NCC Report No. 1 - (IMD), Pune

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Where, Net j denotes the weighted sum of inputs for j th hidden layer neuron which isdefined asNetpj= ∑ Wjixi+ θj,i=1Where W ji denotes the weight between i th input layer neuron & j th hiddenlayer, x i represents the i th element of input pattern and θ j represents the bias weightfor the j th hidden layer neuron. <strong>No</strong>w the output Y is computed as:Y = W H1+ W2H21+δW 1 & W 2 are the weights between output neuron and H 1 & H 2 respectivelyand δ is the bias weight.There are many back propagation training algorithms. We have used theResilient Back propagation algorithm (Riedmiller and Braun 1993) to train thenetwork. For each case, 20 model runs were made by changing the initial guessvalues of weights. The predicted output was then assumed as the average of thevalues obtained during the 20 independent model runs. For the development of theANN models we have used algorithms available in the Matlab software.5. Results and Discussions5.a. EMR Models2Fig.5a shows the R plotted against the number of predictors for all possiblemodels (63 models) derived from the SET-I. Fig.5 a clearly shows that the increasein the number of model predictors need not essentially improve the modelperformance. Fig.5 b shows the same details like Fig.5a but for all possible modelsfrom SET-II. The Tables 4a & 4b respectively show the details of 5 best modelsselected using the maximum2R criteria.18
Further, the second task of identification of best development period wasundertaken. The RMSE and R were calculated for all the possible developmentperiods (8 to 35 years) for each of the 10 MR models listed in the Tables 4a & 4b.Fig.6 shows the variation of R & RMSE with the development period for Model 4shown in Table -4a, which has 5 predictors of SET-I as the input. It is seen that foraround 23 years of development period, the RMSE has its minimum value and the Rhas maximum value indicating the best model performance around this period. Thus,we can assume that the best model development period for this particular modelwas around 23 years. Similar exercise on other models revealed that thebest/correct model development period for all the models were in general around 21-25 years. To keep uniformity in the further analysis, we have taken 23 years as themodel development period for all the models.For the independent verification of the models, independent forecasts weregenerated with the retroactive technique with development period as 23 years. Asthe data period of SET-I was 1951-2005, the independent predictions bycorresponding 5 best models were possible for the period of 32 years (1974 to2005). In the case of SET-II, as the data period was 1958-2005, the independentpredictions by the corresponding 5 best models were possible only for the period of25 years (1981 to 2005).Fig.7 shows the model predictions for the period 1974-2005 by the 5 EMR-1models, and their ensemble average. Similarly, Fig.8 shows the model predictionsfor the period 1981-2005 by the 5 EMR-II models and their ensemble average.Table-5 shows the model performance statistics of EMR-I and EMR-II models. Asseen in the Table-5, RMSE for the period 1981-2004 of the best 5 regression modelsused in the EMR-I model varied in the range of 7.18-8.37 % of LPA. The RMSE ofthe ensemble model was 7.54% of LPA. In the case of EMR-II, the RMSE for thesame period (1981-2004) of the selected 5 best models was in the range of 5.91-6.82 % of LPA and that of the ensemble forecast was 5.89 % of LPA. This indicatesthat the performance of the EMR-II and the individual MR models used in itsensemble was better than that of EMR-I model and the individual MR models usedin its ensemble. The RMSE of predictions based on climatology was 10.3% of LPA.19
Page 2: NEW STATISTICAL MODELS FORLONG RANG
Page 5 and 6: For the long range forecasting (LRF
Page 9 and 10: computed as the average of surface
Page 11: tropical Pacific Ocean in boreal wi
Page 14 and 15: to a model with smallest model size
Page 16 and 17: using the best development period a
Page 18 and 19: the most “interesting” projecti
Page 22 and 23: The climatological forecast for a g
Page 24 and 25: period of 1981-2004 were 6.89% and
Page 26 and 27: chance of failure but no guarantee
Page 28 and 29: EMR-II were based on the data of 19
Page 30 and 31: ReferencesAngell J. K., 1981, Compa
Page 32 and 33: Iyengar R.N and Raghukanth, S.T.G.,
Page 34 and 35: Parthasarathy, B., Rupa Kumar, K. a
Page 36 and 37: Walker, G. T., 1923, Correlation in
Page 38 and 39: Table - 3 : Inter-correlation among
Page 40 and 41: Table - 8: Model statistics of the
Page 42 and 43: SE INDIAN OCEAN SST ANOMALYSTD. ISM
Page 44 and 45: N. ATLANTIC MSLP ANOMALYSTD. ISMR32
Page 46 and 47: ADJUSTED R-SQUARE Vs MODEL SIZE: DA
Page 48 and 49: PERFORMANCE OF ENSEMBLE MODEL: JUNE
Page 50 and 51: 25PERFORMANCE OF ANN MODELS FOR THE

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