Q1: How closely should the monthly satellite-gauge combined precipitation datasets follow the gauge analysis?

A1: The combined precipitation research team at Goddard has major responsibility for the Global Precipitation Climatology Project monthly Satellite-Gauge combined product, the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B43 monthly product (previously), and the IMERG Final Run monthly product.  In each case the multi-satellite data within the product are averaged to the monthly scale and combined with the Global Precipitation Climatology Centre's (GPCC) monthly surface precipitation gauge analysis (see https://www.dwd.de/EN/ourservices/gpcc/gpcc.html).  In each case the multi-satellite data are adjusted to the large-area mean of the gauge analysis, where available (mostly over land), and then combined with the gauge analysis using a simple inverse estimated-random-error variance weighting.  In all three data sets the gauge analysis has an important or dominant role in determining the final combined value for grid boxes in areas with "good" gauge coverage.  Regions with poor gauge coverage, such as central Africa have a higher weight on the satellite input.  The oceans are mostly devoid of gauges and therefore mostly lack such gauge input.  Isolated island stations are deleted from the GPCC gauge analysis before use because they are usually not representative of the surrounding ocean, and frequently not even the island as a whole.

Q2: How closely related are the short-interval multi-satellite precipitation datasets to the monthly satellite-gauge combined precipitation datasets?

A2: The short-interval GPCP is the One-Degree Daily (1DD), the short-interval TMPA is 3B42 (which is 3-hourly), and the short-interval IMERG is the half-hourly.  In each case the short-interval data are adjusted with a simple, spatially varying ratio to force the multi-satellite estimates to approximately average up to the corresponding monthly product, although with controls on the ratios to prevent unphysical results.  Thus, monthly-average values for the short-interval data should be close to the mean values for the monthly datasets, which the developers consider more reliable than the short-interval datasets.  In fact, compared to datasets that lack the adjustment to the monthly satellite-gauge estimates, the 1DD, 3B42, and IMERG Final half-hourly datasets tend to score better at timescales longer than a few days.  This is presumably because the random error begins to cancel out as more samples are averaged together, while the bias error remains. 

As an example, see:

Bolvin, D.T., R.F. Adler, G.J. Huffman, E.J. Nelkin, J.P. Poutiainen, 2009:  Comparison of GPCP Monthly and Daily Precipitation Estimates with High-Latitude Gauge Observations.  J. Appl. Meteor. Climatol., 48(9), 1843–1857.