1. Submitted by: Stephanie L. Johnson
Interpretation of Flow at Un-gaged Stations May 1, CE 394K.2 Hydrology Semester Project Spring Dr. Maidment
Submitted by: Stephanie L. Johnson

2. Outline “The Big Picture” What do we have? What do we want?
Methods to get what we want
Assessment of one method
Conclusion
“Side project”

3. “The Big Picture” The Big Picture
We have some watersheds along the TX coast that need water quality studies done on them. These watersheds have many, many SWQM points throughout them and a few USGS gages. We need to know how to correlate them.

4. Data Collection in the Watersheds
Have USGS flow data at 15-minute intervals for continuous time periods
Have random water quality information at SWQM stations
Sometimes this includes flow (not very often)
Copano Bay watershed:
7 SWQM stations with 32 years of data
1900 total sampling events
Flow recorded at 182 (<10%) of those events

5. Load Duration Curve Derived from a flow duration curve
Basically a cumulative frequency distribution
Load = flow x concentration x conversion factor
Calculate regulatory curve (flow x max concentration)
Add monitoring data as points
Position tells if it’s in compliance

6. Challenge Need flow and water quality information at the same site
In some cases this is already done
In others we need to estimate flows
How to estimate it?
Model with rainfall-runoff model or regression equations from historic data
Estimate from gaged stations
Need a match in “time and space” between flow and water quality

7. Previous Studies Wurbs and Sisson, 1999 (TA&MU)
Performed to analyze options for use in Water Rights Analysis Package (WRAP) model
Explored: rainfall-runoff modeling, regression equations, and estimating from gaged stations from historic data
Recommended estimating from gaged stations
NRCS Curve Number Adaptation Method
Drainage Area Ratio Method
Recommend using N values equal to 1.0
As Clark mentioned – WRAP
Looked at all the options
Recommended estimating from gaged stations
People like the Drainage Area Ratio Method
Easy, based on known information
Widely used
As long as stations are close have similar CN and precip values anyway and reduces to this
Now Used Widely

8. Previous Studies (Cont.)
Asquith et. al, 2006
Follow-up on Wurbs study
Explores N1 (Φ) value in the Drainage Area Ratio Method
Considered nearly 7.5 million records of mean daily streamflow at more than 712 USGS gaging stations across the state of Texas
Considered 34 different streamflow regimes at each of the stations
four quantiles (0-25, 25-50, 50-75, )
the 20 quintiles (0-5, 5-10, …, 90-95, and )
ten 1 percent ranges in the extreme upper and lower 5 percent tails of the distribution (0-1, 1-2, …, 98-99, and )
Concentrating on stations that were within 100-miles of one another, the study recommended 64 values of N1 (termed Φ) for the various flow regimes that were analyzed. These values are listed in the appendix and can be summarized as shown in Table 1.
Summarized Findings
Flow Regime
0-50%
50-65%
65-85%
85-100%
Recommended
N1 (Φ) Value
0.89
0.92
0.93
0.70
Then, K = 1.0

9. Methodology Wurbs Recommendation Asquith Recommendation
Run Drainage Area Ratio Method with N1 (Φ) = 1.0 to calculate a flow
Calculate percent error based on actual flow
Asquith Recommendation
Calculate new Φ value
For complete record and for quantiles
Run Drainage Area Ratio Method with new N1 (Φ) value
Calculate percent error
Asquith Methodology
Scope:
Use USGS data to figure out how well the N1 = 1.0 method works here
Apply Asquith’s methods to the study area and calculate N1 values
Use those numbers to assess how well that worked

10. Copano Bay Watershed Originally was going to do all watersheds
Too many points
Concentrate on Copano Bay watershed
Located on Texas’ gulf coast (near Rockport)
Currently the subject of a Total Maximum Daily Load (TMDL) Study for bacteria
For that study, the TCEQ and EPA want to use load duration curves
Have 5 USGS flow stations with varying time periods of continuous flow data.
We also have 7 SWQM stations with various water quality data.

