Yamamoto Jorge K, Kikuda Antônio T, Rampazzo Guilherme J, Leite Claudio B B
Universidade de São Paulo, Instituto de Geociências, Geologia Sedimentar e Ambiental, Rua do Lago, 563, Cidade Universitária, 05508-900 São Paulo, SP, Brazil.
Universidade Federal de São Paulo, Departamento de Ciências Exatas e da Terra Rua São Nicolau, 210, 09913-030 Diadema, SP, Brazil.
An Acad Bras Cienc. 2018 Aug;90(2 suppl 1):2025-2048. doi: 10.1590/0001-3765201820170589.
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.
