Climate change projections are one of the main inputs for assessing the potential consequences of different socioeconomic development pathways and international climate policy on natural and human systems. Due to the complexity of the systems involved and their interactions, climate projections are inherently uncertain (Curry and Webster, 2011;Gay and Estrada, 2010a;Knutti and Sedláček, 2012). Moreover, computational and technical costs of state-of-the-art physical models allow exploration of only a small fraction of the range of possible climate futures and hinder assessing risk through probabilistic scenarios (Knutti et al., 2010;Sanderson et al., 2015). For most decision-makers and researchers, these costs make it infeasible to explore how current and hypothetical changes in international mitigation policy can influence future warming and its consequences for society. In a time of proactive international mitigation policy, the dynamic nature of projecting future climate becomes even more evident and decision-making requirements can go beyond fixed illustrative emissions scenarios, such as the RCPs (Estrada and Botzen, 2021). For example, Nationally Determined Contributions (NDCs) that represent greenhouse gas emission reductions that countries promise as their contributions to the Paris Agreement are currently a key focus of international climate policy. Moreover, due to the nonlinearity of most climate impacts, even small deviations from a high-warming trajectory can produce large changes in the associated impacts (Estrada and Botzen, 2021;Ignjacevic et al., 2021). International efforts such as the Coupled Model Intercomparison Project (CMIP), which build and host large databases of climate models' simulations publicly available, have significantly contributed to improving the accessibility and utilization of climate scenarios for the wider research community and decision-makers (Knutti and Sedláček, 2012;Thomas F. Stocker et al., 2013;Taylor et al., 2012). However, many users still face the problem of processing large datasets for adapting them to their particular needs (e.g., temporal frequency and spatial domains). As such, studies and decisions are commonly based on a few illustrative greenhouse gases emissions trajectories and a handful of climate models' simulations which are often selected due to their availability and ease of use, such as WorldClim (Fick and Hijmans, 2017). Such a selection of climate model runs can hardly provide a good representation of uncertainty and indicate if a model's projections for a given region may represent extreme realizations in comparison to the majority of other models (Sanderson et al., 2015;Weigel et al., 2010). Even in cases when climate models' performance is assessed, the resulting selection of models does not guaranty that those projections of future climate are reliable (Altamirano del Carmen et al., 2021). Climate model selection remains an unresolved problem as commonly used metrics can be non-informative about the models' ability to reproduce the observed climate change signal and indicate much less about their ability for projecting future climate (Knutti et al., 2010). Uncertainty is a key characteristic of climate change and how it is understood and included in climate impact assessments can have profound effects on the estimates of the consequences of this phenomenon and on the design of policies to address these consequences (Gay and Estrada, 2010a;IPCC-TGICA, 2007). The development of tools and methods for better uncertainty management and for improving the usefulness of the large (thousands of terabytes) databases that are currently available are increasingly relevant research topics. More efficient, simple, and flexible approaches for taking advantage of the available databases can transform data into useful information and knowledge for better assessments of impacts, risks, and climate policy options. Reduced complexity models and emulators of more advanced models allow exploring -at low computational and technical costs for the user-a wide range of possible futures and emissions trajectories, parameterizations, as well as probabilistic assessment of risks for natural and human systems (Blanc, 2017;Estrada et al., 2020;Meinshausen et al., 2011a). Integrated assessment modelling benefits from such models and emulators to provide tools for supporting decisionmaking and providing estimates for cases in which complex climate/impacts model runs are not available. A notable example of the usefulness of such models is the MAGICC software which has made significant contributions to climate change research, particularly in impact, vulnerability and adaptation (IVA) assessments, and integrated assessment modelling (Meinshausen et al., 2011a(Meinshausen et al., , 2011b;;Wigley, 1995). The MAGICC software has been regularly used in the IPCC reports when simulations produced by general circulation climate models are not available and also in the national climate change assessments of several countries (Conde et al., 2011;IPCC, 2021IPCC, , 2018)). Here we present AIRCC-Clim (Assessment of Impacts and Risks of Climate Change -Probabilistic Climate Model Emulator), a simple and flexible climate model emulator for producing probabilistic regional projections of monthly and annual temperature and precipitation, as well as risk measures. AIRCC-Clim emulates the results from 37 atmosphere-ocean coupled general circulation models included in the Fifth Assessment Report of the IPCC (Thomas F. Stocker et al., 2013) with low computational and technical requirements on the user. It is a standalone software for Windows and Linux operating systems that requires no programming or advanced technical skills from the user and runs on computers with standard memory and processing resources. AIRCC-Clim is designed for a variety of applications including IVA assessments, integrated assessment modelling, and the quick evaluation of the consequences on global and regional climate of user-defined experiments of international mitigation. The remainder of this paper is structured as follows: Section 2 describes the AIRCC-Clim model structure and describes in detail each of its modules in terms of data sources, modelling approaches and methods, and their output. This section also describes the file options for exporting climate projections and their characteristics. An application of the model is shown in Section 3 in which the benefits of stringent international mitigation efforts are illustrated in terms of avoided warming, changes in precipitation and risk reduction. Section 4 concludes and discusses model extensions and integration with IVA models. 2. Model structure, data and methods AIRCC-Clim is composed of four main modules: greenhouse gas emission scenario editor; global climate models, a regional scenario generator; and a climate risk index generator (Figure 1).
In the following paragraphs each module is discussed, including detailed descriptions of the modelling approaches, methods and data sources. AIRCC-Clim offers a graphic interface for constructing user-defined emissions scenarios for six climate changing substances: Carbon dioxide (CO2 in MtC/yr), methane (CH4; in MtCH4/yr), nitrous oxide (N2O; MtN2O-N/yr), chlorofluorocarbons (CFC11, CFC12 in kt/yr), and sulfur hexafluoride (SF6 in kt/yr). Four RCP emissions trajectories are included by default and the user can select one of them as starting point for editing. As shown in Figure 2 AIRCC-Clim has three input options for emissions: 1) by means of editing the values displayed on a table; 2) by selecting and plotting the substance of interest and modifying the emissions trajectories directly in a graph; 3) loading an Excel file (.xlsx) with user-defined emissions trajectories for each gas in a predefined format (see the AIRCC-Clim user guide included in the SI). The modified emissions scenario is saved in an Excel (.xlsx) file and used for generating the corresponding climate projections in AIRCC-Clim. Global temperature projections in AIRCC-Clim can be generated by running a simple climate model, as well as by using precalculated projections from two reduced complexity climate models. As described in the following paragraphs, in all cases probabilistic projections are constructed by means of stochastic simulation to represent uncertainty in the climate sensitivity (CS) parameter. The Schneider-Thompson (ST) simple climate model (Schneider and Thompson, 1981) includes three components that allows to calculate the atmospheric concentrations of greenhouse gases, the corresponding change in radiative forcing and the resulting increase in global temperature. Due to its flexibility and low computational cost, this climate model (and modified versions of it) is used in some of the most popular integrated assessment models, such as FUND and RICE (Anthoff and Tol, 2014;Nordhaus and Boyer, 2003). The version of the ST model in AIRCC-Clim builds upon that used in the FUND integrated assessment model (Tol and Fankhauser, 1998) which is available at http://www.fund-model.org/. In this section, the ST model and the modifications that are introduced in AIRCC-Clim. A five box-model (Tol, 2019) is used to convert annual emissions of CO2 (MtC) into atmospheric concentrations (ppm). The initial value for CO2 concentrations is 278 ppm which represent preindustrial times (circa 1750). The carbon cycle model is represented by the following equation:

(1)

where 𝐶 𝑖,𝑡 𝐶𝑂 2 represents the atmospheric concentrations of CO2 in box i=1,..,5 at time t, 𝐸 𝑡 are the CO2 emissions at time t, 𝛼 𝑖 determines how long CO2 remain in box i, while 𝛾 𝑖 is the proportion of emissions that enter box i, and 𝛽 is a scale parameter (𝛽 = 0.00045). These boxes are characterized by different decay times that resemble the slow and fast components of the carbon cycle. However, these boxes do not represent physical processes and are just simple mathematical devices that allow to approximate the observed concentrations (Schneider and Thompson, 1981;Tol, 2019). 𝐶 𝑡 𝐶𝑂 2 is the total concentration of CO2 in the atmosphere at time t. Parameter values are reproduced in Table S1. The radiative forcing from CO2 is calculated as:

Where 𝐶 𝑝𝑟𝑒 𝐶𝑂 2 = 278 represents the preindustrial atmospheric concentrations of CO2. CH4 concentrations are calculated using the following equation:

Where 𝐶 𝑡 𝐶𝐻 4 are the atmospheric concentrations of CH4 at time t, 𝐶 𝑝𝑟𝑒 𝐶𝐻 4 = 721.89 is the preindustrial concentrations of CH4, 𝐸 𝑡 𝐶𝐻 4 are the emissions of CH4 at time t, 𝑎 1 = 0.1057 represents the permanence of CH4 in the atmosphere and 𝑏 1 = 0.3597 is a scaling factor. The atmospheric concentrations of N2O are calculated using an equation similar to that of CH4:

(5)

Where the emissions and atmospheric concentrations of N2O are denoted by 𝐸 𝑡 𝑁 2 𝑂 and 𝐶 𝑡 𝑁 2 𝑂 , respectively, while 𝐶 𝑝𝑟𝑒 𝑁 2 𝑂 = 272.96, 𝑎 2 = 1 120 ⁄ and 𝑏 2 = 0.1550. Calculating the radiative forcing of CH4 and N2O involves an interaction term between these gases to account for their overlap in the absorption bands as represented in the following equations:

𝐼𝑛𝑡 𝑡 𝑁 2 𝑂 = 𝑓(𝑀 0 , 𝑁) -𝑓(𝑀 0 , 𝑁 0 ) ′ (7)

Where these interaction functions are given by:

CFC11 and CFC12 concentrations are calculated as follows:

