THE PROBLEM OF MISSING DATA IN HYDROCLIMATIC TIME SERIES. APPLICATION OF SPATIAL INTERPOLATION TECHNIQUES TO CONSTRUCT A COMPREHENSIVE ARCHIVE OF HYDROCLIMATIC DATA IN SICILY, ITALY

摘要

Planning, management and e ective control of water resource systems, require a considerableudamount of hydrological data variables such as rainfall, temperature, stream-ud ow, etc.. Such data are required when a hydrological model has to be developed,udas well. Very often hydrological data sequences at a given gauge have gaps or areudincomplete, or are not characterized by a good quality or are not su ciently length.udThis can severely a ect, for example, the reliability of the design of a hydropowerudplant, the construction of dams, etc. Furthermore, the problem of missing values isuda common obstacle in time series analysis and speci cally in the context of rainfall,udtemperature and rainfall runo processes modelling.udThere may be various reasons for missing values, for instance equipment failure,uderrors in measurements or faults in data acquisition, and natural hazards such asudlandslides, or even temporary absence of observers, the cessation of measurement orudabsence of observations prior to the commencement of measurement or by limitedud nancial resources. Whatever the reasons, missing values produce a signi cant problemudfor water resources applications. Consequently, nding e cient methods to dealudwith the problem of missing values is an important issue in most hydrological analyses.udHowever, hydrological modellers commonly discard the observations with missingudvalues and only use the observations with complete information, which means thatuda lot of information contained in the dataset is lost. Furthermore, the approach isudinadequate for analyses that require serially complete data. On the other hand, theuduse of the dataset prone to missing data can result in errors that exhibit temporaludand spatial patterns (Stooksburry et al., 1999[Stooksbury1999]). As an alternative toudthis listwise(?) deletion procedure, modellers sometimes replace (or ll in ) a valueudfor the missing values by using, for example, the mean of the observed variables. Suchuda procedure could, however, seriously distort statistical properties like standard variation,udcorrelations or percentiles. But the best alternative to the above mentionedudapproaches consists of lling the gaps in the rainfall, temperature or stream ow timeudseries by estimating the missing values.udIn fact, the most common approach followed in technical literature is the applicationudof either deterministic or stocastic methods to estimate the missing data. Theuddescribed problem is so dramatically important within hydrological research that theudscienti c community has point out a transnational initiative of international researchudgroups, i.e., the ''Decade on Prediction in Ungauged Basins (PUB)'', a wide researchudproject promoted by the International Association of Hydrological Sciences (Sivapalanudet al., 2003). This e ort is particularly focused on the reconstruction of seriallyudincomplete data records in basins with short stream ow records or in ungauged riverudbasins.udIn this scenario, the individuation and application of the most suitable methodsudfor the accurate estimation of hydrological variable values, useful to ll in the incompleteudtime series, is of paramount importance and represents the most promisingudapproach to solve the problem of missing data. In particular, once the hydrologicaludvariable is de ned together with its speci c characteristic, the choice of the estimationudmethods and their comparison is necessary to carry out the best reconstruction of theudconsidered variable dataset.udThe issue of gaps in climatic variables have been the subject of a large number ofudscienti c works where numerous techniques for estimating missing data values haveudbeen implemented and compared. Among these methods, the temporal methods,udthat taking into account the temporal dependence of the considered variables, haveudbeen used and among more advanced methods, the space-time models, i.e. modelsudhandling dependence the spatial and temporal simultaneously, has been applied. Audgroup of methods that are also widely used in literature for the missing data estimationudare the spatial models which represent the spatial distribution of variables overuda speci c duration. Many papers have been dedicated to the comparison betweenuddeterministic and stochastic approaches to reconstruct data records and their resultsudsuggest that often the use of geostatistical techniques improve the results since theyudare able to study the pattern of spatial dependences observed for climatic variables;udin the particular case of estimation of runo , in some works it was highlighted thatudconsidering the runo as an areal process, i.e., considering the strongly dependenceudof runo with the basin area, improves by far the estimates obtained. Another considerationudis common to many works, i.e., that the use of algorithms that incorporateudancillary informations (geographical and morphological) into the spatial estimationudof climatic variables improves the obtained estimates.udThe aim of this thesis is to investigate the methods for the optimal estimation ofudthe missing data in time series of hydrological variables with reference to Sicily (Italy).udIn particular, the following hydrological variables are object of study: precipitation,udtemperature and runo .udIn this thesis only the spatial structural dependence of rainfall, temperature andudruno data is used to reconstruct missing data, neglecting the spatial-temporal dependence.udOn the basis of the variables speci ed, di erent estimation methods have beenudconsidered, described and applied to solve the problem of missing data. With regardudto the variables as precipitation and temperature, that can be represented as pointudprocesses, the following algorithms, used for the spatial interpolation, will be applied:udinverse distance weighting, radial basis function with thin plate spline, simple linearudregression, multiple regression, geographically weighted regression, arti cial neuraludnetwork, ordinary kriging, residual ordinary kriging. With the applications of theseudmethods, serially complete monthly and annual dataset will be obtained.udOn the other hand, for the runo , the proposed investigation stems from theudconsideration that it can be described as an areal process. With this assumption, audmore accurate estimation of the considered variable can be obtained. This approachudhas very few examples in scienti c literature but appears to be very promising inudthe considered eld. For this reason the estimation method, chosen for the runo ,udis a stochastic method to derive gridded maps for ner and ner resolution with audgeostatistical approach. It is, in particular, a stochastic interpolation system that canudbe assimilated to kriging system with the explicit consideration of the runo variableudas an areal process. The application of this methods will give the annual runo udestimated data for the stations that have been out of work in the chosen time windowudof input runo data and that are characterised by a dataset a ected by missing data.udMoreover, it will be possible to obtain the annual runo estimated values also forudthe areas of the basins not provided with gauge stations. The latter values can beudobtained by the gridded map with a certain resolution.udIt is important to highlight that the previous applications of such an approach areuddone in homogeneous climatic contexts with favorable conditions of the ow regime toudapply the procedure. On the contrary, here, for the rst time, the method is appliedudin the Sicilian context where both the climatic and morphological pro les are stronglyudinhomogeneous.