905490001
ESTIMATED LOADINGS FROM SEVEN MICHIGAN
TRIBUTARIES AND RECOMMENDATIONS FOR
TRIBUTARY SAMPLING STRATEGIES
by
Robert M. Day
Surface Water Quality Division
Michigan Department of Natural Resources
Lansing, Michigan 48909
Project Officer
David Rockwell
Project Nos. S-005741-01-2,
S-005741-02-1, S-005741-03
GREAT LAKES NATIONAL PROGRAM OFFICE
REGION V
U.S. ENVIRONMENTAL PROTECTION AGENCY
CHICAGO, ILLINOIS 60605
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ABSTRACT
Annual load estimates of twelve parameters from seven Michigan
tributaries were calculated from 1984 to 1986. Estimates were
calculated by dividing sample concentrations into high and low strata and
applying Scale's Ratio Estimator. The greatest annual loads of the
twelve parameters usually came from the St. Joseph followed by the Black
or Rouge rivers and the lowest annual loads came from either the Pere
Marquette or Ontonagon rivers.
Monte Carlo studies indicate that flow stratified sampling strategies
yield unbiased and relatively precise total phosphorus load estimates
when the samples were selected randomly. Strategies that confine
sampling to the first half of the year or neglect either the rising-area
or falling area of the hydrograph will yield biased load estimates. A
systematic sampling strategy will insure that each sample within each
strata has an equal probability of being selected and usually yields
unbiased total phosphorus load estimates.
Sample sizes necessary to estimated total phosphorus loads were calculated
for four of the seven Michigan tributaries studied using load average and
variance predicted by flow variability versus load variability regression
equations. This method can be used to provide sample size estimates for
many tributaries with little or no prior information about total phosphorus
concentrations but is not reliable for the most event responsive rivers.
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TABLE OF CONTENTS
Page
ABSTRACT i
LIST OF FIGURES ill
LIST OF TABLES iv
ACKNOWLEDGEMENTS v
CONCLUSIONS 1
INTRODUCTION 4
PROJECT DESIGN
-Site Descriptions 6
-Flow Measurements and Estimations 11
ANNUAL LOAD ESTIMATES
-Load Estimation Methods 11
-Annual Loads from Seven Tributaries 13
SAMPLE STRATEGY DEVELOPMENT
-Determining the Necessity of Event Sampling Strategies 18
-Testing for Bias Introduced by Event Sampling Strategies. ... 20
-Flow Stratified Systematic Sampling 25
SAMPLE SIZE ESTIMATION
-Sample Size Estimation Method 28
-Predicting Load Variability for Sample Size Calculation .... 31
-Sample Size Estimates for Michigan Tributaries 37
LITERATURE CITED 42
APPENDICES
-Appendix 1. Project Watershed Maps 43
-Appendix 2. Average Daily Flow vs. Average Daily Load 51
ii
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LIST OF FIGURES
Number Page
1 River mouth stations samples by the Michigan
Department of Natural Resources 7
The relationship between the coefficient of
variation (CV) of total phosphorus daily loads and
average daily flow variability (CVLF5) 35
The relationship between the coefficient of
variation (CV) of total phosphorus daily loads and
average daily flow variability (CVLF5) in the high
flow strata. . 36
The relationship between the coefficient of
variation (CV) of total phosphorus daily loads and
average daily flow variability (CVLF5) in the low
flow strata 36
111
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LIST OF TABLES
Number Pag«
1 Drainage area of the project watersheds 8
2 Land use (%) by watershed 9
3 Soil types (%) by watershed 9
4 Drainage area ratios (DAR) and U.S. Geological Survey
gaging station location by river. . . 12
5 Annual loads from seven Michigan tributaries
(metric tons per year) 14
6 Average daily flow (cfs) , 20th percentile cut-off
flow (cfs) and the number of days in each high flow
and low flow strata for the Black, Clinton, Rouge
and Huron rivers 1984-1986, and the Ontonagon,
Pere Marquette and St. Joseph rivers, 1984 17
7 Total phosphorus average daily load estimates
(Kg/day) and average percent estimated bias from
Monte Carlo-analyses for the Sandusky, Grand and
Raisin rivers 23
8 Low, high and median 95% confidence intervals
calculated on load estimates (Kg/day), from
Monte Carlo subsampling, for the Sandusky, Grand and
Raisin rivers 29
9 Comparison between estimated sample sizes, at
various levels of precision, calculated using
variance and average estimates from the complete data
set and using the CV predicted from the regression
equation 38
10 Predicted number of samples required per year to
estimate total phosphorus loads with 95% confidence
intervals less than or equal to the indicated
precision of the estimate 40
IV
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ACKNOWLEDGEMENTS
Funding for this project was provided by the Environmental Protection
Agency, Great Lakes National Program Office. Event sampling programs
are labor intensive and many Michigan Department of Natural Resources
personnel helped with data collection. Sampling was coordinated and
conducted by Rick Lundgren, Frank Horvath and Bob Wood. Additional
assistance was provided by Jim Rossio, Greg Goudy, Dave Kenaga,
Chris Hull, Jim Young, Amy Peterson, Bruce Rabe and Rob MacLean.
Colleagues who provided comments on earlier drafts include Jim Rossio,
Dave Kenaga, Greg Goudy, Rick Lundgren and Bob Wood. Also, R. Peter
Richards (Heidelberg College) and David M. Dolan (International Joint
Commission) provided comments on an earlier draft of this report.
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CONCLUSIONS
Annual load estimates of total phosphorus, suspended solids,
ammonia, total Kjeldahl nitrogen, nitrate, calcium, sodium, silica,
sulfate, magnesium and potassium were calculated by dividing sample
concentrations into two groups, or strata, and applying Beale's Ratio
Estimator. The sample concentrations were divided into high and low
strata with the cut-off being the historical upper 20th percentile of
flow.
Annual load estimates calculated from 1984 to 1986 on the Black,
Clinton, Rouge and Huron rivers were variable from year to year. Annual
loads seemed to be related to the magnitude of the average annual flows
or to the actual number of high flow days in a year. In 1984 annual
loads were also estimated from the St. Joseph, Pere Marquette, and
Ontonagon rivers. The greatest annual loads of the twelve parameters
usually came from the St. Joseph followed by the Black or Rouge rivers.
The lowest annual loads came from either the Pere Marquette or Ontonagon
rivers.
Event sampling strategies yield excellent load estimates regardless
of the relationship between load and flow. However, event sampling is
resource intensive and not required unless loads of the constituent
increase with increasing flow. Plots of daily average load versus daily
average flow indicate a positive relationship between loads and flow for
all twelve parameters in the Black, Clinton, Rouge, Huron, Ontonagon, and
St. Joseph rivers. Suspended solids and ammonia in the Pere Marquette
1
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River did not increase with flow and therefore loads could be estimated
with a fixed interval sampling program instead of an event sampling
program.
The results of Monte Carlo studies indicate that random sampling is
the only way to insure that load estimates will be unbiased. Strategies
that confine sampling to the first half of the year or neglect either the
rising arm or falling arm of the hydrograph will yield biased total
phosphorus load estimates.
Although it is difficult to develop a completely random sampling
strategy, systematic sampling insures that each sample within each strata
has an equal probability of being selected. The results of Monte Carlo
studies indicate that in most cases systematic sampling yields unbiased
total phosphorus load estimates.
The number of samples required to estimate loads will not be the
same for each river. Sample size estimates were calculated using load
average and variance estimates obtained directly from the complete data
sets. Load estimates from the Monte Carlo studies were usually within
the precision specified by the sample size estimation formula.
The variance of total phosphorus loads can be predicted from flow
variability. The load variability can then be used to predict the number
of high and low flow samples required from each river. Estimated sample
sizes were calculated using load average and variance predicted by flow
variability versus load variability regression equations. This method
2
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can be used to provide sample size estimates for many tributaries with
little or no prior information about the constituent of concern but is
not reliable for the most event responsive rivers.
Sample size estimates were calculated for four of the seven Michigan
tributaries studied using the load variability versus flow variability .
relationship. Sample size predictions were good for the Ontonagon, Huron
and Clinton rivers but poor for the most event responsive Black river.
Low intensity sampling on the more stable Pere Marquette and St. Joseph
rivers yielded relatively precise loads supporting the contention that
rivers with stable flows generally require less intensive sampling
programs.
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INTRODUCTION
The Great Lakes are the largest body of freshwater in the world and
support a variety of human activities. They receive wastes from point
sources such as municipal and industrial facilities as well as from
non-point sources including combined sewer overflows, urban and
rural runoff, and atmospheric deposition. Although complete mass
balances have not been conducted for all the Great Lakes, tributaries
are known contribute large amounts of certain chemical constituents.
Many of these constituents are present and required in trace amounts for
the existence of aquatic life but if present in excess can cause nuisance
conditions or toxicity problems.
The Michigan Department of Natural Resources (MDNR) has monitored
several Great Lakes tributaries for numerous chemical constituents for
more than 30 years. This monitoring has been used to describe trends,
identify emerging problems, document existing conditions for waste
discharge permits and estimate tributary loadings. Tributary Loadings
have historically been calculated by multiplying average monthly flows by
a single monthly sample concentration, but indications are that although
existing monitoring was sufficient for most purposes, it was poorly
suited for calculating loads of most constituents.
Many tributary systems are characterized by loads that are dominated
by non-point sources. Concentrations of some parameters tend to increase
or remain relatively constant with increased flow. Yaksich and Verhoff
(1983) reported that in several Ohio rivers, the greatest loadings
occurred during periods of high flow or high flow runoff events and
Richards and Holloway (1987) stated that in some Lake Erie tributaries as
4
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much as 80% of the annual load of certain constituents was delivered
past a monitoring point during the 20% of the time that the highest flows
occurred. In these cases where most of the annual load occurs during the
20% of the time with the highest flows the distribution of loads is
usually highly skewed. Load estimates from monthly monitoring often
underestimate the true load from these "event responsive" rivers by 15%
to 30% (Yaksich and Verhoff 1983) .
One sampling design that can substantially reduce load estimate
errors is flow stratified sampling. Stratified sampling is performed by
dividing the flow into subgroups or strata and sampling from each strata.
This procedure breaks the flow into groups that are less variable than
the complete flow record. Strata with highly variable loading rates can
be sampled more intensively than the less variable strata so that
estimate errors within each strata are minimized and precision of the
overall estimate is increased (Bierman et al 1988). Also, precision can
be gained by forming strata so that a heterogenous flow record is divided
into fairly homogenous parts (Snedecor and Cochran 1980).
Richards and Holloway (1987) conducted Monte Carlo studies to test
various sampling strategies and load estimation techniques using large
data sets from three Lake Erie tributaries. Based on these studies, they
recommended flow stratified sampling with proportionately more samples
collected during periods of high flow. They found that for event
responsive streams in Ohio, less than 50 samples per year provided
strongly biased and imprecise load estimates. Yaksich and Verhoff (1983)
and Bierman et al (1988) also concluded that sampling strategies should
be stratified by flow in these event responsive rivers. Yaksich and
Verhoff (1983) recommended an event sampling strategy for Lake Erie
5
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tributaries that included 15 to 20 grab samples over two or three of the
largest events with 5 to 10 additional steady flow samples. They stated
that their strategy would yield a load estimate "with a 10% to 20%
standard error. v
The MDNR presently monitors the water quality of several rivers
throughout the state with a fixed station monthly monitoring program. As
previously mentioned, one goal of that program is to provide data to
calculate annual pollutant loads to the Great Lakes from the tributaries.
This project was undertaken to sample several rivers more extensively
during high flow periods in order to obtain better load estimates and to
develop a load estimation sampling strategy that would be applicable to
Michigan rivers.
PROJECT DESIGN " .
Site Descriptions and Sampling Methods
Seven tributaries were selected for study including the Black,
Clinton, Huron, Rouge, Ontonagon, Pere Marquette and St. Joseph rivers
2 2
(Figure 1). River watersheds ranged in size from 1201 Km to 12,124 Km
with the smallest being the Rouge and the largest being the St. Joseph
(Table 1). Land use and soil types varied among watersheds. The
Ontonagon and Pere Marquette drainage basins are mostly forested and
wetlands; the Black, Huron, Clinton and St. Joseph watersheds are
primarily agricultural; and the Rouge watershed is primarily urban and
suburban (Table 2). All the watersheds are predominately loam soils
except for the Pere Marquette, which is mostly sandy soils (Table 3).
