NCC Report No. 1 - (IMD), Pune

More documents

Recommendations

Info

using the best development period and retroactive technique. The ensembleforecast for each year was then computed as the simple average of the forecasts forthat year obtained from the best 5 models.The skill of the models was also measured by calculating the model statisticssuch as C.C. between actual and predicted ISMR (R) and bias in the modelpredictions (BIAS) in addition to RMSE. The BIAS has also the same units as that ofRMSE. The BIAS was computed using the following equation.)∑ (Y − Y)BIAS =k4.b.Principal Component - Regression (PCR) ModelsThe PCR technique is recommended when there is significant intercorrelationamong the predictors. The PCR model avoids the inter-correlation andhelps to reduce the degrees of freedom by restricting the number of predictors. Asseen in the Table-3, there is significant inter-correlation among some of thepredictors in SET-I and SET-II. Singh and Pai (1996) used Principal Component-Regression (PCR) model for the prediction of the seasonal (June-September) ISMRfor the country as a whole based on predictors from the Indian Ocean only.Rajeevan et al. (2000) on the other hand used PCR model for the prediction ofseasonal summer monsoon rainfall over two homogeneous regions of India.To develop a PCR model, Principle Component Analysis (PCA) is first appliedon the predictor set and then few PCs (principle components) having highest C.Cwith the predictand (ISMR) are selected. The selected PCs are than related to therainfall time series using a multiple regression equation. In this study, PCR modelsfor the first and second stage forecasts (PCR-I and PCR-II) were developed usingpredictor sets SET-I and SET-II respectively. The general mathematical formulationof PCR model is given below in brief.A set of time series of ‘m’ inter-correlated standardised variables for ‘n’ yearscan be represented by (nXm) matrix, Z= [Z ij : i=1,…..,n;j=1,…..,m]. Z is transformed14
into E via the matrix transformation, eij=Z ij a ji , using empirical orthogonal functionanalysis (EOFA). Here, e ij is empirical orthogonal variable for j th empirical orthogonalvariable for i th year and a ji for i th empirical orthogonal weight for j th variable. In matrixform above equation can be written as: E = ZAIf in addition, the matrices E and A obtained from EOFA are rescaledaccording to: L= AD 1/2 and F = ED 1/2 ; the complete procedure is called PCA. Here Fis (nXm) matrix of PC scores each having zero mean and unit variance (i.e. the PCscores are standardized), L is (mXm) matrix of PC loadings and D is the (mXm)diagonal matrix whose elements are eigen values of correlation matrix C (= 1/nZ T Z)arranged in descending order of magnitude.If we select any ‘p’ modes of the PC scores (p
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 18 and 19: the most “interesting” projecti
Page 20 and 21: Where, Net j denotes the weighted s
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

NCC Report No. 1 - (IMD), Pune

Create successful ePaper yourself

Delete template?

Save as template?