Cowtan, Kevin, Jacobs, Peter, Thorne, Peter and Wilkinson, Richard (2018) Statistical analysis of coverage error in simple global temperature estimators. Dynamics and Statistics of the Climate System, 3 (1). pp. 1-18. ISSN 2059-6987
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Abstract
Background. Global mean surface temperature is widely used in the climate literature as a measure
of the impact of human activity on the climate system. While the concept of a spatial average is
simple, the estimation of that average from spatially incomplete data is not. Correlation between
nearby map grid cells means that missing data cannot simply be ignored. Estimators that (often
implicitly) assume uncorrelated observations can be biased when naively applied to the observed
data, and in particular, the commonly used area weighted average is a biased estimator under these
circumstances. Some surface temperature products use different forms of infilling or imputation to
estimate temperatures for regions distant from the nearest observation, however the impacts of such
methods on estimation of the global mean are not necessarily obvious or themselves unbiased. This
issue was addressed in the 1970s by Ruvim Kagan, however his work has not been widely adopted,
possibly due to its complexity and dependence on subjective choices in estimating the dependence
between geographically proximate observations.
Objectives. The aim of this work is to present a simple estimator for global mean surface temperature
from spatially incomplete data which retains many of the benefits of the work of Kagan, while being
fully specified by two equations and a single parameter. The main purpose of the simplified estimator
is to better explain to users of temperature data the problems associated with estimating an unbiased
global mean from spatially incomplete data, however the estimator may also be useful for problems
with specific requirements for reproducibility and performance.
Methods. The new estimator is based on generalized least squares, and uses the correlation matrix of the
observations to weight each observation in accordance with the independent information it contributes.
It can be implemented in fewer than 20 lines of computer code. The performance of the estimator is
evaluated for different levels of observational coverage using reanalysis data with artificial noise.
Results. For recent decades the generalized least squares estimator mitigates most of the error
associated with the use of a naive area weighted average. The improvement arises from the fact
that coverage bias in the historical temperature record does not arise from an absolute shortage of
observations (at least for recent decades), but rather from spatial heterogeneity in the distribution of
observations, with some regions being relatively undersampled and others oversampled. The estimator
addresses this problem by reducing the weight of the oversampled regions, in contrast to some
existing global temperature datasets which extrapolate temperatures into the unobserved regions. The
results are almost identical to the use of kriging (Gaussian process interpolation) to impute missing
data to global coverage, followed by an area weighted average of the resulting field. However, the new
formulation allows direct diagnosis of the contribution of individual observations and sources of error.
Conclusions. More sophisticated solutions to the problem of missing data in global temperature
estimation already exist. However the simple estimator presented here, and the error analysis that
it enables, demonstrate why such solutions are necessary. The 2013 Fifth Assessment Report of the
Intergovernmental Panel on Climate Change discussed a slowdown in warming for the period 1998-
2012, quoting the trend in the HadCRUT4 historical temperature dataset from the United Kingdom
Meteorological Office in collaboration with the Climatic Research Unit of the University of East Anglia,
along with other records. Use of the new estimator for global mean surface temperature would have
reduced the apparent slowdown in warming of the early 21st century by one third in the spatially
incomplete HadCRUT4 product.
Item Type: | Article |
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Keywords: | Climate change; historical temperature record; observational coverage; |
Academic Unit: | Faculty of Social Sciences > Geography Faculty of Social Sciences > Research Institutes > Irish Climate Analysis and Research Units, ICARUS |
Item ID: | 11090 |
Identification Number: | 10.1093/climsys/dzy003 |
Depositing User: | Peter Thorne |
Date Deposited: | 24 Sep 2019 15:46 |
Journal or Publication Title: | Dynamics and Statistics of the Climate System |
Publisher: | Oxford University Press |
Refereed: | Yes |
Related URLs: | |
URI: | https://mu.eprints-hosting.org/id/eprint/11090 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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