Maps of the tributaries are included in Appendix 1.
6
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ONTONAGON
PERE MARQUETTE
ROUGE
HURON
ST. JOSEPH
Figure 1. River mouth stations sampled by the Michigan Department of Natural Resources.
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Table 1. Drainage area of the project watersheds
Tributary
Rouge
Black
Pere Marquette
Clinton
Huron
Ontonagon
St. Joseph
sq. mi
467
711
740
760
908
1390
4681
sq. km
1210
1842
1917
1968
2352
3600
12123
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Table 2. Land use (%) by watershed.
Watershed
Ontonagon
Pere Marquette
Black
Huron
Clinton
Rouge
St. Joseph
Urban &
Suburban
0.
0.
2.
8.
25.
73.
3.
1
6
4
2
6
4
1
Agricultural Forest &
& Range Wetlands
13
33
82
67
62
23
72
.0
.2
.8
.4
.8
.6
. 7
83
64
14
22
9
2
22
.8
.8
.8
.4
.9
.8
.9
- Inland-
Waters
3
1
<0
2
1
0
1
.1
.4
.1
.1
.7
.2
.3
Table 3. Soil types (%) by watershed,
Watershed
Ontonagon
Pere Marquette
Black
Huron
Clinton
Rouge
St. Joseph
Clay
36.4
15.8
18.2
10.1
17.4
28.6
8.6
Loam
46.0
7.9
75.0
85.3
71.8
48.4
81.5
Sand
17.6
77.0
6.9
4.6
10.8
23.0
10.0
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The rivers were sampled over a 3-year period during 1984 through
1986. The study was conducted on all seven rivers in 1984, but only the
Black, Clinton, Huron and Rouge were sampled in 1985 and 1986. Three
sampling strategies were used including (1) monthly throughout each year,
(2) weekly during the spring when flows are typically highest (scheduled
samples), and (3) twice daily during periods of high flow caused by
precipitation and/or snow melt (event samples). Water samples collected
using monthly and scheduled strategies were analyzed for suspended
solids, total phosphorus, ammonia, total Kjeldahl nitrogen, nitrates,
chlorides, calcium, sodium, silica, sulfate, magnesium and potassium
while event samples were only analyzed for total phosphorus, total
Kjeldahl nitrogen, nitrates, ammonia, chlorides and suspended solids.
The number of high and low flow samples collected varied among rivers,
years and parameters.
Event sampling was initiated based on weather forecasts and daily
telephone monitoring of river stage heights, measured by the United
States Geological Survey (U.S.G.S.), at gaging stations on each river.
When it was determined that an event was starting, sampling was initiated
focusing primarily on the rising arm, the peak, and initial falling slope
of the event hydrograph. Samples were usually collected twice a day for
seven consecutive days during the high flow event.
Surface water grabs were taken as close to the mouth of each
tributary as possible but upstream of areas influenced by seiches.
Samples were collected with a can sampler at about '30 cm below the
surface in the center of the stream in an area of high flow. Sample
collection, handling and preservation procedures are described in "
Quality Assurance Manual for Water and Sediment Samples" (MDNR 1982
edition).
10
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Flow Measurement and Estimation
Since river sampling stations were downstream of gaging stations, it
was necessary to adjust the' flow value obtained at the gaging stations to
reflect the additional drainage areas between the gages and the sampling
stations. To estimate the discharge at the sampling site near the
tributary mouth, a single gage reading or sum of gage readings was
multiplied by a correction factor. The correction factor used was the
drainage area ratio (DAR), calculated by dividing the drainage area above
the sampling station by the drainage area above the gaging station. The
estimated discharge at sampling stations in the Pere Marquette,
Ontonagon, Huron, Clinton and Black rivers were obtained directly by
multiplying the DAR by the appropriate gage reading (Table 4). Since
there was no gage in the St. Joseph River downstream of the confluence of
either the Dowagiac or the Paw Paw rivers, the flow .at the mouth was
estimated by multiplying the DAR by the sum of the flows at the three
gages. In the Rouge River there were no gages below the confluence of
either the Middle Rouge or Lower Rouge Rivers. Also, the Ford Rouge
Plant continuously discharges 784 cfs of water, drawn from the Detroit
River, to the Rouge River downstream of the gaging station but approxi-
mately 2.5 miles (4 km) upstream of the water sampling station. The Rouge
River flow estimate at the mouth was obtained by multiplying the DAR by
the sum of the three gage flows (Rouge, Middle Rouge and Lower Rouge) and
adding the 784 cfs discharged from the Ford Rouge plant.
ANNUAL LOAD ESTIMATES
Load Estimation Methods
After samples have been collected with a flow stratified sampling
11
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Table 4. Drainage Area Ratios (DAR) and U.S. Geological Survey gaging
station locations by river.
River
Pere Marquette
Ontonagon
Huron
Clinton
Black
St. Joseph
Rouge
Gages
04122500 at Scottville
04040000 near Rockland
04174800 at Ann Arbor
04165500 at Mt. Clemens
04159500 near Fargo
04101500 St. Joseph R. at Niles
04101800 Dowagiac R. at Summerville
04102500 Paw Paw R. at Riverside
04166500 River Rouge at Detroit
04167000 Middle Rouge at Garden City
04168000 Lower Rouge at Inkster
DAR
1.05
1.04
1.21
1.04
1.48
1 .09
1.24
12
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strategy, a variety of methods are available for calculating the annual
load. Dolan et al (1981) tested several load estimation methods,
including means of loads' over time, regression estimators and a ratio
estimator (Beale's ratio estimator) using Monte Carlo studies with a
large data set from the Grand River in Michigan. They found that Beale's
ratio estimator (BRE)- consistently yielded estimates with the least
bias and best precision and concluded that the BRE was the best estimator
for systems with complete daily flow records and relatively little
concentration information. Richards and Holloway (1987) tested Beale's
ratio estimator against other estimators and also concluded that the BRE
provided the most precise and unbiased estimates.
For calculation purposes the flows were divided into two strata.
Although the number of flow strata can be more than two, Dolan et al
(1981) and Richards and Holloway (1987) also divided the flows into two
strata. Dolan et al divided the strata at two times the median flow
while Richards and Holloway divided the flow into the upper 20th
percentile and bottom 80th percentile. In this study the flows were
divided into high and low flow strata with the cut-off being the
historical upper 20th percentile of flow. In other words, the cutoff
flow was exceeded by 20% of the recorded flows and was greater than 80%
of the recorded flows. Percentiles of flow are available (in five
percentile intervals) from U.S.G.S. flow duration analyses.
Annual Loads from Seven Tributaries
The total annual loads of twelve constituents from seven tributaries
were calculated using the BRE and dividing the samples into high and low
flow strata (Table 5). In some cases, estimates of annual loads varied
13
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Table 5. Annual loads froi seven Michigan tributaries (netric tonnes per year).
River and Total
Year Phos,
Black River
1984
Load 184.0
+/-35X C.I. 32.6
nh 47
nl 25
1985
Load 225.4
+/-95X C.I, 90.3
nh 41
nl 48
1988
Lead :39,5
+/-35X C.I. 21.4
nh 45
nl 48
Clinton River
1984
Load" 100.1
+/-95X C.I. 23.5
nh 32
nl 39
1985
Load 167.4
+/-95X C.I. 36.8
nh 48
nl 41
1986
Load '.20.0
+ /-95X C.I. 20.4
nh 75
nl 27
Rouge River
1984
Load 114.2
»/-95X C.I. 16.2
nh 33
nl 36
Load 186.1
t/-35X C.L 36.2
nh 50
nl 45
1986
Load 128.6
+/-95X C.I. 13.4
nh 56
al 37
Total
Suspended
Solids Auonia
79490
22420
48
25
100900
54190
41
49
81S90
26700
43
48
25560
8242
32
41
50120
16060
48
42
36400
11890
73
27
24210
5979
44
26
41920
19930
50
46
25300
6632
54
37
226,1
163.4
7
14
170.6
45.2
41
49
257,4
57.2
45
48
97.67 •
20,84
6
14
130.1
38.3
48
42
.123.5
18.3
75
27
389.9
113.5
4
15
640.1
82.5
50
46
488.8
47.5
56
37
Total
Kjeldahl
Nitrogen
1397
46
47
25
1229
301
41
49
1371
77
48
48
671.4
,56.6
32
40
1387
131
48
42
909.8
56.5
76
27
1110
82
33
36
1858
173
50
45
1328
103
55
37
Total
Nitrate
1462
371
7
14
1317 '
2"9
41
49
1111
173
45
48
1108
218
5
14
1432
157
48
42
1184
230
76
27 -
520.2
211.7
4
15
942.8
109.1
50
46
562.7
44.2
56
37
Total
Calciai
38310
11070
7
14
32250
11260
11
13
•13350
12180
10
17
31110
1820
5
15
51820
5830
4
10
44700
5790
16
12
40830
2770
3
16
54530
3600
12
12
46630
4140
15
11
14
Total
Sodiui
8693
3165
7
14
5945
1993
11
14
7572
3180
10
17
28990
5170
5
15
44450
10920
14
11
49030
15640
16
12
29730
4700
3
16
56170
15880
12
13
42240
11490
15
11
Total
Silica
1197
153
7
14
1331
396
10
14
1521
519
1C
18
'1112
140
6
13
2093
301
i 0
11
1576
2100
17
12
1253
544
4
15
1932
209
11
13
1314
167
16
11
Total
Sulfate
36480
13420
7
14
31780
13310
12
14
28670
9860
11
18
24120
5110
5
14
42180
4930
• r
1 1
i i
27010
6200
19
12
30220
3010
4
15
44430
4180
13
13
32160
3850
18
10
Total
Cloride
16590
6460
•j
14
14530
4770
12
14
15660
2020
45
48
45540
11700
6
14
78S70
17200
15
1 1
i *
55760
3770
74
27
58000
18150
4
15
100400
23860
13
13
79560
9970
55
37
Total
Hagnesiua
11390
3430
7
14
3035
3221
11
14
10000
3570
10
17
9642
598
c
15
14560
2150
14
130SO
1860
16
12
10580
570
0
j
16
13580
900
12
13
12280
1260
15
11
Tctai
Patassiuj
3172
267
7
14
3290
414
11
14
3794
289
10
17
1875'
103
5
:s
2902
2C5
14
11
2553
109
16
12
2242
234
3
16
2637
180
12
13
3119
651
15
11
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Table 5. continued.
River and Total
Tear Phos.
Huron River
1984
Load 35.49
+/-95X C.I. 2.48
nh 36
nl 35
1985
Load 64.39
t/-95X C.I. 7.67
nh 42
nl 53
1986
Load 47.90
+/-95X C.I. 2.85
nh 38
nl 53
Ontonagon River
1984
Load 110.2
+/-95X C.I. 29.6
nh 31
nl 80
Pere Harqaette River
1984
Load 34.00
I/-95X C.I. 3.35
nh 17
nl 8
'St. Joseph River
1984
Load 317.5
t/-95X C.I. 44.9
nh 10
ni 14
Totil
Suspended
Solids
10840
1944
36
36
23680
5386
42
54
15000
1943
38
53
• -104200
505,20
31
80
5900
1554
18
9
80850
22410
10
14
Amonia
38.34
39.89
6
15
120.8
25.5
42
54
78.39
11. §5
38
53
40.18
10.68
3
18
137.5
40.3
15
9
620.1
201.2
9
14
Total
Kjeldahl
Hitrogen
521.3
20.7
36
35
770.8
50.2
42
54
727.0
22.8
33
53
671.3
47.9
31
80
475.2
in o
J U . J
17
8
3972
297.6
10
14
Total
Nitrate
450,3
68.0
5
15
760.7
53.8
42
54
'SO. 5
43.3
38
53
154.7
42.0
7
18
143.2
19.5
15
3
7803
913
10
14
Total
Calciui
29260
1500
5
16
46260
2910
12
12
45460
2050
9
15
18550
580
10
18
3C510
1370
16
3
273900
12130
9
14
Total
Sodiui
14720
1200
5
18
22990
4050
12
13
24520
3100
3
15
4079
365
10
18
6915
645
15
3
50970
3980
9
14
Total
Silica
874,8
294.4
6
15
1714
355
11
13
1375
375
,9
16
4424
288
3
18
2750
312
15
3
11450
2750
3
14
Total
Suifate
25430
1130
6
15
43510
4020
13
13
34080
1080
10
15
8421
933
8
18
13580
705
' 5
8
204800
9800
3
14
Total
Cioride
27240
1970
6
15
43230
6500
13
13
4184C
1710
38
53
3186
378
8
18
10630
1050
16
3
93500
5520
3
14
Total
Xagnesiui
8309
510
5
16
12990
S40
12
13
12920
300
9
15
5156
378
8
18
10500
520
15
0
31720
5170
9
14
Total
Pctassiua
1258
77
5
16
1310
113
12
13
1907
111
9
15
1.712 -
423
8
18
i53,2
51.:
15
Q
3534
286
3
14
nh= umber of high flow saiples
nl= niiiber of low Flow saaples
15
-------
substantially among different years. For example, the annual total
phosphorus load in the Huron River was approximately 83% greater in 1985
than 1984. Most of the estimated loads from the Rouge, Clinton, and
Huron rivers were highest in 1985, intermediate in 1986 and lowest in
1984. This is probably related to annual average daily flows that were
also highest in 1985, intermediate in 1986 and lowest in 1984 (Table 6).
