## 1. Introduction

[2] Reliable at-site estimation of drought quantiles from a small number of observations is important for many engineering projects such as emergency planning, reservoir management, pollution control, and risk calculations. Traditionally, this type of drought quantile estimation is done with parametric methods. In order to do this, one must assume that extreme events are drawn according to a probability density function from some known parameterized family. In practice, there are important problems associated with this assumption. For example, it is clear that drought processes are governed by complex interactions between atmosphere, surface water, soil, vegetation, and groundwater; this suggests it is unlikely that any known parameterized distribution is a true explanation of the drought quantiles.

[3] Researchers have applied several different nonparametric approaches for quantile estimation in hydrology. Nonparametric approaches build a more complicated regression between input and output data. For example, *Apipattanavis et al.* [2010] presented a nonparametric approach based on local polynomial regression for estimating a flood quantile function. They applied the method to synthetic data from mixtures of conventional distributions and to flood records that exhibited mixed population characteristics from the Gila River basin of Arizona. *Moon and Lall* [1994] used a kernel estimator to predict flood quantiles at a gauged site. During the past decades, applications of machine learning theory and neural networks have emerged in function estimation and regression analysis. The support vector machines (SVMs) of *Vapnik* [1995], based on kernel distributions and supervised learning, are recognized as one of the most powerful tools in machine learning and risk minimization. *Shu and Ouarda* [2008] used artificial neural networks (ANN) for flood quantile estimation at ungauged sites.

[4] This paper explores the functionality of nonparametric approaches in drought quantile estimation at ungauged sites. We apply radial basis function (RBF) neural networks and least squares support vector machine regression (SVR) as nonparametric methods and compare the results from these two to the traditional regression model, the most commonly used method for quantile estimation at ungauged sites. Linear regression has been commonly applied for this application, but it has disadvantages such as not fitting the observed data very well, or diverting from tails in skewed data [*Haghighatjou et al.*, 2008]. Both RBF and least squares SVR have rarely been used in extreme quantile estimation and, to the authors' knowledge, least squares SVR was never used in drought quantile estimation. Studies relevant to RBF are those of *Shu and Burn* [2004], *Dawson et al.* [2006], *Reed and Robson* [1999], and *Ahmad and Simonovic* [2005]. Examples of research using SVR are given by *Tripathi et al.* [2006], *Ghosh* [2010], *Lin et al.* [2006], and *Asefa et al.* [2006].

[5] We use a jackknife experiment to train and test the data for all three methods: least squares SVR, RBF, and multiple linear regression (MLR). In the end, we compare the methods and their effectiveness for quantile estimation at ungauged sites.