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A comparison of multiple non-linear regression and neural network techniques for sea surface salinity estimation in the tropical Atlantic Ocean based on satellite data. (English. French summary) Zbl 1338.86015

Summary: Using measurements of Sea Surface Salinity and Sea Surface Temperature in the Western Tropical Atlantic Ocean, from 2003 to 2007 and 2009, we compare two approaches for estimating Sea Surface Salinity : Multiple Non-linear Regression and Multi Layer Perceptron. In the first experiment, we use 18,300 in situ data points to establish the two models, and 503 points for testing their extrapolation. In the second experiment, we use 15,668 in situ measurements for establishing the models, and 3,232 data points to test their interpolation. The results show that the Multiple Non-linear Regression is an admissible solution whether it be interpolation or extrapolation. Yet, the Multi Layer Perceptron can be used only for interpolation.

MSC:

86A32 Geostatistics
86A05 Hydrology, hydrography, oceanography
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[1] : Residual ri= yi- \hat{}yi yiobserved value \hat{}yifitted responsenr2i=ni(yi- \hat{}yi)2 S =i In Figure 4, we show some data points and a regression line, the plotted squares represent the squares of residuals. If we change the slope and/or the intercept of this line, the sizes of squares would be changed. The Least Squares Method find the line that minimizes the total area of these squares [6]. ESAIM: PROCEEDINGS AND SURVEYS71 Second experiment: {\(\beta\)}0= -3.925 {\(\beta\)}1= +0.5998 {\(\beta\)}2= +2.828 {\(\beta\)}3= +0.001887 {\(\beta\)}4= -0.02251 {\(\beta\)}5= -0.05022 1.3. MLP (Multi-Layer Perceptron) Model The Artificial Neural Networks (ANNs) introduced in the 1960s, are based on the human nervous system functioning to design processing information machines [7]. It is composed of two or more layers. Each one contains a set of neurons (e.g layers in Figure 5). The connections between the layers are associated with weights. There are many types of Neural Network (NN). They differ in structure, and the learning algorithm. In this work we proposed to apply the MLP (Multi-Layer Perceptron) that is a supervised method [7]. It requires a desired output in order to learn using a back-propagation algorithm, for more details see [7]. Model that maps the input to the output is then created. The goal is to produce an output when the desired output is unknown. Figure 5 shows the structure of MLP. The standard MLP network that is used for function fitting in the Neural Network Toolbox of MATLABtm, is a two-layer feedforward network, with a sigmoid transfer function (Equation (8)) in the hidden layer and a linear transfer function (Equation (9)) in the output layer [10]. Before learning starts, the default dataset division is made as follow: ●70
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