Sensitivity Analysis of Non-Parametric Ortho-Normal Series Method in Estimation of Annual Maximum-Minimum Temperature Probability Distribution Function

Background and objectives: Estimation of temperature probability distribution function (PDF) is a basic step for risk and uncertainty analysis in hydrology and environment studies. Most researches on temperature PDF estimation have been based on parametric approach while non-parametric approach has been considered in recent years because of some its benefit. The Ortho-Normal Series (ONS) method is a novel non-parametric method with suitable features that has recently been considered in hydrology. This method uses a number of constants with default values for its calculation, but no independent research has taken place about the importance of the default values on the precision of PDF fitting. The objective of this study is sensitivity analysis of ONS constants for precision of temperature PDF estimation which leads to a better understanding of the importance of the coefficients of this method.

Materials and methods: First, the precision of non-parametric ONS method beside four conventional parametric methods (i.e. Gamma, Gumbel, Exponential and Log-Normal) for annual maximum and minimum temperature PDF estimation of Isfahan, Shiraz, Zahedan and Ramsar stations were investigated using Akaike Information criteria (AIC) and Mean Square Error (MSE). The non-parametric ONS method uses CJ0, CJ1, CT and CM coefficients with their default values. The reasonable domains were determined for each coefficient and a certain number of values in each domain were selected. The precision criteria corresponding to the selected value in the domains of coefficients were calculated separately. The sensitivity analysis graphs were drawn using calculated values. The CV of fitting precision criteria of each coefficient was determined considering studied data series for comparison of magnitude of sensitivity of the coefficients.


Results: The ONS coefficients sensitivity analysis show the CT coefficient is most sensitive coefficient to changes relative to its default value. The CM and CJO coefficients have similar magnitude of sensitivity and are less sensitive to CT coefficient while CJ1 coefficient is least sensitive coefficient among all coefficients. The analysis of sensitivity analysis graph reveled that increase in precision with decrease in coefficients values and decrease in pension with increase in coefficients.

Conclusion: The results show sensible decrease or increase on ONS precision with changes in default values of the coefficients. Moreover it is obvious the completely acceptable precision of ONS using its default values for the coefficients but the changes in CT coefficient led to sensible improvement in precision. Therefore it can be concluded that investigation of changes in default values of ONS coefficients are an important and suitable tool to increase the precision of PDF estimation by this method.