measurements  as described  in Section 4.4.   A weather station to measure
and record weather parameters was installed near the center of the MERS.   Solar
radiation was measured with a 50 ^unction Epply pyranometer at 2 m height.  Wind
velocity was measured at 9 m height with a Science Associate's anemometer.
YSI 80 recorders were calibrated and used for recording both wind velocity and
solar radiation.  Air temperature and relative  humidity were recorded on a
Belfort spring wound hygrothermograph,  with a bimetal temperature sensor and
hair hygrothermograph.  The hygrothermograph was calibrated weekly.   When in-
strumentation breakdown occurred, the required  weather data were obtained from
Morthern States Power Company records at the nearby Monticello Power Plant.
Fraction cloud cover was estimated  from NOAA Minneapolis-St. Paul and St. Cloud
local weather data and from the  Epply solar radiation records.  Finally,  cross
sectional area and surface width at each channel segment were determined from
field measurements as in Section 4.1.
     When a convective-diffusive equation such  as Eq.  6-1 is modelled through
finite differences, care must be taken  to insure that the numerical  dispersion
caused by the finite size of the well-mixed control volumes is small when
compared to the physical dispersion.  Longitudinal dispersion is included

-------
in Eq. 6-1 as a diffusive terra.  Banks  (1974) studied a one-dimensional  un-
steady mixed cell model with a concentration front similar to the  temperature
fronts in Section 5.  He found that at an infinite number of cells the model
is equivalent to Eq. 6-1 without the source term where the term  Q
replaced the longitudinal dispersion coefficient  (D  ) .  If we define  an
                                                   L
approximate numerical longitudinal dispersion coefficient,
then the grid Peclet number may be expressed as
                                 Pe = 2 "nun/0!,                         (7'14)

Although  D     is only truly equivalent to a diffusion coefficient at  an
infinite number of cells, it gives a valid estimate of existing numerical
diffusion with a finite number of cells.  It is interesting to note that
the greatest difference between central difference or upstream difference
formulations as described in Section 7.2 occurred at  D    = D .  For the
                                                       num    L
hybrid formulation used here (Eq. 7-4) a small grid Peclet number must  be
used if longitudinal dispersion is important.  The use of various distance
increments indicated that in the four water temperature prediction, Runs A
through D, longitudinal dispersion was crucial only to Run D, where two
temperature fronts were routed through the channel.

Run A:  1800 h January  31 through  2200  h February  4,  1976, with weather data
        averaged over 1 hour time  increments.
...	This" four-dayper rod- -rnciudes~a- temporary- decrease—in-up-stream- water	
temperature-and a severe cold-front.  Upstream-water-temperature  was  mostly  •
"maintained'at 15 C  through  the heat exchangers.  Because of  the artificially '
high water temperature,  air-water  heat  transfer was large.  The mean  channel
flow velocity was constant  at 0.016 m/sec.  Air and dew point  temperatures
were obtained from  records  at the  NSP Monticello weather station.  Computed
water  temperatures  were compared to observed hourly water temperatures  at
channel locations 3, 7, 9,  13, 15, and  17.  The standard error was computed
to be  0.22 C.  When one considers  that  a decrease  in  water temperature  of
                                    102

-------
7°C along the channel was common, this standard error can be considered very
low.  Predicted and observed water temperatures from channel locations 3, 9,
and 17 are shown in Fig. 7.3.

Run B:  0000 h April 3 through 2400 h April 12, 1976, with weather data
        averaged over 3-hour time increments
     For these ten days in early spring the relatively high solar radiation
and low relative humidity are in-contrast to Run A for the winter period.  Air
temperature was mild, between 20 and -3 C.  The mean channel flow velocity
during this period was approximately 0.013 m/sec.  With the large solar radia-"
tion values, a small error in measured solar radiation or predicted water
surface reflectivity can cause significant' errors in computed water tempera-
tures at 1200, 1500, and 1800 hr.  This is shown to occur periodically in
Fig. 7.4, where computed and observed water temperatures for channel locations
3, 12, and 17 are compared.  While longwave, evaporative, and conductive
heat transfer were all of similar values for the winter Run A, the larger
air temperatures and lower relative humidity of Run B decreased the importance
of conductive heat transfer and increased the importance of evaporative heat
transfer.  Residuals of predicted and observed water temperatures were taken
every 3 hours at channel locations 3, 6, 12, and 17, and the standard error
was determined to be 0.22 C.  This standard error compares very well to the
daily variation of 7-8 C at location 17.

Run C:  1500 h June 20 through 2100 h July 19, 1977. with weather data
        averaged over 3 hour increments
     This run encompasses a full month in midsummer when solar radiation is
of the greatest importance.  Large variations in cloud cover, wind velocity,
and solar radiation occurred over the month period.  In declining importance,
most of the air-water heat transfer was due to solar radiation, evaporation,
and longwave radiation.  Convective heat transfer-provided a very small.
contribution.  The mean channel flow velocity throughout the period for
Run C (Period C) was approximately 0.020 m/sec.  Computed and observed water
temperatures for channel locations 3 and 17 are compared in Figs. 7.5a, 7.5b,
and 7.5c.  As with Run A and Run B, upstream water temperature was maintained
10-15 C above ambient so that the heat transfer is about what is expected
from cooling ponds.  The temperature regime which would occur under ambient
                                     103

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O
o
 tu
 Q.

 E
                                       O  Location  3

                                       A  Location  9

                                       Q  Location 17
        Jon 31
Feb I
Feb 2
Feb 3
Feb 4
        Fig. 7.3.  Run A.  Hourly water temperatures at three stations  in channel 1 from January 31
                   through February 4, 1976.  Station locations are  identified  in Fig.  4.13.  Symbols
                   are recorded values; solid lines are values simulated with MNSTREM.

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       22
       20
       18
    o
    <°  I/I
t-   0.1^
       12
       10
        8
-]	1	p	r

 A   Location  3
 D   Location  12
 O   Location  17
                                                                                                       12
                Fig. 7.4.  Run,B.  Three-hour water temperatures at three stations in Channel 1.  Station
                           locations are identified in Fig. 4.13 (3 is upstream and 17 is downstream).
                           Symbols are recorded values; solid lines are values simulated with MNSTREM.

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o
en
                  A  Location 3

                     Location 17'
           Fig.  7.5a.  Run C.  Three-hour water temperatures at Station 3  (upstream)  and  Station 17 (downstream)
                        in Channel  8.  Symbols are recorded values; solid lines are values  simulated with MNSTREM.

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          A  Location  3
          O  Location  17
26  -
                                                                                       8
    Fig. 7.5b.   Run C.   Three-hour water temperatures at Station 3  (upstream) and Station 17
                (downstream)  in Channel 8.  Symbols are recorded values; solid lines are
                values  simulated with MNSTREM.

-------
o
CD
          42
          40
       o
        0)
           36
34
           32
           30
           28
                    A  Location  3
                    O  Locatiqn 17
                  II
                 12
13
14
    15

July 1977
16
17
18
19
              Pig. 7.5c.   Run  C.  Three-hour water temperatures  at Station 3  (upstream) and Station 17
                          (downstream) in Channel 8.   Symbols  are recorded values; solid lines are

                          values  simulated with MNSTREM.

-------
 conditions is shown during the period June 24 through June 26 when  no  addi-
 tional heat was supplied to inflowing water upstream.  Residuals of predicted
 and observed water temperatures were taken every  3 hours at channel locations
 3, 9, and 17, and the standard error was determined  to be 0.29°C.

 Run D:  0000 h November 16 through 2400 h December 5, 1976, with weather
         data averaged over 3 hour increments
      This late fall period includes four temperature fronts  (2  increases  and 2
 decreases), a steady decrease in air temperature  from approximately 5°C to -20°C,
 and-consistently^large wind velocities.  Upstream- water temperatures wer-e
                     o
 maintained around 10 C above ambient.  During the temperature front periods,
 the computational time increment was reduced from 3600 sec to 400 sec  to
 prevent oscillations in the solution matrix.  This is usually required when
 3T/3x  is very large, as in a temperature front or pulse.  Grid Peclet number
 was approximately 1 in the pools, so  D   YD  = 1/2  during this run and  D*
                                        nuin  Lt
 was adjusted accordingly.  The mean channel flow velocity during this  period
 was approximately 0.015 m/sec.  As with Run A, air temperature  and  dew point
 temperature were obtained from weather station records for the  NSP  Monticello
 Power Plant.  The predicted and observed water temperature, from channel
 locations 3 and 17 are compared in Fig. 7.6a and 7.6b.  During much of the
 period predicted downstream temperatures are larger than observed.  This
 could be because the wind direction was predominantly parallel  to the  down-
 stream channel sections, and wind direction is not included in  the  wind
 function determined in section 6.5.  In tne later half of Period D, low air
 temperatures and a variable wind velocity created a highly dynamic  temperature
 regime with large longitudinal gradients.  As with Run A, evaporative, con-
 vective, longwave radiation and solar radiation heat transfer were  all of
-equal—importance. -Residuals-of- predicted.and, observed..water, .temperatures	.    _
 were taken-every--3 hours, at. ctiamiel,J-ocationaJJ^..6J.,12,_._and_.17_, and  the "standard
 error was determined to be-0-.32 CT  ---    -'    -    	'"._.. ..  .._.'_
      The water temperature predictions were chosen to cover all four seasons
 of the year.  Runs A, B, C, and D indicate that MNSTREM accurately  predicted
 water temperatures which were  both ambient and artificially heated  for each
 season of the year.  Upstream  water temperature varied from 0  to 40°C and
 air temperature varied from -25 C to +35 C.   With this wide range of conditions,
                                        109

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        I	'	1	'
          A  Location  3
          O  Location 17
                                         20       21
                                       November  1976
24
25
Fig. 7.6a.   Run D.  Three-hour water temperatures at Station 3 (upstream)  and Station  17  (down-
            stream) in Channel 1.   Symbols  are recorded values; solid lines are  values simulated
            with MNSTREM.

-------
                    A  Location  3
                    O  Location 17
           27       28
             November  1976
    3         4
December 1976
Fig. 7.6b.   Run D.  Three-hour water  temperatures at Station 3 (upstream)  and Station 17 (down-
            stream) in Channel 1.  Symbols "are recorded values; solid lines  are values simulated
            with MNSTREM.

-------
the maximum standard error for any run was 0.316 C, which compares to a calibra-
tion error of 0.10 to 0.2 C for the thermistors which measured water temperature.
The low standard errors are a good indication of MNSTREM's capability for pre-
dicting water temperature, especially when one considers that MNSTREM has no
coefficients determined from the data of any of the predictive Runs A, B, C,
or D.
     When predicting water temperatures over a stream reach,  an  investigator
must decide- what~time peraod~ts* adequate for averaging measured weather para-
meters.  Since hourly averages of weather data were used for Run.A, this period
was used to compare the accuracy of water temperature predictions with weather
data averaged over 1, 3, 6, and 12 hour periods.  The results, given in Table
7.1, indicate that for the period in Run A, averaging weather parameters over
1, 3, and 6 hour periods gave equally good predictions.

            TABLE 7.1.  STANDARD ERROR OF WATER TEMPERATURE
                        PREDICTIONS WHEN WEATHER PARAMETERS
                        ARE AVERAGED OVER 1, 3, 6, AND 12 HR PERIODS
Time
Averaging





Period for
Weather Parameters
(hr)
1
3
6
12
Standard Error of
Prediction
C°0
0.222
0.243
0.239
0.407
It should be noted that Run A was for a winter period when daily variations
of solar radiation are small. " Other weather parameters such" as wind"velocity
and air temperature, however, _were highly variable in Run A.
     Instantaneous values of weather data are more easily obtained than time
averaged values.  Much of the NOAA Local Climatological Data, for example,
is given as instantaneous values every three hours.  To test the accuracy of
water temperature prediction with instantaneous rather than time-averaged
readings of weather data, water temperatures were predicted with 3, 6, and 12
hour instantaneous weather data for Period A.  In addition, the effect of
                                     112

-------
lead time in the input of the instantaneous data  to  the computer model was
studied.  The results are given in Table 7.2.  For six-hour instantaneous
weather data, a lead time of 1.5 hours means the  weather data is applied 4.5
hours before the reading and 1.5 hours after the  reading time.  The results
of Table 7.2 indicate that, for example
     1)  a three-hour instantaneous reading of weather data taken at
         1200 would give the best prediction if applied from 1030 to
         1330, based on the lowest standard error of prediction
     2)  a six-hour instantaneous reading at 1200 should be applied
         from 0830 to 1430, and
     3)  a 12-hour instantaneous reading at 0100  should be applied
         from 0230 to 1430.
The results given in Table 7.2 are only strictly  applicable to the MERS
channels for Period A.  They give an indication of what can be expected in
a shallow channel.
                                  113

-------
      TABLE 7.2.   STANDARD ERROR OF WATER TEMPERATURE PREDICTIONS WITH
                  INSTANTANEOUS READINGS OF WEATHER DATA TAKEN AT 3, 6,
                  AND 12 HOUR INCREMENTS*
Lead Time
in Input of Re
Weather Data e
(hr)
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
,. Standard Error
very: 3 (hrs) 6 (hrs)
<°0 (°C)
0.265 0.379
0.248 0.271
0.278 0.261
0.308
0.420
0.364




*


12 (hrs)
<°C)
0.678
0.474
0.297
0.344
0.534
0.402
0.539
0.649
0.661
0.705
0.793
0.845
*A lead time of 2.5 hours means  the instantaneous data is applied for 2.5 hours
 after the reading time,  and N-2.5  nours before the reading time, where
 N = 3, 6, or 12.
                                     114

-------
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Godfrey, R. G. and B. J. Frederick (1970)  "Stream Dispersion at Selected
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Gulliver, J. S.  (1977)   "Analysis of Surface Heat Exchange and Longitudinal
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Gulliver, J. S. and H.  Stefan  (1980)   "Soil Thermal Conductivity and Tempera-
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Hahn, M. G., J.  S. Gulliver", and H. Stefan  (1978a)  "Operational Water Tempera-
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Hahn, M. G., J.  S. Gulliver, and H. Stefan  (1978b)  "Physical Characteristics
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                                      116

-------
Hahn, M. G. (1978)   "Experimental Studies of Vertical Mixing in Temperature
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Harbeck, G. E. (1958)   "Water Loss Investigations, Lake Mead Studies," U.S.
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Hughes, G. H.  (1964)   "Analysis of Techniques Used to Measure Evaporation
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Idso, S. B. and R.  D.  Jackson (1969)  "Thermal Radiation from the Atmosphere,"
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Jain, S. C. (1976)   "Longitudinal Dispersion Coefficients for Streams," Journal
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Jobson, H. E.  and N.   Yotsukura (1972)   "Mechanics of Heat Transfer in Non-
    Stratified Open Channel Flows," Institute of River Mechanics Paper,
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Koberg, G. E.  (1964)   "Methods to Compute Long-wave Radiation from the
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Limerinos, J.  T.  (1970)  "Determination of the Manning Coefficient from
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Liu, H. and A.H.D.  Cheng (1980)   "Modified Fickian Model for Predicting
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                                      117

-------
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                                         •
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                                      118

-------
               APPENDIX A







TEiMPERATURE FRONT DATA FOR DETERMINATION






OF LONGITUDINAL DISPERSION COEFFICIENT
                   119

-------
TABLE A-l.  CHANNEL 1 CROSS-SECTIONAL AREAS AND SURFACE WIDTHS
            FOR TEMPERATURE FRONT EXPERIMENTS
Section Nr
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Cross-sectional
Area (ra2)
1.17
0.46
1.44
0.48
1.62
0.37
1.64
0.37
1.77
0.37
1.76
0.39
1.83
0.38
1.37
0.38
Surface Width (m)
3.05
2.01
3.35
1.89
3.35
2.04
3.35
1.95
3.35
1.80
3.35
1.80
3.26
1.80
3.20
1.65
   TABLE A-2.  RESIDENCE TIMES TO EACH STATION IN TEMPERATURE
               FRONT EXPERIMENTS (HRS)
Date of
Experiment
11/17/76
11/18/76
11/22/76
12/06/76
12/14/76'

3
0.31
0.37
0.31
0.15
0.29

5
0.76
0.82
0.74
0.56
0.67

7
1.25
1.28
1.20
1.06
1.08
Stations
9
1.72
1.68
1.65
1.50
1.47

1
2.22
2.14
2.06
1.98
1.88

13
2.83
2.58
2.64
2.50
"2.30

15
3.64
3.04
3.13
2.99
2-. 86

17
4.15
3.41
3.58
3.46
- —
                              120

-------
     TABLE A-3.  MEASURED 0 VALUES FOR 11/17/76 TEMPERATURE FRONT (Cont'd)
Time Since
Front Inception
(ht)
.25
.31
.38
.44
.50
.56
.63
.69
.75
.81
.88
.94
1.00
1.13
1.25
1.38
1.50
1.63
1.75
1.88
2.00
2.13
2.25
2.38
2.50
2.63
2.75
2.88
3.00
3.13
3.25
3.38
3.50
3.63__
3.75
4.00 - -
4-.25~- _.. 	
4.50
4.75
5.00
Stations
3

.83
.49
.33
.23
.15
.10
.06
.03
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—_
- 	
	 --
.
—
—

5

1.00
1.00
1.00
1.00
.96 -
.94
.80
.65
.52
.39
.31
.23
.15
.10
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

7

1.00
II
It
n
1.00
1.00
1.00
1.00
1.00
—
—
.99
.94
.76
.49
.32
.21
.14
.09
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

9

1.00
II
n
n
n
ii
it
it
n
1.00
1.00
1.00
1.00
—
—
.97
.83
.63
.46
.32
.21
.15
.11
.06
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

11

1.00
n
it
n
it
n
n
n
it
n
n
n
n
1.00
1.00
1.00
1.00
1.00
—
.90
.78
.60
.47
.37
.29
.22
.18
.14
.11
.08
—
—
—
—
—
—
—
—
—

13

1.00
n
n
it
n
n
II
11
U
n
II
n
n
n
ii
ii
it
n
1.00
1.00
1.00
1.00
.97
.89
.76
.67
.55
.47
.40
.35
.31
.27
.24
—
—
—
—
—
—

15

1.00
It
It
II
II
H
II
It
It
II
II
n
n
u
n
u
n
ti
11
ii
11
u
1.00
1.00
1.00
—
.96
.89
.80
.73
.66
.60
.55
.51
.47
.40
.36
.33
.30
.23
Note: 0  is defined by Eg. 5.5.
      0  = [T(t)  - T(0)]/[T(oo) - T(0)]
                                       121

-------
TABLE A-3.  MEASURED  0 VALUES FOR  11/18/76 TEMPERATURE FRONT  (Cont'd)
Time Since
Front Inception
(hr)
.25-_
.31
.38
.44
.50
.56
.63
.69
.75
.81
.88
.94
1.00
1.13
1.25
1.38
1.50
1.63
1.75
1.88
2.00
2.13
2.25
2.38
2.50
2.63
2.75
2.38
3.00
3.13
""• "3V2S 	 	 •"
3-jJ5-
" .3.50 .. . .
"" 3763 " """" " ~
3.75

3

.89
.66
.51
.38 	
.28
.20
.15
.10
.08
.07
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
	 	 	
—
—
— "
—

5

1.00
"
1.00
—
—
.95
.86
.73
.61
.50
.40
.31
.23
.13
.09
.07
. —
—
—
—
—
—
—
—
—
—
—
—
—
—
-- 	 	

" —

—

7

1.00
"
n
It
it
it
n
it
1.00
1.00
—
—
.91
.72
.53
.45
.22
.13
.08
.07
—
—
—
—
—
—
—
—
—
—

—
~-
- ---
—
Stations
9

1.00
n
ti
- ,«*-
fi
n
n
n
n
n
1.00
1.00
—
—
—
.90
.75
.57
.42
.31
.21
.13
.08
—
—
—
—
—
—
—
- 	 — — — -
—
—
-" -' -- 	
—

