Improvements in global precipitation retrievals from the GPM Microwave Imager (GMI) using dimensional reduction techniques, matched channel resolutions, and optimized land surface classifications,

Swath-level precipitation estimates from the Global Precipitation Measurement (GPM) Core satellite Microwave Imager (GMI) are currently based on the Goddard Profiling (Level 2A GPROF) algorithm (GPM GPROF Algorithm Theoretical Basis Document, 2022). The algorithm employs a Bayesian estimation scheme (Kummerow et al. 2001), applied to a large database of 385 million GMI multichannel microwave brightness temperatures matched with independently estimated near-surface rain rates. These estimates are mainly derived from the GPM Dual-frequency Precipitation Radar (DPR), but under certain surface conditions for which DPR estimates are unreliable, they are obtained surface-based sources such as field campaigns. Under most conditions, the algorithm calculates the "best" rain rate as a weighted average of near-matches within a 9-dimensional channel space.

The microwave brightness temperatures in the original GPROF database are at their native resolutions, implying significant resolution differences between the lower frequencies (starting at 10.7 GHz) and the highest frequencies (up to 89 GHz). As a result, nearby sharp spatial gradients in scene properties, such as coastlines and precipitation edges, can encroach on the fields of view (FOVs) of lower-frequency channels while remaining outside the FOVs of higher-frequency channels (Petty and Bennartz 2017). This introduces an additional geophysical noise term that the retrieval algorithm must successfully reject to avoid retrieval degradation.

Additionally, the application of the Bayesian algorithm in this high-dimensional channel space relies on a relatively simple weighted RMS difference, with an assumed diagonal noise covariance matrix, for identifying matches to a given observation vector. Due to the well-known "curse of dimensionality," data points, which may appear densely packed in lower dimensions, become exponentially sparser in higher-dimensional spaces. Consequently, the number of successful matches in the 9-channel space is often quite low under certain circumstances. An implicit trade-off exists between obtaining sufficient matches and excluding extraneous non-precipitating matches (Petty 2013). There is no guarantee that a satisfactory optimum can be found in all cases.

Moreover, the algorithm is applied to non-overlapping subsets of the full database based on a large set of static land surface classes and near-surface conditions, further increasing the effective dimensionality of the Bayesian retrieval, as surface air temperature and column water vapor become additional "channels" to be considered. The 18 land surface classes primarily derive from a clustering algorithm applied to climatological mean surface emissivities (Aires et al. 2011), with a few additional classes to account for mountainous regions and other special cases. However, this classification does not ensure homogeneity in the climatological multichannel covariances of background brightness temperatures as required for a full optimization of the discrimination of precipitation signatures from background geophysical noise.

In this paper, we investigate the potential for significant performance improvements by 1) employing a dimensionality reduction technique (Petty 2013, Petty and LI 2013) to reduce the search space from 9 channels to 3 pseudochannels, thereby isolating important precipitation signatures from the background noise and greatly increasing the effective sample density; 2) using brightness temperatures that have been processed to be more closely matched in spatial resolution (Petty and Bennartz 2017); and 3) adopting an alternative land surface classification based on the clustering of climatological multichannel covariances (Petty 2022). For each proposed modification, we compare our resulting surface precipitation retrievals (no profiles) with the currently distributed GPROF near-surface retrievals to ascertain whether measurable retrieval improvements result and, if so, whether the additional processing effort is justified.