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CPS1846 Maryam I. et al.
(Morice et al., 2012). As a result of this, a 10,000 member ensemble data is
created. It is an update to the data set discussed in Ilyas et al. (2017). It was
generated using multi-resolution lattice kriging (Nychka et al., 2015) that
estimated the model covariance parameters using a likelihood approach. The
key difference between the two data sets is the inference methodology. The
updated data set is produced by using the ABC based posterior densities of
the multi-resolution lattice kriging covariance parameters. The use of posterior
distribution of the model parameters creates a data set that accounts for the
multi-resolution lattice kriging parametric uncertainties. The ABC posterior
distributions and model parameters of multiresolution lattice kriging are used
to generate an ensemble. This ensemble data is based on HadCRUT4
temperature data. The HadCRUT4 monthly data set consists of 100 sparse
ensemble members. For each of 100 monthly spatial fields of HadCRUT4, a
spatially complete 100 member ensemble is created that samples the
coverage and parametric uncertainties of multi-resolution lattice kriging. It
results in 10,000 ensemble members. These ensemble members are referred
as a hyperparameter temperature ensemble data set. The 100 members of
ensemble generated from a HadCRUT4 ensemble member are the random
fields from the multivariate conditional normal distribution. These sample
fields are drawn by conditioning on the HadCRUT4 available field
measurements, multi-resolution lattice kriging covariance model, and
variogram based ABC posteriors of autoregressive weights and smoothing
parameter. In other words, 10 fields are drawn from the multivariate
conditional normal distribution. These are sampled corresponding to each of
the 10 draws from the ABC posterior distributions of smoothing parameter
and autoregressive weights. This ensemble data set is generated using UCL
High-Performance Computing (HPC) facility.

4. Discussion and Conclusion
This paper proposes a spatial model that can cope with large data settings.
It is based on multi-resolution lattice kriging and variogram based ABC. Multi-
resolution lattice kriging provides flexible framework to handle large data
settings and it is straight forward to paralellize the rejection algorithm of
variogram based ABC. As each iteration of acceptance rejection algorithm is
independent of the remaining iterations. Hence, each iteration can in principle
be carried out to one CPU core. Therefore, variogram based multi-resolution
lattice kriging provides flexible modeling framework for large data settings.
This ABC methodology for multi-resolution lattice kriging is used to create a
temperature data product that accounts for observational, coverage and
multi-resolution parametric uncertainties. This is the updated version of the
data set created in the second chapter. It should be borne in mind that
parametric uncertainties are based on 10 samples drawn from ABC posteriors.

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