Basin Scale Precipitation Data Merging Using Markov Chain

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 3 rd Center Workshop of the International Precipitation Working Group, 23 -27 October, 2006 for Hydrometeorology and Remote Sensing, University of California, Irvine

Outline Ø PERSIANN Rainfall Ø Precipitation Data Merging Ø Grid-Based Precipitation Data Merging Ø Basin Scale Precipitation Data Merging Ø Case Study Ø Summary Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) Products PERSIANN System “Estimation” Hourly Global Precipitation Estimates ANN High Temporal-Spatial Res. Cloud Infrared Images MW-RR (TRMM, NOAA, DMSP Satellites) Sampling Feedback Satellite Data Global IR Error Detection Hourly Rain Estimate Quality Control Ground Observations MW-PR Hourly Rain Rates GPCC & CPC Gauge Analysis Merged Products - Hourly rainfall - 6 hourly rainfall - Daily rainfall - Monthly rainfall Gauges Coverage Center for Hydrometeorology and Remote Sensing, University of California, Irvine for Hydrometeorology and Remote Sensing, University of California, Merging

PERSIANN-CCS (Cloud Classification System) Center for Hydrometeorology and Remote Sensing, University of California, Irvine

PERSIANN Precipitation Products Global PERSIANN: http: //hydis 8. eng. uci. edu/hydis-unesco/ 0. 25 ox 0. 25 o Hourly US PERSIANN-CCS: http: //hydis 8. eng. uci/CCS 0. 04 ox 0. 04 o Hourly 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 High resolution precipitation data are needed for hydrologic applications in SW. PERSIANN CCS (0. 04° 0. 04°) 07/24 -27/2006 Severe storms propagate from 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. Radar beams (3 -km above ground level) are blocked by mountains in southwest United States. Strong convections start over mountains where radar coverage is poor. PERSIANN monitors the lifetimes of storm systems and provides information for early warning. 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 hydis 8. 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

i Hydrologic Models R IA Sacramento Model F t q API Model QR Q t. B VIC Model Mike SHE Model, DHI Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Streamflow Simulation vs. Precipitation Uncertainty: Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Streamflow Simulation vs. Precipitation Uncertainty: Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Streamflow Simulation vs. Precipitation Uncertainty: Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Multiple Sources for Rainfall Estimation Low Orbiting Satellites VIS, IR, MV, and Radar Geosynchronous Satellites VIS, IR, Sounding Radar LABZ Gauge Surface Temperature Soil Moisture Vegetation Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Grid-Based Data Merging Bias Correction and Downscaling of Daily Rainfall to Hourly Rainfall Downscaled to Hourly Rainfall CPC Daily Gauge Analysis Grid size: 0. 04 ox 0. 04 o Daily Rainfall: Summer 2005 PERSIANN Rainfall (non-adjusted) PERSIANN Rainfall (bias adjusted) Grid size: 0. 25 ox 0. 25 o PERSIANN Rainfall CPC Daily Analysis Time Step: Day Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Basin Scale Precipitation Data Merging Center for Hydrometeorology and Remote Sensing, University of California, Irvine

PERSIANN Rainfall Estimates in Hydrologic Simulation OBSERVED vs. SIMULATED DISCHARGE (RADAR/GAGESATELLITE MERGED RAINFALL (TRMM-MULTI RAINFALLESTIMATES) Radar/Gauge 6 -hour Rainfall PERSIANN 6 -hour Observed Radar/Gage Merged TRMM/Multi Satellite Gages used by NWS Leaf River Near Collins Mississippi USGS # 02472000 Basin Area : 753 mi 2 Hydrologic Model Sacramento Soil Moisture Accounting Model (NWS) (RFC parameters) Input time step : 6 hours Output time step : 24 hours Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Basin Scale Precipitation Data Merging Hydrologic Model (SAC-SMA Model) Pg Ps ( g , g) Pi Hydrologic Model ( i) ( s , s) Optimization output Qtcomp Qtobs P : Input Q : Output I : Weighting parameters ( I, Model ) : Errors i : Hydro. Model parameters I : Bias parameters Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Parameter Calibration Probability distribution to be maximized * = observations Flow = simulated flows Hours Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Uncertainty of Parameters Probability distribution to be maximized 95% Uncertainty associated with parameters Total Uncertainty including structural errors Hours Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Bayesian Model Analysis • Learn model parameters from data: • p(ө): • p(D|ө): • p(ө|D): Priori distribution of parameters Likelihood function Posterior distribution of parameters Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Markov Chain Monte Carlo (MCMC) Sampling Probability distribution to be maximized w. r. t Current guess Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Markov Chain Monte Carlo (MCMC) Sampling 100% acceptance of new points having higher probability than the old point >1 Always accept New guess Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Markov Chain Monte Carlo (MCMC) Sampling α% acceptance of new points having lower probability than the old point <1 Accept if a > R ~ Uniform (0, 1) If the a ratio is small, then the probability of acceptance is small Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Gages used by NWS Leaf River Near Collins Mississippi USGS # 02472000 Basin Area : 753 mi 2 Gauge PERSIANN Streamflow (CMSD) Precipitation (mm/day) Rainfall Runoff Time Series Time: Day Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Runoff Forecasting from Gauge, PERSIANN, and Merged Rainfall Gauge Rainfall (mm/day) 100 50 Satellite: PERSIANN Rainfall 100 50 Merged Rainfall 100 50 1000 RMSE Corr. Bias Streamflow (m 3/day) 750 Gauge PERSIANN 51. 82 80. 78 0. 876 0. 706 15. 34 -17. 68 Merged 34. 91 CMSD 0. 901 -3. 52 CMSD 500 250 0 0 200 100 Center for Hydrometeorology and Remote Sensing, University of California, Irvine Time (Day) 300

Parameter Distribution of Merging Parameters(5000 samples) Weighting factor (αg ) Bias parameter (βg ) Weighting factor (αs ) Bias parameter (βs ) Center for Hydrometeorology and Remote Sensing, University of California, Irvine

Parameter: αs Parameter: βg Interaction Between Parameters Parameter: αg Parameter: βs Parameter: αg Parameter: αs Parameter: βg 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

Rainfall (mm/day) 120 Precipitation 95% Uncertainty Bound 80 40 0 99% Uncertainty Bound Streamflow (m 3/day) 800 95% Uncertainty Bound Observed Streamflow 600 400 200 0 0 100 200 Center for Hydrometeorology and Remote Sensing, University of California, Irvine 300