Error Propagation from Radar Rainfall Nowcasting Fields to a FullyDistributed Flood Forecasting Mode

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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
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
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
tL
tL
Lead Time
Vivoni et al. (2006)
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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
Envelope Motion
MIT Lincoln Lab Storm Tracker Model (STNM)
Van Horne et al. (2006)
Small-scale Features
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Distributed Hydrologic Modeling
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
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.
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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 98
Jan 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
BF
DM
Discharge (m3/s)
Discharge (m3/s)
Rainfall (mm/h)
Rainfall (mm/h)
Simulation Hours
Simulation Hours
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Multi-Gauge Model Calibration
January 1998
October 1998
Baron Fork (808 km2)
Dutch Mills (107 km2)
Peacheater Creek (65 km2)
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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
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
Outlet
Outlet
Vivoni et al. (In Press)
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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
Increasing Skill
1-hr
Decreasing Skill
2-hr
At 1-hr Lead Time
Vivoni et al. (2006)
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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 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
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

• 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
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).