Texas HydrologySome Contributions of the USGS Texas Water Science Center

1
Texas Hydrology---Some Contributions of the USGS
Texas Water Science Center

• William H. Asquith, Research Hydrologist
• April 21 and 23, 2009

2
ADCP measurement of streamflowLittle River near
Rockdale, Texas
Design Hydrology comes from Statistical Analysis
of Data
3
Flood Frequency Studies in Texas
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.
1
3
2
4
Visualization of Site-Specific Values
Seven distributions fit to all sites---because,
hey, we do not know true distributional form.
5
PRESS-regressions

• Instead of log10 of drainage area in regression
  use a power transformation.
• The power, press factor, comes from brute force
  minimization of the PRESS statistic.
• Tens of thousands of usual WLS regressions are
  performed to determine optimum press factor for
  each T-year return period.

6
Residuals of Regression
Red overrest.Blue underest.

• Because PRESS statistic appears to be smallest
  for about the 10-year event, focus on the
  residuals of these regressions.
• 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.

Triangles for gt0.15 log-cycle residual
7
Ecoregions of Texas
Residuals generalized into one-degree quads to
form the OmegaEM.

• 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.

Region of high-magnitude flood production?
8
The Latest Equations for Undeveloped
Flood-Frequency Estimation in Texas

• Coming this summer in USGS SIR 2009-5087

A coe. is erased until release.
9
Depth-DurationFrequency ofPrecipitation
AnnualMaxima for TexasTxDOT RMC-3Implementation
Project 5-1301
10
Hydrology (Precipitation and Runoff) Influence
Infratructure

• Sand filtration Best-Management Practice (BMP)
  behindWilliam H. Asquith's house in north Austin
  in Shoal Creek watershed.

11
Atlas ofDepth-Duration Frequency of
Precipitationin Texas
DDF is basis for cost-effective risk-mitigated
design and other more scientific pursuits.

• 96 maps
• 8 recurrence intervals
• 12 durations

Asquith and Roussel (2004)
12
What are L-moments?
L-moments are

• Revolutionary statistical tools
• EXACT analogs to usual product moments
• Linear combinations of the expectations of order
  statisticsstatistics of ordered samples.
• Unbiased (unlike product moments, PM)
• Efficientsmaller sampling errors than PM
• Readily used with quantile functions

13
Dimensionlessor Regional FrequencyCurves

• 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 L-moments (parameter estimation)
  using a mean of unity and the coefficient of
  L-variation as the second L-moment (L-scale).

14
DDF Atlas
Asquith (1998)

• NWS data
• L-moments
• Regionalization of L-moments
• Distribution selection
• Parameter est.
• Parameter regionalization

Figure 23. Location for 7-day duration
15
DDF Atlas
Asquith (1998)
Shape parameter (k) -0.0615
Figure 37. Scale for 7-day duration
16
25-year1-daydurationannualmaxima
DDFAtlas
17
100-year7-daydurationannualmaxima
DDFAtlas
18
Atlas of Interoccurrence IntervalsTxDOT Research
Project 0-4194"another talk"
19
Design StormsDaily Interoccurrence
Exponential Distribution(Poisson Process,
memoryless)
Asquith and Roussel (2003)

• Asquith and Roussel (2003)
• USGS WRIR 034281.

20
Design StormsDaily Interoccurrence

• Previous slide for0.05 inches or more, but this
  one for 1.0 inch or more.
• The regional differences for a single map
  makeclimatological sense.
• The differences between the maps make
  climatological sense.

21
SeasonalCorrectionsto the MeanInteroccurrenceI
ntervals
Design StormsDaily Interoccurrence
22
Design StormsPoisson 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

23
Design StormsDaily Interoccurrence
Negative Correlation

• Influence of elevation on the interoccurrence
  interval of daily precipitation.
• Elevation is important for small rainfall
  magnitudes.
• Elevation is not important for small rainfall
  magnitudes.

No Correlation?
24
Rainfall Hyetographs and Distribution of Storm
Depth TxDOT RMC-3 Research Project 0-4194
Dr. William H. Asquith Research HydrologistUSGS,
Austin

• Research Team
• Meghan C. Roussel, USGS
• Dr. David B. Thompson, TTU
• Dr. Theodore G. Cleveland, UH
• Dr. Xing Fang, Lamar Univ.