11

1.00
ri*
it
~ .» -
n
n
n
n
it
it
n
it
1.00
1.00
1.00
—
—
.95
.88
.76
.64
.52
.37
.27
.17
.10
.05
—
—
—
—
—
—
--
—

13

1.00
, 	 . n
n
*"
n
n
n
n
it
n
n
n
H
ft
It
1.00
1.00
—
—
—
.93
.87
.77
.68
.57
.45
.32
.21
.15
.10
.06
—
—
—
—

15

1.00^
II
II
II
t|
11
"
11
II
II
II
n
n
n
it
n
ii
1.00
1.00
1.00
—
—
—
.92
.87
.79
.68
.62
.52
.42
- -- .34-
.-22"
.16
.10 "
.07
                               122

-------
TABLE A-3.  MEASURED 8  VALUES FOR  11/22/76 TEMPERATURE FRONT  (Cont'd)
Time Since
Front Inception
(hr)
.19
.25
.31
.38
.44
.50
.56
.63
.69
.75
.81
.88
.94
1.00
1.13
1.25
1.38
1.50
1.63
1.75
1.88
2.00
2.13
2.25
2.38
2.50
2.63
2.75
2.88
3.00
3.13
.3.25
3.38
3.50
3.63
3.75
3.88
" 4.00
Stations
3

.99
.76
.46
.30
.18
.12
.07
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
5

1.00
11
11
it
1.00
.96
.86
.75
.57
.47
.37
.28
.20
.14
.09
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
7

1.00
tl
II
II
If
II
tl
It
1.00
1.00
.99
.96
.92
.84
.59
.43
.28
.20
.13
.08
.05
—
—
—
—
—
—
—
—
—
—
	
—
—
—
—
—
—
9

1.00
rt
n
it
n
n
it
n
n
n
tt
n
»
1.00
1.00
.96
.85
.69
.51
.39
.29
.22
.18
.14
.10
.08
.07
.05
—
—
—
— - -
—
—
—
—
—
--
11

1.00
n
n
ii
it
n
tl
it
n
it
n
n
tt
n
n
n
1.00
.98
.96
—
.75
.62
.46
.40
.33
.26
.20
.17
.14
.12
—
.09
—
—
.06
—
—
—
13

1.00
n
ti
n
n
ii
n
n
it
n
ft
tt
11
ii
n
n
it
it
it
ii
1.00
.98
.91
.84
.72
.60
.48
.42
.36
.30
.25
.21
.17
.15
—
.12
—
.09
15

1.00
n
n
n
n
n
ti
n
n
n
it
it
n
n
tt
ii
ti
ti
ti
. H
n
n
1.00
1.00
.97
.92
.85
.77
.68
.59
.50
.42"
.36
.31
.28
.23
.20
.17
                                  123

-------
TABLE A-3.  MEASURED  0  VALUES FOR 12/06/76 TEMPERATURE FRONT  (Cont'd)
Time Since
Front Inception
(hr)
.13
.19
.25
.31
.38
.44
.50
.56
.63
.69
.75
.81
.88
.94
1.00
1.13
1.25
1.38
1.50
1.63
1.75
1.88
2.00
2.13
2.25
2.38
2.50
2.63
2.75
2.38
3.00
3.13
3.25
3.38
3.50
3.75
3.88
4.00
Stations
3

.64
.37
.24
.15
.10
.07
—
—
—
—
—
—
—
—
—
—
—
— •
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
5

1.00
1.00
1.00
—
.95
.84
.69
.50
.36
.27
.21
.15
.12
.08
.07
—
—
— '
—
—
—
--
—
—
—
—
—
—
—
—
—
. —
. —
—
—
—
—
—
	 7_

1.00
if
n
n
ti
"
ti
n
1.00
-~
.97
.93
.87
.77
.63
.38
.26
.18
.12
.08
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
9

1.00
11
11
n
ti
n
n
n
n
ti
1.00
ii
11
1.00

.95
.86
.70 •
.50
.38
.27
.20
.16
.12
.09
.07
--
—
—
—
—
—
—
—
—
—
—
—
11

1.00
II
n
n
ti
n
ti
n
n
n
tr
11
it
n
n
it
it
1.00
—
.91
.77
.62
.47
.35
.27
.21
.14
.11
—
.08
—
—
—
—
—
—
—
--
13

1.00
ft
n
n
n
n
n
"
ii
n
n
it
n
11
ti
ti
ti
11
it
11
1.00
—
.95
.85
.73
.61
.50
.41
.35
.29
.24
.21
.18
.15
—
.11
—
.09
15

1.00
n
n
n
n
n
n
n
n
H
ii
n
n
n
n
n
n
n
n
n
n
ii
n
1.00
1.00
.97
.90
.79
.69
.60
.48
.42
.35
.29
.21
.18
.15
.13
                                   124

-------
TABLE A-3(Cont'd).  MEASURED  9  VALUES FOR 12/14/76 TEMPERATURE FRONT
Time Since
Front Inception 3
(hr)
.25 .72
.31 .42
- -.--..38 ~- -. .26
-- -V44 ~ — ~ - .15'
.50 -.09
- ~ .56 ' * 'rO^S
.63
.69
.75
.81
.88
.94
1.00
1.13
1.25
1.38
1.50
1.63
1.75
1.88
2.00
2.13
2.25
2.38
2.50
2.63
2.75
2.88
3.00
3.13
3.25
3.38
" 3-.50 " -- "
3.63. - .. ". ._—
3.75-
4.00 " —

5

1.00
n
11
Q-G—
- .ati
.61
.45
.34
.25
.21
.16
.13
.08
.05
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
— —
— __ _
—
~ — "

7

1.00
11
"
n
«
n
—
—
.95
.88
.79
.65
.43
.29
.19
.10
.07
—
—
—
—
—
—
—
—
—
—
—
—
—
—
— —
— .
. —
—
Stations
9

1.00
n
n
- ii-
n
n
n
it
it
n
n
1.00
.95
.82
.64
.47
.35
' .24
.16
.11
.06
—
—
—
—
—
—
—
—
—
—
—
...
—
—

11

1.00
II
It
II-
"ll
II
II
n
it
it
it
ii
1.00
—
.95
.90
.79
.66
.51
.39
.29
.21
.15
.11
.10
—
—
—
—
—
—
— —
—

—

13

1.00
n
n
- it
11
n
it
it
n
n
n
n
n
ft
it
11
1.00
—
.95
.88
.81
.69
.55
.45
.36
.29
.24
.19
.16
.12
.10
.09
— —
...07._.
—
~~—

15

1.00
If
tl
II
It
It
It
It
It
II
tt
n
it
ti
ti
it
it
n
1.00
—
.97
.90
.84
.76
.66
.56
.48
.44
.37
.32
.29
. 26
— _
.19
.13
                                  125

-------
                       APPENDIX B







      DATA AND COMPUTATIONS OF BULK SURFACE HEAT





   TRANSFER COEFFICIENT AND WIND FUNCTION PARAMETERS




FROM STEADY-STATE LONGITUDINAL WATER TEMPERATURE PROFILES
                           126

-------
TABLE B-l.  DATA AND COMPUTATIONAL RESULTS FOR DETERMINATION OF BULK SURFACE HEAT TRANSFER
            COEFFICIENT AND WIND FUNCTION PARAMETERS FROM STEADY STATE LONGITUDINAL WATER
            TEMPERATURE PROFILES (Cont'd)
Date

12-4-75
12-4-75
12-19-75
12-21-75
12-21-75
12-24-75
12-26-75
12-28-75
12-29-75
12-30-75
1-5-76
1-8-76
1-9-76
1-9-76
1-11-76
1-13-76
1-14-76
1-15-76
1-17-76
1-19-76
1-22-76
1-25-76
1-27-76
1-31-76
2-2-76
2-5-76
2-6-76
T
a
<°0
-1.4
4.2
-6.7
-17.2
-7.2
-7.2
-6.9
-5.6
-3.3
-3.9
-2.7
-22.8
-20.6
-16.7
-11.7
-8.9
-15
-12.2
-20.6 '
-17.2
-12.2
-8.9
-19.4
-5.6
-21.1
-17.2
-17.2
Td
<°0
-2.9
1.3
-8.3
-17.2
-8.3
-8.3
-7.8
-6.9
-3.9
-5.0
-6.1
r23.9
-21.7
-17.8
-11.7
-10.0
-15
-12.2
-20.6
-18.3
-12.2
-10.0
-19.4
-7.8
-21.1
-18.3
-17.8
T
w
<°0
7.6
9.8
12.5
8.2
8.9
10.1
12.3
11.7
12.2
12.6
12.2
8.8
10.1
11.4
12.0
11.7
11.2
11.1
11.2
9.7
11.2
12.0
9.4
11.3
10.3
10.6
9.3
A6v
<°0
9.2
8.4
20.0
26.1
16.6
17.9
20.1
18.0
16.2
17.3
15.7
33.8
32.2
29.0
24.6
21.4
27.1
24.1
32.7
27.7
24.6
21.8
33.6
17.6
32.6
28.7
28.2
Q
(«/.)
11.7
11.7
21.1
17.8
17.8
22.0
22.0
22.9
22.9
22.0
21.1
21.1
21.1
21.1
21.1
20.2
20.2
20.2
20.2
19.4
19.4
19.4
21.1
20.2
20.2
20.2
19.4
NS/SS

.10
.04
.04
.03
.10
.06
.04
.06
.05
.06
.03
0
.03
.04
.03
.02
.05
.04
.04
.09
0
.03
0
.05
0
.02
.06
W9
(m/sec)
4.5
5.4
2.75
1.1
1.3
5.6
2.9
2.7
4,2
3.1
3.8
3.2
1.6
2.0
2.5
2.2
2.9
3.1
.75
4.9
1.5
2.5
1.8
4.0
.9
2.2
3.1
e/eo
(x=487.7m)
.647
.530
.780
.778
.760
.700
.759
.815
.721
.770
.742
.751
.784
.778
.769
.767
.732
.710
.771
.687
.779
.761
.772
.740
.787
.772
.743
K
s
(cal cm"2
day"1 °C~1
31.1
45.3
32.1
27.3
29.9
48.1
37.2
28.7
44.1
35.2
38.6
37.0
31.5
32.5
34.0
32.9
38.7
36.5
32.2
44.5
27.8
32.4
33.5
37.3
29.1
32.1
35.2
F
w
,
19.4
29.4
20.4
17.8
19.2
35.6
24.8
17.2
29.5
22.2
25.6
27.4
22.0
22.7
23.0
21.7
28.3
25.7
22.7
34.7
17.5
21.2
24.0
25.3
19.6
19.1
25.6
Fw-5.52(A9v)V
(cal cm"2
day"1 mb~ )
7.9
18.1
5.5
1.5
5.1
21.2
9.8
2.8
15.6
8.0
11.8
9.6
4.4
5.7
7.0
6.4
11.7
9.7
5.0
18.0
1.5
5.8
6.2
10.9
2.0
2.2
8.8

-------
         TABLE B-l(Cont'd).  |DATA AND COMPUTATIONAL RESULTS FOR DETERMINATION OF BULK SURFACE  HEAT TRANSFER
                             .COEFFICIENT AND WIND FUNCTION PARAMETERS FROM STEADY STATE LONGITUDINAL WATER
                             ITEMPERATURE PROFILES
to
CO


Date




2-7-76
2-12-76
2-13-76
2-15-76
2-17-76
2-18-76
2-19-76
3-6-76
3-7-76
3-9-76
3-14-76
3-27-76
4-10-76
11-16-76
11-19-76
11-22-76
11-24-76
11-29-76
12-1-76
12-3-76


T
a
i
<°C)
;
-18.3
-1.1
-6.5
3
3
2.5,
1.2
-20.5
-9.5:
-2 >'
-1 l
2.2
10 ;
•3
-2.0
-4.0
-7oO
-14 ,,
-15 '
-13 '
1
1
T, f
1 d :

, (°d
1
-21J1
-3.3
-7^5
2^5
2.5
2J3
, -b
-20J5
-9i8
-2 '
-1J3

8,3
-1.3
-4.0
-4.6
-7,3
-14
-1512
-13.5


T
w

(°c>

9.3
12.3
12.2
11.7
12.7
12.7
12.4
8.0
9.2
11.2
10.8
10.8
19.0
9.1
fl.3
9.2
7.2
8.0
6.8
8.7


A6
V

(°C)

28.2
14.1
20.0
11.1
10.5
11.0
12.1
29.5
19.7
14.1
12.6
9.3
10.2
10.2
10.9
14.0
14.9
23.0
22.7
22.7


Q


U/s)

20.2
19.4
16.3
14.8
14.8
15.5
13.4
15.5
15.5
15.5
14.8
22.9
15.5
29.8
37.9
36 .7
39.1
29.8
29.8
28.8


NS/SS




.06
.96
.04
.11
.13
0
.09
.04
.14
.06
- .04
.10
.08
.10
.03
.04
.08
.05
0
.03

•*
WQ
9

(m/sec)

4.0
2.7
1.6
' 4.0
4.0
2.7
2.5
2.0
1.3
- 1.8
2.9
5.5
3.0
4.25
5.25
8.0
3.25
4.5
4.5
5.75


6/6
o

(x=487.7m)

.758
.760
.711
.578
.586
.622
.632
.693
.717
.680
.616
.750
.623
.809
.819
.783
.851
.796
.832
.806
1 i
1
K !
s

_2
(cal cm '
day'1 V1)
34.3
32.5
34.0
46.1
42.2
45.1
34.2
34.8
31.6
36.6
44.0
42.6
44.9
38.7
46.3
55.0
38.6 '
41.7
32.4
38.0


F
w



25.6
19.6
22.0
28.6
25.1
27.4
20.1
25.3
21.0
22.9
28.9
27.0
21.8
25.1
33.1
40.7
27.5
31.6
22.8
27.8

1 /\
F -5.52(A0t ) '
w v

(cal cm
day mb )
8.8
6.2
7.0
16.3
13.0
15.1
7.4
8.3
6.1
9.6
16.1
15.3
9.8
13.2
20.9
27.4
13.9
15.9
7.1
12.2

-------
        Sample Calculation of Bulk Surface Heat Transfer Coefficient
               and Wind Function Parameters from Steady State
                      Longitudinal Temperature Profile

     A near steady-state longitudinal temperature profile was observed on
strip chart records of water temperature on November 29, 1976.  Weather
                                o
records indicated that  T  = -14 C, W  = 4.5 + 1 m/sec, and relative humidity
                         a           y       —
(RH)was 91 per cent.  Using psychometric tables,- dew point was determined to
be -14 C for the given  T   and RH.--This and all-other-steady-state--per igdsT
                         Cl             "*
occurred during non-daylight hours, so  T  = T   was a good approximation.
                                         £    U
     Water temperatures were adjusted by the corresponding temperature cali-
bration and values of  6/6  = [T(x)-T ]/(T -T )  were computed and plotted on
semi-log paper as shown in Fig. B-l.  A best fit line through all points
gave  6/9  (x=487.7 m)*= .796.  All points, however, are enclosed by maximum
and minimum  9/9  (x=487.7 m) values of .865 and .760, respectively.
Sample Computation:
For  8/eQ = .796, x = 1600 ft = 487.7 m, Q = 473 gpra = 29.8 2,/S
and  b = 9.5 ft = 2.9 m,  K  from Eq. 6-34 = 41.66 cal cm"2 day ~l °C~1
                           5
    T  =8.0 (mean channel water temperature)  C
     w
Then
     3 = from Eq. 6-43 = .4156 mb/ °C .
and
    F  from Eq. 6-42 = 31.59 cal cm"  day   mb
     w
    p  = air pressure = 1013 mb '(assumed)
     3                 ^
  _.. e  = saturation vapor pressure at T  = 8.05-mb      -
   e   = saturation vapor pressure at T  = 1.56 mb .
    clZ                                 Q
Then
   A6v = from Eq. 6-30 = 22.95°C
and
    FW - 5.88(A6y) /  from Eq. 3-45 = 15.91 cal cm"1 day"1 mb"1

*  1600 ft.
                                      129

-------
U)
O
            fi/
            fa
1.0


0.9



0.8



0.7




0.6





0.5
                0.4,
 O  Observed  water temperatures

—— "Best fit"  steady  state profile
                              I
                           I
I
                                100
                             200          300          400

                               Distance  Downstream  (m)
                                                     500
                     Fig. B-l.   Steady  state water temperature profile and "best fit" curve for
                                 November 29, 1976.

-------
     The maximum  AT/At  of all channel locations was  2.0  C/day,  and  the


temperature difference between inflow and outflow temperatures  was  AT =  5.0°C.


Thus the steady state parameter was





                         N§ _     AT/day
                                               =
                         SS   30.39 Q(gpm)(AT)




where   Q = 473 gpm.  The maximum per cent error in  T(x)   from  non-steady-


                                                     3   = T _ T
                                                      o     o     E
state temperatures is  100(1 - 1/1.05) = 5%.  Since  9   = T   - T_  =  15° +  14°
                                                      Q    O    £»
  29°C, from Fig. B-l
                     T{x = 1600 ft) =  .796 9  + T_ =  9.08°C
                                            O    Ct
and the maximum per cent error  Z  in  9/0  (x = 1600  ft)
                             0/9 -[.95T)x = 1600) - T  ]/8

                     Z = 100 —2 - _ - E_o   .  2%





Then the maximum error in  K   calculations is
                            s



                                            In 9/9  -  In (1.0 2  9/9  )

               %(NS/SS) error in K  = + 100 - ."  , ta -  =  + 8.7%
                                  s   —            xn  y/o              —





     At a flow of 473 gpm, the accuracy of flow  rate measurement  in  the MFS


experimental channels is  *• 4 per cent.  Equation 6-34 indicates  that  this


will transfer directly to a  +4 per cent error  in  K   computations.   Thus,
                             ™                       5

there are three significant contributions to errors in K  .



