Interpretation of Flow Interpretation of Flow at Un-gaged Stationsat Un-gaged Stations

May 1, 2007May 1, 2007

CE 394K.2 HydrologyCE 394K.2 HydrologySemester ProjectSemester Project

Spring 2007 - Dr. MaidmentSpring 2007 - Dr. Maidment

Submitted by: Stephanie L. JohnsonSubmitted by: Stephanie L. Johnson

OutlineOutline

““The Big Picture”The Big Picture” What do we have?What do we have? What do we want?What do we want? Methods to get what we wantMethods to get what we want Assessment of one methodAssessment of one method ConclusionConclusion ““Side project”Side project”

““The Big Picture”The Big Picture”

Tres Palacios Bay

Matagorda Bay

/0 10 205 Miles

Tres Palacios BayPalacios, Texas

Data Collection in the Data Collection in the WatershedsWatersheds

Have USGS Have USGS flow dataflow data at 15-minute at 15-minute intervals for intervals for continuouscontinuous time periods time periods

Have Have random water qualityrandom water quality information at SWQM stationsinformation at SWQM stations SometimesSometimes this includes this includes flowflow (not very (not very

often)often) Copano Bay watershed:Copano Bay watershed:

7 SWQM stations with 32 years of data7 SWQM stations with 32 years of data 1900 total sampling events1900 total sampling events Flow recorded at 182 (Flow recorded at 182 (<10%<10%) of those events) of those events

Load Duration CurveLoad Duration Curve Derived from a flow duration curveDerived from a flow duration curve

Basically a cumulative frequency distributionBasically a cumulative frequency distribution Load = flow x concentration x conversion factorLoad = flow x concentration x conversion factor Calculate regulatory curve (flow x max Calculate regulatory curve (flow x max

concentration)concentration) Add monitoring data as pointsAdd monitoring data as points

Position tells if it’s in compliancePosition tells if it’s in compliance

E. Coli Load Duration Curve

1.0E+07

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

1.0E+13

1.0E+14

1.0E+15

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Percent Exceedance

Lo

ad

(#/

da

y)

Target SS Load Target Mean Load Data

ChallengeChallenge

Need Need flow and water qualityflow and water quality information at the information at the same sitesame site In some cases this is already doneIn some cases this is already done In others we need to estimate flowsIn others we need to estimate flows

HowHow to estimate it? to estimate it? ModelModel with rainfall-runoff model or with rainfall-runoff model or

regression equations from historic dataregression equations from historic data EstimateEstimate from gaged stations from gaged stations

Previous StudiesPrevious Studies Wurbs and Sisson, 1999 (TA&MU)Wurbs and Sisson, 1999 (TA&MU)

Performed to analyze options for use in Water Rights Performed to analyze options for use in Water Rights Analysis Package (WRAP) model Analysis Package (WRAP) model

Explored: rainfall-runoff modeling, regression Explored: rainfall-runoff modeling, regression equations, and estimating from gaged stations from equations, and estimating from gaged stations from historic datahistoric data

Recommended estimatingRecommended estimating from gaged stations from gaged stations

NRCS Curve Number Adaptation MethodNRCS Curve Number Adaptation Method

Drainage Area Ratio MethodDrainage Area Ratio Method

Recommend using Recommend using N values equal to 1.0N values equal to 1.0

321 N

gaged

ungagedN

gaged

ungagedN

gaged

ungaged

M

M

CN

CN

A

AC

1N

gaged

ungaged

A

AC

gagedungaged QCQ *

Now Used Widely

Previous Studies (Cont.)Previous Studies (Cont.)

