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Matthew Collins
and
Myles R. Allen

Abstract

The relative importance of initial conditions and boundary conditions in interannual to decadal climate predictability is addressed. A simple framework is developed in which (i) ensembles of climate model simulations with changing external forcing can be measured against climatology to get an estimate of the timescale on which changing boundary conditions can provide predictive skill, and (ii) the rate of spread of ensembles of simulations with small perturbations to the initial conditions can be measured against climatology to assess the timescale at which the information in the initial conditions is degraded by chaotic error growth. A preliminary test of the method on a limited number of climate model simulations is presented.

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Myles R. Allen
and
Leonard A. Smith

Abstract

Singular systems (or singular spectrum) analysis (SSA) was originally proposed for noise reduction in the analysis of experimental data and is now becoming widely used to identify intermittent or modulated oscillations in geophysical and climatic time series. Progress has been hindered by a lack of effective statistical tests to discriminate between potential oscillations and anything but the simplest form of noise, that is, “white” (independent, identically distributed) noise, in which power is independent of frequency. The authors show how the basic formalism of SSA provides a natural test for modulated oscillations against an arbitrary “colored noise” null hypothesis. This test, Monte Carlo SSA, is illustrated using synthetic data in three situations: (i) where there is prior knowledge of the power-spectral characteristics of the noise, a situation expected in some laboratory and engineering applications, or when the “noise” against which the data is being tested consists of the output of an independently specified model, such as a climate model; (ii) where a simple hypothetical noise model is tested, namely, that the data consists only of white or colored noise; and (iii) where a composite hypothetical noise model is tested, assuming some deterministic components have already been found in the data, such as a trend or annual cycle, and it needs to be established whether the remainder may be attributed to noise. The authors examine two historical temperature records and show that the strength of the evidence provided by SSA for interannual and interdecadal climate oscillations in such data has been considerably overestimated. In contrast, multiple inter- and subannual oscillatory components are identified in an extended Southern Oscillation index at a high significance level. The authors explore a number of variations on the Monte Carlo SSA algorithm and note that it is readily applicable to multivariate series, covering standard empirical orthogonal functions and multichannel SSA.

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Myles R. Allen
and
Michael K. Davey

Abstract

A number of linear models of the steady-state response of the tropical atmosphere to sea surface temperature (SST) anomalies have been proposed, all based on the shallow-water equations. Despite their formal similarity, the various models have very different physical interpretations and suggest widely varying values for key parameters, including the mechanical damping rate (or coefficient of Rayleigh friction), the strength of the coupling to SST, and the “effective stability” of the lower troposphere. In order to place empirical constraints on these coefficients, the linear momentum equations are inverted to obtain the scalar forcing fields P′(interpreted as vertically integrated boundary-layer pressure anomalies) that best reproduce observed surface wind anomalies through the period 1984–90. This gives an optimum value for the mechanical damping rate, independent of the coupling parameterization. Direct optimization of a fully linear Gill-type model of ocean-atmosphere coupling reveals that the problem of identifying optimum values for the other two parameters (coupling and stability) is degenerate; if one parameter is fixed, the other is well constrained by the data, but if both are allowed to vary, the cost function (rms error in the model output winds) has no well-defined minimum. Models of this type also suggest a simple relationship between P′ and anomalies of SST and divergence, however. A significant but strikingly different relationship is found between these three quantities derived from the observations. If uniform, linear coupling is assumed, this result suggests that the large-scale response of the tropical atmosphere to SST anomalies is consistent with a moderately moist-unstable boundary layer, with the stability of the response being maintained by turbulent diffusive processes. This may be parameterized most simply by introducing biharmonic diffusion on Pinto the “thermodynamic” equation of a Gill-type model. Simple forms of nonlinear coupling both to SST and to divergence are also investigated. Although the possibility that nonlinear effects are important cannot be excluded, no evidence is found to suggest that either of two widely used nonlinear coupling parameterizations represent an improvement on a fully linear scheme.