11. USGS Gage Data
Station
Drainage Area
(miles2)
Number of
Flow Records
Years
of Data
Maximum
Flow
(cfs)
Minimum
Mean Flow
Median Flow
Percent of Flow
Values Equal to
Zero
693
24,722
7/1/1939 to
Present
67,200
127 12
0.02%
243
15,681
4/1/1964 to
49,300 38 4 3%
203
7,694
3/1/1962 to
9/30/1977
&
9/14/2001 to
46,300 14
45% 39
4,186
9/21/1995 to
2,190 44
60%
138
7,740
7/3/1970 to
9/30/1991
18,900 40
10%
Unfortunately, no flow data at SWQM stations, so have to do this analysis at USGS stations.
5 stations with 15 minute continuous data.
and have longest records – will be used for comparison to others.
Note the size of the basins and the % zero flows.

12. Results of Drainage Area Ratio Method for the Complete Record
Reference Station
Calculated Station
# of Data Points
Compared
Drainage Area
Ratio
Average %
Error with Φ =
1.0
Mean Φ
Average % Error
with Calculated Φ
7,694
0.2933
6890%
3.46
327%
15,681
0.3508
246%
1.40
129%
7,740
0.1988
4419%
2.16
611%
4,186
0.0561
131%
0.73
441%
6,932
0.8360
2122%
14.01
436%
2.8506
103%
211%
0.5667
2373%
3.58
488%
0.1599
219%
0.30
742%
Performed for period from 2000 to present and found similar results.

13. Calculated Φ Values of Quantiles Using Complete Record
Results (cont.)
Calculated Φ Values of Quantiles Using Complete Record
Reference
Station
Calculated
Mean Φ
Average % Error with
Calculated Φ
0-25
25-50
50-75
75-100
Average
1.72
1.20
1.30
1.38
1.40
113%
3.55
2.90
1.84
0.90
2.30
219%
N/A
1.46
0.31
0.89
149%
0.62
1.28
1.51
2.10
103%
8.43
5.98
2.95
-0.84
4.13
199%
1.61
-0.47
0.57
333%

14. Discussion Computed Φ values result in lower errors
Comparison of Average Percent Errors
Analysis
Reference Station:
Reference Station:
With Φ = 1.0
With Calculated Φ
Complete Record
2922%
377%
1204%
469%
Record from 2000 to Present
2359%
265%
2671%
424%
with Quantiles
---
160%
212%
Record from 2000 to Present with Quantiles
58%
57%
Expected since Φ values are calculated based on flow data
Performing on shorter time periods not necessarily better
Using quantiles is more accurate
Particularly important when reference and calculated stations have such different flow regimes

15. Comparison of Calculated Φ Values
Discussion (cont.)
Calculated Φ values much higher than expected
Comparison of Calculated Φ Values
Flow Regime Quantile
Reference Station:
Reference Station:
Asquith et al. Φ Values
Average Φ
Range of Φ
No Quantiles –
Whole Record
1.94
0.73 to 3.46
4.82
0.3 to 14.01
N/A
0-25
2.64
1.72 to 3.55
4.53
0.62 to 8.43
0.89
25-50
2.05
1.20 to 2.90
3.63
1.28 to 5.98
50-75
1.53
1.30 to 1.46
2.02
1.51 to 2.95
0.93
75-100
0.87
0.31 to 1.38
0.27
-0.47 to 2.10
Average
0.89 to 2.30
2.03
0.57 to 4.13
There is evidence that choosing the reference station closest to the calculated station reduces the error in calculation. Using Station to calculate flows at results in an average error of 441%; if Station were used as the reference, however, the error would be 742%. Similar results were found by pairing with and with
Most values are significantly over 1.0
Large Φ value drives areal ratio toward zero (A1<A2)
Non-reference stations all have median flows of 0 cfs
Stations and have 60% and 45% zero flows

16. Remember …..
Station
Drainage Area
(miles2)
Number of
Flow
Records
Years
of Data
Maximum
(cfs)
Minimum
Mean Flow
Median Flow
Percent of Flow
Values Equal to
Zero
693
24,722
7/1/1939 to
Present
67,200
127 12
0.02%
243
15,681
4/1/1964 to
49,300 38 4 3%
203
7,694
3/1/1962 to
9/30/1977
&
9/14/2001 to
46,300 14
45% 39
4,186
9/21/1995 to
2,190 44
60%
138
7,740
7/3/1970 to
9/30/1991
18,900 40
10%
Also suggested since values for Φs are lower than (and watershed is larger, therefore, ratio is lower)

