Monthly mean total precipitation for the Australian continent between 1976-2005. Modelled by fitting a trivariate thin plate smoothing spline function of longitude, latitude and vertically exaggerated elevation to the square roots of observed and estimated monthly 1976-2005 rainfall means at 11,697 Bureau of Meteorology stations. Missing monthly precipitation values were estimated by regression with the long term station that provided estimates of the 1976-2005 monthly means with with the least standard error. This was applied to each station with at least 10 years of record between 1931 and 2012. Automated quality controls were applied to the regression process to remove poor quality data. Thus, an average of 66 values per month were removed, giving an average of 11631 data points for each month. These were commonly associated with stations with an old or short period of record, or with an imprecise location. Station elevations were 0.05 degree local averages of grid values from the GEODATA 9 second DEM version 3 as provided by eMAST_ANUClimate_fx_el05_v1m0. The mean absolute error of individual cross validation residuals provided by the spline analysis at 3518 stations with near complete records, of at least 28 years, is 3.9 mm (6.6% of the mean). A comprehensive assessment of the analysis and the factors contributing to the quality of the final interpolated monthly mean precipitation grids is in preparation.