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F. Hugo Lambert
and
Myles R. Allen

Abstract

A tropospheric energy budget argument is used to analyze twentieth-century precipitation changes. It is found that global and ocean-mean general circulation model (GCM) precipitation changes can be understood as being due to the competing direct and surface-temperature-dependent effects of external climate forcings. In agreement with previous work, precipitation is found to respond more strongly to anthropogenic and volcanic sulfate aerosol and solar forcing than to greenhouse gas and black carbon aerosol forcing per unit temperature. This is due to the significant direct effects of greenhouse gas and black carbon forcing. Given that the relative importance of different forcings may change in the twenty-first century, the ratio of global precipitation change to global temperature change may be quite different. Differences in GCM twentieth- and twenty-first-century values are tractable via the energy budget framework in some, but not all, models. Changes in land-mean precipitation, on the other hand, cannot be understood at all with the method used here, even if land–ocean heat transfer is considered. In conclusion, the tropospheric energy budget is a useful concept for understanding the precipitation response to different forcings but it does not fully explain precipitation changes even in the global mean.

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Gabriele C. Hegerl
and
Myles R. Allen

Abstract

Two approaches to distinguishing anthropogenic greenhouse gas and sulfate aerosol signals in the observed surface temperature record are compared. Both rely on a variant of general regression called “optimal fingerprinting.” One approach is equivalent to a stepwise regression procedure estimating, first, a greenhouse gas signal and, in a second step, the sulfate aerosol signal. This is different from multiple regression, under which both signals are estimated simultaneously and treated symmetrically. The stepwise regression approach is a more powerful means of detecting greenhouse gas influence in the presence of a small and possibly poorly simulated sulfate aerosol signal. However, when both signals are of comparable size, multiple regression provides estimates of the amplitude of the greenhouse and sulfate responses that are, in principle, independent of each other, making it generally simpler to interpret. It is shown that there is a simple linear transform relating the stepwise and multiple regression approaches. Application of this transform to previous results of stepwise regression illustrates that estimated responses to anthropogenic greenhouse gas forcing are very similar between different climate models and are generally consistent with the signal estimated from the observations. The sulfate component of the anthropogenic signal appears to be responsible for the most prominent discrepancies between observations and some of the model simulations considered. The estimated contribution of anthropogenic greenhouse gases to the observed warming over the period of 1949–98 lies in the range of 0.39–1.29 K (50 yr)−1 or 0.28–1.16 K (50 yr)−1 (5%–95% range), depending on the model used to estimate the signal. These ranges depend only on the accuracy of the spatial pattern and the sign of the modeled sulfate forcing and response, not on its amplitude.

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Philip D. Watts
,
Myles R. Allen
, and
Timothy J. Nightingale

Abstract

The emission and reflection properties of a rough sea surface are investigated, with particular emphasis on the wavelengths and viewing geometry relevant to the Along Track Scanning Radiometer. The authors start from Fresnel's equations for a flat water surface and calculate the effect of changing sea state on direct emissivity and reflectivity. The authors then investigate the role of surface-emitted surface-reflected (SESR) radiation, which enhances emissivity at high wind speeds. The effect of foam and whitecaps at high wind speeds is referred to briefly in the appendix but essentially remains an unknown quantity.

Radiative transfer calculations that employ emissivity models also have to consider the reflection of downwelling radiance from the atmosphere. Although energy conservation requires that reflectivity is 1 minus emissivity, the variability of the sky brightness with zenith demands that one consider also the angular distribution of the reflected radiance. Additionally, the extended statistical model is used to investigate what one may call surface-reflected surface-reflected (SRSR) radiance.

It was found that the SESR and SRSR effects, and the reflection of the anisotropic sky radiance, together act to cancel the first-order effect of reduced emissivity with increasing wind speed, such that the approximation of constant emissivity and specular reflection is essentially valid for the Along Track Scanning Radiometer viewing geometry. Finally, parameterizations are derived for the variable emission and reflection of a rough sea surface that are suitable for fast radiative transfer models.

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DáithíA. Stone
,
Myles R. Allen
, and
Peter A. Stott

Abstract

This paper presents an update on the detection and attribution of global annual mean surface air temperature changes, using recently developed climate models. In particular, it applies a new methodology that permits the inclusion of many more general circulation models (GCMs) into the analysis, and it also includes more recent observations. This methodology involves fitting a series of energy balance models (EBMs) to the GCM output in order to estimate the temporal response patterns to the various forcings.