     Equations 6-42 and 6-47 indicate that the magnitude of  the maximum error


in K  , rather than the per cent error, is carried to  both   F   and
    s                                                        w
       _      I-/*! - »-   -  _ _-,_.._ - __  _ ___           - -_ — ___

F  - 5.52(A9 ) --  .  The maximum and minimum values of   K  , F , and- -F-- - 5.52
 wv            _                              sw.w

(A6T )     which would occur due to each .component of error and with  a  combi-


nation of all three errors are given in Table B-2.  With such  a large


potential error, the scatter in Figs. 6-1 through 6-4  is understandable.
                                      131

-------
       TABLE B-2^   MAXIMUM AND MINIMUM VALUES OF  K ,  F ,  and  F -5.52(A9 )  1f  IN SAMPLE
                                                   S   W        W        V

                i'  COMPUTATION DUE TO MAXIMUM POSSIBLE ERRORS IN DATA
                                                                            A i
Best estimate
Ranges of estimates:
                                   K (cal  cm"2 day"1 °C~1)     F (cal cm"2mb~T)
41.66
31.59
                                        Fw-5.52(A8v)
                                                    1/3
       —2    —1   —1
(cal cm   day   mb  )


         15.91
    Including estimate of 6/0
                             o
Maximum
Minimum
Including errors
steady character
temperature ' '
Maximum 3
Minimum « .
Including errbr^
measurement . i
' l
Maximum »'
Minimum --
' 1
i
)
di|e to un-
of water
i
•>
t

in flow

i
1

i
50
26



45
38



43
40

.11 39.83 !
.48 16.79



.28 35.12
.04 28.07



.33 32.22
.0 29.98

24.15
1 1.11
i


19.44
12.38


1
17.54
14.29

Including corabinatipn of
all sources of error
Maximum '
t
Minimum /
1


56

23
.65 46.21

.21 13.61
30.52

- 2.08

-------
                                 APPENDIX C

                       USER'S GUIDE TO THE MINNESOTA
             STREAM WATER TEMPERATURE PREDICTION MODEL (MNSTREM)

      As noted in Section 7.3, the most important parameters for accurate
water temperature prediction with MNSTREM are flow rate,  cross-sectional area,
solar radiation, air temperature, relative humidity, and sometimes longitudinal
dispersion coefficient.  There are also a number of other parameters necessary
in running the model.  This appendix gives a line by line description of the
input file with format specifications given in parenthesis.  Sample data from
Appendix E are given in brackets.
                                     133

-------
 Line 1 (8P 10.2)
       DSTAR,  TSTART, DELX, DTIME, DAY1, TLNGTH  , LAT, ALT

       DSTAR = Dimensionless longitudinal dispersion coefficient = D. B/Q [7.47]
                                                                    L
       TSTART = Starting hour of day (hours.minutes) [00.00]
       DfiLX = Distance increment  (ft)  for computations [12.50]
       DTIME = Time increment (sec)  for computations  [3600]
       DAY1 = Day of month for starting day  [16]
       TLNGTH = Total length of channel reach (ft) [1700]
       LAT = Latitude of study site (degrees)  [45]
       ALT = Altitude of study site (ft)   [1000]

 Line 2 (8F 10.2)
       DATE, CHDATE

       DATE = Month.Day of starting day  [11.16]
       CHDATE = Number of days in month/100   [.30]

 Line 3 (915)
       NHOUR,  MHOUR, NRES, NP, NSECT,  IFLAG, JFLAG, KFLAG, LFLAG

       NHOUR = Total hours of time period for computer run  [480]
       MHOUR = Number of hours between weather data input [3]
       NRES = Number of channel locations with observed water temperatures  [3]
       NF = Number of flow rates read  in  [11]
       NSECT = Number of constant cross-sectional segments in channel reach [17]
       IFLAG = 1 if observed water temperatures are read in
       JFLAG = 0 if the longitudinal dispersion model is used
       JFLAG = 1 if computations are by upstream differences (numerical
               dispersion only)
       KFLAG =1 if D , rather than DSTAR, is specified at each segment
                     Jj
       LFLAG = 1 if test of increment  size is called

 Set  4 (9F5.1)    Two lines
       T0(l)  (TI(I), 1=1, 17)

       T0(l) = inflow temperature for  first time step (°C) [11.3]
       TI(I) = initial temperature at  channel segment I [TI(1)=10.7,TI(16)=8.1]

'Line 5 (10A8)
       HEAD (I), 1=1, 10                .            .            .            .

       HEAD = Heading for output of weather data which includes date and
              time of run
                                     134

-------
 Set 6  (7F 10.4). NHOUR/MHOUR lines
       TA(J), RH(J), RAD(J), W(J), WDIR(J),  P(J),  CC(J),  TIME

       Set 6  is repeated for J=l to J=NHOUR/MHOUR

       TA(J)  = Air temperature (°C) [TA(1)=-10]
       RH(J)  = Relative humidity (%)   [RH(1)=100]
       RAD(J)  = Total solar radiation (cal cm-2 min~l) [RAD(3)=.09]
       W(J)  = Wind velocity (m/sec) [w(4)=3]
       WDIR(J)  =s Wind direction (degrees)  [Blank column  in Appendix E]
       P(J)  = Air Pressure (Bars)   [PA(1)=979]
       CC(J)  = Fraction cloud cover [CC"fl3)=0.5]
       TIME = Time of day (hours), [03 in first row-of Set 6] -
       The last column gives data>-which is "not r.ead-into-
 If IFLAG = 0,  the next set of lines is skipped.

 Set 7(18F 6.2). NHOUR/MHOUR lines
       TO(J),  (TT(IT+1, IT+NSECT)

       Set 7     is repeated for
       J=l to J=NHOUR/MHOUR, where IT=>(J-1) *NSECT

       TT(I)  =  Observed water temperatures.  Use 0.0 if no observed water
                temperature is input at segment.  [Not in Appendix E]
       Temperature measurements taken at a given time would occupy one row.

 Set 8(12F 5.1). NHOUR/12+1 lines
       TO(J),  J-l, NHOUR+1  [TO(1)=11.1, TO(13)=10.8]

       TO(J)  = Upstream water temperature which is read for each hour
       Date and hour given in the last two columns is not read into MNSTREM

 Set 9 (10F 7.0). NF/10+1 lines
       Q(I),  1=1, NF

       Q(I)  = Flow rate  (gpm)  [Q{l)-473, Q(11)=456]
       NF = Number of input flow rates

 Set 10 (1015). NF/10+1 lines
---"  IF(I)y-1=1, NF	   -  --     -  -   ----_-_  --    --  -.-.-.	

       "IF(I)  =~TJumber of hours Q"(I) is "applied  [lF(l)=8i 'IF(II)=192]
 Set 11(10F 7.2).  MSECT/10+1 lines
       A(I),  1=1, NSECT

       A(I) = Cross-sectional area of segment I(ft ) [A(l)=14.2, A(17)=20]

 Set 12 (10F 7.2). NSECT/10+1 lines
       B(I),  1=1, NSECT
                                                   2
       B(I) = surface width of channel segment I(ft )  [B(l)=10.8, B(17)=10.5]
                                      135

-------
Set 13 (10F 7.2).  NSECT/10+1 lines
      DL(I), 1=1, NSECT

      DL(I) = Longitudinal dispersion coefficient for channel segment I
              (m2/sec)  [Not in  Appendix E]
                                    136

-------
            APPENDIX D




PROGRAM LISTING FOR THE MINNESOTA




 STREAM WATER TEMPERATURE MODEL





             MNSTREM
               137

-------
 00001
 00002C
 00003C
 00004C
 00005C
 00006C
 00007C
 00008C
 00009C
 00010C
 00011C
 000 12C
 00014C
 00015C
 0001 AC
 00017C
 0001 8C
 0001 9C
 00020C
 00021C
 00022C
 00023C
 00024C
 00026C
 00027C
 0002BC
 0002°C
 00030C
 0003 1C
 00032C
 00033C
 00034C
 00035C
 00036C
 00037C
 00038C
 00039C
 00040C
 00041C
 00042C
 00043C
 00044C
 0004SC
 00046C
 00047C
 00048C
 00049C
" 00050C
 00051C
 00052C  -
 00053C
 00054C
 00055C
 OOOSoC
 00057C
 ooosac
 00059C
 00060C
 00061C
 00062C
 00063C
 00064C
 00065C
PROGRAM MNSTREM
   ALT = ALTITUDE(M)
   B(K) = SURFACE WIDTH (M)
   CC(I) = FFACTION CLOUD COVER FOR TIME  INCREMENT I
   CHDATE = THE NUMBER OF DAYS IN THE STARTING  MONTH  /100
   DATE = MONTH DAY
   DAY1 = STARTING DAY OF YEAR
   DELX = DISTANCE INCREMENT FOR COMPUTATIONS
   DL = LONGITUDINAL DISPERSION COEFFICIENT  
   DSTAR = DIMENSIQNLESS LONGITUDINAL DISPERSION COEFFICIENT
   DTIME = TIME INCREhENT FOR COMPUTATIONS  (SEC)
   .EKRttAX..= J1AXIH.UJi_£RRa&.IiUC-TJl CM*,NG,e  IN  INCFEr<5NT SIZE
   ERRMEAN- = MEAN ERROR DDUE VO LHANGc IN- INCREMENT SIZE""
   FI s-COEFFIUENT UHZCH. Sr£C:?IES..TJCtl£. STEP METHOD  ,.
   FI =-05 FOI\ CRANtv-NieOLSGh' Irt.'-LICIT hETHOD
   FI- = IX) FOR FULLY  IMPLICIT METHOD           -   - .  	"  :;_."._.
   HEAD = HEADING FOR WEATHER DATA OUTI-UT
   ITEST = 0 IF NO INCREMENT SIZE TEST HAS  OCCURED
   LAT = LATITUHE(RADIANS)
   M= TOTAL NUMBER OF RESIDUALS
   MHOUR= NUMBER OF HOURS BETWEEN WATER TEMPERATURE AND
          UEATHER DATA INPUT
   NITER = NUMBER OF ITERATIONS ON SOURCE TERM  FOR EACH TIME STEP
   Nf= NUMBER OF FLOU RATES READ  IN
   NHOUR= TOTAL HOURS OF TIME PERIOD
   NSECT = NUMBER OF SECTIONS  IN  lOTAL CHANNEl  LENGTH
   NT = TOTAL NUMBER OF TIME INCREMENT STEPS
   F= AIR ^RESSUFE  (MB)
   FRNOUT = A SUBROUTINE FOR OUTPUT OF WATtR TEMPERATURES
                                                                                NSFTN
                                         138

-------
                                             \
00066C        Q =  CHANNEL  FLOU  RATE
00067C        RAD=  INCOMING SHORTWAVE  RADIATION , RESID(4000)
00081      COMMON/C/  TSTART.TLNGTH, IFLAG, JFLAG.M-LAG.JTIME,NSECT,NDELEAT      NSFTN
00082      COMMON/D/  T0(710),TI(18)
00083      COMMON/E/  Q<30),IF(30),NF
00084      COMMON/F/  TA(250) , RH(250>. RAD(250).U<250),UDIR(250),P(250>,CC<250)
00085      COMMON/G/  S(17),SIGMA, DAY1, LAT,ALT,TOLIK 150)
00086      COMMON/H/  A(17).B(17),AK(17),BK(17),CK(17),DL(17), CELX,
00087     tDTIME ,FE(17),FC(17),FI
00088      DIMENSION  HEAD<10)
00089      REAL LAT
00090      EXTERNAL TEMP.FRNOUT
00091C        READ  PARAMETERS AND  FLAGS
00092      READ(7,800)  DSTAR, TSTART, DELX, DTIME,DAY1,TLNGTH,LAT,ALT
00093C        DELX  SHOULD  BE CHOSEN SUCH  THAT  TLENGTH/NSECT/DELX = EVEN NO
00094      READC7.800)  DATE,CHDATE,FI
00075      LAT-LATH3  14/180
00096C        CONVERT TO METRIC
00097      OELX=DELX* 3043
00098      TLNGTH=TLNGTH*  3048
00099      READ(7,810)  NHOUR, MHOUR. NF, NSECT.IFLAG.JFLAG,KFLAG.LFLAG.NITER
00100C        IF IFLAG=0,  NO OBSERVED  WATER  TEMPERATURES  ARE READ
00101C        IF JFLAG=0,  THE LONGITUDINAL DISPERSION MODEL IS USED  ' •
00102C        IF JFLAG  = I/ COMPUTATIONS  ARE  BY UPSTREAM  DIFFERENCES
00103C                       (NUMERICAL DISPERSION ONLY)
00104C        IF KFLAG=0,  CSTAR, RATHER THAN  DL,  IS SPECIFIED
00105C        IF LFLAG=1,  TEST  OF  INCREMENT  SIZE IS CALLED
00106      SIGMA=1  17E-7
00107      NT=NHOUR/MHOUR
00108      ITEST=0
00109      ITER=0
00110      NDELEAT=0                                                           NSFTN
00111C        READ  INITIAL UATER TEMPERATURES
00112      READ(7,320>  T0(1),(TI(I),1=1,17)
00113C        READ  AND  CONVERT  UNITS OF WEATHER DATA
00114      READ(7,030)  (HEAD(I),1=1,10)
00115      PRINT 835,  (HEAD(I),1=1,10)                                        NSFTN
00116-     PRINT 840_           -           ._.-"-        ..-..•-'   NSF-TN
00117  .    TIME=TSTART+FLOAT(MHOUR>
00118      DO 4 J=1,NT                              "
00119      NH=J*MHOUR
00120      ITER=ITER+1
00121      IFdTER EQ 87)  PRINT 840                                            NSFTN
00122      IF(TIME  GE 24 ) TIME=TIME-24
00123      READ(7,850)  TA(J), RH(J), RAtK J),UiJ),UDIR(J>.P(J),CC.TIME       NSFTN
00126      TIME=TIME+FLOAT(MHOUR>
00127 4    CONTINUE
00128      IF(IFLAG EQ  0>  GO TO 7
00129C        READ UATER TEMPERATURE  TEMPERATURE DATA
00130      IT=0
.00131      DO 5 J=1,NT..
                                        139

-------
00132
00133
00134 5
00135 7
00136C
00137C
00138
00139
00140
00141 10
00142C
00143
00144
00145
00146C
00147  •«
00148
0014V 15
00150
00151
00152
00153
00154C
00155
00156
00157 40
00158
00159
00160
00161C
00162
00163
00164
OOloS
00166C
00167
00168
00169
00170
00171
00172
00173
00174
00175C
00176 800
00177 810
00178 820
00179 330
00180 835
00131 840
00182   .
00133
00184 850
00185 360
00186 870
00187 880
00188 890
00189 395
00190 900
00191 910
00192
00193
00194
0019S 920
00196 930
00197 940
 NH=J*MHOUR
 REAIK6.870)  TO, 1 = 1, NF)
 READ(7,895)(IF* 00228* 3048**3
    READ CROSS-SECTIONAL AREAS AND SURFACE UIDTHS
 PRINT 910                                                           NSFTN
 READ(7,900)  (A(I),1=1,NSECT)
 READ(7,900>  * 3048*  3048
 B(I) = B(D* 3048
 PRINT 920, (A(I), 1 = 1,NSECT)                                          NSFTN
 PRINT 930, ,1=1,NSECT)
 PRINT 940,,1 = 1,NF)                                            NSFTN
 PRINT 955.(0(1),1=1,NF)                                             NSFTN
 PRINT 980                                                           NSFTN
    CALl NUMERICAL UA'I ER TEMPERATURE PROGRAM
 CALL TEHF(NT, DSTAR, ITEST, ERRMAX,SUMERR,IT.NITER)
 M'NTfcNSECT-NDELEAT                                                  NSFTN
 CALL rRNOUT'NT,M,DATE,CHDATE>
 IF(LFLAG NE 1)  STOP
    TEST INCREMENT SIZE
 ITEST=!
 SUrlERR=0 0
 ERRMAX=0 0
 DTIME=DTIME/2
 CALL TEMP(NT,DSTAR,ITEST,ERRMAX,SUMERR,IT,NITER)
 ERRMEAN=SQRT(SUMERR/FLOAT 
 FORMAT       PERCENT  LANG/DAY    <  .'
2M/SEC)   UCGREES     MB    -FRACTION*)
 FORMAT(7F10 4)
 FORMATdlO, 7F10  4,F7  2)
 FORMATU8F6 2)
 FOnrtAT(12F5 1)
 FORMATUOF7 0)
 FORMAT(IOIS)
 FORMATUOF7 2)
 FORMAT(///10X, *MORFHOLOGIC AND  LONGITUDINAL MIXING  PARAMETERS*//   NSFTN
160X,*CHANNEL LOCATION*/17X,*    23456
27      3      9       10     11     12     13     14     15      16
3    17     18*/>
 FORMAT(IX,iCRO^B-SECTIONAL*.17F7 2/5X,*AREA        *, 17F7 2)                                 NSFTN
 FORMAT(IX,'DL (h**2/SEC)   '.17F7 2)                                 NSFTN
                                          140

-------
                                    \
 00198  950
 00199  955
 00200  960
 00201
 00202  980
 00203
 00204
 00205
 00206
 00207C
 00208C- -
 00209C
 00210C
 C0211C
 00212C
 00213C
 00214C
 00215C
 00216C
 00217C
 00218C
 00219C
 00220C
 00221
 00222
 00223
 00224
 00225
 00226
 00227
 00228
 00229
 00230
 00231
 00232
 00233
 00234
 00235
 00236
 00237
 00238
 00239
 00240
 00241
 00242 112
 00243
 00244
 00245
 "00246" 7" ~
 00247 115
 00248 120
- 00249
 00250
 00251
 00252 140
 00253
 00254
 00255
 00256
 00257
 00258
 00259C
 00260 300
 00261
 00262
 00263 305
 FORMAT
 END
 SUBROUTINE PRNOUT
 COMMON/C/ TSTART, TLNGTH,IFLAG, JFLAG, KFLAG, JTIME, NSECT, NDELEAT
 COMMON/D/ TO(710),TI(18)
 COMMON/H/ A<17), £«17), AKU7), Bl\( 17), CN( 17), DL<17), DELX,
SDTIME ,FE<17),FC(17),FI
 PRINT 300,DELX,DTIME
 PRINT 305,IX,JTIME,IFOOL,KFOOL
 PRINT 310
 PRINT 330, (Tia), 1 = 1,NSECT)
 MONTH =DATE
 IT=1
 TIME=TSTART
 DO 120 L=l,NT
 TIME=TIrtE+FLOAT(MHOUR>
 IFUIME LT 24  )  GO TO  112
 TIME = TIME-24
 DATE=DATE-IO 01
 IF(DATE-FLOAT(MONTH> GT CHDATE)  DATE=FLOAT(MONTH)-H  01
 MONTH -DATE
 PRINT 315,DATE
 NH=L*MHOUR
 PRINT 320, NH, (TF(I), I = IT, IT-fNSECT-1), TIME
 IFdFLAG EQ 0)  GO TO 115
_ PRINT 330, 
-------
                                                  \
00264 310  FORMAT(<40X,*POOL NUMBER*/15X,* HOUR   23456     NSFTN
00265     *  7     8     9     10    11    12    13    14    15    16     17
00266     «  18      TIME*/)
00267 315  FORMATC4X.F5 2)
00268 320  FORMAT<4X,*EST  TEMP   *,I3.2X,17F6 2.F9 2)                         NSFTN
00269 330  FORMAT(4X,*ACT TEMP*.9X,17F6 2)                                      NSFTN
00270340  FORMAT(4X,*RESIDUAL*,9X,17F6.2)                                      NSFTN
00271 350  FORMAT(//10X,*RESIDUAL SUM OF SQUARES =*.F10 4)                     NSFTN
00272 360  FORMAT(10X,*STANDARD ERROR**,F6  4)                                  NSFTN
00273 370  FQRMAT(10X,*DELEATEri CASES =*,15)                                   NSFTN
00274      END-
00275      SUBROUTINE TEMP  = SURFACE WIDTH (M)
00283C        BBAR= MEAN CHANNEL  WIDTH (COMPLETE CHANNEL)  (M)
00284C        DELX=LENGTH INCREMENT 
00285C        DISPERS =• A SUBROUTINE TO COMPUTE COEFFICIENTS FOR HYBRID
00286C                  DIFFERENCES
00287C        DL =  LONGITUDINAL DISPERSION COEFFICIENT  (M**2/SEC>
00288C        DSTAR = DIMENSIONLESS LONGITUDINAL DISPERSION COEFFICIENT
00289C        DTIME= TIME INCREMENT (SEC)
00290C        ERRMAX = MAXIMUM  ERROR  DUE TO CHANGE IN INCREMENT SIZE
00291C        FC(K) = FLUX COEFFICIENT FOR THE FINITE DIFFERENCE SOLUTION
00292C        FI =  COEFFICIENT  UHICH  SPECIFIES TIME STEP METHOD
00293C        FI =  0 5 FOR CRANK-NICOLSEN IMPLICIT METHOD
00294C        FI =  1 0 FOR FULLY  IMPLICIT METHOD                                  -
00295C        FLOU= FLOW RflTE(M**3/SEC>
00296C        IPOOL=NUMBER CF LENGTH  INCREMENTS IN ONE FOOL OR RIFFLE
00297C        ITEMP = SUBROUTINE TO COMPUTE INITIAL TEMPERATURE PROFILE
00293C        IX= TOTAL NUMBER  OF LENGTH INCERMENTS IN THE CHANNEL
00299C        JTIME=NUMBER OF TIME INCREMENTS IN ONE HOUR
00300C        KPOOL= 1/2 IFOOL
00701C        MHOUR= NUMBER OF  HOURS BETWEEN UATER TEMPERATURE AND
00302C               UEATHER DATA INPUT
00303C        NDELEAT= NUMBER OF  COMPUTED UATER TEMPERATURES FOR UHICH
00304C        NITER = NUMBER OF ITERATIONS  ON SOURCE TERM  FOR EACH TIME STEP
00305C                 THERE IS NO INPUT WATER TEMPERATURE DATA
00306C        N3ECT = NUMBER OF SECTIONS IN TOTAL CHANNEL  LENGTH
00307C        NT =  TOTAL NUMDER OF TIME INCREMENT STEPS
00308C        PE(K) = GRID PECLET NUMBER
00309C        RESID = RESIDUAL, = TF-TT
00310C        ROECF= DENSITY OF UATER (KG/M**3)
00311C        S(I)  = TOTAL HEAT SOURCE FOR LOCATION I (KCAL/SEC/M**2)
00312C     -  SUMERR - SUM OF SQUARES OF THE ERROR-S- IN INCREMEN-T-SIZE--T-E-ST	
00313C  .      T(I,J>= COMPUTED  UATER-TEMPERATURE AZ-USeATION I-ANfr-TIME J-
QO314C.    -    T-IME-  = DAY. HOUR--- -.--.-.----                     -  -     --.--_
00315C        Tr(I>=COMPUTEH UATER TEMPERATURE-AT PROBE LOCATION  I
00316C   "     TLNGHT = TOTAL "LENGTH "OF CHANNEL   '  '  = "   '  '  " *"".      "        '  ~
00317C        TSTART= STARTING  HAY HOUR
00318C        TT(I)= ACTUAL UATER TEMPERATURES
00319C        UPSTREM = A SUBROUTINE TO COMPUTE COEFFICIENTS FOR UPSTREAM
00320C                  DIFFERENCES
00321      EXTERNAL ITEMP,QRATE, HFLUX, DISPERS, UPSTREM                          NSFTN
00322      COMMON/A/ T(150.2),TIME, IX,IFOOL,KPOOL,MHOUR
00323      COMHON/B/ TF(4000), TT(4000), RESID<4000)
00324      COMMON/C/ TSTART,TLNGTH, IFLAG, JFLAG, KFLAG,JTIME,NSECT,NDELEAT       NSFTN
00325      COMMON/D/ T0<710), TI(13)
00326      COMMON/G/ S(17), SIGMA, DAY! , LAT, ALT, TOLIK 150)
00327      COMMON/H/ A(17),B(17), AK(17), BK(17),CK(17),DL(17),DELX,
00329     tDTIME ,FE(17),FC(17),FI
00329      DIMENSION Z(500). G(SOO), F(500), TITER(150)
                                             142

