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A novel Bayesian Monte Carlo integration (BMCI) technique was developed to retrieve geophysical variables from satellite microwave radiometer data in the presence of tropical cyclones. The BMCI technique includes three steps: generating a stochastic database, simulating satellite brightness temperatures using a radiative transfer model, and retrieving geophysical variables such as profiles of temperature, relative humidity, and cloud liquid and ice water content from real observations. The technique also provides uncertainty estimates for each retrieval and can output the error covariance matrix of selected parameters. The measurements from the Advanced Technology Microwave Sounder (ATMS) on board Suomi National Polar-Orbiting Partnership (Suomi NPP) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI) were used as input. A new technique was developed to correct the ATMS and GMI observations for the beam-filling effect, which is due to small-scale variability of precipitation and clouds when compared with the instrument footprint and also the nonlinear relation between the brightness temperature and precipitation. In addition, the assimilation of the BMCI retrievals into the NASA GEOS model is discussed for Hurricane Maria. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns. Two possible factors that may limit the impact of the BMCI retrievals include 1) the resolution of the model (about 25 km), which was too coarse to show the potential of the BMCI data in improving the representation of tropical storms in the model forecast, and 2) the data assimilation system not being able to consider vertically correlated observation errors.

Results from a cloud-resolving model are systematically compared with a variety of observations, both ground based and satellite, in order to better understand the mean background errors and their correlations. This is a step in the direction of developing a background error covariance matrix for use in cloud data assimilation. Observation sources include the Geostationary Operational Environmental Satellite (GOES), the Atmospheric Emitted Radiance Interferometer (AERI), a microwave radiometer (MWR), radiosonde, and cloud radar. When exploring model biases in temperature, precipitable water vapor, and liquid water path, a warm and moist bias at night and a cool and dry bias during the day are observed. Values for the background decorrelation length of water variables are determined. In addition, a dynamic cloud mask is presented to give more control in the assimilation of cloudy satellite radiances, allowing different cloud types to be excluded from the assimilation as well as establishing values for the maximum residuals to be considered.