## 1. Introduction

The importance of cloud to the distribution of radiative heating rates has long been recognised Liou, 1986, as has the importance of representing subgrid-scale cloud inhomogeneity (Cahalan *et** al.* 1994). However, the radiative transfer schemes used in many general circulation models (GCMs) ignore subgrid-scale cloud-water content variability and assume that clouds are vertically overlapped according to the maximum random approximation Geleyn 1979 and Hollingworth, 1979). Barker *et** al.* (1999) showed that these assumptions lead to biases in the calculated fluxes and heating rates, both individually and when combined.

The Monte Carlo Independent Column Approximation (McICA), described by Pincus *et** al.* (2003), is a method for representing cloud inhomogeneity in radiative transfer schemes. It approximates the accurate but costly full Independent Column Approximation (ICA) calculation (Barker et al., 1999) at considerably less computational expense. For the integral over wavelength, at each quadrature point, instead of calculating the monochromatic flux for every subcolumn the monochromatic flux for one or more randomly chosen subcolumns is calculated. For further details, see section 2.

McICA has two major advantages compared with the alternative methods for representing cloud inhomogeneity in GCMs, such as the use of a scaling factor (Cahalan et al., 1994) or ‘Tripleclouds’ (Shonk and Hogan, 2008). Firstly it is unbiased with respect to the full ICA calculation. Secondly and perhaps more importantly it removes the cloud-structure representation from the radiative transfer code and thus allows for a more flexible cloud representation. On the other hand, it introduces conditional random errors, which depend on the choice of subcolumns mapped to each quadrature point. The amount and effect of this noise has been the subject of several articles. However, such articles have generally tended to focus on its impacts in climate models.

Pincus *et** al.* (2003) performed a number of tests on cloud fields from a cloud-resolving model (CRM). They calculated the standard deviation of McICA errors for a short-wave (SW) surface flux of 105 W m^{−2} (approximately 10% of the incident top of atmosphere (TOA) radiation). The effect of this noise on a seasonal forecast model was estimated by randomly perturbing radiative fluxes and heating rates. They found no statistically significant differences from their control.

Raisanen *et** al.* (2005) and Raisanen *et** al.* (2007) investigated the effect of McICA noise on the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) and European Centre Hamburg Model 5 (ECHAM5) climate models respectively, using a low-noise version of McICA as the reference. In both models they found that their noisiest implementations of McICA led to a significant reduction in low cloud fractions. They were able to remove this effect by reducing the level of noise.

More recently, Barker *et** al.* (2008) investigated the effect of McICA noise on several global models. Again using a low-noise version of McICA as the reference, they ran 14 day simulations. They found that some of their models responded significantly to the noisiest tests, but no models displayed significant impacts when noise was reduced.

While the effect of McICA noise on climate models has been quite extensively studied, its effect on numerical weather prediction (NWP) models, particularly where the time and spatial scales of interest are smaller, is not so well documented. McICA has been tested in the European Centre for Medium-Range Weather Forecasts (ECMWF) integrated forecast system (Morcrette *et** al.* 2008) and, as in the climate simulations, the related noise was not found to be detrimental to results. However, the radiation scheme employed at ECMWF has many more quadrature points than most other forecast models and as a result the magnitude of McICA noise in the ECMWF model is significantly smaller.

As McICA noise is generally thought to be of little consequence, only a single article has been published regarding methods for reducing noise. Raisanen and Barker (2004) suggested two methods for minimizing McICA noise. Combining these methods, they found that they could reduce the standard deviation of McICA noise by approximately a factor of three, while increasing the number of monochromatic calculations required by 50%.

This article investigates the effect of McICA noise on the MetUM. In section 2 we consider the McICA scheme in more detail, discuss its implementation in the MetUM and describe the cloud generator that provides the subgrid cloud profiles required. Section 3 considers the magnitude of the noise associated with McICA, introduces techniques for efficiently minimizing this noise and compares these techniques with a previous method. In section 4 we consider the effect of McICA noise on a MetUM NWP simulation, with regards to 1.5 m temperature in particular. Finally, conclusions are presented in section 5.