-------
                                           \
10
00330
00331
00332
00333
00334
00335
00336
00337
00338
00339C
OOJ40
00341
00342
00343
00344
00345C
00346
00347
00348
00349
00350
00351
0035
00353
00354
00355
00356C
00357
00358
00359C
00360
00361 20
00362C
00363 25
00364
00365
00366 30
00367 35
00363
00369
00370C
00371
00372
00373
00374C
00375
00376
00377
00378
00379
00380 -
00381
00302
00383
00384
00385
00336
00387
00388
00389
00390
00391
00392
00393
00394
00395
110
 REAL KS
 ROECP=1000
 IX=TLNGTH/DELX+ 1
 IPOOL=IX/NSECT
 KPOOL=FLOAT/2 +  6
 JJ=1
 TIME=TSTART
 IT=1
 SUMB=0 0
    COMPUTE MEAN CHANNEL UIDTH
 DO 3 K=1,NSECT
 SUMB=SUMB+B
 B8AR=SUMB/FLOAT ( NSECT )
, CALL ITEMP
 NH=0
    BEGIN MAIN LOOP
 DO 300 LOOP=1.NT
 MFLAG=0
 DO 5 1=1, IX
 TITER(I)=T(I, 1)
 TOLD(I)=T(1, 1)
 CALL HFLUX(LOQP,MFLAG)
 DO 200 ILOOP=1,MHOUR
 NH=NH+1
 DTIME-3600
 JTIME=3600 /DTIME+  1
    DETERMINE FLOW RATE
 CALL QRATE ,  FOR POOL  I
 tiO 20 K=l, NSECT
 DL=DSTAR*FLOU/BBrtR                                            -
    COMPUTE PECLET NO  FOR. EACH SECTION
 DO 30 K=l, NSECT
 FC < K ) =FLOU*DTIME/A < Is ) /DELX*FI
 FE(K)=FLOU*OELX/A
 CONTINUE
 DO 200 J=l, jriME
 TIME=TIME+1  /FLOAT( JTIME)
 IF(TIME GE 24 ) TIME=TIME-24
    DETERMINE INFLOW  TEMPERATURE
 R=l -FLOAT(J)/FLOAT(JTIME)
 T( 1, JJ+1 )=R*TN+( 1 -R)*TO(NH+1>
 T<1, JJH)=T(1. JJ + D4-0 2
    SUBSTITUTION AND ELIMINATION SOLUTION FOR TEMP1  PROFILE
 1=2
 K = l
 L=0
•IF(JFLAG EC!  0) CALL  DISPERS(K.L)   -
 IFUFLAG NE 0) CALL UPSTREM(K)
 Z-*T(I, 1>+CK(K)
1*T/IFOOL+1
 L=0
 IF(I EG  IFOOL*(K-1)-H)  L = l
 IFUFLAG EQ  0) CALL  DISPEFS(K,L)
 IFCJFLHG NE 0) CALL UFSTF-EMCK)
 Z+CK(K>
IXTd + l, 1))+S(N)*B(K)*DTIME/A
 I = IX
 K=NSECr
                                                                         NSFTN
                                                                         NSFTN
                                                                         NSFTN
                                                                         NSFTN
                                                                         NSFTN
                                     143

-------
00396
00397
00398
00399
00400
00401
00402
00403
00404C
00405
00406
00407 130
00408
00409 140
00410 200
00411C
00412
00413
00414
00415 2005
00416
00417
00418
00419
00420
00421
00422
00423 201
00424
00425 202
00426
00427
00428C
00429
00430
00431
00432
00433C
00434 205
00435
00436
00437
00438
00439
00440 220
00441
00442
00443
.004.44- .
00445
00-446C-
00447
0044B-
004*9
00450
00451
00452
00453
00454
00455
00456
00457
00458
00459
00460
00461  12
     L=0
     IFUFLAG Ed 0) CALL DISPERS+CK(K>
    1*1(1+1. 1) >+S(K)*B(K)*DTIME/A(K)/ROECP
          <(AK-CK-CK(K»
                                                                     NSFTN
                                                                     NSFTN
300
10
    BACK-SUBSTITUTE FOR WATER TEMPERATURE
 T(IX, JJ+1)=G
 NH=NH-MHOUR
 CALL HFLUX
 DO  201  1=1, IX
 TITER
 GO  TO 10
 DO  220  I=IT, IT+NSECT-1
 II = =0 0
 NOELEAT=NDELEAT+1
 CONTINUE
 IT=IT+NSECT
 CONTINUE
 RETURN
 ENtt ____            - -- —  -     -     —
 SUBROUTINE ITEMP           '       ------
    THIS SUBROUTINE ..SETS. UP. THE INIT.IAt. UATER TEMPERATURE PROFILE
 COMMON/ A/. TU50, 2), TIME, IX, IPOOL. KPOOL, MHOUR
-COMMON/DV-TOt71O)-, TIC187' -----  ~
 1 = 1
 11 = 1
 IF(TI<17) LT 0 1) TK17>=TI<16>- 5*/FLOAT
-------
                                                 \
5
10
 00462  13
 00463  15
 00464
 00465
 00466
 00467  20
 00468
 00469
 00470
 00471
 00472
 00473  40
-004Z4-  __-
 00475
 00476
 00477C
 00478
 00479
 00480
 00481
 00482
 00483
 00484
 0048J
 00486
 00487
 00488
 00489C
 00490C
 00491C
 004920
 00493C
 00494C
 00495C
 00496C
 00497C
 00498C
 00499C
 00500C
 00501C
 00502C
 00503C
 00504C
 00505C
 00506C
 00507C
 0050GC
_ £.05.0.9.0 __
 00510C
 00511C
 00512C
 00513C -
 00514C
 00515C
 00516C
 00517C
 00518C
 00519C
 00520C
 00521C
 00522C
 00523C
 00524C
 00525C
 0052oC
. 00527C -
IF(fT, /FLOAT (KFOOL-1)
T*(1 -R)+R*TKI>
GO TO 40
R=FLOAT (II) /FLOAT ( IPOOL)
T =  FRACTION CLOUD COVER FOR TIME INCREMENT  I
   CL  =  LATENT  HEAT OF VAPORIZATION (CAL/G)
   CR  =  CLOUDINESS RATIO  =  1 -RAD RADiATioN(CAL/PAY/CM**2)
   HSO = SOLAR  RADIATION  INCIDENT ON THE ATMOSPHERE 
-------
                                                        \
00528C        SINA = MEAN SINE OF THE SOLAR ANGLE
00529C        SUNDEC = DECLINATION OF THE SUN(RADIANS)
00530C        T(I,J)= COMPUTED UATER TEMPERATURE AT LOCATION  I  AND  TIME  J
00531C        TIME= DAY HOUR
00532C        TA= AIR TEMPERATURE (C) AT 2M.
00533C        TDEU = DEU POINT TEMPERATURE CO
00534C        U= WIND VELOCITY AT 9M  (M/SEC)
00535C        UDIR= UIND DIRECTION (DEGREES)
00536C        UFTN = UIND FUNCTION FOR EVAPORATIVE AND CONNECTIVE HEAT
00537C               LOSSES (CAL/CM**2/DAY/MB>
00538      COMMON/A/ T<150,2)  TIME, IX, IPOOL, KPOOL,MHOUR
00539      COMMON/C/ TSTART,TLNGTH, IFLAG. JFLAG, KFLAG.JTIME.NSECT.NDELEAT
00540      COMMON/F/ TA(250), RH(250), RAD(250), U<250>, UDIR(250),P(250),CC(250)
00541      COMMON/G/ S( 17), SIGMA, HAY1, LAT, ALT, TOLDU50)
00542      REAL LAT
00543      IF(MFLAG GE 1) GO TO 8
00544C        CLEAR SKY SOLAR RADIATION
00545      Cl=l 0
00546      C2=l 0
00547      IF(RADCNH) GT 0 0)  GO TO 5
00548      HS=RAD(NH)
00549      GO TO 7
00550C        COMPUTE AVERAGE SINE OF SOLAR ALTITUDE,SINA
00551 5    HOUR1=0 262*(TIME-12 >
00552      IF
00556      SUHDEC=0 409*COfa<0 017I*<172 -DAY))
00557      HOURO=ACOS(-SIN(LAT>*SIN(SUNDEC>/COS(LAT)/COS(SUNDEC»
00558      1F(COS(HOUR1) LT COS.) HOUR1=C1*HOURO
OOC59      IF(COS(HOUR2) LT  COS(HOURO)) HOUR2=C2*HOUFn
00160      SINA=<(HOUR2-HOUR1)*SIN*X5 256
00567      AMASS=FALT/(SINA+0 15/+3 885>**1 253)
00568C        COMPUTE ATMOSPHERIC MOISTURE CONTENT,AMC (CM)
00569      CftH=l -RH(NH)/100
00570      TDEU=TA(NH)-CRH*<14 55+0 114*TA(NH))-(CRH*(2 5+ 007*TA(NH))>**3
00571     4-(15 9+0 117*TA)*CRH*K14
00572      AMC=0 85*EXP(0 11+0 0614*TDEU>
00573C        COMPUTE CLEAR  SKY SOLAR RADIATION,  HSM (LANGLYS/DAY)
00574      A1=£XP(AMASS*(-0 4o5-0 t30*AriC)*(0  179+0 421*EXP(- 721*AMASS)))
00575      A2=EXP(AMASS*(-0 4o5-0 13-UAMC>*(0 129+0 171*EXF(- 880*AMASS))>
00574      HSM=HSO*(A1+0 5*(1  -A2»
00577C     -   COMPUTE-CLOUDINESS RATIO
00578      IF(RAD(NH) GT HSM>  GO TO 6
00579      CR=1 -R'AD(NH)/HSM -  '
00580  6  -IF(RAIKNH) GT HSM)  CR=0 0
00581C        SHORTWAVE REFLECTIVITY WITH ANDERSONS EON
00582      A=2 ?0+CR**0 7/4 -«.CR**0 7-0 4)**2/0 16
00533      B=-l 02+CR**0 7/16  +**2>*<1 - 261*EXP(- 74E-4*TA(NH>**2»
00593  8   DO 10 I=1,NSEC1
NSFTN
                                          146

-------
                                                 \
10
00594
00595C
00596
00597
00598C
00599
00600
00601
00602
00603
00604
00605
00606
00607C
00608
00609C
00610
00611C
00612
00613
00614
00615
00616 100
00617
00618
00619C
00620C
00621
00622
00623
00624
00625
00626
00627
00628
00629C
00630C
00631
00632
00633
00634
00635
00636
00637
 II=I*IPOOL-KPOQL-H
     COMPUTE NET LONGUAVE RADIATION,HLR.
 TUS=/2
 HLR=SIGMA* 97*«TUS+273 >**4-EPS*+273.>**4)
     COMPUTE EVAPORATIVE HEAT TRANSFER,HE
 ES=6 1078*EXP(17 26939*TUS/aUS+309 ))
 DELTV=>-+273.>
** + 0053*U(NH)
 E=UFTN*(ES-EA)
 CL=597 5- 592*TUS
 HE=E* FOR  POOL I
 SU> = 
 CONTINUE
 RETURN
 FORMATU5, 13F10 4)
 ENH
 SUBROUTINE BISPERS, BK(17),CK(17),DL(17),DELX,
•EDTIME ,FE<17),FC<17),FI
 AN(K)=FC(K)*<1 +AMAXKO .(1 -0 1*PE(K-L»X*5/FE(K-L>))
 CK(K)=FC(K)*AMAX1(0 ,<1 -0  1*FE(K))**S/FE(K))
 BK,DELX,
•SDTIME ,PE(17).FC(17),FI
 AK(K)=FC(K)
 CK(K)=0 0
 BK(K)=1
 RETURN
 END
                                                                         NSFTN
                                                                         NSFTN
                                                                         NSFTN
                                                                         NSFTN
                                    147

-------
          APPENDIX E
SAMPLE INPUT DATA FOR MNSTREM
 Variable names and formats
 are specified in Appendix C
             148

-------
7 47
11.16
480
11 3

WEATHER
-10.
-11 1
-10
2
7
3 5
-3.
5
5
0.0
-1
& 5
10.
6
1
-2 5
-4 5
-3
3
12
13
8 5
4 5
4
2
1
0
5 5
7
2 5
-1
-4
-6 5
-11
-8
0
2 5
' 1 S
5
- 5
-1
-2
-1 5
1 5
S
- 5
-2
-2 5
-3 5
-4
-4
-3 5
-3 5
-5
-7
-9
-9
-9
-3
00.00
30
3 11
10 7
9 0
DATA FROM
100
100
100
64
42
52
75
61
65
69
68
37
36.
44
58
76
87
71
46
47
37
34
36
38
43
50
56
46
40
49
63
80
94
100
98
61
69
96
97
97
97
90
30
S3
72.
81
85
82
82
84
85
80
71
72
76
83
82
79
77
12 50
7
17 1
9

11-16-76

00
09
46
38
06




11
46
43
05




00
29
32
03




09
46
43
06




03
11
08
03




08
25
.09





00
09
09
01




01
3600 16

000
9
8 1
THROUGH12-06-76

00 0

3
6 5
3 5
2.
4
4
3 5
4
7
10
8 5
3
2 5
2
3
5
8 5
12
8
6
7
6
5 5
4 5
6
6 5
4 5
2
1 5
0
00

1 5
4
4
7
8
5
7
8.
9
B
8 5
9
8
8
7 5
6 5
6
7
6 5
6
5.5
3
6
4 5
            1700.
45.
                                 1000
THREE-HOURLY AVERAGE
979
979
979
979
979
979
979
979
971.
971
971
971
971.
971
971
971
969
969
969
969
969
969
969
969
975
975
975
975
975
975
975
975
975
975
975
975
975
975
975
975
980
980
980
980
980
980 -
980
980
985
985
985
985
985
985
985
985
985
985
985

0 0

0 0
0 0
0 0
0 0
0 0

0.0
0 0
0 0
0 5
0 0
0 0
0 0
0 0
9
1 0
6
5
3
0 0
0 0
0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
1 0
1 0
1 0
1 0
1 0
7
1 0
1 0
5
7
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
6
1 0
1 0
I 0
03 11-16-7
06 11-16
09 11-16
12 11-16
15 11-16
18 11-16
21 11-16
24 11-16
03 11-17
06 11-17
09 11-17
12 11-17
15 11-17
18 11-17
21 11-17
24 11-17
03 11-18
06 11-18
09 11-18
12 11-18
15 11-18
18 11-18
21 11-18
24 11-18
03 11-19
06 11-19
09 11-19
12 11-19
15 11-19
10 11-19
21 11-19
24 11-19
03 11-20
06 11-20
09 11-20
12 11-20
15 11-20
18 11-20
21 11-20
24 11-20
03 11-21
06 11-21
09 11-21
12 11-21
15 11-21
--18 11-21
21 11-21
24 11-21
03 11-22
06 11-22
09 11-22
12 11-22
15 11-22
18 11-22
21 11-12
24 11-22
03 ll-
-------
-6 5
-5 5
-7
-7
-8
-7 5
-5 5
-4.
-1.
4 5
3.
0
-5.
-4.5
-2.5
- 5
2
1 5
1.
1.
1.
- 5
-3 5
-4 5
Z
-2 5
-4 5
-8
-10
-12.
-14 5
-16
-13
-11 5
-14
-16
-17 5
-19
-18 5
-19 S
-15
-13
-12 5
-16 5
-17
-16 5
-15 5
-15
-10 5
-9 5
-13
-IS
-16 5
-18
-20
-21
-14
-10
-11.5
-15 5
-13 5
-13 5
-15
-13 5
-10 5
-9
70
64.
72.
75
79
92.
96
92
72
53
68
92
100
100
100
96
77
98
100
100
99
95
100
97
93.
92.
83.
68.
65
64
75
82
74
59
61
74
87
92
86
86
73
62
68
81
85
90
91
88
73
62
69
78"
84
39
91
90
77
58
73
93
85
83
84
as
79
75
15
20
02
02
22
28
00
00
02
00
00
08
15
09
00
03
40
49
06
08
49
46
06
06
52
49
03
11
46
43
05
02
 17
20
4 5
5 5
4
3.
3
3.5
3.
3 5
3
4 5
3
1.5
1.
1.
2 5
3.
4 5
5 5
4 5
4
5.5
4 5
4
4.5
7
6 5
8
8
9.
9
8.
6 5
7.
7 5
6
3.
1.
2. 5
4 5
4
6
6 5
4 5
2 5
6 5
4 5
3 5
4
6 5
8
6 5
6
4 5
2 5
1 5
2.5
4.
4.
2 5
  5
3.
4 5
3 5
4 5
6
5 5
985
985
985
985.
985.
985
974.
974
974
974.
974
974
974
965
965.
965
965
965.
965.
965
965.
974
974
974
974
974
974
974
974.
985.
985.
985.
985
985.
985
985
985.
985.
985
985
985
985
985.
985
985
985
985
985.
985
985.
985.
985.
985
985
985
985
985.
985
985.
985
985.
985
985
985
985
985
1 0
1 0
1 0
1 0
3
1 0
1.0
1.0
9
.9
1 0
1 0
6
.9
4
1.0
1 0
1 0
1 0
1 0
1 0
.5
2
1 0
1 0
1 0
1 0
1 0
1.0
1 0
1 0
1 0
6
6
6
0 0
0 0
4
5
0 0
3
8
8
0 0
0 0
8
1
.5
7
6
6
5
2-
0 0
0 0
0 0
0 0
1
5
6
1 0
1 0
1 0
1 0
1 0
1 0
12 11-22
15 11-22
18 11-22
21 11-22
24 11-22
03 11-24
06 11-24
09 11-24
12 11-24
15 11-24
18 11-24
21 11-24
24 11-24
03 11-25
06 11-25
09 11-25
12 11-25
15 11-^5
18 11-25
21 11-25
24 11-25
03 11-26
06 11-26
09 11-26
12 11-26
15 11-26
18 11-26
21 ll-?6
24 11-26
03 11-27
06 11-27
09 11-27
12 11-27
15 11-27
18 11-27
21 11-27
24 11-27
03 11-28
06 11-28
09 11-28
12 11-28
15 11-23
18 11-28
21 11-28
24 11-2S
03 11-29
06 11-29
09 11-29
12 11-29
15 11-29
18 11--29
21 11-29
24 11-29
03 11-20
06 11-30
09 11-30
12 11-30
15 11-30
18 11-30
21 11-30
24 11-30
03 12-01
06 12-01
09 12-01
12 12-01
15 12-01
               150

