Short and Medium Range Ensemble Streamflow Prediction John
Short and Medium Range Ensemble Streamflow Prediction John Schaake COMET Advanced Hydrologic Sciences Class August 6, 2008
Elements of a Hydrologic Ensemble Prediction System QPE, QTE, Soil Moisture QPF, QTF Data Assimilator Hydrology & Water Resources Models Streamflow Ensemble Post. Processor Parametric Uncertainty Processor Ensemble Verification System Ensemble Pre. Processor Hydrology & Water Resources Ensemble Product Generator Fig 1
Some Elements of Hydrologic Forecasting ESP forecasts typically are made for many forecast points in a river basin using a distributed (or quasidistributed) hydrologic model River basins are partitioned into connected segments (which may include elevation zones, reservoirs, river routing segments, etc. ) Hydrologic models are calibrated (i. e. parameters are estimated) using historical data Recent observations (precipitation, temperature, SWE, streamflow are used to estimate inititial conditions at the time a forecast is created.
ESP Forecast Process Raw Atmospheric Forecasts Intitial Conditions EPP ESP Model Parameters Raw ESP Hydrographs
ESP Input Requirements • Forecast precipitation and temperature ensemble forcing: – For every forecast segment – Member time series at ~6 hr step for entire forecast period – Individual members must be “consistent” over all segments and for the entire forecast period.
ESP Input Requirements (cont’d) • Statistical Properties: – Ensembles must be unbiased at all time and space scales and for all lead times – Ensembles must account for space/time scale dependency in the variability of precipitation and temperature and in the forecast uncertainty at all space and time scales – Each member must be equally likely to occur (i. e. a random sample)
precip. depth (mm) spa RA H ( ce 4 c ns) sp ace bi P A (HR precip. depth (mm) 4 a ins Pb ) s) 4 b 4 d A spa c spa HR e( c in Pb ) ins Pb RA H ( e precip. depth (mm)
Hydrology is Sensitive to Precipitation Variability: Spatial Scale Dependency Example • Total runoff from 64 x 64 4 km grid domain • Several years of Stage III, 1 -hr, QPE • 7 Area Segmentations: 1, 2, 4, 6, 16, 32, 64 pixels • Same model/parameters used for each segmentation • Graph shows different runoff totals vs size of area segment • Some models more scale dependent than others • Scale dependency is a result of non-linearity THEREFORE: Space/Time Variability of Ensemble Forcing Will Have a Primary Effect on Hydrologic Ensemble Response
Example Ensemble Inputs and ESP Output for American River Basin, CA
Ensemble Temperature Forecast
Ensemble Precipitation Forecast
Ensemble Streamflow Forecast
Raw Atmospheric Forecasts Viewed from a Hydrologic Perspective
NCEP Global Ensemble Forecasts
Rank Histogram
Uncertainty Analysis of Global Ensemble Precipitation Forecasts
Illustration of the scale-dependent skill in GFS ensemble mean winter season precipitation forecasts for the North Fork of the American River Basin. The curve labeled “moving 6 hr window” shows how the correlation between 6 hr precipitation forecasts and corresponding observations decreases with increasing forecast lead time. The curve labeled “average from t=0” shows the correlations averages accumulated over windows beginning at t=0 and corresponding observations decreases as the time to the end of the window increases. The remaining curves are for similar averages that begin at different times after t=0. Fig 5
Forecast Window Width (6 -hr periods) GFS Precipitation Forecast Correlation Coefficient: Temporal Scale-Dependency NFDC 1 HUP – January 15 Forecasts 2 1 w ee ks e it m d ast a le ec g or n f i as of riod e cr nd pe In o e t we ek Forecast Lead Time to Beginning of Forecast Window (6 -hr periods)
Ensemble Pre-Processor (EPP) Objectives • • Produce ensemble forcing for ESP Remove bias in atmospheric forecasts Correct spread problems Preserve space-time variability and uncertainty structure • Downscale atmospheric to forecast basins
EPP 2 – Step Process Raw Atmospheric Forecasts This step assures that members are “consistent” over all basins for the entire forecast period Estimate Probability Distributions Assign Values to Ensemble Members (Schaake Shuffle) This step includes downscaling, and correction of bias and spread problems ESP Input Forcing
Estimate Probability Distributions for each: Time-step, Aggregate Sub-period and Forecast Sub-Area (segment) • Use historical singlevalue forecasts and observations (for a common period of time)
Estimate Probability Distributions (Cont’d) • Estimate climatological distributions of forecasts and observations • Use climatologies to transform forecasts and observations to Standard Normal Deviates • Estimate correlation parameter of Joint Distribution
Calibration Sample Space NQT 0 X Correlation(X, Y) Forecast PDF of STD Normal Joint distribution Y Model Space Observed Y PDF of STD Normal PDF of Observed Joint distribution NQT X Forecast July 15 -17, 2008 National DOH Workshop, Silver Spring, MD
Ensemble Generation Joint distribution Model Space xfcst X Probability 1 Observed Y Conditional distribution given xfcst x 1 … xn Ensemble members Forecast 0 x 1 xi xn Ensemble forecast Obtain conditional distribution given a singlevalue forecast xfcst July 15 -17, 2008 National DOH Workshop, Silver Spring, MD