In which 𝑎 3 and 𝑎 4 are equal to 1 45 ⁄ and 1 100 ⁄ while 𝑏 3 = 0.0423 and 𝑏 4 = 0.0481. The radiative forcing from CFCs is calculated by multiplying it by a scaling factor equal to 0.25/1000 in the case of CFC11 and 0.32/1000 for CFC12. Finally, the concentrations of 𝑆𝐹 6 are obtained using the following equation:

Where 𝑎 5 = 1 3200 ⁄ and 𝑏 5 = 0.0393. The radiative forcing of 𝑆𝐹 6 is calculated as 𝐹 𝑡 𝑆𝐹 6 = 0.00052 * 𝐶 𝑡 𝑆𝐹 6 . The ST model uses the following two interlinked equations to produce annual mean global air and ocean surface temperatures:

Following Tol (2019) we use the following parameter values as the initial calibration: 𝜆 1 = 0.0256, 𝜆 2 = 1.14891, 𝜆 3 = 0.00738, and 𝜆 4 = 0.00568. The CS of this model is calculated as 𝜆 2 [5.35ln ( 2)] and it is the main parameter for calibrating the model to reproduce observed or projected annual mean global air surface temperature. A limitation with this approach is that the accuracy of its projections will depend on which temperature series is used for calibration. To illustrate this, we use the projections obtained from the MAGICC6 model for the RCP8.5, RCP6, RCP4.5 and RCP2.6 for the period 2005-2100. The calibration procedure used was to minimize the sum of the squared residuals between the TS and the MAGICC6 projections using ordinary least squares. The CS values that calculated for each scenario are 3.27 (RCP8.5), 2.70 (RCP6), 2.64 (RCP4.5) and 2.23 (RCP2.6).
Choosing any single value of this parameter to project all the RCP scenarios would lead to over-or underestimating future temperatures, particularly in the case of extreme scenarios (RCP2.6 and RCP8.5). As such, this approach could have an impact on, for example, the evaluation of the benefits of mitigation policies. The level of warming is closely related to the total cumulative emissions of CO2 (TCRE). The relationship between global temperature change and TCRE is relatively constant over time and independent from the emissions scenario used, but it is dependent of the global climate model CS and transient climate response (Collins et al., 2013). Figure 1 shows that in the case of MAGICC6 this assumption holds as the cumulative amount of CO2 is linearly related to the estimated CS. Given this relationship, we propose a dynamic CS parameter for the ST model that is calculated based on the cumulative CO2 emissions, which are dominant in any RCP, SRES or other realistic emissions scenario. The CS is thus calculated prior to projecting global temperatures with the ST model. The regression equation that relates the CS and the cumulative CO2 emissions is 𝐶𝑆 = 2.05 + 6.18 × 10 -7 ∑ 𝐶𝑂 2 (𝑅 2 = 0.96; Figure 2). To get a better approximation for the lowest and highest cumulative scenarios, we also fitted a line based on the CS values for RCP2.6 and the RCP8.5. The results were compared to the projections in the IPCC Fifth Assessment Report (AR5) and were optimized to reproduce the best estimates. The final extreme CS values are 2.1ºC and 3.3ºC for the RCP2.6 and RCP8.5 scenarios, respectively. The final equation relating CS and cumulative CO2 emissions is

In which the CS values are restricted to the interval [2.1, 3.3]. Table 2 shows the projections of the modified ST model and the best estimates and likely ranges in the AR5. For all four RCP emissions scenarios and both short-and long-term horizons, the average difference is about 0.08ºC and the maximum 0.23ºC. This illustrates that the modified ST model very closely resembles the IPCC AR5 temperature projections. To extend the ST model to account for the uncertainty in CS values and to produce probabilistic projections, we represent the model's CS with a triangular distribution. In this distribution the most likely value is given by equation 19 above, and the lower and upper limits are the calculated CS value plus/minus some constants that are to be calibrated. The equations for the upper (𝐶𝑆 ℎ𝑖𝑔ℎ ) and lower limits (𝐶𝑆 𝑙𝑜𝑤 ) of the triangular distribution for CS are:

The ℎ 1 and ℎ 2 constants are calibrated to match the likely ranges reported in the IPCC's AR5. Simulations of 10,000 realizations were used and the 5 th and 95 th percentiles were chosen to construct the ST likely ranges. The parameter values that provided good fit for all RCPs are ℎ 1 = 1.1 and ℎ 2 = 1.5. Table 1 shows that the likely ranges of the modified ST model closely reproduce those reported in the IPCC for both short-and long-term horizons, showing almost exact overlap with differences in upper and lower limits typically smaller than 0.2ºC. 2.2.2. Generating probabilistic global temperature projections using precalculated runs from MAGICC6 and the Thermodynamic Climate Model. The MAGICC6 and the Thermodynamic Climate Model (TCM) are reduced-complexity climate models that were designed for different objectives. MAGICC is composed of a set of coupled models that include gas cycles and climate and ice-melt models designed to explore the effects of anthropogenic emissions of greenhouse gas concentrations, radiative forcing, and changes in global mean annual temperature and sea level (Meinshausen et al., 2011a(Meinshausen et al., , 2011b;;Wigley, 1995). The TCM was originally conceived as a weather forecast model for the northern hemisphere and then extended to the global scale for studying the climate of Earth and of other planets in the Solar System (Adem, 1991). In the case of MAGICC6, precalculated projections of global temperature are included in AIRCC-Clim for the emissions scenarios RCP2.6, RCP4.5 RCP6 and RCP8.5, while in the case of the TCM the precalculated that were available are the RCP4.5, RCP6 and RCP8.5. To account for the uncertainty in CS values and to produce probabilistic projections, we propose a simple method based on linear regression and statistical simulation. Due to the availability of climate models' output we base our calculations on MAGICC6. Projections for each RCP scenario were obtained using of MAGICC6 for three different CS values that represent medium CS (3.0ºC), low CS (1.5ºC) and high CS (4.5ºC). To emulate MAGICC's results for high and low climate sensitivities, we propose the use of some scaling weights 𝑤 that would approximate them when multiplied by the global temperature obtained using a medium CS value. Such weights can be obtained by means of the following regression:

