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We present a new reconstruction of surface air temperature and sea surface temperature for the Last Glacial Maximum. The method blends model fields and sparse proxy-based point estimates through a data assimilation approach. Our reconstruction updates that of Annan and Hargreaves (2013), using the full range of general circulation model (GCM) simulations which contributed to three generations of the PMIP database, three major compilations of gridded sea surface temperature (SST) and surface air temperature (SAT) estimates from proxy data, and an improved methodology based on an ensemble Kalman filter. Our reconstruction has a global annual mean surface air temperature anomaly of -4.5±0.9 ∘C relative to the pre-industrial climate. This is slightly colder than the previous estimate of Annan and Hargreaves (2013), with an upwards revision on the uncertainty due to different methodological assumptions. It is, however, substantially less cold than the recent reconstruction of Tierney et al. (2020). We show that the main reason for this discrepancy is in the choice of prior. We recommend the use of the multi-model ensemble of opportunity as potentially offering a credible prior, but it is important that the range of models included in the PMIP ensembles represent the main sources of uncertainty as realistically and comprehensively as practicable if they are to be used in this way.

Observational constraints on the equilibrium climate sensitivity have been generated in a variety of ways, but a number of results have been calculated which appear to be based on somewhat informal heuristics. In this paper we demonstrate that many of these estimates can be reinterpreted within the standard subjective Bayesian framework in which a prior over the uncertain parameters is updated through a likelihood arising from observational evidence. We consider cases drawn from paleoclimate research, analyses of the historical warming record, and feedback analysis based on the regression of annual radiation balance observations for temperature. In each of these cases, the prior which was (under this new interpretation) implicitly used exhibits some unconventional and possibly undesirable properties. We present alternative calculations which use the same observational information to update a range of explicitly presented priors. Our calculations suggest that heuristic methods often generate reasonable results in that they agree fairly well with the explicitly Bayesian approach using a reasonable prior. However, we also find some significant differences and argue that the explicitly Bayesian approach is preferred, as it both clarifies the role of the prior and allows researchers to transparently test the sensitivity of their results to it.

Version 1.1 of the editorial of Geoscientific Model Development (GMD), published in 2015 (GMD Executive Editors, 2015), introduced clarifications to the policy on publication of source code and input data for papers published in the journal. Three years of working with this policy has revealed that it is necessary to be more precise in the requirements of the policy and in the narrowness of its exceptions. Furthermore, the previous policy was not specific in the requirements for suitable archival locations. Best practice in code and data archiving continues to develop and is far from universal among scientists. This has resulted in many manuscripts requiring improvement in code and data availability practice during the peer-review process. New researchers continually start their professional lives, and it remains the case that not all authors fully appreciate why code and data publication is necessary. This editorial provides an opportunity to explain this in the context of GMD. The changes in the code and data policy are summarised as follows: The requirement for authors to publish source code, unless this is impossible for reasons beyond their control, is clarified. The minimum requirements are strengthened such that all model code must be made accessible during the review process to the editor and to potentially anonymous reviewers. Source code that can be made public must be made public, and embargoes are not permitted. Identical requirements exist for input data and model evaluation data sets in the model experiment descriptions. The scope of the code and data required to be published is described. In accordance with Copernicus' own data policy, we now specifically strongly encourage all code and data used in any analyses be made available. This will have particular relevance for some model evaluation papers where editors may now strongly request this material be made available. The requirements of suitable archival locations are specified, along with the recommendation that Zenodo is often a good choice. In addition, since the last editorial, an “Author contributions” section must now be included in all manuscripts.

We present new reconstructions of global climatological temperature fields for the Last Glacial Maximum and the mid-Pliocene Warm Period.The method is based on an Ensemble Kalman Smoother which combines globally complete modelled temperature fields, with sparse proxy-based estimates of local temperature anomalies. This ensures spatially coherent fields which respect physical principles and which are also tied closely to observational estimates. For the Last Glacial Maximum, we use the full set of PMIP2/3/4 model simulations, and we combine this with a wide range of proxy-based SST and SAT estimates of local temperature to ensure the best possible global coverage. Our reconstruction has a global mean surface air temperature anomaly of -5.3 +- 0.9C relative to the pre-industrial climate, and thus lies roughly half-way between the estimates of Annan and Hargreaves (2013) and Tierney et al (2020). We examine the reasons for these differences and discuss their implications.For the mid-Pliocene Warm Period, we use the PlioMIP 1 and 2 model simulations and the PRISM proxy estimates for the 3.2 Ma time slice. These data are considerably more sparse and uncertain than for the LGM and our reconstruction is correspondingly more uncertain. We obtain an estimate of 5.6 +- 1.6C which is considerably warmer than most previous estimates, suggesting a significant discrepancy between the models and the data. We investigate the reasons for this and discuss the implications.

We assess evidence relevant to Earth's equilibrium climate sensitivity per doubling of atmospheric CO 2, characterized by an effective sensitivity S. This evidence includes feedback process understanding, the historical climate record, and the paleoclimate record. An S value lower than 2 K is difficult to reconcile with any of the three lines of evidence. The amount of cooling during the Last Glacial Maximum provides strong evidence against values of S greater than 4.5 K. Other lines of evidence in combination also show that this is relatively unlikely. We use a Bayesian approach to produce a probability density function (PDF) for S given all the evidence, including tests of robustness to difficult-to-quantify uncertainties and different priors. The 66% range is 2.6–3.9 K for our Baseline calculation and remains within 2.3–4.5 K under the robustness tests; corresponding 5–95% ranges are 2.3–4.7 K, bounded by 2.0–5.7 K (although such high-confidence ranges should be regarded more cautiously). This indicates a stronger constraint on S than reported in past assessments, by lifting the low end of the range. This narrowing occurs because the three lines of evidence agree and are judged to be largely independent and because of greater confidence in understanding feedback processes and in combining evidence. We identify promising avenues for further narrowing the range in S, in particular using comprehensive models and process understanding to address limitations in the traditional forcing-feedback paradigm for interpreting past changes.

