Influence of the evolution of a daily rain gauges network on the observation of the rainy surfaces according to their area
The most usual rainfall risk assessment, based on a stochastic approach, or an accurate quantiles estimation, requires long series of observations. Most of the time when long periods of observation are considered, the available information consists of data from daily rain gauge networks which are evolving in space and time during these periods. As the rainy surfaces which generate the highest intensities are localised in space, the intergauge distances may be too large to "observe" all the rainfall events occurring over a given network. Thus it could bias the stochastic results based on values sampled from such a network, especially when extreme rainfall events are considered. The aim of this paper is to estimate the capacity of a daily rain gauge network to intercept rainy surfaces according to their area and the network density. The results have been used to estimate the bias introduced in rainfall risk assessment using the regional frequencies of isohyets areas observed in the studied region. The network studied is the Languedoc-Roussillon daily rain gauge network, in a French region along the Mediterranean sea. The network has been developed by Météo-France since 1870. The number of gauges put into service has varied during the 1870-1993 period of observation: from 3 gauges in 1870, the maximum reached was 353 gauges in 1969 and 1972, which represented a spatial mean density of 12.6 gauges/ 1000 km2. Since 1972 the number of gauges has decreased; in 1993 the gauge density was the same as in 1963, with 10.6 gauges/ 1000 km2. Nevertheless the clustered gauges have been reduced, as have the maximum intergauge distances, and the network has become more homogeneous over the region. Using simulation, the percentage of rainy surfaces which have affected the region, and which have been observed by the rain gauge network, has been estimated, as a function of the rainy surfaces area and the rain gauge density. It could be interpreted as the empirical expression of the probability to observe a given rainy surface with a given network configuration. Two periods have been considered, 1870-1957 and 1958-1993. Two simulation methods have been used: in the first the rainy surfaces have been considered to be static and in the second their motion has been taken into account. It has appeared that considering the motion of rainy surfaces yields the same results as the static method but with a different rainy surface geometry. The small differences between the percentage of rainy surfaces observed by the network in both cases can be explained by the simulation methods. It has been shown that the average probability over the period from 1870 to 1957 of observing a given rainy surface is 2 to 4 times less than the average probability over the 1958-1993 observation period, during which the gauge density has increased and the network has become more homogeneous over the region: over the 1870-1957 period the rain gauge network intercepted 50% at least of the rainy surfaces equal to or larger than 700 km2 but in the 1958-1993 period 50% at least of the rainy surfaces were observed if their area exceeded 80 km2. If the rainfall event which affected the N"mes hydrological system on 2-3 October 1988 is considered, these results have shown that the average probability over the 1870-1957 observation period to observe such an event is 2 times less than over the 1958-1993 observation period. In a recent study, a rainfall risk assessment has been made over the Languedoc-Roussillon region, using the frequencies of the isohyets areas defined for different rain thresholds, for 24-hour and 48-hour durations. These isohyets areas have been estimated on the basis of a sample of 93 rainfall events selected over the Languedoc-Roussillon region from 1958 to 1993 (Neppel et al., 1998). A method to estimate the bias introduced by the network in the estimation of the isohyets area return periods has been carried out, using this empirical probability estimated with the static simulation method. It has been shown that the bias only affects the more frequent isohyets area quantiles, corresponding to return period of 1 year for 48-hour duration and 1 to 3 years for 24-hour duration. Moreover, for this sample and this network, it has been shown that the bias would be negligible compared to the quantiles 5% confidence limits, whatever the return period and the time step. It must be noted that with this sample the 5% confidence limits of the quantiles sometimes reach 100% of the quantiles. The results are related to the sample and the network configuration, and they should not be extended to other areas or other samples: a larger sample over the same region could lead to narrower confidence limits, in which case the bias might no longer be negligible. In particular, the use of historical data needs to consider the longest observation period. Usually the rain gauge density decreases over such observation periods, which leads to a lower empirical probability of observing rainy surfaces according to their area. Thus the bias influence may increase, especially compared with the quantiles 5% confidence limits which are reduced when the sample is enlarged. Nevertheless the method described here is general and may be transposed to other geographical zones, provided that the isohyets area frequencies and the empirical probability of observing a rainy surface according to its area, corresponding to the network under consideration, are known. The current tendency in France is to reduce the number of daily rain gauges, managed by volunteers, and to replace them by automatic rain gauges. However in such a case the density would decrease and reach that observed in 1900. When rainfall risk assessment is considered, this study has shown the drawbacks of such a policy.