steps: an empirical treatment of forecast uncertainty alan seed bmrc weather forecasting group
TRANSCRIPT
STEPS: An empirical treatment of forecast uncertainty
Alan Seed
BMRC Weather Forecasting Group
Outline
Where does uncertainty come from? Can we get rid of it? How can we quantify it? Where to from here?
Sources of forecast uncertainty
Radar rainfall estimation Field motion estimation Development during forecast period
Radar Measurement Error
Major contribution to forecast error in the first hour
0
2
4
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8
10
0 15 30 45 60 75
Lead Time (min)
MS
E (
mm
/h)^
2
Mean square error of rainfall forecast (1km, 15min) as a function of lead time based on a 5-day storm, 200 rain gauges for ground truth
Radar Measurement Error
Radar measurement errors are highly variable in time
0
2
4
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14
12/05/200300:00
13/05/200300:00
14/05/200300:00
15/05/200300:00
16/05/200300:00
17/05/200300:00
18/05/200300:00
Time
Mea
n S
td E
rro
r (m
m/h
)
Radar QPE 60Min
0
2
4
6
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14
12/05/200312:00
12/05/200318:00
13/05/200300:00
13/05/200306:00
13/05/200312:00
Time
Mea
n S
td E
rro
r (m
m/h
)
Radar QPE 60Min
Errors increase in significant convective weather
Errors Due to Changes in Field Velocity
Bowler et al 2005; submitted to QJR
Development during the forecast lead time
Climatology- topography, diurnal cycle Rate of temporal development depends on
scale- predictability limits Situation dependent
Effect of topography
Effect of Topography
Predictability is a Function of Scale
Can We Get Rid of Uncertainty?
•No, but
we can reduce it
we can understand it
we can tell our users about it
Quantifying Forecast Uncertainty
Physical ensembles Statistical ensembles
Multi Model Ensemble
3500 campers were evacuated ahead of a flood at Tamworth after a qualitative assessment of risk based on the ensemble mean.
Gordon McKay, Beth Ebert
Short Term Ensemble Prediction System
Generate a deterministic nowcast based on radar data
Estimate the error for the nowcast and a NWP forecast over a hierarchy of spatial scales
Merge the nowcast with the NWP forecast using weights that are a function of the forecast error and spatial scale
Generate an ensemble by perturbing the deterministic blend with a stochastic component
256-
128
km
64-32 km
8-4 km
32-1
6 km
4-2
km
128-
64 k
m16
-8 k
m
Spectral Decomposition
Temporal Development Model
The Lagrangian temporal development for each level in the
cascade is forecast using an AR(2) model
AR(2) parameters are estimated at each time step for each level
The innovation term is spatially correlated, temporally uncorrelated
)()1()()()()1(ˆ,,,,2,,,1,,, tntXtntXtntX jikjikkjikkjik
Forecast Skill
Model skill is taken to mean the fraction of the observed variance that is explained by the model, r2
Skill of Nowcast is given by the AR-2 model Skill of the NWP is calculated as the
correlation between the NWP cascade and radar cascades
Telling the users
Observation uncertainty Forecast uncertainty
Observation Uncertainty
15-min average interpolated from gauge network
Error as a fraction of the rain field variance
15-min rainfall accumulation forecast- 20 member stochastic nowcast ensemble
Ensemble mean Ensemble standard deviation
Stochastic nowcast model does not yet include the observation error model
Way Forward: Heuristic Probabilistic Forecasting?
Held a workshop in Montreal- presentations can be found at http://www.radar.mcgill.ca/~cwrp/
• NWP has improved significantly but errors will remain• Use persistence of NWP errors to develop post-processing
systems to mitigate the error• Need to model initiation, growth, decay• Conceptual probabilistic models are likely to be useful• Would like to develop a common framework and to
collaborate on developing probabilistic forecast models
Thank you