25
Texas Hyetograph Related Publications

• Al-Asaadi (2002) M.S. thesis
• 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

26
Classical Hyetographs
27
Runoff-Producing Storms in Texas
28
Dimensionless Hyetographs
Grey lines represent individual storms. The
connected stars are the median ordinate for
2.5-percent 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
29
Triangular Hyetographs
30
Huff-likeHyetographs
F.A. Huff (1967 and 1990)

• Hyetographs for runoff producing storms in Texas
• Independent analytical direction from the core
  Asquith (2003) approach.

31
Empirical Hyetographs
32
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
33
Some Questions Answeredby 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.
34
Statistics of Storms
0428 Austin Camp Mabry, Texas
Total Depth
Total Depth
Duration
Interevent time
Duration
12 hour MIT

• 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

35
90th Percentile Storm Depths
COUNTY MEAN_08hr_DEPTH 8hr-90th El Paso 0.233
in 0.59 in Lubbock .406 in 1.02
in Travis .494 in 1.24 in Hays .564
in 1.42 in Harris .590 in 1.49 in
2.52 is the8 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
2.49 is the24 hour -90 percent frequency factor
36
Storm Statistics Data
EVENT DEPTH DURATION INTERVAL (no.)
(in.) (hrs) (days) 1 0.34 4
12.0 2 1.6 7 3.25 3
.76 2 .5 4 3.00
14 23.0 MEAN 1.43 6.75 9.69
and then compute other "moments" (L-moments)
37
Statistics of Storms 652 p.

• 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

38
Basic Steps for defining a Frequency Curve from
Data
Observed data
Distribution characterization(Moment
computation)Sample L-moments
Frequency Curve
Distribution modelquantile functionsother
formulations
Parameter Estimation
39
Autocorrelation Analysis
Autocorrelation analysis determines a suitable
minimum interevent time in which storms can be
considered statistically distinct.
40
Autocorrelation Analysis
There appears to be limited spatial influenceon
the auto-correlation coefficients of hourly
rainfall in Texas
41
Effects of Minimum Inter-event Time on Storm
Statistics
Statistics with dimension must increase with
increasing minimum interevent time.
42
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.
43
Mean Storm Depth for8-hour MIT
Large east-to-west gradient Maps used with
dimensionless frequency curve to generate storm
depth distribution. 21 maps provided
44
Mean Storm Depth for24-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.
45
L-moment diagrams are the state-of-the-art tool
for selection of distributions to model
environmental data.Distribution L-moments
compared to dataL-moments. Differences between
distributions are clear and unambiguous.
L-moment diagrams

• Kappa (4 parameters)
• Pearson Type III (3 para.)
• Gamma (2 parameters)
• Exponential (2 parameters)

Kappa dist. is MOST REPRESENTATIVE.
46
DimensionlessKappa Distribution Frequency Curves
MIT has LIMITED influence on the curve--so does
geographic location EASY TO USE
47
Dimension-less Kappa Distribution Frequency
Curves
"frequency factors"

• Limitedspatialdifferences
• Flexible
• Unambiguous
• Easy to use

48
Comparison of DimensionlessExponential, Gamma,
Kappa Distributionsof Storm Depth
Exponential used in analytical BMP equations. EPA
and others suggest Gamma. Kappa most accurate
(cutting-edge) and throws greater outliers.
49
Distribution Parameter Estimates
Dimensionless Exponential Gamma Kappa
50
Mean Storm Arrival Rate for8-hour MIT
51
Distribution of Storm Interoccurrence
Exponential distribution with MIT correction
POISSON PROCESS
52
Mean Storm Duration for8-hour MIT
53
Summary and DiagnosticStatistics of Countywide
Maps
These statistics provide nice analytical closure.
54
Project 0-4193Regional 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

55
Background

• Substantial progress on the Texas hydrograph
  method has been made over the past 7 years or so
  ...
• 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 modelexcess
  rainfall
• Complete the loop Rainfall --gt Excess Rainfall
  --gt Runoff
• Motivation for 2-year extension request . . .

56
Primary 0-4193 Objectives

• Is the NRCS dimensionless unit hydrograph
  representative of Texas hydrology? SORT
  OF (at times)
• If not, can alternative methods be developed?
  certainly YES
• 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)

57
0-4193 Approach

• Common database (93 watersheds and 1,600 events)
• Joint but INDEPENDENT data processing . . .
• Assumption of differing LOSS-MODELS--A necessary
  step
• Unit Hydrograph Computations
• 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.)