Estimated loads from the Black River did not follow this pattern
even though the annual average daily flows did. In the Black River, from
1984 to 1986, the lowest annual average daily flow occurred in 1984
followed by 1986 and 1985. However, more high flow days, or days in
which the daily average flow exceeded the historical upper 20th
percentile cut-off flow of 347.8 cfs, occurred in 1984 followed by 1986
and 1985. Estimated annual loads of total phosphorus and suspended
solids were highest in 1985 and lowest in 1986 following the pattern of
the relative magnitude of annual daily average flows. At the same time,
estimated annual loads of total Kjeldahl nitrogen, nitrate, calcium,
sodium, sulfate and chloride were highest in 1984, the year with the most
high flow days. It may be that the number of high flow days was more
important than the magnitude of flow on high flow days. In such a case,
loads of some parameters may be less in years with a few large events
than in years with many smaller events.
Estimates of annual loads from the Ontonagon, Pere Marquette and St.
Joseph rivers are available for 1984. Fewer samples were collected in
the Pere Marquette and St. Joseph rivers compared to the other
tributaries but sampling effort on the Ontonagon River was relatively
intense. Scheduled samples from the Ontonagon were collected by an MDNR
Conservation Officer stationed at White Pine and event samples were
16
-------
Table 6. Average daily flow (cfs), 20th percentile cut-off flow
(cfs) and the number of days in each high flow and low
flow strata for the Black, Clinton, Rouge and Huron
rivers, 1984-1986, and the Ontonagon, Pere Marquette and
St. Joseph rivers, 1984.
Flow
River Year Cut-off
Black
1984
1985
1986
Clinton
1984
1985
1986
Rouge
1984
1985
1986
Huron
1984
1985
1986
Ontonagon
1984
347
347
347
713
713
713
1143
1143
1143
904
904
904
1518
.8
.8
.8
.1
.1
.1
.9
.9
.9
High
Flow
Days
143
109
129
65
140
140
67
129
117
62
99
71
62
Low
Flow
Days
223
256
236
301
225
225
299
236
248
304
266
294
304
Ave .
High
Flow
1633
2927
2195
1472
1971
1323
1731
1877
1654
1187
1671
1408
3602
Ave .
Low
Flow
140
97
131
342
356
439
932
953
979
350
444
552
924
Annual
Ave .
Daily
Flow
.0
.84
.0
.5
.0
.8
.6
.9
.0
. 7
.0
. 7
. 1
723
942
860
543
975
778
1079
1280
1195
492
776
719
1378
.3
.7
.5
. 1
.5
.6
.4
.8
. 1
Pere Marquette
1984 879.9
St. Joseph
1984
5927
161
91
205
275
1097
7842
705.6
3841
877.8
4836
17
-------
collected by park rangers from Porcupine Mt. State Park. The precision
estimates for these three rivers were comparable to the other four
tributaries, but if annual load estimates are as variable as those from
the four eastern tributaries, then caution should be used in extra-
polating estimates to other years.
In 1984 the greatest annual loads of twelve parameters usually came
from the St. Joseph River followed by the Black or Rouge rivers. Large
•K.
loadings from the St. Joseph river are not surprising since the average
daily flow in the St. Joseph river was more than 3.5 times the daily
average flow in any of the other rivers and nearly 73% of the watershed
is developed for agriculture. Also, both the Black and Rouge river
watersheds have large urban or agricultural areas that may be non-point
sources of some constituents. The smallest annual loadings of each
constituent came from either the Pere Mar-quette or Ontonagon rivers.
Both of these watersheds are relatively undeveloped and dominated by
forests and wetlands.
SAMPLE STRATEGY DEVELOPMENT
Determining the Necessity of Event Sampling Strategies
Yaksich and Verhoff (1983) found that event sampling strategies
yielded excellent load estimates in all cases regardless of the relation-
ship between concentration and flow. However event sampling is more
resource intensive than other sampling strategies and is not required
unless loads of the constituent increase with increasing flow. When
concentration and flow are not related annual loads can be estimated with
fixed interval sampling programs.
18
-------
To determine which constituents in each tributary actually required
a flow stratified sampling strategy, daily average loads were plotted
against the corresponding daily average flow. Daily average loads were
calculated on each day samples were collected by multiplying daily
average flow (cfs) by parameter concentration (mg/1) and by a conversion
factor of 2.45 (cfs x mg/1 x 2.45 = Kg/day). Least squares linear
regression estimates were calculated and a t-test was used to demonstrate
•v
that the loads of some parameters were related to flow.
Plots of loads versus flow of twelve parameters in Seven tributaries
are included in Appendix 2 and the regression of loads on flow in the
Black, Rouge, Clinton, Huron, Ontonagon and St. Joseph rivers indicate a
statistically significant (alpha 0.05) positive relationship between
loads and flows for all parameters. The variability tended to increase
with increased flow which is otie.reason for taking a proportionately
higher number of samples during high flow periods.
In the Clinton and Rouge rivers, sodium and chloride concentrations
tended to increase with flows but loads were highly variable at all
flows. This may have been due to chloride uses not related to flow, such
as seasonal use of road deicers. Urban areas, where large amounts of
deicers are used, are much more extensive in the Clinton and Rouge
watersheds than in the other five tributaries monitored.
In the Pere Marquette River, loads of suspended solids and ammonia
were not related to flow. Therefore, load estimates of suspended solids
and ammonia from the Pere Marquette River do not require event sampling
and could be obtained with a less labor intensive fixed interval sampling
program. All other constituent loads require event sampling to obtain
reliable estimates.
19
-------
Testing for Bias Introduced by Event Sampling Strategies
Another objective of the project was to develop a sampling strategy
that would yield relatively precise and accurate load estimates (in this
case total phosphorus loads) from Michigan tributaries. To test several
different high flow sampling strategies, Monte Carlo runs were conducted
on three large data sets of total phosphorus concentrations. The data
sets selected were the Sandusky River (1834 total phosphorus samples
collected during calendar years 1982-1985) the Raisin River (1237 total
phosphorus samples collected during water years 1983 to 1986) and the
Grand River (361 samples collected between March 1, 1976 and March 1,
1977). These data sets were obtained through STORET, the Environmental
Protection Agency's data storage and retrieval computer system. All
three had duplicate samples on some days, missing values on some days, or
both. Therefore, the data sets were adjusted so that there was a single -
total phosphorus concentration recorded for each day. Average
concentrations were calculated on days with multiple samples and
concentrations were estimated by linear interpolation on days when no
samples were.collected. A "known" annual load and average daily load
were calculated using the adjusted daily total phosphorus concentrations
and daily average flows recorded at U.S.G.S. gaging stations. Although
the true load cannot be "known", these data sets were the most complete
available.
The next step was to assess different methods of stratified random
sampling by drawing subsamples from the complete data sets and comparing
estimates to the "known" load. The data sets were broken down into
individual years within each tributary so that there were a total of nine
complete data sets (four each from the Sandusky and Raisin and one from
20
-------
the Grand). Subsamples were drawn and average daily loads were
calculated two hundred and fifty times for each of the nine different
adjusted data sets and each of the five different sampling strategies.
The number of samples selected for each subsample was calculated using a
sample size estimation formula that requires an estimate of average and
variance of the load as well as a specified confidence interval.
A precision of +/- 50% was selected for the estimates of average
load calculated from the Monte Carlo runs. This precision was selected
for the Monte Carlo runs because the data sets were adjusted to have one
.sample per day and the estimated sample size could not exceed the number
of days in each strata. Also, a relatively small estimated sample size
provides a larger number of random combinations of subsamples.
Investigators estimating tributary loads generally require more precise
estimates than +/- 50% and to achieve a greater precision more
samples are required. However, conclusions about the best sampling
strategy, based on Monte Carlo studies, will be independent of the
precision of load estimates.
Daily average loading rates and 95% confidence intervals were
calculated for each estimate along with bias, which was the percent
difference between the "known" load and the estimated load. Each group
of runs was tested for deviations from a normal distribution using a test
for skewness and a test for kurtosis. The average estimated load from
each group of runs that was normally distributed, or could be transformed
to a normal distribution, was tested for deviation from the known load
using a t-test. Median estimates were calculated for all subsets with
distributions that could not be transformed to normal.
21
-------
The first flow stratified sampling strategy tested on each data set
was random sampling from each strata. Individual daily total phosphorus
samples were selected using a Lotus 123 random number generator. One
data set was non-normal and had a median bias of -4.05%; but the average
bias of the other seven estimates of average daily loads (Kg/day) ranged
from -0.605% to 0.266% and none of the averages of daily loads were
significantly different than the known load (Table 7). This indicates
-^
that "random" sampling of high and low flow days is a strategy that would
usually provide estimates that, on average, are unbiased. Unfortunately
it is impossible to use random numbers to select sampling days without
having prior knowledge of the number and date of occurrence of high and
low flow days in an upcoming year. Therefore, several flow stratified
sampling programs were tested to document any bias introduced by
non-random sampling and to propose an alternative program.
Previous studies have indicated that daily load estimates may be
influenced by season. In spring 1977, MDNR personnel collected total
phosphorus samples from several southeastern Michigan tributaries during
high flow conditions. They found the highest total phosphorus concen-
trations during the first event of the season despite relatively low
flows during the event (Schroeter 1978). Peak total phosphorus
concentrations tended to decline with each of the first three successive
events, regardless of flow, in each of the tributaries sampled. These
data suggest that if a disproportionate number of high and low flow
samples were to be collected in the spring, the resulting annual load
estimate may be biased.
To test this hypothesis, Monte Carlo runs were conducted using
subsamples drawn randomly from the first half of the available high and
low flow days to simulate a sampling strategy that concentrates sampling
22
-------
Table ?, Total phosphorus average dailj load estimates Ug/sayl and average percent estlntsd
bias fro« Honte Carlo analyses for the Sandusky, Grand and Ra.sin rivers.
•up ling
Strategy
"known Load"
Randot
•«*
Seasonal
No Rising Hydro
No Failing Hydro
Ranaoi Gr:u?s
"known Load"
lUadoa
Seasonal
No Rising Hydro
No Falling Hydro
Randoj Groups
"known Load"
Randoi
Seasonal
No Rising Hydro
No tailing Hydro
Randoa Groups
Average Estimated Percent Eias
Sandusky River
1332 1983
1670 998.5
1668 -0.119X 998,9 0.04COX
1522 ** -7.0"X 1123 ** 12. 5X
1738 ** 4.075 10C1 G.250X
17.19 ** 4, 135 1107" 10.35
1E55 H 0.39SX 333.: D.C30IX
Grand River
3/1/76-2/28/7?