Where 𝑇 𝑡 𝑠𝑒𝑛𝑠 * is the global temperature projection obtained with MAGICC6 using either low or high CS, while 𝑇 𝑡 𝑚𝑒𝑑𝑖𝑢𝑚 corresponds to the global temperature projection obtained with medium CS; 𝜔 is the slope parameter and 𝜀 𝑡 are the regression residuals. In all cases, the 𝑅 2 is higher than 0.99; note that the objective of these models is not to make inference about parameter values, but just to produce a close fit of projections using different values of CS. The values of parameter 𝜔 for the different combinations of CS and for each RCP emissions scenario are provided in Table 2. The estimated parameter values are very similar for different RCPs with an average value of 1.34 and 0.57 for high and low CS values, respectively. As shown in Figure 3, these values allow to closely approximate the simulations of MAGICC6 produced using high/low CS values by scaling a simulation of the same model calculated with medium sensitivity. The approximation is less precise when used on scenarios that lead to stabilization (Figure 3d), but the error is still very small (0.17ºC for the high CS projection using the RCP2.6).
To produce probabilistic scenarios using the ST model, we use a triangular distribution to scale the MAGICC6 runs obtained with a medium CS. The parameters of the triangular distribution are 1 for the mode or most likely value and, 0.5679 and 1.3414 for the lower and upper limits, respectively (Table 2). These parameter values allow to emulate the projections that would be obtained with MAGICC6 randomly choosing CS values contained in the interval 1.5ºC to 4.5ºC, assigning a larger probability of occurrence to values that are closer to the medium sensitivity of 3ºC. CS is high uncertainty (Cox et al., 2018;Freeman et al., 2015;Friedrich et al., 2016;Knutti et al., 2017;Lewis and Curry, 2015;Rogelj et al., 2014;Tan et al., 2016). However, the consensus is that the CS is probably within the 1.5ºC to 4.5ºC interval with a central estimate of 3ºC (Bony et al., 2013;Callendar, 1938;Freeman et al., 2015;Santer et al., 2019;Stocker et al., 2013). This CS range encompasses the range produced by the state-of-the-art models included in the Coupled Model Intercomparison Project 5 (CMIP5) (Jonko et al., 2018;Stocker et al., 2013). Given that in the TCM the CS is not an explicit parameter as in MAGICC6, but an emerging property of the model, there are no high/low CS projections that can be used to find the corresponding parameters in Table 2. As such we apply the same scaling parameters we found for MAGICC6 to represent uncertainty in CS values and to extend the TCM projections to be probabilistic. Figure 3. Actual MAGICC6 projections for different RCP scenarios and projections of high/low CS approximated using the parameters in Table 2. M, H, L denote projections using medium, high, and low CS values, while the symbol * indicates the projections are obtained using the average scaling parameters in Table 2. Pattern scaling is a technique for producing regional scenarios based on the robust finding documented in the literature of stationarity in geographical patterns of change in some climate variables, in particular temperature and precipitation (Collins et al., 2013;Santer et al., 1990;Tebaldi and Arblaster, 2014). These patterns can be scaled by global temperature change to produce regional climate change scenarios in a simple and computationally efficient manner that provide a useful approximation to those produced by complex global climate models. The performance of pattern scaling techniques has been evaluated in the literature in several occasions (Cabré et al., 2010;Collins et al., 2013;Herger et al., 2015;Kravitz et al., 2017a;Mitchell, 2003;Osborn et al., 2018;Tebaldi and Arblaster, 2014;Tebaldi and Knutti, 2018;Zelazowski et al., 2018). These techniques produce adequate approximations for variables such as annual/seasonal temperature and precipitation and other variables excluding extreme events and time-scales in which natural variability is dominant. These patterns are also adequate for most of  the emissions scenarios, including low-warming policy trajectories and most regions except where local forcing is strong and time-varying (Collins et al., 2013;Estrada and Botzen, 2021). The pattern scaling technique can be described as follows (Collins et al., 2013;Estrada and Botzen, 2021;Tebaldi and Arblaster, 2014): represents is an error term due to both natural variability and the limitations of the pattern scaling methodology (Collins et al., 2013;Estrada and Botzen, 2021). The patterns 𝑝(𝑖, 𝑗, 𝑦, 𝑠) were calculated for monthly and annual air surface temperature and precipitation using simulations from a battery of coupled ocean-atmosphere general circulation models (Table S2) under the RCP8.5 emissions scenario and that are available at the CMIP5 data portal (https://esgf-node.llnl.gov/search/cmip5/). All simulations were bilinearly interpolated into a common grid with a spatial resolution of 2.5º x 2.5º. The Hodrick Prescott filter (Hodrick and Prescott, 1997) was applied to the time series from each grid point from the climate models' simulations to remove the effects of high frequency variability. Then, temperature/precipitation time series from each grid cell were regressed on the global mean temperature and the slope coefficients were stored as maps that represent the scaling patterns (Kravitz et al., 2017b;Lynch et al., 2017). For producing the regional climate change scenarios, global mean temperature projections from section 2.2 are used to scale the patterns produced in this section. The projections are expressed in ºC for changes in temperatures and in percentage of change for precipitation, with respect to preindustrial conditions (c. 1750). AIRCC-Clim allows the user to select the scaling patters for any given climate model, as well as to generate probabilistic scenarios combining all of them. This stochastic version of AIRCC-Clim uses a uniform distribution which assigns the same probability to each of the climate models. A variety of approaches for assigning probabilities to climate models' output have been proposed in the literature (Knutti et al., 2010;Mendlik and Gobiet, 2016;Xu et al., 2010) but there is no agreement on which would be the best way of doing it (Deser et al., 2014;Knutti, 2010;Notz, 2015;Stephenson et al., 2012). The uniform distribution follows the Principle of Insufficient Reason which is the maximum entropy distribution in absence of any additional information (Gay and Estrada, 2010b;Jaynes and Bretthorst, 2003;Jaynes, 1957). Other probability distributions based on performance evaluation or model dependence could be implemented, however these distributions may be as arbitrary as assigning equal probabilities to each model and may lead to unjustified dismissal of uncertainty (Altamirano del Carmen et al., 2021;Gay and Estrada, 2010b;Potter and Colman, 2003). Climate change scenarios for temperature and precipitation can be exported as geotiff and netCDF files for three time horizons: 2030 (2021-2040), 2050 (2041-2060) and 2070 (2061-2080). Maps of changes in temperature and precipitation for any year between 2005-2100 can be exported as high-quality PNG and as netCDF files. AIRCC-Clim uses the probabilistic nature of its projections to produce user-defined risk measures based on thresholds. The current version of the model includes two types of risk metrics: probabilities of exceedance and the dates when the selected threshold is exceeded. The threshold values are selected by the user to reflect his perceptions of risk and information needs. The calculation of the risks indices is done following the same procedure as CLIMRISK (Estrada and Botzen, 2021).
First, the indicator function is used to identify in which simulations and grid cells the threshold is exceeded. In the case of changes in temperature T, we have:

𝐼𝑅𝑇 𝑖,𝑗,𝑡,𝑠𝑖𝑚 = 𝐼(𝑇 𝑖,𝑗,𝑡,𝑠𝑖𝑚 > 𝑇 * ) 24

where 𝐼𝑅𝑇 𝑖,𝑗,𝑡,𝑠𝑖𝑚 is a four-dimensional matrix in which 𝑖, 𝑗 are the longitude and the latitude that define the location of the gird cell, 𝑡 is time, 𝑠𝑖𝑚 is the number that identifies each of the realizations of the simulation experiment, and 𝑇 * is the user-defined threshold in ºC. For cases in which the threshold 𝑇 * is exceeded the indicator function returns a value of 1 and zero otherwise. In the case of the change in precipitation P, the threshold of interest 𝑃 * can be positive or negative and thus the indicator function is applied as follows:

𝐼𝑅𝑃 𝑖,𝑗,𝑡,𝑠𝑖𝑚 = { 𝐼(𝑃 𝑖,𝑗,𝑡,𝑠𝑖𝑚 > 𝑃 * ) 𝑖𝑓 𝑃 * > 0 𝐼(𝑃 𝑖,𝑗,𝑡,𝑠𝑖𝑚 < 𝑃 * ) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (25)

𝐼𝑅𝑃 𝑖,𝑗,𝑡,𝑠𝑖𝑚 is a four-dimensional matrix defines as above in which the indicator function returns a value of 1 if the threshold 𝑃 * is exceeded and zero otherwise. Estimates of the probabilities of exceeding the thresholds 𝑇 * and 𝑃 * can be obtained by summing over the 𝑠𝑖𝑚 dimension: Where 𝑃𝐼𝑅𝑇 𝑖,𝑗,𝑡 and 𝑃𝐼𝑅𝑃 𝑖,𝑗,𝑡 , are three-dimensional matrices containing probability estimates. The estimated probability maps can be exported as PNG and netCDF files for any year in the period 2005-2100. These probability estimates of exceeding critical thresholds are used to estimate the expected dates when such thresholds would be attained. These dates can be computed as follows:

𝐼𝐷𝑇 𝑖,𝑗,𝑡 = 𝐼(𝑃𝐼𝑅𝑇 𝑖,𝑗,𝑡 ≥ 𝛾) (28)

𝐼𝐷𝑃 𝑖,𝑗,𝑡 = 𝐼(𝑃𝐼𝑅𝑃 𝑖,𝑗,𝑡 ≥ 𝛾)

Where the parameter 𝛾 represents the percentage of simulations that is required by the user to declare the threshold has been exceeded. 𝐼𝐷𝑇 𝑖,𝑗,𝑡 and 𝐼𝐷𝑃 𝑖,𝑗,𝑡 are matrices in which the entries take the value 1 if the confidence level 𝛾 is attained or exceeded and zero otherwise. In AIRCC-Clim and CLIMRISK, this value is called confidence level and can vary with the risk tolerance of different users. The default value in AIRCC-Clim is 50%. The estimated dates for exceeding the risk threshold are obtained by mapping into a year index the first occurrence of the value 1 in the time dimension of all gird cells in 𝐼𝐷𝑇 𝑖,𝑗,𝑡 and 𝐼𝐷𝑃 𝑖,𝑗,𝑡 . The maps of the dates of exceedance can be exported as PNG and netCDF files. In this section we provide an example application of AIRCC-Clim in which the effects on climate from a high-emissions trajectory (RCP6.0) are compared to those of a deep mitigation scenario (RCP2.6) consistent with the goals of the Paris Agreement and to those in which such mitigation effort is delayed ten years. Figure S1 shows the trajectories of 𝐶𝑂 2 , 𝐶𝐻 4 and 𝑁 2 𝑂 for the RCP6.0, RCP2.6 and the modified version of the RCP2.6 scenarios in which mitigation is delayed for 10 years, starting in 2020. The modified version of the RCP2.6 was edited in Excel and directly loaded to AIRCC-Clim using the user-defined option for emissions scenarios. The RCP6.0 and the RCP2.6 scenarios produce contrasting results in terms of their effects on climate. While the first produces a mean increase in global temperature of about 3ºC at the end of this century, and up to 4ºC when the 95 th percentile is considered, the RCP2.6 limits warming below 2ºC for the ensemble mean (about 1.7ºC), although this limit is exceeded for the 95 th percentile (Figure 4). The MAGICC model produces similar results, with a mean increase in global temperature of 3.1ºC and 1.6ºC for the end of the century under the RCP6.0 and RCP2.6 scenarios, respectively (Figure S2). The TCM produces a considerably larger mean increase for the RCP6.0 (3.9ºC), but that still lies within the likely range of the CMIP5 experiment (Table 1). The ST simulations for the modified RCP2.6 in which the mitigation effort is delayed for 10 years, show that the mean increase in global temperature reaches 2ºC in 2100, and up to 3ºC in the 95 th percentile. Figures 5 and6 show the changes in annual mean temperature and total annual precipitation at the grid cell level for the three emissions scenarios and two time-horizons (2050 and 2100). Temperature increase is much larger in high latitudes of the northern hemisphere due to the Arctic Amplification phenomenon (Pithan and Mauritsen, 2014), reaching about 6ºC for the mid-century and more than 8ºC in 2100, under the RCP6.0 scenario (see Figure S3 and S4 for results using the precalculated MAGICC6 and TCM runs). Most of the continents would experience temperature increases in 2050 of about 2ºC to 3ºC and of about 4ºC to 5ºC in 2100. Apart from the Arctic region, midlatitudes in North America and in Eurasia would have the largest increases (5ºC-6ºC) in temperature by the end of the present century, followed by Southern Asia and the Middle East, North and South Africa, parts of the west coast of North America, Mexico and the Amazonian region and the northern part of Brazil. Large changes are also expected in precipitation under the RCP6.0 scenario, with large increases in high latitudes, the equatorial Pacific Ocean and some parts of the Middle East, and large decreases in the Mediterranean, the Caribbean, Mexico, and the southern part of the US, as well as in southern parts of Africa and America (Figure S3 and S4). The implementation of a deep mitigation effort consistent with the goals of the Paris Agreement would significantly limit these changes in climate. Under the RCP2.6 most of the Arctic would not exceed a warming of 5ºC during this century, most continents would not exceed 3.5ºC, and precipitation change would be notably smaller. AIRCC-Clim portraits the risks of climate change, and the benefits of mitigation, in a clearer way due to its probabilistic nature and its capacity to produce maps of probabilities and of dates of exceedance.
Figures 7 and8 show the probabilities of exceeding a 2.5ºC increase in annual temperatures and a decrease of 15% in annual precipitation in 2050 and 2100. Under the RCP6.0, by 2050 the probabilities of exceeding 2.5ºC increase in annual temperatures are higher than 60% for most of the continents, while the Arctic region and the high latitudes of the northern hemisphere are virtually certain to exceed this threshold by mid-century (Figure S5). These simulations also show that a 2.5ºC warming would be exceeded in all continents by 2100 and that there is a high probability (above 60%) that this threshold would be crossed in all oceans, except for parts of the southern hemisphere and the Atlantic. The probabilities of exceeding a decrease of 15% in total annual precipitation in 2050 are higher than 50% for several areas of the world such as the Mediterranean, parts of Northern, Western and Southern Africa, the Caribbean and Mexico (Figure S5). For 2100, these probabilities increase to more than 60% in those regions and extend to parts of South America and West Australia. If the emissions trajectory described in by the RCP2.6 is achieved, by 2050 the probability of exceeding 2.5ºC would be lower than 40% over the continents, except for the Arctic and parts of the midlatitudes in the northern hemisphere where the probabilities range from 60% to 100% (Figure 7). Likewise, the probabilities of exceeding decreases in precipitation of at least 15% are considerably smaller in comparison to the RCP6.0. However, by the end of