stations are best fitted or forecasted by the MLR- method, for a good number of stations the climate, namely, the precipitation, is better predicted by the ARIMAex- model. However, this observation does not disprove the earlier statements that forecasts of the precipitation in the study region are less reliable than those of the temperatures (see also Table 4.24).
Table 4.25. Number of climate stations with the best models from one of the groups of MLR- and ARIMAex (ARex)- models for the annual and seasonal predictions for the vrf1- and vrf2- calibration/verifications schemes.
calibration/
verification
period predictand
number of stations1,2
annual optimal model
seasonal optimal model
dry pre-monsoon monsoon1 monsoon2 MLR ARex MLR ARex MLR ARex MLR ARex MLR ARex cal: 1971-1985
vrf: 1986
Tmax 2 2 4 4 4 2 2
Tmin 2 2 3 1 4 3 1 2 2
PCP 18 6 18 6 17 7 19 5 18 6
cal: 1971-1999 vrf: 2000
Tmax 3 1 4 3 1 4 1 3
Tmin 4 4 4 4 3 1
PCP 21 3 19 5 15 9 21 3 18 6
1number of stations add up to 4 for Tmin and Tmax and to 24 for PCP for each season
2mostly selected models for each climate variable and season are highlighted in bold italics
To depict the inter-season forecasts in more detail, the 1986- one-year-ahead MLR- and ARIMAex- predicted climate series (vrf1 scheme) at temperature stations 48459 and precipitation station 459201 are exhibited, together with the observed series, in the three panels of Figure 4.11. One can recognize from Figure 4.11a that for the maximum temperature the ARIMAex- method works better than the MLR- model, as the latter underestimates the observed temperatures significantly from the beginning to the end of the monsoon seasons (April-October). The predicted and observed minimum temperature series of Figure 4.11b exhibit that the ARIMAex- forecast works better at the beginning and the MLR- one better for the second half of the year.
Finally, for the precipitation series in Figure 4.11c, the MLR- method provides overall a better forecasting skill than ARIMAex. Nonetheless, MLR can better simulate the first peak of the observed rainfall at the beginning of the first monsoon season, whereas ARIMAex works slightly better for representing the observed rainfall peak of the second monsoon season. These results show that for good seasonal climate forecasting, the selection of an optimal seasonal forecasting model should not only be based on its average annual prediction skill, but should also consider its seasonal performances.
MLR- model enhancements by using ocean teleconnections
Figure 4.11. Observed and 12-month-ahead predicted climate time-series of a) maximum and b) minimum temperatures at station 48459 and c) precipitation at station 459201 for year 1986 (calibration/verification scheme vrf1), using the MLR- and the ARIMAex- model.
30 31 32 33 34 35 36
temperature (°C)
obs Tmax
MLR (HiRes+SSTs) :NS=0.66 ARIMAex (Hi-Res.tmp) :NS=0.86
16 18 20 22 24 26 28
temperature (°C)
obs Tmin
MLR (SSTs) :NS=0.81
ARIMAex (ep.lag -1) :NS=0.88
0 2 4 6 8 10 12
precipitation (mm/day)
obs PCP
MLR (HiRes) :NS=0.70
ARIMAex (Hi-Res.pre) :NS=0.66
a) Tmax, stat: 48459
b) Tmin, stat: 48459
c) PCP, stat: 459201
used in the MLR- models with the corresponding number of climate stations using them. More specifically, climate series are predicted for stations, where an MLR- model with a combination of GCMs+SSTs- predictors show the best prediction skill, with 1) both GCMs+SSTs -predictors turned on, and 2) only GCMs – predictors with the +SSTs- predictors turned off. By comparing the prediction performances of these two MLR- variants, one gets an idea on the possible benefits of using +SSTs teleconnections in climate prediction.
The three panels of Figure 4.12 show a typical result of this vast modeling exercise, namely, the 1986-1987, 24-month-ahead, predicted climate series of the two monthly temperatures at station 48459 and of the precipitation at station 48150, based on calibration/verification scheme vrf1,i.e.
calibration for the 1971-1985 time period. One may notice that, generally, the pattern of the predicted climate series of the MLR- models with and without +SSTs- teleconnection predictors are nearly similar and both follow the variations of the observed climate series reasonably well.