In this study we introduce a Bayesian framework, which is flexible and explicit about the prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on Ordinary Least Squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (1.1 - 4.8, 5 - 95 percentiles) using the PMIP2, PMIP3 and PMIP4 data sets for the LGM, and 2.4 K (0.4 - 5.0) with the PlioMIP1 and PlioMIP2 data sets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (1.1 - 4.3) using the LGM and 2.4 K (0.4 - 5.1) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a slightly tighter constraint of 2.6 K (1.1 - 3.9). We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95% probability of climate sensitivity mostly below 5 and never exceeding 6 K. The approach is compared with other approaches based on OLS, a Kalman filter method and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, suggesting a higher bound by construction in case of weaker correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation of their potential use in future probabilistic estimation of climate sensitivity.

Coronavirus has claimed the lives of over half a million people world-wide and this death toll continues to rise rapidly each day. In the absence of a vaccine, non-clinical preventative measures have been implemented as the principal means of limiting deaths. However, these measures have caused unprecedented disruption to daily lives and economic activity. Given this developing crisis, the potential for a second wave of infections and the near certainty of future pandemics, lessons need to be rapidly gleaned from the available data. We address the challenges of cross-country comparisons by allowing for differences in reporting and variation in underlying socio-economic conditions between countries. Our analyses show that, to date, differences in policy interventions have out-weighed socio-economic variation in explaining the range of death rates observed in the data. Our epidemiological models show that across 8 countries a further week long delay in imposing lockdown would likely have cost more than half a million lives. Furthermore, those countries which acted more promptly saved substantially more lives than those that delayed. Linking decisions over the timing of lockdown and consequent deaths to economic data, we reveal the costs that national governments were implicitly prepared to pay to protect their citizens as reflected in the economic activity foregone to save lives. These ‘price of life’ estimates vary enormously between countries, ranging from as low as around $100,000 (e.g. the UK, US and Italy) to in excess of $1million (e.g. Denmark, Germany, New Zealand and Korea). The lowest estimates are further reduced once we correct for under-reporting of Covid-19 deaths. Electronic supplementary material The online version of this article (10.1007/s10640-020-00466-5) contains supplementary material, which is available to authorized users.

Paleoclimate simulations are widely used as a test of the ability of climate models to simulate climate states that are substantially different to the present day, and quantitative reconstructions of these climate states is an essential component of model evaluation. With there being no large network of instrumental observations from these periods, we must rely on inferences from a relatively modest number of unevenly distributed proxy records which are believed to be quantitatively indicative of the climate state. In order to robustly establish climatic conditions over global scales, we require methods for smoothing and interpolating between these sparse and imperfect estimates. In recent years, we have worked on this problem and created a global reconstruction of the Last Glacial Maximum [Annan and Hargreaves, 2013, Climate of the Past] using the data and models which were available at that time. The method uses scaled patterns from the PMIP ensemble of structurally diverse climate simulations, combined with sparse sets of proxy data, to produce spatially coherent and complete data fields for surface air and sea temperatures (potentially including the seasonal cycle) along with uncertainty estimates over the whole field. This approach is more robust than alternative methods, which either perform a purely statistical interpolation of the data or at best combine the data with a single climate model. Here, we aim to improve the method, update the inputs, and apply the same technique to both Last Glacial Maximum and mid Pliocene climate intervals. As well as generating spatially complete and coherent maps of climate variables, our approach also generates well-calibrated uncertainty estimates.

This study discusses how much of the biases in top-of-atmosphere (TOA) radiation and clouds can be removed by parameter tuning in the present-day simulation of a climate model in the Coupled Model Inter-comparison Project phase 5 (CMIP5) generation. We used output of a perturbed parameter ensemble (PPE) experiment conducted with an atmosphere–ocean general circulation model (AOGCM) without flux adjustment. The Model for Interdisciplinary Research on Climate version 5 (MIROC5) was used for the PPE experiment. Output of the PPE was compared with satellite observation data to evaluate the model biases and the parametric uncertainty of the biases with respect to TOA radiation and clouds. The results indicate that removing or changing the sign of the biases by parameter tuning alone is difficult. In particular, the cooling bias of the shortwave cloud radiative effect at low latitudes could not be removed, neither in the zonal mean nor at each latitude–longitude grid point. The bias was related to the overestimation of both cloud amount and cloud optical thickness, which could not be removed by the parameter tuning either. However, they could be alleviated by tuning parameters such as the maximum cumulus updraft velocity at the cloud base. On the other hand, the bias of the shortwave cloud radiative effect in the Arctic was sensitive to parameter tuning. It could be removed by tuning such parameters as albedo of ice and snow both in the zonal mean and at each grid point. The obtained results illustrate the benefit of PPE experiments which provide useful information regarding effectiveness and limitations of parameter tuning. Implementing a shallow convection parameterization is suggested as a potential measure to alleviate the biases in radiation and clouds.

The concept of independence has been frequently mentioned in climate science research, but has rarely been defined and discussed in a theoretically robust and quantifiable manner. In this paper we argue that any discussion must start from a clear and unambiguous definition of what independence means and how it can be determined. We introduce an approach based on the statistical definition of independence, and illustrate with simple examples how it can be applied to practical questions. Firstly, we apply these ideas to climate models, which are frequently argued to not be independent of each other, raising questions as to the robustness of results from multi-model ensembles. We explore the dependence between models in a multi-model ensemble, and suggest a possible way forward for future weighting strategies. Secondly, we discuss the issue of independence in relation to the synthesis of multiple observationally based constraints on the climate system, using equilibrium climate sensitivity as an example. We show that the same statistical theory applies to this problem, and illustrate this with a test case, indicating how researchers may estimate dependence between multiple constraints.

We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used trends in observational time series to constrain equilibrium climate sensitivity, it has also been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed, and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. It is only when the sensitivity is very low that the variability can provide a tight constraint. Our investigations take the form of “perfect model” experiments, in which we make the optimistic assumption that the model is structurally perfect and all uncertainties (including the true parameter values and nature of internal variability noise) are correctly characterised. Therefore the results might be interpreted as a best-case scenario for what we can learn from variability, rather than a realistic estimate of this. In these experiments, we find that for a moderate sensitivity of 2.5 ∘C, a 150-year time series of pure internal variability will typically support an estimate with a 5 %–95% range of around 5 ∘C (e.g. 1.9–6.8 ∘C). Total variability including that due to the forced response, as inferred from the detrended observational record, can provide a stronger constraint with an equivalent 5 %–95 % posterior range of around 4 ∘C (e.g. 1.8–6.0 ∘C) even when uncertainty in aerosol forcing is considered. Using a statistical summary of variability based on autocorrelation and the magnitude of residuals after detrending proves somewhat less powerful as a constraint than the full time series in both situations. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity but suggest caution in the interpretation of precise results.

