Prediction of terrestrial and extraterrestrial parameters by modelling and extrapolating their natural regularities

Extrapolation of dominant modes of fluctuations after fitting suitable mathematical function to the observed long period time series is one of the approaches to long-term weather or short-term climate prediction. Experiences suggest that reliable predictions can be made from such approaches provided the time series being modeled possesses adequate regularity. Choice of the suitable function is also an important task of the time series modelling-extrapolation-prediction, or TS-MEP, process. Perhaps equally important component of this method is the development of effective filtering module. The filtering mechanism should be such that it effectively suppresses the high frequency, or unpredictable, variations and carves out the low frequency mode, or predictable, variation of the given series. By incorporating a possible solution to these propositions a new TS-MEP method has been developed in this paper. A Variable Harmonic Analysis (VHA) has been developed to decompose the time series into sine and cosine waveforms for any desired wavelength resolution within the data length (or fundamental period). In the Classical Harmonic Analysis (CHA) the wavelength is strictly an integer multiple of the fundamental period. For smoothing the singular spectrum analysis (SSA) has been applied. The SSA provides the mechanism to decompose the series into certain number of principal components (PCs) and then recombine the first few PCs, representing the dominant modes of variation, to get the smoothed version of the actual series.   Twenty-four time series of terrestrial and extraterrestrial parameters, which visibly show strong regularity, are considered in the study. They can be broadly grouped into five categories: (i) inter-annual series of number of storms/depressions over the Indian region, seasonal and annual mean northern hemisphere land-area surface air temperature and the annual mean sunspot number (chosen cases of long term/short term trends or oscillation); (ii) monthly sequence of zonal wind at 50- hPa, 30-hPa levels over Balboa (representative of quasi-biennial oscillation); (iii) monthly sequence of surface air temperature (SAT) over the India region (strongly dominated by seasonality); (iv) monthly sequence of sea surface temperature (SST) of tropical Indian and Pacific Oceans (aperiodic oscillations related to El Nino/La Nina); and (v) sequence of monthly sea level pressure (SLP) of selected places over ENSO region (seasonality and oscillation). Best predictions are obtained for the SLP followed by SAT and SST due to strong domination of seasonality and/or aperiodic oscillations. The predictions are found satisfactory for the lower stratospheric zonal wind over Balboa, which displays quasi-periodic oscillations. Because of a steep declining trend a reliable prediction of number of storms/depressions over India is possible by the method. Prediction of northern hemisphere surface air temperature anomaly is not found satisfactory.