A mathematical theory of de-integrating long-time integrated rainfall statistics. Part II: from 1day to 1minute

作者：Matricciani Emilio^*

来源：International Journal of Satellite Communications and Networking, 2013, 31(2): 77-102.

DOI：10.1002/sat.1021

• applied meteorology
• climatology
• hydrology
• radio propagation
• rainfall intensity
• rain rate
• de-integration
• disaggregation

We have developed, tested and discussed a theory for de-integrating the probability distribution (PD) of the daily rain rate to the PD of the rain rate integrated in 1min, through many simple steps, with a good or very good precision, for a large range of probabilities and in many sites. The theory can also estimate the number of rain events (in the sense of rainstorms), NR, their average duration and the (conditional) PD of daily rainy time. The theory needs only three inputs, measured on site: the daily rain rate PD, the number of rainy days, ND (only for finding NR) and the PD of the rain rate integrated in two consecutive and disjoint couples of days. The theory contains two complementary parts, both successfully tested: the first deals mainly with duration of daily rainy time and rain events, and the second deals with the main issue, namely de-integrating daily rain rate PDs in 1-min PDs. We have tested the theory on duration of rainy time in Spino d'Adda, Gera Lario, Fucino and Prague and subsequently with real (blind) field tests in Milan, Lugano, many sites in the USA, and Canada. The sites tested belong to very different climatic regions. Nevertheless, the predictions are generally very close to the experimental data. The theory, and its powerful predictions, can be useful for several research communities: radio propagation, agriculture, climatology, hydrology and applied meteorology. For all disciplines and applications, seasonal studies or even monthly studies could be pursued because the data banks available can be very large, even for restricted sub-data banks. The theory will estimate its parameters on on-site seasonal, or monthly, measurements. Future developments could deal with de-integrating large-area and long-time integrated rain rate, observed by means of meteorological satellites, for obtaining point' 1-min rain rate PDs concerning a small homogeneous area. We have tested the theory to sites with very different climates and for latitudes between 65 degrees N and 28 degrees N. Therefore, we think that the theory can be applied globally in this latitude range because its parameters are derived from local measurements and, perhaps, down to the tropics. Because of the simplicity of the theory, and its use of few local measurements, it may be applied also to equatorial sites. This, however, is only a conjecture because we have not tested the theory directly there.

• 出版日期2013-4