17. Conclusions Important to admit your failures …
Method not accurate for stations with ephemeral flows
Potential that highly dynamic weather conditions on the coast make the Drainage Area Ratio Method less accurate
But……
Asquith Φ values more accurate than Wurbs’ suggestion of N1=1.0
Use Asquith flow regime specific Φ values to calculate flows at un-gaged stations

19. References
Asquith, W. H., Roussel, M.C., and Vrabel, J Statewide Analysis of the Drainage-Area Method for 34-Streamflow Percentile Ranges in Texas. US Geological Survey Scientific Investigations Report 2006-____.
Wurbs, R., and Sisson, E Comparative Evaluation of Methods for Distributing Naturalized Streamflows from Gaged to Ungaged Sites. Texas Water Resources Institute Technical Report No. 179.

20. Questions?

21. National Climatic Data Center (www.ncdc.noaa.gov)
Weather Stations
National Climatic Data Center (
Figure 1 shows the location of the only NCDC precipitation gage station within the Copano Bay watershed (Beeville 5N). The nearest USGS gage station to the precipitation station is USGS Station This gage station, however, lies in a different watershed than the precipitation station (Figure 2). If one assumes that the spatial variation in precipitation is small, the precipitation at Beeville 5 NE should be an accurate estimate of the precipitation experienced at USGS Station The USGS gage station , however, lies within the same watershed boundary as the precipitation gage. Precipitation data at the gage could, therefore, be used to estimate the precipitation experienced in the watershed upstream of this USGS gage. Due to its proximity to these two USGS gage stations and the issues discussed, the precipitation data from Beeville 5 NE station will be used to model flow at both USGS gage station and

22. Linear Regression Model
Where: Q0 = Average daily flow at the USGS gage station on the day to be forecast (cfs)
Q-n = Average daily flow at the USGS gage station n days before the day modeled (cfs)
P0 = Total precipitation at the weather station on the day to be forecast (inches)
P-n = Total precipitation at the weather station n days before the day modeled (cfs)
an = Calculated constant
The relationship between the current flow in the river, the previous days’ flow in the river, and the precipitation over the watershed were first assumed to be related through a linear model. A general form of this model is shown below.
The first station combination to be analyzed was that between the Beeville 5N precipitation station and the USGS Station This analysis covered 15,515 data points between 4/1/1964 and 9/24/ During this time the 15,515 USGS mean daily flow values were compared to the 2,328 rain events at the Beeville station.

23. Beeville 5 NE vs. USGS Station 08189700
Summary of Data for Analysis
Min Date
Max Date
No. of Events
No. of Events > 0
Min Event
Max Event
Average Event
Beeville 5N (Events in inches)
4/3/1964
9/24/2006
15,515
2,328
11.41
0.08
USGS Station (Events in cfs)
15,083
49300
37.98
Variables’ Correlation to Current Day Flow: Beeville 5N versus USGS Station
The calculated t-stat values can be compared to a t distribution value of 1.96 (α = 0.05 and (n-k) = degrees of freedom). Under these circumstances, eachof the t stat values is greater than the t distribution value signifying the fact that the slope value is significantly different from zero. The “P-value” computed for each of the variables (shown in the appendix) confirms this by always being less than 0.05.
Q-1
Q-2
Q-3
Q-4 P0
P-1
P-2
P-3
P-4
Correlation

