Using Canonical Correlation Analysis to produce dynamically-based highly-efficient statistical observation operators

Observation operators (OOs) are a central component of any data assimilation system. As they project the state variables of a numerical model into the space of the observations, they also provide an ideal opportunity to correct for effects that are not or not sufficiently described by the model. In such cases a dynamical OO, an OO that interfaces to a secondary and more specialised model, often provides the best results. However, given the large number of observations to be assimilated in a typical atmospheric or oceanographic model, the computational resources needed for using a fully dynamical OO mean that this option is usually not feasible. This paper presents a method, based on canonical correlation analysis (CCA), that can be used to generate highly-efficient statistical OOs that are based on a dynamical model. These OOs can provide an approximation to the dynamical model at a fraction of the computational cost. One possible application of such an OO is the modelling of the diurnal cycle of sea surface temperature (SST) in ocean general circulation models (OGCMs). Satellites that measure SST measure the temperature of the thin uppermost layer of the ocean. This layer is strongly affected by the atmospheric conditions and its temperature can differ significantly from the water below. This causes a discrepancy between the SST measurements and the upper layer of the OGCM, which typically has a thickness of around 1 m. The CCA OO method is used to parametrise the diurnal cycle of SST. The CCA OO is based on an input dataset from the General Ocean Turbulence Model (GOTM), a high-resolution water column model that has been specifically tuned for this purpose. The parameterisations of the CCA OO are found to be in good agreement with the results from GOTM, showing the potential of this method for use in data assimilation systems.