Abstract Arithmetic map operations are very common procedures used in GIS to combine raster maps resulting in a new and improved raster map. It is essential that this new map be accompanied by an assessment of uncertainty. This paper shows how we can calculate the uncertainty of the resulting map after performing some arithmetic operation. Actually, the propagation of uncertainty depends on a reliable measurement of the local accuracy and local covariance, as well. In this sense, the use of the interpolation variance is proposed because it takes into account both data configuration and data values. Taylor series expansion is used to derive the mean and variance of the function defined by an arithmetic operation. We show exact results for means and variances for arithmetic operations involving addition, subtraction and multiplication and that it is possible to get approximate mean and variance for the quotient of raster maps.

Neste artigo examina-se a influência da variável secundária como função da correlação com a variável primária na cokrigagem colocalizada. Para este estudo cinco bases de dados completas foram geradas no computador a partir das quais amostras com 60 e 104 pontos de dados foram retirados através do método de amostragem aleatória estratificada. Estas bases de dados completas foram geradas partindo-se de um par de variáveis, primária e secundária, que apresentam boa correlação. Então sucessivos conjuntos foram gerados adicionando-se uma quantidade de ruído branco de modo que a correlação se tornasse menor. Utilizando-se estas amostras foi possível encontrar o quanto as informações primária e secundária são utilizadas na estimativa de um ponto não amostrado conforme o nível de correlação.

In this paper the influence of a secondary variable as a function of the correlation with the primary variable for collocated cokriging is examined. For this study five exhaustive data sets were generated in computer, from which samples with 60 and 104 data points were drawn using the stratified random sampling method. These exhaustive data sets were generated departing from a pair of primary and secondary variables showing a good correlation. Then successive sets were generated by adding an amount of white noise in such a way that the correlation gets poorer. Using these samples, it was possible to find out how primary and secondary information is used to estimate an unsampled location according to the correlation level.