this century the probabilities of exceeding this threshold would be close to 50% for the southern region of Spain, parts of North and West Africa (Morocco, Mauritania, Mali, Senegal, Sierra Leone and Guinea), and about 40% for parts of the Caribbean, Central and South America (Colombia and Venezuela; Figure 8). Figure 9 shows the dates when the 2.5ºC threshold would be exceeded. The default confidence level (𝛾 = 50) was used for the estimates presented in this section. The results show that under the RCP6.0, most of the planet except for part of the southern oceans and part of the North Atlantic, would exceed the 2.5ºC threshold during this century and that some parts of the world already exceeded it (Figure S5). The date of exceedance for the Arctic occurred during the 2000s, while for much of the high latitudes in the northern hemisphere, the Middle East, parts of South Asia, and West and South Africa, the exceedance is expected to occur in the 2020s-2030s. The remainder of the continents and the Antarctic region would go over this threshold during the period 2040-2060 and most of the oceans above the 20ºS would exceed the 2.5ºC threshold during this century. The regions in which reductions of at least 15% in annual precipitation is exceeded are fewer and form well-defined geographical patterns that cover the Mediterranean, parts of North, West and South Africa, Central America and the Caribbean, Mexico and Colombia and Venezuela in South America, as well as the west part of Australia and part of the southern Pacific Ocean (Figures 9 andS5). The dates for exceedance on these regions are typically reached in the 2050-2060 decades, although regions of Spain and West Africa could exceed this threshold as early as the 2040s. Achieving RCP2.6 would prevent exceeding these thresholds for most of the world during this century (Figure 9). However, as mentioned above, some regions such as the Arctic and the high latitudes of the northern hemisphere already have exceeded the 2.5ºC temperature threshold or will do so during the next decade, regardless of the emission scenario that is selected. For parts of the midlatitudes, the RCP2.6 represents delaying reaching the 2.5ºC threshold for about 20 years, which buys time for adapting to the projected changes and to reduce risks and damages. The occurrence of this threshold would also be delayed until 2060 in some parts of the Sahara, South Africa, the Middle East and India. Exceeding decreases in precipitation of more than 15% would not occur during this century, with the exception of a few grid cells in Africa, Spain and Central America. AIRCC-Clim runs illustrate that delaying the deep mitigation efforts of the RCP2.6 by ten years would significantly increase the risks of climate change during this century. The bottom rows of Figures 7 and8 show that, under delayed international action, the probabilities of exceeding 2.5ºC in annual temperature and a decrease of at least -15% annual precipitation in 2100 are similar to those obtained in 2050 for the RCP6.0 and much higher than those of the original RCP2.6. The consequences of delaying for ten years the mitigation efforts described in the RCP2.6 are clearly illustrated by Figure 9: North and South Africa, South America, the Middle East and Central Asia would exceed a 2.5ºC increase in temperatures around 2060, when this threshold was not reached during this century under the original RCP2.6 trajectory. Parts of Australia would exceed this threshold at the end of the present century if mitigation efforts were postponed. In terms of precipitation reductions, the Mediterranean region would be most affected, as the dates of exceedance of decreases of at least 15% in precipitation would occur as soon as 2040-2050 for the south of Spain and North Africa and at the end of this century for Greece. Western Africa would go over this threshold in 2040, and parts of Central America and South Africa would see decreases of more than 15% in the 2050-2060 period. However, it is important to note that this delayed action scenario still provides important benefits in comparison with the RCP6.0, which is commonly used to represent current international mitigation commitments. Some of the most affected regions due to warming would buy time (about 2 decades) for adapting to a 2.5ºC under the delayed version of the RCP2.6.
This is not so clear with regard to exceeding -15% decrease in annual precipitation for the most affected regions, as in comparison with the RCP6.0, the delayed version of the RCP2.6 would buy them only 5-10 years for implementing adaptation actions. Monthly estimates of changes in precipitation and temperature are commonly needed for assessing the impacts of climate change in natural and human systems. AIRCC-Clim also generates estimates of monthly temperature and precipitation change, as well as estimates of probabilities and dates of exceedance for user-defined thresholds. Figure 10 illustrates this feature for the RCP6 emissions scenario and for the central month of winter and summer (i.e., February and July). During the coldest months in the northern hemisphere's winter, the threshold of 2.5ºC was exceeded at the beginning of this century in the Arctic, while for parts of the midlatitudes it will be exceeded during this decade of in the 2030s (Figure 10a). In most of the remaining parts of the northern hemisphere the 2.5ºC threshold in temperatures during February would be exceeded in the 2030-2050 decades. For parts of North and Central America, the driest months occur in winter and precipitation in February in those areas would decrease at least 15% as soon as 2030. In the case of regions in southern hemisphere, such as Australia, Central and South Africa, as well as most of South America, the temperature threshold