Authors:Cowtan K; Jacobs P, Thorne P, et al. Abstract: BackgroundGlobal 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.ObjectivesThe 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.MethodsThe 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.ResultsFor 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.ConclusionsMore 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. PubDate: Fri, 20 Jul 2018 00:00:00 GMT DOI: 10.1093/climsys/dzy003 Issue No:Vol. 3, No. 1 (2018)

Authors:Ashwin P; David Camp C, von der Heydt A. Abstract: It is well known that periodic forcing of a nonlinear system, even of a 2D autonomous system, can produce chaotic responses with sensitive dependence on initial conditions if the forcing induces sufficient stretching and folding of the phase space. Quasiperiodic forcing can similarly produce chaotic responses, where the transition to chaos on changing a parameter can bring the system into regions of strange non-chaotic behaviour. Although it is generally acknowledged that the timings of Pleistocene ice ages are at least partly due to Milankovitch forcing (which may be approximated as quasiperiodic, with energy concentrated near a small number of frequencies), the precise details of what can be inferred about the timings of glaciations and deglaciations from the forcing are still unclear. In this article, we perform a quantitative comparison of the response of several low-order nonlinear conceptual models for these ice ages to various types of quasiperiodic forcing. By computing largest Lyapunov exponents and mean periods, we demonstrate that many models can have a chaotic response to quasiperiodic forcing for a range of forcing amplitudes, even though some of the simplest conceptual models do not. These results suggest that pacing of ice ages to forcing may have only limited determinism. PubDate: Tue, 08 May 2018 00:00:00 GMT DOI: 10.1093/climsys/dzy002 Issue No:Vol. 3, No. 1 (2018)

Authors:Kondrashov D; Chekroun M, Ghil M. Abstract: Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound socio-economic implications. Of particular interest are reliable methods for SIE forecasting on subseasonal time scales, in particular from early summer into fall, when sea ice coverage in the Arctic reaches its minimum. Here, we apply the recent data-adaptive harmonic (DAH) technique of Chekroun and Kondrashov, (2017), Chaos, 27 for the description, modeling and prediction of the Multisensor Analyzed Sea Ice Extent (MASIE, 2006–2016) data set. The DAH decomposition of MASIE identifies narrowband, spatio-temporal data-adaptive modes over four key Arctic regions. The time evolution of the DAH coefficients of these modes can be modelled and predicted by using a set of coupled Stuart–Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time. Retrospective forecasts show that our resulting multilayer Stuart–Landau model (MSLM) is quite skilful in predicting September SIE compared to year-to-year persistence; moreover, the DAH–MSLM approach provided accurate real-time prediction that was highly competitive for the 2016–2017 Sea Ice Outlook. PubDate: Tue, 27 Mar 2018 00:00:00 GMT DOI: 10.1093/climsys/dzy001 Issue No:Vol. 3, No. 1 (2018)