Optimising assimilation of hydrographic profiles into isopycnal ocean models with ensemble data assimilation

- Constructing the innovation vector in observations coordinates is more accurate.
- Horizontal localisation radius varies with latitude (a bimodal Gaussian function).
- Assimilation of hydrographic profiles reduces efficiently error and bias.
- The ensemble simulation is found statistically reliable in most regions.

Hydrographic profiles are crucial observational datasets for constraining ocean models and their vertical structure. In this study, we investigate a key implementation setup for optimising their assimilation into isopycnal ocean models. For this purpose, we use the Norwegian Climate Prediction Model (NorCPM), which is a fully-coupled climate prediction system based on the Norwegian Earth System Model and the ensemble Kalman filter. First, we revisit whether it is more accurate to assimilate observations in their original coordinate (z-level coordinate) or to transform them into isopycnal coordinates prior to assimilation. The analysis is performed with a single assimilation step using synthetic observations that mimic the characteristic properties of hydrographic profiles: varying vertical resolutions, profiles of only temperature and observations only in the top 1000 m. Assimilating profiles in their native coordinate (z-level coordinates) performs best because converting observations into isopycnal coordinates is strongly non-linear which reduces the efficiency of the assimilation. Secondly, we investigate how to set the horizontal localisation radius for our system. A radius that varies with latitude following a bimodal Gaussian function fits the system well. Thirdly, we estimate observation error, which consists of both instrumental error and representativeness error. In the proposed formulation only the instrumental error decreases with the number of observations during superobing, because the representativeness error is dominated by model limitation. Finally, we demonstrate the impact of assimilating hydrographic profiles from the observational EN4 dataset into NorCPM. An analysis of 10 years with monthly assimilation is performed with special focus on assessing the accuracy and the reliability of our analysis. The assimilation of hydrographic profiles into NorCPM is found to efficiently reduce the model bias and error, and the ensemble spread is found to be a reliable estimator for the forecast error in most regions.