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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 ScienceNew 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
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
Quantitative Flood Forecasts (QFFs) using Distributed Hydrologic Modeling
Nowcasting of Radar Quantitative Precipitation
Estimate (QPE)
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The distributed QPF and QFF models are combined using a method denoted as the Interpolation Forecast Mode.
Combined Rainfall-Flood Forecasting
tL tLLead Time
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 QPFsfused 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.
Vivoni et al. (2006)
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MIT Lincoln LabStorm Tracker Model (STNM)
Rainfall forecasting using scale-separation extrapolation allows for predictability in the space-time distribution of future rain.
STNM Radar Rainfall Nowcasts
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
Large-scale Features
Small-scale Features
Envelope Motion
Van Horne et al. (2006)
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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.
Distributed Hydrologic Modeling
TIN-based Real-time Integrated Basin Simulator (tRIBS) is a fully-distributed model of coupled hydrologic processes.
Ivanov et al. (2004a,b)
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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 km2 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, tC) used for model flood forecasts.
3.320.84106.9115
12.590.86808.3914
9.260.84610.6013
0.190.310.7812
0.550.774.2911
1.500.8721.1810
2.160.8749.079
5.440.82182.918
6.270.82365.257
7.250.84450.266
0.510.831.415
0.930.772.674
1.670.8112.143
4.030.8365.062
5.780.99108.231
tc (h)D (km-1)A (km2)Basin
Baron Fork
808 km2
Basin 12 0.8 km2
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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.
Oct 98Jan 98
Simulation Hours Simulation Hours
Dis
charg
e (
m3/
s)
Dis
charg
e (
m3/
s)
Rain
fall
(m
m/
h)
Rain
fall
(m
m/
h)
Fall Squall Line:
• Concentrated rain accumulation.• Decaying flood wave produced in Dutch Mills.
BF DM
Winter Front:
• Banded rain accumulation.• 7-yr flood event at Baron Fork.
Jan 98 Oct 98
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Multi-Gauge Model Calibration
January 1998 October 1998
Baron Fork
(808 km2)
Dutch Mills
(107 km2)
PeacheaterCreek
(65 km2)
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Rainfall and Runoff Forecasts
Vivoni et al. (In Press)
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
MAP MAP
OutletOutlet
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Lead-Time Dependence Catchment Scale Dependence
Increasing Skill
At 1-hr Lead Time
QPE
1-hr
2-hr
Decreasing Skill
Flood Forecast Skill
Flood forecast skill decreases as a function of lead time and increases with basin area for the two storm events.
Vivoni et al. (2006)
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• Bias defined as:
where F = forecast meanO = 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.
Radar Nowcast Error Propagation
Statistical measures of error propagation show that nowcastingerrors are amplified in the flood forecast as lead time increases.
Bias Propagation Mean Absolute Error Propagation
OFB =
∑=
−=N
iii FO
NMAE
1
1
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
Vivoni et al. (In Press)
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 Bratio 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.
rain
dis
BBB =ratio
rain
dis
MAEAMAEMAE*
ratio =
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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, anext 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).