Uncertainty assessment of monthly water balance models
based on Incremental Modified Fuzzy Extension Principle
method
M. Nasseri, B. Zahraie, A. Ansari and D. P. Solomatine
ABSTRACT
In this paper, a new method, namely Incremental Modified Fuzzy Extension Principle (IMFEP), is
proposed for uncertainty assessment of conceptual water balance models. IMFEP is based on a new
modification of fuzzy extension principle using fuzzy approximate. The most important feature of the
IMFEP method lies in its realistic superposition of convex fuzzy membership functions of model
inputs at different fuzzy α-cuts. To evaluate the IMFEP method, four other fuzzy-based approaches
have been used to assess the uncertainties in simulating monthly water balance in basin scale and
their results are compared with IMFEP. These approaches, one based on simple fuzzy mathematics,
Vertex method, UNcertainty Estimation based on local Errors and Clustering (UNEEC) and Modified
Fuzzy Extension Principle (MFEP) have been previously used for uncertainty estimation of water
models. The nonlinear monthly water balance models calibrated for the two basins in Iran and
France and their outputs with the five aforementioned methods have been compared. For both
basins, IMFEP and MFEP methods have shown the best performance followed by UNEEC and Vertex
methods (however, the differences in the underlying assumptions of the UNEEC method have to be
taken into account). It can be concluded that the IMFEP method shows strong performance of
uncertainty propagation in all evaluated fuzzy α-cuts.
M. Nasseri (corresponding author)
School of Civil Engineering,
University of Tehran, Tehran,
Iran
E-mail: mm_nasseri@yahoo.com;
mnasseri@ut.ac.ir
B. Zahraie
Center of Excellence for Engineering and
Management of Civil Infrastructures,
School of Civil Engineering,
University of Tehran, Tehran,
Iran
A. Ansari
International Institute of Earthquake Engineering
and Seismology (IIEES), Tehran,
Iran
D. P. Solomatine
UNESCO-IHE Institute for Water Education,
Delft,
The Netherlands
and
Water Resources Section,
Delft University of Technology,
The Netherlands
Key words | fuzzy reasoning, mathematical fuzzy operator, modeling uncertainty estimation,
monthly water balance, UNEEC
INTRODUCTION
Uncertainty assessment in environmental sciences has
recently received significant attention. Various methods
have been used to assess the uncertainty of simulations.
There is a wide range of uncertainty evaluation methods
which can be classified in the three important categories:
probabilistic, possibilistic, and hybrid methods, as shown
in Figure 1. Probabilistic methods typically refer to cdf
(cumulative distribution function) or pdf (probable distri-
bution function) of parameters, input, or output variables.
This class employs different approaches, such as analytical
(Tung ), statistical (Melching ; Langley ) and
all sampling-simulation and iterative approaches, such as
Monte Carlo, Markov Chain Monte Carlo, mostly under a
Bayesian framework (Beven & Binley ; Kuczera &
Parent ; Thiemann et al. ; Krzysztofowicz ;
Montanari & Brath ; Ruessink ; Mishra ).
Broadness of uncertainty projection methods and their
inevitable statistical assumptions are the most important
weakness of probabilistic uncertainty simulation methods
(Montanari ). The four major difficulties of using these
methods can be listed as follows:
•
Difficulty or impossibility of analytical derivation of stat-
istical functions in case of complex models.
•
Imprecision in identifying suitable statistical distribution
of model parameters and variables (Montanari ).
1340 © IWA Publishing 2013 Journal of Hydroinformatics | 15.4 | 2013
doi: 10.2166/hydro.2013.159
Downloaded from https://iwaponline.com/jh/article-pdf/15/4/1340/387192/1340.pdf
by guest
on 07 December 2018