Multivariate statistics and time series analysis of weather conditions and phenological parameters of cocoa tree (Theobroma cacao L.) under several irrigation strategies

The goals of this paper were to evaluate the interactions between a set of meteorological elements and sets of phenological variables of cocoa trees under three levels of supplemental irrigations, as well as between the sets of phenological variables themselves, in the "transversal" time steps. The experiment was carried out in Linhares, in the state of Espírito Santo, Brazil, during September of 1989 through August of 1993. The treatments were: no water restriction, supplemental irrigations in the stages of inflorescence and flowering (October to April) and no supplemental irrigations. The set of meteorological data series was made by maximum, minimum and average temperatures, global solar irradiation, and sunshine duration, wind speed at two meters height, estimated evapotranspiration, rain and supplemental irrigation. The sets of phenological variables included leaf flushing, leaf drop, flowering intensity, fruit setting and cherelle wilt. The canonical analysis was efficient to detect high correlations between the sets of meteorological and phenological variables, even in time series analysis. This technique showed time persistency of the effects of meteorological events on phenology of cocoa trees up to five months later, insinuating annual periodicities in interrelations of sets of variables. This technique was able to differentiate the treatments, suggesting higher similarities among the treatments with irrigation. Principal components analysis was an efficient tool to detect which meteorological variables held higher amounts of information; however it was not able to detect the important meteorological variables to be used in posterior analysis as expected. The problem was that meteorological variables that held large amount of information are those derived from several other environmental parameters interactions. Therefore, these variables were not the primary cause. Also, these procedures tended to discard variables associated with water in the atmosphere, like relative humidity and rainfall. The Fourier’s harmonic analysis was the better procedures to enlighten the more relevant results. The autocorrelation function was capable to show the intrinsic periodicities of each one of the variables, meteorologicals and phenologicals. The cross-correlation function was able to reveal invisibles tints interrelating the variables. Considering that biological systems do not always show a perfect response to any input variable, the most surprising result was the phenological response to photoperiod, which is essentially an astronomical variable, therefore a primary cause, which is clearly the effect of supplemental irrigation strategies. Unfortunately, the spectral analysis did not elucidate particularly any aspect, or added consistent information to that disclosed by harmonic analysis. A possible reason of these discrepancies would be the lengths of time series used, no longer enough, in terms of number of values of each series, for the spectral analysis to show its mathematical robustness and consistency.