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Nicholas Lewis

Abstract

Insight is provided into the use of objective-Bayesian methods for estimating climate sensitivity by considering their relationship to transformations of variables in the context of a simple case considered in a previous study, and some misunderstandings about Bayesian inference are discussed. A simple model in which climate sensitivity (S) and effective ocean heat diffusivity (K υ) are the only parameters varied is used, with twentieth-century warming attributable to greenhouse gases (AW) and effective ocean heat capacity (HC) being the only data-based observables. Probability density functions (PDFs) for AW and HC are readily derived that represent valid independent objective-Bayesian posterior PDFs, provided the error distribution assumptions involved in their construction are justified. Using them, a standard transformation of variables provides an objective joint posterior PDF for S and K υ; integrating out K υ gives a marginal PDF for S. Close parametric approximations to the PDFs for AW and HC are obtained, enabling derivation of likelihood functions and related noninformative priors that give rise to the objective posterior PDFs that were computed initially. Bayes’s theorem is applied to the derived AW and HC likelihood functions, demonstrating the effect of differing prior distributions on PDFs for S. Use of the noninformative Jeffreys prior produces an identical PDF to that derived using the transformation-of-variables approach. It is shown that similar inference for S to that based on these two alternative objective-Bayesian approaches is obtained using a profile likelihood method on the derived joint likelihood function for AW and HC.

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Nicholas Lewis

Abstract

A detailed reanalysis is presented of a “Bayesian” climate parameter study (as exemplified by Forest et al.) that estimates climate sensitivity (ECS) jointly with effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multidecadal observations with simulations by the Massachusetts Institute of Technology 2D climate model at varying settings of the three climate parameters. Use of improved methodology primarily accounts for the 90% confidence bounds for ECS reducing from 2.1–8.9 K to 2.0–3.6 K. The revised methodology uses Bayes's theorem to derive a probability density function (PDF) for the whitened (made independent using an optimal fingerprint transformation) observations, for which a uniform prior is known to be noninformative. A dimensionally reducing change of variables onto the parameter surface is then made, deriving an objective joint PDF for the climate parameters. The PDF conversion factor from the whitened variables space to the parameter surface represents a noninformative joint parameter prior, which is far from uniform. The noninformative prior prevents more probability than data uncertainty distributions warrant being assigned to regions where data respond little to parameter changes, producing better-constrained PDFs. Incorporating 6 years of unused model simulation data and revising the experimental design to improve diagnostic power reduces the best-fit climate sensitivity. Employing the improved methodology, preferred 90% bounds of 1.2–2.2 K for ECS are then derived (mode and median 1.6 K). The mode is identical to those from Aldrin et al. and [using the same Met Office Hadley Centre Climate Research Unit temperature, version 4 (HadCRUT4), observational dataset] from Ring et al. Incorporating nonaerosol forcing and observational surface temperature uncertainties, unlike in the original study, widens the 90% range to 1.0–3.0 K.

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Nicholas Lewis and Thorsten Mauritsen

Abstract

Recently it has been suggested that natural variability in sea surface temperature (SST) patterns over the historical period causes a low bias in estimates of climate sensitivity based on instrumental records, in addition to that suggested by time variation of the climate feedback parameter in atmospheric general circulation models (GCMs) coupled to dynamic oceans. This excess, unforced, historical “pattern effect” (the effect of evolving surface temperature patterns on climate feedback strength) has been found in simulations performed using GCMs driven by AMIPII SST and sea ice changes (amipPiForcing). Here we show, in both amipPiForcing experiments with one GCM and by using Green’s functions derived from another GCM, that whether such an unforced historical pattern effect is found depends on the underlying SST dataset used. When replacing the usual AMIPII SSTs with those from the HadISST1 dataset in amipPiForcing experiments, with sea ice changes unaltered, the first GCM indicates pattern effects that are indistinguishable from the forced pattern effect of the corresponding coupled GCM. Diagnosis of pattern effects using Green’s functions derived from the second GCM supports this result for five out of six non-AMIPII SST reconstruction datasets. Moreover, internal variability in coupled GCMs is rarely sufficient to account for an unforced historical pattern effect of even one-quarter the strength previously reported. The presented evidence indicates that, if unforced pattern effects have been as small over the historical record as our findings suggest, they are unlikely to significantly bias climate sensitivity estimates that are based on long-term instrumental observations and account for forced pattern effects obtained from GCMs.

