Estimation of flow accumulation uncertainty by Monte Carlo stochastic simulations

Abstract

Very often, outputs provided by GIS functions and analysis are assumed as exact results. However, they are influenced by certain uncertainty which may affect the decisions based on those results. It is very complex and almost impossible to calculate that uncertainty using classical mathematical models because of very complex algorithms that are used in GIS analyses. In this paper we discuss an alternative method, i.e. the use of stochastic Monte Carlo simulations to estimate the uncertainty of flow accumulation. The case study area included the broader area of the Municipality of Čačak, where Monte Carlo stochastic simulations were applied in order to create one hundred possible outputs of flow accumulation. A statistical analysis was performed on the basis of these versions, and the 'most likely' version of flow accumulation in association with its confidence bounds (standard deviation) was created. Further, this paper describes the most important phases in the process of estimating uncertainty, such as variogram modelling and chooses the right number of simulations. Finally, it makes suggestions on how to effectively use and discuss the results and their practical significance.

Izlazni rezultati dobijeni primenom GIS funkcija i alatki za analizu, obično se podrazumevaju kao tačni, međutim i oni su podložni nesigurnostima koje mogu uticati na odluke bazirane na tim istim rezultatima. Ocena uticaja nesigurnosti rezultata je veoma kompleksna i često nemoguća primenom standardnih matematičkih metoda s obzirom na veoma kompleksne algoritme koji se koriste u GIS analizama. U ovom radu razmatrano je alternativno rešenje kod ocene nesigurnosti prostorne koncentracije oticaja, primenom Monte Karlo stohastičkih simulacija. Za područje šireg obuhvata opštine Čačak generisano je sto mogućih izlaznih verzija rezultata prostorne koncentracije oticaja primenom Monte Karlo stohastičkih simulacija. Na osnovu njih, uz odgovarajuće statističke analize dobijena je 'najverovatnija' verzija prostorne koncentracije oticaja uz pripadajući interval poverenja odnosno standardne devijacije dobijenih rešenja. U radu su opisane najznačajnije faze u procesu ocene nesigurnosti, poput modeliranja variograma i odabira broja simulacija. Takođe je data i preporuka kako najefikasnije primeniti i diskutovati dobijene rezultate i njihovu značajnost.