Page 245 - Contributed Paper Session (CPS) - Volume 2

CPS1846 Maryam I. et al.
to 1200 km of the prediction location (Hansen et al., 2010). The weight of each
sample point decreases linearly from unity to zero. This interpolation scheme
computes estimates by weighting the sample points closer to the prediction
location greater than those farther away without considering the degree of
autocorrelation for those distances. On the other hand, the JMA (Ishii et al.,
2005) records use covariance structure of spatial data and are based on
traditional kriging. Formal Gaussian process regression is used by the BEST to
produce spatially complete temperature estimates (Rhode et al., 2013). It is
worth noting that these interpolation approaches do not consider the multi-
scale feature of geophysical processes. Additionally, regional coverage
uncertainty estimates are not available for these data sets. Recently, a new
monthly temperature data set (Ilyas et al., 2017) is created. It results from the
application of the multi-resolution lattice kriging approach (Nychka et al.,
2015) that captures variation at multiple scales of the spatial process. This
multi-resolution model quantifies gridded uncertainties in global
temperatures due to the gaps in spatial coverage. It results in a 10,000 member
ensemble of monthly temperatures over the entire globe. These are spatially
dense equally plausible fields that sample the combination of observational
and coverage uncertainties. The data are open access and freely available at:
https://oasishub.co/dataset/global-monthly-temperature-ensemble-1850-
to-2016. This paper provides an update on Ilyas et al. (2017) data set. Here, a
new version of this data is produced that incorporates the parametric
uncertainties in addition to the observational and coverage errors. To account
for the model parametric uncertainties, an approximate Bayesian inference
methodology is proposed for multi-resolution lattice kriging (Nychka et al.,
2015). It is based on variogram that is a measure of spatial variability between
spatial observations as a function of spatial distance.

2. Methodology

2.1 Multi-resolution lattice kriging using ABC
Multi-resolution lattice kriging (MRLK) has been introduced by Nychka et
al. (2015). It is a linear approach that models spatial observations in terms of
a Gaussian process, linear trend and measurement error term. This
methodology extends spatial methods to very large data sets accounting for
all scales. It is a methodology for spatial inference and prediction. This
approach has the advantage of being computationally feasible for large data
sets by the virtue of sparse covariance matrices. The MRLK models the
underlying spatial process as the sum of independent processes each of which
is the linear combination of the basis functions. The basis functions are fixed
and co-efficients of the basis functions are random. Consider observations
at spatial locations , , … . , in the spatial domain . The aim is to

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