High precision estimation of modeled aerosol direct radiative forcing

Aerosol radiative forcing can be difficult to quantify both accurately and precisely in global climate models. Long climate model integrations are often required and levels of statistical uncertainty can be substantial for some of the diagnostic methods and diagnosed forcings. Instantaneous estimates of sulfate aerosol direct radiative forcings in the present-day climate are compared to forcings that were determined using different diagnostic methods based on nudged climate model simulations with specified sea surface temperatures and sea ice. Our results show that the accuracy and precision of aerosol radiative forcing estimates vary considerably among different methods. Nudging of model trajectories to constrain natural meteorological variability in the simulations leads to highly accurate and precise estimates of sulfate radiative forcings for a wide range of nudging parameters. The radiative forcing of black carbon aerosols, for which instantaneous estimates of the direct radiative forcing are not available, was also assessed using these methods. We show that the nudging process also significantly increases the precision of these radiative forcing estimates. 11


Introduction
stantaneous RFs can be diagnosed as the radiative flux perturbation after an climate forcing agent 41 is introduced, usually by performing additional radiation calculations in the GCM with fixed mete-42 orological conditions. However, this method cannot be used if RFs are intimately tied to changes 43 in clouds, water vapor, and temperature. This is particularly important for aerosol semi-direct 44 and second indirect effects. RF methods that account for dynamic interactions of atmospheric 45 processes are needed to account for these changes. For example, RF can be determined as the dif-46 ference in radiative fluxes between two simulations, with and without the radiative effects of the 47 original forcing agent included. Such approaches are based on the assumption that meteorological 48 variables respond rapidly to the introduction of a RF agent so that impacts of RFs on sea surface 49 3 This paper is a non-peer reviewed preprint submitted to EarthArXiv. temperatures (SSTs) and sea ice (e.g. Lohmann et al. 2010;Boucher et al. 2013) or surface air 50 temperatures (Hansen et al. 2005) can be neglected in order to separate RFs from climate feedback 51 processes.

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As simulated radiative fluxes vary in time and space due to model internal variability, the diag-53 nosis of statistically meaningful aerosol radiative forcings often requires multi-decade long simu-54 lations or an ensemble of shorter simulations. This fact is particularly important for forcing agents 55 that produce radiative forcings which are much smaller than cloud and snow radiative effects in 56 the simulations, which can easily mask the radiative forcings. However, much shorter model inte-57 grations are frequently used in practice, especially for models with costly treatments of complex 58 aerosol and chemical processes. This raises concerns about the precision of these forcing esti-59 mates, with potential implications for the accuracy of climate assessments that are based on these 60 estimates.  Since uncertainties in diagnostic methods may contribute to overall uncertainties in radiative 70 forcings, it is useful to both quantify and reduce these uncertainties. In the following, the accu- This paper is a non-peer reviewed preprint submitted to EarthArXiv.   Aerosol direct RFs are diagnosed in this study using different methods, as we will now discuss. proposed the following radiative forcing estimate where δ T s is the global surface air temperature change and λ is the equilibrium climate sensitiv- This paper is a non-peer reviewed preprint submitted to EarthArXiv.
estimates are therefore based on relatively small differences in the means of highly variable quanti- The subscripts m and p denote the nudged and prescribed model states, respectively, andτ is 120 the relaxation time constant. In general, the nudging is only applied to a subset of model fields.

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In the current study, different model fields and time scales are used to examine the sensitivity of 122 the method to these choices. In the following, we will refer to nudged effective radiative forcing 123 (NERF) and Hansen nudged radiative forcing (Hansen NERF).

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In addition to sulfate, the methods described above were also applied to diagnose RFs for black 125 carbon. However, ERF methods do not filter out responses of clouds to changes in atmospheric 126 heating rates so black carbon RF estimates also include semi-direct effects. Consequently, instan-127 taneous direct radiative forcing estimates cannot be used to evaluate black carbon RFs. This paper is a non-peer reviewed preprint submitted to EarthArXiv. member model ensembles were generated without contributions of sulfate aerosol or black carbon 135 to radiative transfer, respectively.

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In order to compute the RFs for the nudged simulations, several different 6-member model en-137 sembles were generated. In the first ensemble, the horizontal winds and temperatures were nudged  Table 1. Figure 1 shows the corresponding RFs for individual ensemble members.

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For sulfate RF, the Hansen RF produces slightly better agreement with the true RF than the ERFs.  (Table 1).

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To assess differences in ensemble-mean RF estimates between different methods, Nudging leads to a slightly higher true RF than in the free control run (Table 1), which can only 162 be explained by small changes in simulated climate with this approach. While differences are 163 significant (Table 2), they are very small.

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P-values among individual RF diagnostic methods are summarized in Table 3. Results in Table 3 165 confirm that the Hansen method improves the agreement between the ERF and true RF for sulfate.

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Interestingly, the most strongly constrained nudging approach producing the highest precision (D), 167 results in a RF that is significantly different from the true forcing, even with the Hansen correction  In addition to global RFs, spatial patterns of RF are of interest for studies of regional climate 172 processes. Figure 2  This paper is a non-peer reviewed preprint submitted to EarthArXiv. This paper is a non-peer reviewed preprint submitted to EarthArXiv. This paper is a non-peer reviewed preprint submitted to EarthArXiv. This paper is a non-peer reviewed preprint submitted to EarthArXiv. This paper is a non-peer reviewed preprint submitted to EarthArXiv.