Transcript Texas Hydrology---Some Contributions of the USGS Texas Water Science Center

Texas Hydrology---Some
Contributions of the USGS
Texas Water Science Center
William H. Asquith, Research Hydrologist
April 21 and 23, 2009
U.S. Department of the Interior
U.S. Geological Survey
Design Hydrology comes from
Statistical Analysis of Data
ADCP measurement of streamflow
Little River near Rockdale, Texas
Flood Frequency
Studies in Texas
1
Numerous studies of the relation
between T-year discharge and
watershed characteristics. New
report coming this summer is best
yet and cover art is not yet
complete.
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2
U.S. Department of the Interior
U.S. Geological Survey
Seven distributions
fit to all sites--because, hey, we
do not know true
distributional form.
Visualization of
Site-Specific
Values
PRESS-regressions
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Instead of log10 of drainage area in
regression use a power transformation.
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The power, press factor, comes from
brute force minimization of the PRESS
statistic.
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Tens of thousands of usual WLS
regressions are performed to determine
optimum press factor for each T-year
return period.
Residuals of Regression
·
Because PRESS statistic
appears to be smallest
for about the 10-year
event, focus on the
residuals of these
regressions.
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To clarify, at about the
10-year event (90th
percentile) the
interaction of basin
characteristics
describing flood
magnitude and relatively
low error in fitting
distributions provide
“most” favorable
regressions.
Red: overrest.
Blue: underest.
Triangles for >0.15
log-cycle residual
Ecoregions of
Texas
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Structure to the residuals and
in particular the residuals for
the 10-year event.
The algorithm has elucidated
spatial context likely not to be
seen in generalized skew or in
index-flood-like methods.
Residuals generalized into
one-degree quads to form the
OmegaEM.
Region of high-magnitude
flood production?
The Latest
Equations for
Undeveloped FloodFrequency
Estimation in Texas
·
Coming this
summer in USGS
SIR 2009-5087
A coe. is erased until release.
Depth-Duration
Frequency of
Precipitation Annual
Maxima for Texas
TxDOT RMC-3
Implementation
Project 5-1301
U.S. Department of the Interior
U.S. Geological Survey
Hydrology (Precipitation and Runoff) Influence
Infra$tructure
Sand filtration Best-Management Practice (BMP) behind
William H. Asquith's house in north Austin in Shoal Creek watershed.
DDF is basis for cost-effective
risk-mitigated design and
other more scientific pursuits.
Atlas of
Depth-Duration
Frequency of
Precipitation
in Texas
• 96 maps
Asquith and Roussel (2004)
• 8 recurrence
intervals
• 12 durations
What are L-moments?
L-moments are:
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Revolutionary statistical tools
EXACT analogs to usual product moments
Linear combinations of the expectations of order
statistics—statistics of ordered samples.
Unbiased (unlike product moments, PM)
Efficient—smaller sampling errors than PM
Readily used with quantile functions
Dimensionless
or “Regional”
Frequency
Curves
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“Dimensionless” points are created
by dividing the data points for a
given station by the mean of the
data for the station.
“Dimensionless” curves are created
by performing the method of Lmoments (parameter estimation)
using a mean of unity and the
coefficient of L-variation as the
second L-moment (L-scale).
Asquith (1998)
DDF Atlas
1. NWS data
2. L-moments
3. Regionalization
of L-moments
4. Distribution
selection
5. Parameter est.
6. Parameter
regionalization
Figure 23. Location for 7-day duration
Asquith (1998)
DDF
Atlas
Shape parameter
(k) = -0.0615
Figure 37. Scale for 7-day duration
DDF
Atlas
25-year
1-day
duration
annual
maxima
DDF
Atlas
100-year
7-day
duration
annual
maxima
Atlas of
Interoccurrence
Intervals
TxDOT Research
Project 0-4194
"another talk"
Design Storms—Daily Interoccurrence
Exponential Distribution
(Poisson Process, memoryless)
F=nonexceedance prob.
n=number of events
x=time
l=1/interoccurrence = L
Asquith and Roussel (2003)
USGS WRIR 03–4281.
