Deriving estimates of the storm-wide distribution of vertical wind speed w in convective storms from satellite microwave radiometer observations when radar-derived estimates of w are available over a small portion of the storm (as in the EarthCARE, AOS and INCUS missions)

Much progress has been made in the past decade in bringing satellite microwave radiometer observations of convective storms to bear on numerical weather prediction models. Several centers have implemented all-sky radiance assimilation schemes which try to reconcile the signatures of condensed water in the observed brightness temperatures with the synthetic atmospheric state (including condensed water fields) represented by the model. However two essential issues remain in these all-sky approaches. The first is that in convective storms, apparently different states can actually be essentially equivalent i.e. produced by essentially the same (slightly perturbed) initial conditions. Indeed, tiny perturbations in the initial state can produce convective plumes that are different in number, location, timing, shape and intensity from those produced by the unperturbed state, implying that the discrepancy in the possible outcomes (all due to essentially the same initial conditions) can be quite complex, and quite different from the "additive independent unbiased noise" uncertainty model. This is a fundamental obstacle for the pointwise assimilation of the microwave data. The second issue is that the assimilation of the observations in the individual radiometer beams inevitably requires local adjustments to the state which are not consistent with the conservation equations that the model is designed to enforce.

We have developed an alternate approach which considers jointly all the radiometer observations over the storm, assuming that a satellite radar made simultaneous observations over at least one convective core in the storm, from which estimates of Ice Water Path (IWP) and vertical wind speed (w) can be derived. These radar data are used as tie points to derive the function F which produces the storm-wide histogram Hw of high-(radar)-resolution w from a storm-wide histogram Hi of high-resolution IWP. This is preceded by the derivation of the function G which produces Hi from the histogram Hc of coarse-(radiometer)-resolution values of IWP and cloud-columns structure (height and the top two vertical principal components) as derived from the radiometer observations. Applying the chain rule, G(Hc) is Hi and F(Hi) is Hw. The uncertainty on G depends on the radiometer channels and their resolutions, and the uncertainty on F depends on the number of radar observations. The 0th moment of Hw is akin to the storm-wide convective mass flux, a single scalar derived observation with additive unbiased noise whose assimilation is very straightforward.