Reduced Adjoint Variational Data Assimilation for Estimation of Soil Moisture Profile

Spatially distributed soil moisture profiles are required for watershed applications such as drought and flood prediction, crop irrigation scheduling, pest management, and determining mobility with lightweight vehicles. Soil moisture is highly variable in space and time owing to the dynamics in soil hydraulic properties. Therefore, measurement and simulation of soil moisture pattern are of particular importance.

Satellite-based soil moisture can be obtained from passive microwave, active microwave, and optical sensors, although the coarse spatial resolution of passive microwave and the inability to obtain vertically resolved information from optical sensors limit their usefulness for watershed-scale applications.

In a synthetic study the potential of using surface soil moisture measurements obtained from different satellite platforms to retrieve soil moisture profiles and soil hydraulic properties, will be explored using reduced order variational data assimilation procedures and a 1D mechanistic soil water model. Adjoint techniques namely variational data assimilation (4DVAR) is a well-known method for estimation of the unknown parameters of a physical system. This method improves a model consistency with available data by minimizing a cost function measuring the model–data misfit with respect to some model inputs and parameters. Associated with this type of method, however, are difficulties related to the coding of the adjoint model, which is needed to compute the gradient of the 4DVAR cost function. Proper orthogonal decomposition (POD) is a model reduction technique that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called POD modes. Two distinct approaches for POD in 4DVAR will be explored in this study. In the first approach, an optimization algorithm is applied in order to minimize the cost function entirely in the POD-reduced space. The second approach uses POD to approximate only the adjoint model. The accuracy and feasibility of the proposed approaches will be investigated through a synthetic study. The effect of assimilation strategy, measurement frequency, accuracy in surface soil moisture measurements, and soils differing in textural and hydraulic properties will be investigated. The approach will be able to assess the value of periodic space-borne observations of surface soil moisture for soil moisture profile estimation and for identifying the adequate conditions (e.g. temporal resolution and measurement accuracy) for remotely sensed soil moisture data assimilation.