Représentation statistique des alternances pluie-non pluie à partir des séries pluviographiques Applications à Montpellier-Bel Air (1920-1971) et Paris-Montsouris (1949-1978)

Statistical representation of the alternation of dry and rainy spells using rainfall series -Applications at Montpellier - Bel Air (1920-1971) and Paris-Montsouris (1949-1978)

Université des Sciences et Techniques du Languedoc, Montpellier

Abstract

This is an attempt at the statistical portrayal of a succession of showers at a station using the shortest possible time interval. Two long numerised rainfall series are used: Montpellier - Bel Air, provided by the Ministry of Agriculture and Paris Montsouris, supplied by the national meterorological agency. The discrete units used are a thousandth of a day for time and a tenth of a millimeter for water heights. Successive precipitations are given schematically by an alternating series of dry spells (Ds) and rainy spells (Dh); the latter are also characterised by a continuous rainfall height H. The statistical properties of this process are studied separately for each month of the year. The marginal distribution of continuous rainfall heights H is characterised by a high frequency of heights lower than or equal to a threshold Ho (0.4 mm at Montpellier - 0.2 mm in Paris). The frequency distribution of these low heights is well described by an exponential law whose parameter is associated with the frequency of H ≤ Ho. The distribution of values H' higher than the Ho [H' = H - (Ho + 0.05)] is either protrayed by an exponential law after a parabolic transformation of the variable (Montpellier) or by a Weibull law (Paris). The couples (Ds - H) are log-linearly dependent. The value of the correlation coefficient is between 0.6 and 0.8 according to the season. Residual precipitation has a somewhat symmetrical distribution around the regression line, with a constant variance. The frequency distribution of dry spells is bimodal. The first mode corresponds to short dry spells between successive showers, and the second to much longer spells of true good weather. This distribution is described by combining the two lognormal lanes in a proportion p. The successive variables: spells and heights are all but independent. The tests carried out always lead to a slightly higher number of rejections than acceptances of the hypotheses of independence, for parametrical testing using the linear auto-correlation coefficient pl, for non-parametrical testing, distinguishing between two states on either side of a numerical value, and for scrutiny of the average duration of chronological sequences which are lower or higher than a given quantile. However, when comparing the rejections under various tests of each hall' of a series, the same seasons are never systematically found. Independence has thus been accepted, subject to it providing accurate results during simulation tests. Simulation offers no particular difficulty in the conditions stated above. To make a judgement of the results, rainfall heights have been added over 24 consecutive hours to obtain a series similar to a rainfall series in which successive rainy days have been cumulated. The observed and simulated series can then be compared at the level of the first two moments of the variables characterising a daily rainfall model: length in days of dry and rainy spells and the corresponding height of the latter. The comparison can also be made using monthly totals. The first simulation shows reasonably satisfactory results, except for the standard deviations of length of dry spells (overestimated) and heights during rainy spells (under estimated). The first anomaly is easily corrected by setting the maximum value observed as boundary to the dry spells (Ds). This touches on the problem of statistical portrayal of a physically bounded variable by a non-bounded law. The second anomaly is linked to a typology of daily spells : some corresponding to cyclonic disturbances involve only light showers; by contrast, others associated with convective phenomena, involve only heavy showers. It is found that a simulation distinguishing type of spell arbitrarily by drawing only from a small part of the law governing H (but preserving the law governing H over ail the spells) improves the results. The portrayal of a succession of showers at a station remains to be perfected by a typological study of spells and completed by a study of the succession of rain intensity within continuous spells of rainfall.