Instrumental global temperature records are derived from the network of in situ measurements of land and sea surface temperatures. This observational evidence is seen as being fundamental to climate science. Therefore, the accuracy of these measurements is of prime importance for the analysis of temperature variability. There are spatial gaps in the distribution of instrumental temperature measurements across the globe. This lack of spatial coverage introduces coverage error. An approximate Bayesian computation based multi-resolution lattice kriging is developed and used to quantify the coverage errors through the variance of the spatial process at multiple spatial scales. It critically accounts for the uncertainties in the parameters of this advanced spatial statistics model itself, thereby providing, for the first time, a full description of both the spatial coverage uncertainties along with the uncertainties in the modeling of these spatial gaps. These coverage errors are combined with the existing estimates of uncertainties due to observational issues at each station location. It results in an ensemble of 100,000 monthly temperatures fields over the entire globe that samples the combination of coverage, parametric and observational uncertainties from 1850 to 2018 on a 5° by 5° grid.

The 100,000 equally-plausible ensemble members are stored in a series of separate netcdf files each containing 1000 realisations.

Additionally, there is 100-realisation subsample that provides an estimate of the uncertainty in the full ensemble. This has been created using conditional Latin hypercube sampling across 25 key regions of the globe. It many cases it would be sufficient to analyse just this 100-member subsample, for example to compute a likely range in a quantity. It is recommended that full 100,000 member ensemble is only investigated in those situations where the precise shape of the uncertainty distribution is required. NetCDF files at both the annual and monthly resolution are provided for this subsample.