Chapter 13 - Outlier robust extreme learning machine: Predicting river water temperature in the absence of air temperature

Abstract

Modeling river water temperature using air temperature is broadly discussed in the literature, and up to now, all proposed models were based on establishing a direct relationship between water and air temperatures variables at different timescale. The need for a stronger link between these two variables was strongly emphasized, and the number of published work has substantially increased during the last few years, and it was demonstrated that the proposed models were robust, accurate and worked with unusually high level of precision, presumably due to the greater effect of air temperature on water temperature. In the absence of air temperature, the developed models do not therefore seem to be possible to use. In the present investigation, we demonstrate that it is now possible to predict river water temperature without the need of air temperature, and using only another weather variable which is the barometric pressure. We apply and compare four nontuned machines learning namely, (i) the original extreme learning machines, (ii) outlier robust extreme learning machine, (iii) regularized extreme learning machines, and (iv) weighted regularized extreme learning machines. The proposed models were developed using large data set collected from four stations in the Columbia River, United States. We demonstrate here that the inclusion of the periodicity represented by the component of the Gregorian calendar, that is, year number, month, day, and the hour of day, will substantially help in improving the models accuracies, and a high level of correlation was found between in situ measured data and predicted data, reaching an average values of correlation coefficient (R) and Nash-Sutcliffe (NSE) efficiency of 0.990 and 0.980, respectively, while the root mean square error and mean absolute error were below 0.650°C and 0.500°C, respectively. With the excellent results obtained, we are showing that this new modeling approach is being confirmed and consolidated.