1734
1734
150" ** -7.32»
1583 " -2.34X
1745 0.534X
1727 -0.402X
Raisin ?.iver
1983 1384
589,8 452.2
591.1 0.220X 453.1 0.199X
4?2.5 ** -19. 9X 465.0 ** 2. 335
573.1 ** -2.33X 423.3 ** -8.39
5?;. 1 ** 14. 2X 541.9 ** 19. 8X
591.3 K 0.333X 441.0 M -2.48X
1384 1985
1581 1133
1517 K -4.05X M 1136 0.262X
1383 «* -12. 2X 1229 ** 3.39X
1550 i -1.96X K 1151** -2.70X
1351 ** 17. IX 1353 ** H.8X
1542 H 2.35X M 11S6 M 1.1CX
1385 1936
563.3 396.2
554.2 C.266X 393.8 -0.505*,
601.2 ** 5.73X 339.3 ** -14.15
521.7 ** -7.29 397.' 0.3"35
630.1 ** 22. EX 431,3 ** 3.C1X
555.3 * 0.5345 397.8 0.404X
* significantly different than :he known load (alpha=0.05l
** significantly different than the known load lalpha=0.01)
U: Hedian value was calculated due to non-norial distribution of the averages.
23
-------
effort during the first part of a year. The sample sizes remained the
same even though samples from days toward the end of the year were
excluded from all subsets. All of the average estimates calculated were
significantly biased, but the direction of the bias was not predictable.
The range of bias estimates was from -19.9% to 12.5% with four of the
average bias estimates positive and five negative (Table 7). Therefore,
sampling should not be unproportionately concentrated in one season or
•^
bias may be introduced. Data collected from the Rouge and Clinton rivers
indicate that this type of seasonal variability may be especially
pronounced with chloride concentrations.
Schroeter (1978) also compared total phosphorus concentrations from
the rising and falling arms of event hydrographs and concluded that total
phosphorus concentrations were generally higher during the rising
hydrograph. This indicates that.if a sampling strategy were to
systematically neglect either the rising arm or the falling arm, then
bias may be introduced by the sampling strategy.
To test this hypothesis, high flow samples were divided into three
categories. The first category included samples on the rising arm of the
hydrograph, the second category included samples at the peak of an event
hydrograph while the third category included samples from the falling arm
of the event hydrograph. To test a strategy that consistently missed the
beginning of an event hydrograph, high flow subsamples were selected
exclusively from high flow days in categories two and three and low flow
samples were selected randomly from the entire number of low flow days.
This type of sampling strategy may be implemented accidentally if field
crews are unable to respond fast enough to an event and subsequently miss
the beginning of each event.
24
-------
Six of the nine average daily load estimates were significantly
biased, two were not significantly biased, and one set of estimates was
non-normal and not tested but had a median bias of -1.96%. Average bias
ranged from -7.39% to 4.07% and of the average biases that were
significantly different than zero, five were negative and one was
positive (Table 7). Although this strategy did not introduce bias in all
cases, two-thirds of the average estimates were biased and one was
«^
untested indicating the potential for this strategy to yield inaccurate
estimates.
To assess the effects of missing samples at the end of an event,
Monte Carlo runs were made with subsets that included high flow samples
randomly selected from high flow days in categories one and two and low
flow samples selected randomly from the entire low flow data set. Again,
this type of strategy may be implemented accidentally if field crews are
consistently unable to continue sampling a site for the duration of an
event, and the falling arm of an event hydrograph is sampled less often
than earlier portions of the hydrograph. All the average daily load
estimates from the nine sets of runs were significantly different than
the known load except for the Grand River average estimate. The average
bias estimates were positive and ranged from 0.634% to 22.5% (Table 7).
Therefore, it appears that strategies that consistently miss samples on
the falling arm of the hydrograph may be introducing bias.
Flow Stratified Systematic Sampling
It appears that the key to developing an unbiased stratified
sampling strategy is to insure that within each strata, each sample has
the same probability of being selected. However, it is difficult to
25
-------
develop a plan to sample randomly without prior knowledge of future
flows. One method would be to use a systematic sampling strategy where
samples are drawn at regular intervals based on the percentage of
subsamples desired (See Snedecor and Cochran 1980 for further information
on systematic sampling). For example, if the historical upper 20th
percentile of flow is used as a cut-off between high and low flow strata,
then an average year will have 72 high flow days (365 x 20% = 72). If
the estimated high flow strata sample size is 24 then it is necessary to
collect samples on one third of the high flow days. If the high flow
days are arranged chronologically and "counted off" into groups of three,
then in an average year there would be three groups of 24 samples each.
A number between one and three could be randomly selected and would
designate a particular group of samples.
For example, assume that in an average year the number one was
selected randomly, high flow sampling would be initiated on the first
high flow day of the year and samples would be collected on high flow
days 1,4,7,10, 64,67,70 for a total of 24 samples. However, most
years would not have exactly 72 high flow days and 72 is not divisible by
all estimated sample sizes. If 72 is not divisible by the estimated
sample size then the investigator will have to use a rounded "real
number" spacing interval. For example, if the estimated sample size is
30 then a sample should be collected every 2.4 days. If the sampling
started on day one then the sampling interval should be 1, 3.4, 5.8, 8.2,
10.6,....65.8, 68.2, 70.6 but samples would actually be collected on
days 1,3,6,8,11 66,68,71.
To test a systematic sampling strategy, high flow days in each of
the data sets from the Sandusky, Raisin and Grand rivers were arranged in
26
-------
chronological order, counted off based on the estimated sample size, and
divided into groups. Each subsample used to estimate a load consisted of
a randomly selected group of high flow samples combined with low flow
samples selected randomly from the entire low flow data set.
Distributions of estimates from five of the Monte Carlo runs were
non-normal and not transformable, usually due to bimodal distributions
based on the high flow group randomly selected to calculate an individual
estimate. Four of the average estimates were tested against the "known"
and one was significantly biased (alpha 0.05). Median bias ranged from
3.86% to -2.48% and average bias ranged from -0.403% to 0.534% with
0.534% being statistically different than zero (Table 7).
If a monitoring program were conducted over many years the average
number of samples per year could be predicted but for any one year the
number of samples collected could be highly variable. During a wet year
with more than the average number of high-flow days additional samples
would need to be collected since indications are that discontinuing
sampling before the end of the year would introduce bias to the sampling
strategy. However, a potential benefit of a systematic sampling strategy
is that additional samples are collected during years with more than
average high flow days and this should improve estimates by sampling more
often during more variable years. Also, fewer samples would be collected
during dry years without a loss in precision.
The assumption was made that low flow samples will be collected
"randomly". Less attention is paid to low flow sampling because
generally the low flow strata contributes less to the annual load and is
less variable. Although no strategies for random sampling in the low
flow strata were tested, collecting the samples over the entire year (i.e
regular fixed interval sampling) should be sufficient.
27
-------
SAMPLE SIZE ESTIMATION
Sample Size Estimation Method
The number of samples required to estimate loads is an important
aspect of any sampling strategy. Generally sample sizes can be predicted
by using the following formula:
n =(t2 x S2)/(D2 x X2)
^ CO U
where:
n = estimated sample size
est v
2
t = student's t value squared
2
S = variance of the daily load
2
D = precision, as a percentage of the
average, squared (ie. D=0.5 would
indicate a precision of +/- 50%)
2
X = average daily load squared
The approach taken was to estimate the sample size within each flow
strata, so an estimate of the daily average load and variance of the
daily average load within both the high and low flow strata was required.
Again, sample size estimates for Monte Carlo studies were predicted
using average and variance estimates calculated from the complete data
sets. If predictions of variance and average are accurate then the
estimated 95% confidence interval should have been within +/- 50% of the
estimate. Confidence intervals for loads to the Sandusky River,
calculated from random sampling, ranged from +/- 8.29% to +/- 51.3% of
the estimate (Table 8). Confidence intervals for loads to the Grand and
Raisin rivers, ranged from 7.62% to 40.9%, and 7.30% to 47.0%,
28
-------
Table 8. Low, high and ledian 95X confidence intervals calculated on lead estimates
(Kg/day), froi Honte Carlo subsanpling, for the Sandusky, Grand and
Raisin rivers.
River and
Year Strategy
Sandusky River
ftandoi
1982
1983
1984
1385
Seasonal
1982
1983
1984
1985
No Rising
1982
1983
1984
1985
No Palling
1982
1983
1984
1985
Systenatic
1982
1982
1984
1385
Grand River
3/1/77 to Randoi
3/1/78
Seasonal
No Rising
Ho Falling
Systeiatic
Saiple
Size
66
65
56
66
56
66
56
66
Hydro.
56
66
56
66
fljdro.
"6
66
56
66
Saiphng
35-96
75
71
77
13
13
Hydro.
13
Hydro.
13
saipling
16-17
+/- 95X
low
106.3
67.42
131.2
98.39
151.3
86.53
170.6
134.5
•5. 07
76.31
135.5
99.99
:59,5
122.0
159.5
134.7
399.6
118.5
225.4
130.0
127.3
116.3
151.0
123.1
159,6
confidence
high
906.4
203.9
778.0
223.1
754.0
171.8
243.4
230.3
357.3
205.1
792.3
207.4
933.3
203.2
730.9
207.6
472.0
156.1
539.8
154,5
824.1
322.5
702.3
748.8
3:i,5
interval
ledian
584,0
138.9
302.3
176.0
595.3
159.9
215.5
203.5
552.2
149.0
320.1
157.0
?46.1
190.0
718.9
189,4
407.5
153.9
534,3
157.2
316.7
352.?
336.9
23:. 3
303.1
I/- 95X
X low
9.43X
8.29X
9.28X
9.27X
14.6)1
3.64X
12. 6X
11. 3X
?.81X
3.91X
10. 2X
9.02X
14. IX
12. OX
10. OX
10.31
24. 4X
11. 3X
14. 5X
11. 2X
7.62X
8.08X
8. SOX
7.54X
3.51X
confidence
X high
51.25
20. 4X
47. OX
18.81
49. 5X
16, OX
18. 5X
18, 5X
4S.2X
20. IX
48. 3X
18. OX
53, 3X
18. 8X
41. 5X
15. 3X
17 o*
u ( * Cti*
:5.6X
32, 'X
•3.CX
40. 9X
iQ QV
'to • OS
*
-------
Table 8. Continued,
River and
Year Strategy
Raisin River
Randan
iff 1983
»Y 1334
Iff 1935
mr 1986
Seasonal
Iff 1983
»Y 1984
KY 1985
BY 1986
No Rising
KY 1983
»Y 1984
»Y 1335
»Y 1986
Mo Falling
Iff 1933
VY 1984
»Y 1985
Iff 1986-
Systenatic
»Y 1983
WY 1984
Iff 1985
Iff 1986
Saiple
Size
39
39
39
39
39
39
39
39
Hydro.
29
i 0
33
33
Hydro,
39
39
39
39
Saapling
67-68
60-61
42-43
56
•/- 35X
low
43.39
47.50
75.84
24.56
30.54
51.29
100.4
21.34
40.33
15.32
43.49
29.23
55.18
50.81
130.4
23.44
124.5
55.8
108.5
40,0
confidence
high
301.6
115.5
151.1
104.2
92.35
91.58
153,3
53.13
305.3
105.4
:35.c
110.6
278.3
106.4
147,5
104.0
171.1 ,
73.1
132,3
80.0
interval
aedian
177.7
81.11
121,2
52.94
56.44
78.24
144,5
23.31
157.3
73. 15
112.7
68,74
234.7
84.84
132.7
87.30
141.4
67,46
115,1
68.23
+/- 95S
X low
9.80X
11. 3S
14. OX
7, SOX
7.24X
11. OX
2C-.SX
5."4X
10. 3X
11. 3X
1D.7X
8.20X
11. IX
10.2!
18. IX
7.83X
20. 2X
11. «
18. 6X
10.1!!
confidence
X high
47. OX
23. 4X
28. 7X
25. 8X
18. Sv,
20. 2X
25. IX
17. K
47. 7X
26. OX
21. 3X
27. IX
41. IX
19. 5X
21. 2X
23. 7X
27. 4X
17. 7X
2G.8X
20. OX
interval
X ledian
29. 6X
17. 9X
21. 4X
16. 2X
11.9J
15. 4X
23. 3X
3.83X
32. 3X
17, 4X
21. 5X
17.51
31. 8X
15.7*
19. 3X
19. 3X
23. 3X
15, 5X
20. 3X
17. OX
30
-------
respectively. Calculated 95% confidence intervals from the systematic
sampling strategy ranged from 11.2% to 37.2% of Sandusky River loads,
9.51% to 43.0% of Grand River loads, and 10.1% to 27.4% of the Raisin
River loads. Confidence intervals rarely exceeded +/- 50% and were
usually much less than +/- 50%.