Asquith and Roussel (2003)
Design Storms—Daily Interoccurrence
Previous slide for
0.05 inches or
more, but this one
for 1.0 inch or
more.
The regional
differences for a
single map make
climatological
sense.
The differences
between the maps
make
climatological
sense.
Design Storms—
Daily
Interoccurrence
Seasonal
Corrections
to the Mean
Interoccurrence
Intervals
Design Storms—Poisson Process
PROBLEM: Compute
the 90th percentile
number of events in a one
year period for an
interoccurrence interval
of 10.5 days per event.
Assume that the process
is Poisson (memoryless).
SOLUTION: 42 events
• CDF of Poisson
distribution
• One parameter model
Negative Correlation
Design Storms—
Daily
Interoccurrence
Influence of elevation on the
interoccurrence interval of
daily precipitation.
• Elevation is important for
small rainfall magnitudes.
No Correlation?
• Elevation is not important for
small rainfall magnitudes.
Rainfall Hyetographs and Distribution of
Storm Depth TxDOT RMC-3 Research
Project 0-4194
Dr. William H. Asquith
Research Hydrologist
USGS, Austin
U.S. Department of the Interior
U.S. Geological Survey
Research Team
Meghan C. Roussel, USGS
Dr. David B. Thompson, TTU
Dr. Theodore G. Cleveland, UH
Dr. Xing Fang, Lamar Univ.
Texas Hyetograph Related Publications
•
Al-Asaadi (2002): M.S. thesis
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Asquith (2003): Ph.D. diss.
•
Asquith, Bumgarner,
Fahlquist (2003): J.A.W.R.A.
•
Asquith and Thompson (2003): ASCE-Texas
Proceedings
•
Asquith, Roussel, Thompson, Cleveland, and
Fang (2004): TxDOT 0-4194-4
•
Sether-Williams, Asquith, Cleveland, Fang, and
Thompson (2004): USGS SIR2004-5075
Classical Hyetographs
Runoff-Producing Storms in Texas
Dimensionless
Hyetographs
Grey lines represent individual
storms. The connected stars are
the median ordinate for 2.5percent wide intervals. Quartiles
and deciles are shown.
The lower figure shows means
and sample sizes of the data.
In general “runoff producing
storms in Texas are front loaded.”
0-12 HOUR
DURATION
Triangular
Hyetographs
Huff-like
Hyetographs
F.A. Huff (1967 and 1990)
• Hyetographs for
runoff producing
storms in Texas
• Independent
analytical direction
from the core
Asquith (2003)
approach.
Empirical Hyetographs
Which hyetograph(s) are optimal for
the initial-abstraction and constant
loss model using the gamma unit
hydrograph?
Answer is not known
and remains perhaps
THE open question
remaining for a type of
design hydrology in
Texas
Some Questions Answered
by Detailed Storm Statistics
• Expected depth in BMP (expected
hydraulic head)
• Expected spill volume
• BMP contents at beginning (or end) of next
event
• Probabilistic wet pond assessment
• Detailed cost-benefit analysis
• Multiple reservoir analysis
• Average number of spills per year
• BMP maintenance scheduling
• Revegetation studies
Some questions have analytical solutions; whereas others must
be solved using continuous simulation models.
Statistics of Storms
Duration
Interevent time
12 hour MIT
Duration
0428 Austin Camp Mabry, Texas
• Storms are distinguished by a minimum interevent time.
• Brief periods of zero rainfall within a "storm" are common.
• Storms are characterized by arrival, total depth and
duration, and temporal distribution of intensity
90th Percentile Storm Depths
COUNTY MEAN_08hr_DEPTH
El Paso
0.233 in
Lubbock
.406 in
Travis
.494 in
Hays
.564 in
Harris
.590 in
2.49 is the
24 hour -90
percent
frequency
factor
8hr-90th%
0.59 in
1.02 in
1.24 in
1.42 in
1.49 in
2.52 is the
8 hour - 90
percent
frequency
factor
COUNTY MEAN_24hr_DEPTH 24hr-90th%
El Paso
0.275 in
0.68 in
Lubbock
.522 in
1.30 in
Travis
.672 in
1.67 in
Hays
.743 in
1.85 in
Harris
.810 in
2.02 in
Storm Statistics Data
EVENT
(no.)
