Transcript Downscaling in time

Downscaling in time
Weather and climate
• Aim is to make a probabilistic description of
weather for next season
– How often is it likely to rain, when is the rainy season likely
to begin, how long are dry spells likely to be?
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• Weather: a particular daily sequence drawn from the
population of weather sequences (climate)
– Probabilistic description is central because weather is
unpredictable more than 2 weeks ahead
bridging Climate into Risk Management
.. crop model can act as a non-linear temporal integrator
Approaches to temporal
downscaling
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1.
Historical analog techniques
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2.
Use various subsets of past data based on a seasonalmean predictor(s), or even daily GCM output
Stochastic weather generators
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3.
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Parameters estimated from seasonal (or monthly)
GCM predictions
Hidden Markov model
Statistical transformation of daily GCM output
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Local scaling
Why do we need to “downscale”
in time?
• GCMs have approx. 15 min. timestep!!
– Not analogous to spatial downscaling, where
GCMs have approx. 300-km gridboxes
• GCM predictions on sub-seasonal time scales
tend to be dominated by “weather noise”
• GCMs do not simulate sub-monthly weather
phenomena well
Example of GCM
vs. Station Daily
Rainfall
Distributions
(Queensland in Summer)
… need for calibration
Some statistics
we need to get right
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1. Precipitation occurrence
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Probability of rain
Wet/dry spell lengths
Spatial correlations between stations
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Log-odds ratio (odds of rain at one station vs. rain
at another)
2. Precipitation amount
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Daily histogram
Daily Precipitation
Occurrence Probabilities
Hidden Markov model for Kenya (March–May)
Probability
of a wet-day
Lodwar
Wet/Dry Spell Durations
Historical Analogs
• Simplest approach
• Take daily sequences of weather observed
during past events as possible scenarios for a
predicted event
• An event can be defined according to the
threshold of an index, such as Niño-3 SST, or
a GCM-predicted seasonal-mean quantity
(e.g. regional precip.)
K-Nearest Neighbors
• Refinement of the analog approach, retaining its
advantages and partially solves the sampling
problem
• Past years’ daily sequences Dt are again selected
from the historical record according to the value of
some (seasonal-mean or daily) predictor x* …
• … but here the past year t is “resampled” according
to the distance |xt - x*|
*
x
• So we select the k nearest neighbors of in
the historical record, estimate appropriate
weights to assign to each, and resample Dt
accordingly
• The resulting superensemble of years (each is
repeated many times) can then be fed to a
crop model
Weather generators
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• Use concept of “Monte Carlo” stochastic simulation
– Let computer generate a large number of daily
sequences using a stochastic model
• Honor the statistical properties of the historical data
of the same weather variables at the site
– Precipitation frequency and amount, dry-spell length
etc
– Daily max and min temperatures, solar radiation …
• Cast seasonal prediction in terms of changes in these
statistical properties
Multi-site extension
• Run a series of WG’s in parallel
• Use spatially correlated random numbers
(Wilks, 1998)
• Use a Hidden Markov Model
downscaling daily weather sequences with a
Non-homogeneous Hidden Markov Model
Transition
probabilities
modulated by X
GCM
predictors
states
Rainfall is
conditionally
dependent on the
weather state
station
network
rainfall
.. daily sequence of rainfall vectors
toolboxes for downscaling in time
• toolboxes for constructing
stochastic daily weather
sequences conditioned on GCM
outputs
‣ HMM
‣ KNN/weather typing
http://iri.columbia.edu/climate/forecast/stochasticTools/index.html
Rainfall amount distributions
From Queensland Australia (Oct–Apr)
Non-zero amounts modeled by mixed exponential distribution
Statistical transformation of daily
GCM output: Local scaling
• Use nearest GCM gridpoint
• Calibrate GCM’s precipitation so that it’s
distribution matches that of local station data
– no spatial calibration