-------
-10
-13.:
-18
-21 :
-24 !
-25 :
-21 !
-19
-18
-16 :
-15
-13 !
-13
-12.!
-11
-8 !
-9
-13
-12
-13
-13
-15
-7
-5
-6.
-5
-7
-12
-16
-17
-12
-a
-7
-6
-3
11 1
10 3
1 2
1 2
10 4
9 8
10 1
9 8
9 6
B 6
9 2
9 2
3
	 2_
"V" a
a 4.
a 6
7 6
7 a
7 7
7 6
10 2
10 2
9 8
9 4
10 0
9 5
9 5
8 6
3 9
5
5
5
5
5
5-
5-
5
5
5
5
5
5
5
5
5
5
5
5
5
12
11 *?
i £
10 2
1 4
1 1
10 6
9 7
9
9 7
9 7
7 5
9 3
9 4
8
	 7_
10 0
R T
" 8 2
"7 6
7 6
7 6
7 5
12 6
10 3
9 9
9 4
10 1
9 4
9 3
8 6
8 9
75
79
72.
73
76
74
61
60
65
67
70
83
85
- 90
92
80
88
100
99
96.
97
98
92
92
99
99
97
100
99
97
99
96
100
100
100
12 3
1 A O
10 V
10 2
1 6
1 1
10 6
9 6
4 6
9 6
9 8
7 6
9 4
9 6
8
. 	 7_
10 2
a. 4
8
- 7
7 6
7 6
3
12 2
10 2
a 7
9 5
10 0
9 4
9 2
8 6
8 9



11 6
10 8
10 1
1 7
1 1
10 6
9 6
4 6
9 5
9 8
8 6
9 4
9 6
9
„ ..&.-
3 4
8 5
a
7-
7 6
7 5
3 6
12 0
10 0
3 2
9 5
9 9
9 5
9 2
Q 6
8 9
0
o:
3
.3
0
0
1
2
0
. 0
2
1
0
0
2
1
0

11 2
10 8
10 1
1 6
1 1
10 6
9 6
10 2
9 3
9 9
9 2
9 4
9 6
9
.- -6.
a 6
R 5.
7 9
7 8
7 6
7 5
9 0
12.1
10 0
8 4
9 6
9 8
9 5
9 2
8 7
a a
5
5
8
7
2
0
5
3
2
6
8
8
2
3
2
7
1

10 9
1 rt >£.
1 \J O
10 0
1 6
1 1
10 5
9 5
10 2
9 2
10 1
9 4
9 4
9 6
9
4f
a 6
8 6.
7 9
- 7 7
7 5
7 4
9 3
12 2
9 9
9
9 6
10 0
9 5
9 0
8 8
8 3
5
5
5.
4.
4
2
1.
2
4
5
6.
~~ 67
-- 5
3.
2.
3
2.
2
2
2
2
3
5
4
3
4.
3
1
2
3
3
4.
5
10 8
10 0
1 5
1 1
10 5
9 5
10 2
9 2
10 1
9 3
9 3
9 6
9
	 6--
8 5
a, 6
7 8
7 7'
7 6
7 9
9 2
12 3
10 1
9 4
9 7
10 0
9 4
3 3
8 3
a a
S
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5

10 6
9 8
1 4
I 2
10 4
9 3
10 0
9 1
10 0
9 I
9 3
9 6
8
	 ^.£_
8 6
a. 6-
7- 8
7 6-
7 6
7 8
9 3
12 2
10 0
9 1
9 8
10 0
9 4
8 9
8 8
8 8



11 0
9 8
1 4
1 2
10 2
9 2
10 0
9 1
9 9
9 1
9 3
9 6
8
_ . 6-
3 o
a 6
7 7
•7 6
7 6
7 8
9 6
12 1
10 0
9 2
9 8
9 9
9 4
9 0
3 9
8 9



11 0
9 9
1 4
1 2
10 1
9 4
9 o
9 2
9 8
9 0
9 3
a
a
--9 4--
8 6
8- 6
7 7
7-6
7 6
7 6
9 5
11 7
10 0
9 2
9 8
9 7
9 4
8 3
8 7
8 9
985
985.
985
991
991
991
991
991
991
991
991
980
980
980
980
980
980
980
980
986
986
986
986
986
986
986
986
989
989
989
989
939
989
989
989
3 6
9
1 3
11
10 0
9 6
9 7
9 4
9 7
9 1
9 3
8
8
-9_2-
8 5
-8 7
7 6
-7 7
7 6
7 <<>
9 4
11
10 0
9 3
9 9
9 6
9 4
8 3
8 3
9 1



10 6
1 rt
1 \J
1 0
1 2
10 2
9 9
9 8
9 9
9 6
9 6
9 1
9 3
8
7
-9 -4~
8 6
& 8
7 6
7 S
7 6
7 9
9 4
6
9 8
9 4
10 0
9 5
9 4
9 0
8 8
9 0
10 18 12-01
8 21 12-01
6 24 12-01
.0 03 12-02
00 06 12-02
5 09 12-02
5 12 12-02
7 15 12-02
8 18 12-02
10 21 12-02
10 24 12-02
10 03 12-03
10 06 12-03
1 0 09 12-03
10 12 12-03
10 15 12-03
10 18 12-03
10 21 12-03
10 24 12-03
10 03 12-04
10 06 12-04
.2 09 12-04
8 12 12-04
10 15 12-04
10 18 12-04
10 21 12-04
10 24 12-04
7 03 12-03
4 06 12-05
10 09 12-05
10 12 12-0"5
1.0 IS 12-05
10 18 12-05
8 21 12-05
10 24 12-05
11-16-76 00
11—1 A — ~?A 1 *^
11 lO /O 1^-
11-17-76 00
11-17-76 12
11-18-76 00
11-18-76 12
11-19-76 00
11-19-76 12
11-20-76 00
11-20-76 12
11-21-76 00
11-21-76 12
11-22-76 00
11-22-76 12
U-2-3--76-OO 	
11-23-76 12
11-24-76- 00-
11-24-76 12
11-25-76-0-0
11-25-76 12
11-26-76 00
11-26-76 12
11-27-76 00
11-27-76 12
11-28-76 00
11-28-76 12
11-29-76 00
11-29-76 12
11-30-76 00
11-30-76 12
12-01-76 00
151

-------
"9.0 9
939
9.6 9
« ft ft * ft
IV U i V
949
11 0 10
10 S 10
10.6 10.
10 6 10
10 4 10
473
456
8
192
14 2
17 7
10.8
11 0
189
292
798
If ft t
IV i
293
8 10 8
4 10 7
- 4 10 4
6 10 7
4
601
24 24
3 4
3 0
6 6
5 9
909
9 1 9
10 0 10
1 ft 4 4 ft
Iv 1 Iv
2 0 10
10 9 10
10 5 10
10 7 10
10 6 10
582.
48
16 7
18 5
11 0
10 9
0 9
3 9
0 9
01 A
lu
0 10
7 10
5 10
4 10
.6 10
601
72
4 0
3 2
6 2
5 4
"0 9.0
292
.999
01 n rt
IV v
2 10 6
8 10 8
5 10 5
8 10 6
4 10 4
582.
24 24
18 2
17 2
10 9
10 8
929
929
10 0 9
10 5 10
10 7 10
10 5 10
10 6 10
10 4 10
620.
24
4 0
2 3
6.7
5.6
.292
2 9.2
9 9.7
8 11.0
8 10 6
5 10 5
5 10 6
4 10 5
601
48 48
17 8
20 0
11 9
10 5
9 1
9 3
9 9
10 9
10 7
10 6
10 6
10.5
582.
3 3
6 4
9
9
10
11
10
10
10
10

1
. 4
0
.0
.6
4
6
2
45
17.
11
12-01-76
12-02-76
12-02-76
1*% /N^ -7 1
c.— QJi — /o
12-03-76
12-04-76
12-04-76
12-05-76
12-05-76
6 473
0 3.2
3 5.9
12
00
12
S\/\
Ov
12
00
12
00
12

152

-------
             APPENDIX F
PARTIAL SAMPLE OUTPUT FROM MNSTREM
                153

-------
"HAIER"  JEMPE'SAIURE^FKOH FINIIE  DIFFERENCE MODEL  «f?V"
~ X-INCREMENI (HI = 3.81
TIME INCREMENT tiEC) =3600.00
L^ ' IX = 136 JTIME= 1 IPOOL= 8""
*" •= ACI. IEMP
J ESF. ItHP
v, AC i. r tip
PfJIDUAL
ESI. ItMP
^ AC1.UHP
RESIOUIL
ESI. TEMP
>^ ACI.IENP
RESIDUAL
ESI. ItHP
x, ACT.fEHP
P^. P£ SI DUAL
o| fSt . TEMP . .
L ,H ACT. It HP
f) RE M DUAL,
O ESI. TEMP
x, «-( An.TtMP
cr> PFSIOUAL
ESI. IEMP
». AC I . I VMP
PESIOUAL
11.17
^ fSI. IEMP
AC I.I tlf
RESIDUAL
x_ FSI. IEMP
ACI. JEMP
RESIDUAL
^, ' ESI. IEMP_.
ACI. TEMP
PESIDUAl _„
W - ESI. IENP
" ACI. TEMP
RESIDUAL
^ ESf. IEHP._
ACI. It HP
RESIDUAL
\^. ESI. IEMP
>. ACI. It HP
RESIDUAL
^ rsi. IEHP
ACI . TtH^•
<'£•,10UAL
HOUR i ' i
10.33 10.70
3 11.83 11.78
0 12.10
0 -.32
6 10.88 10.72
0 10. BO
0 -.08
9 11.11. 11.03
" a J.L.IO
0 -.Q8
12 11.33 11.26
0 .16
15 __10.99 11.02
0 10.90
18 10. H '10.11.
0 10.00
0 .11.
21 9.72 . 9.60
0 .00

-------
in
in
«C i 1 UU we.
ESI. I£r"p 1,05 8
ACI. IEMP
RESIDUAL
12.03
ESI. IEMP 	 f;08_ 	 B
ACI. IEMP"
RESIDUAL
LSI. IEMP 1.11 y
«CI. IEMP
PESIOUAL
ESI. IEMP i, I it 8
ACI. IEMP
RESIDUAL
ESI. IEMP 1,17 8
ACI. IEMP
RESIDUAL -
.ESI. UMP 	 1,20 	 3
ACI. IEMP
PESinilAL
tSI. IEMP 1,23 J
ACI. IE1P
PESIDUAL
ESI. IFMP 1.26 10
ACI. IEMP
RESIDUAL
ESI. IEMP 1.29 11
ACI. IEMP
Rf SI DUAL
12.01,
ESI. IEMP 1,32 11
ACI. IEMP 	
RESIDUAL
ESI. IEMP 1.35 10
ACI. TEMP
PESIDUAL
tSI. IEMP 1,38 10
ACI . IEMP
REJ10UAL
ESI. IEMP 1,1.1. _JO
ACI . IEMP
RESIDUAL
ESI. IEMP 1.1.1. 10
ACI. IEMP
RESIDUAL
FSI . IEMP_ . 1.1,7 	 10
ACI. IEMP
PCSI (1UAL
ESI. UMP 1.50 10
ACI. IEMP
RESIDUAL
LSI. IfMP 1.53 10
ACI. IEMP
RESIDUAL
.65 . 8.1.2 • 8.12
Q 8.1.0 ' 0
If .02 0
.90 8.62 '_8;2J
0 8.70 0
0 -.04 0
.00 8.73 ' 8.36
0 8.70 0
0 .03 0
0 8-'<> »
0 -.06 0
,6«' 8.1,2 8.13
0 8.1,0 '. 0
p .02 u
.Z\ 8.93 8.51
0 8.30 ' 0
0 .63 , 0
.79 <«.92 6.1.5
0 7.60 , 0
0 *2.68 0
.51, 10.1,6 10. 17
g iO.i.0 o
0 -06 ' 0
.01 1U .75 10.58
0 10.50 0
0 .25 0
.05 10.83 10.52
0 10.50 0
0" .33 " 0
.91 10.66 10.32
0 10.80 i 0
0 -.1U 0
. flt, 10.60 10.27
0 10.70 0
g -.10 o
.68 10.1,7 10.18
0 io.i>0 0
0 	 ,.07 _ .0
,b<, 10.55 10.1,5
q 10. 6Q 0
"O -.05 0
.66 1Q.55 10.36
0 10.50 , 0
0 '.05 0
.5? IP. 39 10.11.
0 10.1,0 0
9 -.01 o
.58 10.1.2 10.20
' g 10.60 0
. i -•!«. . . o
7.90
0
0
0
0
8.11
0
0
0
0
7.93
0
0
8.1.29
0
0
7.01,
0
0
2.76
0
0
10. 13
0
0
10.32
0
0
10.09
0
0
10.05
0
0
9.97
0
0
10.37
0
0
10.22
0
0
9.97
0
0
10.05
0
• o
7.59 7
7.50
.. .09
7 .55 7
7.1.0
.15
.35 7.00 	 6
0 0
0 0
•T6_6,
0
0
J.3__6.§1 	 5.90 5_i69 5
0 " 0 'S.TO "fl
0 0 .20 0
»!-0__5..21
0 0
0 0
0 1..60
0 .16
•27._6.J6 	 6.60 6.25 6.02 5.70 5.1.9 5.20 	 5.01 I.. 73 it. 51,
ooooo 5.50 o o o g I..30
00000 .20 OOOOO
7.75 7.50 7.11 6
7.70 0 0
.05 0 0
7.69 7.1,6 7.11 6
7.60
.09
7.65 7
7.60
.05
_ . 8 . 0 0 	 7.
7.90
•10 ._
7.79 8
t>.30
0
8.70 8
9.50
-.80
9.77 9
9 50
.27
10.03 9
9.30
.23
9.10 9
9.60
.20
9.75 9
9.50
.25
9.68 9
9.50
..18
10.26 10
10.00
.26
10.01 9
9.80
.21
9.73 9
9.60
.13
9.81. 9
9.80 "
.01.
0 0
o o
.1.5 7.15 6
0 0
0 0
.83 7.58 7
0 0
0 _ 0
.01 8.21 8
0 0
0 0
.•_S5_7_I0".90 " 0
0 .27 0
.61 9.1.0 9.28 9
0 8.90 0
0 .50 0
.30 9.18 9.09 	 9
0 8.70 0
0 .1.8 0
.85 8.67 8.55 8
0 8.30 0
0 .37 0
,.95 8.71, e_,61 «
0 8.1.0 0
0 .31, 0
.37 5.16
0 0
0 0
.53 5.31,
0 0
0 0
.70 5.52
0 0
0 0
JL.H5 	 6_,Jl
0 0
0 _ 0
.57 7.1,14
0 0
0 0
.59 5.60
0 0
0 0
.26 6.93
0 -0
0 0
.09 7.92
__o 	 g
o g
.00 7.81,
0 0
.81. 7.67
0 0
" "o b
J12_JJ.5S
0 0
0 0
.03 8.90
0 0
0 0
..?8_8._9Q
0 0
0 0
.38 8.27
0 0
0 0
,1,0 8,27
o a
0 0
i<. 81, 1..61,
	 0 .Jt.20
o o
	 S..J15 	 h.86
0 <>.10
0 0
5.25 5.07
0 1..30
0 0
6.08 5.93
0 5.10
0 .83
7.21 7.09
0 6.00
0 1.09
5.M 5.71
0 ** • *i 0
0 0
6.36 6.06
0 6.60
0 -.51,
7.66 7.1,9
0 7 . 1*0
0 ~ .09
7,60 7.1.1,
0 7.50
0 -.06
7.1.3 7.27
0 7.50
0 -.23
_£.30__7,13
0 7.1.0
0 -.27
8.65 8.52
0 8.20
0 .32
g~8.i.g
0 .31
- 8.12 8.01
0 7.90
0 .11
a.Oe 7.96
0 8.20
	 0 -.21.
0
0
I..28
0
0
1..33 3
0
0
0
0
1..79 9
0
0
5.68 12
0
_ 0
6.81. 15
0
0
5.33 18
0
0
5.52 21
0
0
7.19
	 0
0
_7,2Q ' 3
0
0
7.01. 6
0
0
*" 0
0
8.21. 12
0
0
«j^9 15
0
0
7.89 I 18
' 0 ''
0
-L.78 ; zi
0
- 0 . .
till) 	
0
.00
.00
.00
.00
,o"o
.00
.00
0
,00 	
.00
,00 	 	
.00
. 00 	
.go
.00

14
m
20
72
4
26
It
30
32
34
36
36
40
42
44
46
48
50
52
34
itl
56
60
62'
64'
1

-------
Ul
Ol

CO
o
01
o
-
-
-;



12.05
EST. IEHP 456
ACT. TEMP
PESIDUAL
r.SI . It HP 459
ACI . Tt HP
RESIDUAL
ESI. TEMP 442
ACI. ItMP
FESIDUAL
ESI. IE1P 465
ACI. IEMP
ESI. IcMP 4b8
ACI.IEHP
PESKIUAL
ISI. ItMP 471
JCI. IEHH
PESIOUAL
ESI. IEMP 474
ACI.TtMP
PESIOUAL
ESI. ItMP 477
ACI. ItMP
PESIDUAL
12.06
ESI. IEMP 480
ACI.IEHP
RESIDUAL
BtSIOUAL SUM
I
• i .
10.6V 10. Jb 10.06
0 10. btl 0
0 -.24 0
10.66 10.37 9.94
0 10 .SO 0
a - . rt o
10.69 10. tit 10.14
0 10.4P 0
o • o$ i o
10. be 10. lit 10.10
. .0 io,6l> : o
o -.20 i a
10.70 10.55 ^0.36
0 10.70 I 0
0 -.15 . 0
10. 72 10.59 110.39
o 19.50 o
0 .09 | 0
10.46 10.28 {10.05
0 10..50 0
O1 T.2ZJ 0
10.54 10.33 110.05
0 10.30 | 0
0 '.03 ! 0
10.42 10.2,2 ' 9.98
0 10.. 40 1 0
-i T.»; o
Oh SQUARES = 55

9.8/ 9.60
0 9.40
0 .20
9.74 9.41
0 9.20
0 .21
9.91 9.58
0 9.10
0 .28
9.90 9.64
0 9.40
0 .24
10.24 10.06
0 10.00
0 .06
10.26 10.06
0 9.40
0 .26
9.90 9.69
0 9.40
0 .29
9.86 9.60
0 9.40
0 .20
9.84" 9.65
0 9.20
0 .45
.2382

9.41
0 "
0
9.19
0
0
9.35
0
0
9.45
0
0
9.92
0
0
9.92
0
0
9.i>4
0
0
9.42
0
0
0
0


9.14 8
0
0
8. 87 II
0
0
9.00 8
0
0
9.17 8
0
0
9.71 9
0~
0
9.71 9
0
0
9.33 9
o""
0
9.15 8
0
0
9.30 9
0
0


.96 a.
0
0
.66 8.
0
0
.77 a.
0
0
.98 'a.
0
0
.57 9.
0
0
.57 "9.
0
0
.18_,_8_.
0
.98 8.
0
0
.1&"~8.
0
o".