Use EPP Forecast Probability Distributions to Assign Values to Members) • Divide total forecast period into sub-periods for: – Individual time-steps – Aggregate time periods • Estimate forecast probability distribution for each time-step and each sub-period • Construct ensemble members using “Schaake Shuffle” • Resolve differences between member values for aggregate periods and time-step periods Example Cascade Of Sub-Periods Aggregate periods Individual time steps
Schaake Shuffle For each segment, at each time step, associate forecast ensemble members (left panel) with historical ensemble members (right panel) by rank (and hence year) Historical ensemble distribution 1 1 Probability Conditional distribution given xfcst Probability • 0 0 x 1 xi (1996) xn y 1 yi (1996) yn Historical Ensemble Forecast Ensemble July 15 -17, 2008 National DOH Workshop, Silver Spring, MD
National Weather Service Hydrologic Ensemble Pre-Processor (EPP) GFS Subsystem J. Schaake, R. Hartman, J. Demargne, L. Wu, M. Mullusky, E. Welles, H. Herr, D. J. Seo, and P. Restrepo Average observed values of 6 -hour precipitation corresponding to RFC and GFS forecasts (mm) 6 hr RFC QPF Verifications Files and Operational MAPs RFC-specific Utility Historical 6 hr RFC Operational MAP QPF Data files Operational RFC QPF Files 6 hr MAP Calibration Files MAP Conversion Utility Raw Historical Data Files 6 hr MAP Unformatted Calibration Data Files Continuous Rank Probability Skill Score (CRPSS) for 6 -hour precipitation forecasts Operational GFS Files RFC single-value forecasts Operational Forecast Files Operational Ensemble MAPs Historical GFS Ensemble Mean Precipitation Forecasts (mm) Average forecast values of 6 -hour precipitation for RFC and GFS Pre-Processor Precipitation Algorithms Historical 6 hr RFC Operational MAP Observed Data Files Precipitation Parameters Parameter Estimator Ensemble forecasts based on RFC single-value forecasts Ensemble Generator Hindcast Ensemble MAPs GFS Processor Historical Data Sets GFS single-value forecasts (mm) MAP Area Locations MAP Time Series Identifiers Precipitation Verification Index Files (mm) CFS Ensemble Forecast (Application Under Construction) Data Analysis Ensemble forecasts based on GFS single-value forecasts Verification Results Statistics Average observed values of daily minimum temperature corresponding to RFC and GFS forecasts RFC TMX/TMN Forecast Verification Files and Operational Observed TMX/TMN MOS TMX/TMN Forecast Verification Files Precipitation Ensemble Pre-Processor RFC Historical Operational Observed TMX/TMN RFC-specific Utility RFC Historical Operational Forecast TMX/TMN MOS Utility MAT Analysis Pre-Processor Temperature Algorithms Operational RFC QTF Files Continuous Rank Probability Skill Score (CRPSS) for daily minimum temperature forecasts Operational GFS Files RFC single-value forecasts Operational Forecast Files Operational Ensemble MATs MOS Historical Forecast TMX/TMN Temperature Parameters Parameter Estimator Ensemble forecasts based on RFC single-value forecasts Ensemble Generator Hindcast Ensemble MATs Average forecast values of daily minimum temperature for RFC and GFS 6 hr MAT Calibration Files 6 hr to TMX/TMN Raw Historical Data Files TMX/TMN Calibration Data Conversion Utility CFS Ensemble Forecast (Application Under Construction) TMX: maximum temperature TMN: minimum temperature Historical GFS Ensemble Mean Temperature Forecasts GFS single-value forecasts MAT Area Locations MAT Time Series Identifiers Stations used for MAT Analysis Temperature Normals Temperature Verification Index Files Unformatted TMX/TMN Calibration Data Files Ensemble forecasts based on GFS single-value forecasts Verification Results GFS Processor Historical Data Sets Temperature Ensemble Pre-Processor
CNRFC Ensemble Prototype Smith River Mad River Salmon River Van Duzen River Navarro River American River (11 basins)
Example EPP Hindcast Results for CNRFC Basins
Some EPP Parameters North Fork American River Observed POP Forecast POP Observed CAVG Forecast CAVG
Correlation Coefficient GFS Precipitation Forecast vs Observation North Fork American River Forecast Uncertainty Depends on both Lead-Time and Aggregation. Time Aggregate periods
Bias – NFDC 1 HUF Precipitation Raw Forecasts Ensemble Mean RFC Forecasts GFS Forecasts
GFS Precipitation Forecast Verification North Fork American River Bias Day of Year CRPSS Day of Year Raw GFS Ensemble Mean Forecast Period GFS EPP Prototype Forecast Period
Example ESP Hindcast Results for CNRFC Basins
Short-term Ensemble Prototype NF American (upper subarea) 5 -day Temperature Ensembles
Short-term Ensemble Prototype NF American (upper subarea) 5 -day Precipitation Ensembles QPF = 1. 5 inches in two successive 6 -hr periods, otherwise zero
Short-term Ensemble Prototype NF American 5 -day Streamflow Ensembles
Short-term Ensemble Prototype NF American 5 -day Streamflow Distribution
NFDC 1 – Forecasts and Simulations
CREC 1 – Forecasts and Simulations
NFDC 1 – March 15 Forecasts Cumulative Rank Histograms
Thank You
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