Cyclone generation Algorithm including a THERmodynamic module for Integrated National damage Assessment (CATHERINA 1.0) compatible with CMIP climate data

. Tropical cyclones are responsible for a large share of global damage resulting from natural disasters and estimating cyclone-related damage at a national level is a challenge attracting growing interest in the context of climate change. The global climate models, whose outputs are available from the Coupled Model Intercomparison Project (CMIP), do not resolve tropical cyclones. The Cyclone generation Algorithm including a THERmodynamic module for Integrated National damage Assessment (CATHERINA) presented in this paper, couples statistical and thermodynamic relationships to generate synthetic 5 tracks sensitive to local climate conditions and estimates the damage induced by tropical cyclones at a national level. The framework is designed to be compatible with the data from CMIP models offering a reliable solution to resolve tropical cyclones in climate projections. We illustrate this by producing damage projections in Representative Concentration Pathways (RCP) at the global level and for individual countries. The algorithm contains a module to correct biases in climate models based on the distributions of the climate variables in the reanalyses. This model was primary developed to answer the need 10 of the economic and ﬁnancial community that is seeking quantitative signals that would allow for a better quantiﬁcation of physical risks in the long term, to estimate, for example, the impact on sovereign debt.


Introduction
Climate-related physical risks pose a growing threat to humanity, and the design and implementation of adequate adaptation and mitigation measures require assessing future physical risks at a national and global scale. One important source of information about the future climate are the projections of the global climate models, however the spatial resolution of these global models is unfortunately still not sufficient to fully resolve extreme events, particularly tropical cyclones. On the other side of the 15 spectrum, Integrated Assessment Models (IAM) directly assess the impact of climate on economic activity. Most of these models embed a physical damage module, usually limited to a very generic damage function. Tools to assess the impact of tropical cyclones on the economy under future climate are thus lacking in the literature. The objective of this paper is to fill this gap: we build synthetic cyclones based on the climate data produced by the global climate models, and evaluate the economic damage of these synthetic cyclones under various assumptions. 20 The physics of tropical cyclones has been intensively studied in the literature. The thermodynamic cyclone theory builds upon the seminal contributions by Emanuel (1988) followed by Holland (1997) and Emanuel (1999). Concerning the impact of Framework from climate models allowing to define locally the maximum potential intensity based on the simplified expression in Holland (1997). Some controls such as the maximum pressure drop observed for the corresponding temperature and the decay relationship for cyclones evolving over land are also fitted for each basin and applied in the synthetic tracks generation algorithm.

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Extracting the climate variables from different models allow us to correct the biases and evaluate model uncertainty. Then, we use the physical asset values (Eberenz et al., 2020b) and regional damage functions from the CLIMADA module to evaluate the cyclone-related damage at a national level. This step requires to extract the local physical asset values and aggregate them on tiles of length defined proportionally to the average radius to maximum wind (∼ 50 km) along the cyclone path. Summing the losses along tracks for each year and for each country allows us to establish a national assessment of the damage generated 65 by tropical cyclones.
The paper is organized as follows. Section 2 describes the datasets used to fit the model on ERA-5 and to generate synthetic cyclones based on both ERA-5 and CMIP5 models datasets. Section 3 describes the statistical calibration process and the details of the thermodynamic instrumental variables. Section 4 recalls the calibration methods implemented in the CLIMADA environment to fit the regional damage functions, defines the parameters of these functions using Eberenz et al. (2020a) and applies them along the synthetic tracks produced to study the distribution of national annual damages. Section 5 explores the properties of the produced synthetic tracks, with ERA-5 and 7 CMIP models, assesses climate uncertainty and introduces the bias correction module in the context of changing climate conditions. To close this section, we present the global and regional projections of cyclone damage between 2070 and 2100 obtained with CATHERINA.
2 Input data 75 In the CATHERINA framework, we fit the properties of historical cyclones (IBTrACS database) on past climate reanalyses  in the perspective of describing future cyclones based on global climate models outputs (CMIP), having a lower spatial and temporal resolution. This perspective constrains us to use monthly data.