In some cases there was a relatively large range in confidence
intervals. Data from a tributary, year and subsample that by chance
yield a low confidence interval, should not be taken as an indication
that fewer samples could be collected in the next year. For example, one
combination of samples taken from the Sandusky River in 1982 yielded an
estimate with a 95% confidence interval of +/- 9.48%, while another
combination of samples from the same tributary and year yielded an
estimate with a 95% confidence interval of +/- 51.3%. A decision to
change the sample size based on either of these confidence intervals may
lead to wasted resources on unnecessary precision or an estimate less
precise than desired. A better way to adjust sample size estimates after
one year of sampling would be to use improved estimates of average daily
load and variability in the sample size estimation formula.
Sample size estimates of 13 for the more stable Grand River would
not be considered intensive event sampling. However, the precision of
the calculated estimates was always less than the desired +/- 50%
indicating that the sample size was adequate. This method of sample size
estimation may save investigators from making arbitrary decisions about
the intensity of flow stratified sampling.
Predicting Load Variability for Sample Size Calculations
Many tributaries will not have extensive concentration data on each
parameter of concern-. While an approximation of the average load in each
31
-------
strata may be available from monthly monitoring data, variance estimates
typically require more information. Richards (in press) found that one
way to predict the variance of the daily load of a particular parameter
was to relate it to the variance of the average daily flow. He quantified
a relationship between the daily suspended solids load variance and the
average daily flow variance using complete, or nearly complete, suspended
solids and flow data sets from 11 tributaries to lakes Michigan, Erie and
Ontario. These tributaries ranged from event responsive systems in which
flow was highly variable, to stable systems with less variable flows and
2 2
the watersheds ranged in size from 16,395 Km to 44 Km .
Richards used the coefficient of variation (standard deviation
divided by the average) of the logs of the set of percentiles of flow
(5%,10%,15%,20% 80%,85%,90%,95%) (CVLF5) to quantify flow
variability. The CVLF5 is provided in U.S.G.S. flow duration analyses.
All flows were in cfs and Richards pointed out that CVLF5 is affected by
the units used to measure flow. The variability of the daily suspended
solids load was quantified by calculating the coefficient of variation
(CV) of the logarithms of daily suspended solids loads. A least-squares
linear regression between the CVLF5 and the CV of the log of daily loads
for nine of the eleven tributaries yielded a predictor equation of Y=
0.0482 + 0.7197(CVLF5) with R= 0.99. Two tributaries were excluded as
outliers because Richards felt that the watersheds were small and the
period of flow record was short. This equation enabled him to predict
the CV of the log of suspended solids loads on any tributary which had a
complete flow record.
32
-------
A similar type of relationship was developed, for this project,
between flow variability and total phosphorus daily load variability.
Data sets from six Great Lakes tributaries with complete or nearly
complete records of daily total phosphorus concentrations were used. The
six tributaries were the Sandusky River, Honey Creek, (classified by
Richards as event responsive) Raisin River, Maumee River, Cuyahoga River
(variable responsive) and the Grand River (stable responsive). As stated
earlier, the total phosphorus concentrations used from the Sandusky River
were recorded during calendar years 1982-1985 and included 1834 total
phosphorus measurements. From the Raisin River, 1237 total phosphorus
samples were collected during water years 1983 to 1986 and 361 total
phosphorus samples were collected from the Grand River between March 1,
1976 and March 1, 1977. The additional three data sets included 2359
total phosphorus samples from the Cuyahoga Rj.ver, 2431 total phosphorus
samples from Honey Creek and 2564 total phosphorus samples from the
Maumee River collected between January 1, 1982 and December 31, 1986.
To quantify load variability the.CV of the total phosphorus load was
estimated for each of these rivers by calculating the antilog of the
standard deviation of the logs of daily loads. For example, the standard
deviation of the logs of daily average loads in the Grand River was 0.305
and the antilog of 0.305 is 2.018. A standard deviation of +/-0.305 in
the logarithm of the load can be transformed back to a non-logarithmic
standard deviation equal to the mean load multiplied (or divided) by
2.018. So if the standard deviation of the logarithms equaled 0.305 then
the standard deviation of the geometric mean would equal +/- 1.018% of
the mean. Standard deviations expressed as percentages of the mean are
coefficients of variation (CV).
33
-------
A Plot of the CV of total phosphorus daily loads versus CVLF5
indicates that there is a linear relationship between flow variability
and load variability and that Honey Creek seems to be an outlier (Figure
2). The least squares linear regression equation, based on five points,
was CV=-2.505+(CVLF5*32.2797) with R2= 0.872. Honey Creek was the
smallest and most variable of the six watersheds. The relationship may
not be linear at the upper range of CVLFS's or the size of the watershed
may influence the relationship between load and flow variabilities.
In order to estimate sample sizes in each strata, it is necessary to
know the parameter variability within each flow strata, not just the
parameter variability for the range of flow conditions within a given
year. Therefore, the same type of parameter variability versus flow
variability relationship was developed within each of the two flow
strata.
2
In the high flow strata there was a linear relationship (R =0.967)
between CVLF5 and' the CV of daily high flow loads excluding Hone}' Creek
(Figure 3). In the low flow strata there was also a linear relationship
2
(R =0.847 when Honey Creek was excluded) between daily load and daily
flow variability (Figure 4). The CV of daily total phosphorus load in
the high flow strata could be estimated by using the high flow predictor
equation CV=0.08381 +(CVLF5*7.0478) and the CV of the low flow strata can
be estimated by CV=-0.8528 +(CVLF5*11.8341).
Estimated sample sizes were calculated for the high and low flow
strata of each of the five rivers using variance estimates from the
complete data sets and estimates calculated from the predictor equations.
These two different sample size estimates were not always close and the
magnitude of the absolute difference between the two estimates increased
34
-------
i
O.OS
0.45
Figure 2. The Relationship between the Coefficient of Variation (CV)
of Total Phosphorus Daily Loads and Average Daily Flow
Variability (CVLtfS).
35
-------
1.S -
1 -
as -
CVLF5
Figure 3. The Relationship between the Coefficient of Variation (CV)
of Total Phosphorus Daily Loads and Average Daily Flow
Variability (CVLF5) in the High Flow Strata.
.x
2
o.os
0.45
Figure 4. The Relationship between the Coefficient of Variation (CV)
of Total Phosphorus Daily Loads and Average Daily Flow
Variability (CVLFB) in the Low Flow Strata.
36
-------
with increased flow variability. At a precision of +/-50% the absolute
difference between estimated Grand River sample sizes was one and the
absolute difference between Sandusky River sample sizes was seventy-eight
(Table 9). This method of predicting sample size requirements is one
procedure that can be used when sampling programs are desired on
tributaries with little or no prior information about the constituent of
concern but it seems that estimates are less reliable for the more event
responsive rivers.
Flow variability versus load variability relationships may be
quantified for other constituents that vary with flow. Parameters that
tend to be more variable than total phosphorus will require more sampling
effort to achieve the same precision while parameters that are less
variable will require fewer samples.
Sample Size Estimates for Michigan Tributaries
Sampling requirements were estimated for four of the seven Michigan
tributaries using the predictor equation and methods described above.
The predictor equations were developed using five tributaries with
CVLF5's ranging from 0.08469 to 0.26547 so the CV should only be
estimated for rivers with CVLFS's in this range since the slope or
relationship may change outside of this range. The CVLF5 at the mouth of
each tributary was 0.03092 for the Rouge, 0.04679 for the Pere Marquette,
0.05724 for the St. Joseph, 0.08245 for the Ontonagon, 0.09867 for the
Huron, 0.13991 for the Clinton, and 0.28044 for the Black rivers. The
CVLFS's for the Clinton and Huron Rivers fell within this range and
sample size estimates were calculated. The CVLF5 for the Ontonagon River
was near the lower end of the predictor equations and the Black River was
37
-------
Table 9. Coiparison between estiiated saaple sizes, at various levels of precision,
calculated using variance and average estiaates froa the coaplete data set
and using the CV predicted froa the regression equation.
Tributary
precision
(X of estiaate) Sandusky
A.
+/-
+/-
t/-
*/-
+/-
t/-
High Flow
SOX
40X
30X
25X
20X
10X
Strata
C*
32
48
84
120
185
732
P**
61
94
166
238
371
1476
Kauaee
C
21
32
54
77
119
467
P
37
56
98
140
218
865
Raisin
C
30
45
77
no
173
670
P
29
43
74
:os
163
647
Cuyahoga
C
37
56
98
140
218
865
P
24
37
63
90
140
551
Grand
C
8
12
13
26
33
147
P
10
14
22
31
47
180
B. Lo» Flow Strata
+/- 50X
+/- 40X
+/- 30X
t/- 25X
+/- 20X-
t/- 10X
C
34
P
83
51 128
88 226
126 324
195 506
775 2013
C
21
32
55
P
37
57
98
77 140
120 218
468 364
C ?
9 24
13 35
20 54
23 89.
42 138
181 546
C
11
16
27
37
P
18
27
46
86
58 101
221 398
C. Total Nuaber of Saaples
C
5
6
9
11
"16
57
P
2
2
4
4
5
11
+/-
+/-
t/-
+/-
+/-
*/-
D.
*/-
SOX
40X
30X
25X
20X
10X
Absolute
50X
C
56
99
172
246
380
1507
Difference
78
P
144
222
392
562
877
3489
C
42
64
109
154
239
935
P
74
113
196
280
436
1729
32
C
39
58
97
138
212
331
P
53
73
138
194
301
1193
14
C
48
72
125
1"7
276
1086
P
42
64 •
103
156
241
349
6
C
13
18
28
37
55
204
P
12
16
26
35
52
191
1
* Saaple size eatiiates calculated using variance and average estimates froa the
coaplete data sets.
** Saaple size estiaates calculated using the CVLF5 and the predictor equations
38
-------
near the upper end of the range so sample size estimates were also
calculated for these tributaries. Although sample size predictions should
not be made for rivers with a CVLF5 below 0.08469, sampling requirements
will decrease with a decrease in flow variability and the corresponding
load variability.
The CVLF5 was lowered dramatically in the Rouge River by the Rouge
Ford plant diversion. This constant addition of 784 cfs, to a median
upstream flow of 129 cfs, increased the flow at the mouth without
influencing the magnitude of the range between high and low flows. The
Rouge River CVLF5 calculated using flows above the diversion was 0.19993
and would indicate flow variability greater than all study rivers except
the Black River. At the mouth the CVLF5 was 0.03092 indicating flow
variability less than all of the rivers studied. Actual Rouge River
sampling yielded relatively precise 95% confidence intervals of +/-14%
of the estimate in 1984 (n=69), +/-19% in 1985 (n=95) and +/-!!% in 1986
(n=93). Although, these estimates are relatively precise, the results of
Monte Carlo studies indicate that large ranges of confidence intervals,
using the same sample size, are common. A calculated precision from any
single subset, within the group, may not be a good indicator of the
required sample size. On the other hand there is no evidence indicating
that additional sampling would have been beneficial.
The estimated sample sizes are presented in Table 10 so that the
predicted precision can be contrasted with the actual precision estimate.
Comparing the estimated number of samples (171) to the actual number of
samples collected in the Black River indicates that this tributary should
have been sampled more intensely to insure a precision of at least +/-
50%. However, 95% confidence intervals ranged from 10.8% (n=93) to 40.1%
39
-------
Table 10. Predicted number of samples required per year to
estimate total phosphorus loads with 95% confidence
intervals less than or equal to the indicated precision
of the estimate.
Tributary
Precision
(% of estimate) Ontonagon
A. High Flow Strata
+/- 50%
+/- 40%
+/- 30%
+/- 25%
+/- 20%
+ /- 10% 1
B. Low Flow Strata
+/- 50%
+/- 40%
+/- 30%
+/- 25%
+/- 20%
+ /- 10%
C. Total Number of
+/- 50%
+/- 40%
+/- 30%
+/- 25%
+/- 20%
+/- 10% 1
10
13
21
30
45
72
2
3
4
4
5
9
Samples
12
16
25
34
50
81
Huron
12
17
28
40
61
236
4
5
7
9
12
40
16
22
35
49
73
276
Clinton
20
30
51
73
112
449
13
18
30
42
65
250
33
48
81
115
177
699
Black
70
107
191
275
430
1719
101
156
275
395
615
2457
171
263
466
670
1045
4176
40
-------
(n=89) and it is likely that, as in the case of the Sandusky River, the
predicted sampling requirements are more rigorous than necessary.
