## 1. Introduction

The increasing availability of gridded, multivariate, climatological data sets calls for new methodologies to visualize and explore the relationships between different variables. These relationships are often difficult to detect when the variables are plotted separately. One particular solution to reduce the dimensionality of the visualization was proposed by Taylor (2001), who showed that all components of the spatial covariance between two variables (i.e. their variances and correlation) can be summarized in a single radial diagram. This type of diagram is especially suited when a suite of different models is evaluated against observations. The spatial structure of the underlying data, however, is not considered. Other solutions for visualization can be found by making use of some of the properties of common colour schemes.

A colour model is a mathematical description of how a colour is constructed from its components. Most colour models have two or more components (or degrees of freedom), for instance, the amount of red, green and blue (RGB model) or the hue, saturation and brightness value (HSV model). Changing any of the components (with some exceptions) results in a different and unique colour. In theory, these degrees of freedom can be utilized to map an equal number of variables to colour, so that all colours on the map correspond to a combination of variables rather than a single variable. For three degrees of freedom, this requires some way of displaying the legend in more than two dimensions. Triangular colour maps were used previously by Nemani *et al.* (2003, Figure 1A) and Albani *et al.* (2006, Figure 6). The triangular legend, however, has two rather than three degrees of freedom (i.e. the position along two axis of the triangle determines the third), which limits its applicability to variables that always sum up to same number.

In this study, we propose a method that uses a purely two-dimensional (2-D) colour mapping. Its main advantage over other visualization methods is that the distribution of any two variables, along with their covariance, can be condensed in a single map without loss of information and in a way that is easy to interpret (Olsen, 1981). This is illustrated in Figure 1. This method is especially suited to map two variables that are physically linked, but for which their correlation varies regionally. To our best knowledge, such a plot was first used for climate analysis by Teuling *et al.* (2009, Figure 1). In this study, we present more objective and general methods to construct the colour legend than that used by Teuling *et al.* (2009) and provide extended examples for both sequential and diverging data.