A hybrid deterministic-fuzzy rule based model for catchment scale nitrate dynamics

Summary Current understanding of nitrate export from catchments indicates that the transport dynamics are mainly driven by hydrological processes characterised by complex nonlinear relationships. The aim of this paper is to develop a hybrid deterministic–fuzzy rule based model capable of simulating catchment scale nitrate transport on the basis of the relationships between driving and resultant variables. The deterministic water balance model WaSiM-ETH is used for the simulation of hydrological flow components. The simulated flow components from the WaSiM-ETH model together with observations are used to develop a fuzzy rule based nitrate transport model. The fuzzy rules are derived using a simulated annealing optimisation procedure supplemented by knowledge about data relationships. The study is undertaken using daily time step data from the Weida catchment in the North-Eastern Germany, which is a 100 km2 subcatchment of the Weisse Elster river in the Elbe river basin. The models show reasonable performance with regards to the magnitude and dynamics of the streamflow, and nitrate-N concentration and load. The superior performance of the fuzzy rule based model in comparison to a multiple linear regression model indicates a complex nonlinear relationship between driving and resultant variables. The assessment of the rules provides explicit insights on the qualitative and quantitative relationships between different variables and their relative importance. The subsurface flow is found to be the most important variable which corresponds to the prevailing understanding that the nitrate transport processes are mainly driven by it. The relative importance of temperature as an input variable indicates the effect of seasonal variability. The hybrid model is valid for present land use characteristics and management practices, which can be extended to include additional variables that affect nitrate entry to subsurface flow.

[1]  Paul Quinn,et al.  Scale appropriate modelling: representing cause-and-effect relationships in nitrate pollution at the catchment scale for the purpose of catchment scale planning , 2004 .

[2]  Keith Beven,et al.  A fuzzy decision tree to predict phosphorus export at the catchment scale , 2006 .

[3]  Sergei Ovchinnikov,et al.  Fuzzy sets and applications , 1987 .

[4]  G. Lischeid,et al.  Comparative simulation of the nitrogen dynamics using the INCA model and a neural network analysis: implications for improved nitrogen modelling , 2004 .

[5]  Luis Samaniego,et al.  Fuzzy rule-based classification of remotely sensed imagery , 2002, IEEE Trans. Geosci. Remote. Sens..

[6]  Karl-Erich Lindenschmidt,et al.  Physically-based hydrological modelling for non-point dissolved phosphorus transport in small and medium-sized river basins / Modélisation hydrologique à bases physiques et du transport de phosphore dissous diffus en bassins versants de petite et moyenne tailles , 2004 .

[7]  Application of a conceptual catchment scale nitrate transport model on two rural river basins , 1998 .

[8]  Timothy A. Cohn,et al.  Load Estimator (LOADEST): A FORTRAN Program for Estimating Constituent Loads in Streams and Rivers , 2004 .

[9]  András Bárdossy,et al.  The use of fuzzy rules for the description of elements of the hydrological cycle , 1996 .

[10]  D. Legates,et al.  Evaluating the use of “goodness‐of‐fit” Measures in hydrologic and hydroclimatic model validation , 1999 .

[11]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[12]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[13]  Michael Rode,et al.  Investigation of parameter uncertainty and identifiability of the hydrological model WaSiM-ETH , 2006 .

[14]  Jörg Schulla,et al.  Hydrologische Modellierung von Flussgebieten zur Abschätzung der Folgen von Klimaänderungen , 1997 .

[15]  Chantal Gascuel-Odoux,et al.  Seasonal and interannual variations of nitrate and chloride in stream waters related to spatial and temporal patterns of groundwater concentrations in agricultural catchments , 2004 .

[16]  Wayne Woldt,et al.  Fuzzy rule-based approach to describe solute transport in the unsaturated zone , 1999 .

[17]  M. Sivapalan,et al.  Nitrate attenuation in agricultural catchments: Shifting balances between transport and reaction , 2006 .

[18]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[19]  N. Null.  Artificial Neural Networks in Hydrology. I: Preliminary Concepts , 2000 .

[20]  Harald Kunstmann,et al.  High resolution distributed atmospheric-hydrological modelling for Alpine catchments , 2005 .

[21]  H. Riedwyl.  Goodness of Fit , 1967 .

[22]  James P. McNamara,et al.  An approach to understanding hydrologic connectivity on the hillslope and the implications for nutrient transport , 2003 .

[23]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[24]  Peter A. Troch,et al.  Spatial and temporal variations in surface water nitrate concentrations in a mixed land use catchment under humid temperate climatic conditions , 2000 .

[25]  Vladimir M. Krasnopolsky,et al.  A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components , 2006 .

[26]  K. Bencala,et al.  Hydrological controls on dissolved organic carbon during snowmelt in the Snake River near Montezuma, Colorado , 1994 .

[27]  Lawrence E. Band,et al.  Regulation of Nitrate‐N Release from Temperate Forests: A Test of the N Flushing Hypothesis , 1996 .

[28]  M. Fink.  Regionale Modellierung der Wasser- und Stickstoffdynamik als Entscheidungsunterstützung für die Reduktion des N-Eintrags : am Beispiel des Trinkwassertalsperrensystems Weida-Zeulenroda, Thüringen , 2004 .

[29]  A. Bárdossy,et al.  Development of a fuzzy logic-based rainfall-runoff model , 2001 .

[30]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

[31]  Modelling nitrogen dynamics for a mesoscale catchment using a minimum information requirement (MIR) concept / Modélisation des dynamiques de l'azote pour un bassin versant de taille moyenne, utilisant le concept de besoin minimum d'information , 2002 .

[32]  Valentina Krysanova,et al.  Automatic fuzzy-rule assessment and its application to the modelling of nitrogen leaching for large regions , 2003, Soft Comput..

[33]  Herbert Lang,et al.  Advanced flood forecasting in Alpine watersheds by coupling meteorological observations and forecasts with a distributed hydrological model , 2002 .

[34]  Lucien Duckstein,et al.  Fuzzy Rule-Based Modeling of Reservoir Operation , 1996 .

[35]  Karl-Erich Lindenschmidt,et al.  Distributed sediment and phosporus transport modeling on a medium sized catchment in central germany , 2001 .

[36]  Lucien Duckstein,et al.  Fuzzy Rule-based Methodology for Estimating Monthly Groundwater Recharge in a Temperate Watershed , 2002 .

[37]  L. Zadeh,et al.  Fuzzy sets and applications : selected papers , 1987 .