Validation of the downscaling models 3.6
3.6.4 Distributional properties of the optimal downscaling models
Figure 3.23. Kernel density estimations of monthly observed and simulated (using the multi-domain GCMs+HiRes /MLR-method) maximum and minimum temperatures, humidity and solar radiation at station 48478, and precipitation and wet-day rate at station 48092 for the verification period 1986-1999.
Extreme value analysis of the downscaled climate variables 3.6.4.2
The examination of the general probability distributions of the GCM/MLR- models downscaled climate predictions provides some evidence for extreme value deviations of the empirical density distributions from a normal distribution. In this section, the extreme value probabilities are investigated further. Such an extreme values analysis is important in studies of climate change and its impacts, for example, to understand the future occurrences of droughts, or storms and floods. Again, frequency analysis of the observed and modeled climate variables, with an emphasis of the analysis of the tails of the empirical distribution is applied for that purpose (Reynard et al. 2005, Salathé 2005, Rodrigo 2009, Friederichs 2010, Hashmi et al. 2011).
To assess the extremes of the climate variables temperatures and precipitation, probability distributions of the monthly observed or downscaled extreme rainfall are usually fitted by specific extreme-value distributions (Friederichs 2010, Hashmi et al. 2011, Huang et al. 2012). As
maximum temperature (C) minimum temperature (C)
humidity (%) solar radiation (MJ/m2)
precipitation (mm/day) probability of wet day (%)
Table 3.26. Absolute bias (error) (observed –modeled) of various statistical attributes of the modeled ECDF computed on annual and four-season bases for verification period 1986-1999.
predictor season
mean absolute error of the estimated parameters (%) percentile
mean SD
25% 50% 75%
Tmax (C)
annual 0.2 0.5 0.6 0.4 0.3
dry 0.3 0.6 0.7 0.6 0.3
premonsoon 0.5 0.5 0.8 0.6 0.4
monsoon1 0.2 0.4 0.7 0.5 0.3
monsoon2 0.3 0.2 0.4 0.3 0.3
Tmin (C)
annual 0.5 0.2 0.3 0.3 0.1
dry 0.6 0.4 0.4 0.3 0.1
premonsoon 0.4 0.2 0.2 0.3 0.2
monsoon1 0.2 0.3 0.4 0.3 0.1
monsoon2 0.5 0.3 0.3 0.4 0.0
HMD (%)
annual 1.6 0.9 0.5 0.9 0.6
dry 0.9 0.6 0.6 0.6 1.2
premonsoon 1.6 0.9 0.6 0.9 1.0
monsoon1 1.4 1.0 0.9 1.1 1.0
monsoon2 0.8 1.5 1.2 1.1 0.5
SLR (MJ/m2)
annual 0.5 0.5 0.1 0.3 0.4
dry 1.0 0.1 0.1 0.4 0.8
premonsoon 0.5 0.1 0.7 0.1 0.4
monsoon1 0.5 0.2 0.2 0.2 0.4
monsoon2 1.3 0.9 0.5 0.7 0.6
PCP (mm/day)
annual 0.5 0.8 0.5 0.2 0.8
dry 0.3 0.4 0.4 0.3 0.4
premonsoon 0.8 0.6 0.8 0.5 1.0
monsoon1 0.8 0.7 1.3 0.7 1.5
monsoon2 0.4 0.9 1.0 0.5 0.6
%Wet (day/day)
annual 0.03 0.06 0.05 0.03 0.03
dry 0.02 0.03 0.03 0.02 0.02
premonsoon 0.06 0.05 0.07 0.04 0.05
monsoon1 0.04 0.06 0.09 0.04 0.06
monsoon2 0.03 0.06 0.06 0.03 0.03
discussed in Section 2.5.2, the GEV and the Gumbel models turned out to be best for fitting the extreme-value distributions of the climate series in the study area. For this reason, they are also used also in the following extreme value analysis.
From the quantiles q(p) for a given exceedance- probability p which is the inverse of the return period T, i.e. T=1/p, the monthly extreme (exceedance) values as a function of the return period are computed. The results of this extreme value analysis are shown for one temperature- and two precipitation stations in Figure 3.24. More specifically, the figure illustrates the extreme values (exceedance) of the observed 1971-1999 and simulated downscaled climate variables, obtained with the optimal multi-domain MLR-model, calibrated with the observations between years 1971-1985 and fitted with the Gumbel- and GEV- models as a function of the return period.
One may notice that although the simulated extreme maximum temperatures in Figure 3.24a fit the observations rather well, this is less so the case for the extreme minimum temperature in Figure 3.24b, where there is a systematic underestimation of the minimum temperatures which gets bigger for larger return periods. The bias of the extreme monthly precipitation estimation is even higher than those of the two temperatures, as one can see from the Figure 3.24c, d.
Figure 3.24. Extreme values (exceedance) of observed and simulated downscaled monthly data between years 1971-1999, fitted with Gumbel and GEV for various return periods of max (a) and min (b) temperatures at station 48478 and rainfall at stations 48092 (c) and 459201 (d).
