Error Propagation from Radar Rainfall Nowcasting Fields to a Fully-Distributed Flood Forecasting Model

Enrique R. Vivoni

1

, Dara Entekhabi

2

and Ross N. Hoffman

3

1. Department of Earth and Environmental Science New Mexico Institute of Mining and Technology 2. Department of Civil and Environmental Engineering Massachusetts Institute of Technology 3. Atmospheric and Environmental Research, Inc.

ERAD 2006 Conference, Barcelona, Spain

Motivation

Radar nowcasting and distributed watershed modeling can improve prediction of hydrologic processes across basin scales.

Nowcasting of Radar Quantitative Precipitation Estimate (QPE)

Combined Radar QPF-Distributed QFF

Quantitative Precipitation Forecasts (QPFs) using Radar Nowcasting

• How does rainfall forecast skill translate to flood forecast skill?

• What are the effects of lead time and basin scale on flood forecast skill? • Does a hydrologic model dampen or amplify nowcasting errors? Why?

• How do errors propagate into the flood predictions as a function of scale?

Quantitative Flood Forecasts (QFFs) using Distributed Hydrologic Modeling

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Combined Rainfall-Flood Forecasting

The distributed QPF and QFF models are combined using a method denoted as the Interpolation Forecast Mode.

Interpolation Forecast Mode t L

Lead Time

t L Vivoni et al. (2006) Interpolation Forecast Mode

• Multiple QPEs available at a specific time interval (depending on radar estimation technique).

• Nowcasting QPF generated from available QPEs to ‘fill in’ periods with no radar observations. • QPEs + Radar Nowcasting QPFs fused according to lead time prior to forcing input into distributed model.

• Forecast lead time (t

L

) is varied from 15-min to 3-hr to introduce radar nowcasting errors into QFF.

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STNM Radar Rainfall Nowcasts

Rainfall forecasting using scale-separation extrapolation allows for predictability in the space-time distribution of future rain.

Large-scale Features STNM Nowcasting Model

• Predictability in rainfall over 0-3 hr over regional, synoptic scales.

• Forecast of space-time rainfall evolution suited for linear storm events (e.g. squall lines).

• Tested over ABRFC over 1998-1999 period using NEXRAD, WSI data.

• Skill is a function of lead time, rainfall intensity and verification area.

Unfiltered Radar Rainfall

MIT Lincoln Lab Storm Tracker Model (STNM)

Envelope Motion Van Horne et al. (2006) Small-scale Features 4

Distributed Hydrologic Modeling

TIN-based Real-time Integrated Basin Simulator (tRIBS) is a fully-distributed model of coupled hydrologic processes.

Surface-subsurface hydrologic processes over complex terrain. Ivanov et al. (2004a,b) Distributed Hydrologic Modeling

• Coupled vadose and saturated zones with dynamic water table.

• Moisture infiltration waves. • Soil moisture redistribution.

• Topography-driven lateral fluxes in vadose and groundwater.

• Radiation and energy balance.

• Interception and evaporation.

• Hydrologic and hydraulic routing.

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Study Area

Radar rainfall over ABRFC used as forcing to hydrologic model operated over multiple stream gauges in the Baron Fork, OK.

NEXRAD-based Rainfall

• WSI (4-km, 15-min) NOWrad • STNM nowcasting algorithm • Transformed to UTM 15 • Clipped to Baron Fork basin

Basin QPFs

• 808, 107 and 65 km 2 basins • 52, 13 and 10 (4 km) radar cells

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Basin Data and Interior Gauges

Soils and vegetation distribution used to parameterize tRIBS model. Fifteen gauges (range of A, t C ) used for model flood forecasts.

Baron Fork 808 km 2 Basin 12 0.8 km 2

Basin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A (km 2 ) 108.23

65.06

12.14

2.67

1.41

450.26

365.25

182.91

49.07

21.18

4.29

0.78

610.60

808.39

106.91

D (km -1 ) 0.99

0.83

0.81

0.77

0.83

0.84

0.82

0.82

0.87

0.87

0.77

0.31

0.84

0.86

0.84

t c (h) 5.78

4.03

1.67

0.93

0.51

7.25

6.27

5.44

2.16

1.50

0.55

0.19

9.26

12.59

3.32

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Hydrometeorological Flood Events

Two major flood events: January 4-6, 1998 and October 5-6, 1998 varied in the basin rainfall and runoff response.

Jan 98 Winter Front: Oct 98 Fall Squall Line:

• Banded rain accumulation.

• 7-yr flood event at Baron Fork.

• Concentrated rain accumulation.

• Decaying flood wave produced in Dutch Mills.

