Nonlinear data assimilation for clouds and precipitation using a gamma inverse‐gamma ensemble filter

Abstract

Where clouds occur, their water content is always positive definite, and may be near zero. In addition, it is common for errors in remote‐sensing observations of clouds and rainfall to be represented as a fraction of the measurement. Furthermore, there is nonlinearity in the relationships among cloud environment, cloud microphysical processes, and the amount and distribution of cloud and precipitation. For these reasons, data assimilation algorithms that rely on linearity and assumptions of Gaussian probability distributions may have difficulty in assimilating observations in cloudy regions, as well as producing an analysis that realistically represents the actual distribution of clouds and precipitation. A recently developed ensemble filter algorithm, the Gamma, Inverse‐Gamma, and Gaussian Ensemble Kalman Filter (GIGG‐EnKF), allows for fractional observation errors and positive‐definite quantities. As such, it has promise for producing more effective and accurate data assimilation and retrievals of clouds and precipitation. This study evaluates the effectiveness of the GIGG‐EnKF by using it to estimate the values of warm rain cloud microphysical parameters in a cloud model using observations of precipitation. GIGG‐EnKF estimates of cloud parameters and rainfall are compared with a Bayesian reference solution returned by a Markov chain Monte Carlo algorithm, and with a perturbed‐observations Ensemble transform Kalman filter (ETKF). The ETKF produces an ensemble with a substantial number of negative (non‐physical) precipitation rates and parameter values. In contrast, the GIGG‐EnKF precipitation analysis is positive definite, and is able to adapt to changes in the observation value (and observation uncertainty). Nonlinearity in the parameter–precipitation relationship is handled by implementing an iterative outer loop regression from the observation space to state space. The positive‐definite constraint and natural accommodation of fractional error, along with the iterative outer loop, produces an accurate reproduction of the Bayesian analysis of the precipitation rate and cloud microphysical parameter values.

Why Are Radar Data so Difficult to Assimilate Skillfully?

“…Measurements or retrieved properties can then be assimilated to improve precipitation simulation. While some benefits are observed in rain, the unknown and complex relationship between modelsimulated properties such as hydrometeor type, number, and mixing ratio, and radar observations in ice remains an obstacle (e.g., Posselt et al 2015).…”

“…In parallel, for variables like precipitation that are positive definite and non-Gaussian, ensemble data assimilation approaches that are based on non-Gaussian statistics may also need to be explored (Posselt and Bishop 2018;Anderson 2019).…”

Non-Gaussian Deterministic Assimilation of Radar-Derived Precipitation Accumulations

“…However, it also prevents the analysis from approaching the observed value if it is greater than the largest value within the ensemble or less than the smallest value. This is in contrast with standard Gaussian DA approaches that only use the ensemble for estimating background error covariances and therefore can produce analysis states with nonphysical values [e.g., negative humidity or accumulated precipitation; Posselt and Bishop (2018)]. However, for highly non-Gaussian distributions, such ''extrapolation'' outside the range of values within the ensemble may produce inaccurate results.…”

Techniques and challenges in the assimilation of atmospheric water observations for numerical weather prediction towards convective scales

“…for variables that are not Gam, IG or Gaussian distributed, and for multivariate distributions. It has though been tested successfully by Posselt and Bishop () who estimated microphysical cloud parameters assumed to have a Gam prior and observations of precipitation rates assumed to have an IG likelihood. The method presents a step forward for certain classes of problems, pertinent to the analysis of AW variables.…”