Table 3.27. Average (using all climate stations) absolute differences, i.e. errors between the fits of the GEV- and the Gumbel- models to the observed and simulated (multi-domain MLR- monthly downscaling) climate variables between years 1971-1999 at the annual and the four-season time-scales for different return periods.
station season mean absolute error of the extreme value estimations
GEV Gumbel
2-yr 5-yr 10-yr 20-yr 50-yr 100-yr 2-yr 5-yr 10-yr 20-yr 50-yr 100-yr
Tmax
(°C)
annual 0.3 0.4 0.7 1.0 1.5 1.8 0.2 0.5 0.7 0.9 1.2 1.5 dry 0.2 0.3 0.6 0.9 1.3 1.7 0.2 0.3 0.5 0.7 1.0 1.2 pre-monsoon 0.2 0.4 0.6 0.9 1.2 1.4 0.2 0.4 0.7 0.9 1.2 1.4 monsoon1 0.1 0.3 0.6 0.8 1.2 1.5 0.1 0.3 0.5 0.7 0.9 1.0 mosoon2 0.2 0.3 0.5 0.7 1.0 1.2 0.2 0.3 0.4 0.6 0.8 1.0 Tmin
(°C)
annual 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.1 dry 0.1 0.4 0.5 0.6 0.6 0.7 0.1 0.5 0.7 0.9 1.2 1.4 pre-monsoon 0.1 0.4 0.5 0.6 0.8 0.9 0.1 0.5 0.7 0.9 1.1 1.3 monsoon1 0.1 0.3 0.6 0.8 1.2 1.6 0.1 0.3 0.5 0.6 0.8 1.0 mosoon2 0.0 0.1 0.2 0.2 0.2 0.2 0.0 0.2 0.4 0.5 0.7 0.9 PCP
/day)(mm
annual 1.7 3.3 4.5 5.6 7.2 8.7 1.6 3.4 4.6 5.7 7.2 8.3 dry 0.2 0.6 1.2 1.9 3.0 4.1 0.2 0.6 1.0 1.3 1.8 2.1 pre-monsoon 0.9 2.2 3.0 3.8 4.8 5.6 0.9 2.2 3.1 3.9 5.0 5.8 monsoon1 0.3 1.8 3.2 4.8 7.5 10.0 0.5 1.8 2.6 3.5 4.6 5.4 mosoon2 0.4 1.8 3.1 4.5 6.4 7.9 0.2 1.8 2.9 4.0 5.4 6.4
a) extreme Tmax b) extreme Tmin
c) extreme PCP (48092) d) extreme PCP (459201)
(°C) (°C)
observation obs. with GEV obs. with Gumbel simulation sim. with GEV sim. with Gumbel
observation obs. with GEV obs. with Gumbel simulation sim. with GEV sim. with Gumbel
observation obs. with GEV obs. with Gumbel simulation sim. with GEV sim. with Gumbel
observation obs. with GEV obs. with Gumbel simulation sim. with GEV sim. with Gumbel
annual precipitation (interval : 100 mm/year)
observed annual average predicted annual average In Table 3.27, the results of the extreme value analysis for the averages of the climate variables for all stations are summarized. More precisely, the absolute differences, i.e. errors between the fits of the GEV- and the Gumbel-model to the observed and simulated - using the multi-domain MLR- monthly downscaling - climate variables between years 1971-1999 at the annual and the four-season time-scales are listed for different return periods. From the numbers in the table no clear statement with regard to which extreme value model is better can be made. For example, for the two extreme temperatures the errors in the estimated exceedance values at the 50-year return period for both models are between 1.0 and 1.5°C, whereas those of the extreme precipitation at the same return period go up to 7 mm/day, corresponding to 210 mm/month.
It will be interesting to see whether the rather poor extreme-value estimation of the monthly rainfall obtained above can be improved when the monthly climate series are rescaled into daily ones by using the stochastic climate generation method to be developed in Chapter 5.
Spatial distribution of the downscaled precipitation 3.6.4.3
Regarding the spatial distribution of climate data, that of the rainfall is of particular interest in climate assessment. Figure 3.25 shows the spatial distribution plots of the average observed and simulated (predicted) precipitation obtained by interpolating the (observed and predicted) data at the 24 rainfall gauges using the IDW method (see Section 2.4.3), wherefore the predicted rainfall is based on the (1971-1985- calibrated) multi-domain MLR-model, verified for years 1986-1999.
The two panels of Figure 3.25 demonstrate that the general pattern of the observed- and predicted rainfalls are similar. In general, the average rainfall is lowest in the southwestern- and highest in the eastern part of the study area. However, the spots of low-magnitude rainfall (light green color) for the predicted distribution on the west side of the KY-watershed indicate some underestimation of the observed rainfall of the order of 100-200 mm/year.
Figure 3.25. Spatial distributions of observed- (left panel) and downscaled (right panel) 14-year annual average precipitation from 24 sites for verification period 1986-1999.