Submitted by: Stephanie L. Johnson

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Presentation transcript:

Submitted by: Stephanie L. Johnson Interpretation of Flow at Un-gaged Stations May 1, 2007 CE 394K.2 Hydrology Semester Project Spring 2007 - Dr. Maidment Submitted by: Stephanie L. Johnson

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”

“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.

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

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

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

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

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, 75-100) the 20 quintiles (0-5, 5-10, …, 90-95, and 95-100) ten 1 percent ranges in the extreme upper and lower 5 percent tails of the distribution (0-1, 1-2, …, 98-99, and 99-100) 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

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

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.

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 08189500 693 24,722 7/1/1939 to Present 67,200 127 12 0.02% 08189700 243 15,681 4/1/1964 to 49,300 38 4 3% 08189300 203 7,694 3/1/1962 to 9/30/1977 & 9/14/2001 to 46,300 14 45% 08189200 39 4,186 9/21/1995 to 2,190 44 60% 08189800 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. 08189500 and 08189700 have longest records – will be used for comparison to others. Note the size of the basins and the % zero flows.

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 08189500 08189300 7,694 0.2933 6890% 3.46 327% 08189700 15,681 0.3508 246% 1.40 129% 08189800 7,740 0.1988 4419% 2.16 611% 08189200 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.

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 08189500 08189700 1.72 1.20 1.30 1.38 1.40 113% 08189800 3.55 2.90 1.84 0.90 2.30 219% 08189200 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%

Discussion Computed Φ values result in lower errors Comparison of Average Percent Errors Analysis Reference Station: 08189500 Reference Station: 08189700 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

Comparison of Calculated Φ Values Discussion (cont.) Calculated Φ values much higher than expected Comparison of Calculated Φ Values Flow Regime Quantile Reference Station: 08189500 Reference Station: 08189700 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 08189500 to calculate flows at 08189200 results in an average error of 441%; if Station 08189700 were used as the reference, however, the error would be 742%. Similar results were found by pairing 08189700 with 08189800 and 08189500 with 08189300. 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 08189200 and 08189300 have 60% and 45% zero flows

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 08189500 693 24,722 7/1/1939 to Present 67,200 127 12 0.02% 08189700 243 15,681 4/1/1964 to 49,300 38 4 3% 08189300 203 7,694 3/1/1962 to 9/30/1977 & 9/14/2001 to 46,300 14 45% 08189200 39 4,186 9/21/1995 to 2,190 44 60% 08189800 138 7,740 7/3/1970 to 9/30/1991 18,900 40 10% Also suggested since values for 08189500 Φs are lower than 08189700 (and watershed is larger, therefore, ratio is lower)

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

References Asquith, W. H., Roussel, M.C., and Vrabel, J. 2006. 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. 1999. Comparative Evaluation of Methods for Distributing Naturalized Streamflows from Gaged to Ungaged Sites. Texas Water Resources Institute Technical Report No. 179.

Questions?

National Climatic Data Center (www.ncdc.noaa.gov) Weather Stations National Climatic Data Center (www.ncdc.noaa.gov) 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 08189300. 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 08189300. The USGS gage station 08189700, 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 08189300 and 08189700.

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 08189700. This analysis covered 15,515 data points between 4/1/1964 and 9/24/2006. During this time the 15,515 USGS mean daily flow values were compared to the 2,328 rain events at the Beeville station.

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 08189700 (Events in cfs) 15,083 49300 37.98 Variables’ Correlation to Current Day Flow: Beeville 5N versus USGS Station 08189700 The calculated t-stat values can be compared to a t distribution value of 1.96 (α = 0.05 and (n-k) = 15508 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 0.34007 0.05687 0.01283 0.00788 0.19599 0.48339 0.23065 0.04945 0.01514

Beeville 5 NE vs. USGS Station 08189700 (cont.) Multiple Regression Output: Beeville 5N versus USGS Station 08189700 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 -41.114 31.73 15.64 58.51 3.467 -9.912 Mult Reg2 (Q-1, P, P-1 ) 489.28 0.5543 0.30726 0.256 173.9 669.6 -38.558 37.58 15.69 59.28 -9.442 Mult Reg3 (P, P-1, P-2) 504.72 0.5127 0.26286 167.6 707.6 226.7 -49.295 14.66 60.75 19.83 -11.539 Mult Reg4 (Q-1, P-1, P-2) 492.94 0.5449 0.29687 0.241 699.4 46.46 -30.271 31.23 62.22 3.690 -7.344 Mult Reg5 (Q-1, P-1) 493.14 0.5443 0.29626 0.255 704.4 -27.488 37.14 63.09 -6.781 Mullt Reg6 (P-1) 514.58 0.4834 0.23367 785.6 -24.233 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 08189700 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:

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 0818300 (Events in cfs) 4,169 46,300 17.09 Variables’ Correlation to Current Day Flow: Beeville 5N versus USGS Station 08189300 Q-1 Q-2 Q-3 Q-4 P0 P-1 P-2 P-3 P-4 Correlation 0.3236324 0.070952053 0.006218348 0.001906395 0.140978 0.447149 0.264259 0.030691 0.004609 Similar to the analysis done at the USGS Station 08189700, the calculated t-stat values between Beeville 5N and USGS Station 08189300 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.

Beeville 5 NE vs. USGS Station 08189300 (cont.) Multiple Regression Output: Beeville 5N versus USGS Station 08189300 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 -48.645 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 -41.237 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 -58.026 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 -43.513 21.16 39.61 6.997 -7.501 Mult Reg5 (Q-1, P-1) 486.28 0.5188 0.2692 0.265 624.4 -36.179 26.72 41.17 -6.321 Mullt Reg6 (P-1) 508.78 0.4471 0.1999 681.5 -36.092 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 08189300 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:

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.

Questions?