Asquith et. al, 2006Asquith et. al, 2006 Follow-up on Wurbs studyFollow-up on Wurbs study Explores N1 (Φ) valueExplores N1 (Φ) value in the Drainage Area in the Drainage Area

Ratio MethodRatio Method

2

1

2

1

A

AK

Q

Q

Flow RegimeFlow Regime 0-50%0-50% 50-65%50-65% 65-85%65-85% 85-100%85-100%

Recommended Recommended N1 (Φ) ValueN1 (Φ) Value 0.890.89 0.920.92 0.930.93 0.700.70

Summarized Findings

gaged

N

gaged

ungagedungaged Q

A

AQ *

1

Then, K = 1.0

MethodologyMethodology

Wurbs RecommendationWurbs Recommendation RunRun Drainage Area Ratio Drainage Area Ratio

Method Method with N1 (Φ) = 1.0 with N1 (Φ) = 1.0 to calculate a flowto calculate a flow

Calculate percent error Calculate percent error based on actual flowbased on actual flow

Asquith RecommendationAsquith Recommendation Calculate new ΦCalculate new Φ value value

For complete record and For complete record and for quantilesfor quantiles

RunRun Drainage Area Ratio Drainage Area Ratio Method Method with new N1 (Φ)with new N1 (Φ) valuevalue

Calculate percent errorCalculate percent error

0.1K

2

1

2

1

A

AK

Q

Q

2

1

2

1

log

log

AAQ

Qi

i

i

n

i

in

Mean1

1

Asquith Methodology

694,7

1 2

2

08189500

08189300

693203log

log

694,7

1

n

i

milesmiles

QQ

Mean

08189700

0.1

08189700

*QA

AQ ungagedungaged

Copano Bay WatershedCopano Bay Watershed

USGS Gage DataUSGS Gage Data

StationStationDrainage AreaDrainage Area

(miles(miles22))Number of Number of

Flow RecordsFlow RecordsYearsYears

of Dataof Data

MaximumMaximum FlowFlow(cfs)(cfs)

MinimumMinimum FlowFlow(cfs)(cfs)

Mean FlowMean Flow(cfs)(cfs)

Median FlowMedian Flow(cfs)(cfs)

Percent of FlowPercent of Flow Values Equal toValues Equal to

ZeroZero

0818950008189500 693693 24,72224,722 7/1/1939 to7/1/1939 to PresentPresent 67,20067,200 00 127127 1212 0.02%0.02%

0818970008189700 243243 15,68115,681 4/1/1964 to4/1/1964 to PresentPresent 49,30049,300 00 3838 44 3%3%

0818930008189300 203203 7,6947,694

3/1/1962 to3/1/1962 to 9/30/19779/30/1977

&&9/14/2001 to9/14/2001 to

PresentPresent

46,30046,300 00 1414 00 45%45%

0818920008189200 3939 4,1864,186 9/21/1995 to9/21/1995 to PresentPresent 2,1902,190 00 4444 00 60%60%

0818980008189800 138138 7,7407,740 7/3/1970 to 7/3/1970 to 9/30/19919/30/1991 18,90018,900 00 4040 00 10%10%

ResultsResultsResults of Drainage Area Ratio Method for the Complete Record

Reference StationReference Station Calculated StationCalculated Station # of Data Points# of Data Points ComparedCompared

Drainage AreaDrainage Area RatioRatio

Average % Average % Error with Φ =Error with Φ =

1.01.0Mean ΦMean Φ

Average % Error Average % Error with Calculated Φwith Calculated Φ

0818950008189500 0818930008189300 7,6947,694 0.29330.2933 6890%6890% 3.463.46 327%327%

0818950008189500 0818970008189700 15,68115,681 0.35080.3508 246%246% 1.401.40 129%129%

0818950008189500 0818980008189800 7,7407,740 0.19880.1988 4419%4419% 2.162.16 611%611%

0818950008189500 0818920008189200 4,1864,186 0.05610.0561 131%131% 0.730.73 441%441%

0818970008189700 0818930008189300 6,9326,932 0.83600.8360 2122%2122% 14.0114.01 436%436%

0818970008189700 0818950008189500 15,68115,681 2.85062.8506 103%103% 1.401.40 211%211%

0818970008189700 0818980008189800 7,7407,740 0.56670.5667 2373%2373% 3.583.58 488%488%

0818970008189700 0818920008189200 4,1864,186 0.15990.1599 219%219% 0.300.30 742%742%

Performed for period from 2000 to present and found similar results.

Results (cont.)Results (cont.)