This paper arose from a workshop at the Bishop Museum Honolulu in March 2012 organised by the PAGES CLIVAR Intersection Panel. ABSTRACT: We present a selection of methodologies for using the palaeo climate model component of the Coupled Model Intercomparison Project (Phase 5) (CMIP5) to attempt to constrain future climate projections using the same models. The constraints arise from measures of skill in hindcasting palaeo climate changes from the present over three periods: the Last Glacial Maximum (LGM) (21 000 yr before present ka) the mid Holocene (MH) (6 ka) and the Last Millennium (LM) (850–1850 CE). The skill measures may be used to validate robust patterns of climate change across scenarios or to distinguish between models that have differing outcomes in future scenarios. We find that the multi model ensemble of palaeo simulations is adequate for addressing at least some of these issues. For example selected benchmarks for the LGM and MH are correlated to the rank of future projections of precipitation/temperature or sea ice extent to indicate that models that produce the best agreement with palaeo climate information give demonstrably different future results than the rest of the models. We also explore cases where comparisons are strongly dependent on uncertain forcing time series or show important non stationarity making direct inferences for the future problematic. Overall we demonstrate that there is a strong potential for the palaeo climate simulations to help inform the future projections and urge all the modelling groups to complete this subset of the CMIP5 runs.

We investigate the consistency of various ensembles of climate model simulations with the Multiproxy Approach for the Reconstruction of the Glacial Ocean Surface (MARGO) sea surface temperature data synthesis. We discover that while two multi-model ensembles, created through the Paleoclimate Model Intercomparison Projects (PMIP and PMIP2), pass our simple tests of reliability, an ensemble based on parameter variation in a single model does not perform so well. We show that accounting for observational uncertainty in the MARGO database is of prime importance for correctly evaluating the ensembles. Perhaps surprisingly, the inclusion of a coupled dynamical ocean (compared to the use of a slab ocean) does not appear to cause a wider spread in the sea surface temperature anomalies, but rather causes systematic changes with more heat transported north in the Atlantic. There is weak evidence that the sea surface temperature data may be more consistent with meridional overturning in the North Atlantic being similar for the LGM and the present day. However, the small size of the PMIP2 ensemble prevents any statistically significant results from being obtained.

Paleoclimate simulations provide us with an opportunity to critically confront and evaluate the performance of climate models in simulating the response of the climate system to changes in radiative forcing and other boundary conditions. Hargreaves et al. (2011) analysed the reliability of the Paleoclimate Modelling Intercomparison Project, PMIP2 model ensemble with respect to the MARGO sea surface temperature data synthesis (MARGO Project Members, 2009) for the Last Glacial Maximum (LGM, 21 ka BP). Here we extend that work to include a new comprehensive collection of land surface data (Bartlein et al., 2011), and introduce a novel analysis of the predictive skill of the models. We include output from the PMIP3 experiments, from the two models for which suitable data are currently available. We also perform the same analyses for the PMIP2 mid-Holocene (6 ka BP) ensembles and available proxy data sets. Our results are predominantly positive for the LGM, suggesting that as well as the global mean change, the models can reproduce the observed pattern of change on the broadest scales, such as the overall land–sea contrast and polar amplification, although the more detailed sub-continental scale patterns of change remains elusive. In contrast, our results for the mid-Holocene are substantially negative, with the models failing to reproduce the observed changes with any degree of skill. One cause of this problem could be that the globally- and annually-averaged forcing anomaly is very weak at the mid-Holocene, and so the results are dominated by the more localised regional patterns in the parts of globe for which data are available. The root cause of the model-data mismatch at these scales is unclear. If the proxy calibration is itself reliable, then representativity error in the data-model comparison, and missing climate feedbacks in the models are other possible sources of error.

The mid-Pliocene Warm Period (mPWP) is the most recent interval in which atmospheric carbon dioxide was substantially higher than in modern pre-industrial times. It is, therefore, a potentially valuable target for testing the ability of climate models to simulate climates warmer than the pre-industrial state. The recent Pliocene Model Intercomparison Project (PlioMIP) presented boundary conditions for the mPWP and a protocol for climate model experiments. Here we analyse results from the PlioMIP and, for the first time, discuss the potential for this interval to usefully constrain the equilibrium climate sensitivity. We observe a correlation in the ensemble between their tropical temperature anomalies at the mPWP and their equilibrium sensitivities. If the real world is assumed to also obey this relationship, then the reconstructed tropical temperature anomaly at the mPWP can in principle generate a constraint on the true sensitivity. Directly applying this methodology using available data yields a range for the equilibrium sensitivity of 1.9–3.7 °C, but there are considerable additional uncertainties surrounding the analysis which are not included in this estimate. We consider the extent to which these uncertainties may be better quantified and perhaps lessened in the next few years.

We investigate the identifiability of the climate by limited proxy data. We test a data assimilation approach through perfect model pseudoproxy experiments, using a simple likelihood-based weighting based on the particle filtering process. Our experimental set-up enables us to create a massive 10 000-member ensemble at modest computational cost, thus enabling us to generate statistically robust results. We find that the method works well when data are sparse and imprecise, but in this case the reconstruction has a rather low accuracy as indicated by residual RMS errors. Conversely, when data are relatively plentiful and accurate, the estimate tracks the target closely, at least when considering the hemispheric mean. However, in this case, our prior ensemble size of 10 000 appears to be inadequate to correctly represent the true posterior, and the regional performance is poor. Using correlations to assess performance gives a more encouraging picture, with significant correlations ranging from about 0.3 when data are sparse to values over 0.7 when data are plentiful, but the residual RMS errors are substantial in all cases. Our results imply that caution is required in interpreting climate reconstructions, especially when considering the regional scale, as skill on this basis is markedly lower than on the large scale of hemispheric mean temperature.

© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. Global constraints on momentum and energy govern the variability of the rainfall belt in the intertropical convergence zone and the structure of the zonal mean tropical circulation. The continental-scale monsoon systems are also facets of a momentum- and energy-constrained global circulation, but their modern and palaeo variability deviates substantially from that of the intertropical convergence zone. The mechanisms underlying deviations from expectations based on the longitudinal mean budgets are neither fully understood nor simulated accurately. We argue that a framework grounded in global constraints on energy and momentum yet encompassing the complexities of monsoon dynamics is needed to identify the causes of the mismatch between theory, models and observations, and ultimately to improve regional climate projections. In a first step towards this goal, disparate regional processes must be distilled into gross measures of energy flow in and out of continents and between the surface and the tropopause, so that monsoon dynamics may be coherently diagnosed across modern and palaeo observations and across idealized and comprehensive simulations. Accounting for zonal asymmetries in the circulation, land/ocean differences in surface fluxes, and the character of convective systems, such a monsoon framework would integrate our understanding at all relevant scales: from the fine details of how moisture and energy are lifted in the updrafts of thunderclouds, up to the global circulations.

Understanding past climate should help reduce uncertainties in projections of future climate. This Review of palaeosimulation evaluations suggests that existing models capture broad patterns of climate change, but that further improvement is needed.

We demonstrate the application of an efficient multivariate probabilistic parameter estimation method to a spectral primitive equation atmospheric GCM. The method, which is based on the Ensemble Kalman Filter, is effective at tuning the surface air temperature climatology of the model to both identical twin data and reanalysis data. When 5 parameters were simultaneously tuned to fit the model to reanalysis data, the model errors were reduced by around 35% compared to those given by the default parameter values. However, the precipitation field proved to be insensitive to these parameters and remains rather poor. The model is computationally cheap but chaotic and otherwise realistic, and the success of these experiments suggests that this method should be capable of tuning more sophisticated models, in particular for the purposes of climate hindcasting and prediction. Furthermore, the method is shown to be useful in determining structural deficiencies in the model which can not be improved by tuning, and so can be a useful tool to guide model development. The work presented here is for a limited set of parameters and data, but the scalability of the method is such that it could easily be extended to a more comprehensive parameter set given sufficient observational data to constrain them.

We review progress in model and proxy-based reconstruction of the surface temperature field of the Last Glacial Maximum. Both approaches have converged towards a climate state substantially colder than the present day, with the temperature anomaly field showing strong polar amplification and land-sea contrast. The magnitudes of the large-scale changes are increasingly well-constrained, with a recent model-data synthesis generating a value of 4 °C, which suggests a moderate equilibrium climate sensitivity of about 2.5 °C. However, significant areas of uncertainty remain, particularly in the tropical sea surface temperature change. At finer sub-continental spatial scales, there is limited agreement between models and data regarding the patterns of change.

This study discusses how much of the biases in top-of-atmosphere (TOA) radiation and clouds can be removed by parameter tuning in the present-day simulation of a climate model in the Coupled Model Inter-comparison Project phase 5 (CMIP5) generation. We used a low-resolution version of the Model for Interdisciplinary Research on Climate version 5 (MIROC5) Atmosphere-Ocean General Circulation Model (AOGCM) and compared the output of a perturbed parameter ensemble (PPE) experiment in the pre-industrial control setting with satellite observation data. The model biases and the parametric uncertainty of the biases are evaluated with respect to TOA radiation and clouds. We used the output of the PPE experiment without flux adjustment, which is consistent with the experimental design of the CMIP5. The results indicate that removing or changing the sign of the biases by parameter tuning alone is difficult. Especially, the cooling bias of the shortwave cloud radiative effect in low latitudes could not be removed, neither in the zonal mean nor at each latitude–longitude grid point. The bias was related to the overestimation of both cloud amount and cloud optical thickness, which could not be removed by the parameter tuning either. However, they could be alleviated by tuning parameters such as the maximum cumulus updraft velocity at the cloud base. On the other hand, the bias of the shortwave cloud radiative effect in the Arctic was sensitive to parameter tuning. It could be removed by tuning such parameters as albedo of ice and snow both in the zonal mean and at each grid point. The obtained results illustrate the benefit of PPE experiments which provide useful information regarding effectiveness and limitations of parameter tuning.

What are the predictions of climate models, should we believe them, and are they falsifiable? Probably the most iconic and influential result arising from climate models is the prediction that, dependent on the rate of increase of CO2 emissions, global and annual mean temperature will rise by around 2–4°C over the 21st century. We argue that this result is indeed credible, as are the supplementary predictions that the land will on average warm by around 50% more than the oceans, high latitudes more than the tropics, and that the hydrological cycle will generally intensify. Beyond these and similar broad statements, however, we presently find little evidence of trustworthy predictions at fine spatial scale and annual to decadal timescale from climate models. For further resources related to this article, please visit the WIREs website. Conflict of interest: The authors have declared no conflicts of interest for this article.

In 2008, the first volume of the European Geosciences Union (EGU) journal Geoscientific Model Development (GMD) was published. GMD was founded because we perceived there to be a need for a space to publish comprehensive descriptions of numerical models in the geosciences. The journal is now well established, with the submission rate increasing over time. However, there are several aspects of model publication that we believe could be further improved. In this editorial we assess the lessons learned over the first few years of the journal's life, and describe some changes to GMD's editorial policy, which will ensure that the models and model developments are published in such a way that they are of maximum value to the community. These changes to editorial policy mostly focus on improving the rigour of the review process through a stricter requirement for access to the materials necessary to test the behaviour of the models. Throughout this editorial, "must" means that the stated actions are required, and the paper cannot be published without them; "strongly encouraged" means that we encourage the action, but papers can still be published if the criteria are not met; "may" means that the action may be carried out by the authors or referees, if they so wish. We have reviewed and rationalised the manuscript types into five new categories. For all papers which are primarily based on a specific numerical model, the changes are as follows: – The paper must be accompanied by the code, or means of accessing the code, for the purpose of peer-review. If the code is normally distributed in a way which could compromise the anonymity of the referees, then the code must be made available to the editor. The referee/editor is not required to review the code in any way, but they may do so if they so wish. – All papers must include a section at the end of the paper entitled "Code availability". In this section, instructions for obtaining the code (e.g. from a supplement, or from a website) should be included; alternatively, contact information should be given where the code can be obtained on request, or the reasons why the code is not available should be clearly stated. – We strongly encourage authors to upload any user manuals associated with the code. – For models where this is practicable, we strongly encourage referees to compile the code, and run test cases supplied by the authors where appropriate. – For models which have been previously described in the "grey" literature (e.g. as internal institutional documents), we strongly encourage authors to include this grey literature as a supplement, when this is allowed by the original authors. – All papers must include a model name and version number (or other unique identifier) in the title. It is our perception that, since Geoscientific Model Development (GMD) was founded, it has become increasingly common to see model descriptions published in other more traditional journals, so we hope that our insights may be of general value to the wider geoscientific community.

