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. The interaction between radiation and clouds represents a source of uncertaintyin numerical weather prediction (NWP) due to both intrinsic problems of one-dimensional radiation schemes and poor representation of clouds.The underlying question addressed in this study is how large the NWP radiative bias is for shallow cumulus clouds and how it scales with various input parameters of radiation schemes, such as solar zenith angle, surface albedo, cloud cover and liquid water path. A set of radiative transfer calculations was carried out for a realistically evolving shallow cumulus cloud field stemming from a large-eddy simulation (LES). The benchmark experiments were performed on the highly resolved LES cloud scenes (25 m grid spacing) using a three-dimensional Monte Carlo radiation model. An absence of middle and high clouds is assumed above the shallow cumulus cloud layer.In order to imitate the poor representation of shallow cumulus in NWP models, cloud optical properties were horizontally averaged over the cloudy part of the boxes with dimensions comparable to NWP horizontal grid spacing (several kilometers), and the common δ -Eddington two-stream method with maximum-randomoverlap assumption for partial cloudiness was applied (denoted as the “1-D” experiment).The bias of the 1-D experiment relative to the benchmark was investigated in the solar and thermal parts of the spectrum, examining the vertical profile of heating rate within the cloud layer and the net surface flux.It is found that, during daytime and nighttime, the destabilization of the cloud layer in the benchmark experiment is artificially enhanced by an overestimation of the cooling at cloud top and an overestimation of the warming at cloud bottom in the 1-D experiment (a bias of about −15  K d −1 is observed locally for stratocumulus scenarios).This destabilization, driven by the thermal radiation, is maximized during nighttime, since during daytime the solar radiation has a stabilizing tendency.The daytime bias at the surface is governed by the solar fluxes, where the 1-D solar net flux overestimates (underestimates) the corresponding benchmark at low (high) Sun.The overestimation at low Sun (bias up to 80 % over land and ocean) is largest at intermediate cloud cover, while the underestimation at high Sun (bias up to −40  % over land and ocean) peaks at larger cloud cover (80 % and beyond).At nighttime, the 1-D experiment overestimates the amount of benchmark surface cooling with the maximal bias of about 50 % peaked at intermediate cloud cover.Moreover, an additional experiment was carried out by running the Monte Carlo radiation model in the independent column mode on cloud scenes preserving their LES structure (denoted as the “ICA” experiment).The ICA is clearly more accurate than the 1-D experiment (with respect to the same benchmark).This highlights the importance of an improved representation of clouds even at the resolution of today's regional (limited-area) numerical models, which needs to be considered if NWP radiative biases are to be efficiently reduced.All in all, this paper provides a systematic documentation of NWP radiative biases, which is a necessary first step towards an improved treatment of radiation–cloud interaction in atmospheric models.

Quantifying the bias of radiative heating rates in numerical weather prediction models for shallow cumulus clouds