during one of the hottest months (February) would occur before 2060 and, in some parts of these region, this threshold could be exceeded 20 years earlier. The hottest months in the northern hemisphere occur during the boreal summer. As shown in Figure 10c, exceeding the threshold a 2.5ºC increase in July would happen in this decade for regions in the Mediterranean such as Spain, France, Italy, Greece, and parts of North Africa. In these regions, exceeding this threshold in temperatures during July would be accompanied by decreases of at least 15% in precipitation before 2050 in the same month, which is one of the driest in the Mediterranean. a) b) c) d) Figure 10. Estimates of dates of exceedance during February and July for 2.5ºC and -15% thresholds in temperature and precipitation, respectively. Moreover, due to its capabilities for exporting output, AIRCC-Clim can be easily combined with other products to address the user's specific information needs. Figure 11 combines population count projections from the SSP3 scenario that were obtained from CLIMRISK (Estrada and Botzen, 2021) with two risk measures produced with AIRCC-Clim to provide a first approximation of risk and exposure. Climate and population projections show that by 2050 some regions of the world will have high exposure and high probabilities of experiencing large changes in climate. In the bivariate map shown in Figure 11a dark magenta color indicate regions for which large population and high probabilities of exceeding 15% decrease in precipitation are projected. These high-risk, high-exposure regions include large fractions of the Mediterranean, Central America and parts of the Middle East and South Asia. Light yellow areas indicate regions characterized by large population but low probabilities of decreases in precipitation of at least 15%. These include high latitude regions in the northern hemisphere for which most climate models' projections suggest an increase in precipitation. This combination of population and precipitation change would be found in parts of India, China, parts of central, northern and eastern Europe, northern US and Canada. Light blue regions such as Australia, large parts of Noth Africa and South America, are where decreases in precipitation of at least 15% are highly likely but where population counts are low. Figure 11b shows a bivariate map of population counts and the probability of exceeding 2.5ºC in annual temperature change by year 2050. Regions such as the eastern part of the US, Central America, most of Europe, India, China, the Middle East and parts of Africa are shown in dark magenta color. These regions are characterized by high probabilities of exceeding 2.5ºC and large population counts. Regions in light blue hue represent places where the probability of exceeding a warming of at least 2.5ºC in 2050 are high, but population in those areas is not large. This is the case of high latitudes in the northern hemisphere, Australia, the Amazon rainforest, the Sahara, Namib and the Arabian deserts. Moreover, Figures 11 helps to identify risk hotspots in which population counts will be high in the future and significantly dryer and hotter conditions will likely occur. Such combination of factors has been associated with higher risks of human conflict and migration (Barrios et al., 2006;Hodler and Raschky, 2014;Hsiang et al., 2013;Puente et al., 2016;World Bank, 2016), as well as impacts on biomass production and more frequent wildfires (De Dato et al., 2008;Stevens-Rumann et al., 2018). Here we present AIRCC-Clim, an emulator of complex climate models included in the IPCC's Fifth Assessment Report that allows generating probabilistic climate change projections and risk measures for RCP emissions scenarios, as well as for user-defined emissions scenarios. Global temperature projections are produced using a modified version of the ST model and precalculated runs of the MAGICC and TCM models. AIRCC-Clim has a spatial resolution of 2.5º x 2.5º and produces monthly and annual temperature and precipitation scenarios. This is a user-friendly, stand-alone software aimed for students, decision-makers, and researchers that allows for quick estimates of changes in climate, as well as of the probabilities and dates of exceedance of userdefined thresholds. The AIRCC-Clim model attempts to fill users' needs for models that have low technical and computing requirements, but that are able to emulate complex climate models' output and produce spatially explicit, probabilistic projections and risk measures. AIRCC-Clim extends the ST climate model to include a dynamic climate sensitivity that takes advantage of the well-established approximately linear relationship between cumulative CO2 emissions and global temperature increase. This extension of the ST model, combined with stochastic simulation, allows to closely approximate the best estimate and likely range included in the Fifth Assessment Report of the IPCC.
By means of a simple stochastic simulation procedure, we account for the uncertainty in the climate sensitivity parameter and produce probabilistic scenarios based on MAGICC and TCM precalculated runs. Extensions and future development of this model include the integration with IVA and integrated assessment models, such as simple agricultural emulators and climate-economy models (Estrada et al., 2020;Estrada and Botzen, 2021;Ignjacevic et al., 2021Ignjacevic et al., , 2020)); the inclusion of additional climate variables (e.g., minimum and maximum temperatures and bioclimatic indices), as well as complementary uni-and multivariate risk measures. . Comparison between the best estimates and likely ranges of annual mean global air surface temperature reported in the IPCC's AR5 and those obtained with the modified ST model.