Jan 98 Oct 98 BF DM Simulation Hours 8 Simulation Hours

Multi-Gauge Model Calibration

January 1998 October 1998 Baron Fork (808 km 2 ) Dutch Mills (107 km 2 ) Peacheater Creek (65 km 2 ) 9

Rainfall and Runoff Forecasts

Radar nowcasting QPFs and distributed QFFs are tested in reference to the radar QPE and its modeled hydrologic response.

January 1998 MAP October 1998 MAP Multiple QPF and QFF Realizations Outlet Vivoni et al. (In Press) Outlet

• Solid black lines represent QPE Mean Areal Precipitation (MAP) and Outlet discharge at Baron Fork.

• Thin gray lines are Nowcast QPF MAP and Outlet discharge for 12 different lead times (t

L

). • Two events had varying rainfall amounts and runoff transformations: • January Q/P = 1.20 • October Q/P = 0.24 • January Recurrence = 6.75 yr • October Recurrence = 1.43 yr • January Basin Lag = 13.3 hr • October Basin Lag = 15.3 hr

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Flood Forecast Skill

Flood forecast skill decreases as a function of lead time and increases with basin area for the two storm events.

Lead-Time Dependence Catchment Scale Dependence QPE 2-hr Vivoni et al. (2006) Increasing Skill

At 1-hr Lead Time

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Radar Nowcast Error Propagation

Statistical measures of error propagation show that nowcasting errors are amplified in the flood forecast as lead time increases. Bias Propagation

Slope = 1.3 for January = 2.6 for October

Mean Absolute Error Propagation

Slope = 0.099 for January = 0.105 for October

• Bias defined as:

B



F O

where F = forecast mean O = QPE mean indicates discharge bias increases more quickly than rainfall bias.

• Mean Absolute Error defined as:

MAE

 1

N i N

  1

O i



F i

shows that increase in rainfall MAE leads to higher discharge MAE.

• Note the strong impact of the increasing forecast lead time.

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Error Dependence on Basin Scale

Propagation of radar nowcasting errors is reduced with increasing catchment scale (area) over range 0.8 to 800 km 2 .

1-hr Lead Time 2-hr Lead Time

• Bias Ratio defined as:

B

ratio 

B dis B rain

indicates comparable bias for large basins and large variability in B ratio for small basins.

• Mean Absolute Error ratio is:

MAE

ratio 

MAE dis A

*

MAE rain

shows small basins either amplify or dampen errors, while at large scales errors tend to cancel out.

Vivoni et al. (In Press) 13

Final Remarks

We have analyzed the propagation of radar nowcasting errors to distributed flood forecasts using two forecast models. The study results reveal:

(1) Increasing the forecast lead time results in nowcasting errors which are amplified in the flood forecast at the basin outlet.

(2) Catchment scale controls whether rainfall forecast errors are strongly amplified or dampened (in small basins) or effectively comparable to (in large basins) flood forecast errors.

(3) Differences in storm characteristics (winter air mass vs. fall squall line) have a strong effect on the error propagation characteristics.

To best utilize the distributed nature of the forecast models, a next step would be utilizing spatial metrics to assess error propagation from rainfall to soil moisture fields.

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References

Ivanov, V.Y., Vivoni, E.R., Bras, R.L. and Entekhabi, D. 2004a. Preserving High-Resolution Surface and Rainfall Data in Operational-scale Basin Hydrology: A Fully-distributed Physically-based Approach. Journal of Hydrology. 298(1-4): 80-111. Ivanov, V.Y., Vivoni, E.R., Bras, R. L. and Entekhabi, D. 2004b. Catchment Hydrologic Response with a Fully-distributed Triangulated Irregular Network Model. Water Resources Research. 40(11): W11102, 10.1029/2004WR003218. Van Horne, M.P., Vivoni, E.R., Entekhabi, D., Hoffman, R.N. and Grassotti, C. 2006. Evaluating the effects of image filtering in short-term radar rainfall forecasting for hydrological applications. Meteorological Applications. 13(3): 289-303. Vivoni, E.R., Entekhabi, D., Bras, R.L., Ivanov, V.Y., Van Horne, M.P., Grassotti, C. and Hoffman, R.N. 2006. Extending the Predictability of Hydrometeorological Flood Events using Radar Rainfall Nowcasting. Journal of Hydrometeorology. 7(4): 660-677. Vivoni, E.R., Entekhabi, D. and Hoffman, R.N. 2006. Error Propagation from Radar Rainfall Nowcasting Fields to a Fully-Distributed Flood Forecasting Model. Journal of Applied Meteorology and Climatology. (In Press).

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