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We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and - importantly - about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

This paper describes GCAM v5.1, an open source model that represents the linkages between energy, water, land, climate, and economic systems. GCAM is a market equilibrium model, is global in scope, and operates from 1990 to 2100 in 5-year time steps. It can be used to examine, for example, how changes in population, income, or technology cost might alter crop production, energy demand, or water withdrawals, or how changes in one region's demand for energy affect energy, water, and land in other regions. This paper describes the model, including its assumptions, inputs, and outputs. We then use 11 scenarios, varying the socioeconomic and climate policy assumptions, to illustrate the results from the model. The resulting scenarios demonstrate a wide range of potential future energy, water, and land uses. We compare the results from GCAM v5.1 to historical data and to future scenario simulations from earlier versions of GCAM and from other models. Finally, we provide information on how to obtain the model.

Earth system models (ESMs) and general circulation models (GCMs) are heavily used to provide inputs to sectoral impact and multisector dynamic models, which include representations of energy, water, land, economics, and their interactions. Therefore, representing the full range of model uncertainty, scenario uncertainty, and interannual variability that ensembles of these models capture is critical to the exploration of the future co-evolution of the integrated human–Earth system. The pre-eminent source of these ensembles has been the Coupled Model Intercomparison Project (CMIP). With more modeling centers participating in each new CMIP phase, the size of the model archive is rapidly increasing, which can be intractable for impact modelers to effectively utilize due to computational constraints and the challenges of analyzing large datasets. In this work, we present a method to select a subset of the latest phase, CMIP6, featuring models for use as inputs to a sectoral impact or multisector dynamics models, while prioritizing preservation of the range of model uncertainty, scenario uncertainty, and interannual variability in the full CMIP6 ensemble results. This method is intended to help impact modelers select climate information from the CMIP archive efficiently for use in downstream models that require global coverage of climate information. This is particularly critical for large-ensemble experiments of multisector dynamic models that may be varying additional features beyond climate inputs in a factorial design, thus putting constraints on the number of climate simulations that can be used. We focus on temperature and precipitation outputs of CMIP6 models, as these are two of the most used variables among impact models, and many other key input variables for impacts are at least correlated with one or both of temperature and precipitation (e.g., relative humidity). Besides preserving the multi-model ensemble variance characteristics, we prioritize selecting CMIP6 models in the subset that preserve the very likely distribution of equilibrium climate sensitivity values as assessed by the latest Intergovernmental Panel on Climate Change (IPCC) report. This approach could be applied to other output variables of climate models and, possibly when combined with emulators, offers a flexible framework for designing more efficient experiments on human-relevant climate impacts. It can also provide greater insight into the properties of existing CMIP6 models. [ABSTRACT FROM AUTHOR]

Hector is an open-source reduced-complexity climate–carbon cycle model that models critical Earth system processes on a global and annual basis. Here, we present an updated version of the model, Hector V3.2.0 (hereafter Hector V3), and document its new features, implementation of new science, and performance. Significant new features include permafrost thaw, a reworked energy balance submodel, and updated parameterizations throughout. Hector V3 results are in good general agreement with historical observations of atmospheric CO 2 concentrations and global mean surface temperature, and the future temperature projections from Hector V3 are consistent with more complex Earth system model output data from the sixth phase of the Coupled Model Intercomparison Project. We show that Hector V3 is a flexible, performant, robust, and fully open-source simulator of global climate changes. We also note its limitations and discuss future areas for improvement and research with respect to the model's scientific, stakeholder, and educational priorities. [ABSTRACT FROM AUTHOR]

Hector, an open-source reduced complexity climate-carbon cycle model. Hector is a computationally efficient source of climate information, capable of completing a run in a fraction of a second. Hector models critical Earth system processes on a global and annual basis. Here we present an updated version of the model, Hector V3. In this manuscript, we document Hector's new features, and implementation of new science (e.g., radiative forcing calculations, carbon cycle, etc.). Hector V3 results are in good agreement with historical observations of CO2 concentrations and global mean surface temperature, and its future temperature projections are consistent with more complex Earth System Model output data from the Sixth Coupled Model Intercomparison Project. We document that Hector V3 is a flexible, performant, and robust simulator of contemporary and 21st-century global climate, and in closing, discuss future areas of improvement and research with respect to the model's scientific, stakeholder, and educational priorities. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a range of extreme metrics. While we exploit existing large ensembles contributed to the CLIVAR Large Ensemble Project, our perspective is that of a modeling center wanting to estimate a-priori such sizes on the basis of an existing small ensemble (we use five members here). We therefore ask if such small-size ensemble is sufficient to estimate the population variance in a way accurate enough to apply a well established formula that quantifies the expected error as a function of n (the ensemble size). We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extreme metrics as a function of n by applying the population variance derived by five members in the formula. For a range of spatial and temporal scales, forcing levels (we use RCP8.5 simulations), and both models considered here as our proof of concept, CESM1-CAM5 and CanESM2, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, which remains true when extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation, and - importantly - about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. When an F-test is applied to the ratio of the variances in question, one estimated on the basis of only 5 or 10 ensemble members, one estimated using the full ensemble (up to 50 members in our study) we do not obtain significant results even when the analysis is conducted at the grid-point scale. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, like physics parameter settings, when designing ensemble simulations. [ABSTRACT FROM AUTHOR]