Precalibrating an intermediate complexity climate model

Credible climate predictions require a rational quantification of uncertainty, but full Bayesian calibration requires detailed estimates of prior probability distributions and covariances, which are difficult to obtain in practice. We describe a simplified procedure, termed precalibration, which provides an approximate quantification of uncertainty in climate prediction, and requires only that uncontroversially implausible values of certain inputs and outputs are identified. The method is applied to intermediate-complexity model simulations of the Atlantic meridional overturning circulation (AMOC) and confirms the existence of a cliff-edge catastrophe in freshwaterforcing input space. When uncertainty in 14 further parameters is taken into account, an implausible, AMOC-off, region remains as a robust feature of the model dynamics, but its location is found to depend strongly on values of the other parameters

Multi-variate factorisation of numerical simulations

Factorisation (also known as "factor separation") is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the factorisation, and the factorisation. We show that, when more than two variables are being considered, none of these three methods possess all four properties of "uniqueness", "symmetry", "completeness", and "purity". Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations - the "linear-sum"factorisation, the "shared-interaction"factorisation, and the "scaled-residual"factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical in the case of four or fewer variables, and we conjecture that this holds for any number of variables. We present the results of the factorisations in the context of three past studies that used the previously proposed factorisations

Applications of the Local critique plot

The use of the Local critique plot is illustrated by three different applications. The applications involve directed acyclic graph (DAG) models of varying complexity and structure, and they illustrate different aspects and abilities of the plots. We see examples where the posterior is a trade off of tail specifications because of conflict between the local prior and the lifted likelihood. Hence model choices made on these tails are, perhaps unexpectedly, identified as influential. We also see how the local critique plot can reveal local prior or lifted likelihood domination. The applications also illustrate that diagnostic warnings from the local critique plot prompt us to reconsider the statistical model, but that sometimes a reexamination can assure us that the choices are justified

A data-driven approach for assessing ice-sheet mass balance in space and time

Combinations of various numerical models and datasets with diverse observation characteristics have been used to assess the mass evolution of ice sheets. As a consequence, a wide range of estimates have been produced using markedly different methodologies, data, approximation methods and model assumptions. Current attempts to reconcile these estimates using simple combination methods are unsatisfactory, as common sources of errors across different methodologies may not be accurately quantified (e.g. systematic biases in models). Here we provide a general approach which deals with this issue by considering all data sources simultaneously, and, crucially, by reducing the dependence on numerical models. The methodology is based on exploiting the different space-time characteristics of the relevant ice-sheet processes, and using statistical smoothing methods to establish the causes of the observed change. In omitting direct dependence on numerical models, the methodology provides a novel means for assessing glacio-isostatic adjustment and climate models alike, using remote-sensing datasets. This is particularly advantageous in Antarctica, where in situ measurements are difficult to obtain. We illustrate the methodology by using it to infer Antarctica\u27s mass trend from 2003 to 2009 and produce surface mass-balance anomaly estimates to validate the RACMO2.1 regional climate model

Resolving the Antarctic contribution to sea-level rise: a hierarchical modelling framework

Determining the Antarctic contribution to sea-level rise from observational data is a complex problem. The number of physical processes involved (such as ice dynamics and surface climate) exceeds the number of observables, some of which have very poor spatial definition. This has led, in general, to solutions that utilise strong prior assumptions or physically based deterministic models to simplify the problem. Here, we present a new approach for estimating the Antarctic contribution, which only incorporates descriptive aspects of the physically based models in the analysis and in a statistical manner. By combining physical insights with modern spatial statistical modelling techniques, we are able to provide probability distributions on all processes deemed to play a role in both the observed data and the contribution to sea-level rise. Specifically, we use stochastic partial differential equations and their relation to geostatistical fields to capture our physical understanding and employ a Gaussian Markov random field approach for efficient computation. The method, an instantiation of Bayesian hierarchical modelling, naturally incorporates uncertainty in order to reveal credible intervals on all estimated quantities. The estimated sea-level rise contribution using this approach corroborates those found using a statistically independent method. © 2013 The Authors. Environmetrics Published by John Wiley & Sons, Ltd