The Gaussian Quadrature Independent Column Approximation for Computing Domain-average Radiative Flux Profiles in Large-scale Atmospheric Models (Invited Presentation)

This talk introduces and assesses the Gaussian Quadrature (GQ) Independent Column Approximation (GQ-ICA). The GQ-ICA method is applied in the CCCma radiation algorithm, assessed using A-Train satellite data, and contrasted against its conventional Monte Carlo counterpart, which is known as McICA, as well as McICA augmented by judiciously selected additional samples. Like McICA, GQ-ICA uses N stochastically-generated subgrid-scale cloudy columns that get sorted, from the smallest to largest, cloud water path, and ultimately performs full solar and infrared spectral integrations on n_G << N sub-columns. The n_G sub-columns are identified by rules governing GQ, and the resulting flux profiles are weighted appropriately and summed to give domain-averages. Several sorting procedures were considered. For solar radiation, n_G = 1 GQ-ICA can produce significant bias errors, but its random errors are comparable to those for the conventional McICA. These biases are almost eliminated by n_G = 2 and have corresponding random errors, for net fluxes at surface and top-of-atmosphere, which are typically 30% - 50% of McICA’s. This is partly because solar and infrared solvers operate on the same sub-columns. GQ-ICA’s random errors for heating rates are comparable to McICA's; even for the computationally burdensome version of n_G = 3. An amendment to the initial GQ-ICA helps reduce heating rate noise, but introduces biases that have proven to be difficult to eliminate.