24. Beeville 5 NE vs. USGS Station 08189700 (cont.)
Multiple Regression Output: Beeville 5N versus USGS Station
Standard Error
Multiple r r2
Coefficients (a0, a1, a2,…)
t Stat
Q-1 P0
P-1
P-2
Intercept P
Mult Reg (Q-1, P, P-1, P-2)
489.11
0.5548
0.3078
0.243
173.3
665.1
43.32
31.73
15.64
58.51
3.467
-9.912
Mult Reg2 (Q-1, P, P-1 )
489.28
0.5543
0.256
173.9
669.6
37.58
15.69
59.28
-9.442
Mult Reg3 (P, P-1, P-2)
504.72
0.5127
167.6
707.6
226.7
14.66
60.75
19.83
Mult Reg4 (Q-1, P-1, P-2)
492.94
0.5449
0.241
699.4
46.46
31.23
62.22
3.690
-7.344
Mult Reg5 (Q-1, P-1)
493.14
0.5443
0.255
704.4
37.14
63.09
-6.781
Mullt Reg6 (P-1)
514.58
0.4834
785.6
68.77
-5.730
Based upon this analysis, the Mult Reg (Q-1, P, P-1, P-2) model is the most accurate estimate of flow at USGS Station based on precipitation data from Beeville 5N. The resulting model is therefore shown below.
This model shows that the most important parameter (from those considered) effecting flow is the precipitation on the day preceding the flow. Precipitation on the current day is the second most important parameter.
Governing Equation:

25. Beeville 5 NE vs. USGS Station 08189300
Summary of Data for Analysis
Min Date1
Max Date1
Min Date2
Max Date2
No. of Events
No. of Events > 0
Min Event
Max Event
Average Event
Beeville 5N (Events in inches)
3/1/1962
9/30/1977
9/14/2001
9/30/2006
7,536
1,091
11.41
0.08
USGS Station (Events in cfs)
4,169
46,300
17.09
Variables’ Correlation to Current Day Flow: Beeville 5N versus USGS Station
Q-1
Q-2
Q-3
Q-4 P0
P-1
P-2
P-3
P-4
Correlation
Similar to the analysis done at the USGS Station , the calculated t-stat values between Beeville 5N and USGS Station were compared to a t distribution value of 1.96 (α = 0.05 and (n-k) = 7529 degrees of freedom). The computed t-stat and “P-value” values obtained for this combination showed that the slope values given by the regression are significantly different from zero.

26. Beeville 5 NE vs. USGS Station 08189300 (cont.)
Multiple Regression Output: Beeville 5N versus USGS Station
Standard Error
Multiple r r2
Coefficients (a0, a1, a2,…)
t Stat
Q-1 P0
P-1
P-2
Intercept
Mult Reg (Q-1, P, P-1, P-2)
483.84
0.5260
0.2767
0.233
82.35
589.7
119.2
21.24
5.393
37.75
7.042
-8.290
Mult Reg2 (Q-1, P, P-1 )
485.40
0.5215
0.2719
0.266
81.70
607.4
26.82
5.333
39.26
-7.120
Mult Reg3 (P, P-1, P-2)
498.09
0.4831
0.2334
80.01
608.2
274.3
5.089
37.87
17.45
-9.633
Mult Reg4 (Q-1, P-1, P-2)
484.74
0.5234
0.2739
0.232
607.0
118.6
21.16
39.61
6.997
-7.501
Mult Reg5 (Q-1, P-1)
486.28
0.5188
0.2692
0.265
624.4
26.72
41.17
-6.321
Mullt Reg6 (P-1)
508.78
0.4471
0.1999
681.5
43.38
-6.027
This combination of precipitation and flow data also showed that the Mult Reg (Q-1, P, P-1, P-2) scenario has the least amount of error of the linear models considered. The resulting linear equation to relate flow at the USGS Station to precipitation at the Beeville precipitation stations is, therefore, shown below.
Once again, the most important parameter (from those considered) effecting flow is the precipitation on the day preceding the flow. In this situation, however, the precipitation 2 days in advance of the current day is the second most important parameter.
Governing Equation:

27. Non-linear Regression Modeling
Log transformed:
Natural log (ln) transformed:
Non-Linear Modeling
A second type of modeling that allows the researcher to determine the relationship between the current flow in the river, the previous days’ flow in the river, and the precipitation over the watershed is non-linear modeling. In this type of modeling, the parameters are transformed before the linear regression is performed. A typical transformation to make is the log or natural log transform. General equations for these models are shown below.
Log Transformation:
Natural Log (ln) Transformation:
Since the majority of the precipitation values in these analyses are equal to zero, however, these types of transformations cannot be preformed in our modeling. (The log and natural log of zero are undefined numbers.)
Not possible to do these models since precipitation is equal to zero for the majority of the time.

28. Questions?