72 8
0
0
ID 8
0
0
45 8
0
0
71 8
n
0
0
0
38 9
0
0
98 a
"o "
0
74 8
0
0
94 ~8
0
0


.56
0
0
.19
0
0
"n
0
.51
0
0
.21
0
0
.26
0
0
.85
0
0
.59
0
0
."so~
0
0


4.35 8.20 8.01
7.90 0 0
.45 0 0
7.94 7.76 7.52
7.70 0 0
.24 0 0
7.94 7.74 7.45
7.50 0~ " 0
.44 0 0
6.Z7 8.09 7.81
7.80 0 0

7.8B' 7
) "
7~.3p! 7
0
7.27' 7
0
0
7 . 6]4 7
'fl
.47 0 0 )0
8.99 8.65 a. 61 8. . 4*7 8
8.70 000
.29 0. 0 ,0
9.09 8.97 8.80 " a. 70 8
».60 '0 0 0
.49 0 0
8.67 8.54 8.39
8.00 0 0
.67 0 0
8.38 B. 23 8. 04
7.90 0 0
.48 0 0
8.59 8.~44 872Z
7.90 0 0
.69 0 0

0
8.Z6 8
0
0
7.9;l 7
0
»°
8."09, 7
;o
53 8.42 8
0 8.40
a .02
.10 7.99 7
0 7.70
0 .29
.73 7.61 7
0 7.50
0 .11
.~88 7.7S"~7
0 Z.60
0 .15


.40 0 j vJ
0
0 4
.00 1. 00 ~J
0
0
.57 6. Oil 8 -J
0
. 0 lu
.91 9.00 ~J
0 i?
o ,
.86 12.00 u *J i
0
0 i
.25 IS. 00 J
0 ,K
0
.84 18.00 ,u — '
" 0
0 )?
.45 21.00 ->
a 3.
0 ?
."54 0 "i
0 IB '
0 ^
u

                      SI4NOBKD EKKOK=
                      OllEAItO CASES =
                                                                                                                                                                       -36


                                                                                                                                                                        IB


                                                                                                                                                                        40
                                       r   !'

-------
                                  APPENDIX G
                            MERS WEATHER STATION

     The MERS channel water temperatures are controlled by inflow and
weather conditions.  A station to measure and record weather parameters was
therefore installed near the center of the field station.  Solar radiation
and wind velocity were recorded since December 3, 1975.  A 50 - junction Epply
pyranometer and a Science Associate's anemometer were mounted at 2 m and 9 m,
respectively, above the ground.  A Belfort hydrothermograph, with a bimetal
temperature sensor and hair hydrometer, were mounted in a weather shelter
and recorded air temperature and relative humidity since January 29, 1976.
A Texas Electronics wind direction vane and transmitter, mounted at 4 m, with
power supply unit and Rustrak recorder was put in operation on April 2, 1976.
Sample strip chart records are shown in Figs. G-l and G-2.  The weather station
is shown in Fig.  G-3.   A one-year  cycle of measured air temperatures is shown
in Fig.  G-4.
                                      157

-------
Solar Radiation (cal
Ul

00

H-
iQ
•
_^
1
t-1

1
CL l/>
^' |j
n> -o
n — '
r*- fC
O l/>
3 (-+• a
. -I 0)
-•• •<
O> XD
3 • n:
o. o o
3- C
O T
OJ I/I Is
-J 2
-t»
-so o
O.
-• $: T3
cu -i. 2
(-*• 3 — '
-•• a.
0
3 <
• a>
o
O Q-JO
"•*' 
— ' ""a.
n <& ~*^
o
n -j
o 3
•o
|£»l4
O
' I
to
>Q-
>' !
'.©,.-;.
V
t
««)-4 •
i®
H ;
JO--
>
^0 5
^ *
c
'^"W
ni)'- '
* ' ,1 '
:o ' -
^ i
/ O ~6 * •
i *
J1 yN* •*
^ ^J --*-
< 1 *"
' *i
i* iO "—•-•
} ' »-*
/ /" V.
f V *%.
' ~\ J^**!
: U- 7r*
>\V 'i
' ^ -1-"
' >''
O-- <^;
t i
• i"\'


                          2  -1
                        cm min  )
                        I !l '," I" 11

                         •' I'1 ..illil.
Uind Direction (degrees)
     —•  ro
  

n Wind Velocity (m/sec) .

n ' co CD ip Cj3 C 5 CD CJ> CJ J^fcHt-F-rrT I ' i . i—j ! * *' i •' I I ' i ' I i I ^trlJ^jlTm ^itr! rrtTTTrrr ir^rmTnlTTi b'lJJj.vJ-L.L '3!-JX-{J4- I ! !' V,1 I I i i' IXTI^!.! _[:. j). ->_,_1'_1.^ • T_"' 1 *»':• . •<.<*• ——>x-»i- > • .V- ,• ;Jr"' ' II _LH o. --r--:-;-1-- * 11 '.^,'. ' O1 ' ' I , ! __.T-'}''^ x' ! ' I I ' II , „ ;.,,vvi—K. 1 —I'r- o'-iiilL-^"1.'-!:1..!:..'::!'].^ **l i I _ «V.i-,- i ii ii ' Q^II'!^ i''1.^'.1!.:..'.^.!1:.1']!1. ^iT?l'r:'!ii'^"!!^^ ol-^ll1!!^


-------
                          '   !     MONDAY	v	TUESDAY	v	WEDNESDAY	v	THURSDAY	v	
                          1   ' 4- S 8 lO^IJa 4-68 lO^Jta 4-68 lOXIf? 468 lofjl 2 468 /qXJfS 468 10WS f 6 Q IQXffS 4-68 10^2 » 6 t
                         ^   —~—————~———————————————~~      ———•   '~
si
                      Fig. Gr2  - Sample  hygrothermograph  strip chart for degrees £e1c'ius air  temperature
                                  (top) and percent relative  humidity (bottom).   *

-------
                  r
Fig. G-3.  Weather station with hygrothermograph and shelter,
           pyranometer, wind vane, and anemometer.  Top - complete
           weather station.  Bottom - hygrothermograph, small
           weather shelter, and pyranometer.

                                  160

-------
  35


  30


  25

  20


   15

   10

o
t.  5
o
h-
<"  c
I"5
 -15


-20

-25

-30

-35
                                    Highest oir temperature for one
                                    week
                                    Weekly mean of fhe dally  high
                                    temperature
                                    Weekly mean  temperature
                                     ©Weekly mean of  the doily low
                                     temperature

                                 ^  Lowest  air temperature for one
                                 ^  week
        Feb     Mar    Apr   May     Jun    Jul    Aug     Sept    Oct     Nov     Dec   Jan
                                                1976

        Fig.  G-4.  One-year cycle  of air temperatures.   February  1976 through
                    January 1977.
                                                                                      1977

-------
                           APPENDIX H
           SAMPLE OUTPUT FROM PROGRAM WTEMP1
               WATER TEMPERATURE- STATISTICS

                            ********
                       WATER TEKPERATUPE STUDY
            US EPA NONTICELLO ECOLOGICAL RESEARCH STATION
                          "CONDUCTED 8Y~"
                       UNIVERSITY Of (IIMNSSOTA
                ST.  ANTHONY FALLS HYDRAULIC  LABORATORY
     STATISTICAL ANA'LYS'IS OF "OPERATIONAL" MATE'R  TENPERATURES FOR  "
                       CHANNEL *» STATIQN~~2

                               NOTES»
»ERICD CT ANALYSIS  IS  FROM   10/20/76 TO  9/19/77.  ALL STATISTICS
DECOROED ARE SLIDING    7-DAILY PARAMETERS.  COMPUTED ft OH THREE-HOURLY
DiTt.  ALL STATISTICS,  EXCEPT SKEVNESS*  ARE RECORDED IN DEGREES CEL-
CIU5. SKEVNESS IS  OInENSIONLESS.  ALL CALENDAR  WEEKS START ON  SUNDAY.
                                162

-------
           otrE
                    CALENDAR
                    OAY/UEEK
 DAY OF
THE WEEK
  nlHlHUH
TERPEBATUBE
CTl
Ul
f>eo6A8HiTies IN PERCENT
 99.0     50.0      5.0
  KAKIKUK
TEMPERATURE
                                                                                                    NEAN
STANDARD
DEVIATION
                                                                                                                       COEFFICIENT
NO. OF ESF.
DATA POINTS
J J * *"
^•10-23-76
3MO-24-76
-O10-36-76
10-37-76
-10-3»-76
10-3«-76
IP-30-76
10-31-76
11- 1-76
11- 3-76
11- 3-76
11- 4-76
11- 5-76
11- 6-76
11- 7-76
'11- 0-76
-11- 9-76
"11-10-76
11-11-76
-11-13-76
11-13-76
11-14-76
11-15-76
11-16-76
U-17-76
11-18-76
11-19-76
11-20-76
11-31-76
11-33-76.
11-33-76
-11-34-76
11-35-76
11-36-76
-11-37-76
11-38-76
'11-39-76
-11-30-76
13- 1-76
12- >-76
13- 3-76
13- 4-76
12- 5-76
12- 6-^6
13- 7-7*
-12- d-76
13- 9-76
13-10-76
13-11-76
-13-13-76
13-13-76
13-14-76
12-15-76
12-16-76
12-17-76
17-1(1-76
13-19-76
13-30-76
13-31-76
397/43
398*44
399/44
300/44
301/44
302/44
303/44
304/44
'05/45
J06/45
307/45
308/45
109/45
31O/45
311/45
312/46
313/46
314/46
31 V46
316/46
317/46
316f 46
319/47
330/47
331/47
333/47
333/47
334/47
335/47
326/4«
327/48
328/4»
329/4H
330/48
331/46
332/4P
333/49
334/49
335/49
336/49
337/49
338/49
339»49
340/50
341/«0
343/50
343/50
344/50
?45/50
346/50
347/il
34P/51
349/51
350/51
'51/51
353/51
353/51
354/53
S»T, 4.4 7.
SUN. 3.4 6.
BOW. 3.4 6.
TUEt 3.4 6.
UEO. 3.4 6.
THU. 3.4 6.
FBI. 3.4 6.
sir. 3.4 6.
SUN. 3.6 6.
HON. 3.4 6.
TUE, 3.1 6.
UFO. 2.7 6.
THU. 1.4 6.
FBI. .8 6.
SAT. .7 5.
SUN. .7 3.
MPN. .t 3.
TUE. .6 3.
WEO. .6 3.
THU. .5 3.
FBI. .5 3.
SAI. .9 3.
SUN. .5 3.
urn. .{ 3.
TUE. .5 3.
WED. .5 2.
THU. .5 2.
FRI. .6 3.
SAT. .6 3.
SUN. .6 3.
HON. .5 3.
TUE. .5 3.
UEO. .5 3.
THU. .5 3.
FBI. .5 3.
SAT. .5
SUN. .5
HON. .5 .
TUE. .5
WEO. .6
Tt'U'. .5
FBI. .5
5AT. .5
SUN. .5
VON. .4
TUE. .4
UEO. .4
THU. .4
FBI. .4
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SUN. .4
HON. .3 .
TUE. .3
uEp. .3
THU. .3
"»«I. " "" ~" .2 .
StT. .2
SUN. .2
m|f. .z
TUE. .2
) 5.7 4.6 7
I 9.4 3.8 6
> 5.3 3.7 6
1 5.1 3.7 6
i 5.1 3.7 6
i 5.1 3.7 6
' 5.1 3.7 6
6.0 3.7 7
6.0 3.9 7
6.0 3.6 7
t.O 3.2 7
f.O 2.9 7
3.6 1,6 7
3.3 .9 7
2.9 .6 6
l.« .7 4
1.3 .6 4
1.1 .6 3
1.0 .6 3
.9 .6 3
.9 .5 3
.9 .5 3
.6 .5 3
.9 .5 3
3 .9 .9 2
> 1.0 .5 2
> 1.0 .5 3
! 1.1 .7 3
S 1.3 .7 3
5 1.1 .7 3
5 1.0 .6 3
> .8 .5 3
S .8 .5 3
i .7 .5 3
k .7 .9 3
9 .7 .5
B .7 .5
9 .7 .5
» .7 .7 1
9 .7 ".7 1
) .7 .6 1
9 .7 .5 1
9 .7 .5 1
» . .5 1
» . .5 1
9 . .4
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b . .4
5 . .4
5 .5 .4
S .9 .4
9 .5 .4
5 .5 .4
3 .4 .3.1
4 .4 .3 1
4 .4 " .3 1
4 .4 .3 1
4 .4 .2 1
S .4 .2 1
J .5 .2 1

*
•
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•
•
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•
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•
•
•
•
•
•
•
•
•
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•
•
•
•
*
•
•
•
•
3

0
0
0
0
0
0
0
2
4
4
9
5
5
5
5
5
5
1
1
6
6
6
6
6
6
6
5
6
8
6
0
0
0
0
0
0
0
9
7
7
7
7
7
7
5
5
5
5~
5
S
5
5
5
5
5
5
5
5
5
S
5
5
5
4
4
3
2
2
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1
1
1
1
1
1
1
1
1
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.'l
.0
.1
.2
.3
.6
.6
.7
.4
.'s
.5
.7
.1
.7
.5
.3
.1
.1
.0
.1
.1
.1
.1
.3
.5
• 5
.4
.2
.1
.1
.9
.7
.7
.7
.7
.7
.7
,7
.7
.6
.6
.6
.9
.5
.5
.5
.5
.4
.5
.5
.5
.5
.5
.7
.6
.66
.71
.71
.72
.64
.91
.00
.06
.93
.06
.33
.92
.73
.64
.46
.16
.02
.66
.67
.69
.67
.67
.67
.69
.47
.47
.43
.66
.62
.84
.86
.90
.91
.93
.69
.09
.08
.06
.07
.07
.09
.10
.12
.13
.14
.10
.06
.09
.05
.05
.06
.07
.06
.35
.32
.33
.34
.39
.45
.51

-
-

1
2
2
2
1
1
1
1
1
' 1
1
2
9
1
1
1
3
2
2
2
1
.30
.62
.54
.39
.14
.09
.14
.59
.71
.81
.56
.07
.40
.39
.26
.79
.69
.71
.37
.30
.41
.29
.92
.61
.72
.70
.82
.38
.36
.49
.82
.96
.03
.23
.44
.48
.63
.79
.61
.37
.91
.91
.76
.12
.26
.51
.62
.79
.61
.63
.36
.53
.19
.36
.14
.19
.66
.95
.29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

-------
"«
         CAIEHOAB
         04V/WEEK
" 0»lt OF
IHE WEEK
  HINIHUH
TEHt>ERATU>£
PROBABILITIES  IN PERCENT
 99.0     »0.0      5.0
  HAXInUH
IEMP£RATURE
                                                                                       HE AN
STANDARD
DEVIATION
 SKEWNESS
COEFFICIENT
NO. OF ESI.
DATA POINTS
•^1
f -r
oil
i_ i
i
i
i
i
i
i
D
Reproduced from jj»%
best available copy. ^|§P
2-22-76 357/52 UEO. .2 1.5 .8 .2 1. .9 .53 .02 0
2-25-76 360»5i
2-26-76 '61/
2-27-76 362/
2-2«-76 363/
J-29-76 36<>"
2-30-76 365/
2-31-76 366>
- 1-T7 If
- 2-77 It
- 3-77 	 3/_
- 5-77 It
- 6-77 6/
- 7-77 7/
- e-77 e/
- 9-77 9/
-10-77 10*
-11-77 ll/
-12-77 12/
-13-77 13/
-14-77 Ht
-15-77 15/
-16-77 16 /
-17-77 17/
-18-77 lt»
-19-77 111
-20-77 20/
-21-77 21/
-22-77 tit
-23-77 23/
-M-77 24/
-25-77 25/
-26-77 26/
-27-77 27r
-Z8-77 Zfl/
-29-77 29»
-30-77 30/
-31-77 31/
- 1-77 3?f
- 2-77 33/
T»U. .J 1.6
FRI. .3 1.6
SAT. .3 1.6
SUN. .8 1.6
HON. 1.3 1.6
TUE. 1.3 1.6
yep. 1.3
THU. 1.3
FRI. 1.0
SAT. 1.0
SUN. 1.0
HON. 1.0
TUE. i.o
WEO. 1.0
THU. i.o
FRI. 1.0
SAT. 1.0 """
SUN. 1.0
NQH. 1.1
TUE. 1.1
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THU. 1.1
FRI. 1.0
SAT. 1.0
.8
.8
.8
.8
.6
.6
.6
.8
.3
.3
.3
.3
.3
.3
.3
.3
.3
.3
SUN. 1.0 1.3
HON. 1.0 1.3
TUE. .9 1.2
WED. .9 1.2
THU. .9 .2
FRI. .9 .2
SAT; .9 ,j
SUN. .9 .2
TUE. .9
WED. .9 1.
THU. .9 1.
FRI. .9
SAT. .9
SUN. .9
HON. .9
TUE. .9
b WEO. .9
- 4-77 35/ 6 FBI. .7
- 5-77 36f 6 SAT. .5
- 6-77 37f 7 SUN. .5
- 7-77 »•/ 7 HON. .4
- »-77 39> 7 TUE. .4
- 9-77 IQI'1 WEO. .<
-10-77 41r 7 THU. .4
2-11-77 42/ 7 FRI. .4
2-12-77 43/ 7 SAT. .4
2-13-77 44f SUN. .4
2-14-77 45f tt(lN. .4
2-15-77" *57~ TUfi "3 ~
2-16-77 «7/ WED. .3
2-17-77 4«/ THU. .3
2-18-77 49f FRI. .3
2-19-77 50f SAT. .3
1 •
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• 1
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.1
.1
.1
.1
.4
.<•
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.4
.4
.5
.5
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.2
.2
.2
.2
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.2
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.2 1.
.3 1.
.4 1.
.3 1.
.3 1.
.3 1.6
.3 1.9
.3 1.9
.1 1.9
.1 1.9
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.1 1.9
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.1 1.8
.1 1.3
.1 1.3
.1 ~ 1.3
.1 1.3
.1 . 1.4
.1 1.4
.1 1.4
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.1 ~ 1.4
.0 1.4
.0 1.4
.0 1.3
t.O 1.3
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.9 1.3
.9 1.3
.0 .9 1.2
.0 .9 1.2
.0 .9 1.2
.0 .9 1.2
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.9
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.9 1.4
.9 1.4
.9 1.4
.9 1.4
.8 1.4
.6 1.4
.5 1.4
.5 1.1
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.0 .55 -.33 0
.2 .46 -.98 0
.3 .34 -2.02 0
.4 .12 -2.52 0
.4 .09 - .21 0
.5 .08 -.26 0
.5 .13 .90 0
.5 .15 .63 0
.5 .21 -.20 0
.4 .24 .01 0
.4 .26 .18 0
.3 .28 .48 0
.3 .28 .90 0
.2 .21 1.68 0
.2 .08 .12 0
.2 .07 -.09 0
.2 .07 -.29 0
.2 .07 -.19 3
.2 .Ob .19 3
.2 .06 .18 4
.2 .06 .28 4
.2 .06 .28 4
.2 .07 -.51 6
.2 .10 -.67 11
.2 .09 -.65 8
.2 .08 -.82 8
.1" .09 -.73 7
.1 .11 -.46 7
.1 .12 -.03 7
.0 .11 .20 5
.0 .10 .05 0
.0 .09 .33 0
.0 .08 .38 0
.0 .07 .56 0
.0 .07 .24 0
.0 .07 .13 0
.0 .07 .41 0
.0 .07 .52 0
.0 .07 .51 0
.0 .10 1.70 0
.0 .10 1.43 0
.0 .10 1.19 0
.0 .11 .83 ~0
1.0 .11 .58 0
.9 .16 -.59 0
.9 .IS -.18 0
.8 .19 -.57 0
.8 .19 -.19 0
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.0 .6 .5 l.X .7 .17 .60 0
.9 .6 .5 1.1 .6 .11 1.02 0
.9 .6 .5 l.l .6 .15 1.06 0
.U .6 .5 1.1 .6 .16 1.12 0
.0 .6 .5 1.1 .6 .17 1.13 0
.0" ".6 " .<•"""" "1.0 .6 " .16 " .82" 0
.0 .6 .4 1.0 .6 .17 .82 0
.0 .6 . <• 1.0 .6 .17 .70 0
.0 .A .* 1.0 .6 .18 .77 0
.0 .6 .» 1.0 .6 .17 .73 0

