LMRFC March, 2009

Calibration at Finer Time and Space Scales

LMRFC March, 2009

Hydrologic Modeling Challenges• We cannot directly apply physical laws to some

components of the hydrologic cycle because boundary conditions and system properties are unknown at all locations, e.g.– Exact soil depth or plant rooting depth is unknown – Soil matrix hydraulic properties are unknown (e.g. hydraulic

conductivity)– Underground flow paths are unknown

• Errors and uncertainty in data an models• Model and data errors tend to increase at higher

resolutions• Modeling ungauged locations

– Difficult to verify models– Difficult to determining warning thresholds

LMRFC March, 2009

Calibration with NEXRADat smaller spatial and temporal scales

Anytime a model is calibrated at one spatial and temporal scale it should be recalibrated if the

time/space scale changes

LMRFC March, 2009

surface

supplemental

TCI

direct

interflow

primary

Sub-basin scale in HRAP bins

1X1 2X2 4X4 8X8 16X16 32X32 64X64

Relative sensitivity of SAC runoff components to sub-basin scale.Runoff values have been normalize by the value at the 8X8 scale.

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Sca

led

runo

ff v

alue

LMRFC March, 2009

(a) Lumped Basin

(c) Basin disaggregatedInto 16 cells

(d) Basin disaggregated into 100 cells

(b) Basin disaggregatedinto 4 cells

“Truth Scale” and“Truth Simulation”

Expectations: Effect of Data Errors and Modeling Scale

LMRFC March, 2009

Expectations: Effect of Data Errors and Modeling Scale

Relative Sub-basin Scale A/Ak

1 10 100

10

15

20

25

30

0

5Re

lativ

e e

rro

r, E

k , %

(lumped) (distributed)

Noise 0% 25% 50% 75%

Data errors (noise) may mask the benefits of fine scale modeling. In some cases, they may make the results worse thanlumped simulations.

Sim

ulat

ion

erro

r c

ompa

red

to fu

lly d

istr

ibut

ed

‘Truth’ is simulation from 100 sub-basin model

clean data

LMRFC March, 2009

Model Errors as a Function of Scale

0

20

40

60

80

10 100 1000 10000

Area (km2)

Ave

rag

e %

A

bs.

Pe

ak

Flo

w E

rro

rs

0.0

0.3

0.6

0.9

1.2

Rq

Flash floods

260

Distributed model (uncalibrated). Each point is an average peak flow error from approximately 25 events over an eight year study period Oct 1996-Sept.2004.

Scaling relationship for an uncertainty index (Rq) from Carpenter and Georgakakos (2004) (secondary axis)

Log-linear regression for distributed model data

LMRFC March, 2009

Rmod Calibrated All Periods

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Basin (smallest to largest)

Mod

ified

Cor

rela

tion

Coe

ff R

mod

ARS

AZ1

AZ2

CEM

DH1

DH2

EMC

ILL

LMP

NEB

OHD

RMS

UAE

UOK

VU2

VUB

ave uncal

ave calb

Overall Rmod vs Basin SizeCalibrated Models

Sprin Wsilo Caves Dutch KNSO2 Elm Powel Connr Savoy Lanag ELDO2 BLUO2 SLOA4 TIFM7 TALO2

DMIP 2 Results

37 sq km 2484 sq km

LMRFC March, 2009

Tools

• XDMS spatial display (ABRFC)

• ICP PLOT-TS time series display

• Stat-Q statistics program

• Calibration Assistance Program (CAP)– Soils– Parameters

• Calb MAPX

• Calb MAP (1 hour)

LMRFC March, 2009

July 1, 1999 event. Rain fall on 6/30/99 hours 10,11,12, and 13

TALO2

TALO2

TALO2

TALO2

T=10

T=12

T=11

T=13

Basin Shape: Case 2 - XDMS Plots of Radar Rainfall

You can use XDMS now!

LMRFC March, 2009

Distributed Model Implementation

• Use with, not instead of, lumped model at same time step

• Part of natural progression to finer scalesLumped 6-hr Lumped 1-hour Distributed 1-hour

• Calibration is good training process for forecasting

• Current:– DHM: operation in NWS for headwaters, locals– HL-RDHM: Large area, soil moisture, FFG, etc

• Feedback to OHD

LMRFC March, 2009

Hydrograph at Location A

Hydrograph at Location B

Hydrographs at Basin Outlet

0

40

80

120

160

200

4/3/99 0:00 4/3/99 12:00 4/4/99 0:00 4/4/99 12:00 4/5/99 0:00 4/5/99 12:00 4/6/99 0:00

Flo

w (

CM

S)

0

40

80

120

160

200

4/3/99 0:00 4/3/99 12:00 4/4/99 0:00 4/4/99 12:00 4/5/99 0:00 4/5/99 12:00 4/6/99 0:00

0

40

80

120

160

200

4/3/99 0:00 4/3/99 12:00 4/4/99 0:00 4/4/99 12:00 4/5/99 0:00 4/5/99 12:00 4/6/99 0:00

Flo

w (

CM

S)

B

A Distributed

Lumped

ObservedF

low

(C

MS

)

Use with, not instead of lumped model

Distributed and Lumped Operations

LMRFC March, 2009

Case 1: October 23, 2007

24-hour RainfallBlack Creek near Brooklyn, Miss.

Distributed Modeling for Operational River Forecasts

5 inches in 24 hours

Basin Location

LMRFC March, 2009

Actual River Forecast: Black Cr. At Brooklyn, Miss.Oct. 23, 2007

Distributed Modeling for Operational River Forecasts

Lumped model

Observed flow

Distributed model