Climate model data (CMIP)
CATHERINA aims at generating cyclones tracks with properties drawn from climate models to enable national damage as-80 sessments, bridging the gap between AOCGM outputs and damage assessments. To reduce the bias in the variables produced by climate models 1 and evaluate the performance of CATHERINA on past data by comparing the simulated cyclone damages to the realized ones we use historical simulations (as opposed to future climate projections) from the Coupled Model Intercomparison project (Phase 5) models (Taylor et al., 2012). We use the historical climate simulations at the monthly frequency for the relative humidity (RH) at two meters, sea surface temperature (SST), sea level pressure (MSLP) and tropauspose tem-85 perature (T tropo ) (at pressure level of 50 hPa) from Copernicus climate data store 2 . CMIP5 data are used in the 5th assessment report of the Intergovernmental Panel on Climate Change (IPCC). The latest synthesis Report in progress in 2021 is IPCC AR6 3 , which uses CMIP6 datasets but in the present paper, we use CMIP5 data because of broader availability of climate variables.
We use models from the following climate centers: NASA, Goddard Institute for Space Studies (GISS-E2-H, USA), Institut and Analysis (CanESM2, Canada). The spatial resolution goes from 0.75°to 2.5°depending on the model (See Table 1). Each climate model produces a potentially biased estimate of multiple climate variables at the spatial resolution given in Table 1   To reduce the influence of these biases, we use a large number of models and consider the distribution of results provided by all the models. Then we correct, variable by variable, and for each basin, and each model, the biases with respect to the reanalysis along the same tracks.

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Climate reanalyses describe the historical climate conditions, obtained by assimilating all available observations into the models. They provide numerical estimates of atmospheric parameters (e.g. air temperature, pressure and wind) at different altitudes / pressure levels, and surface parameters (such as rainfall, soil moisture content, ocean-wave height and sea-surface temperature) on a single level. We use reanalyses to calibrate the cyclone generation algorithm based on the most realistic available estimates of climate variables. 105 We use ERA-5 reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF) to fit CATHERINA model 4 . This dataset covers the Earth on a 30 km grid (∼ 0.25°) and resolves the atmosphere using 137 levels from the surface up to a height of 80 km. In this paper, to ensure compatibility with CMIP5 models, we extract mean sea level pressure (MSLP), sea surface temperature (SST), sea level relative humidity (RH), and tropopause temperature (T tropo ) at the monthly frequency.
Because reanalysis resolves past tropical cyclones, the historical mean sea level pressure values in ERA-5 are influenced by 110 their presence. Consequently, we retrieve the mean sea level pressure 500 km (∼ 5°longitude) away from the storm center to extract a value for P env , that is meant to represent the pressure -at a given latitude and season -in normal environmental conditions.  allowing to define the total asset (A tot ) for each country. This value is distributed to each grid cell proportionally to the light intensity L i times the local population P pix 8 : .

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The physical asset value is expressed in USD as of 2014. Using this dataset in the future might require correcting (either simulated or reported damages) by inflation using for instance consumer price index 9 .   Table   A1 for details).

Global disaster database (EM-DAT)
The fitting of the damage functions was performed by Eberenz et al. (2020a) on reported damages in the EM-DAT database (Guha-Sapir et al., 2018) 10 . Filtering the database by sub-type 'tropial cyclone' allows to extract 1 855 tropical cyclones in the 140 period between 1980 and 2021, among which 1 101 events have a reported total damage cost in USD. In terms of damage, tropical cyclones are, using the full set of observations from 1980 to 2021, the most damaging events reported (see Figure   4). This database includes a start date field (day, month and year) allowing us to map 455 events with the events reported in IBTrACS using start year and month and country 11 . We use this database to validate our simplified estimation process.

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Our model structure follows Bloemendaal et al. (2020) with three main modeling steps: genesis, displacement of the eye and calibration of the cyclone properties. The STORM model relies on statistical relationships (James and Mason, 2005;DeMaria and Kaplan, 1994;Kaplan and DeMaria, 1995). This simulation method differs from the purely thermodynamic approach developed by Kerry Emmanuel (Emanuel, 1999;Emanuel et al., 2008). 10 available at : www.emdat.be. 11 Eberenz et al. (2020a) functions are fitted on a similar sample of 376 tropical cyclones used for calibration.  The major change in our specification compared to Bloemendaal et al. (2020) is that we use a the local definition of maximum 150 available thermodynamic intensity (MPI) based on climate data. In particular, we use relative humidity (RH) and tropopause temperature (at 50 hPa, T tropo ), for better representation of the physics underlying the intensification process. In this section, we present process of generating synthetics tracks, characterized by the maximum wind (V t ) and central pressure (P c t ) at each time step, given the climate conditions extracted from climate models.

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Although thermodynamic descriptions of cyclone genesis exist in the literature (Gray, 1975;DeMaria et al., 2001), there is still too much uncertainty about how climate change will affect the frequency of cyclones to justify the integration of multiple additional variables at this step. For this reason, we choose to rely on a simple statistical model based on past frequencies for the genesis. The number of synthetic cyclones each year is determined by the Poisson distribution in each basin, with parameter λ B defined as the average number of cyclones per year in the historical data. We use the parameters λ B given in 160 Bloemendaal et al. (2020) i.e. 14.5 for the East Pacific (EP), 10.8 for the North Atlantic (NA), 2.0 for the North Indian (NI), 12.3 for the South Indian (SI), 9.3 for the South Pacific (SP), and 22.5 for the West Pacific (WP) 12 . Similarly, the temporal and spatial initial positions of synthetic future cyclones (longitude x, latitude y and starting month m) are generated by independent sampling from the historical distribution of these variables. Figure 6 shows the geographical distribution of cyclones retrieved from IBTrACS (i.e. x obs , y obs ) and the histograms in Figure 7 show the monthly distribution (m obs ) of cyclones in each basin.

