Coupling of Atmospheric and Hydrologic Models:

A Hydrologic Modeler’s Perspective

George H. Leavesley1, Lauren E. Hay1, Martyn P. Clark2, William J. Gutowski, Jr.3, and

Robert. L. Wilby4

1U.S. Geological Survey, Denver, CO 2University of Colorado, Boulder, CO 3Iowa State University, Ames, IA 4King’s College London, London, UK

Topics

• Water resources issues

• Hydrologic modeling approaches

• Spatial and temporal distribution issues

• Hydrologic forecasting methodologies

• Downscaling approaches and applications

Water Resources Simulation and Forecast Needs

• Long-term Policy and Planning (10’s of years)

• Annual to Inter-annual Operational Planning (6 - 24 months)

• Short-term Operational Planning (1 - 30 days)• Flash flood forecasting (hours)• Land-use change and climate variability

PRMS

PRMS Snowpack Energy-Balance Components

LUMPED MODELSLUMPED MODELS - No account of spatial variability of processes, input, boundary conditions, and system geometry

DISTRIBUTED MODELSDISTRIBUTED MODELS - Explicit account of spatial variability of processes, input, boundary conditions, and watershed characteristics

QUASI-DISTRIBUTED MODELSQUASI-DISTRIBUTED MODELS - Attempt to account for spatial variability, but use some degree of lumping in one or more of the modeled characteristics.

SPATIAL CONSIDERATIONS

MAXIMUM TEMPERATURE-ELEVATION RELATIONS

PRECIPITATION-ELEVATION RELATIONS

Precipitation and Temperature Distribution

Methodologies• Elevation adjustments

• Thiessan polygons

• Inverse distance weighting

• Geostatistical techniques

• XYZ method

• …

Monthly Multiple Linear Regression (MLR) equations

developed for PRCP, TMAX, and TMIN using the predictor

variables of station location (X, Y) and elevation (Z).

XYZ Methodology

XYZ DISTRIBUTION

San Juan Basin Observation Stations 37

XYZ Spatial Redistribution

of Precipitation & Temperature

1. Develop Multiple Linear Regression (MLR) equations (in XYZ) for PRCP, TMAX, and TMIN by month using all appropriate regional observation stations.

2. Daily mean PRCP, TMAX, and TMIN computed for a subset of stations (3) determined by the Exhaustive Search analysis to be best stations

3. Daily station means from (2) used with monthly MLR xyz relations to estimate daily PRCP, TMAX, and TMIN on each HRU according to the XYZ of each HRU

Precipitation and temperature stations

XYZ Spatial Redistribution

Z

PR

CP

2. PRCPmru = slope*Zmru + intercept

where PRCPmru is PRCP for your modeling response unit

Zmru is mean elevation of your modeling response unit

x

One predictor (Z) example for distributing daily PRCP from a set of stations:

1. For each day solve for y-intercept

intercept = PRCPsta - slope*Zsta

where PRCPsta is mean station PRCP and

Zsta is mean station elevation

slope is monthly value from MLRs Plot mean station elevation (Z)

vs. mean station PRCP

Slope from monthly MLR used to find the

y-intercept

XYZ Methodology

XYZ DISTRIBUTIONEXHAUSTIVE SEARCH ANALYSIS

• Select best station subset from all stations

• Estimate gauge undercatch error for snow events (Bias in observed data)

• Select precipitation frequency station set (Bias in observed data)

Forecast Methodologies

- Historic data as analog for the future

Ensemble Streamflow Prediction (ESP)

-Synthetic time-series

Weather Generator

- Atmospheric model output

Dynamical Downscaling

Statistical Downscaling

Animas River @ Animas River @ DurangoDurangoMeasureMeasure

ddSimulatedSimulated

Animas Animas Basin Basin Snow-Snow-

covered covered Area Area Year 2000Year 2000SimulateSimulate

dd

MeasurMeasured ed

(MODI(MODIS S

SatellitSatellite)e)

Error Range <= Error Range <= 0.10.1

ESP Animas River @ Durango

0

2000

4000

6000

8000

10000

120004/

3/20

05

4/17

/200

5

5/1/

2005

5/15

/200

5

5/29

/200

5

6/12

/200

5

6/26

/200

5

7/10

/200

5

7/24

/200

5

8/7/

2005

8/21

/200

5

9/4/

2005

9/18

/200

5

Str

eam

flo

w (

cfsd

)

1981 (.68)

1982 (.45)

1983 (.23)

1986 (.50)

1987 (.95)

1988 (.73)1989 (.99)

1990 (.09)

1991 (.91)

1992 (.86)

1993 (.64)

1994 (.59)

1995 (.14)