We investigate the performance of the newest generation multi-model ensemble (MME) from the Coupled Model Intercomparison Project (CMIP5). We compare the ensemble to the previous generation models (CMIP3) as well as several single model ensembles (SMEs), which are constructed by varying components of single models. These SMEs range from ensembles where parameter uncertainties are sampled (perturbed physics ensembles) through to an ensemble where a number of the physical schemes are switched (multi-physics ensemble). We focus on assessing reliability against present-day climatology with rank histograms, but also investigate the effective degrees of freedom (EDoF) of the fields of variables which makes the statistical test of reliability more rigorous, and consider the distances between the observation and ensemble members. We find that the features of the CMIP5 rank histograms, of general reliability on broad scales, are consistent with those of CMIP3, suggesting a similar level of performance for present-day climatology. The spread of MMEs tends towards being “over-dispersed” rather than “under-dispersed”. In general, the SMEs examined tend towards insufficient dispersion and the rank histogram analysis identifies them as being statistically distinguishable from many of the observations. The EDoFs of the MMEs are generally greater than those of SMEs, suggesting that structural changes lead to a characteristically richer range of model behaviours than is obtained with parametric/physical-scheme-switching ensembles. For distance measures, the observations and models ensemble members are similarly spaced from each other for MMEs, whereas for the SMEs, the observations are generally well outside the ensemble. We suggest that multi-model ensembles should represent an important component of uncertainty analysis.

Some recent compilations of proxy data both on land and ocean (MARGO Project Members, 2009; Bartlein et al., 2011; Shakun et al., 2012), have provided a new opportunity for an improved assessment of the overall climatic state of the Last Glacial Maximum. In this paper, we combine these proxy data with the ensemble of structurally diverse state of the art climate models which participated in the PMIP2 project (Braconnot et al., 2007) to generate a spatially complete reconstruction of surface air (and sea surface) temperatures. We test a variety of approaches, and show that multiple linear regression performs well for this application. Our reconstruction is significantly different to and more accurate than previous approaches and we obtain an estimated global mean cooling of 4.0 ± 0.8 °C (95% CI).

This study proposes a systematic approach to investigate cloud-radiative feedbacks to climate change induced by an increase of CO2 concentrations in global climate models (GCMs). Based on two versions of the Model for Interdisciplinary Research on Climate (MIROC), which have opposite signs for cloud–shortwave feedback (ΔSWcld) and hence different equilibrium climate sensitivities (ECSs), hybrid models are constructed by replacing one or more parameterization schemes for cumulus convection, cloud, and turbulence between them. An ensemble of climate change simulations using a suite of eight models, called a multiphysics ensemble (MPE), is generated. The MPE provides a range of ECS as wide as the Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel ensemble and reveals a different magnitude and sign of ΔSWcld over the tropics, which is crucial for determining ECS. It is found that no single process controls ΔSWcld, but that the coupling of two processes does. Namely, changing the cloud and turbulence schemes greatly alters the mean and the response of low clouds, whereas replacing the convection and cloud schemes affects low and middle clouds over the convective region. For each of the circulation regimes, ΔSWcld and cloud changes in the MPE have a nonlinear, but systematic, relationship with the mean cloud amount, which can be constrained from satellite estimates. The analysis suggests a positive feedback over the subsidence regime and a near-neutral or weak negative ΔSWcld over the convective regime in these model configurations, which, however, may not be carried into other models.

In this study, we constructed a perturbed physics ensemble (PPE) for the MIROC5 coupled atmosphere–ocean general circulation model (CGCM) to investigate the parametric uncertainty of climate sensitivity (CS). Previous studies of PPEs have mainly used the atmosphere-slab ocean models. A few PPE studies using a CGCM applied flux corrections, because perturbations in parameters can lead to large radiation imbalances at the top of the atmosphere and climate drifts. We developed a method to prevent climate drifts in PPE experiments using the MIROC5 CGCM without flux corrections. We simultaneously swept 10 parameters in atmosphere and surface schemes. The range of CS (estimated from our 35 ensemble members) was not wide (2.2–3.2 °C). The shortwave cloud feedback related to changes in middle-level cloud albedo dominated the variations in the total feedback. We found three performance metrics for the present climate simulations of middle-level cloud albedo, precipitation, and ENSO amplitude that systematically relate to the variations in shortwave cloud feedback in this PPE.

In the present study we investigate the performance of climate models which con- tributed to the past 3 Intergovernmental Panel for Climate Change (IPCC) assessment reports for the Gangetic West Bengal region of east India (6° × 6°). Analysing present-day seasonal rainfall and temperature over the domain, we compare the results of the models (from the 6 modelling centres common to the second, third and fourth assessment reports—SAR, TAR and AR4, respec- tively) in order to judge to what extent these global models have improved on a regional scale. Metrics for model evaluation are not yet firmly established in the literature, so in this paper we compare and contrast the results from a number of different statistics used in previous studies. We also analyse the impact of topography on the results obtained for the AR4 models. We find that most models improved from SAR to AR4, although there is some variation in this result depending on seasons, variables and on which statistical methods are used in the analysis. The multi-model mean of the 6 models improves from SAR to TAR to AR4. The overall best performance in this region in the AR4 is the Japanese model, MIROC, but the best model in terms of improving skill from SAR to AR4 is the GFDL model from the United States. Correcting for errors in the model topographies produced an overall improvement of spatial patterns and error statistics, and greatly improves the performance of 1 model (CGCM) which has poor topography, but does not affect the ranking of the other models.

