Stochastic Weather Generators

Transcription

From WGEN to BayGEN
Will Kleiber
Department of Applied Mathematics
University of Colorado
Boulder, CO
Workshop on Stochastic Weather Generators, Vannes, France
May 17, 2016
Acknowledgements
Balaji Rajagopalan
Andrew Verdin
Rick Katz
Guillermo Podestá
Federico Bert
Branden Olson
Will Kleiber (CU Applied Mathematics)
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Motivation
“It is arguable that the artificiality of agricultural production
systems make them less flexible, and therefore more
vulnerable to climatic change than the naturally occurring
species of the ecosystem within which they fit, and that the
more unstable the climate the greater this vulnerability is
likely to be.”
- Oram (1985)
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Agriculture: Colorado
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Agriculture: France near Paris
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The Pampas: 750,000 km2
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Productive region:
soybean, cereal, maize,
wheat
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Very flat: little
subsurface flow, lack of
drainage
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Strong human systems
and natural systems
coupling
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The Pampas: 750,000 km2
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Pampas climate & land use change
Alternating wet and dry epochs:
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Early 1900s floods.
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1930-50 drought.
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Increasing precipitation
1960-2000.
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Agricultural expansion: 51 million
metric tons of soy per year.
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1997-2003 flooding.
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2008 drought.
1200
1000
800
600
Total Precip (mm)
→ Extremes & frequency.
1960
1970
1980
1990
2000
2010
Year
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Agricultural planning in the Pampas
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Crop simulation models (DSSAT).
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Analyze different management strategies.
. . . the need for data.
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Observed record limited.
Respond to seasonal forecasts.
All at ungauged locations.
→ Stochastic weather generation!
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−33
Study region & data
3
5
2
−34
●
●
●
6
4
●
7
8
●
lat
−35
●
●
11 ●
−36
●
9
1
10 ●
●
●
16 ●
12
−37
13 ● 14
●
17 ●
−65
−64
−63
15 ●
−62
−61
lon
1961–2013 daily precipitation, maximum and minimum temperature
(area ≈ 200,000 km2 ).
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Agricultural, ecological, hydrological models often require daily
weather (e.g. precipitation, minimum/maximum temperature, solar
radiation)
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On grid
In the future
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Stochastic Weather Generators (SWGs) can be used to produce
infinitely long series of synthetic weather, for observation network
infilling, or climate model downscaling
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SWGs are statistical models whose simulated values “look like”
observed weather
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Daily statistics
Interannual statistics
SWGs are not forecast models
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Short History
Gabriel and Neumann (1962): First SWG for rainfall occurrence
(persistence via Markov chain)
p01 = P(rain today | no rain yesterday)
p11 = P(rain today | rain yesterday)
Buishand (1977): Geometric distributions for spell lengths
Todorovic and Woolhiser (1975): Rainfall amounts (skewed distribution
via exponential pdf)
f (y|rain) = λ exp(−λy)
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for
y>0
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Short History
Richardson (1981), Richardson and Wright (1984): WGEN
(precipitation, minimum temperature, maximum temperature, solar
radiation)
Given precipitation (non)-occurrence,
 TX (t)−µX (t) 
σX (t)





TN (t)−µN (t)
σN (t)
R(t)−µR (t)
σR (t)


 ∼ MVNormal(0, Σ)