58
GUGAS SHAPE PARAMETER
NRCS
59
COMPARISON OFGUH TO NRCS DIMENSIONLESS UH
Undeveloped watershed DUH is more symmetrical and
peaky than developed watershed DUH and the NRCS
DUH.
60
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

UNDEVELOPED WATERSHEDS
61
Comparison of GUHs
62
Comparison of GUHs
63
ESTIMATION OF TIME TO PEAK FROM TIME OF
CONCENTRATION
64
TWO METHODS FOR TIME TO PEAK
65
0-4193 Implications

• Watershed development influences UH shape and
  time scale.
• GUH of same order of NRCS GUH.
• GUH shape can be predicted and uncertainty
  computed.
• K function(L,D)
• GUH Time-to-Peak (Tp) can be predicted without
  Time-of-Concentration (Tc) and uncertainty
  computed.
• Tp function(L,S,D)
• GUH Tp can be predicted with Tc and uncertainty
  computed.
• Tp function(Tc, D)
• THE TWO Tp METHODS COMPLIMENT EACH OTHER!

66
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

67
Unit Hydrographs TxDOT 0-4193-4 Timing
Parameters TxDOT 0-4696-2 Loss Models USGS SIR
2007-5243
Rainfall-Runoff Modeling
68
TxDOT Publicationscan be found atUniversity of
Texas at AustinCenter for Transportation
Research (Library)

• http//library.ctr.utexas.edu/dbtw-wpd/textbase/we
  bsearchcat.htm

Search for author Asquith and separately for
Roussel
69
Some Terms

• Time-to-Peak
• Time from inception of runoff to peak discharge
  value. Often used as a parameter in hydrograph
  models.
• 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.

70
Some Terms

• Unit Hydrograph
• The unit hydrograph is the direct runoff
  hydrograph produced by a unit depth of excess
  precipitation on the watershed.
• Loss Model
• A mathematical construct that accounts for ALL
  rainfall losses on a watershed. The equation
  that converts precipitation to excess
  precipitation.

71
HYDROGRAPHS
72
Study Area--92 watersheds

• Over 1,600 storms analyzed.
• Multiple approaches for unit hydrograph
  estimation.
• Multiple approaches for time parameter
  estimation.
• Multiple approaches for loss model estimation.

73
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.
74
Gamma Unit Hydrographs

• Perform analysis of rainfall and runoff data.
• Use gamma distribution as hydrograph model.
• Match Tp and Peak Discharge at all costs.
• Statistically summarize Tp and GUH shape.
• Perform regression analysis.

The TxDOT unit hydrograph report.
75
Regionalizationof time-topeak
Multiple linear regression is used to define a
relation between watershed characteristics and
time-to-peak.
76
Comparison of GUHs
77
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

UNDEVELOPED WATERSHEDS
78
Time-to-Peak
DEVELOPED WATERSHEDS

• 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

79
Time-to-Peak vs. Time-of-Concentration
80
(No Transcript)
81

• Ok--We can now estimate the gamma unit hydrograph
  for a watershed.
• Let us use that GUH with real rainfall to
  estimate the parameters of an initial-abstraction,
  constant-loss model.
• 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.

82
Optimal loss models produce UNBIASED peak
discharges.
83
INITIAL ABSTRACTION
84
CONSTANT LOSS
85
Some Rules of Thumb?

• Urbanization cuts time to peak in half, which
  substantially increases peak discharge.
• Unit hydrographs can be reliably estimated for
  many watersheds.
• Understand time and one understands the
  hydrograph.
• Dimensionless hydrograph shapes for developed and
  undeveloped watersheds are similar.

• 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?

86
Initial-Abstraction, Constant-Loss Model

• Regional analysis of watershed-specific,
  loss-model parametersby conventional
  regression.
• 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.
87
Initial-Abstraction, Constant-Loss Model
INITIAL ABSTRACTION
CONSTANT LOSS

• Regional analysis ofloss-model parametersby
  Regression Trees

88
Standard Residual Plots
INITIAL ABSTRACTION

• Comparison of residual plots for regression
  equations (top) and regression trees (bottom).

CONSTANT LOSS
89
Error Analysis Peak, Volume, and Time
PEAK

• 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.

VOLUME
TIME
90
Estimation of Peak Discharge using GUH and
combined loss-model parameters

• Note unbiased appearance

91
CONCLUSION In one word?
GUH optimal loss parameters

• UNBIASED- PEAK-DISCHARGE

GUH and combined model of losses
note hyphens
92
THANKS

• 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

• Our research partners, colleagues, and friends at
  Texas Tech University, University of Houston, and
  Lamar University
• David Thompson (fmr TTU)
• Ted Cleveland (fmr UH, now TTU)
• Xing Fang (fmr Lamar, now Auburn)