1. Downscaling in time

2. 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

3. .. crop model can act as a non-linear temporal integrator bridging Climate into Risk Management

4. 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 ……

5. 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

6. Example of GCM vs. Station Daily Rainfall Distributions … need for calibration (Queensland in Summer)

7. 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 ……

8. Daily Precipitation Occurrence Probabilities Hidden Markov model for Kenya (March–May) Lodwar Probability of a wet-day

9. Wet/Dry Spell Durations

10. 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.)

11. K-Nearest Neighbors Refinement of the analog approach, retaining its advantages and partially solves the sampling problem Past years’ daily sequences D t 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 |x t - x * |

12. So we select the k nearest neighbors of x * in the historical record, estimate appropriate weights to assign to each, and resample D t accordingly The resulting superensemble of years (each is repeated many times) can then be fed to a crop model

13. 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 ……

14. Multi-site extension Run a series of WG’s in parallel Use spatially correlated random numbers (Wilks, 1998) Use a Hidden Markov Model

15. downscaling daily weather sequences with a Non-homogeneous Hidden Markov Model states station network rainfall GCM predictors Transition probabilities modulated by X Rainfall is conditionally dependent on the weather state.. daily sequence of rainfall vectors

16. 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

17. Rainfall amount distributions From Queensland Australia (Oct–Apr) Non-zero amounts modeled by mixed exponential distribution

18. 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