Downscaling climate parameters

Rasmus E. Benestad & Abdelkader Mezghani

Rasmus.benestad@met.no

Example: precipitation

What information can we use?

f(x) = 1/µ exp{-x/µ}

µ is the wet-day mean

How to estimate parameters for precipitation.

Number of data points → expectation values (central limit theorem)

Parameters as variables

Parameters as variables

Simple model for wet-day amount

Simple model for wet-day amount

“Heavy precipitation”

A test

Different quantities

x = fx = fww µµ

Mean = (wet-frequency) • (wet-mean)

How sensitive are the parameters?

Probabilities for all days

Pr(X>x) = fPr(X>x) = fw w ee

-x/-x/µµ

How often does it rain? ffww (fraction) (fraction)

How often does it rain?

The 24-hr precipitation amounts

Pr(X>x) = fPr(X>x) = fw w ee

-x/-x/µµ

How much does it rain when it rains?

µ µ (mm/day)(mm/day)

How much does it rain when it rains?

The question: more heavy rain events?

• Observations: annual mean µ- Downscaled from 107 CMIP5 GCMs (RCP4.5)

PRELIMINARY RESULTS

Temperature

library(esd)data(ferder)y=anomaly(ferder)hist(coredata(y),breaks=seq(-21,15,by=0.5),col='pink',freq=FALSE,xlab='Temperature anomaly (deg C)',main='Ferder lighthouse')lines(x,dnorm(x,mean(y,na.rm=TRUE),sd=sd(y,na.rm=TRUE)),lwd=4)text(-20,0.15,expression(f(x)==1/(sqrt(2*pi) * sigma) * e^-((x - mu)^2/(2 *sigma^2))),pos=4)

Temperature

Two parameters: µ and σ

Temperature

Dependency on the large-scale conditions?

From parameters to weather

How to use the probabilities

Pr(X>x) = fPr(X>x) = fw w ee

-x/-x/µµ

How to use the probabilities

Pr(X>x) = fPr(X>x) = fw w ee

-x/-x/µµ

Pr(X>x) = Pr(X>x) = 1/(21/(2σσ ) e) e-(x--(x-µµ )/)/σσ

How to predict number of events

p=Pr(X>x) = fp=Pr(X>x) = fw w ee

-x/-x/µµ

Pr(X=k) = Pr(X=k) = nnCCkk p pkk

(1-p)(1-p)n-kn-k

The number of heavy rain events

Predicting number of heavy rain events

Disaggregation: synthesizing daily series from parameters

Weather generators

Different kinds

The specific question

Input from climate parameters– Temporal structure?

• ρ1, LTP, f

w, n

cdd, n

cwd

– Spatial structure?

Validation

Different types:

Traditional:• Cross-validation

– Correlation, RMSE.

• GCM: common EOFs

Non-traditional:• Probabilities: binomial

• Non-stationarity test.