Tutorial

Other post-processing approaches …1) Bayesian Model Averaging (BMA) –

Raftery et al (1997)

2) Analogue approaches –Hopson and Webster, J. Hydromet (2010)

3) Kalman Filter with analogues –Delle Monache et al (2010)

4) Quantile regression –Hopson and Hacker, MWR (under review)

5) quantile-to-quantile (quantile matching) approach –Hopson and Webster J. Hydromet (2010)

… many other approaches …

Significance of Weather Forecast Uncertainty Bangladesh Discharge Forecasts

3 day 4 day

Precipitation Forecasts

1 day 4 day

7 day 10 day

1 day 4 day

7 day 10 day

Discharge ForecastsTransformedinto

Calculating the rank histogram …

obs ForecastPDF

Flow rate [m3/s]

obs ForecastPDF

Flow rate [m3/s]

First occurrence

Second occurrence

=> Count in bin 6

=> Count in bin 3

Get data from shared disk: AfricaColloqData.txtPlace in working directory (desktop will work) and read in spreadsheet

… Generate histogram plot using spreadsheet

Next, redo in R

BS =1n

yi −oi( )2

i=1

n

∑Brier Score

y = forecasted event occurenceo = observed occurrence (0 or 1)i = sample # of total n samples

=> Note similarity to MSE

Brier skill score

refref

ref

BS

BS1

BS0

BSBSBSS

-- Next, approximately determine 75th quantileFrom the July observation data (let me know your answer before proceeding further)

-- Then calculate the Brier score for probabilityof occurrence below this threshold.

-- Then, using the climatology mean (using theJuly obs data – what is the value?), calculateThe Brier skill score for this reference forecast(what’s your answer?). Is there a better reference forecast? Try this. Answer?

-- Finally, using this same threshold, calculateThe reliability diagram values (4 probabilities)And plot using spreadsheet (what are theProbabilities?)

Note: for this exercise, we will use a more“discrete” form for the ensemble probability,in which you just count the # ofensemble members above or belowthe threshold to calculate the probability(arguably less exact then interpolating)

Next steps … do both in spreadsheet and R

Reliability Diagram

From Eumetcal module on forecast verification