Monthly runoff forecasts by bivariate distributions
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Abstract
Forecasting the runoff that enters in a reservoir is very important for water use planning purposes. In this paper, Fuerte river’s monthly runoff is studied, which is used to irrigate the valley with the same name in the state of Sinaloa in northern México. Summer’s runoffs, due to the Mexican Monsoon, are correlated and represent 85% of the annual Fuerte river´s runoff. The objective of this paper is to present a method, which uses the correlation between monthly runoffs to forecast runoff with bivariate distributions. With this purpose a generalization of Moran´s bivariate distribution is used, this distribution can be constructed with the marginal distributions of best fit to monthly runoffs (based in statistical criteria). This distribution has the advantage of expressing the dependency between variables by the correlation coefficient. Runoffs forecasting, in this approach, are obtained with the mean value of the conditional distribution, which in some sense, is a generalization of the simple regression equation. Results show that the conditional mean is better than the forecast given by the regression equation, which is not suitable if variables are not normally distributed.
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