Anomaly-based daily interpolationBackground field can be calibrated on full historical dataCan be extended to sites with modest numbers of records –beyond what is available day by dayTopographic dependence can be (largely) incorporated into thebackground field parametersAnomalies from the background field have broader scale spatialpatterns, with little or no dependence on topography – supportsday by day interpolation from limited numbers of sitesHow to do this for daily rainfall?
Censored power of normal distributionRainα = μ + σz α 0.3 – 0.9 z standard normal variable, z ≥ -μ/σ μ/σ -3.0 to 2.0 P(W) = Φ(μ/σ)
Regression extension of short period records – for 1976-20056400 stations with at least 20 years of recordAdditional 3200 stations with at least 10 years of recordWithout regression RMSE = 20%With regression RMSE = 10%Cross validation RMSE of interpolated long period stns = 15%Cross validation MAE of interpolated long period stns = 7% (3172 stations, at least 28 years of record)
Interpolation of anomaliesAdaptive thin plate smoothing spline interpolation of anomaliesMore knots for positive rainfall, fewer for latent negatives: – up to 5000 for positives (amounts) – 1500 for negatives (occurrence)Tune the placement and relative weighting of the latent negativesto minimise the RMS of cross validated normalised rainfall valuesPlacement: 0.25, weighting: 4.0Monitor cross validation of occurrence structureMonitor goodness of fit – amounts and occurrence
Statistics for 6 Representative DaysStatistic Cross Validation Residuals of FitRMS of normalised 0.223valuesMAE (mm) 1.43 0.940RMS (mm) 3.62 2.25MAE of positive rain 2.9(mm)Class average of 82.2% 90.6%occurrenceKappa statistic of 0.668 0.810occurrence
Daily Rainfall over NE Qld on 12/02/1999 Rainfall (mm) High : 460 Low : 113
Daily Maximum Temperature over NE Qld on 12/02/1999 Temperature (C) High : 28.7 Low : 19.0
ConclusionCensored square of normal distribution provides a stable parameterisation ofthe background daily rainfall distributionAlso provides stable statistical assessment of rainfall extremes and of variousinterpolation statistics – applicationsNot perfect – smoothed interpolation of actual daily extremes – seasonalaggregations reasonableAnomaly-based interpolation is being applied to the other daily and monthlyvariablesDownscale climate drivers to any pointDownscale climate change scenarios to a grid