1
2
3
4
MEAN =
DEPTH
(in.)
0.34
1.6
.76
3.00
1.43
DURATION
(hrs)
4
7
2
14
6.75
INTERVAL
(days)
12.0
3.25
.5
23.0
9.69
and then compute other "moments" (L-moments)
Statistics of Storms: 652 p.
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eNM, OK, TX
NWS hourly data
155 million values
774 stations
MIT: 6, 8, 12, 18, 24,
48, and 72 hours
• Storm Arrival, Depth,
and Duration
– percentiles
– L-moments
– dist. eq. form
• Hyetographs
– new analysis
• Example Problems
Basic Steps for defining a Frequency
Curve from Data
Observed data
Distribution characterization
(Moment computation)
Sample L-moments
Frequency Curve
Distribution model
quantile functions
other formulations
Parameter Estimation
Autocorrelation Analysis
Autocorrelation
analysis determines
a suitable minimum
interevent time in
which storms can be
considered
statistically distinct.
Autocorrelation Analysis
There
appears to be
limited spatial
influence
on the autocorrelation
coefficients of
hourly rainfall
in Texas
Effects of Minimum Interevent Time on Storm Statistics
Statistics with dimension must increase
with increasing minimum interevent time.
Countywide Mean Tables
Tables listing countywide mean values for storm arrival rate,
depth, and duration for eNM, OK, and TX are provided.
Countywide tables are convenient as many administrative
jurisdictions are coincident with county boundaries.
Mean Storm
Depth for
8-hour MIT
Large east-to-west gradient
Maps used with
dimensionless frequency
curve to generate storm
depth distribution.
21 maps provided
Mean Storm
Depth for
24-hour MIT
Maps for Arrival Rate
Maps for Storm Depth
Maps for Storm Duration
(Tables also provided.)
Easy to use, consistent, and
logical with many
administrative jurisdications.
L-moment diagrams
L-moment diagrams are
the state-of-the-art tool
for selection of
distributions to model
environmental data.
Distribution L-moments
compared to data
L-moments. Differences
between distributions
are clear and
unambiguous.
1. Kappa (4 parameters)
2. Pearson Type III (3 para.)
3. Gamma (2 parameters)
4. Exponential (2 parameters)
Kappa dist. is MOST REPRESENTATIVE.
Dimensionless
Kappa
Distribution
Frequency Curves
MIT has LIMITED
influence on the
curve--so does
geographic location
EASY TO USE
Dimensionless Kappa
Distribution
Frequency
Curves
• Limited
spatial
differences
• Flexible
• Unambiguous
• Easy to use
"frequency factors"
Comparison of
Dimensionless
Exponential, Gamma,
Kappa
Distributions
of Storm Depth
Exponential used in
analytical BMP equations.
EPA and others suggest
Gamma.
Kappa most accurate
(cutting-edge) and throws
greater outliers.
Distribution Parameter Estimates
Dimensionless
Exponential
Gamma
Kappa
Mean Storm
Arrival Rate
for
8-hour MIT
Distribution of Storm Interoccurrence
POISSON PROCESS
Exponential distribution with MIT correction
Mean Storm
Duration for
8-hour MIT
Summary and Diagnostic
Statistics of Countywide Maps
These statistics provide nice analytical closure.
Project 0-4193
Regional Characteristics of
Unit Hydrographs
David B. Thompson, Texas Tech, RS
George R. Herrmann, TxDOT, PD
William H. Asquith, U.S. Geological Survey, Co-PI
Xing Fang, Lamar University, Co-PI
Theodore G. Cleveland, University of Houston, Co-PI
U.S. Department of the Interior
U.S. Geological Survey
Background
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Substantial progress on the “Texas” hydrograph method
has been made over the past 7 years or so ...
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Design storm depth and temporal distribution--DONE
Weakness in Curve Number method documented--DONE
Unit hydrographs--almost DONE
Time parameters--almost DONE
What is left? A temporal loss rate model=excess rainfall
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Complete the loop: Rainfall --> Excess Rainfall --> Runoff
Motivation for 2-year extension request . . .