-------









































o~x>
 2-2?-77
<~> 2-23-77
2-2*-77
2-25-77
'-'6-77
'-27-77
2-2P-17
3- 1-77
' 3- ?-77
3- 3-77
3- *-77
1- *-77
3- 6-77
3- 7-77
3- fl-77
- 3- 9-77
3-10-77
' 3-11-7'
3-12-77
J-13-77
3-1*-77
3-19-77
3-16-77
' 3-17-77
3-1 "-77
1-19-77
3-20-77
3-21-77
3-22-77
3-23-77
. 3-2*-77
* 3-25-77
3-26-77
3-27-77
3-2'-77
3-20-77
3-30-77
3-31-77
*- 1-77
*- 2-7T
4- 3-77
4- 4-7'
*- 5-77
4- fc-77
«- 7-77
»- 1-77
4- 9-77
4-10-77
4-| 1-77
4-12-77
4-13-77
4-1 4-77
4-l"-77
4-1, -77
4-17-7T
*-) 0-77
4-10-77
4-1Q-77
CALENDAR PAT OF i hiNimtn
PROBABILITIES IN
f»r/UEE« THE WEEK (EnPERATURE 95.0
•I/ o ,
52/ 9
53' o
54/9 ,
".1 9
•,•- 1 9
57/0
*P / 1 0
50/10
>-0/10
/•i no
62/10 '
63/10
^4 / 10
»-5/ll
66/11
f.7/11
6* / 1 1
69/11 '
70/11
71/11 |
^2/12
73/12 i
74/12
7J/12 i
7»MZ
77/12
t*t\t
70/13
60/13
"1/13 '
e?/n '
83/13
f 4/13
85/13
•"t'14
P7/14
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•9/14
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91/1*
92/1* '
01/15
94/15
91/15
96/15 '
97/15 '
98/15 '
9"/15
100/ 16
101/1*
102/16
103/16
104/1*-
10* M6
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' 107/17
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100/17
110/17
SUN. j
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TUE. ,
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THU. .
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SIT .
SI'N. 1
PON. I
Hit. !
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SUN. I
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WED.
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TUE. i
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SUN.
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THU.
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.2
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.2
.2
.2
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.3
.3
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.1
.3
.3
.3
.1
.3
.3
.3
.2
.2
.2
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.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
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1.6
2.1
2.1
2.1
2.1
?.l
2.1
2.3
2.3
2.3
2.3
2.3
2.3
3.2
4.6
5.9
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10.4
10.*
10.5
10. P
10. 1
11.2
11.2
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.9
.9
.9
.9
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1.5
3.9
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4.5
4.5
4.5
4.5
4.5
* . 9
4.2
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3.8
3.9
3.9
5.2
6.1
6.3
11.2
12.7
12.7
12.7
12.7
13.2
13.5
14.1
1*.4
14.4
14.4
14.4
14.6
14.9
50.0
.5
.5
.9
.4
. *
.*
.4
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K
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.6
.6
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1.0
2.7
3.2
3.2
3.3
3.1
3.2
3.0
3.0
3.0
3.2
3.2
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3.5
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5.5
6.8
9.6
11.0
11.2
11.*
11.6
12.5
13.2
13.6
13.7
13. "
13.9
PERCENT
HAxinun
5.0 TcHPERATURE

.2
.2
.2
.2
.2
.2
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.3
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.3
.3
.3
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.2

.2
.2
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.3
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1.8
2.2
2.2
2.2
2.2
2.2
2.*
2.*
2.*
2.*
2.*
2.4
2.6
3.2
5.1
6.0
b. 6
10.5
10.5
10.6
11.1
11.2
11.7
11.7
1.0
1.2
1.2
1.2
1.2
1.2
1.2
1.2
.9
.9
.9
.9
.9
.9
.9
.9
.9
.9 »
.9
.9
.9
.9
.9
.9
.9
.9
.9
.9
1.0
2.1
4.0
4.6
4.6
4.6
4.6
4.6
4.6
4.6
4.5
4.2
4.2
4.2
4.2
5.5
6.5
8.7
11.*
13.9
13.5
13.5
13.5
13.5
13.6
14.1
1*.6
14.6
1* . 6
14.6
1-1.8
15.2
STANDARD SKEUNESS NO. OF EST.
MEAN
.6
.5
.9
.5
.5
.9
.*
.9
.5
.9
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
.6
f5
.9
.9
.*
.9
.9
.8
1.*
1.9
2.*
2.7
3.0
3.3
3.*
3.2
3.1
3.1
3.1
3.1
3.3
3.6
*.2
9.2
6.4
7.9
1.1
9.8
10.7
11.6
12.1
12.*
12.9
13.2
13.3
13.6
U.7
DEVIATION COEFFICIENT DATA POINTS
.17
.20 '
.20
.20
.20
.21
.19
.20
.16
.19
.16
.16
.19
.19
.14
.19
.19
.14
.14
.19
.16
.17
.16
.16
.19
.21
.21
.21
.21
.37
.97
1.99
1.70
1.6*
1.43 ,
1.16
.79
.67
.97
.48
.47
.90
.48
.69
1.03
1.99
2.93
3.36
3.4*
3.10
2.92
1.87
1.20
1.1*
1.31
1.29
1.13
1.01
.ft
.6*
.66
.63
1.01
1.17
1.3*
1.29
1.37
1.19
.6*
.6*
.39
.2*
.11
.02
-.1)
-.31
-.30
— • 16
.00
.31
.52
.36
.36
.43
jZ2
.22
.11
.26
.29
2.42
2,19
1.15
.47
-.07
-.9*
-.66
-.30
.13
.31
.09
.06
.01
-.09
1.66
1.23
1.26
1.06
.61
- .05
-.36
-.79
-1.23
-.*0
.32
.07
-.45
-.79
-1.08
-1.06
-1.22
0
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
o
0
0
0
7
15
1)
15
19
19
19
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0








-------
- , OATe
^ 4-21-77
— *-22-77
CD *-23-77
~i «-2*-77
*-25-77
*-26-77
4-27-77
»-2f-77
4-29-77
'-30-77
°- 1-77
5- 2-77
5- 3-77
a- 4-77 "
5- 5-77
5- 6-77
•!- 7-77
5- »-77
9- 9-77
"5-16-77
9-11-77
5-12-77
9-13-77
9-14-77
5-15-77
5-16-77
5-17-77
9—1 8—7^
5-19-77
5-20-77
a-2 1-77
5-22-77
5-23-77
5-2*-77
5-25-77
*-;>6-77
5-27-77
9-29-77
5-'9-77
5-30-71
	 5-31-77
a a> °~ 1-77
2.-0 h- 2-77
0 (.- 3-7T
< 0- f,- ^-77
2.n *- 5-77
0)2 6- 6-'7
21 6- 7-77
0 ~ 6- 8-77
o § 6- 9-77 ~
0 3 »-)0-77
3 t-U-77
f-12_f7
-jjjfgj^ f-| 3-77
^9& ' - 1 * - ' 7
^fe|^ »,-j«_77
6-16-77
^17-77
f-n-77
6-19-77
CALENDAR
OIY/HEEK
111/17
112/17
113/17
114/18
11S/H
116/10
1 17/1"
1 Ifl/ 1 ^
119/lt
1 ?0/lf
121/19
122/19
121/19
124/19
125/19
126/19
127/19
12P/20
120/20
1 30/20
131/20
132/20
133/20
134/20
135/21
" 136/2T
137/21
13P/21
139/21
1*0/21
1*1 / ?1
r*2/ 22
1*3/22
l**/22
1*5/22
1*6/22
1*7/22
I A*/22
1 *°/ 23
150/23
151/23
152/23
153/23
1 51/23
155/23
156/2*
157/2*
1 56 / 2*
1 5°/2*
160/2*
1M/2*
162/2*
1 63/25
16*/25
1*5/25
16* /?5
lf-7/25
It'/ 25
169/25
170/26
OAK Of
THE HEEK
T>IU.
"I*
SAT.
SUN.
Finn.
TUE. '
WED,
TMU. '
F»I.
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SUN,
CON".
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THU.-
FR 1 1
S AT t
SUNl '
JIPN.
TU£; 	
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TUE.
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THU,.
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SOT.
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HON.
TUE.
WED.
THU.
fRJ.
S AT\
SUN.
"ON. ;
TUE.
uEP.i '
T"U.!
" rut. '
SAT.,

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THU.
"I.
5AT.
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HfN. ^ I
TUI . '
U£0. 1
THU. |
en. I
SA7.
su»'. !
nlNlfUH POU6A8 11 [TIES IN
TSHPE»'IU»E 95.0 50.0
11.2
ir.2
il.2
11.2
12.6
12.7
12.7
12.7
13.2
13.*
11.*
!*.>
It. 8
i*.a
1*.6
i*.e
I*. 6
15.7
15.9
15.9
16.*
17.1
17.1
17.4
16.*
' 20.0 '
20.0
20.0
19.6
18.8
16.8
1 a . o
18.8
18.8
18.8
16.8
21.2
~ 21.1
20.0
20.0
20.0
20.0
20.0
" 20.0 '
20.0
20.5
20.0
1 * • 7
18.7
1 g; 7
1". 7
18.7
18.7
11.7
20.0
?0,0
2C.O
tO.*
20.*
20.*
1*.9
~1*.9 '
15.2
15.8
15.8
16.*
17.1
17.2
17.2
17.2
' 17.2
17.6
17.7
17.8
18.6
18.9
19.1
19.5
20.*
22.2
22.8
22.6
22.9
22.9
23.8
2* . 9
2*. 9
2*.«
2*. 9
2*.«
2*. 9
"" " "25".*"
25.8
29.8
25.8
25.8
25.6
	 zs:s
25.8
25.5
25.5
25.1
2*.*
	 23.7 —
23.7
23.7
23.7
23.7
23.7
~ "23.3 "
23.3
23.2
23.2
23.2
23.5
23.3
23.3
23.3
23.2
23.2
13.9
13. P
13.6
13.9
1*.2
1*.S
1*.8
15.2
15.6
15.6
15.4
IS. 9
16.0
16.3
16.*
16.6
17.1
17. S
17.8
16.*
1*.9
19.6
20.*
21.1
21.*
"ZJ'.O"
22.3
22.1
21.7
21.7
21.6
22.*
22.*
22.*
23.3
23.7
2*.0
23.8
23.*
23.0
22.*
22.2
22.1
22.0
22.0
22.2
22.1
22.0
21.9
22.0
21.6
21.3
21.1
21.2
21.*
21.6
21.6
21.7
21.7
21 .7
PERCENT
3.0
11.7
11.7 "
11.7
11.7
12.8
13.0
13.0
13.2
13.5
1 * .2
1*.2
It. 8
1*.9
1*.9
1*.9
1*.9
1*.9
15. J
16.*
16.*
16.7
17.2
17.2
18.2
18.6
26.2
20.3
20.3
19.8
19.2
19.2
i"9;j~
19.2
14.2
19.2
19.2
21. S
22 . 1
20.3
20.3
20.3
20.3
20.3
20.)
20.3
20.8
20.7
19.1
19.1
19.1 '
19.1
19.1
19.1
19.1
20.3
20.3
20.3
20.4
20.*
20.*
NABIHUN
TEMPERATURE
15.2
15.2
15.7
16.2
16.2
16.9
17.6
17.6
17.6
17.6
17.6
17.9
17.9
16.0
19.1
19.1
19.3
19.8
21.0
22.9
23.0
23.0
23.3
23.3
2*. 6
25.7
2*. 7
25.7
25.7
25.7
25.7
25.'8
26.6
26.6
26.6
26.6
26.6
26.6
26.6
25.8
25.8
25.8
25.0
"" 2*.) ~"
2*. 3
2*. 3
2*. 3
2*. 3
2*. 3
23. S
23.5
23.}
23. i
23.3
23.8
23.8
23. a
23.8
23.9
23.8
PEAN
13.7
13.7
13.7
l*oO
1*.3
1*.5
i*.e
15.2
15.6
19.8
15.7
16.0
16.2
16.3
16.5
16.7
17.1
17. S
18.0
18.6
19.3
19.9
20.*
20.9
21.)
2i7l
22.)
22.2
21.9
21. 8
21.9
~ 22.1
22.2
22.3
22.3
23.*
23.9
" "23.9
23.5
23.0
22.7
22.*
22.1
" ~ 21.9
22.0
22.2
22.1
21.8
21.8
21.7
21.5
21.*
21.3
21.3
21.7
21.7
21.7
21.8
21.8
21.8
STANDARD
DEVIATION
.66
.66
.9*
1.11
.91
.96
1.16
1.21
1.07
.90
.90
.6*
.6*
.86
1.03,
1.1*
1.18
.Ob
.19

.1 1
• "
. 2
.< 6
.; 9
.19"
.. 2
0 ' *?

. I
. 2
. ^
B i
. 16
. 16
. '8
. 0
. 9
. >3
. 18
1. *
1. .1 ,
1. 6 1
. Ifl "'
.91 1
. 0 1
•e5
i.lzo
l.i*
~" 1.16
1.17
1.17
1.10
l.'l*
1..03
J99
.98
.40
.82
.8.1
SKEHNE5S
COEFFICIENT
-1.10
-.90
-.47
-.28
.18
.31
.32
-.06
-.21
-.13
-.06
.36
.29
.15
.53
.24
-.01
.20
a*9
" .71
.*2
.10
-.17
-.*9
-.18
.75
.56
.60
.*0
.23
.20
.1*
.20
.12
-.3*
-.87
-.23
.08
-.3S
-.13
.26
,58
.60
.15
.13
.26
.11
-.77
-.59
'-.«*""
-.**
-.2*
-.07
-.09
.26
.22
.22
.27
.29
.32
NO. Of EST.
DMA POINTS
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0







0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

-------
C1LEND1R   RAY Or
                                     PROBABILITIES  IN  PERCENT
                                                                                        STANDARD
                                                                                                     JKEWNESS
CJ "ATE
LO — ™— — — —
«y 6-20-77
CT> 6-21-77
(T> A-22-T7
^° 6-J3-77
6-24-77
- 6-25-77
" 6-26-77
6-27-77
' 6-28-77
" A-29-77
6-30-77
7- 1-77
7- 2-77
71-3-77"
1 7- 4-77
7- 5-77
_I 7- 6-77
- 7- 7-77
-0 7- 8-77
t 7- 9-77
- 7-10-77
. 7-11-77
^ 7-12-77
7-13-77
. 7-14-77
7-15-77
' 7-16-77
7-17-77
7-ll«-77
T-19-77
7-20-77
7-21-77
~ 7-22-77
. 7-23-77
• 7-24-77
7-25-77
7-26-77
7-27-77
1 7-2P-77
.3 7-29-77
7-30-77
-- 7-31-77
) - 1-77
J - 2-77
- 3-77
- 4-77
~ - 5-77
' - 6-77
- - 7-77
- - 9-77
-10-77
-U-77
-12-77
-13-77
-14-77
-15-77
-17-77
-18-77
PAY/WEEK
1 71/26
172/26
173/26
174/26
175/26
176f26
177/27
170/27
179/27
ldO/27
IM m
ll>2/27
183/27
184/2"
187/28
] 86.2*
169/26
190/28
191/29
192/29
193/20
194/20
195/70
106/20
197/29
196/30
199/30
200/30
201/30
202/30
203/30
204/JO
205/31
206/31
207/31
208/31
200/31
210/31
211/31
212/32
213/32
214/32
215/32
216/32
217/32
210/33
220/13
221/33
222/33
'23/33
224/31
225/1J
?26/3»
? 27/ 34
2 2 P / 34
2?o/3t
23"/34
THE WEEK
HPM.
rut.
WEO.
THU.
FPI.
SAT.
5UH.
HON..
TUE.
WED,
THU.
FPI.
SAT.
SDH.
HON.
TUE. '
WEO.
THU.
FBI.
SAT.
SUN.
MON.
TUE.
WEO.
Tl'U.
FBI.
SM.
SUN.
HON.
TUE.
WEO.
THU. '
FBI.
SAT.
SUM.
HON.
TUE.
WEO.
THU.
FRI.
SAT.
SUN.
HHN.
TUE.
WEO.
THU.
m.
SAT.
SUN.
HON.
TUE.
WEO.
TM(/.
FBI.
5»T.
SUM.
KPN.
TUE.
WEO.
TEMPERATURE
20.1
20.1
20.1
20.1
20.1
20.1
20.1
21.5
20.4
20.4
20.4
20.4
20.4
20.4
20.4
21.7
23.1
23.1
22.3
22.3
22.3
22.3
22.3
22.3
22.3
23.2
23.2
23.8
23.6
24.0
24.0
24.0
24.0
22.4
22.4
21.7
21.7
21.7
21.0
20.
20.
20.
20.
20.
20.
20.
20.2
20.2
20.2
19.5
19.2
19.2
19.2
19.0
19.0
1 7.9
17.9
17.9
17.9
05.0
23,9
25.3
25.8
26.3
26.7
26.7
26.7
26.7
26.7
26.7
26.3
26.4
26.9
26.9
27.2
27.2
27.2
27.2
27.2
27.2
27.2
26.5
26.1
26.9
26.9
27.6
28.7
28.7
26.7
"28.7
26.7
28.7
26.5
27.3
27.0
26.7
26.6
26.6
26.4
25.6
25.6
29.6
25.6
24 '.7
24.9
25.3
25.3
25.0
25.0
25.0
25.0
24.8
23.9
23.0
21.0
23.0
22.8
22.5
22.3
50.0
	 21.7 .
21.6
22.1
22.6
24.1
24.3
24.5
24.4
24.1
• 23.7
23.4
23.4
23.7
24.2
25.6
25.9
25.9
25.8
25.3
25.0
24!4
24.3
24.6
25.0
2S.1
25.8
" 26.1
26.3
26.4
26.1
26.0
25.9
25.4
25.0
24. »
24.6
24.0
23.8
23.3
22.8
22.9
22.8
22.4
22.0
22.4
22.8
22.6
22.6
22.3
22.2
22.3
22.1
21.6
21.0
20.8
20.5
20.5
20.3
2C.4
5.0
20. S
20.5
20.5
20.5
20.5
20.5
20.5
21.8
20.9
20.9
20.9
20.9
20.9
20.9
20.9
21.9
23.2
23.3
22.4
22.4
22.4
22.4
22.4
"22.4"
22.4
23.2
23.5
24.4
24.0
24.6
24.5
24.3
24.3
23.7
23.3
22.0
22.0
22.0
21.4
20.5
20.
20.
20.
20.
20.
20.2
20.7
' 20.7
20.7
20.1
19. i
19.5
19.5
19.5
19.2
19.2
18.9
18.5
18.5
11.5
TEMPERATURE
24.6
25.9
26.2
27.0
27.0
27.0
27.0
27.0
27.0
27.0
26.7
26.6
27.2
27.2
27.6
27.6
27.6
27.6
27.6
27.6
27.6
26.8
26.8
27.5
27.5
26.7
29.0
29.0
29.0
29.0
29.0
29.0
29.0
26.0
27.1
27.0
27.0
27.0
26.7
26.5
26.5
26.5
26.5
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
24.
23.
23.
23.
23.
23.
22.4
MEAN DEVIATION
21.9 .97
22.2
22.6
23.1
23.7
24.0
24.2
24.4
23.9
23.7
23.5
23.6
23.6
24.4
24.6
25.5
25.7
25.6
25.2
25.0
24.6
24.4
24.3
24.5
24.9
25le
26.3
26.1
26.4
26.2
26.1
26.0
25.5
25.0
24.7
24.4
24.3
23. 7_
23.1
22.6
22.8
22.8
22.5
22.2
22.4
22.8
22.9
22.7
22.4
22.2
22.2
22.0
21.6
21.1
20.9
20.7
20.6
20.4
20.4
.36
.67
.94
.03
.90
.69
.33
.68
.69.
.60
.66
.84
.01
.06
.55
.17
.23
.48
.47
.34
.14
.01
.24
.28
.29
.40
.23
.28
.19
.21
.31
.22
.14
.10
.31
.35
.30
.44
.47
.43
.49
.45
.26
.21
.34
.32
.26
.25
.41
.56
.51
.42
.23
.15
.15
.26
.24
.15
.08
COEFFICIENT
.76
1.11
.66
.32
-.19
-.55
-.75
, -.10
-.20
.09
.14
.18
.10
-.65
-1.09
-.79
-.59
-.37
-.02
.36
.11
.12
.34
-.18
.42
.31
.26
.03
.1)
.35
.39
.39
-.11
-.02
-.36
-.16
.18
.08
-.01
.22
.41
.38
.22
.42
.3)
.26
.16
.25
.26
.13
.19
.16
.15
.10
.36
.20
.19
.23
-.07
DATA POINTS
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

