Elsevier

Environmental Modelling & Software

Volume 38, December 2012, Pages 89-100
Environmental Modelling & Software

Predicting and managing reservoir total phosphorus by using modified grammatical evolution coupled with a macro-genetic algorithm

https://doi.org/10.1016/j.envsoft.2012.05.006Get rights and content

Abstract

A model that predicts the monthly water quality for a subtropical deep reservoir was constructed based on a newly developed programming system, the incremental grammatical evolution (IGE). IGE was designed to execute Grammatical Evolution (GE) by iteratively introducing the optimal solution until convergence, and to explore complex veiled relationships between inputs and outputs when physical models cannot be defined in advance. A disadvantage of traditional GE is that it tends to select the most significant input variables and may become trapped in a local optimum. The IGE adequately manages the large input dimensionality by incrementally expanding the search depth. From three IGE runs, we extracted four significant input variables from 15 input variables, including watershed chemical loads, precipitation, inflow, and outflow, and expressed them appropriately in a sophisticated mathematical manner with accepted complexity. The IGE-derived equation yields the optimal predictive capability, especially for peak total phosphorous (TP) values, compared to traditional multilinear regression (MLR) and back-propagation neural network (BPNN) models. The sensitivity analyses reconfirm the effectiveness of the selected variables in the nonlinear mathematical equations. Although BPNN and IGE demonstrate similar performances, we preferred the latter because of its transparency in providing a formula with measurable parameters. After obtaining the IGE-derived model, a Macro-evolutionary Genetic Algorithm (MEGA) was applied to enhance searching efficiency and genetic diversity during optimization, and subsequently deduced the reduction rates of TP loads from various input sources to achieve the water quality requirement of the reservoir. This practice benefits the reservoir management by revealing the forcing functions that are manageable to prevent reservoir eutrophication.

Introduction

Eutrophication is one of the major water quality problems in river and reservoir systems (Garnier et al., 2005). Reservoirs, lakes, and a number of estuaries act as “nutrient traps”, meaning that many water bodies have progressed along a sequence from low productivity or oligotrophic settings to productive mesotrophic conditions to over-enriched hypertrophic or eutrophic conditions, with subsequent increases in the algal or cyanobacterial mats and anoxia, changes which reduce overall biodiversity (Carpenter et al., 1969; Likens, 1972). Phosphorus and nitrogen from point and non-point sources in the upstream watershed are the two essential nutrients for algal growth, of which phosphorus has been recognized as the limiting nutrient in most freshwater bodies (Raymont, 1980). Therefore, the addition of phosphorus can have detrimental effects on aquatic systems by increasing the biological productivity of surface water (Mau and Christensen, 2000). Development of strategies to prevent reservoir eutrophication requires information about the forcings, the specific nutrient sources and quantification of their relative contributions (Diogo et al., 2008). However, the complexity of the physical, chemical, and biological processes make prediction of the nutrient loading and eutrophication status and subsequent development of a management strategy very difficult (Kao et al., 2004; Kuo et al., 2007; Huang et al., 2010).

Artificial neural networks (ANNs) have recently offered an effective alternative tool for water quality modeling and forecasting (Zou et al., 2002; Kralisch et al., 2003; Kuo et al., 2006). Although ANN is considered a nonlinear black-box model, unable to express explicit functions or improve the understanding of physical mechanisms (Chen et al., 2011), ANN models can be used to predict the output from new independent input data through training processes, and are therefore suitable for simulating water quality trends in environments with complex hydrological dynamics superimposed by nonlinear ecological responses. Lee et al. (2003) used ANN to successfully predict the algal bloom dynamics of the coastal waters of Hong Kong. Maier et al. (2004) used ANNs to derive the optimal alum doses and treated water quality parameters. Maier et al. (2010) indicated that the vast majority of studies focus on flow prediction, with much less applications to water quality.

Conversely, evolutionary computation techniques are based on survival of the fittest, a powerful principle of evolution. The evolutionary computation techniques approach demonstrates an advantage over traditional statistical methods because it is distribution-free. As with ANN, no prior knowledge of the statistical distribution in the data is required. The genetic algorithm (GA) is one of the most widely used search algorithms among these methods, though it has a number of disadvantages, such as fixed-length encoding and premature convergence (Chen and Chang, 2007). Genetic programming (GP) demonstrated significant success in the automatic generation of programs or equations between the inputs and outputs; however, it is difficult to construct a tree-type data structure in GP (Chen, 2003a, b). One of these difficulties is to choose the appropriate size of a fix-designed tree to express a meaningful equation in advance. The recently developed grammatical evolution (GE) technique is a biologically efficient approach that performs the evolutionary processes on simple variable-length binary strings. The data structure in GE is flexible, thereby allowing researchers to maximize the applicability of genetic algorithms. Chen et al. (2008) applied GE to improve the remote monitoring on water quality in a subtropical reservoir with satellite imagery. Chen and Wang (2010) proved that GE is more efficient and robust in generating relatively smaller root mean square errors (RMSEs) by comparing the predicting accuracies between an improved real-coded GE and a GP. However, GE cannot acquire a satisfactory solution when the number of input variables is too high.

Using historical data, we compared three methods for developing an optimal model with a lead-time to forecast the behavior of nutrient loads and the in-reservoir nutrient status. Our case study tested GE as an optimal tool for watershed management, one which indicates how to maintain a reasonable balance between water quality and farming requirements. We introduce the GE algorithm concerning the incremental running process to improve prediction accuracy. The total phosphorus (TP) forecasting model of the Feitsui Reservoir in Northern Taiwan is demonstrated as a case study. The incremental GE (IGE) was used and compared with the traditional GE regarding performance. Additionally, multilinear regression (MLR) and back-propagation artificial neural network (BPNN) were implemented for comparison. The macro-evolutionary genetic algorithm (MEGA) was integrated into our IGE model to optimize the water quality management and control of nutrient loads from the watershed.

Section snippets

Grammatical evolution

Grammatical evolution (GE) is an evolutionary automatic programming type system that combines a variable length binary string genome and Backus-Naur Form (BNF) grammar to evolve interesting structures. Variable length binary string genomes are used with each codon representing an integer value where codons are consecutive groups of 8 bits. The integer values are used in a mapping function to select an appropriate production rule from the BNF definition; the numbers generated always represent

Feitsui Reservoir

Feitsui Reservoir at 25°27′ N and 121° 33′ E is the most important reservoir of northern Taiwan, supplying drinking water for more than five million people in Taipei City. The main dam is located downstream of Peishih Creek, a tributary of Hsintien Creek (Fig. 2). Agricultural activities surround the catchment area. There are no industrial activities in the catchments. Atmospheric influx, domestic sewage and agricultural fertilizers are the primary sources for most of the anthropogenic

Summary and conclusions

This paper provides an example of using the IGE method coupled with the macro-evolutionary genetic algorithm (MEGA) to predict the total phosphorous (TP) concentration of a reservoir in Taiwan and to provide strategic control for maintaining the water quality standard. The IGE process overcomes the multivariable nonlinear problems by running the traditional GE several times to achieve higher precision when deriving an appropriate model to simulate the TP concentration. From the results of the

Acknowledgments

This work was supported by the National Science Council of the Republic of China (NSC 97-2221-E-216-022-MY2, NSC 100-2621-M-001-003-MY3).

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