Annual rainfall values show good correlation between historical stations on the island of Puerto Rico, suggesting uniform causes for drought episodes. The absolute value of the interannual variability increases while the percentage variability decreases with increasing mean values. This is consistent with annual rainfall variability on the island of Oahu, Hawaii. For 94 years of area-averaged annual rainfall in Puerto Rico, 22 showed 100% or more change in interannual variability. Of these 22 years, the number of stations with the same sign as the area-averaged variability outnumber by 18 to 1 the number of stations of opposite sign. Thus, in cases of marked departures from one year to the next, the entire island is affected uniformly. The exact station location will dictate the absolute amounts, but will have only minor influence on the sign change between successive years.
Marked positive departures of rainfall in a given year tend to be followed by negative departures in the following year and vice versa. In 15 of the 22 cases of extreme interannual variability, the subsequent sequence of years show a reversal of sign of the change. These rainfall excesses and deficiencies are modulated by the quasi-biennial oscillation (QBO) on the interannual time scale. This is revealed through a singular spectrum analysis (SSA) on the annual rainfall time series (specifically, the series of monthly rainfall departures from the mean). The leading component represents the QBO.
The two leading components are statistically significant with respect to white noise. A time series of monthly rainfall departures may be reconstructed from each component. Since they are linearly independent, we may sum them to emulate a filtered surrogate for the actual rainfall time series. The filtered series are devoid of random noise, suggesting potential for long lead forecasts.
We test this potential by fitting an autoregressive (AR) model to each of the two reconstructed time series. The model provides 12 steps-ahead forecasts (12 steps-ahead forecasts from one initialization represents one year). The pearson product moment coefficient of correlation between forecast and filtered amounts are 0.98 and 0.97 for components one and two respectively. When the two component forecasts are summed, thereby representing a surrogate for monthly rainfall departures, the coefficient between predicted and actual is only 0.11. This indicates that the time series of monthly rainfall departures is dominated by noise processes. This is corroborated by the fact that the two components modeled represent only 12% of the total variance. Furthermore, while these components are marginally significant with respect to white noise, they are not significant with respect to an AR(1) process. Therefore, to any statistical standard more rigorous than an AR(1) process, all of the variance of monthly rainfall departures is explained by noise. These results cast doubt on the ability of univariate time series methodology to predict tropical rainfall in Puerto Rico.