A data assimilation technique to account for the nonlinear dependence of scattering microwave observations of precipitation
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A data assimilation technique to account for the nonlinear dependence of scattering microwave observations of precipitation
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    Journal of Geophysical Research-Atmospheres, 120(11), 5548-5563.
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  • Description:
    Satellite microwave observations of rain, whether from radar or passive radiometers, depend in a very crucial way on the vertical distribution of the condensed water mass and on the types and sizes of the hydrometeors in the volume resolved by the instrument. This crucial dependence is nonlinear, with different types and orders of nonlinearity that are due to differences in the absorption/emission and scattering signatures at the different instrument frequencies. Because it is not monotone as a function of the underlying condensed water mass, the nonlinearity requires great care in its representation in the observation operator, as the inevitable uncertainties in the numerous precipitation variables are not directly convertible into an additive white uncertainty in the forward calculated observations. In particular, when attempting to assimilate such data into a cloud-permitting model, special care needs to be applied to describe and quantify the expected uncertainty in the observations operator in order not to turn the implicit white additive uncertainty on the input values into complicated biases in the calculated radiances. One approach would be to calculate the means and covariances of the nonlinearly calculated radiances given an a priori joint distribution for the input variables. This would be a very resource-intensive proposal if performed in real time. We propose a representation of the observation operator based on performing this moment calculation off line, with a dimensionality reduction step to allow for the effective calculation of the observation operator and the associated covariance in real time during the assimilation. The approach is applicable to other remotely sensed observations that depend nonlinearly on model variables, including wind vector fields. The approach has been successfully applied to the case of tropical cyclones, where the organization of the system helps in identifying the dimensionality-reducing variables.
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