Despite considerable spread in estimated EBM parameters, characteristics of model performance, such as the transient climate response, appear to be more constrained for each of the forcings. The resulting estimated response patterns are provided as input to the standard fingerprinting method used in previous studies. The estimated GCM responses to changes in greenhouse gases are detected in the observed record for all of the GCMs, and are generally found to be consistent with the observed changes; the same is generally true for the responses to changes in stratospheric aerosols from volcanic eruptions. GCM responses to changes in tropospheric sulfate aerosols and solar irradiance also appear consistent with the observed record, although the uncertainty is larger. Greenhouse gas and solar irradiance changes are found to have contributed to a best guess of ∼0.8 and ∼0.3 K warming over the 1901–2005 period, respectively, while sulfate aerosols have contributed a ∼0.4 K cooling. This analysis provides an observationally constrained estimate of future warming, which is found to be fairly robust across GCMs. By 2100, a warming of between about 1.5 and 4.5 K can be expected according to the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios (SRES) A1B emissions scenario.

These results indicate an emerging constraint for global mean surface temperature responses to external forcings across GCMs, which is corroborated in the observed record. This implies that observationally constrained estimates of past warming and predictions of future warming are indeed becoming robust.

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Reto Knutti
,
Gerald A. Meehl
,
Myles R. Allen
, and
David A. Stainforth

Abstract

The estimated range of climate sensitivity has remained unchanged for decades, resulting in large uncertainties in long-term projections of future climate under increased greenhouse gas concentrations. Here the multi-thousand-member ensemble of climate model simulations from the climateprediction.net project and a neural network are used to establish a relation between climate sensitivity and the amplitude of the seasonal cycle in regional temperature. Most models with high sensitivities are found to overestimate the seasonal cycle compared to observations. A probability density function for climate sensitivity is then calculated from the present-day seasonal cycle in reanalysis and instrumental datasets. Subject to a number of assumptions on the models and datasets used, it is found that climate sensitivity is very unlikely (5% probability) to be either below 1.5–2 K or above about 5–6.5 K, with the best agreement found for sensitivities between 3 and 3.5 K. This range is narrower than most probabilistic estimates derived from the observed twentieth-century warming. The current generation of general circulation models are within that range but do not sample the highest values.

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Nathan P. Gillett
,
Vivek K. Arora
,
Damon Matthews
, and
Myles R. Allen

Abstract

The ratio of warming to cumulative emissions of carbon dioxide has been shown to be approximately independent of time and emissions scenarios and directly relates emissions to temperature. It is therefore a potentially important tool for climate mitigation policy. The transient climate response to cumulative carbon emissions (TCRE), defined as the ratio of global-mean warming to cumulative emissions at CO2 doubling in a 1% yr−1 CO2 increase experiment, ranges from 0.8 to 2.4 K EgC−1 in 15 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5)—a somewhat broader range than that found in a previous generation of carbon–climate models. Using newly available simulations and a new observational temperature dataset to 2010, TCRE is estimated from observations by dividing an observationally constrained estimate of CO2-attributable warming by an estimate of cumulative carbon emissions to date, yielding an observationally constrained 5%–95% range of 0.7–2.0 K EgC−1.

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Nathan P. Gillett
,
Gabriele C. Hegerl
,
Myles R. Allen
,
Peter A. Stott
, and
Reiner Schnur

Abstract

Anthropogenic influences on surface temperature over the second half of the twentieth century are examined using output from two general circulation models (HadCM2 and ECHAM3). Optimal detection techniques involve the comparison of observed temperature changes with those simulated by a climate model, using a control integration to test the null hypothesis that all the observed changes are due to natural variability. Two recent studies have examined the influence of greenhouse gases and the direct effect of sulfate aerosol on surface temperature using output from the same two climate models but with many differences in the methods applied. Both detected overall anthropogenic influence on climate, but results on the separate detection of greenhouse gas and sulfate aerosol influences were different. This paper concludes that the main differences between the results can be explained by the season over which temperatures were averaged, the length of the climatology from which anomalies were taken, and the use of a time-evolving signal pattern as opposed to a spatial pattern of temperature trends. This demonstration of consistency increases confidence in the equivalence of the methodologies in other respects, and helps to synthesize results from the two approaches. Including information on the temporal evolution of the response to different forcings allows sulfate aerosol influence to be detected more easily in HadCM2, whereas focusing on spatial patterns gives better detectability in ECHAM3.

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