Hydraulic Head Interpolation in an Aquifer Unit Using ANFIS and Ordinary Kriging
In this study, Ordinary Kriging (ok ), and Adaptive Neuro Fuzzy based Inference System (anfis ) are evaluated for assessing hydraulic head distribution in an aquifer unit covering 40 km2. Cartesian coordinates of the samples were used as inputs of anfis .
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Mu˘gla University, Geological Engineering Department, 48000 Kotekli Mu˘gla, Turkey [email protected] http://geoe.mu.edu.tr 2 MINES ParisTech, Geosciences Department 35 rue Saint-Honor´e,77305 Fontainebleau, France [email protected] http://www.geosciences.mines-paristech.fr/ CNRS/UPMC, UMR Sisyphe 7619, BP 105, Tour 55-56, 4 place Jussieu, 75252 Paris, France 4 Cemagref, UR Hydrosystems and Bioprocesses, P.B. 44, 92163 Antony Cedex, France
Abstract. In this study, Ordinary Kriging (OK), and Adaptive Neuro Fuzzy based Inference System (ANFIS) are evaluated for assessing hydraulic head distribution in an aquifer unit covering 40 km2 . Cartesian coordinates of the samples were used as inputs of ANFIS. Calibrated models are used to interpolate the hydraulic head distribution on a 50 m square - grid. Both simulations have realistic pattern (R2 > 0.97) even if OK performs slightly better than ANFIS at sampling location. The two methods capture different patterns. The Comparison of the two distributions allow for identifying area of estimate uncertainty, what can be used to improve the sampling network.
1 Introduction A hydrosystem is defined as a ”part of space [where atmosphere overlap soil surface and subsurface] through which water flows. Physical and biogeochemical phenomena occur in all hydrosystem because of reactions due to water moving through a media” [1]. Many earth scientists (hydrologists, geologists, biogeochemists,) do interest in understanding the behaviour of such a complex system. Usually they first do experiments/observations in the field at specific locations and then try to distribute these observations/measurements in space and time using modelling techniques which are based on abstractions. In this paper our focus is to distribute punctual hydraulic head measurements on a grid that covers a part of an experimental basin. One technique often used in earth sciences and especially in hydrogeology is kriging [2,3,4,5,6,7,8,9,10,11,12]. For a few years hydrologists started to use fuzzy logic and Adaptive neuro-fuzzy inference system (ANFIS) to estimate groundwater parameters [13], to predict reservoir level [14,15], river discharge [16,17,18,19,20,21,22,23] and karstic spring discharge [24], for groundwater management [25,26,27], and for assessing pollutant fluxes at the basin scale [28,29]. ANFIS was also used to model the hydrological cycle [30]. Nevertheless only K. Madani et al. (Eds.): Computational Intelligence, SCI 343, pp. 265–276. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com
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Legend Geology
Lprm, Silt and clay
g1a, Priabonian mudstone
C, Colluvions
Rm, Clay
e7b, Bartonian marl
Fz, Alluvium
Lpg2, Silt and sand
e7a, Bartonian limestone
LP, Silt
g2, Stampian sand
e6b, Bartonian limestone and marl
LPg1b, Silt
g1b, Rupelian limestone
Orgeval watershed Piezometers Training Avenelles watershed Validation stream network Test
Fig. 1. Geological Map of the Orgeval watershed, location of wells and springs divided int
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