Comparing the estimated total phosphorus sample size for the Clinton
River to the actual sample size indicates that precision should have been
within 40% in 1984 and 30% in 1985 and 1986. The actual precision was
better than the predicted precision in all three cases and was +/- 23.4%
(n-71), +/- 12.0% (n-89) and +/- 17.0% (n-103) in 1984, 1985 and 1986,
respectively. Sampling conducted on the Huron River should have yielded
95% confidence intervals within approximately +/- 25% of the estimate and
actual confidence intervals ranged from +/- 6.0% (n=91) in 1986 to +/-
11.8% (n=95) in 1985.
Sampling effort in the Ontonagon River should have yielded a total
phosphorus estimate with a 95% confidence interval of within approxi-
mately +/- 25% and the actual 95% confidence interval was just outside
the predicted range at 26.9%. This could be related to problems
extending the predictor line past the lowest point, variability of the
estimate derived from the predictor equation, higher than normal total
phosphorus load variability in the Ontonagon River in 1984 or a
combination of these factors.
No sample size estimates were calculated for the Pere Marquette or
St. Joseph rivers, but relatively low intensity sampling on both rivers
(25 samples from the Pere Marquette and 24 samples from the St. Joseph
rivers) yielded 95% confidence intervals of +/- 14.2% and +/- 9.8% for
the Pere Marquette and St. Joseph rivers respectively. As mentioned
earlier, calculated confidence intervals are variable and are not always
good indicators of sampling requirements, but these estimates were
relatively precise and support the contention that rivers with
stable-flows generally require less intensive sampling programs.
41
-------
LITERATURE CITED
Bierman, V.J. Jr., S.J. Preston and S.E. Silliman. 1988.
Development of estimation methods for tributary loading
rates of toxic chemicals. Dept. Civil Eng., Notre Dame
Univ. Tech. Rept. No. 183
Dolan, D.M., A.K. Yui, and R.D. Geist. 1981. Evaluation of
River Load Estimation Methods for Total Phosphorus. J.
Great Lakes Res. 7(3): 207-214.
Richards, R.P. (in press). Measures of Flow Variability
and a New Classification of Great Lakes Tributaries. Water
Quality Laboratory, Heidelberg College, 310 E. Market Street
Tiffin, Ohio.
Richards, R.P. and J. Holloway. 1987. Monte Carlo Studies of
Sampling Strategies for estimating Tributary Loads. Water
Res. Res. 23: 1939-1948.
Schroeter, J. 1978. Total Phosphorus-Flow Relationship in
Southeastern Michigan Tributaries. Mich. Dept. Nat. Res.,
Environmental Services Division, Pub No. 4833-5082.
Snedecor, G.W. and W.G. Cochran. 1980. Statistical Methods.
Seventh ed. Iowa St. Univ. Press. Ames, Iowa.
Yaksich, S.M., and F.H. Verhoff. 1983. Sampling Strategy for
River Pollutant Transport. J. of the Envir. Eng. Div., ASC
109 (No. EE1): 3-8.
42
-------
Appendix 1. Watershed Maps and Locations in Michigan
43
-------
\
0
Black
ver Basn
Sanilac Co
Lapeer Co,
10
Scale of Miles
St, Cla.ir Co,
vvvvvvvvvvvvwvv
v Lake Huron
\ vvvvvvvvvvv
\
•\
\
\ vvvvvw
H
44
-------
r\
\J
\ !
ve
Scale of Miles
Lapeer Co
r>. I ni , p
it LiQir Co,
Oakland Co,
Wayne Co,
\Haconb Co,
vvvvvvvvvv
vvvvvvvvvv
vvvvvvvvvvvvvvvvvvvv
45
-------
9*7
-------
Huron Rver
c~
r
!
Inghan Co,
Jackson Co,
/Oakland Co,
Scale of Miles
Vash-fcenaw Co
Monroe Co,
vvvvvvvvvvvvvvvv
vvvvvvvvvvvvvvwv
Lake Er
vvvvvvvvvvvvvvvvvvvvvvvvv
47
-------
.40
AAAAAAAAAA
AAAAAAAAAAAAA
-------
vvwvvvvw
vvvvvvvvvvvvv
Dere
Hasoii Co,
v
\_
/
Lake Co,
' Dceana Co,
Neroygo Co,
11
Scalp of Hiles
\
49
-------
CD
H5
O
CO
O
in
-------
Appendix 2. Relationship between Average' Daily Load
and Average Daily Flow.
51
-------
700
a
a a a
468
(Thouiand*)
Avarag* Daly How (cf •)
10
12
Average Daily Load of Calcium versus Average Daily Flow in the
Black River {1984-1986).
300
280
260
240
220
200
180
160
140
120
100
ao
60
40
20
0
a a
n
0
a a
a
a
a
a
a
10
12
Daly
Average Daily Load of Chloride versus Average Daily Flow in the
Black River (1984-1986).
52
-------
••
"5
1
**
*i
i'
•*• 9
si
*
1
5
90 -
ao -
70 -
60 -
so -
4O -
3D -
Q
a
a
a
a
a
a
a
a
20 -\
a
10 -I QpO*3
Q l^r . , . . . . , , ,
4 6
(Thousand*)
Axcrag* Ocily Row (cf»)
10
12
Average Daily Load of Potassium versus Average Daily Flow in the
Black River (1984-1986).
•^
^
£
11
^ a
2|
t
1
4
iao -
170 -
160 -
1SO -
140 -
130 -
120 -
11O -
100 -
so -
ao -
70 -
60 -
so -
° 0
a °
0 a
a a
a
cm
40 -I QlQ
1 PT^
3D -\ £
20 -\Sa
10 -If
0 -I
9
0 2 4 68 10 1
CThouKirid*)
Average Daily Row (cf»)
Average Daily Load of Magnesium versus Average Daily Flow in the
Black River (1984-1986).
53
-------
f
^
tl
.98
^ a
"0*
I
9
|
<
I
^v
9
Vjf
g "J
J !
ti
8
0
1
no -
130 -
120 -
no -
100 -
so -
80 -
70 -
60 -
SO -
4O -
30 -
a
a
0 a Q
a
a
a ^
i?
a
D
a a
B>
rT0 0
20 -1 rffi&
\jffn
10 -jpu
0 2 4 6 8 10 1
CThouiand*)
Avorag* Ddly Plow (cf»)
Average Daily Load of Sodium versus Average Daily Plow in th
Black River (1984-1986).
10 -
9 -
8 -
7 -
6 •«
s -
4 -
3 -
2 -
i _
i —
o -
a D
B° B .
a a °
a
a D B
a
a a
a
B
8
a a D
a B 0
B a D
^Q_ D
00°° m °
^HtaBrn ^"
8
10
12
Plow (cf»)
Average Daily Load of Ammonia versus Average Daily Plow in the
Black River (1984-1986).
54
-------
35 -
Avorao* Ddfcr Load
(TKoiMK)nd»)
0 W 8 M 8
0 H
C
a
a a
a
a ° a °
a ° o a a
if a ° °
eft a a
a a
a
Q g a
a a
_ o a a
a g
a
^=
^^^^^l" 1 1 1 I 1 1 1 1 I I
) 246 8 10 13
1. 1 rmimanamj
Avarag* Daly Plow (cf»)
45 -
35 -
1 »-
*.^
"8"§ 25 -
tj 20-
Qt
1 1S "
10 -
S -
n -
Average Daily Load of Nitrate versus Average Daily Flow in the
Black River (1984-1986).
a
a
a n
a
a
a
a
j^t,n
46
^ThouK
A\«raa» Daly Flow
10
12
Average Daily Load of Silicate versus Average Daily Flow in the
Black River (1984-1986).
55
-------
600
500 -
«,-
200 -
100
4 6
CThouKind*)
Avwog* Deily Flow («f
1O
12
Average Daily .Load of Sulfate versus Average Daily Plow in the
Black River (1984-1986).
8 -
7 -
1 *~
I? 5"
H 4-
a
| 3 -
2 -
1 -
0 -
C
a
a
a
a a a
B
a a a
§ a a D
an a n
^^^^^^^^^""""" 1 I 1 1 I 1 11 I I
)' 2 4 6 3 10 1
1, 1 1 iwuBunuv^
Average Ocily Plow (cf»)
Average Daily Load of Suspended Solids versus Average Daily
Flow in the Black River (1984-1986).
56
-------
1
1*
II
*
I
<
•5
.g
>£>%
"B-S
11
•*!
al
I
•
<
60 -
SO -
40 -
30 -
20 -
10 -
0 -
a
a
Q n
0 I a a° n
* • °
a _r, a o a
B afl a ^ a
a ^
—ft ^
?a On Q
g g a a
DQ| a
^^gflffW
0 246 8 10 1
Axorog* Daly Flow (cf»)
Average Daily Load of Total Kjeldahl Nitrogen versus Average
Daily Flow, in the Black River (1984-1986).
15 -i
14 -
13 -
12 -
11 -
10 -
9 -
8 -
7 -
6 -
5 -
4 -
3 -
2 -
0 -I
a
a
g
a
• o "' H
a | a 8 D P
0 a m ° 9 °
a V* a H H
a a a Da
° a a
•^a^P1*0^
4 6
CThouKind*)
Avvrogo Da'ly Flow (cf
10
12
Average Daily Load of Total Phosphorus versus Average Daily Flow
in the Black River (1984-1986).
57
-------
1
!l
|4
!
1
Q^
700 -T
6QO -
SOO -
•400 -
300 -
200 -
100 -
0 -
(
1.4 -
1.3 -
1.2 -
1.1 -
1 -
Q9 -
08 -
a? -
06 -
as -
04 -
03 -
02 -
Q1 -
a -
a
a
a
a
a
aq
°ifa a
a
cB
f
1 1 1 1 1 1 1 * '
) 2 4 € 8 11
(Thousand*)
Average Daly Plow (cf»)
Average Daily Load of Calcium versus Average Daily Flow in the
Clinton River (1984-1986).
a
a a
„ ° ° • =
ft D
° a D
a
.s °J B
l^f
j^n °
4 6
(Thouiand*)
Avarag* Daly Plow (cf»)
10
Average Daily Load of Chloride versus Average Daily Flow in the
Clinton River (1984-1986).
58
-------
I
20 -
4O -
30 -
30 -
10 -
D 24 € 8 10
(Thousand*)
Avaroge Daly Plow (cf »)
Average Daily Load of Potassium versus Average Daily Flow in
the Clinton River (1984-1986).
1
^
11
*i
at
i
1
l/U -
1SO -
14O -
130 -
130 -
110 -
100 -
SO -
ao -
70 -
eo -
so -
40 -
30 -
20 -
10 -
a
a
a
a
0
°
a
On J]
*
a
0 24 681
Average Oeily Plow (cf»)
Average Daily Load of Magnesium versus Average Daily Flow in
the Clinton River (1984-1986).
59
-------
aoo
TOO -
I
!l
>i
2l
aoo i
•400 -
300 -
aoo -
100 -
10
Averog* Doily Flew
Average Daily Load of Sodium versus Average Daily Flow in the
Clinton River (1984-1986).'
•
s
7 -
5 -
4 -
3 -
1 -
B
a
a
a
a
a
OB
a
4 6
CThouKmdB)
Average Doily Flow (cf»)
a
a
10
Average Daily Load of Ammonia versus Average Daily Flow in the
Clinton River (1984-1986).
60
-------
1
1^
ll
5
{1
c
J
JJ;
j
V
F"
j]
si
|
I
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10-
8 -
6 -
4 -
2 -
0 -
u
0 °
Q
a
a
a a a o
o
a a ° 0
a a Q
Oapa ° ° 1 D
Q*^ a
J Mi a a
o OFo
0 Jllf D
tjEiP a
Jlfc B
*"
i i i i i 1,1 i i
024681
(Thouiond*)
Average Dcily Plow (<*•)
Average Daily Load of Nitrate versus Average Daily Flow in th«
Clinton River (1984-1986).
