Hydrologic Applications of Ensemble Forecasts Extra Slides

1
Hydrologic Applications of Ensemble
ForecastsExtra Slides

• Julie Demargne
• Hydrology Laboratory
• Office of Hydrologic Development
• NOAA/National Weather Service

Ensemble User Workshop, NCEP, Oct. 31-Nov. 2, 2006
2
Hydrologic Products and Services
River Basin with Forecast Points
Major River System
National
Forecast Group
Headwater Basin and Radar Rainfall Grid
High Resolution Basins
3
Long-Term ESP Methodology

• Better estimate true climatological distribution
  based on data pooling process use adjacent
  events to increase sample size
• Better sample climatological distribution based
  on Schaake Shuffle method to generate stratified
  ensembles

T1
T2
T3
Historical Sampling Distribution
Historical Sampling Distribution
Historical Sampling Distribution
1
1
1
Climatological Distribution
Climatological Distribution
Climatological Distribution

Probability
Probability
Probability
1964
1996
1975
1996
1975
1964
1964
1975
1996
0
0
0
Precipitation Amount
Precipitation Amount
Precipitation Amount
By re-scaling climatological observations,
space-time properties of resulting time series
are similar to the historical events properties
4
Long-Term ESP Methodology

• Climate Adjustment (optional) integrates days
  1-365 meteorological forecasts/climate outlooks
  from NCEP/CPC to adjust stratified ensembles of
  precipitation and temperature using the CPC
  pre-adjustment technique.

5
Short-Term ESP Methodology

• 1. Joint Distribution Calibration at each time
  step of the whole year, estimate the parameters
  of the joint distribution of observed and
  forecast values from archived data

Parameters describing the joint distribution of
forecasts and observations
Joint distribution
Normal Space
Archived data
ZY
Y
Observed
Observed
NQT
ZX
zY0
Forecast
X
0
zX0
Forecast
The single-value forecast could be the NCEP/HPC
forecast as modified by RFC (operational
deterministic forecast)
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Short-Term ESP Methodology

• 2. Conditional Probability Distribution at each
  time step of the forecast period, compute the
  parameters of the conditional distribution of
  future values given the single-value forecast

Conditional distribution
Joint distribution
Normal Space
Normal Space
ZY
1
Probabilistic forecast given the single-value
forecast
Inverse NQT
Observed
Single-value forecast
Probability
NQT
P ( ZY ZX zX )
ZX
Forecast
zY0
ZX
0
For the forecast zX
z0
Observed
zX0
The single-value forecast could be the NCEP/HPC
forecast as modified by RFC (operational
deterministic forecast)
7
Short-Term ESP Methodology

• 3. Distribution Mapping at each time step of the
  forecast period, generate ensemble points given
  the conditional distribution of future events by
  sorting and then re-scaling climatological
  observations

T1
T2
T3
Conditional Distribution
Conditional Distribution
Conditional Distribution
1
1
1
Climatological Distribution
Climatological Distribution
Climatological Distribution

Probability
Probability
Probability
1964
1996
1975
1996
1975
1964
1964
1975
1996
0
0
0
Precipitation Amount
Precipitation Amount
Precipitation Amount
Ensemble forecasts capture skill of single-value
forecasts. Space-time properties of resulting
time series are similar to the historical events
properties.
8
Short- to Medium-Term ESP GFS Ensemble Mean
Forecasts

• Under development use ensemble mean forecasts
  from daily global model ensemble forecasts
  produced from a frozen version of the Global
  Forecast System (GFS) of NOAA/NWS/NCEP.
• Available forecasts 2-week ensembles archived on
  a 2.5 degree grid, for the 1979 - 2005 period
• Issues
• Bias varies with location, season, and forecast
  lead time
• Scale-dependency in space and time

Lead Day 1
Lead Day 3
Lead Day 5
Coefficient of correlation between GFS ensemble
mean forecast and observed precipitation for
January at 2.5 degree grid
9
Short- to Medium-Term ESP GFS Ensemble Forecasts

• Under verification at CBRFC use 2 week ensemble
  forecasts produced from a a frozen version of the
  Global Forecast System (GFS) of NOAA/NWS/NCEP.
• Methodology
• downscale GFS ensembles to estimate conditional
  probability distribution
• synthesize ensembles based on spatially
  correlated fields of random numbers

10
Current ESP System Streamflow Forecasts

• Run hydrologic model up to the start of the
  forecast period to estimate basin initial
  conditions.
• Run hydrologic model into the future using
  hydrometeorological ensemble forecasts.
• Under development data assimilation methods

Historical Data
Forecasts
Hydrologic Model
SWE
SM
Q
Historical Simulation
time
Past
Future
11
Multi-model Ensembles

• Better performance with multimodel ensembles

Mean of multimodel ensemble (arrow) is superior
to the best single model simulation (cross hair)
Illinois river at Savoy
All DMIP basins
Probabilistic prediction using multimodel
ensemble has larger economic value than single
model results
From Georgakakos et al. 2004