the 3rd workshop of the international precipitation working group, 23-27 october, 2006

Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Basin Scale Precipitation Data Merging Using Markov Chain Monte Carlo Method

K. Hsu, F. Boushaki, S. Sorooshian, and X. GaoCenter for Hydrometeorology and Remote Sensing

University of California Irvine

The 3rd Workshop of the International Precipitation Working Group, 23-27 October, 2006


PERSIANN RainfallPERSIANN Rainfall

Precipitation Data MergingPrecipitation Data Merging

Grid-Based Precipitation Data MergingGrid-Based Precipitation Data Merging

Basin Scale Precipitation Data MergingBasin Scale Precipitation Data Merging

Case StudyCase Study

SummarySummary

Outline


PERSIANN System “Estimation”

Global IR

MW-RR (TRMM, NOAA, DMSP Satellites)

Merged Products- Hourly rainfall- 6 hourly rainfall- Daily rainfall- Monthly rainfall

ANN

Error Detection

QualityControl

Merging

Sat

elli

te D

ata

Gro

un

d O

bs

erv

ati

on

s

Products

High Temporal-Spatial Res.Cloud Infrared Images

Fee

db

ack

Hourly Rain EstimateSampling

MW-PR Hourly Rain Rates

Hourly Global Precipitation Estimates

Gauges Coverage

GPCC & CPCGauge Analysis

Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN)



PERSIANN-CCS (Cloud Classification System)


Global PERSIANN:http://hydis8.eng.uci.edu/hydis-unesco/

US PERSIANN-CCS:http://hydis8.eng.uci/CCS

0.25ox0.25o Hourly 0.04ox0.04o Hourly

PERSIANN Precipitation Products


A SHORT MOVIE OF PERSIANN PRODUCTS (PERSIANN: Precipitation estimation from Remote Sensing Information using Artificial Neural Network)

PERSIANN (0.25° 0.25°)07/25-27/2006

PERSIANN CCS(0.04° 0.04°)07/24-27/2006

High resolution precipitationdata are needed for hydrologicapplications in SW.

Severe storms propagatefrom mountains to low-elevated areas.

Acknowledgement. This research is partially funded by NSF/SAHRA and NASA/GPM programs


RESEARCH TO SUPPORT MODELING EFFORTS Flash Flood Monitoring (7/27-28/2006)

Poor radar coverage over mountainous southwest can result in missing flood warning for the areas radar network does not cover (Maddox et al., 2003). The demo shows our on-going study to check how the missing portions of a severe storm can be retrieved by the concurrent PERSIANN storm images and also reduce false warning.

Strong convections start over mountains where radar coverage is poor. PERSIANN monitors the lifetimes of storm systems and provides information for early warning.

Radar beams (3-km above ground level) are blocked by mountains in southwest United States.

Differences between PERSIANN and radar images exist.

Red: PERSIANN Rain vs. Radar No Rain

Blue: PERSIANN No Rain vs. Radar Rain


6-Hour Accumulated Rainfall: Hurricane Ivan

hydis8.eng.uci.edu/CCS


Precipitation Measurement is one of the KEY

hydrologic Challenges


Hydrologic Models

Q

B

QR

t

q

RIA

i

t

API Model INTERFLOWSURFACERUNOFF

INFILTRATIONTENSION

TENSION TENSION

PERCOLATION

LOWERZONE

UPPERZONE

PRIMARYFREE

SUPPLE-MENTAL

FREE

RESERVED RESERVED

FREE

EVAPOTRANSPIRATION

BASEFLOW

SUBSURFACEOUTFLOW

DIRECTRUNOFF

Precipitation Sacramento Model

Mike SHEModel, DHI

VIC Model


)(%20)( tPt

Streamflow Simulation vs. Precipitation Uncertainty:


)(%25)( tPt



)(%50)( tPt



RadarGauge

Surface TemperatureSoil MoistureVegetation

LABZ

Multiple Sources for Rainfall Estimation

Geosynchronous SatellitesVIS, IR, Sounding

Low Orbiting SatellitesVIS, IR, MV, and Radar


Bias Correction and Downscaling of Daily Rainfall to Hourly Rainfall

Time Step: Day

CPC Daily Analysis

PERSIANN Rainfall (non-adjusted)

PERSIANN Rainfall (bias adjusted)

PE

RS

IAN

N R

ain

fall

Daily Rainfall: Summer 2005

Downscaled to Hourly Rainfall

Grid size: 0.25ox0.25o

Grid size: 0.04ox0.04o CPC Daily Gauge Analysis

Grid-Based Data Merging


Basin Scale Precipitation Data Merging

INTERFLOWSURFACERUNOFF

INFILTRATIONTENSION

TENSION TENSION

PERCOLATION

LOWERZONE

UPPERZONE

PRIMARYFREE

SUPPLE-MENTAL

FREE

RESERVED RESERVED

FREE

EVAPOTRANSPIRATION

BASEFLOW

SUBSURFACEOUTFLOW

DIRECTRUNOFF

Precipitation


Gages used by NWS

Hydrologic ModelHydrologic ModelSacramento Soil Moisture Accounting Model (NWS)Sacramento Soil Moisture Accounting Model (NWS)

