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Several Meteorological service agencies have developed Extended Kalman Filter based land data assimilation systems that, in principle, can analyse any model land variable. Such systems can make use of a wide variety of observation types, such as screen level (2 meters above the surface) observations and satellite based estimates such as retrieved surface soil moisture and retrieved skin temperature. Indirect measurements can be used and information propagated from the surface into the deeper soil layers. A key component of the system is the calculation of the Jacobians of the observation operator which describe the link between the observations and the land surface model variables. The Jacobians are estimated using finite difference by performing short model forecasts with perturbed initial conditions. This paper examines the Jacobians that link observations of screen level variables, satellite derived surface soil moisture and satellite derived skin temperature to model soil temperature and moisture. The calculated Jacobians that link screen level variables to model soil moisture show that there is strong coupling between the screen level and the soil. The coupling between the topmost model level soil moisture and the screen level is found to be due to a number of processes including bare soil evaporation, soil thermal conductivity, soil thermal capacity as well as transpiration by plants. Therefore, there is significant coupling both during the day and at night. The sign of the Jacobians linking screen level temperature to topmost model level soil moisture are usually negative during the day and tends to be positive during the night. The coupling between the screen level and soil moisture in the deeper model layers is primarily through transpiration by plants. Therefore the coupling is only significant during the day and the vertical variation of the coupling is found to be significantly affected by the vegetation root depths. The calculated Jacobians that link screen level temperature to model soil temperature are found to be largest for the topmost model soil layer and become very small for the lower soil layers. These Jacobians are largest during the night and generally positive in value. It is found that the Jacobians that link observations of surface soil moisture to model soil moisture are strongly affected by the soil hydraulic conductivity. Generally, for the Joint UK Land Environment Simulator (JULES) land surface model, the coupling between the surface and root zone soil moisture is weak. Finally, the Jacobians linking observations of skin temperature to model soil temperature and moisture are calculated. These Jacobians are found to have a similar spatial pattern to the Jacobians for observations of screen level temperature. Where the linear assumption is valid, the calculated values of the Jacobians should be nearly independent of the sign of the perturbations used. This is investigated by comparing Jacobians calculated using perturbations of opposite signs. Jacobians values that are significantly affected by the sign of perturbation used are assumed to contain a gross error and not used by the data assimilation. A simple quality control scheme is developed to detect land points where the computed Jacobians contain such gross errors. Analysis is also performed of the sensitivity of the calculated Jacobians to the magnitude of the perturbations used.

Analysis of the linearised observation operator in a land surface data assimilation scheme for numerical weather prediction