Abstract
<p>Initial-condition large ensembles with ensemble sizes ranging from 30 to 100 members have become a commonly used tool to quantify the forced response and internal variability in various components of the climate system. However, there is no consensus on the ideal or even sufficient ensemble size for a large ensemble.</p><p>Here, we introduce an objective method to estimate the required ensemble size. This method can be applied to any given application. We demonstrate its use on the examples that represent typical applications of large ensembles: quantifying the forced response, quantifying internal variability, and detecting a forced change in internal variability.</p><p>We analyse forced trends in global mean surface temperature, local surface temperature and precipitation in the MPI Grand Ensemble (Maher et al., 2019). We find that 10 ensemble members are sufficient to quantify the forced response in historical surface temperature over the ocean, but more than 50 members are necessary over land at higher latitudes. </p><p>Next, we apply our method to identify the required ensemble size to sample internal variability of surface temperature over central North America and over the Niño 3.4 region. A moderate ensemble size of 10 members is sufficient to quantify variability over North America, while a large ensemble with close to 50 members is necessary for the Niño 3.4 region.</p><p>Finally, we use the example of September Arctic sea ice area to investigate forced changes in internal variability. In a strong warming scenario, the variability in sea ice area is increasing because more open water near the coastlines allows for more variability compared to a mostly ice-covered Arctic Ocean (Goosse et al., 2009; Olonscheck and Notz, 2017). We show that at least 5 ensemble members are necessary to detect an increase in sea ice variability in a 1% CO<sub>2</sub> experiment. To also quantify the magnitude of the forced change in variability, more than 50 members are necessary.</p><p>These numbers might be highly model dependent. Therefore, the suggested method can also be used with a long control run to estimate the required ensemble size for a model that does not provide a large number of realisations. Therefore, our analysis framework does not only provide valuable information before running a large ensemble, but can also be used to test the robustness of results based on small ensembles or individual realisations.</p><p><em><strong>References</strong><br>Goosse, H., O. Arzel, C. M. Bitz, A. de Montety, and M. Vancoppenolle (2009), Increased variability of the Arctic summer ice extent in a warmer climate, Geophys. Res. Lett., 36(23), 401–5, doi:10.1029/2009GL040546.</em></p><p><em>Olonscheck, D., and D. Notz (2017), Consistently Estimating Internal Climate Variability from Climate Model Simulations, J Climate, 30(23), 9555–9573, doi:10.1175/JCLI-D-16-0428.1.</em></p><p><em>Milinski, S., N. Maher, and D. Olonscheck (2019), How large does a large ensemble need to be? Earth Syst. Dynam. Discuss., 2019, 1–19, doi:10.5194/esd-2019-70.</em></p>
Highlights
Single model initial-condition large ensembles (SMILEs) are a valuable tool for cleanly separating a model’s forced response from internal variability and improving our understanding of the observed trajectory of the climate system in the past, as well as its projected future evolution (Zelle et al, 2005; Deser et al, 2012a; Rodgers et al, 2015; Kay et al, 2015; Maher et al, 2019; Branstator and Selten, 2009; von Känel et al, 2017; Kirchmeier-Young et al, 2017; Frankignoul et al, 2017; Stolpe et al, 2018).The ensemble sizes currently available for individual global coupled climate models greatly differ
To quantify how effective the separation of forced response and internal variability is, we show the root-meansquare error (RMSE) of ensemble means for different ensemble sizes compared to the 200-member mean
If the acceptable error (RMSE) is 0.1 ◦C, 10–30 ensemble members are sufficient over the tropical ocean, while more than 50 ensemble members are required over most land regions
Summary
Single model initial-condition large ensembles (SMILEs) are a valuable tool for cleanly separating a model’s forced response from internal variability and improving our understanding of the observed trajectory of the climate system in the past, as well as its projected future evolution (Zelle et al, 2005; Deser et al, 2012a; Rodgers et al, 2015; Kay et al, 2015; Maher et al, 2019; Branstator and Selten, 2009; von Känel et al, 2017; Kirchmeier-Young et al, 2017; Frankignoul et al, 2017; Stolpe et al, 2018). Some studies argue that the pre-industrial control simulation is sufficient to quantify internal variability and no large ensemble is required. Thompson et al (2015) argue that the pre-industrial control simulation can be used to provide a robust estimate of internal variability and represent future internal variability, implying that a single ensemble member for each model may be sufficient. This approach only works if the internal variability does not change over time. Realisations 101–200 were added later and use the same configuration as the first 100 realisations but are initialised from different years of the preindustrial control simulation
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