28 -
26 -
24 -
22 -
20 -!
18 -
16 -
14 -
12 -
10 -
a -
6 -
4 -
2 -
Q -
a a
a a
0
a
a
a
a
a a
a a
4 6
(ThouKind*)
Average Daly Plow (cf»)
10
Average Daily Load of Silicate versus Average Daily Flow in the
Clinton River (1984-1986).
61
-------
600
£00 -
•400 -
300 -
200 -
100 -
OB
Do °
46
(ThouaondiO
Avaroge Daly Ftew (cf»)
3
10
Average Daily Load of Sulfate versus Average Daily Flow in the
Clinton River (1984-1986).
•^
1
II
ii
0
1
I
2,8 -
26 -
24 -
22 -
2 -
1.8 -
1.6 -
1.4 -
1.2 -
1 -
aa -
0,6 -
d4 -
0,2 -
o -
a
a
a
B B
9
a a a a
a
n°° a Q
a
a a a
D D_ 0
Q So
°B aa^a Bg
^^i^^ffla optt D
32468
CThouKind*)
Averog* Obly Plow (cf»)
Average Daily Load of Suspended Solids versus Average Daily
Flow in the Clinton River (1984-1986).
62
10
-------
*s
.-8
•••• D
2£
&
*
at-
€0
so -
20 -
B
4 6
CThouKind*)
Average Doily Plow (cf»)
8
10
Average Daily Load of Total Kjeldahl versus Average Daily Plow
•in the Clinton River (1984-1986).
10
9
a
7
6
n
a
4 6
0houiand»)
Daly Plow (<*»)
10
Average Daily Load of Total Phosphorus versus Average Daily
Plow in the Clinton River (1984-1986).
63
-------
"5
^
1C
—•^
1
>• Q
Jl
|
1
|
»
~^
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H
Q
A
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k
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BOO -
4SO -
400 -
350 -
530 -
3SO -
200 -
ISO -
100 -
D
a
a
aa
a° a
tfi
a
J*
1
0 24681
Average Oa'ly Plow (cfe)
Average Daily Load of Calcium versus Average Daily Flow in the
Rouge River (1984-1986).
1.6 -
1.S -
1.4 -
1.3 -
1.2 -
1.1 -
1 -
as -
aa -
07 -
06 -
as -
O3 -
02 -
01 -
Q -
a
a
a
a
Q
a
a a
a
a
Q n
a_ S
Q ^a
°w£ ° °
2w
aa
4 6
CThouiande)
Average Daly Plow (cf»)
10
Average Daily Load of Chlorides versus Average Daily Flow in the
Rouge River (1984-1986).
64
-------
1
^
14
ft
•3 |
ii
|
I
^
1
•w^.
•B .2
a
1
II
&
1
28 -
26 -
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
a
a a
a
a
a
°°D °°
a
PI ^3
^tt^^
^L Q
U Q
ao
Q
qfr °
3
B^
i i i i i i i i i
0 24681
CThouKind»)
Average Ocily Flew (cf»)
Average Daily Load of Potassium versus Average Daily Flow in th
Rouge River (1984-1986).
100 -
so -
80 -
70 -
60 -
SO -
40 -
30 -
20 -
10 -
a
a
0 °
a
a
a
a£
0
3
J
fa
»
4 6
CTHpiiinnciB^
Ocily Hew (cf»)
8
1O
Average Daily Load of Magnesium versus Average Daily Flow in the
Rouge River (1984-1986).
65
-------
1"
t?
3 i
TJ-2
at-
|
i
<
|
£
Tf
31
3
si
f
aoo -
TOO -
€00 -
SCO -
400 -
300 -
200 -
100 -
Q
a
o a
Q a
D
D
n
ad ijjgb a
1
024 681
(Thousand*)
Average Daly Plow Ccf»)
Average Daily Load of Sodium versus Average Daily Flow in the
Rouge River (1984-1986).
13 -
12 -
11 -
10 -
9 -
a -
7 _
6 -
S -
4 -
3 -
2 -
1 -
O -
a
a
a a
o a
o a _
aa a §
D 0
a n
a QQ n
" B a
a ° t
OHO a a a H
dST a a
%S SjPol
ȣi"a
4 €
CThounnd*)
Avvrag* Doily Flow (cf»)
10
Average Daily Load of Ammonia versus Average Daily Flow in the
Rouge River (1984-1986).
66
-------
•s
J
£
I??
3§
tl
g
1
-5.
-g
i
v^.
^i
te
*
s
J
35 -
3D -
25 -
20 -
IS -
10 -
s -
a
a
a
a
a
0
a
a o° °
DQB DQ B
iflf5 m°
^^S S a D
dA9
u 1 I 1 1 1 1 1 1 1 1 1
0 2 4 6 8 1(
CTrjouoonde)
Average Daily Flow (cfe)
Average Daily Load of Nitrate versus Average Daily Flow in the
Rouge River (1984-1986).
28 -
26 -
24 -
22 -
20 -
18 -
1C -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
a
a
a a
a
Ba B
a
U Q
JB H g
•GL Q
mf
0 2 4 6 8 1O
CThouiand*)
Average Daily Flow (cfe)
Average Daily Load of Silica versus Average Daily Flow in the
Rouge River (1984-1986).
67
-------
•st
1
il
v 3
sl
&
1
sou -
460 -
400 -
35O -
300 -
2SO -
200 -
ISO -
100 -
SO -
O -
O
a
a
o
a
an
a B a
go °
Ba
Jofl
s
4 6
CThouaand*)
Average Daily Plow (cf»)
10
Average Daily Load of Sulfate versus Average Daily Flow in the
Rouge River (1984-1986).
u
.3.2
I
IS
a
3 -J
1.S -
1 -
as -
a
a
Ha
a
a a
a
4 6
(Thousand*)
Daly How (cf»)
10
Average Daily Load of Suspended Solids versus Average Daily Flow
in the Rouge River (1984-1986).
68
-------
I
"w%^
ll
•
>l
si
8>
|
^
^J
J
f*
I g
^3
24
32-
30 -
38 -
26-
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
Q
a
a
a °
a a
o a o
a
o
a
a
9 o a
a %
a a *
o JB ° a
a c»i
n_^P TI ^
nr pip
HQ " 'I^Jj C^*
_-r^fft3 i3 *
^ftflEDQ
&^^^ 9
i i i i i i i > i
O 2 4 6 8 K
CThouKind*)
A\«rag» Deity Flow (cf»)
Average Daily Load of Total Kjeldahl Nitrogen versus Average
Daily Flow in the Rouge River (1984-1986).
€ -
S -
4 -
3 -
2 -
1 -
Q -
a
a a
a
a
n °
a a
a a B
a
a
°a Q B
cP B«g aa
a a a a
•• Ja« B
jjjjjfi
-------
•8
SCO -
«*-
300 -
200 -
100 -
a a
I i r i i i I i i i i
0.4 0.8 1.2 1.6 2 2.4
(TKouKjndt)
Averag* Daly Plow (cf»)
2.8
3.2
Average Daily Load of Calcium versus Average Daily Flow in the
Huron River (1984-1986). •
aoo
TOO -
600-
900 -
400-
300-
200 -
100 -
m
a
n
aa
T I i
0.4 0.8
1.2 1.6 2
(Thousand*)
Average Daly Plow (cf»)
2.4
2.8
3.2
Average Daily Load of Chloride versus Average Daily Flow in the
Huron River (1984-1986).
70
-------
•~ g
s£
19 -
18 -
17 -
16 -
15 -
14 -
13 -
12 -
11 -
10 -
9 -
8 -
7 -
6 -
S -
4 -
3 -
2 -
oa
cP
0.4 0.8 1.2 1.6
CThoueande)
Average Daily Flow (cf»)
2.4
2.8
3.2
Average Daily Load of Potassium versus Average Daily Flow in the
Huron River (1984-1986). '
•"5
o
^
£>%
!l
•**!
at
g
I
140 -
130 -
120 -
11O -
1OO -
9O -
80 -
TO -
60 -
SO -
4O -
30 -
20 -
10 -
0 -
a
a
a
a ^
a °
mn g° n
a *™
°rj3rn°
^B^^
^r
cff
0.4 0.8 1.2 1.6
(Thousand*)
Average Dcily Flow (cf»)
2.4
2.8
3.2
Average Daily Load of Magnesium versus Average Daily Flow in the
Huron River (1984-1986).
71
-------
?
I
11
ot
1
1
^
^
V?
X
•"•JJ.
"8"g
j i
•^ o
T3-2
at
400 -
4OO -
350 -
300 -
250 -
200 -
ISO -
100 -
so -
0
0 0
1 Q Q
™* D 0^3 n
^&&°*"
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.
Average Da'ly Row (cf»)
Average Daily Load of Sodium versus Average Daily Flow in the
Huron River (1984-1986).
2.8 -
2.6 -
2,4 -
2.2 -
2 -
1.8 -
1.6 -
1.4 -
1.2 -
1 -
0.8 -
0.6 -
Q4 -
Q2 -
O -
L
B c
s
a a
a
a
a
a
a
a
D
o a
"^a a
DjB ° C*3 030 a
ndr, Qa Q Q °
Bin n Q D
O S SuRF? Q n Q ^^ me
nnCMiS^tJ^^iPteg i S> "^3 D
0.4 0.8 1.2 1.6 2
CTheuiand*)
Average Daly Plow (cf»)
2.4
2.8
3.2
Average Daily Load of Ammonia versus Average Daily Flow in the
Huron River (1984-1986).
72
-------
L
f
1
^B
Qt
|
"*
14 -
13 -
12 -
11 -
10 -
9 -
8 -
7 -
6 -
S -
4 -
3 -
2 -
1 -
O -
C
26 -i
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
O -
D
C
D DQ
a a QQ
4-£D "
G a * - ^
BBn °°
B aa a a a
D_n
ni
&R3 i* a
[}] g rj Ti ^
9tSS^i
) 0.4 0.8 1.2 1.6 2 2.4 2.8 3.
CThouiandft)
Average Dcily Flow (cf»)
Average Daily Load of Nitrate versus Average Daily Flow in the
Huron River (1984-1986). .
a
Q§ a
"
a
D a
a
D
a *]
D ODD °
aa^°^ d1
n Qm^ n Q
0 0.4 0.8 1.2 1.6 2
(Thouwnd*))
Average Daly Plow (cf»)
Average Daily Load of Silicate versus Average Daily Flow in the
Huron River (1984-1986).
73
-------
14
13
12
11
10
9
8
7
€
S
4
3
2
1
0
QD
0.4 0.8 1.2 1.6 2
CThou»and»)
Average Daily Row (cf»)
2.4
2.8
3.2
Average Daily Load of Total Kjeldahl Nitrogen versus Average
Daily Flow in the Huron River (1984-1986).
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Q9
0.8
0.7
0.6
OS
Q4
O3
0.2
Q1
0
Q
a
0.4 0.8 1.2 1.6 2
CThoiMand*)
Average Daly Plow (cf»)
2.4
2.8
3.2
Average Daily Load of Total Phosphorus versus Average Daily
Plow in the Huron River (1984-1986).
74
-------
ofc-
460
4OO -
360 -
300 -
2SO -
200 -
1SO -
10O -
SO -
a
ag
°
QB
a o
0.4 0.8 1.2 1.6 2
CThou»and»)
Average Dcily Plow C^»)
2.4
2.2
3.2
Average Daily Load of Sulfate versus. Average Daily Flow in the
Huron River (1984-1986).
x
•8
•8i
O
1.2
1.1
1
0.9
O.8
0.7
Q6
as
Q4
Q3
Q2
Q1
0
B
Average Daly Row (cf»)
Average Daily Load of Suspended Solids versus Average Daily
Flow in the Huron River (1984-1986).
75
-------
1.9 -
1.7 -
1.6 -
1.S -
1.4 -
1.3 -
1.2 -
1.1 -
1 -
0.9 -
08 -
Q7 -
0.6 -
OS -
Q.4 -
0.3
EP
a a
a
9
-i 1 1 1 1—
6 8 10
CThouiand»)
Average Daly Plow (cf»)
—[—
12
14
Average Daily Load of Calcium versus Average Daily Flow in the
St. Joseph River (1984-1986).
