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Basin Scale Precipitation Data Merging Using Markov Chain Monte Carlo Method K. Hsu, F. Boushaki, S. Sorooshian, and X. Gao Center for Hydrometeorology and Remote Sensing University of California Irvine. The 3rd Workshop of the International Precipitation Working Group, 23-27 October, 2006. - PowerPoint PPT Presentation
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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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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)
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
PERSIANN-CCS (Cloud Classification System)
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
6-Hour Accumulated Rainfall: Hurricane Ivan
hydis8.eng.uci.edu/CCS
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Precipitation Measurement is one of the KEY
hydrologic Challenges
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
)(%20)( tPt
Streamflow Simulation vs. Precipitation Uncertainty:
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
)(%25)( tPt
Streamflow Simulation vs. Precipitation Uncertainty:
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
)(%50)( tPt
Streamflow Simulation vs. Precipitation Uncertainty:
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
RadarGauge
Surface TemperatureSoil MoistureVegetation
LABZ
Multiple Sources for Rainfall Estimation
Geosynchronous SatellitesVIS, IR, Sounding
Low Orbiting SatellitesVIS, IR, MV, and Radar
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Basin Scale Precipitation Data Merging
INTERFLOWSURFACERUNOFF
INFILTRATIONTENSION
TENSION TENSION
PERCOLATION
LOWERZONE
UPPERZONE
PRIMARYFREE
SUPPLE-MENTAL
FREE
RESERVED RESERVED
FREE
EVAPOTRANSPIRATION
BASEFLOW
SUBSURFACEOUTFLOW
DIRECTRUNOFF
Precipitation
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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)
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
.)|*(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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
.)|*(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%
*
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Markov Chain Monte Carlo (MCMC) Sampling
Probability distributionto be maximized w.r.t
.)|( tp
t
Current guess
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Always accept
.)|( tp
t
New guess
.)|1( tp
1t
.)|( tp
.)|1( tp > 1
Markov Chain Monte Carlo (MCMC) Sampling
100% acceptance of new points having higher probability than the old point
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Markov Chain Monte Carlo (MCMC) Sampling
α% acceptance of new points having lower probability than the old point
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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)
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
Confidence Interval of Merged Rainfall (95%)
95% confidence interval
Center for Hydrometeorology and Remote Sensing, University of California, Irvine
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
99% Uncertainty Bound
95% Uncertainty Bound
Observed Streamflow
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