Copyright© Biological and Agricultural Engineering Department, Texas A&M University1

Introduction to Load Duration Curves

Lucas GregoryTexas Water Resources Institute

Kyna McKeeR. KarthikeyanBiological and Agricultural EngineeringTexas A&M University

Copyright© Biological and Agricultural Engineering Department, Texas A&M University2

Flow Duration Curves (FDCs)

• Flow Duration Curve

– A graph showing the flow rate versus the time

– Time is illustrated as percentage of the year

– Graph shows the relative percentage of the year that

stream flow exceeded a designated flow level

– Flow rates split standard categories

• Low flows

• Dry conditions

• Mid-range flows

• Moist conditions

• High flows

EPA suggested flow categories

- Can be different if desired

- Often modified based on flow

conditions or data availability

Copyright© Biological and Agricultural Engineering Department, Texas A&M University3

Flow Duration Curve: Flow categories

• Can be the standard flow categories– High flows: 0 to 10% exceedance

– Moist conditions: 10 to 40% exceedance

– Mid-range flows: 40 to 60% exceedance

– Dry conditions: 60 to 90% exceedance

– Low flows: 90 to 100% exceedance

• Can develop your own flow categories based on the flow duration curve– Measured or simulated daily stream flow data over multiple

years is preferred

– Intermittent instantaneous data also works

– Create flow breaks based on change in slope in FDC graph

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 10 20 30 40 50 60 70 80 90 100

Stre

am F

low

(cf

s)

Percent of Days Flow Exceeded

Flow Duration Curve

Low Flows

High Flows

Mid-Range Flows

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Load Duration Curves (LDCs)

• Load Duration Curve

– Combines concentrations of a pollutant with flow at

the same time to develop a load

– The LDC illustrates the load of a pollutant versus the

time that a given load is exceeded

– Time is illustrated as percentage of the year

– Able to see if a stream is exceeding the standard in

terms of load (flow and concentration)

– Able to calculate a percent reduction based on flow

categories

Load Duration Curve

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

0 10 20 30 40 50 60 70 80 90 100

Percent of Days Load Exceeded

Da

ily

Av

era

ge

Lo

ad

s

(cfu

/da

y)

Load Duration Curve With Observed Loads

During Different Flow Conditions

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

0 10 20 30 40 50 60 70 80 90 100

Percent of Days Load Exceeded

Lo

ad

(cfu

/day)

High Flows

MoistConditions

Mid-range

Dry Conditions

Low Flows

Load DurationCurve with10% MOS

Load Regression Model on Load Duration Curve

Plot

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

0 10 20 30 40 50 60 70 80 90 100

Percent of Days Load Exceeded

Lo

ad

(c

fu/d

ay

)

High Flows

Moist Conditions

Mid-range

Dry Conditions

Low Flows

Load Duration Curve

with 10% MOS

Load Regression

Curve

64.7%

51.4%

26.9%

Load Regression Model on Load Duration Curve

Plot

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

0 10 20 30 40 50 60 70 80 90 100

Percent of Days Load Exceeded

Lo

ad

(c

fu/d

ay

)

High Flows

Moist Conditions

Mid-range

Dry Conditions

Low Flows

Load Duration Curve

with 10% MOS

Load Regression

Curve

64.7%

51.4%

26.9%

LDC Usefulness (source ID based on LDC)

• Estimate load regression curve with USGS LOAD ESTimator(LOADEST) program

• Input matching flow and E. coli concentration data• Apply regression models and choose which fits best

– 1: a0 + a1lnQ (typically best for limited flow data)– 2: a0 +a1lnQ +a2lnQ2 (typically best for more flow data)

• Have modified version of LOADEST that has E. coli constituent variables

• Calculate load regression curve from output variables and observed or simulated flow with equation:– 1: EXP(a0+a1*(LNQ- “center” of lnQ))– 2: EXP(a0+a1*(LNQ- “center” of lnQ)+a2*(LNQ- “center” of

lnQ)^2)

Copyright© Biological and Agricultural Engineering Department, Texas A&M University10

Load Regression Curve: LOADEST

Calculating Percent Reduction

• Percent Reduction calculated using formula:

– ((Loadest – TMDL) /Loadest) *100

• Percent reduction is calculated for each point and then points within a flow condition are averaged together to get the percent reduction for a flow condition

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Continuous flow nitrate LDC

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

0 10 20 30 40 50 60 70 80 90 100

Nit

rate

Lo

ad (

g/d

ay)

Percent of Load Exceeded

Haberle Rd Load Duration Curve

Maximum Allowable Nitrate Load with 10% MOS

Load Regression Curve

Mid-Range

Low Flows

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Developed Flow Conditions: Percent Reductions

Flow Conditions Percent Reduction Flow Percentage

High Flows 82 0-10%

Mid-Range 83 10%-75%

Low Flows 85 75%-100%

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Flow grab sample E. coli LDC

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Standard Flow Categories: Percent Reductions

Flow Condition Percent Reduction Flow (cfs)

High Flows 20 34.5 - 17

Moist Conditions 21 12.2

Mid-Range 23 5

Dry Conditions 25 3

Low Flows 26 2