Statistical forecasting of daily precipitations

From the time series of daily precipitation observed in Modena (Italy) since 1830, a model for the daily statistical forecasting has been built. The main tool of the model is an urn which contains balls labelled by \uabwet\ubb and \uabdry\ubb. The daily extraction from the urn determines whether, on that day, there will be a precipitation,i.e. if that day will be \uabwet\ubb or \uabdry\ubb. If the day is dry, the content of the urn is changed by adding other balls some labelled by dry and some other labelled by wet. The numbers of added balls depend on the day of the year (seasonal dependence). If the day is wet, the urn is reset to an initial condition, which depends on the day of the year (seasonal dependence). Moreover, if the day was wet, the likely quantity of precipitation is deduced from a gamma distribution with parameters which are seasonally dependent. All the seasonally dependent parameters in the statistical processes previously discussed can be expressed by Fourier expansions, having one year as fundamental period. The observed distributions are adequately fitted by expansions which do not exceed the second harmonic. Although the model has been tuned on the observations in Modena, it can presumably be extended to the entire region having same climate,i.e. the Po Plain. \uc8 presentato un modello per la previsione statistica giornaliera di precipitazione, messo a punto mediante la serie temporale delle osservazioni giornaliere a Modena (Italia) che inizia dal 1830. Si tratta di un modello ad \uaburna\ubb la quale contiene palline etichettate \uabpioggia\ubb e \uabsecco\ubb. L'estrazione giornaliera dall'urna determina se in quel giorno ci sar\ue0 precipitazione, ossia se il giorno \ue8 di pioggia\ubb o \uabsecco\ubb. Se il giorno \ue8 secco, il contenuto dell'urna \ue8 variato con l'aggiunta di altre palline etichettate da \uabsecco\ubb e \uabpioggia\ubb. Il numero di palline aggiunte dipende dal giorno dell'anno (dipendenza stagionale). Se il giorno \ue8 piovoso, il contenuto dell'urna \ue8 riportato ad una condizione iniziale, che dipende dal giorno dell'anno (dipendenza stagionale). Inoltre, nel caso di giorno piovoso, la quantit\ue0 di pioggia \ue8 dedotta da una distribuzione gamma con parametri dipendenti dal tempo. Tutti i parametri con dipendenza stagionale del precedente processo statistico sono stati espressi mediante uno sviluppo in serie di Fourier, avente un periodo fondamentale di un anno. Le distribuzioni osservate sono adeguatamente rappresentate da sviluppi in serie che non superano la seconda armonica. Questo metodo di previsione statistica giornaliera pu\uf2 essere facilmente combinato con metodi di previsione giornaliera dinamica, poich\ue9 le previsioni (sia statistica che dinamica) sono effettuate ogni giorno. Sebbene il modello sia stato messo a punto mediante le osservazioni di precipitazione a Modena, presumibilmente esso pu\uf2 essere esteso all'intera regione climaticamente omogenea, ossia la Pianura Padana. \u418\u437 \u432\u440\u435\u43c\u435\u43d\u43d\u43e\u439 \u43f\u43e\u441\u43b\u435\u434\u43e\u432\u430\u442\u435\u43b\u44c\u43d\u43e\u441\u442\u438 \u441\u443\u442\u43e\u447\u43d\u44b\u445 \u432\u44b\u43f\u430\u434\u435\u43d\u438\u439 \u43e\u441\u430\u434\u43a\u43e\u432, \u437\u430\u440\u435\u433\u438\u441\u442\u440\u438\u440\u43e\u432\u430\u43d\u43d\u44b\u445 \u432 \u41c\u43e\u434\u435\u43d\u435 (\u418\u442\u430\u43b\u438\u44f) \u441 1830 \u433., \u43f\u43e\u441\u442\u440\u43e\u435\u43d\u430 \u43c\u43e\u434\u435\u43b\u44c \u434\u43b\u44f \u441\u443\u442\u43e\u447\u43d\u43e\u433\u43e \u441\u442\u430\u442\u438\u441\u442\u438\u447\u435\u441\u43a\u43e\u433\u43e \u43f\u440\u43e\u433\u43d\u43e\u437\u438\u440\u43e\u432\u430\u43d\u438\u44f. \u41e\u441\u43d\u43e\u432\u43d\u43e\u439 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