Primary 0-4193 Objectives
· Is the NRCS dimensionless unit hydrograph representative
of Texas hydrology?
SORT OF (at times)
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If not, can alternative methods be developed?
certainly YES
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Can an alternative loss model to NRCS curve number
method be developed from the existing database and
resulting UH? Can a loss model “tuned” to the UH
procedures that will result from 0-4193 to date?
(Requested modification)
0-4193 Approach
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Common database (93 watersheds and 1,600 events)
Joint but INDEPENDENT data processing . . .
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Assumption of differing LOSS-MODELS--A necessary step
Unit Hydrograph Computations
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Gamma UH fit to Qp and Tp (USGS): Shape and Tp parameters
Rayleigh IUH fit by error minimization (Univ. of Houston)
Linear programming fit by error minimization (Lamar Univ.)
Traditional method (Texas Tech Univ.)
GUGAS SHAPE PARAMETER
NRCS
COMPARISON OF
GUH TO NRCS DIMENSIONLESS
UH
Undeveloped watershed
DUH is more symmetrical
and peaky than developed
watershed DUH and the
NRCS DUH.
Time to Peak
• Equation to estimate
time to peak from main
channel length, main
channel slope, and
development classification
has been developed.
• Measure of equation
applicability
• Measure of equation
prediction accuracy.
UNDEVELOPED WATERSHEDS
• Handy nomograph
Comparison of GUHs
Comparison of GUHs
ESTIMATION
OF TIME TO
PEAK FROM
TIME OF
CONCENTRA
TION
TWO METHODS FOR TIME TO PEAK
0-4193 Implications
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Watershed development influences UH shape and time scale.
GUH of same order of NRCS GUH.
GUH shape can be predicted and uncertainty computed.
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K = function(L,D)
GUH Time-to-Peak (Tp) can be predicted without Time-of-Concentration (Tc) and
uncertainty computed.
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Tp = function(L,S,D)
GUH Tp can be predicted with Tc and uncertainty computed.
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Tp = function(Tc, D)
THE TWO Tp METHODS COMPLIMENT EACH OTHER!
Initial-Abstraction
and Constant Loss
Model for a Gamma
Unit Hydrographs
David B. Thompson, Texas Tech, RS
George R. Herrmann, TxDOT, PD
William H. Asquith, U.S. Geological Survey, Co-PI
Xing Fang, Lamar University, Co-PI
Theodore G. Cleveland, University of Houston, Co-PI
U.S. Department of the Interior
U.S. Geological Survey
Unit Hydrographs: TxDOT 0-4193-4
RainfallRunoff
Modeling
U.S. Department of the Interior
U.S. Geological Survey
Timing Parameters: TxDOT 0-4696-2
Loss Models: USGS SIR 2007-5243
TxDOT Publications
can be found at
University of Texas at Austin
Center for Transportation Research
(Library)
· http://library.ctr.utexas.edu/dbtwwpd/textbase/websearchcat.htm
Search for author “Asquith” and separately for “Roussel”
Some Terms
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Time-to-Peak
· Time from inception of runoff to peak discharge
value. Often used as a parameter in hydrograph
models.
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Time-of-Concentration
· Time required for parcel of water to travel from the
most hydraulically distance point in a watershed
to the outlet. Common basis for hydrologic
engineering design to get to a time-to-peak.
Some Terms
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Unit Hydrograph
· The unit hydrograph is the direct runoff
hydrograph produced by a unit depth of excess
precipitation on the watershed.
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Loss Model
· A mathematical construct that accounts for ALL
rainfall losses on a watershed. The “equation” that
converts precipitation to excess precipitation.
HYDROGRAPHS
Study Area--92 watersheds
1. Over 1,600 storms
analyzed.
2. Multiple
approaches for unit
hydrograph
estimation.
3. Multiple
approaches for time
parameter
estimation.
4. Multiple
approaches for loss
model estimation.
Tc (Kerby-Kirpich) vs. Drainage Area
A reliable method for
estimation of time of
concen-tration is the
Kerby (overland
flow) Kirpich
(channel flow)
method.
