# Presentation: 066127

## 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

## 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)

**Notes:**
Other studies have shown that one QPF/nowcast technique may produce the best rainfall field in terms of RMSE compared with an observed rainfall field while a different technique produces the best hydrograph (Berenguer and RJ Moore)

We also have proposed work ingesting forecast fields from a high resolution dynamic weather model (WRF)

## NWS Flash Flood Guidance (FFG)

**(1) River Forecast Center (RFC)**
**Maintains 6 hr Lumped Model**

- Forecast points

**(2) RFC Runs Flash Flood Guidance System**

**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 km****2**).

- TR = Threshold runoff

**Notes:**
The River Forecast Center generates a rainfall-runoff curve in real-time for each duration of interest and each basin defined in their river models.
Threshold runoff values are used to derive the amount of rain needed to cause a flood

FFG is the depth of rain required over a specific duration (1 hr, 3 hr, 6 hr) to cause flooding in an area
Threshold runoff (ThreshR) is the depth of runoff required over a specific duration (1 hr, 3 hr, 6 hr) to cause flooding in an area

Two issues:  1 is the Issue of modeling scale (both spatial and temporal scales) [science issue] and another is the issue of update scales [operational issue].  

Bob Davis at WFO Pittsburgh has rules of thumb:  
FF0: minor flooding (0 difference between rainfall accumulation and FFG)
FF1: significant flooding
FF2: serious flash flooding
FF3 or higher:  disastrous flash flooding 

## High Resolution Modeling Brings Potential Benefits but Also Increased Uncertainty 

- 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

## A Statistical-Distributed Model for Flash Flood Forecasting at Ungauged Locations 

- Forecast
- frequencies

**A Statistical-Distributed Model for Flash Flood Forecasting at Ungauged Locations**

- Historical

- Real-time

- Simulated peaks distribution (Qsp) (unique for each cell)

- Statistical
- Post-processor

- Distributed hydrologic model

- Distributed hydrologic model

- Max forecast
- peaks

-   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.

- Local/regional knowledge

**Compare**

## 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)

## 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)

**Notes:**
Explicit soil rainfall/runoff modeling on each computational element. 

Koren, V.I., Reed, S.M., Smith, M., Zhang, Z., Seo, D.J., 2004:  Hydrology laboratory research modeling system (HL-RMS) of the US national weather service. Journal of Hydrology, 291, 297-318.

## Study Basins

- OK

- AR

- INX Radar

- SRX Radar

**Interior,**
**Flash flood**
**basins**

- Basins are well covered by either the INX or SRX radar

**Notes:**
Estimated as the average difference between the time of maximum rainfall and maximum discharge for several events.

## Distributed Model Simulations Compared to FFG-Like Simulations

- 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.

**Distributed Model Simulations Compared to FFG-Like Simulations**
**for the 5 Smallest Basins**
- (for events from Oct. 1996 – Sept. 2004)

**Correlation coefficients**

**Average absolute percent peak flow errors**

- (37 km2)

- (49 km2)

- (65 km2)

- (105 km2)

- (90 km2)

**Notes:**
Note:  I think the reason that the statistical adjustment doesn’t help in Christi may be because two events in the historical record are high overestimates which makes the statistical model tend to want to reduce the flows even though forecasts for most other events are underestimates. I need to look into this further.  I discovered this when looking at the MPE reanalysis results. 

Initial results show gains over the lumped approach even from an uncalibrated distributed model at interior points. 

 Inherent bias adjustment in the statistical-distributed model further improves results.

 Further gains are possible with distributed model calibration (not shown here)

## 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.

## Gain from Inherent Bias Adjustment

- Worst basin: inherent adjustment degrades peak results by 1% on average

- Best basin:  inherent adjustment improves peak results by 14% on average

- One inconsistently simulated event has a big impact

## Maximum Forecast Frequencies at 4 Times on 1/4/1998 

- 14 UTC

- 15 UTC

- 16 UTC

- 17 UTC

- 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)

- In these examples, frequencies are derived from routed flows, demonstrating the capability to forecast floods in locations downstream of where the rainfall occurred.

**Notes:**
Each cell contains the frequency of the maximum flow forecasted in the next 4 days at the given forecast time.
Note that the model can forecast floods in counties downstream of where the primary rainfall/runoff occurs.

## 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)