**1. Introduction**

240 Genetic Programming – New Approaches and Successful Applications

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The Ebro River is located in north-eastern Spain. After crossing the Catalan coastal mountain system, the Ebro reaches the sea. Along the lower part of the river, about 100 km from the mouth, there is a system of three reservoirs: Mequinenza (1500 hm3), Ribarroja (210 hm3) and Flix (11 hm3). These reservoirs regulate the hydrologic regime of the lower part of the river until it reaches the sea. The Mequinenza and Ribarroja reservoirs were finished in the late 1960s (in 1966 and 1969, respectively), while the Flix reservoir was completed in 1945. About 5 km downstream from the Flix reservoir is the Ascó nuclear power plant, which began its activity in December 1984 [1].

Ascó Nuclear Power Station, located on the Ebro River in Spain (Figure 1), takes river water for cooling purposes. The temperature of discharged water must be less than 13 ºC, however five kilometers downstream a water temperature of nearly 14ºC was estimated and such an anomaly was reported to the nuclear center. A detailed analysis shows the relationship between water temperature variation and the presence of a cascade dam system upstream of the Ascó Nuclear Power Station. Water temperature decreases downstream in the outlets of cascade dam systems [1]. During the winter period there also exists thermal stratification within the river, whereby water temperatures near deep intake areas are considerably less than the ambient temperature. Such a situation impacts water taken for cooling purposes by Ascó Nuclear Power Station.

Throughout the years, the human being has made use of fluvial ecosystems. Some actions have caused changes in the thermal regimes of rivers (eg. [2 ,3]).

© 2012 Arganis et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Arganis et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reservoirs and the use of water for cooling are the most important sources of water temperature modifications caused by humans. The use of water for cooling, usually by power plants, causes the water to become warmer [4]. This is often called "thermal pollution".

Comparison Between Equations Obtained by Means of Multiple

Linear Regression and Genetic Programming to Approach Measured Climatic Data in a River 243

regression (MLR) in this study, it was possible to identify the relative significance of each

Tests were made from data collected at the Ribarroja Station, which is located on the Ebro

**Figure 1.** Location of reservoirs and climatic stations on the Ebro River in Spain (Val, 2003 and

Evolutionary Computation (EC) are learning, search and optimization algorithms based on the theories of natural evolution and genetic. The steps of the basic structure of this kind of algorithms are shown in Figure. First, an initial population of potential solutions is randomly created (in the case of a Simple Genetic Algorithm (SGA), the initial population is composed of binary individuals). Then, the individuals of this population are evaluated considering the problem to be solved (environment) where a fitness value is assigned to each individual depending on how close individuals are to the optimum. A new generation is created by selecting the fitter solutions of previous generation and then, genetic operators such as crossover and mutation (Alter P(t) of Figure 2) are applied to selected individuals in order to create a new population (offsprings) which improve their fitness values in comparison to previous generation. This new population is evaluated and selection, crossover and mutation are again applied. This process continues until a termination criterion is reached (this is commonly established as the maximum number of generation).

climatic variable in estimating water temperature.

River in Spain (Figure 1).

google.com.mx)

**2. Methods** 

**2.1. Genetic programming** 

Reservoirs can cause various effects, depending on various factors such as the climate, the size of the impoundment, the residence time, the stability of the thermal stratification and the depth of the outlet [5]. Due to thermal stratification occurs, the water from deep-release reservoirs is cooler in the summer and warmer in the winter than it would be without the reservoir [6,7]. Water diversions can also alter water temperature regimes because they reduce discharge, which causes water temperature range to increase throughout the year [8]. Irrigation is also known to decrease discharge and increase water temperature [9].

In order to preserve the ecological balance it is very important to have a continuous inspection of water quality in that portion of the river. Freshwater organisms are mostly ectotherms and are therefore largely influenced by water temperature. Some of the expected consequences of a water temperature increase are life-cycle changes [4, 10], and shifts in the distribution of species with the arrival of allochthonous species [11, 12] and the expansion of epidemic diseases [13] as a possible result. Also, aquatic flora and fauna depend on dissolved oxygen to survive and this water quality parameter is a function of water temperature as well.

Water temperature variation analysis, in a river with a cascade dam, involves several hydrological and environmental aspects because of the dams impact on aquatic flora and fauna as shown by [14,15,16,1,17,18,19].

Because temperature is a water quality parameter that affects aquatic flora and fauna, it is important to have mathematical models which allow one to make estimations of water temperature behavior. These models are based on climatic data such as solar radiation, net radiation, relative humidity, air temperature, and wind speed. Accurate water temperature modeling may help diminish the environmental impact of increased water temperature on aquatic flora and fauna within the river.

Genetic programming (GP) algorithms have been used to derive equations which estimate the ten minute average water temperature from known variables such as relative humidity, air temperature, wind speed, solar radiation, and net radiation [20]. Only air temperature and relative humidity were associated with water temperature in some of the resulting equations, even though solar radiation is known to increase water temperature in rivers and ponds.

A correlation analysis could prove the implicit participation of solar radiation as a variable in air temperature, even though an explicit solar radiation term does not appears in the equation. Solar radiation was assumed to be independent with respect to water temperature resulting from neglecting the lag time between a change in the solar radiation value and the corresponding change in water temperature, [1] estimated this lag time to be nearly 160 minutes. By inputting data to both the genetic programming algorithm and multiple linear regression (MLR) in this study, it was possible to identify the relative significance of each climatic variable in estimating water temperature.

Tests were made from data collected at the Ribarroja Station, which is located on the Ebro River in Spain (Figure 1).

**Figure 1.** Location of reservoirs and climatic stations on the Ebro River in Spain (Val, 2003 and google.com.mx)
