Spatial and temporal behavior of hydrochemical parameters in groundwater can be studied using tools provided by geostatistics. The cross-variogram can be used to measure the spatial increments between observations at two given times as a function of distance (spatial structure). Taking into account the existence of such a spatial structure, two different data sets (sampled at two different times), representing concentrations of the same hydrochemical parameter can be analyzed by cokriging in order to reduce the uncertainty of the estimation. In particular, if one of the two data sets is a subset of the other (i.e. an under-sampled set), cokriging allows us to study the spatial distribution of the hydrochemical parameter at that time, while also considering the statistical characteristics of the full data set established at a different time. Cokriging Estimation Variance (CEV) is a useful tool in order to determine the influence of the spatial configuration of monitoring networks on the estimations. Then it can be useful for evaluating an optimal arrangement of the wells of a monitoring network for estimating the parameter values in a given number of target sites. Nevertheless, an optimal pattern of a monitoring wells suffers of the uncertainties on the variogram parameters caused by the variographer's choices. Using a fuzzy approach to represent these uncertainties, it is possible to describe the variogram parameters as fuzzy numbers and the parameter uncertainties by means of membership functions. Using such fuzzy variograms, the cokriging method produces membership functions of both the estimation and the CEV. Such optimization procedure has been tested on real cases.
Il comportamento spazio-temporale di parametri idrochimici di inquinamento della falda acquifera può essere studiato attraverso gli strumenti della geostatistica. I cross-variogrammi costruiti incrociando le variazioni spaziali di due set di valori della stessa variabile campionata in periodi diversi sono modelli in grado di esprimere la continuità spaziale e la relativa persistenza temporale del parametro in falda. Per questo essi permettono di migliorare la stima del parametro nei periodi in cui ci sia stato un numero più limitato di prelievi. Tale proprietà è stata utilizzata per implementare una procedura di ottimizzazione al fine di individuare la migliore configurazione di campionamento, per stimare le concentrazioni in siti critici. La determinazione di una configurazione ridotta, ottimale, soffre delle incertezze legate all'ipotesi sui parametri dei variogrammi. L'uso di un approccio fuzzy per rappresentare tali incertezze permette di descrivere i parametri del variogramma come numeri fuzzy. Usando tali variogrammi fuzzy, il metodo del cokriging produce numeri fuzzy sia per la stima che per la varianza di stima. L'algoritmo di ottimizzazione con l'approccio fuzzy è stato testato su casi reali.
L'ottimizzazione delle Reti di Monitoraggio con Tecniche Fuzzy
Passarella G;Vurro M;
2000
Abstract
Spatial and temporal behavior of hydrochemical parameters in groundwater can be studied using tools provided by geostatistics. The cross-variogram can be used to measure the spatial increments between observations at two given times as a function of distance (spatial structure). Taking into account the existence of such a spatial structure, two different data sets (sampled at two different times), representing concentrations of the same hydrochemical parameter can be analyzed by cokriging in order to reduce the uncertainty of the estimation. In particular, if one of the two data sets is a subset of the other (i.e. an under-sampled set), cokriging allows us to study the spatial distribution of the hydrochemical parameter at that time, while also considering the statistical characteristics of the full data set established at a different time. Cokriging Estimation Variance (CEV) is a useful tool in order to determine the influence of the spatial configuration of monitoring networks on the estimations. Then it can be useful for evaluating an optimal arrangement of the wells of a monitoring network for estimating the parameter values in a given number of target sites. Nevertheless, an optimal pattern of a monitoring wells suffers of the uncertainties on the variogram parameters caused by the variographer's choices. Using a fuzzy approach to represent these uncertainties, it is possible to describe the variogram parameters as fuzzy numbers and the parameter uncertainties by means of membership functions. Using such fuzzy variograms, the cokriging method produces membership functions of both the estimation and the CEV. Such optimization procedure has been tested on real cases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
