A Statistical-Distributed Hydrologic Model for Flash Flood Forecasting

1. A Statistical-Distributed Hydrologic Model for Flash Flood Forecasting International Workshop on Flash Flood Forecasting March 13, 2006 Seann Reed1, John Schaake1, Ziya Zhang1,3 1Hydrology Laboratory, Office of Hydrologic Development NOAA National Weather Service, Silver Spring, Maryland 2Consultant to Office of Hydrologic Development, Annapolis, MD 3University Corporation for Atmospheric Research

2. Flash Flood Forecasting Goals and Strategies • Goals • Improve accuracy • Improve lead times • Hydrologic Modeling Strategies • Investigate a statistical-distributed hydrologic model • Understand model errors at flash flood scales • Compare distributed model results to FFG results • Validate inherent bias correction of the statistical-distributed model • Investigate the use of high resolution, short-term QPF grids to force the statistical-distributed model • Force the model with grids from the Multisensor Precipitation Nowcaster (MPN)

3. Wet 285 km2 Runoff Depth Dry TR 1650 km2 800 km2 FFGW FFGD Rainfall Depth Scale mismatch! NWS Flash Flood Guidance (FFG) (1) River Forecast Center (RFC) Maintains 6 hr Lumped Model TR = Threshold runoff (2) RFC Runs Flash Flood Guidance System Forecast points 1 hr Gridded FFG (3) RFC transmits FFG to Weather Forecast Offices (WFO) (4) Forecaster compares mean areal basin rainfall (ABR) to FFG in in small, flashy basins (5 - 260 km2).

4. Distributed model (uncalibrated). Each point is an average peak flow error from approximately 25 events over an eight year study period. Log-linear regression for distributed model data Scaling relationship for an uncertainty index (Rq) from Carpenter and Georgakakos (2004) (secondary axis) High Resolution Modeling Brings Potential Benefits but Also Increased Uncertainty • FFG system uses lumped (260 – 4000 km2) soil moisture states. • A distributed hydrologic model can make computations at spatial and temporal scales consistent with flash flooding. • Model errors tend to increase at smaller modeling scales. • Will increased model errors in small basins mask the benefits of making calculations at the appropriate scales? Flash floods 260

5. A Statistical-Distributed Model for Flash Flood Forecasting at Ungauged Locations Real-time QPE/QPF simulated historical peaks (Qsp) Archived QPE Initial hydro model states Frequency thresholds Real-time Historical • The statistical-distributed model produces gridded flood frequency forecasts. • We express flood frequencies in terms of the Average Recurrence Interval (ARI) associated with the annual maximum flood. Distributed hydrologic model Distributed hydrologic model Simulated peaks distribution (Qsp) (unique for each cell) Max forecast peaks Statistical Post-processor Local/regional knowledge Compare Forecast frequencies

6. Why a frequency-based approach? • Frequency grids provide a well-understood historical context for characterizing flood severity; values relate to engineering design criteria for culverts, detention ponds, etc. • Computation of frequencies using model-based statistical distributions can inherently correct for model biases. • This hypothesis is validated through probability matching at gauged locations (results in slide 10)

7. Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) • This implementation of HL-RDHM uses: • 2 km grid cell resolution • 8 years of hourly, 4 km QPE and QPF grids are resampled to 2 km (nearest neighbor resampling) • Gridded SAC-SMA • Hillslope routing within each model cell • Cell-to-cell channel routing • Uncalibrated, a-priori parameters for Sacramento (SAC-SMA) and channel routing models (Koren et al., 2004) • Similar HL-RDHM implementations showed good performance in the Distributed Model Inter-comparison Project (DMIP) (Smith et al., 2004; Reed et al., 2004) • An operational prototype version of HL-RDHM is running at two NWS River Forecast Centers (slated for official delivery in Fall 2006)

8. Study Basins N INX Radar AR OK SRX Radar Basins are well covered by either the INX or SRX radar Interior, Flash flood basins

9. Distributed Model Simulations Compared to FFG-Like Simulations for the 5 Smallest Basins (for events from Oct. 1996 – Sept. 2004) Average absolute percent peak flow errors Correlation coefficients (37 km2) (49 km2) (65 km2) (90 km2) (105 km2) • Peak flow errors are averages from approximately 25 events over an eight year study period. Peak flow errors are computed regardless of time. • Correlation coefficients are based on the same events.

10. Inherent Bias Adjustment • We suggest that the comparing model-calculated frequencies to frequency-based thresholds can produce an inherent bias correction. • To validate this concept, we compute inherent adjustments at validation points using probability matching. This adjustment is only done for validation as we do not have the techniques and data to make explicit adjustments at ungauged locations.

11. Distributed, Uncalibrated Distributed, Uncalibrated w/ Adjustment 2 year flood flow Gain from Inherent Bias Adjustment Best basin: inherent adjustment improves peak results by 14% on average Worst basin: inherent adjustment degrades peak results by 1% on average One inconsistently simulated event has a big impact

12. Maximum Forecast Frequencies at 4 Times on 1/4/1998 (Generated in hindcast mode using QPE up to the forecast time and 1 hr nowcast QPF beyond) 14 UTC 15 UTC In these examples, frequencies are derived from routed flows, demonstrating the capability to forecast floods in locations downstream of where the rainfall occurred. 16 UTC 17 UTC

13. Conclusions • At scales down to 40 km2, results show gains from the distributed model over the current FFG method even from an uncalibrated distributed model • Inherent bias adjustment in the statistical-distributed model further improves results • Even further gains are possible with distributed model calibration (not shown here) • In forecast mode, gridded QPF data from MPN can be used to force the model and gain lead time • We have begun evaluating forecast case studies using both QPE and QPF (not shown here)