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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

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

Enrique R. Vivoni1, Dara Entekhabi2 and Ross N. Hoffman3

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

September 21, 2006

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Motivation Fully-Distributed Flood Forecasting Model

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

  • Combined Radar QPF-Distributed QFF

  • 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 Precipitation Forecasts (QPFs) using Radar Nowcasting

Nowcasting of Radar Quantitative Precipitation Estimate (QPE)

Quantitative Flood Forecasts (QFFs) using Distributed Hydrologic Modeling

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Combined Rainfall-Flood Forecasting Fully-Distributed Flood Forecasting Model

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

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

Interpolation Forecast Mode



Lead Time

Vivoni et al. (2006)

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STNM Radar Rainfall Nowcasts Fully-Distributed Flood Forecasting Model

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

Envelope Motion

MIT Lincoln Lab

Storm Tracker

Model (STNM)

Van Horne et al. (2006)

Small-scale Features

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Distributed Hydrologic Modeling Fully-Distributed Flood Forecasting Model

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

  • 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.

Surface-subsurface hydrologic processes over complex terrain.

Ivanov et al. (2004a,b)

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Study Area Fully-Distributed Flood Forecasting Model

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 km2 basins

  • 52, 13 and 10 (4 km) radar cells

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Baron Fork 808 km Fully-Distributed Flood Forecasting Model2

Basin 12 0.8 km2

Basin Data and Interior Gauges

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

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Hydrometeorological Flood Events Fully-Distributed Flood Forecasting Model

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

Jan 98

Oct 98

  • Fall Squall Line:

  • Concentrated rain accumulation.

  • Decaying flood wave produced in Dutch Mills.

  • Winter Front:

  • Banded rain accumulation.

  • 7-yr flood event at Baron Fork.

Jan 98

Oct 98



Rainfall (mm/h)

Discharge (m3/s)

Rainfall (mm/h)

Discharge (m3/s)

Simulation Hours

Simulation Hours

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Multi-Gauge Model Calibration Fully-Distributed Flood Forecasting Model

January 1998

October 1998

Baron Fork

(808 km2)

Dutch Mills

(107 km2)

Peacheater Creek

(65 km2)

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Rainfall and Runoff Forecasts Fully-Distributed Flood Forecasting Model

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

January 1998

October 1998

  • Multiple QPF and QFF Realizations

  • 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 (tL).

  • 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





Vivoni et al. (In Press)

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Flood Forecast Skill Fully-Distributed Flood Forecasting Model

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


Increasing Skill


Decreasing Skill


Vivoni et al. (2006)

At 1-hr Lead Time

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Radar Nowcast Error Propagation Fully-Distributed Flood Forecasting Model

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

  • Bias defined as:

    • where F = forecast mean

    • O = QPE mean

  • indicates discharge bias increases more quickly than rainfall bias.

  • Mean Absolute Error defined as:

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

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

  • Mean Absolute Error Propagation

    Bias Propagation

    Slope = 1.3 for January

    = 2.6 for October

    Slope = 0.099 for January

    = 0.105 for October

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    Error Dependence on Basin Scale Fully-Distributed Flood Forecasting Model

    Propagation of radar nowcasting errors is reduced with increasing catchment scale (area) over range 0.8 to 800 km2.

    1-hr Lead Time

    2-hr Lead Time

    • Bias Ratio defined as:

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

    • Mean Absolute Error ratio is:

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

    Vivoni et al. (In Press)

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    Final Remarks Fully-Distributed Flood Forecasting Model

    • We have analyzed the propagation of radar nowcasting errors to distributed flood forecasts using two forecast models.

    • The study results reveal:

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

    • 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.

    • 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 Fully-Distributed Flood Forecasting Model

    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).