## 1. The Tripleclouds scheme

Clouds are recognised as a major source of uncertainty in climate models (Randall, *et al.*2007). It is therefore imperative that parametrizations of cloud properties describe the cloud and its processes as realistically as possible. However, most radiation schemes in general circulation models (GCMs) represent clouds as plane-parallel and align them using maximum-random overlap, whereby vertically continuous clouds are overlapped maximally and clouds separated by layers of clear sky are overlapped randomly. The use of these approximations causes large, systematic biases in the radiative fluxes above and below the clouds (e.g. Barker, *et al.*1999, Carlin, *et al.*2002).

Shonk and Hogan (2008) introduced a new cloud representation scheme, referred to as ‘Tripleclouds’, that improves on the conventional plane-parallel cloud scheme by partitioning the cloud in each layer of a gridbox into two homogeneous regions of equal fractional area. One of these regions contains the optically thinner half of the cloud in that layer; the other contains the optically thicker half. A third region contains the clear sky. The two values of water content for the cloudy regions are defined to approximately represent the standard deviation of water content in the layer. In an operational GCM, the standard deviation could either be specified using an empirical value or, in some recent schemes, taken from an explicit representation of variance (e.g. Tompkins 2002). A review of a number of studies by Shonk, *et al.* (2010), hereafter ‘Part I’, sought to quantify this spread in terms of fractional standard deviation, defined as the quotient of the standard deviation of water content and its mean:

We found *f*_{w} to be 0.75 ± 0.18, with no systematic dependence on cloud type, observation type or gridbox size. Tripleclouds was implemented in the Edwards–Slingo radiation code (Edwards and Slingo 1996), and tests using radar data scenes in Part I showed that significant additional biases are not introduced into the radiation fields when using this mean value, and a mean plane-parallel bias in cloud radiative forcing (CRF) of 8% could be reduced to less than 1% using Tripleclouds.

Hogan and Illingworth (2000) proposed an overlap scheme that we refer to as ‘exponential-random’ overlap, where vertically continuous cloud is overlapped not maximally or randomly, as in all previous schemes, but according to an ‘overlap parameter’, *α*, whose value varies from zero for random overlap to one for maximum overlap. They found the value of *α* to decay roughly inverse-exponentially with layer separation for layers within vertically continuous clouds, over a decorrelation scale of order 1.5 km for a midlatitude location. In Part I, we combined this with results from the cloud radar measurements of Mace and Benson-Troth (2002) to derive a simple latitudinal relationship for this decorrelation scale. We introduced a slightly different form of overlap parameter, *β*, with a definition that allowed exponential-random overlap to be applied to three-region systems as well as two-region systems. We converted the *α* decorrelation scales of Hogan and Illingworth (2000) and Mace and Benson-Troth (2002) to *β* decorrelation scales and found the best-fit latitude relationship to be:

where *Z*_{0β} is decorrelation height in kilometres and Φ is absolute latitude in degrees. Seasonal effects were found to cause a variation of order ±0.5 km in *Z*_{0β}. For a three-region system with one clear-sky region and two cloudy regions, a decorrelation height of *Z*_{0β} is applied to the clear-sky region only and a height of *Z*_{0β}/2 is applied to the cloudy regions. This choice is based on the results of Räisänen, *et al.* (2004), within the limitations discussed in Part I.

In this paper, we combine Tripleclouds with exponential-random overlap and apply it to the European Centre for Medium-Range Weather Forecasts (ECMWF) re-analysis (ERA-40) data to investigate the impact of cloud structure on the global radiation budget for a realistic distribution of clouds. The individual radiative effects of the modification of horizontal inhomogeneity and vertical overlap are investigated and compared. The method used to investigate these contributions is discussed in section 2. In section 3, the radiation calculations are performed and the global radiation budget from our ERA-40 data compared with radiation budget measurements derived from the Clouds and the Earth's Radiant Energy System (CERES) project. The individual effects of the horizontal and vertical components of the Tripleclouds scheme are considered, along with the total effects, in section 4, both in terms of radiation and cloud cover. Finally, the paper is concluded in section 5.