1996 (.05)

1997 (.41)

1998 (.55)

1999 (.36)2000 (.82)

2001 (.32)

2002 (.77)

2003 (.18)

2004 (.27)

Probability of Exceedance

ESP – Animas River @ DurangoESP – Animas River @ Durango(Frequency Analysis on Peak Flows)

ESP – Animas River @ DurangoESP – Animas River @ DurangoESP Animas River @ Durango

0

2000

4000

6000

8000

10000

120004/

3/20

05

4/17

/200

5

5/1/

2005

5/15

/200

5

5/29

/200

5

6/12

/200

5

6/26

/200

5

7/10

/200

5

7/24

/200

5

8/7/

2005

8/21

/200

5

9/4/

2005

9/18

/200

5

Str

eam

flo

w (

cfsd

)

1981

1982

1983

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

Forecast 4/2/05 Observed 4/3 – 6/30/05

Representative Elevation of

Atmospheric ModelOutput based on Regional Station

Observations

Elevation-based Bias Correction

Performance Measures

Coefficient of Efficiency E

Nash and Sutcliffe, 1970, J. of Hydrology

Widely used in hydrology Range – infinity to +1.0 Overly sensitive to extreme values

Nash-Sutcliff Coefficient of Efficiency Scores Simulated vs Observed Daily

StreamflowAnimas River, Colorado USA

Statistical Statistical vs vs

Dynamical Dynamical DDownscaling

NNational CCenters for EEnvironmental

PPrediction/National Center for Atmospheric Research

Reanalysis NCEPNCEP

Global-scale model

NCEP

210 km grid spacingRetroactive 51 year recordEvery 5 days there is an 8-day forecast

Compare SDS and DDS output by using it to drive the distributed hydrologic model

PRMS in 4 basins

(DAY 0)

East Fork of the Carson

Cle Elum

Animas

Alapaha

Snowmelt Dominated922 km2

Snowmelt Dominated526 km2

Snowmelt Dominated1792 km2

Rainfall Dominated3626 km2

Study Basins

Statistical Downscaling

Carson

Cle Elum

Animas

Alapaha

NCEP Grid nodes

Basins

500km Buffer radius

Dynamical Downscaling

52 km grid node spacing

10 year run

Regional Climate Model – RegCM2

nested within NCEP

Dynamical Downscaling

East Fork of

the Carson

Cle Elum

Animas

Alapaha

Animas River Basin

RegCM2 grid nodes

Buffer

52 km

Dynamical Downscaling

Use grid-nodes that fall within 52km buffered area

Climate Stations

1. Station Data

- BEST-STAStations used to calibrate

the hydrologic model

Input Data Sets used in Hydrologic ModelInput Data Sets used in Hydrologic Model

Climate Stations

1. Station Data

- BEST-STA

Input Data Sets used in Hydrologic ModelInput Data Sets used in Hydrologic Model

- ALL-STAAll stations within the RegCM2 buffered area (excluding BEST-STA)

RegCM2 Grid Nodes

1. Station Data

- BEST-STA

Input Data Sets used in Hydrologic ModelInput Data Sets used in Hydrologic Model

2. DDS

- ALL-STA

1. Station Data

- BEST-STA

Input Data Sets used in Hydrologic ModelInput Data Sets used in Hydrologic Model

2. DDS

3. SDS

- ALL-STA

NCEP Grid Nodes

NCEP Grid Nodes

1. Station Data

- BEST-STA

Input Data Sets used in Hydrologic ModelInput Data Sets used in Hydrologic Model

2. DDS

3. SDS

4. NCEP

- ALL-STA

Nash-Sutcliffe Goodness of Fit StatisticComputed between measured and simulated runoff

Best-Sta

Nash-Sutcliffe Goodness of Fit StatisticComputed between measured and simulated runoff

Best-Sta

INPUT TIME SERIES:

Test1

Best-Sta PRCP

Bias-DDS TMAXBias-DDS TMIN

Test2 Bias-DDS PRCPBest-Sta TMAXBias-DDS TMIN

Test3Bias-DDS PRCP

Bias-DDS TMAX

Best-Sta TMIN

Nash-Sutcliffe Goodness of Fit StatisticComputed between measured and simulated runoff

Best-Sta

R-Square Values between Daily “Best” timeseries and:

All-Sta, Bias-All, DDS, Bias-DDS, NCEP, Bias-NCEP, and SDS

Minimum TemperatureMaximum TemperaturePrecipitationAlapahaAnimasCarsonCle Elum

R-S

quar

e

R-S

quar

e

R-S

quar

e

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

Rainfall-dominated basin – highly controlled by daily variations in precipitation