In the climate-carbon cycle system, the terrestrial ecosystem feedback is significant. In studies on feedback analysis, the ecosystem feedback is divided into the sensitivity of carbon storage to atmospheric CO2 concentration (bL), and temperature change (gL). Although ecosystems include many nonlinear processes, the scenario- and time-dependency of bL and gL have not been explicitly discussed. To check the validity of this simplification and its robustness, we carried out two, 1% per year (p.a.) increase and RCP4.5 scenario, experiments, using a processbased terrestrial ecosystem model forced by an existing GCM output, combined with an energy moisture balance model for the latter experiment, with 300 ensemble members perturbing twelve important and a priori unconstrained parameters. In the 1% p.a. experiment, bL peaked around 500 ppm and then gradually decreased with increasing CO2 level, while gL decreased with some inter-annual variability as temperature increases. The

Climate sensitivity is one of the most important metrics for future climate projections. In previous studies the climate of the last glacial maximum has been used to constrain the range of climate sensitivity, and similarities and differences of temperature response to the forcing of the last glacial maximum and to idealized future forcing have been investigated. The feedback processes behind the response have not, however, been fully explored in a large model parameter space. In this study, the authors first examine the performance of various feedback analysis methods that identify important feedbacks for a physics parameter ensemble in experiments simulating both past and future climates. The selected methods are then used to reveal the relationship between the different ensemble experiments in terms of individual feedback processes. For the first time, all of the major feedback processes for an ensemble of paleoclimate simulations are evaluated. It is shown that the feedback and climate sensitivity parameters depend on the nature of the forcing and background climate state. The forcing dependency arises through the shortwave cloud feedback while the state dependency arises through the combined water vapor and lapse-rate feedback. The forcing dependency is, however, weakened when the feedback is estimated from the forcing that includes tropospheric adjustments. Despite these dependencies, past climate can still be used to provide a useful constraint on climate sensitivity as long as the limitation is properly taken into account because the strength of each feedback correlates reasonably well between the ensembles. It is, however, shown that the physics parameter ensemble does not cover the range of results simulated by structurally different models, which suggests the need for further study exploring both structural and parameter uncertainties.

The Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel ensemble has been widely utilized for climate research and prediction, but the properties and behavior of the ensemble are not yet fully understood. Here, some investigations are undertaken into various aspects of the ensemble’s behavior, in particular focusing on the performance of the multimodel mean. This study presents an explanation of this phenomenon in the context of the statistically indistinguishable paradigm and also provides a quantitative analysis of the main factors that control how likely the mean is to outperform the models in the ensemble, both individually and collectively. The analyses lend further support to the usage of the paradigm of a statistically indistinguishable ensemble and indicate that the current ensemble size is too small to adequately sample the space from which the models are drawn.

In this study, we used two novel methods to estimate urban contamination in the Japanese temperature record of the last century. First, we tested different criteria for choosing the rural stations, and found little sensitivity to the method, though the presence of a decreasing local population trend appeared to be a useful indicator. Second, we investigated the relationship between the regional sea surface temperature (SST) and surface air temperature over land, and found a very strong relationship across the coupled model intercomparison project phase 3 multi-model ensemble. Applying this relationship to observational SST data indicates little or no contamination of the trends from the stations identified as rural. Copyright © 2011 Royal Meteorological Society

Analyses of skill are widely used for assessing weather predictions, but the time scale and lack of validation data mean that it is not generally possible to investigate the predictive skill of today's climate models on the multidecadal time scale. The predictions made with early climate models can, however, be analyzed, and here we show that one such forecast did have skill. It seems reasonable to expect that predictions based on today's more advanced models will be at least as skillful. In general, assessments of predictions based on today's climate models should use Bayesian methods, in which the inevitable subjective decisions are made explicit. For the AR4, the Intergovernmental Panel on Climate Change (IPCC) recommended the Bayesian paradigm for making estimates of uncertainty and probabilistic statements, and here we analyze the way in which uncertainty was actually addressed in the report. Analysis of the ensemble of general circulation models (GCMs) used in the last IPCC report suggests there is little evidence to support the popular notion that the multimodel ensemble is underdispersive, which would imply that the spread of the ensemble may be a reasonable starting point for estimating uncertainty. It is important that the field of uncertainty estimation is developed in order that the best use is made of current scientific knowledge in making predictions of future climate. At the same time, it is only by better understanding the processes and inclusion of these processes in the models, the best estimates of future climate will be closer to the truth. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website

The equilibrium climate sensitivity (ECS) of the two perturbed physics ensembles (PPE) generated using structurally different GCMs, Model for Interdisciplinary Research on Climate (MIROC3.2) and the Third Hadley Centre Atmospheric Model with slab ocean (HadSM3), is investigated. A method to quantify the shortwave (SW) cloud feedback by clouds with different cloud-top pressure is developed. It is found that the difference in the ensemble means of the ECS between the two ensembles is mainly caused by differences in the SW low-level cloud feedback. The ensemble mean SW cloud feedback and ECS of the MIROC3.2 ensemble is larger than that of the HadSM3 ensemble. This is likely related to the 1XCO2 low-level cloud albedo of the former being larger than that of the latter. It is also found that the largest contribution to the within-ensemble variation of ECS comes from the SW low-level cloud feedback in both ensembles. The mechanism that causes the within-ensemble variation is different between the two ensembles. In the HadSM3 ensemble, members with large 1XCO2 low-level cloud albedo have large SW cloud feedback and large ECS; ensemble members with large 1XCO2 cloud cover have large negative SW cloud feedback and relatively low ECS. In the MIROC3.2 ensemble, the 1XCO2 low-level cloud albedo is much more tightly constrained, and no relationship is found between it and the cloud feedback. These results indicate that both the parametric uncertainties sampled in PPEs and the structural uncertainties of GCMs are important and worth further investigation.

We use an ensemble of runs from the MIROC3.2 AGCM with slab-ocean to explore the extent to which mid-Holocene simulations are relevant to predictions of future climate change. The results are compared with similar analyses for the Last Glacial Maximum (LGM) and pre-industrial control climate. We suggest that the paleoclimate epochs can provide some independent validation of the models that is also relevant for future predictions. Considering the paleoclimate epochs, we find that the stronger global forcing and hence larger climate change at the LGM makes this likely to be the more powerful one for estimating the large-scale changes that are anticipated due to anthropogenic forcing. The phenomena in the mid-Holocene simulations which are most strongly correlated with future changes (i.e., the mid to high northern latitude land temperature and monsoon precipitation) do, however, coincide with areas where the LGM results are not correlated with future changes, and these are also areas where the paleodata indicate significant climate changes have occurred. Thus, these regions and phenomena for the mid-Holocene may be useful for model improvement and validation.