•^
1
*
3^
%-"Jfr
"8 -a
if
at
&
1
•*
suu -
480 -
460 -
440 -
420 -
400 -
380 -
360 -
34O -
320 -
300 -
280 -
260 -
240 -
220 -
200 -
180 -
i«o -
a °
n
u a
aa
a
n
Da * *
a
a a D
QCb
QQ
a Q
Q ^f00
^3
U
6 8
CTho
Average Daly Plow
1O
12
14
Average Daily Load of Chloride versus Average Daily Flow in the
St. Joseph River (1984-1986).
76
-------
S*J -
80 -
j^ TO -
1 -
*i
3| so-
& 40 -
< 30 -
2O -
10 -
4
4
£60 -
SCO -
4SO -
•v 400 -
"g| 3SO -
.38
*% s00 -
1 2SQ -
200 -
1SO -
100 -
a
a
a
a a
a
* o
a « a
a a a
E^ff °
a rf™ Q
t 4 6 8 10 12 14
CThouiand*)
AuBroge Oaly Plow C«*»)
Average Daily Load of Potassium versus Average Daily Flow in the
St. Joseph River (1984-1986).
a
a
a a
a
a B
8 a
*
D D
fF
1 a
1 1 1 1 1 1 » 1 1 i i i
2 4 6 8 10 12 14
CThouKind*)
Daly Plow (cf»)
Average Daily Load of Magnesium versus Average Daily Flow in the
St. Joseph River (1984-1986).
77
-------
if^
X
!
>£>•<.
Til
I
fl
r
5
>
^c
1
*••»
5 "B
.98
^ 3
ll
4
p
5
"*
25O -
24O -
230 -
220 -
210 -
200 -
190 -
180 -
170 -
1«0 -
ISO -
140 -
130 -
120 -
110 -
100 -
SO -
D
Q
a
D-
a a
a
PD a
a a
a a
a a
J fl
D
o =«, =
a
a
D n o
o _ D a
D 0,°
a ~ a
a
ifl
a
a
2 4 6 8 10 12 14
(Thoueande)
Average Dcily Plow (cf»)
Average Daily Load of Sodium versus Average Daily Flow in the
St. Joseph River (1984-1986).
& -
4 -
3 -
2 -
1 -
0 -
a
a a ig,
° a
a
a D a a
a a
U
a B - a
u
a a ° a
a
a
° 0
D t °
cJPo
8 10
(Thouiand*)
Average Daly Plow (cf»)
12
14
Average Daily Load of Ammonia versus Average Daily Flow in the
St. Joseph River (1984-1986).
78
-------
70 -
"S *° "
•8
^
£ SO -
1?
••* Q
•w JE
at
& 30 -
\
< 2Q -
10 -
a
a
a
a
a a
a
a a
Q
a
Q
a "
D %
QL. D a D
D D
cPa a a
*^3° %
ftF^
1 1 1 1 1 1 1 1 1 i < f
2 46 8 10 12 14
(Thousand*)
Axwroge Drily Plow (cf»)
Average Daily Load of Nitrate versus Average Daily Flow in th
St. Joseph River (1984-1986).
* ^^w — •
90 -
ao -
•5
•8 70 -
&JJ. eo -
\l
•*\ so -
^ a
ot- .«_
*
^
Q
| 30 -
20 -
10 -
Q -
a
a a
a
a
a
^ Q
or D a
a °a
a
a
a
a
a
a
a a
a a
"^3 a a a *
a n
a 10 12
(Thousand*)
AxcnagB Drily Plow (cf»)
14
Average Daily Load of Silicate versus Average Daily Flow in the
St. Joseph River (1984-1986).
79
-------
I
1.4
1.2 -
1.1 -
1 -
a» -
as -
0.7 -
Q6 -
as -
Q4 -
0.3 -
Q2
a a
B
D a
03
a
a
8 10
CThouKind*)
Average Dcily Plow (cf»)
12
14
Average Daily Load of Sulfate versus Average Daily Flow in the
St. Joseph River (1984-1986).
1
T~
4
T
I I I—
3 10
(Thousand*)
Average Daly Plow (cf»)
—I—
12
—I—
14
Average Daily Load of Suspended Solids versus Average Daily Flow
in the St. Joseph River (1984-1986).
80
-------
TO -
eo -
1 «.
ft »'
$ 20 -
10 -
0 -
C
a
a
8
o a a a °
i a
n a a a a
B afl a °
n. Q
rP1 a
a B °° ° °
a nfl a
a0 J
--* ,
, 2 4 € 8 10 12
1, l nouMjnu mj
Average Daly Plow (cf»)
IS -
14 -
13 -
12 -
^ 11 -
i .0.
VJ-L 9 -
11 8 "
*| 7-
Ot 6 -
* s
3 -
2
1
n
Average Daily Load of Total Kjeldahl Nitrogen versus Average
Daily Flow in the St. Joseph River (1984-1986).
a
a
a
a
a
a
% °f S «B ° B
a a g °°
a a
n ° D
468
Average Daly Plow (cf»)
10
12
Average Daily Load of Total Phosphorus versus Average Daily Flow
in the St. Joseph River (1984-1986).
81
-------
1
i
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11
fl
I
<
1
IT
}\
^ a
2|
ft
y
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160 -
150 -
no -
130 -
120 -
110 -
100 -
90 -
90 -
70 -
eo -
so -
t
D
QQ D D Q
° n D
Da an
0 ° §
a °Q o S |
Q^l •••
••
aa
a
a °
*> a
1 t I i I 1 i i i i i i
O.S 0.7 0.9 1.1 1.3 1.5 1.7
CThou«ond»)
Average Daly Flow (cf»)
Average Daily Load of Calcium versus Average Daily Plow in the
Pere Marquette River (1984).
•fis
eo -
56 -
SO -
«-
35 -
30 -
25 -
20 -
IS -
a
a*
c
a
a
a
aa a o
a a
aDDaaaaa Q
9.Q aa a
a° Da a° ° ° a
° "6 D D
a
O.S
0.7
0.9 1.1 1.3
CThouiond»)
Average Ocily Flow (df»)
1.S
1.7
Average Daily Load of Chloride versus Average Daily Flow in the
Pere Marquette River (1984).
82
-------
to -
8 -
I -
•^ j-
f* ^m1 *"
fl ft-
St 4 .
K 3-
™J
<
2 -
«
1 -
c
a
a 8 a °
a § a oa
_ a n_S_
a a ° 0SiPg
^a-aff •
D a
a
0.5 0.7 0.9 1.1 1.3 1.5 1.7
Average Doily Flow (cf»)
Average Daily Load of Potassium versus Average Daily Flow in the
Pere Marquette River (1984). '
3D -1'
SO -
1 -
TS
£ 40-
-------
1
9
^.
"8i
Q B
•J •
V 3
at
1
<
34 -
32 -
30 -
28 -
26 -
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
a
a
Q
B
a
a
a
a „ a a °B °
° * 3 ° Q
Q a a a
0 a a
a
a
a
a
l l l 1 l l
O.S 0.7 O.S 1.1
a
a D £
D a °
§
1 1 1 1 1 1
1.3 1.5 1.7
CTSouKind*))
Average Doily Flow (cf»)
Average Daily Load of Sodium versus Average Daily Flow in the
|
£
Q
3
5
I
Ul
i
Pere Marquette River (1984).
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700 -
600 -
SCO -
400 -
300 -
200 -
100 -
0 -
a
a °
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a a
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0.7
0.9 1.1 1.3
CThouiand*)
Average Dcily Flow Ccf»)
1.5
1.7
Average Daily Load of Ammonia versus Average Daily Flow in the
Pere Marquette River (1984).
84
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1.1 -
1 -
0,9 -
3 0.8 -
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5 0.7 0.9 1.1 1.3 1.5 1.7
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Average Doily Plow (cf»)
Average Daily Load of Nitrate versus Average Daily Flow in the
Pere Marquette River (1984).
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0.7 0.9 1.1 1.3 1.5
(Thousand*)
Daly Plow
1.7
Average Daily Load of Suspended Solids versus Average Daily
Flow in the Pere Marquette River (1984).
85
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4
£
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22 -
21 -
20 -
19 -
18 -
17 -
16 -
15 -
14 -
13 -
12 -
11 -
10 -
9 -
8 -
7 -
6 -
5 -
4 -
0
60 -
55 -
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45 -
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35 -
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5 0.7 0.9 1.1 1.3 1.5 1.7
CThouKind»)
AvBroge Daily Plow (,cf»)
Average Daily Load of Sulfate versus Average Daily Flow in tne
Pere Marquette River (1984).
t
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0.5
0.7
0.9 1.1
Average Daily Plow
1.3
1.5
1.7
Average Daily Load of Silica versus Average Daily Flow in the
Pere Marquette River (1984).
86
-------
1
£
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DAILY LOAI
(Thoueondi
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32 -
3 -
28 -
26 -
24 -
22 -
2 -
1.8 -
1.6 -
1.4 -
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Average Daly Row (cf»)
1.S
1.7
Average Daily Load of Total Kjeldahl Nitrogen versus Average Daily
Flow in the Pere Marquette River (1984).
2SO
240 -
230 -
210
200 •
190
iao
170
160
150
140
13O
120
110
100
90
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70
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1.1 1.3
(Thousand*!)
Average Daly Row (cf»)
1.5
1.7
Average Daily Load of Total Phosphorus versus Average Daily
Flow in the Pere Marquette River (1984).
87
-------
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Ody Load
(ThoiMand
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1
14O -
130 -
130 -
110 -
100 -
90 -
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60 -
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40 -
30 -
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(Thousand*)
Average Daly Flow (cf»)
Average Daily Load of Calcium versus Average Daily Plow in the
Ontonagon River (1984).
at
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
S
4
3
2
(Thousand*)
Average Daily Flow (cf»)
Average Daily Load of Chloride versus Average Daily Flow in the
Ontonagon River (1984).
88
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32 -
30 -
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24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
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(Thousand*)
Average Daly Row (cf»)
Average Daily Load of Potassium versus Average Daily Flow in the
Ontonagon River (1984).
90 -
80 -
70 -
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30 -
20 -
10 -
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Average Daly Row (cf»)
10
Average Daily Load of Magnesium versus Average Daily Flow in the
Ontonagon River (1984).
89
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•3 I 30 -
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Average Daly Row (ef»)
Average Daily Load of Sodium versus Average Daily Flow in the
Ontonagon River (1984 J.
1
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Avorage Ocily Plow (cf•)
Average Daily Load of Ammonia versus Average Daily Flow in the
Ontonagon River (1984).
90
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Average Dcily Plow (cf »}
Average Daily Load of Nitrate versus Average Daily Flow in tne
Ontonagon River (1984).
32 -
30 -
28 -
26 -
24 -
22 -
20 -
18 -
16 -
14 -
12 -
10 -
8 -
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CThouiand*)
Average Dcily Plow (cf»)
8
Average Daily Load of Silicon versus Average Daily Flow in the
Ontonagon River (1984).
91
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70 -
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10 -
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Average Ocily Flew (cf»)
Average Daily Load of Sulfate versus Average Daily Flow in the
Ontonagon River (1984).
14 -
13 -
12 -
11 -
1O -
9 -
a -
7 -
6 -
5 -
4_
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3 -
2 -
1 -
n -
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(Thousand*)
Average Ocily Flow (<:?•)
Average Daily Load of Suspended Solids versus Average Daily Flow
in the Ontonagon River (1984).
92
-------
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19 -
18 -
17 -
16 -
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14 -
13 -
12 -
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10 -
9 -
8 -
7 -
6 -
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4 -
3 —
2 -
1 -
0 -
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02468
Average Dcily Flow (cf»)
Average Daily Load of Total Kjeldahl Nitrogen versus Average
Daily Flow in the Ontonagon River (1984).
10 -|-
9 -
8 -
7 -
6 -
S -
4 -
3 -
2 -
1 -
0 -
a
a
° a
a
a Ba D
a a
B-? a ° DD
_^fmmmmmSAn° "*n
Avarag» Dkily Flow (eft)
Average Daily Load of Total Phosphorus versus Average Daily
Flow in the Ontonagon River (1984).
93
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