## 1. Introduction

[2] Various interpolation methods have been applied to rainfall with many papers comparing interpolation methods [*Hwang et al*., 2011]. Recently, the use of copulas for interpolation of spatial data has come to prominence [*Bárdossy and Li*, 2008; *Kazianka and Pilz*, 2009, 2011]. Copulas are multivariate distributions with uniform marginal distributions which are used to describe dependence between a set of variables. In the context of spatial interpolation, this dependence is modeled as a function of the distance separating points and expressed in the form of rank correlations which are independent of the marginal distributions. The interpolated value is then calculated as an expected value of the copula density at the unknown location.

[3] The advantage of using copulas over traditional interpolation methods such as kriging is that copulas can model different dependence structures for different quantiles of a variable [*Bárdossy*, 2006]. As a result, this makes copulas an attractive prospect for interpolating rainfall as high precipitation events tend to be associated with convective rainfall which is more localized in nature than lower and more widespread events associated with stratiform rainfall. Interpolation using copulas has been shown to outperform kriging when applied to groundwater quality data [*Bárdossy and Li*, 2008], radiation data [*Kazianka*, 2012], and rainfall [*Bárdossy and Pegram*, 2012].

[4] The use of copulas for interpolation, however, requires assumptions about the parameters describing the marginal distribution of the data set, the shape of the correlation function as it varies with distance, and the copula itself. This prompts the following question: as these assumptions are made for an entire spatial domain, could the estimation of the parameters that describe these relationships be improved by using a local neighborhood? Initial experiments suggested that although local estimation of parameters can improve estimation at unknown locations, this improvement is not consistent. At some locations an improvement is observed, while at others prediction errors increase.

[5] Model forecast combinations have been previously used to improve temporal prediction [see, for example, *Chowdhury and Sharma*, 2009, 2011]. In this paper, we present a novel approach for combining predictions in a spatial context by modifying the forecast combination methodology of *Bates and Granger* [1969]. In particular, this methodology is demonstrated by combining global and local copula interpolation of rainfall at unknown sites.

[6] The remainder of this paper is structured as follows. Section 'Data' introduces the test data, while section 'Methodology' provides an outline of the proposed methodology. Section 'Copula Interpolation' presents the results of the application of the methodology to several data sets. Finally, section 'Forecast Combinations' presents a discussion of the success of combining forecasts.