Analysis of the linearised observation operator in a soil moisture and temperature analysis scheme

Abstract. Several weather forecasting agencies have developed advanced 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 m above the surface) observations and satellite based measurements of surface soil moisture and 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 linearised observation operator matrix (Jacobian matrix) which describes the link between the observations and the land surface model variables. The elements of the Jacobian matrix (Jacobians) are estimated using finite difference by performing short model forecasts with perturbed initial conditions. The calculated Jacobians show that there can be strong coupling between the screen level and the soil. The coupling between the screen level and surface soil moisture is found to be due to a number of processes including bare soil evaporation, soil thermal conductivity as well as transpiration by plants. Therefore, there is significant coupling both during the day and at night. The coupling between the screen level and root-zone soil moisture is primarily through transpiration by plants. Therefore the coupling is only significant during the day and the vertical variation of the coupling is modulated 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 values 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. Analysis is also performed of the sensitivity of the calculated Jacobians to the magnitude of the perturbations used.