The equilibrium climate response to anthropogenic forcing has long been one of the dominant, and therefore most intensively studied, uncertainties in predicting future climate change. As a result, many probabilistic estimates of the climate sensitivity (S) have been presented. In recent years, most of them have assigned significant probability to extremely high sensitivity, such as P(S > 6C) > 5%. In this paper, we investigate some of the assumptions underlying these estimates. We show that the popular choice of a uniform prior has unacceptable properties and cannot be reasonably considered to generate meaningful and usable results. When instead reasonable assumptions are made, much greater confidence in a moderate value for S is easily justified, with an upper 95% probability limit for S easily shown to lie close to 4°C, and certainly well below 6°C. These results also impact strongly on projected economic losses due to climate change.

When an averaging method is used for model future projection with weights determined according to the model performance in the present climate, generally, the stationarity of the model performance between present and future is implicitly assumed. Here we investigate this assumption using multi-model data. We consider the correlation between inter-model similarities in the spatial pattern for the present-day climate and future climate change for surface air temperature, precipitation and sea level pressure on global and zonal domains in the seasonal time scale. We further extend previous work by devising a bootstrap method to estimate the statistical significance of all correlations, which have previously not been estimated. Most of the correlation coefficients for precipitation were significant, but moderate or low in the absolute value. Many of those for the other variables were not significant. Also, we discuss the magnitude of the inter-model similarity used in this work.

International audience; We have extended the 3-D ocean based "Grid ENabled Integrated Earth system model" (GENIE-1) to help understand the role of ocean biogeochemistry and marine sediments in the long-term (~100 to 100 000 year) regulation of atmospheric CO2, and the importance of feedbacks between CO2 and climate. Here we describe the ocean carbon cycle, which in its first incarnation is based around a simple single nutrient (phosphate) control on biological productivity. The addition of calcium carbonate preservation in deep-sea sediments and its role in regulating atmospheric CO2 is presented elsewhere (Ridgwell and Hargreaves, 2007). We have calibrated the model parameters controlling ocean carbon cycling in GENIE-1 by assimilating 3-D observational datasets of phosphate and alkalinity using an ensemble Kalman filter method. The calibrated (mean) model predicts a global export production of particulate organic carbon (POC) of 8.9 PgC yr?1, and reproduces the main features of dissolved oxygen distributions in the ocean. For estimating biogenic calcium carbonate (CaCO3) production, we have devised a parameterization in which the CaCO3:POC export ratio is related directly to ambient saturation state. Calibrated global CaCO3 export production (1.2 PgC yr-1) is close to recent marine carbonate budget estimates. The GENIE-1 Earth system model is capable of simulating a wide variety of dissolved and isotopic species of relevance to the study of modern global biogeochemical cycles as well as past global environmental changes recorded in paleoceanographic proxies. Importantly, even with 12 active biogeochemical tracers in the ocean and including the calculation of feedbacks between atmospheric CO2 and climate, we achieve better than 1000 years per (2.4 GHz) CPU hour on a desktop PC. The GENIE-1 model thus provides a viable alternative to box and zonally-averaged models for studying global biogeochemical cycling over all but the very longest (>1 000 000 year) time-scales.

We examined the flows of nitrogen in two batch incubations of plankton assemblages under controlled conditions, using mesopelagic seawater from different depths. Observations included concentrations of nutrients, organic matter (particulate and dissolved) and plankton (biomass by species). Because nitrogen flows were not observed directly (as is generally the case), we examined them using a multi-element ecosystem model developed to simulate these experiments. Dynamic changes in the observed bulk POC/PON ratio (C/N ratio of particulate organic matter, POM) were consistent with a quota model for phytoplankton. To relate these changes to the regeneration of nitrogen, we included such a quota model and all major planktonic groups observed. By assimilating the data (all observations of carbon and nitrogen concentrations, including living carbon biomasses) into the model using the Monte Carlo Markov Chain, we accurately simulated the changes in bulk POC/PON ratio and its difference between incubations. Changes in phytoplankton composition dominated the changes in bulk POC/PON ratio. Bacteria dominated the regeneration of nitrogen in both incubations, and changes in bacterial regeneration strongly affected the bulk POC/PON ratio. After nitrate depletion, gross nitrogen regeneration varied inversely with observed POC/PON ratio and was constrained by this ratio. Thus, we have demonstrated a powerful new approach to constraining the flows of nutrients through ecosystems. Our results suggest that simultaneous observations of POC and PON could place an additional constraint on the supply of inorganic nitrogen in models of the oligotrophic ocean.

We use a recently-developed efficient probabilistic estimation technique to estimate the sensitivity of the Earth’s temperature to a doubling of atmospheric carbon dioxide. The method is based on the ensemble Kalman filter which we apply to the CCSR/NIES/ FRCGC AGCM (the atmospheric component of MIROC 3.2) at T21L20 resolution coupled to a slab ocean. The method combines prior beliefs about the model, with observational data, to simultaneously estimate 25 model parameters in an efficient and objective manner. We perform a sensitivity analysis to investigate the effect of different assumptions regarding model error, since this is a necessarily subjective input which has not yet been well characterised. We attempt to validate the resulting ensembles against out-of-sample data by comparing their hindcasts of the Last Glacial Maximum (LGM) to paleoclimate proxy data, and demonstrate through this that our ensembles of simulations are probably biased towards too high a sensitivity. Within the framework of our single-model ensemble experiment, we show that climate sensitivity of much greater than 6° Ci s hard to reconcile with the paleoclimate record, and that of greater than 8°C seems virtually impossible. Our estimate for the most likely climate sensitivity is in the region of 4.5°C. Although these results are reasonably consistent with the most widely accepted estimates of climate sensitivity, they disagree with some recent research which has suggested a significant probability of sensitivities well in excess of these values. These results suggest that paleoclimatic evidence could provide a useful, albeit imprecise, constraint on ensemble forecasts of future climate change.