-------
CilfNPAH
D>V/UEEK
I OAT OF
DIE MEEK
  niiu nun
TEHPEDATURE
PSOB48I11TIES IN PERCENT
 95.0     50.0      5.0
  nAMnun
TEMPEfUTUBE
                                                                                FIEAN
STAI.O&RD
DEVIATION
 SKEWMESS     NO.  OF  ESI.
COEFFICIENT   DATA POINTS
^- 0-19-77
C> 8-21-77
•J~> 8-22-77
8-23-77
«-2*-J7
8-2?-77
8-26-tr
,' 6-27-77
8-28-77
B-29-77
1-10-77
"-31-77
"9- 1-77
- 9- 2-77
9- 3-77
- 9- *-77
- 9- 5-77
' 9- 6-77
" 9-7-77'
9- 8-77
; 9- 9-77
- 9-10-77
9-11-77
_ 9-12-77
231/3*
232/3*
233/35
23*/35
235/35
236/35
237/35
238/35
239/35
2*0/36
2*1/36
2*2/36
2*3/36
	 2*4/36"
2*5/36
246/36
2*7?37
2*8/37
2*0/37
251/37
252/37
233/37
25*13"
255/38
- 9-13-77 256/38
9-14-77 257/38
9-15-77 258/38
9-16-77 259/3»
FBI.
SAT,
SUN, ,
HON. '
TUE. ,
MED.
THU.
FBI.' 1
SAT. .
S'JN.
i ttON.
Tt'E.
UEO.
, THU.
FBI.
SUN.
HOH.
THE.
WED, '
THU.
I FBI. '
,' SAT.
SUN.
HON.
TUE.
WED.
THU.
i ,FB1.
17.9
17.9
17.9
18.6
18.7
18.7
18.7
18.7
18.7
ic.a
18.9
18.9
IP. 5
ial*
IB.*
18. i
18.0
17.0
17.0
17.0
17.0
17.0
17.0
17.0
17.1
17.1
17.1
22.3
22.3
22.3
22.3
22.3
22.3
22.0
22.0
22.0
22.0
22.0
22.0
21.*
21.3
21.2
21.2
20.7
" 20.8 " ~
20.8
20.8
20.8
20.9
20.6
21.5 '
22.1
22!l
22.1
22.1
20.*
20.5
20.*
20.*
20.3
20.5
20.6
20.5
20.3
20.3
20.3
20.3
20.0
19.8'
19.8
19.6
19.8
19.7
19.6
19.3
19.1
18.7
_18.5
18.5
18.8
19.3
20.9
20.9
18. 5
18.5
18.9
la.e
18.8
ie.8
18. B
18.8
18.8
18. 8
19.0
19.0
19.0
19.0
18.7
18.7
18.6
16.2
Ifl.l
17.5
17.5
17.3
17.*
17.2
17.2
" tt.Z
17.5
17.5
17.7
22.4
22.*
22.4
22.4
22.4
22.1
22.3
22.3
22.3
22.3
22.3
22.1
21.8
2i:a "
21.8
21.8
20.9
21.0 '
21.0
ZloO
2i.O
21.0
21.0
" 22.2
22.2
22. i'" '
22.2
" 22.2 ~
22.2
20.4
20.4
20.4
20.*
20.3
20.4
20.3
20.2
20.2
20.3
20.4
20.4
20.1
19.9"
19.8
19.8
19.7
19.6
19.9
i<*!i
18.9
18.7
18.7
19.0
19.1
19.8
" 20.1 "
20.4
.10
.10
.14
.13
.11
.1Z
.09
.03
.90
.96
.85
.83
_j'7*
.64
.63
.66
.37
.70
.78
' .98 '
a 99
1.02
.93
1.18
1.54
i:69
l!&6
1.41
-.10
-.15
-.10
.12
.2*
.04
-.07
.04
.14
.12
.16
.22
.28
.79
.92
.51
-.20
-.24
-.24
-»38
.01
.37
.70
1.36
.99
-.02
-.51
-1.04
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

-------
                                                                WATER  TEMPERATURE DATA
1 NUKBER OF DATS •
j NUCBER OF STATIONS TO BE AVERAGED -
CHANNEL NUMBER •
| STATION NUMBER •
335 '
4
2
1
                OATf   tinus. 00
                                   03
                                               00
                                                     12
                                                            15
                                                                  IS
                                                                        21
                                                                                  DATE   HOUR* 00
                                                                                                     09
                                                                                                           06
                                                                                                                        IZ
                                                                                                                              19
                                                                                                                                    18
                                                                                                                                          21
en
ID
10-?0-76 7.0 6.7 6.5 t
10-?2-76 5.6 5.3 5.0 «
10-24-76 5.6 5.7 f.f i
10-26-76 4.3 4.f> 3.8 3
10-30-76 6.2 _[ 6,1 6.0 5
11- 3-76 6.2 5.8 S.4 5
11- 7-76 2.6 2.3 1.9 1
11- 9-76 " 1.0 ' ' .9 r^8
11-11-76 .6 .6 ' .6
11-15-76 .5 .* .5
11-17-76 .6 ',7 . .7
11-19-76 1.8 1V6 1.* 1
11-21-76 1,2 ' 1,1 1.0
11-23-76 3.4, 1 3,i4 3.) i
11-25-76 .6 ! .'i .6
11-27-76 .5 ' .7 , .6
11-29-7* .7 .7 1 .7
12- 1-76 .7 Jl . .7
12- 3-76 .9 .'9 ll.O
12- 5-7t .6 .5 1 .6
12- 7-76 .5 ' IS 1 .5
2-11-76 .5 ' ','5 ! .5
.2-13-76 .5 . ,4 ' .4

12-21-76 .3 .'3 ' .3
12-23-76 .6 , 1J3 . .3
12-27-76 .4 IJ4 , .5
12-29-76 .". IjS | .5
1- 2-77 . g j;7 .8
1- 4-77 .1 ll'fl .2


-12-77 .3 101i,l 101. 1 10
-14-77 .3 l!.3 101. 1
-16-77 .2 1.2 ,1.2
-18-77 101.0 1,01.0 101.0 10
-24-77 1.0 1.9 .9
-26-77 1.0 1.0 1.0
.4 {
.7 5
.3 5
.6 3
.8 6
.1 A
.6 1
.7 1
.6 1
.'
.7 1
.3 1
, 1

•
.4

.3
.4
.5
.4
.8
.1
, 2

.1
.3
.2
.0 10
.1
.9
.6 1
.0 6
.4 5
.9 
.2 -11-77
.3 -13-77
.2 -15-77
.3 -17-77
.2 -19-77
.1 -21-77
1.0 -25-77
1.0 1-27-77
.6 5,
.5 4
.1 4
.6 6
.0 3
.0 2
.1
.1
.0
.7
.8 1
.6 1
.8
.6
.9
.6
.5
.5
.5
.4
.3
.4 1
.5
.4

.2


.2
.2
.2
.1
.0
.0
.0
5.3 5.2 5,3
5.6 J,4 ».3
3.8 3.<. 3.7
6.0 5,7 6.1
3.6 3.4 3.4
2.7 2.7 2.9
.a ,e i.o
.6 !.7 ,9
3.J 3^1 1.9
.7 i7 .9
1.0 1.1 1.6

6 .6 .6 .6
• .8 .7 '.7
6 .6 .6 .6
5 .5 .5 .i
4 .4 .5 .5
5 .5 .5 .5
.4 .3 .6 1.2
.3 .4 .4 .5
4 .4 1.4 .4
»5 .9 .<• *3
3 .<•!.* *4

.1 .1 .1 .1


.2 .3 .3 .3
.1 .2 .2 .2
.1 .2 .2 .2
.0 .1 .1 .0
.1 1.0 .1 1.1
.0 .9 .0 1.0
5.7 5.8 I
4.4 4.6 4
6.6 6.6 6
3.8 i. a 3
3.1 3.0 2
1.1 1.0 1
1.0 .9
2.0. 3.4 2
1.2 1.0
2.0 2.1 2

.6 .5
.7 .7
.6 .6
.9 .5
.7 .5
.5 .4
1.5 1.) 1
.9 .9
1.4 1.4 1
.4 .4 1
_ -5 •» 1

.1 .11


.4 .3 1
.2 .2 1
.2 .11
.1 .0
.1 .01
.0 .0 1
a
9
»
3
5
••
9
0
7
0
9
0
5
i
6
5
5
4
3
8
4
4
6
1
1
2
3
3
2
0
0
9
O
0

-------
1-28-77
1-30-77
2- 1-77
2- 3-77
2- 5-77
2- 7-77
2- 9-77
2-11-77
2-13-77
2-15-77
2-17-77
2-19-77
2-21-77
2-23-77
2-25-77
2-27-77
1- 1-77
3- 3-77
1- 5-77
3- 7-77
3- 9-77
3-11-77
3-15-77
	 3-17-77
3-19-77
3-21-77
3-23-77
3-25-77
3-31-77
4- 2-77
4- 4-77
4- 6-77
4- f-77
' ' 4-10-77
4-12-77
4-14-77
4-16-77
4-1P-77
4-20-77
4-22-77
4-24-77
4->6-77
4-2C-77
4-30-77
5- 2-77
~"5- 4-77 "
5- 6-77
5- 8-77
5-10-77
5-17-77
9-14-77
" 5-16-77
•-1S-77
5-20-77
5-22-77
5-24-77
5-?6-77
	 !-2«-77 	
5-30-77
6- 1-77
6- J-77
6- J-77
6- 7-77
1.0 1.0 1.0 1.0
.9 .9 .9 .9
.9 .9 " 1.0 1.1
.9 .9 .9 1.0
.9 .9 .9 1.0
.6 .7 .6 .9
.5 .9 .5 .5
.5 .5 .5 .7
.5 .5 .4 .7
.6 .6 .6 .5
.4 .5 .5 .5
.2 .2 .2 .3
.5 .5 .4 .5
.3 , .4 .5 .7
.5 .4 .5 .7
.7 .7 ,7 .»
.5 .6 .6 .8
.6 .5 .6 .8
1.0 1.0
1.0 .9
1.1 " 1.1
1.4 1.1
1.0 .9
1.1 .6
.7 .6
1.0 .9
1.0 .9
.5 .9
.7 .6
.5 .5
.4 .4
.8 .7
.6 .6
.6 .6
.7 .7
.9 .6
.5 .4 .4 .8 .9 .8
.4 160.6 100.5 lOO.f 100.8 100.8
.4 .3 .2 .2 .3 .3
.t .2 ' .2 .3 " ' .6 .6
.6 .6 .6 .6 1.0 .7
l.a 1.6" 1.7 ~ 2.4 3.1 3.9
3.2 • 372 3.0 2.9
5.1 5.1 4.8 4.6
8.6' B.7 8.8 4.0
11.5 11.9 10.8 10.4
11.7 11.8 11.7 11.6
13.0 12.8 12.5 12.5
113.6 113. a 114.0 114.2
14.2 14.2 13.9 13.7
1J.4 13.2 " 12.8 12:6
14.1 14.0 13.4 12.8
" 13.9 13.9 13.5 13.2
15.0 14.5 14.0 13.4
16.0 15.9 15.6 19.3
16.0 15.6 15.3 15.2
15. 2 15.0 14.9 14.6
17.0 16.7 16.5 16.4
16.6 16.4 16.4 16.7
17.7 17.2 17.1 17.2
19.2 18.9 1«.5 IB. 4
21.4 21.1 20.9 21.0
20.7 20.2 20.0 20.3
21.6 21.2 21.0 21.4
23. a 23.2 23.1 22. «
20.0 19. a 19.6 19.7
21.5 21.2 21.2 21.6
23. a 23.4 21.3 23.4
	 25.4 2i;0~22.» 23.1
24.1 23.4 23.0 22.9
20.7 20.2 24.0 20.3
21. P 21.5 21.2 21.0
21.6 21.6 21.4 21.2
?2.3 22.0 21.8 21.7
3.0 3.1
5.3 6.2
~r&72 mr
11.0 11.4
11.4 11.1
12.6 13.5
114.4 14.6
13.9 13.4
1 3 *2 1 *> • 6
13.6 14.5
14.0 15.2
14.2 15.5
16.0 17.2
15.8 16.8
U.9 1576
17.2 17.7
17.0 16.9
18. 0 19.0
19.3 20.4
22.0 23.0
21.4" 22JT
22.6 23.9
22.6 23.0
19.9 20.1
22.8 24.2
24.4 26.6
24.0" 24.4
24.0 25.0
21.3 21.9
21.3 22.2
22.4 23.8
22.3 23.4
.1
.9
"l.l
1.1
1.0
.a
.6
.5
.8
.8
.9
.5
.6
.4
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.6
75
.6
.6
.9
.9
"1.0
1.0
• 7
• 6
.6
. 5
.4
. 4
.4
. 4
.4
.5
.4
.5 -
.5
.5 .4
100.7 100.6
.2 .2
" ;* .3 "
.6 .4
4.0 3.9
3*1
6.5
— ITTT"
11.2
11.1
13.8
14.4
13.8
~Tf7S~
14.7
15.7
15.7
17.6
17.2
U.9
17.8
19.1
19.3
21.0
22.8
23.3
24.6
22.9
20.4
24.6
25.8
~ 25.5
25.0
21.8
22.6
24.3
23.2
-29-77
-31-77
- 2-77
- 4-77
- 6-77 "
- 8-77
-10-77
-12-77
-14-77
-16-77
-18-77
-20-77
-22-77
-24-77
-26-77
-28-77
- 2-77
- 4-77
- 6-77
- 8-77
-10-77
-12-77
-16-77
-18-77
-20-77
-22-77
-24-77
-26-77
2.6 3-30-77
3.4
6.1
1T72 	
11.0
11.2
13. a
14.2
12.3
14.4
13.9
15.*
15.1
17.1
16. a
*- 5-77
i>- 7-77
i- 9-77
4-11-77
4-13-77
4-15-77
*-17-77
4-19-77
4-21-77
i-23-77 	
4-25-77
4-27-77
4-29-77
5- 1-77
5- 3-77
15.8 S- 5-77
17.4 5- 7-77
18.5 5- 9-77
18.8 5-11-77
20.7 5-13-77
22.0 5-15-77
22.9 ~ 5-17-77
23.8 5-19-77
22.6 5-21-77
20.0 5-23-77
24.0 5-25-77
24.9 5-27-77
24.9 5-29-77
24.2 5-31-77
21.4 6- 2-77
22.4 6- 4-77
23. T 6- 6-77
22.8 6- 9-77
.9
.9
.9
1.0
.a
.6
.6
.6
.5
.6
.5
.4
.2
.3
.4
.4
.5
.3
.4
100.6
.3
."2
.2
4.1
..... ^
.0
.0
11.2
10.7
11.2
13.9
14.0
12.0
	 1172"
15.1
15.0
16.7
16.6
IS. 8
17.1
16.0
18.5
20.4
21.4
"227 T
23.1
21.6
19.6
23.3
23.9
24.3
22.9
21.0
22.1
23.0
22.4
1.0 1.0
.9 .9
.9 .9
1.0 1.0
.a .9
.5 .5
.9 .4
.6 .»
.5 .5
.3 .4
.4 .4
.5 .5
.2 .2
.3 .4
.4 .4
.3 .5
.6 .5
.3 .4
.3 .4
100.6 100.6
.3 .3
.2 .2
.2 .3
273 2.2
3.0 3.0
J.9 5.9
11.3 11.4
10.6 10.5
11.0 10.8
14.0 14.1
13.9 13.7
11.7 11.2
14.0 13.$
19.1 14.8
15.0 14.7
16.5 16.3
16.4 16.1
16.7 16.2
17.5 17.2
18.2 17.9
20.3 20.2
21.4 21.0
2176 2H7
22.7 22.6
21.0 20.7
19.2 18.6
22.7 22.4
23.4 23.2
24.0 23.7
22.4 22.2
20. a 20.5
22.1 21.7
22.4 22.0
22.2 21.0
.9
1.0
1.0
1.1
.9
.7
.8
.6
.6
.a
.5
.8
1.2
.5
.6
.6
.7
.5
.6
100.7"
.3
.4
.5
2.2
2.9
6.0
12.0
10.5
11.2
114.1
13.6
11.4

14.6
14.5
16.1
1».6
1577"
15.9
17.1
17.8
20.3
21.2
21.6
22. a
20.8
19.0
22.6
23.3
23.7
22.2
20.6
21.9
21.5
21.5
1.1 1.1
1.1 1.1
1.1 1.1
1.1 1.0
..9 .6
- .9 .8
.6 .6
.7 .8
.8 .7
.7 .7
1.0 .8
100.6 100.3
.5 .4
.a .a
.9 .9
.8 .7
" .5" .6"
.8 .7
100.7 100.7
.3 .2
.6 .6
1.0 1.5
2.8 3.2
7.0 8.3
J12.8 13.5
11.9 12.7
12.1 13.2
14.1 14.0
14.0 14.6
12.6 13.8
"14.4 is. r
15.3 16.2
15.2 16.4
15.9 17.0
15.* 15.*
16. S 17.6
16.* 17.*
17.8 16.9
18.) 19.5
21.3 22.6
22.2 22.7
"2177 2270"
23. a 25.2
21.1 21.1
20.2 21.9
23. a 25.3
24.4 25.6
24.6 25.5
22.4 122.1
21.3 22.3
22.6 22.4
22.1 23.0
22.2 23.0
.9
1.0
1.1
1.0
1.0
.a
.7
.6
.6
.4
.7
.2
.*
.6
.5
.7
.5
.7
100.6
.2
.6
2.1
3.0
8* 7
12:7
12.7
13.2
13.6
14. «
13.9
15.2
16.2
16.9
17.3
15.*
17.9
18.0
19.1
19. a
22.9
22.3
25l7
20.6
22.5
25. a
25.2
25.8
21.8
22.6
22.6
23.0
23.3
1.0
.9
.9
.6
.6
.9
.5
.6
.4
.6
.2
.6
.4
.5
.7
.5
.7
100.4
.2
.6
1.7
2.8
a. 6
11.6
12.0
13.0
13. 4
14.2
13.4
14.4
15.6
16.4
16.7
15.3
17.5
17.6
10.4
19.5
22.1
21.6
22.2
24.9
20.3
22.2
24.8
24.2
25.0
21.1
22.2
22.0
22.5
22.7

-------
6- 9-77
6-11-77
6-13-77
6-15-77
6-17-77
6-19-77
6-21-77
6-23-77
6-J5-77
6-27-77
6-29-77
7- 1-77
7- 3-77
7- 5-77
7- 7-77
7- e-77
7-11-77
7-13-^7
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