Downscaling in time

• 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?

Weather and climate

……• 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

.. crop model can act as a non-linear temporal integrator

bridging Climate into Risk Management

Approaches to temporal downscaling

1. Historical analog techniques– Use various subsets of past data based on a seasonal-

mean predictor(s), or even daily GCM output

2. Stochastic weather generators – Parameters estimated from seasonal (or monthly)

GCM predictions– Hidden Markov model

3. Statistical transformation of daily GCM output– 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

… need for calibration

(Queensland in Summer)

Some statistics we need to get right

1. Precipitation occurrence– Probability of rain

– Wet/dry spell lengths

– Spatial correlations between stations• Log-odds ratio (odds of rain at one station vs. rain

at another)

2. Precipitation amount– Daily histogram

……

Daily Precipitation Occurrence ProbabilitiesHidden Markov model for Kenya (March–May)

Lodwar

Probability of a wet-day

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*|

• So we select the k nearest neighbors of x* 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

• 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

states

stationnetworkrainfall

GCMpredictor

s

Transition probabilities modulated by X

Rainfall is conditionally dependent on the weather state

.. 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