Calculated Φ Values of Quantiles Using Complete Record

ReferenceReference StationStation

Calculated Calculated StationStation

Mean ΦMean Φ Average % Error withAverage % Error with Calculated ΦCalculated Φ

0-250-25 25-5025-50 50-7550-75 75-10075-100 AverageAverage

0818950008189500 0818970008189700 1.721.72 1.201.20 1.301.30 1.381.38 1.401.40 113%113%

0818950008189500 0818980008189800 3.553.55 2.902.90 1.841.84 0.900.90 2.302.30 219%219%

0818950008189500 0818920008189200 N/AN/A N/AN/A 1.461.46 0.310.31 0.890.89 149%149%

0818970008189700 0818950008189500 0.620.62 1.281.28 1.511.51 2.102.10 1.381.38 103%103%

0818970008189700 0818980008189800 8.438.43 5.985.98 2.952.95 -0.84-0.84 4.134.13 199%199%

0818970008189700 0818920008189200 N/AN/A N/AN/A 1.611.61 -0.47-0.47 0.570.57 333%333%

DiscussionDiscussion

Computed Φ values result in Computed Φ values result in lower errorslower errorsComparison of Average Percent Errors

AnalysisAnalysis

Reference Station: 08189500Reference Station: 08189500 Reference Station: 08189700Reference Station: 08189700

With Φ = 1.0With Φ = 1.0 With Calculated ΦWith Calculated Φ With Φ = 1.0With Φ = 1.0 With Calculated ΦWith Calculated Φ

Complete RecordComplete Record 2922%2922% 377%377% 1204%1204% 469%469%

Record from 2000 to PresentRecord from 2000 to Present 2359%2359% 265%265% 2671%2671% 424%424%

Complete RecordComplete Recordwith Quantileswith Quantiles ------ 160%160% ------ 212%212%

Record from 2000 to Present Record from 2000 to Present with Quantileswith Quantiles ------ 58%58% ------ 57%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

Discussion (cont.)Discussion (cont.)

Calculated Φ values Calculated Φ values muchmuch higher than expectedhigher than expectedComparison of Calculated Φ Values

Flow Regime Flow Regime QuantileQuantile

Reference Station: 08189500Reference Station: 08189500 Reference Station: 08189700Reference Station: 08189700

Asquith et al. Φ Asquith et al. Φ ValuesValuesAverage ΦAverage Φ Range of ΦRange of Φ Average ΦAverage Φ Range of ΦRange of Φ

No Quantiles –No Quantiles –Whole RecordWhole Record 1.941.94 0.73 to 3.460.73 to 3.46 4.824.82 0.3 to 14.010.3 to 14.01 N/AN/A

0-250-25 2.642.64 1.72 to 3.551.72 to 3.55 4.534.53 0.62 to 8.430.62 to 8.43 0.890.89

25-5025-50 2.052.05 1.20 to 2.901.20 to 2.90 3.633.63 1.28 to 5.981.28 to 5.98 0.890.89

50-7550-75 1.531.53 1.30 to 1.461.30 to 1.46 2.022.02 1.51 to 2.951.51 to 2.95 0.930.93

75-10075-100 0.870.87 0.31 to 1.380.31 to 1.38 0.270.27 -0.47 to 2.10-0.47 to 2.10 0.870.87

AverageAverage 1.531.53 0.89 to 2.300.89 to 2.30 2.032.03 0.57 to 4.130.57 to 4.13 0.890.89•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

StationStationDrainage AreaDrainage Area

(miles(miles22))

Number ofNumber of Flow Flow

RecordsRecords

YearsYearsof Dataof Data

MaximumMaximum FlowFlow(cfs)(cfs)

MinimumMinimum FlowFlow(cfs)(cfs)

Mean FlowMean Flow(cfs)(cfs)

Median FlowMedian Flow(cfs)(cfs)

Percent of FlowPercent of Flow Values Equal toValues Equal to

ZeroZero

0818950008189500 693693 24,72224,722 7/1/1939 to 7/1/1939 to PresentPresent 67,20067,200 00 127127 1212 0.02%0.02%

0818970008189700 243243 15,68115,681 4/1/1964 to 4/1/1964 to PresentPresent 49,30049,300 00 3838 44 3%3%

0818930008189300 203203 7,6947,694

3/1/1962 to 3/1/1962 to 9/30/19779/30/1977

&&9/14/2001 to 9/14/2001 to

PresentPresent

46,30046,300 00 1414 00 45%45%

0818920008189200 3939 4,1864,186 9/21/1995 to 9/21/1995 to PresentPresent 2,1902,190 00 4444 00 60%60%

0818980008189800 138138 7,7407,740 7/3/1970 to7/3/1970 to 9/30/19919/30/1991 18,90018,900 00 4040 00 10%10%

Remember …..Remember …..