Snowmelt-dominated basins – highly controlled by daily variations in temperature and radiation

Minimum TemperatureMaximum TemperaturePrecipitationAlapahaAnimasCarsonCle Elum

R-S

quar

e

R-S

quar

e

R-S

quar

e

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

All-

Sta

DD

S

Bia

s-A

llB

ias-

DD

SN

CE

PB

ias-

NC

EP

SD

S

Compare SDS and ESP Compare SDS and ESP Forecasts using PRMSForecasts using PRMS

Perfect model scenario

-Ensemble Spread• Range in forecasts

-Ranked Probability Score• measure of probabilistic forecast skill• forecasts are increasingly penalized as more probability is assigned to event categories further removed from the actual outcome

Ranked Probability Skill Score (RPSS) for forecast Ranked Probability Skill Score (RPSS) for forecast days 0-8 and month using measured runoff and days 0-8 and month using measured runoff and simulated runoff produced using: (1)simulated runoff produced using: (1) SDSSDS output output

and (2)and (2) ESPESP techniquetechnique

For

ecas

t D

ay

Month MonthJ F M A M J J A S O N D J F M A M J J A S O N D

8

6

4

2

0

8

6

4

2

0

0.1 0.3 0.5 0.7 0.9

RPSSRPSS

ESPSDS

Perfect Forecast: RPSS=1

Forecast Spread for forecast days 0-8 and month Forecast Spread for forecast days 0-8 and month using measured runoff and simulated runoff using measured runoff and simulated runoff produced using: (1)produced using: (1) SDSSDS output and (2)output and (2) ESPESP

techniquetechnique

For

ecas

t D

ay

Month MonthJ F M A M J J A S O N D J F M A M J J A S O N D

8

6

4

2

0

8

6

4

2

0

500 1500 2500 3500 4500Forecast SpreadForecast Spread

ESPSDS

Comparison of hydrologic model inputs -- Precipitation

For

ecas

t D

ay

Month MonthJ F M A M J J A S O N D J F M A M J J A S O N D

8

6

4

2

0

8

6

4

2

0

0.1 0.2 0.3 0.4 0.5Pearson CorrelationPearson Correlation

ESPSDS

R-square values calculated between daily basin-mean measured and (1) SDS and (2) ESP precipitation values

Daily basin precipitation mean by month and

forecast day for ESP (red line) and SDS (boxplot)

Comparison of hydrologic model inputs – Maximum Temperature

For

ecas

t D

ay

Month MonthJ F M A M J J A S O N D J F M A M J J A S O N D

8

6

4

2

0

8

6

4

2

0

0.1 0.3 0.5 0.7 0.9Pearson CorrelationPearson Correlation

ESPSDS

R-square values calculated between daily basin-mean measured and (1) SDS and (2) ESP maximum temperature values

Daily basin maximum temperature mean by

month and forecast day for ESP (red line) and SDS

(boxplot)

Nested Domains for MM5

Evaluating MM5 Output Using PRMS

HRU Configurations

Daily Precipitation Mean by

Month

Percent Rain Days by Month

XYZ vs MM5

Daily Basin Maximum and Minimum Temperature Mean by Month

XYZ vs MM5

HRU HRU ConfigurationsConfigurations

Results

Wet period

Dry period

5 Years of data

2-yr calibration

3-year evaluation

Improving Flash Flood Prediction Through a Synthesis of NASA

Products, NWP Models and Flash Flood Decision Support Systems

NASA NOAA NCAR USGS

Proposed Flash Flood Prediction Program

Components• 1km Noah LSM in the LIS framework (ensemble mode) • WRF (ensemble runs) • DSS – USGS Modular Modeling System (MMS)

– Sacremento

– CASC2D

– PRMS

• Forecasts– 15 minutes out to 24 hours

– 1 km resolution

USGS Modular Modeling System (MMS)Toolbox for Modeling,

Analysis, and DSS Development and

Application

Summary

• Statistical and dynamical downscaling can provide reasonable input to drive hydrologic models for a variety of applications.

• Statistical downscaling with XYZ distribution– handles spatial and elevation effects– most effective for frontal type storms – limited value for convective storm systems– based on historic climatology which may limit use

for future climate scenarios

Summary• Dynamical downscaled output handles spatial

and elevational effects, and frontal and convective storm types. However bias correction required which results in similar limit on use with future climate scenarios.

• Statistical downscaling shows improvements over ESP based simulations for short-term forecasts.

Summary• Demonstrated higher degree skill of one

method over the over varies with the climatic and physiographic region of the world and the performance measures.

• Need for hydrologic and atmospheric modelers to work collaboratively to improve downscaling methods. Each community can provide valuable feedback to the other.