Modeling rainfall-runoff process using soft computing techniques
Highlights
► We model rainfall-runoff relationship by genetic programming (GEP) technique. ► GEP results are compared with neuro-fuzzy (ANFIS) and neural network (NN) methods. ► Comparison results show that the GEP model performs better than the other models.
Introduction
Accurate estimation of the runoff by using rainfall, evaporation and other hydrologic variables is an important issue in hydrology and water resources engineering. The rainfall-runoff process is a complex non-linear outcome of various hydrologic parameters, i.e., precipitation intensity, evaporation, geomorphology of catchment, infiltration of water into the soil and depression storage as well as interactions between groundwater and surface water flows and cannot be modeled by simple models.
In the recent past, the use of Artificial Intelligences (AI) techniques, e.g., Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Genetic Programming (GP) in water resources engineering has become viable. So far, numerous works have been reported in literature regarding the application of ANNs in modeling rainfall-runoff and other hydrologic factors (e.g., Smith and Eli, 1995, Guven and Gunal, 2008, Minns and Hall, 1996, Mason et al., 1996, Dawson and Wilby, 1998, Fernando and Jayawardena, 1998, Tokar and Johnson, 1999, Tayfur and Singh, 2006, Tayfur et al., 2007, Kisi, 2008, Kisi, 2007, Kim, 2011).
ANFIS is another data-driven modeling approach, first proposed by Jang (1993), as a combination of an adaptive ANN and a fuzzy inference system. ANFIS is capable of accurately approximating any real continuous function on a compact set of parameters (Jang et al., 1997). ANFIS identifies a set of parameters through a hybrid learning rule combining both the back propagation gradient descent error and least square error methods. There are two approaches for fuzzy inference systems, namely the approach of Mamdani (Mamdani and Assilian, 1975) and the approach of Sugeno (Takagi and Sugeno, 1985). The main difference between both approaches arises from the output membership functions of each fuzzy model: Mamdani's approach uses fuzzy membership functions, while linear or constant functions are used in Sugeno's approach. ANFIS system uses Sugeno's fuzzy inference system which is more compact and computationally efficient than Mamdani's system.
Kisi (2006) compared ANFIS to ANNs for estimating daily pan evaporation values from available climatic data and found ANFIS to outperform ANNs. Chang and Chang (2006) used ANFIS for predicting of water level in reservoir during the flood periods. Yarar et al. (2009) compared ANFIS to ANN and seasonal auto regressive integrated moving average (SARIMA) models for modeling level change in lakes and found the ANFIS model to outperform the ANN and SARIMA. Ozger and Yildirim (2009) applied ANFIS for determining turbulent flow friction coefficient. Shiri and Kisi (2010) introduced a new wavelet-neuro-fuzzy conjunction model for predicting short term and long term stream flows. Based on the results obtained by Shiri and Kisi (2010), introducing the periodicity component of the target streamflow values (day of year, DOY) improves the models’ performance to great extent. Shiri et al. (2011a) compared ANFIS to ANN in estimating daily pan evaporation values and found ANFIS to be better than ANN both in “at station” and “cross-station” applications. Shiri et al. (2011b) used ANFIS for predicting short-term operational sea water levels and compared with the results of ANNs, Auto Regressive and MLR methods, which emphasized on ANFIS superiority to the applied techniques. Kisi and Shiri (2012a) introduced a wavelet-neuro-fuzzy conjunction model for predicting groundwater table depth fluctuations. Azamathulla et al. (2012) introduced an ANFIS based approach for predicting sediment transport in clean sewer.