0818970008189700

*QA

AQ ungagedungaged

ConclusionsConclusions

Important to admit your failures …Important to admit your failures … Method Method not accuratenot accurate for stations with ephemeral flows for stations with ephemeral flows Potential that Potential that highly dynamic weather conditionshighly dynamic weather conditions on on

the coast make the Drainage Area Ratio Method the coast make the Drainage Area Ratio Method less less accurateaccurate

Asquith Asquith Φ values more accurateΦ values more accurate than Wurbs’ than Wurbs’ suggestion of N1=1.0suggestion of N1=1.0

Use Asquith flow regime specific Φ values to Use Asquith flow regime specific Φ values to calculate flows at un-gaged stationscalculate flows at un-gaged stations

But……

Flow Duration Curve

SWQM Station 12948 (9/23/1968 to Present)

0.01

0.1

1

10

100

1000

10000

100000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Exceedance

Flo

w (

cfs)

Flow Duration Curve

SWQM Station 12930 (10/9/1968 to 11/5/1972)

0.01

0.1

1

10

100

1000

10000

100000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Exceedance

Flo

w (

cfs)

Flow Duration Curve

SWQM Station 12943 (10/30/1975 to Present)

0.01

0.1

1

10

100

1000

10000

100000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Exceedance

Flo

w (

cfs)

Flow Duration Curve

SWQM Station 12932 (12/18/1972 to 8/28/2002)

0.01

0.1

1

10

100

1000

10000

100000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Exceedance

Flo

w (

cfs)

Flow Duration Curve

SWQM Station 17592 (2/18/1998 to 4/9/2002)

0.1

1

10

100

1000

10000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Exceedance

Flo

w (

cfs)

ReferencesReferences

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?Questions?

Weather StationsWeather StationsNational Climatic Data Center (www.ncdc.noaa.gov)National Climatic Data Center (www.ncdc.noaa.gov)

Linear Regression ModelLinear Regression Model

......,...),,,...,,,( 22110221102103210 PaPaPaQaQaaPPPQQQfQ nnn

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

Beeville 5 NE vs. USGS Station Beeville 5 NE vs. USGS Station 0818970008189700

Summary of Data for Analysis

Min DateMax Date

No. of Events

No. of Events > 0

Min Event Max EventAverage

Event

Beeville 5N (Events in inches) 4/3/1964 9/24/2006 15,515 2,328 0 11.41 0.08

USGS Station 08189700 (Events in cfs) 4/3/1964 9/24/2006 15,515 15,083 0 49300 37.98

Variables’ Correlation to Current Day Flow: Beeville 5N versus USGS Station 08189700

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 Beeville 5 NE vs. USGS Station 08189700 (cont.)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 Q-1 P P-1 P-2 Intercept

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

210121010 323.4314.66532.1732439.0114.41),,,( PPPQPPPQfQ

Governing Equation:

Beeville 5 NE vs. USGS Station Beeville 5 NE vs. USGS Station 0818930008189300

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 0 11.41 0.08

USGS Station 0818300 (Events in cfs) 3/1/1962 9/30/1977 9/14/2001 9/30/2006 7,536 4,169 0 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

Beeville 5 NE vs. USGS Station Beeville 5 NE vs. USGS Station 08189300 (cont.)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 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

Governing Equation:

210121010 22.11978.589359.822331.0645.48),,,( PPPQPPPQfQ

Non-linear Regression Non-linear Regression ModelingModeling

...logloglog...loglog,...)log,log,log,...,log,log,(loglog 22110221102103210 PaPaPaQaQaaPPPQQQfQ nnn

...lnlnln...lnln,...)ln,ln,ln,...,ln,ln,(lnln 22110221102103210 PaPaPaQaQaaPPPQQQfQ nnn

Log transformed:

Natural log (ln) transformed:

Not possible to do these models since precipitation is equal to zero for the majority of the time.

Questions?Questions?