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Nicholas Lewis and Judith Curry

Abstract

Energy budget estimates of equilibrium climate sensitivity (ECS) and transient climate response (TCR) are derived based on the best estimates and uncertainty ranges for forcing provided in the IPCC Fifth Assessment Report (AR5). Recent revisions to greenhouse gas forcing and post-1990 ozone and aerosol forcing estimates are incorporated and the forcing data extended from 2011 to 2016. Reflecting recent evidence against strong aerosol forcing, its AR5 uncertainty lower bound is increased slightly. Using an 1869–82 base period and a 2007–16 final period, which are well matched for volcanic activity and influence from internal variability, medians are derived for ECS of 1.50 K (5%–95% range: 1.05–2.45 K) and for TCR of 1.20 K (5%–95% range: 0.9–1.7 K). These estimates both have much lower upper bounds than those from a predecessor study using AR5 data ending in 2011. Using infilled, globally complete temperature data give slightly higher estimates: a median of 1.66 K for ECS (5%–95% range: 1.15–2.7 K) and 1.33 K for TCR (5%–95% range: 1.0–1.9 K). These ECS estimates reflect climate feedbacks over the historical period, assumed to be time invariant. Allowing for possible time-varying climate feedbacks increases the median ECS estimate to 1.76 K (5%–95% range: 1.2–3.1 K), using infilled temperature data. Possible biases from non–unit forcing efficacy, temperature estimation issues, and variability in sea surface temperature change patterns are examined and found to be minor when using globally complete temperature data. These results imply that high ECS and TCR values derived from a majority of CMIP5 climate models are inconsistent with observed warming during the historical period.

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Nicholas Lewis and Judith Curry

Abstract

Cowtan and Jacobs assert that the method used by Lewis and Curry in 2018 (LC18) to estimate the climate system’s transient climate response (TCR) from changes between two time windows is less robust—in particular against sea surface temperature bias correction uncertainty—than a method that uses the entire historical record. We demonstrate that TCR estimated using all data from the temperature record is closely in line with that estimated using the LC18 windows, as is the median TCR estimate using all pairs of individual years. We also show that the median TCR estimate from all pairs of decade-plus-length windows is closely in line with that estimated using the LC18 windows and that incorporating window selection uncertainty would make little difference to total uncertainty in TCR estimation. We find that, when differences in the evolution of forcing are accounted for, the relationship over time between warming in CMIP5 models and observations is consistent with the relationship between CMIP5 TCR and LC18’s TCR estimate but fluctuates as a result of multidecadal internal variability and volcanism. We also show that various other matters raised by Cowtan and Jacobs have negligible implications for TCR estimation in LC18.

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Lewis J. Allison, George W. Nicholas, and James S. Kennedy

Abstract

The High Resolution Infrared Radiometer (HRIR) carried by the Nimbus I meteorological Satellite provided detailed nighttime cloud information in the vertical as well as in the horizontal dimension. When the instantaneous field of view of the HRIR is completely filled by either a cloud or the earth's surface through clear skies, the temperature of the radiating surface can be inferred. Cloud top heights can, therefore, be deduced by relating the equivalent blackbody temperature from the satellite to the temperature-height profile of the atmosphere, providing the temperature decreases monotonically with height. Equivalent blackbody temperatures average 5K colder than air shelter temperatures based on 40 stations reporting clear skies. Cloud patterns over water are well defined from daytime HRIR data, but over land some clouds tend to be indistinguishable from land when the sum of the thermal emission and the reflected solar radiation from the cloud equals that from the land. The capability of both the photofacsimile displays and the computer maps to depict synoptic information demonstrates that HRIR data from future meteorological satellites should provide a new operational tool.

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Ryan O’Donnell, Nicholas Lewis, Steve McIntyre, and Jeff Condon

Abstract

A detailed analysis is presented of a recently published Antarctic temperature reconstruction that combines satellite and ground information using a regularized expectation–maximization algorithm. Though the general reconstruction concept has merit, it is susceptible to spurious results for both temperature trends and patterns. The deficiencies include the following: (i) improper calibration of satellite data; (ii) improper determination of spatial structure during infilling; and (iii) suboptimal determination of regularization parameters, particularly with respect to satellite principal component retention. This study proposes two methods to resolve these issues. One utilizes temporal relationships between the satellite and ground data; the other combines ground data with only the spatial component of the satellite data. Both improved methods yield similar results that disagree with the previous method in several aspects. Rather than finding warming concentrated in West Antarctica, the authors find warming over the period of 1957–2006 to be concentrated in the peninsula (≈0.35°C decade−1). This study also shows average trends for the continent, East Antarctica, and West Antarctica that are half or less than that found using the unimproved method. Notably, though the authors find warming in West Antarctica to be smaller in magnitude and find that statistically significant warming extends at least as far as Marie Byrd Land. This study also finds differences in the seasonal patterns of temperature change, with winter and fall showing the largest differences and spring and summer showing negligible differences outside of the peninsula.

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Igor Shulman, James K. Lewis, Alan F. Blumberg, and B. Nicholas Kim

Abstract

An optimization approach is derived for assimilating tidal height information along the open boundaries of a numerical model. The approach is then extended so that similar data along transects inside a model domain can also be optimally assimilated. To test the application of such an optimized methodology, M 2 tidal simulations were conducted with a numerical ocean model of the Yellow Sea, an area with a strong tidal influence. The use of the optimized open boundary conditions and internal data assimilation leads to a significant improvement of the predictive skill of the model. Average errors can be reduced by up to 75% when compared to nonoptimized boundary conditions.

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