The TxDOT
watershed
timing report.
Gamma Unit
Hydrographs
1. Perform analysis of
rainfall and runoff data.
2. Use gamma distribution
as hydrograph model.
3. Match Tp and Peak
Discharge at all costs.
The TxDOT unit hydrograph report.
4. Statistically summarize
Tp and GUH shape.
5. Perform regression
analysis.
Regionalization
of time-to
peak
Multiple linear
regression is used to
define a relation
between watershed
characteristics and
time-to-peak.
U.S. Department of the Interior
U.S. Geological Survey
Comparison of GUHs
Time-to-Peak
• Equation to estimate
time to peak from main
channel length, main
channel slope, and
development classification
has been developed.
• Measure of equation
applicability
• Measure of equation
prediction accuracy.
UNDEVELOPED WATERSHEDS
• Handy nomograph
DEVELOPED WATERSHEDS
Time-to-Peak
• Equation to estimate
time to peak from main
channel length, main
channel slope, and
development classification
has been developed.
• Measure of equation
applicability
• Measure of equation
prediction accuracy.
• Handy nomograph
Time-to-Peak vs. Time-of-Concentration
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Ok--We can now estimate the gamma unit
hydrograph for a watershed.
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Let us use that GUH with real rainfall to estimate
the parameters of an initial-abstraction, constantloss model.
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Estimate the loss-model parameters through
optimization by constraining the parameters to
reality, constraining the optimization to volume
match, and minimizing on the residuals of the
modeled and observed hydrographs.
Optimal loss models produce
UNBIASED peak discharges.
U.S. Department of the Interior
U.S. Geological Survey
INITIAL ABSTRACTION
CONSTANT LOSS
Some Rules of Thumb?
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Urbanization cuts time to peak in
half, which substantially increases
peak discharge.
Unit hydrographs can be reliably
estimated for many watersheds.
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Understand time and one
understands the hydrograph.
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Dimensionless hydrograph shapes
for developed and undeveloped
watersheds are similar.
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Constant loss is about 0.62 in/hr
(undeveloped) and 0.51 in/hr
(developed).
Initial abstraction is about 1.1 in.
(undeveloped) and 0.69 in.
(developed).
Urbanization cuts initial
abstraction by about half.
Urbanization apparently has
limited influence on constant
loss for macrowatersheds?
Initial-Abstraction, Constant-Loss Model
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Regional analysis of
watershed-specific, lossmodel parameters
by conventional
regression.
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Watershed: Length, Rock,
Curve Number (CN),
watershed Development
INITIAL ABSTRACTION
CONSTANT LOSS
Equations appear to be not unreasonable predictors of watershed loss, but many
Many MANY variables exist: Ante. Moisture, Rain in space.
Initial-Abstraction, ConstantLoss Model
INITIAL ABSTRACTION
CONSTANT LOSS
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Regional analysis of
loss-model parameters
by Regression Trees
Standard Residual Plots
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Comparison of
residual plots for
regression
equations (top)
and regression
trees (bottom).
INITIAL ABSTRACTION
CONSTANT LOSS
Error Analysis:
Peak, Volume, and
Time
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Loss Model research
suggested four
competitive models.
We gave up on
selecting one, use all
FOUR together and
average peak
discharge, volume, and
time of peak.
PEAK
VOLUME
TIME
Estimation of Peak Discharge using GUH and
combined loss-model parameters
Note unbiased
appearance
GUH: optimal loss
parameters
UNBIASEDPEAKDISCHARGE
note hyphens
CONCLUSION: In
one word?
GUH and combined
model of losses
THANKS
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A special thanks is needed to
this research supported by
TxDOT through the Research
and Technology
Implementation office for
seven years of support on this
subject!!!!!!!
The numerous colleagues at
TxDOT who to name a few
would miss many.
USGS Cooperative Water
Program
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Our research partners,
colleagues, and friends at
Texas Tech University,
University of Houston, and
Lamar University
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David Thompson (fmr TTU)
Ted Cleveland (fmr UH, now
TTU)
Xing Fang (fmr Lamar, now
Auburn)