(RFC parameters)(RFC parameters)Input time step : 6 hoursInput time step : 6 hours

Output time step : 24 hoursOutput time step : 24 hours

Leaf River Near CollinsMississippi

USGS # 02472000

Basin Area : 753 mi2

PERSIANN Rainfall Estimates in Hydrologic Simulation

Observed

Radar/Gage Merged

OBSERVED vs. SIMULATED DISCHARGE (RADAR/GAGE MERGED RAINFALL ESTIMATES)

Radar/Gauge 6-hour Rainfall

Observed

Radar/Gage Merged

TRMM/Multi Satellite

OBSERVED vs. SIMULATED DISCHARGE (TRMM-MULTI SATELLITE RAINFALL ESTIMATES)

PERSIANN 6-hour Rainfall

3.0

1)1( 3.0

flowflowdtransforme


Basin Scale Precipitation Data Merging

ii : Hydro. Model parameters : Hydro. Model parametersQ : Output Q : Output

P : Input P : Input : Errors: ErrorsI : Weighting parameters

I : Bias parameters

outputoutput

HydrologicModel (i)

Optimization

QQttobsobs

Qttcompcomp

((I, Model ))

(g , g)

(s , s)

Pi

Ps

Pg

)1()()1()()( sssgggm tPtPtP Hydrologic Model (SAC-SMA Model)


.)|*(pProbability distribution

to be maximized

*

180 190 200 210 220 230 240 250 260 270 2800

5

10

15

20

= observations

= simulated flows

*

Hours

Flo

w

Parameter Calibration


.)|*(p

Uncertainty of Parameters

*

Hours180 190 200 210 220 230 240 250 260 270 2800

5

10

15

20

Uncertaintyassociatedwith parameters

Total Uncertaintyincluding structuralerrors

Probability distributionto be maximized

95%

*


Bayesian Model Analysis

• Learn model parameters from data:

• p(ө): Priori distribution of parameters• p(D|ө): Likelihood function• p(ө|D): Posterior distribution of parameters

)(

)()|()|(

Datap

pDatapDatap


Markov Chain Monte Carlo (MCMC) Sampling

Probability distributionto be maximized w.r.t

.)|( tp

t

Current guess


Always accept

.)|( tp

t

New guess

.)|1( tp

1t

.)|( tp

.)|1( tp > 1


100% acceptance of new points having higher probability than the old point


Accept if R ~ Uniform (0,1)

MCMC – Acceptance of New Points Having Lower Probability than the Old Point is Probabilistic

If the ratio is small, then the probability of acceptance is small

.)|( tp

.)|1( tp 1t t

.)|( tp

.)|1( tp < 1


α% acceptance of new points having lower probability than the old point


Rainfall Runoff Time Series

Gages used by NWS

Leaf River Near CollinsMississippi

USGS # 02472000

Basin Area : 753 mi2 Str

eam

flow

(C

MS

D)

Pre

cipi

tatio

n(m

m/d

ay)

Ga

ug

eP

ER

SIA

NN

Time: Day


Runoff Forecasting from Gauge, PERSIANN, and Merged Rainfall

0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

900

1000

Time: Day

Str

em

flow

: C

MS

-Day

Streamflow Simulation

Gauged Rain SimulatedSatellite-based Rain SimulatedMerged Rain SimulatedObserved

50100

50100

50100 Gauge Rainfall

Satellite: PERSIANN Rainfall

Merged Rainfall

Rai

nfa

ll (m

m/d

ay)

500

1000

0

250

750

Str

eam

flo

w

(m3

/day

)

Gauge PERSIANN MergedRMSE 51.82 80.78 34.91 CMSD Corr. 0.876 0.706 0.901Bias 15.34 -17.68 -3.52 CMSD

0 100 200 300

Time (Day)


Parameter Distribution

Distribution of Merging Parameters(5000 samples)

-1 -0.5 0 0.5 10

100

200

300

400

500

Bias(Gauge): Bg

Sam

ple

Cou

nts

-1 -0.5 0 0.5 10

100

200

300

400

500

Bias(Satellite): Bs

Sam

ple

Cou

nts

0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

Weight(Satellite): Ws

Sam

ple

Cou

nts

0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

Weight(Gauge): Wg

Sam

ple

Cou

nts

Weighting factor (αg ) Weighting factor (αs )

Bias parameter (βg ) Bias parameter (βs )

)1()()1()()( sssgggm tPtPtP


Interaction Between Parameters

Parameter: αg Parameter: αg

Parameter: αs Parameter: βg

Par

amet

er:

βg

Par

amet

er:

αs

Par

amet

er:

βg

Par

amet

er:

βs

)1()()1()()( sssgggm tPtPtP


Confidence Interval of Merged Rainfall (95%)

95% confidence interval


0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

900

1000

Time: Day

Str

eam

flow

: C

MS

-D

95% Conference Bounds of Simulated Streamflow

Ra

infa

ll (

mm

/da

y)

40

80

120

0

0

200

400

600

800

Str

ea

mfl

ow

(m

3/d

ay

)

0 100 200 300

Precipitation

95% Uncertainty Bound



Observed Streamflow

the 3rd workshop of the international precipitation working group, 23-27 october, 2006

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