Rainfall Seasonal Forecast by Spectral Analysis of the Large Water Body Levels

The large water body level time series may serve as a natural proxy for a seasonal forecast of the precipitation tendency over the corresponding catchment area and even a whole neighborhood. The method presented here may serve as a useful complement to the statistical models which are trying to overcome the problem of infinity of precipitation-bearing processes and their interactions. The example presented here is the Dead Sea level monthly time series for the period of 1930-2019.

The Dead Sea catchment area is crossed by the westerlies from the Mediterranean Sea which bring the major part of regional precipitation during a rainy season. A certain part of precipitation flows back into the Mediterranean Sea. Still, there is a significant part that flows through the numerous tributaries into the Dead Sea during and after the rainy season.

A basis of the method is the spectral decomposition of the long-term Dead Sea level monthly time series. This spectrum presents the relative contributions of both the natural processes and artificial activities into the Dead Sea level time series variability. The main natural process grossly affecting the Dead Sea levels is evaporation from its surface, which is treated in this method as a long-term nonlinear trend. The detrended Dead Sea level spectrum has a negative slope. The low-frequency part of the level spectrum, being associated with innumerable natural processes and their interactions, has nevertheless some distinguishable features, or bandpasses. The artificial activities, main of which is water consumption from the Jordan River, have a non-regular character and represented as a high-frequency noise in the fading part of the level spectrum which therefore may be ignored in the following frequency analysis.

Note: It is worth to mention that we first tried to apply the spectral decomposition method directly to the precipitation time series of the Jerusalem station which is one of the most representative regional stations located on the axis of the Judaean Mountains range, between its western Mediterranean-side slopes and eastern Dead-Sea-side slopes. We have found that the high-frequency noisy part of the precipitation spectrum is more powerful then its low-frequency distinguishable bands. This means that any results of the frequency analysis of the precipitation spectrum would be undermined. Therefore, instead of the precipitation time series, the corresponding large water body level time series was chosen for the frequency analysis.

After detrending the Dead Sea level monthly time series, its spectrum has one high pick that corresponds to the one-year cycle and obscures other spectral components. After removal of the seasonal component, the whole spectrum fades even more rapidly. Now, it is possible to divide the level spectrum into the three main spectral components and high-frequency noise which may be ignored in further processing. Each main spectral component is being separated with a Butterworth filter. Each filtered series is then fitted with its partial analogous function which may be easily extrapolated. Then, all partial fitting functions are summed up. Verification showed that the best results are being obtained with the filter order of 2, and with each partial fitting function consisting of two sinusoids whose total of 6 parameters are optimized with the Nelder-Mead simplex method. Defining an optimal first-guess set of only the six parameters for finding the best local solution is workable based of the corresponding data waveform. The final fitting analogous function consists of six sinusoids.

The whole algorithm was verified for the rainy seasons of 1991/1992, 2002/2003, and 2018/2019 as if forecasted in the previous summer. That is, the Dead Sea level monthly time series was truncated by Aug 1991, Aug 2002, and Aug 2018, respectively. The seasonal forecast was evaluated with the method as described above. It was found that the tendency of the extrapolated fitting analogous function reflects the tendency of the changes in the Dead Sea level preprocessed time series. This time series, in its turn, is in a good correlation with the total precipitation time series, in spite of the frequency analysis of the latter was found as being much less promising. The proposed method may help in evaluation of the precipitation tendency for the coming rainy season.

We have investigated a possibility of applying of this method to two-year forecasting, and found that the differences in the direction of a tendency at this extent may either do come as in "1992/1993 forecast from Aug 1991" verification, or not, as in "2003/2004 forecast from Aug 2002" verification. The possible approach for increasing a forecasting period may be optimization of building a first-guess set of the input parameters of a simplex method.

Meanwhile, for a seasonal forecast, the described method is definitely may be recommended.