We describe the development of an efficient method for parameter estimation and ensemble forecasting in climate modelling. The technique is based on the ensemble Kalman filter and is several orders of magnitude more efficient than many others which have been previously used to address this problem. As well as being theoretically (near-)optimal, the method does not suffer from the `curse of dimensionality' and can comfortably handle multivariate parameter estimation. We demonstrate the potential of this method in identical twin testing with an intermediate complexity coupled AOGCM. The model's climatology is successfully tuned via the simultaneous estimation of 12 parameters. Several minor modifications arc described by which the method was adapted to a steady state (temporally averaged) case. The method is relatively simple to implement, and with only O(50) model runs required, we believe that optimal parameter estimation is now accessible even to computationally demanding models.

We describe the use of a Monte Carlo Markov Chain (MCMC) method based on Bayes' Theorem and the Metropolis-Hastings algorithm for estimation of model parameters in a climate model. We use the model of Saltzman and Maasch (1990). This is a computationally simple model, but with seven free parameters and substantial non-linearity it would be difficult to tune with commonly used data assimilation methods. When forced with solar radiation, the model can reproduce mean ocean temperature, atmospheric CO2 concentration and global ice volume reasonably well over the last 500 ka. The MCMC method samples the multivariate probability density function of model parameters, which makes it a powerful tool for estimating not only parameter values but also for calculating the model's sensitivity to each parameter. A major attraction of the method is the simplicity and the ease of the implementation of the algorithm. We have used cross-validation to show that the model forecast for the next 50–100 ka is of similar accuracy to the hindcast over the last 500 ka. The model forecasts an immediate cooling of the Earth, with the next glacial maximum in around 60 ka. An anthropogenic pulse of CO2 has a short-term effect but does not influence the model prediction beyond 30 ka. Beyond 100 ka into the future, the model ensemble diverges widely, indicating that there is insufficient information in the data which we have used to determine the longer term evolution of the Earth's climate.

Henriksson et al. (2010), hereafter HALTL10, criticize Annan and Hargreaves (2006a) (AH06) primarily on the grounds that we assumed that different sources of data were conditionally independent given the climate sensitivity. While we consider this approximation to have been a reasonable one under the circumstances (and provided arguments to justify this approach), we also acknowledged its importance in our original paper and performed several sensitivity analyses. The alternative calculations presented by HALTL10 appear to strengthen rather than contradict our conclusion. HALTL10 additionally criticize Annan and Hargreaves (2009) (AH09) for proposing a Cauchy type prior (as an alternative to the use of a uniform prior, which was widespread up to that time) "without sufficient support", and further claim that anticipated economic damages were used as a means of selecting the prior. We are surprised by these claims, especially considering that the proposed prior was justified at some length both on the basis of both the "Charney report" (National Research Council, 1979) and basic physical arguments, and also in light of our elementary demonstration of the pathological failings of the most commonly-used alternative. Thus, these claims are factually incorrect.

An intensive series of observations off the Holderness coast was followed by a related set of modelling applications. Observations included: aircraft and satellite remote sensing, H.F. and X-band radar, ship surveys and in situ instruments on the sea bed and at the sea surface. These observations aimed to monitor, over three successive winter periods, the dynamics and sediment distributions in the vicinity of this rapidly eroding coastline. Associated modelling applications included components simulating: (i) tides and surge currents; (ii) wave evolution; (iii) vertical distributions of turbulence and SPM (suspended particulate matter) and (iv) resulting spatial patterns of sediment transport in the region. Simulations of tidal currents confirmed the accuracy of such models, given accurate fine-resolution bathymetry and appropriate boundary conditions. New developments of WAM, the spectral wave model required for fine-resolution applications in shallow water (described by Monbaliu et al. [Monbaliu, J., Padilla-Hernandez, R., Hargreaves, J.C., Carretero Albiach, J.C., Luo, W., Sclavo, M., Gunther, H., 2000. The spectral wave model WAM adapted for applications with high spatial resolution. This volume.]) are tested here. A number of additional features pertaining to shallow water are revealed including the sensitivity to specification of wind directions and the excessive temporal spreading of short-lived distant events. Likewise, the application of the generic single-point models for vertical profiles of turbulence and SPM (described by Baumert et al. [Baumert, H., Chapalain, G., Smaoui, H., McManus, J.P., Yagi, H., Regener, M., Sundermann, J., Szilagy, B., 2000. Modelling and numerical simulation of turbulence, waves and suspended sediment for pre-operational use in coastal seas. This volume]), are tested and also shown to be appropriate for simulating localised resuspension of SPM. This simulation also illustrates how, in shallow water ( Some preliminary simulations of net sediment movement are included, involving an integration of the above effects. These simulations emphasise how, in all but the shallowest water, the mobility of coarse grain sediments is limited to occasions of extreme waves. By contrast, the movement of fine sediments follows that of the residual tidal current streamlines, i.e., primarily longshore with attendant cross-shore dispersion. However, significant variation between closely-spaced observations indicates the irregularity and complexity of such distributions. It is concluded that because of the inability to prescribe the spatial distribution of available surficial sediments (including size distributions) such simulations can only be expected to reproduce the essential statistical characteristics of SPM concentrations. The availability of extensive remote sensing or in situ data can help to circumvent this problem.

In a recent paper, Chylek and Lohmann (2008) used data from the Vostok ice core together with simple energy balance arguments to simultaneously estimate both the dust radiative forcing effect and the climate sensitivity, generating surprisingly high and low values for these respective parameters. However, their results depend critically on their selection of single unrepresentative data points from time series which exhibit a large amount of short-term variability, and are highly unstable with respect to other arbitrarily selected data points. When temporal averages are used in accordance with accepted norms within the paleoclimate community, the results obtained are entirely unremarkable and in line with previous analyses.

In this paper, a novel interpolation technique based on a greatly simplified Kalman filtering approach is presented which enables satellite sea surface temperature observations to be assimilated into a three-dimensional baroclinic model of the North Sea. A series of numerical experiments of the annual cycle of seasonal stratification demonstrate a large improvement in the predictive ability of the model, and show good agreement with theoretical calculations of expected performance.