GP was first proposed by Koza (1992), as a generalization of Genetic Algorithms (GAs) (Goldberg, 1989) and is particularly suitable where interrelationships among relevant variables are poorly understood; theoretical analysis is constrained by assumptions and therefore their solutions are of limited use; small improvements in performance are routinely measured, easily measurable and highly prized and there is a large amount of data in computer readable forms requiring tedious processing (Banzhaf et al., 1998). The relationships between independent and dependent variables are often referred to as the model, program or solution. The evolution starts from a initially selected random population of programs (initial population), where the fitness value of each model is evaluated against the fitness cases (using the values of the independent and dependent variables). As the population evolves from one generation to another, new models replace the old ones by having demonstrably better performance. The programs are then selected according to their own fitnesses (their performance in that particular environment). The mentioned process is repeated until a good solution can be found for the studied phenomenon. The selection method used in the present study is referred to as the Gene Expression Programming (GEP) based on evolving computer programs of different sizes and shapes encoded in linear chromosomes of fixed lengths (Ferreira, 2001a, Ferreira, 2001b). GEP is comparable to GP yet evolves computer programs of different sizes and shapes encoded in linear chromosomes of fixed lengths. There are two main players in GEP (Ferreira, 2006a): the chromosomes (which are usually composed of more than one gene of equal length) and the expression trees [programs] which are the expressions of the genetic information encoded in chromosomes.
Aytek and Kisi (2008) applied GP to suspended sediment, and found it to perform better than conventional rating curve and multi-linear regression techniques. Guven and Gunal (2008) predicted the local scour downstream the hydraulic structures, using a GP approach. Shiri and Kisi (2011a) compared GEP to ANFIS for predicting groundwater table depth fluctuations and found GEP to be better than ANFIS in this regard. Kisi and Shiri (2011) introduced new wavelet-GEP model for predicting rainfall values. Shiri and Kisi (2011b) applied AI techniques (i.e., ANFIS, ANN and GP) to estimate daily pan evaporation by using available and estimated climatic data in Iran and found the GEP to outperform the other applied models. Kisi et al. (2011) applied various wavelet conjunction models for predicting hourly as well as daily wind speed and found the GP hybrid model as the best model among others. Kisi et al. (2012) applied GEP, ANFIS, ANN and Auto Regressive Moving Average (ARMA) models for predicting daily lake levels. Based on their results, GEP surpassed the other applied techniques. Shiri et al. (2012) compared GEP to ANFIS in modeling daily reference evapotranspiration and found GEP better than ANFIS in this regard, with both local and regional data set. Kisi and Shiri (2012b) applied various AI models for estimating river suspended sediment load by implicating climatic variables. From the resulst it was found that the GEP outperforms the other applied methodologies. Drecourt (1999) compared GEP and ANN models in modeling rainfall runoff. Also, Savic et al. (1999), Muttil and Liong (2001), Babovic and Keijzer (2002), Liong et al. (2002) and Aytek and Alp (2008) applied GP to rainfall-runoff modeling.
The objective of the present study is to compare the accuracy of GEP, ANFIS and ANN techniques in modeling rainfall-runoff process. The paper is organized as follows. The next section presents a description of the methods applied in this study along with the information about the used data and statistical indexes. The applicability of the models on rainfall-runoff process modeling and the results are examined in the third section. Finally, the last section provides concluding remarks.
Section snippets
Used data
In the present paper, daily rainfall and runoff (discharge) data of the Kurukavak Catchment, a sub-basin of the Middle Sakarya basin in the Northwestern Turkey were used for modeling rainfall-runoff process. Fig. 1 represents the geographical position of the Kurukavak Catchment and the gauge stations. Kurukavak is located in Bilecik province and has a drainage area of 4.25 km2. Kurukavak catchment's soil has shallow and over shallow depths of soil, and, has the structure of etiher sandy loan, or
Preliminary investigation on optimal input combination by ANNs
The present paper aims at modeling rainfall-runoff process by GEP, ANFIS and ANN models, using recorded rainfall and runoff data. Several input combinations of runoff and rainfall were evaluated for modeling. The inputs present the previously recorded daily Q and P values (Qt−3, Qt−2, Qt−1, Pt−3, Pt−2 and Pt−1) and the output corresponds to the present runoff data (Qt), where the subscript t represents the time step. Consequently, several input combinations of Q and P data were constructed (as
Conclusions
A modeling study is reported in the present paper that develops ANN, ANFIS and GEP models for simulating rainfall-runoff process in the Kurukavak Catchment, a sub-basin of the Sakarya Basin (Northwestern Turkey). The comparison of the results provided that the employed models could successfully be applied to model rainfall-runoff process. The obtained results indicated that the GEP model is superior to ANFIS and ANN models in this regard from the statistical indexes viewpoint. Beside, GEP can
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