watershed slope lower bounds for methods ewri-2012 21 may 2012

Watershed Slope Lower Bounds for Methods

EWRI-2012 21 MAY 2012

Acknowledgements

• Texas Department of Transportation; “0-6384 Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods”

Project Team

• Theodore G. Cleveland - Texas Tech University

• Ming-Han Li – Texas A&M University• William H. Asquith – USGS• Xing Fang – Auburn University• David B. Thompson – R.O. Anderson Inc.

Why does slope matter?

• Magnitude

Why does slope matter?

• Direction

Rainfall Intensity

Rainfall Intensity

Why does slope matter?

• Losses/Storage

Why does slope matter?

• Drainage channel has capacity – but water “slow” to get there.

Why does slope matter?

• Simple expression of time in terms of speed and distance

• Expression for time in hydrology

€

T =X

V

€

T =nαLβ

iγSδ

Why does slope matter?

• Consequences of “slope” in denominator– As slope vanishes time becomes huge.– Huge time impacts intensity estimate.– Huge time impacts unit hydrograph behavior.

What we did

• Defined low slope– Literature interpretation– Experiments (Physical and Numerical)

• Developed alternative methods– Parametric study using numerical model– Created an “adjustment” for low-slope hydrology

• Developed plan for future monitoring– Emerging technologies needed

Defining Low Slope

• Literature interpretation

€

S < 0.5%

Low Slope Alternate Methods

• Experiments– Rainfall simulator– Small plot – paved– Small plot – grass

Low Slope Alternate Methods

• Small Plot “Paved”

Low Slope Alternate Methods

• Small Plot – “Grass”

Low Slope Alternate Methods

• Experiment Purpose– Obtain data for validating a computer model– Computer model used for the parametric study to

develop guidelines for low-slope hydrologic computations.

• Experiment Summary– Simulator slopes range from 0 to 5%– Field slopes are 0.25% (0.0025)– Paved, grass, bare-earth surfaces represented

Low Slope Alternate Methods

• Experimental Data Interpretation– Diffusion-Hydrodynamic-Model (DHM) to

interpret experimental results– Use DHM to examine behavior in a parametric

study to develop alternative estimation tools.

Low Slope Alternate Methods

• Experimental Data Interpretation– Literature Studies

Low Slope Alternate Methods

• Experimental Data Interpretation– Literature Studies

Low Slope Alternate Methods

• Experimental Data Interpretation– Our Experiments

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Dis

char

g e (

cfs )

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Rai

nfal

l (in

/ hr)

0.0 3.0 6.0 9.0 12.0 15.0Time (hr)

0.0 3.0 6.0 9.0 12.0 15.0

Discharge (Observed)Discharge (Simulated)

Rainfall

Rainfall intensity and discharge flow rate (Concrete Plot, 0911~12-5 min Data, Diffusion Approximation)

Low Slope Alternate Methods

• Parametric Study

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Dis

char

g e (

cfs )

0

5

10

15

20

25

30

35

40

Rai

nfal

l (in

/ hr)

0 30 60 90 120 150 180Time (min)

0 30 60 90 120 150 180

T3-S1 (S=10%)T3-S2 (S=5%)T3-S3 (S=1%)T3-S4 (S=0.1%)T3-S5 (S=0.05%)T3-S6 (S=0.01%)T3-S7 (S=0%)

Rainfall

T1-S: Discharge Variation for Different Bed Slope(Plot Length=1000 ft, Width=2 ft , Rainfall=3.5in/hr, Manning's n=0.02)

Rainfall =3.5 in/hr

Low Slope Alternate Methods

• Parametric Study

1

10

100

1000

0.000001 0.00001 0.0001 0.001 0.01 0.1 1

Tc (m

inut

es)

Slope

Simulated by DHMRegression for S > 0.0005Regression S > 0.003

Low Slope Alternate Methods

• Additional support for where “low slope” begins – about 0.5% or smaller

• Use the DHM to investigate alternate method for time in hydrologic models

€

T =nαLβ

iγ (S + SLB )δ

Low Slope Alternate Methods

• Impermeable surfaces– Low slope starts at 0.005

€

T = (1.612 −1.196S

SLB + S)(

n0.6175L0.551

i0.388(S + SLB )0.436)

€

SLB = 0.0005

Low Slope Alternate Methods

• Permeable surfaces– Low slope starts at 0.005– A unified general equation could not be found,

instead three based on dominant soil type– Mathematical structure same, exponents are

different by soil, the offset lower bound is the same.

Aggregate Observational Database

• 100+ watersheds– Low and

moderate slopes– Small and large

areas– All plot along

similar pattern except for two.

Monitoring Plan

• Discovered that current measurement technologies are not low-slope compatible.– Use existing culverts as gaging stations, should the

need arise.– Emergent (low-cost) technologies that can make

the measurements in low-slope conditions• Laser and reflective targets• Visible/IR image interpretation• Pressure sondes

Conclusions

• Defined low slope, about 0.3% and smaller.• Alternative timing model to use in such

conditions. • Emerging technology needs to be deployed to

measure discharges on low slope.• Guidance in final report on how to use these

findings. (available July 2012)