However, it is apparent from Figure 4.12a and Figure 4.12b, that the MLR- models with both GCMs+SSTs- predictors simulates the two observed temperature series better, particularly, at their low and high peaks, than the models without SSTs- predictors included. For the precipitation shown in Figure 4.12c, the improvement of the model fit by addition of the SST- predictors in the MLR- model is obvious for the rainfall peaks for the first forecast year 1986, though less so for the second forecast year 1987. In any case, the NS- values listed for each of the model cases in the three panels of Figure 4.12 indicate that the MLR+GCMs- predictor models with additional SSTs included are all better than those without them.
The model prediction enhancements by using additional SSTs- predictors are examined further on the seasonal scale, i.e. for the four seasons of a year. Table 4.26 lists these improvements in terms of the percentage-reduction of the RMSE between predicted and observed climate time series, relative to the predictions without SSTs- teleconnectors, for the one-year-ahead and the seasonal forecasts for the vrf1 (year 1986)- and vrf2 (year 2000)- calibration/verification schemes.
Table 4.26 shows that, while the reduction of the RMSE by adding SSTs to the MLR+GCMs-model predictor set for the maximum temperature are only 13% at the annual scale (complete 12 months) for year 1986 (vrf1), they go up significantly to values ranging between -18% and -54%
for the three monsoon seasons. For the minimum temperature and the precipitation, the prediction improvements are less spectacular, but are still higher for the two monsoon seasons than for the complete year. For the vrf2- scheme (year 2000), although the predictions for none of the three climate variable are improved when adding SSTs in the model, the seasonal predictions of the maximum temperature and the precipitation are still benefiting from doing so.
Table 4.26. Average enhancements of the one-year-ahead (annual) and seasonal prediction performances by adding SSTs- teleconnectors in the MLR+GCMs- predictor models, as measured by the percentage reduction of the RMSE for the vrf1- and vrf2- calibration/verification schemes.
calibration/
verification
period predictand reduction of the RMSE (%)
annual dry pre-monsoon monsoon1 monsoon2 cal: 1971-1985
vrf: 1986
Tmax -13 -3 -54 -18 -35
Tmin -3 -2 -4 -17 0
PCP -5 -5 -5 -6 -11
cal: 1971-1999 vrf: 2000
Tmax 0 0 -56 -7 0
Tmin 0 -7 0 -3 0
PCP -0.1 -1 -7 -1 -6
Figure 4.12. Observed and 24-month-ahead predicted climate series of monthly a) maximum and b) minimum temperature at station 48459 and c) precipitation at station 48150, for the two years 1986-1987, using MLR+GCMs- predictor models with and without SSTs-teleconnection predictors added and calibrated under the calibration/verification- scheme vrf1.
30 31 32 33 34 35 36
temperature (°C)
obs Tmax
HiRes+SSTs (with teleconnection) : NS = 0.78 HiRes (no teleconnection) : NS = 0.76
15 17 19 21 23 25 27 29
temperature (°C)
obs Tmin
SSTs (with teleconnection) : NS = 0.87
GCMs+HiRes (no teleconnection) : NS = 0.80
0 2 4 6 8 10 12 14
precipitation (mm/day)
obs PCP
HiRes+SSTs (with teleconnection) : NS = 0.79 HiRes (no teleconnection) : NS = 0.71
a) Tmax, stat: 48459
b) Tmin, stat: 48459
c) PCP, stat: 48150
Thus, in conclusion of the results of the climate prediction, experiments carried out in this section, i.e. from Figure 4.12 and Table 4.26. There is evidence of the advantage of using SSTs- teleconnectors as additional predictors in the MLR/GCMs- predictor models, namely, in terms of a better representation of the seasonal variations of the climate fluctuations, particularly, for the pre-monsoon and monsoon seasons. However, the mixed results obtained for some of the prediction experiments may also hint of vagaries in the models and, particularly, in the data, as the latter come from various sources.