Computation of domain‐average radiative flux profiles using Gaussian quadrature
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abstract
A method for calculating domain‐average radiative flux profiles, called Gaussian Quadrature Independent Column Approximation (GQ‐ICA), is introduced and assessed using cloud properties retrieved from A‐Train satellite data. This method could be suitable for use in large‐scale atmospheric models. Like the Monte Carlo ICA (McICA), GQ‐ICA uses N stochastically generated subgrid‐scale cloudy columns. The independent variable is the sorted, from smallest to largest, sequence of N sub‐column values of liquid and ice cloud water paths. The integrand is essentially the radiative transfer equation. Accurate GQ integration requires integrands to be relatively smooth functions. Unlike McICA, GQ‐ICA performs full solar and infrared spectral integrations on nG < < N sub‐columns which are identified by rules governing nG‐node GQ. The nG flux profiles are appropriately weighted and summed to give domain averages. Several sorting procedures were considered, and all results are based on the CCCma radiation algorithm. For solar radiation, 1‐node GQ‐ICA can produce significant bias errors, but its random errors are generally less than McICA's. These biases, however, are almost eliminated by 2‐node GQ‐ICA. For GQ‐ICA to better McICA's random errors for infrared fluxes, at least the 2‐node version is needed. Ultimately, 2‐node GQ‐ICA random errors for net fluxes at surface and top‐of‐atmosphere are typically 30–50% of McICA's. This is partly because solar and infrared solvers operate on the same sub‐columns. GQ‐ICA random errors for atmospheric heating rates are comparable to McICA's even for 3‐node GQ‐ICA. Computational times required for the 2‐ and 3‐node GQ‐ICA are, respectively, ∼180 and ∼230% of McICA's.