Ailliot et al. (2015) overview: focus on hierarchical models.
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Multi-site weather generators
Resampling:
[Yates et al., 2003; Apipattanavis et al., 2007; Sharif & Burn, 2007]
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Resample observed vector of variables.
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Preserves (exact) spatial dependence and climatological statistics.
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Restricted to historical extremes.
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Difficult to simulate at ungauged locations.
Model-based:
[Wilks, 1998, 1999; Qian et al., 2002; Baigorria & Jones, 2010; Khalili et al.,
2009]
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Climate variables modeled consistent with single site.
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Spatially-varying parameters.
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Can be difficult to preserve space-time dependence.
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Extendable to simulate at ungauged locations.
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The Research Thread
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WGEN (Richardson 1981; Richardson and Wright 1984)
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Covariates via generalized linear models (Stern and Coe 1984;
Chandler 2005; Furrer and Katz 2007)
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Marginal spatial GLMs (Kleiber et al. 2012, 2013)
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Joint SWGs (Verdin et al. 2015)
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Actual seasonal/multidecadal forecasting (Verdin et al. 2016)
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Fully Bayesian implementation (Verdin et al., in prep)
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Generic Methodology
Precipitation occurrence
O(s, t) = 1[WO (s,t)≥0]
WO (s, t) ∼ GP(XO (s, t)T β O (s), CO )
Precipitation amount
A(s, t) ∼ Gamma(αA (s), αA (s)/µA (s, t))
µA (s, t) = exp(XA (s, t)T β A )
Temperature
ZN (s, t) = XN (s, t)T β N (s) + WN (s, t)
ZX (s, t) = XX (s, t)T β X (s) + WX (s, t)
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Seasonal Forecasting
Goal: Generate space-time weather scenarios consistent with
seasonal forecasts and multidecadal trends, for resources planning
and management.
Include seasonal climate information in the form of additional
covariates.
Downscaling coarse scale information.
Enables translation of seasonal forecasts or climate model projections
for decision support systems.
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Seasonal forecast (International Research Institute)
1. Sample ensemble of
climatatology OND, A:N:B as
weights.
OND 2010 Precipitation: (15:35:50) (A:N:B)
OND 2010 Temperature: (40:35:25) (A:N:B)
2. SWG simulation per
ensemble member
(covariates).
3. Ensemble of weather
reflects uncertainty.
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Seasonal forecast
Differences in ensemble mean (unconditional minus conditional):
Precip
Max Temp
Min Temp
0.6
100
0.4
50
0.5
0.2
0
0.0
0.0
−0.2
−50
−0.5
−0.4
−100
−0.6
Differences in 95% ensemble spread (unconditional minus conditional):
Precip
Max Temp
Min Temp
1.5
200
2
100
1
0.5
0
0
0.0
−100
−1
−0.5
−200
−2
1.0
−1.0
−1.5
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Seasonal forecast
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BayGEN
BayGEN: Incorporate parametric uncertainty in weather generation.
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Variability between ensemble members
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Better estimates of crop production risk
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Better interannual statistics
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Local climate estimates at ungauged locations
Treat model parameters as random variables, posterior sampling
propagates variability to weather simulations.
β j (s) ∼ GP(β̂j (s), Cβj ) for j = O, A, N, X
αA (s) ∼ GP(α̂A (s), CαA )
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Gridded simulation
October 1 − Total Precipitation
October 1 − Minimum Temperature
October 1 − Maximum Temperature
30
162
40
92
25
35
53
20
30
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30
15
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10
10
6
4
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2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
17 / 21
Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
WGEN to BayGEN
SWG 2016
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Gridded simulation
30
162
40
92
25
35
53
20
30
17
30
15
25
10
10
6
4
20
5
15
2
0
10
1
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Extremes
(a) Domain max of max temps
(b) Domain min of max temps
(c) Domain min of min temps
(d) Domain max of min temps
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Assessments of Risk
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100 weather trajectories from both GLMGEN and BayGEN
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Propagated through DSSAT for soybean yield
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Assessments of Risk
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100 weather trajectories from both GLMGEN and BayGEN
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Propagated through DSSAT for soybean yield
Probability of < 2500 kg ha−1 (break even yield):
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≈ 17% (GLMGEN)
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≈ 32% (BayGEN)
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Discussion
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GLM space-time weather generator (GLMGEN).1
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Conditional GLMGEN.2
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Complete spatial simulations of “weather”
Downscaling and seasonal forecasts
Bayesian space-time weather generator (BayGEN).3
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1 Verdin
More comprehensive uncertainty quantification
et al., (2015). Coupled stochastic weather generation using spatial and generalized
linear models. Stochastic Environmental Research and Risk Assessment, 29(2), 347–356.
2 Verdin
et al., (2016). A conditional stochastic weather generator for seasonal to multi-decadal
simulations. Journal of Hydrology.
3 Verdin
et al., (2016, In Preparation). BayGEN: A Bayesian space-time stochastic weather
generator. In preparation.
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What might the future hold?
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Incorporate other variables (e.g., wind, solar, relative humidity)
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High time resolution simulation (see later: Koch, Sun)
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Physically constrained simulation (see later: Groyer, Guilloteau,
Bessac, Atencia)
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Large-domain applications (see later: Sommer)
WGEN to BayGEN
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Stochastic Weather Generators

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