The representation of physical processes by a climate model depends on its structure, numerical schemes, physical parameterizations and resolution, with initial conditions and future emission scenarios further affecting the output. The extent to which climate models agree is therefore of great interest, often with greater confidence in robust results across models. This has led to climate model output being analysed as ensembles rather than in isolation, and quantifying the sources of variation across these ensembles is the aim of many recent studies. Statistical attempts to do this include the use of variants of the mixed-effects analysis of variance or covariance (mixed-effects ANOVA/ANCOVA). This work usually focuses on identifying variation in a variable of interest that is due to differences in model structure, carbon emissions scenario, etc. Quantifying such variation is important in determining where models agree or disagree, but further statistical approaches can be used to diagnose the reasons behind the agreements and disagreements by representing the physical processes within the climate models. A process-based approach is presented that uses simulation with statistical models to perform a global sensitivity analysis and quantify the sources of variation in multi-model ensembles. This approach is a general framework that can be used with any generalised linear mixed model (GLMM), which makes it applicable to use with statistical models designed to represent (sometimes complex) physical relationships within different climate models. The method decomposes the variation in the response variable into variation due to 1) temporal variation in the driving variables, 2) variation across ensemble members in the distributions of the driving variables, 3) variation across ensemble members in the relationship between the response and the driving variables, and 4) variation unexplained by the driving variables. The method is used to quantify the extent to which, and diagnose why, precipitation varies across and within the members of two different climate model ensembles on various different spatial and temporal scales. Change in temperature in response to increased CO2 is related to change in global-mean annual-mean precipitation in a multi-model ensemble of general circulation models (GCMs). A total of 46% of the variation in the change in precipitation in the ensemble is found to be due to the differences between the GCMs, largely because the distribution of the changes in temperature varies greatly across different GCMs. The total variation in the annual-mean change in precipitation that is due to the differences between the GCMs depends on the area over which the precipitation is averaged, and can be as high as 63%. The second climate model ensemble is a perturbed physics ensemble using a regional climate model (RCM). This ensemble is used for three different applications. Firstly, by using lapse rate, saturation specific humidity and relative humidity as drivers of daily-total summer convective precipitation at the grid-point level over southern Britain, up to 8% of the variation in the convective precipitation is found to be due to the uncertainty in RCM parameters. This is largely because given atmospheric conditions lead to different rates of precipitation in different ensemble members. This could not be detected by analysing only the variation across the ensemble members in mean precipitation rate (precipitation bias). Secondly, summer-total precipitation at the grid-point level over the British Isles is used to show how the values of the RCM parameters can be incorporated into a GLMM to quantify the variation in precipitation due to perturbing each individual RCM parameter. Substantial spatial variation is found in the effect on precipitation of perturbing different RCM parameters. Thirdly, the method is extended to focus on extreme events, and the simulation of extreme winter pentad (five-day mean) precipitation events averaged over the British Isles is found to be robust to the uncertainty in RCM parameters.

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