An idealized study of coupled atmosphere-ocean 4D-Var in the presence of model error

Atmosphere only and ocean only variational data assimilation (DA) schemes are able to use window lengths that are optimal for the error growth rate, non-linearity and observation density of the respective systems. Typical window lengths are 6-12 hours for the atmosphere and 2-10 days for the ocean. However, in the implementation of coupled DA schemes it has been necessary to match the window length of the ocean to that of the atmosphere, which may potentially sacrifice the accuracy of the ocean analysis in order to provide a more balanced coupled state. This paper investigates how extending the window length in the presence of model error affects both the analysis of the coupled state and the initialized forecast when using coupled DA with differing degrees of coupling. Results are illustrated using an idealized single column model of the coupled atmosphere-ocean system. It is found that the analysis error from an uncoupled DA scheme can be smaller than that from a coupled analysis at the initial time, due to faster error growth in the coupled system. However, this does not necessarily lead to a more accurate forecast due to imbalances in the coupled state. Instead coupled DA is more able to update the initial state to reduce the impact of the model error on the accuracy of the forecast. The effect of model error is potentially most detrimental in the weakly coupled formulation due to the inconsistency between the coupled model used in the outer loop and uncoupled models used in the inner loop.

The impact of two coupled cirrus microphysics-radiation parameterizations on the temperature and specific humidity biases in the tropical tropopause layer in a climate model

The impact of two different coupled cirrus microphysics-radiation parameterizations on the zonally averaged temperature and humidity biases in the tropical tropopause layer (TTL) of a Met Office climate model configuration is assessed. One parameterization is based on a linear coupling between a model prognostic variable, the ice mass mixing ratio, qi, and the integral optical properties. The second is based on the integral optical properties being parameterized as functions of qi and temperature, Tc, where the mass coefficients (i.e. scattering and extinction) are parameterized as nonlinear functions of the ratio between qi and Tc. The cirrus microphysics parameterization is based on a moment estimation parameterization of the particle size distribution (PSD), which relates the mass moment (i.e. second moment if mass is proportional to size raised to the power of 2 ) of the PSD to all other PSD moments through the magnitude of the second moment and Tc. This same microphysics PSD parameterization is applied to calculate the integral optical properties used in both radiation parameterizations and, thus, ensures PSD and mass consistency between the cirrus microphysics and radiation schemes. In this paper, the temperature-non-dependent and temperature-dependent parameterizations are shown to increase and decrease the zonally averaged temperature biases in the TTL by about 1 K, respectively. The temperature-dependent radiation parameterization is further demonstrated to have a positive impact on the specific humidity biases in the TTL, as well as decreasing the shortwave and longwave biases in the cloudy radiative effect. The temperature-dependent radiation parameterization is shown to be more consistent with TTL and global radiation observations.