Cyclone trajectories
A rich literature focuses on cyclone tracking algorithms, see e.g., Neu et al. (2013) for a comprehensive review. Although more advanced definitions have been proposed (Hall and Jewson, 2007;Fabregat et al., 2016), we choose, in line with Bloemendaal et al. (2020), to implement a simple auto-regressive model for cyclone coordinates. Following James and Mason (2005), the 12 The parameters λ B would have been smaller if estimated using our filtered database. However, we maintain these parameters to take into consideration the fact that some events will be generated in conditions not favorable for the development of cyclones, and be cleared out of the database.   Each bar gives the probability for each cyclone to be allocated to a given month. time evolution of the latitude and longitude of the cyclone center is described by the following stochastic dynamics: Here x t and y t are the latitude and longitude of the cyclone center sampled with a 3 hour time step; ∆x t = x t − x t−1 , ∆y t = y t − y t−1 , ε x t and ε y t are i.i.d. noises independent from one another, and the constants a 0 , a 1 , b 0 , b 1 , b 2 , σ x and σ y are fitted on IBTrACS data independently for each basin by least squares regression. Their values are provided in the Appendix. The 175 nonlinear term in the incremental variation of the latitude is justified by the tendency for cyclones to move away from the equator, especially at very low latitudes (James and Mason, 2005, p. 183). We found this formulation sufficient for global assessment despite its lack of consideration for dependencies in the latitudinal and longitudinal variations (James and Mason, 2006) 13 . A sample of the resulting tracks is provided in Figure 8.

Thermodynamic description of cyclone intensity 180
The intensity of cyclones in our model is defined through the following five steps described in the subsequent paragraphs. The wind-pressure relationship (WPR) links the central pressure to the maximum 10 minute-sustained wind speed. The maximum potential intensity (MPI) is determined from local meteorological variables. The maximum pressure drop (MPD) is determined from historically observed pressures. The depression dynamics (DD) along tracks is defined using an autoregressive stochastic equation. When the cyclone arrives on land, a statistical decay relationship (SDR) dictates the evolution.

Wind-pressure relationship (WPR)
We describe the cyclone intensity through its central pressure P c t , which is linked with the maximum wind through an empirical relationship. Let V t be the maximum 10-min sustained wind speed (in m.s −1 ) 14 of the cyclone at time t. This maximum wind is observed around 50 km away from the storm center on average 15 and reported in IBTrACS dataset for historically observed cyclones. The wind-pressure relationship (WPR) is calibrated on the whole cyclone database as follows: where P env (x, y, t) is the mean sea level pressure (MSLP) extracted 500 km away from the eye location at this time in ERA-5 and P c t is the central pressure extracted from IBTrACS. This relationship is illustrated in Figure 9 and the parameters a and b are fitted on ERA-5 and IBTrACS data using nonlinear least squares. 13 To reduce this effect and better encompass the dependency of the cyclone displacement on the location of the eye, and following Bloemendaal et al.
(2020), we fitted these relationships locally using an additional grouping by 5°longitude and latitude sections.
14 For the data from the World Meteorological Organisation (WMO) and the agencies reporting 1 or 3-minutes sustained wind speed, we performed the conversion to 10 minutes sustained wind speed using the coefficients suggested by Knapp et al. (2010). See Figure A1 in the Appendix for more details about the agencies and reporting bias. 15 Radii of maximum wind are also reported in IBTrACS but this information is not central for national level assessment.

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We compute the local maximum potential intensity (MPI) following Holland (1997) and using thermodynamic relationships.
This is particularly relevant in the context of a national damage assessment under changing climate. Indeed, greenhouse gas emissions not only warm up the oceans, but also cool down the lower stratosphere (Butchart et al., 2000;Forster et al., 2007;Ramaswamy et al., 2006). Thus, the tropopause temperature T tropo (that is, temperature corresponding to a pressure of 50 hPa or to an altitude of approximately 20 km) ) must be included in the modeling of the intensification process. Indeed, the 200 thermodynamic efficiency factor E t proportional to the difference between tropopause and sea surface temperatures plays an essential role in the determination of the central pressure of tropical cyclone. The relative humidity (RH) is also an influential parameter allowing for a better description of MPI 16 . Adding these two climate variables allows the CATHERINA model to better take into account the additional energy potential due to the widening of temperature difference between sea surface and upper troposphere and variation in moist entropy.

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Following the seminal formulation in Emanuel (1988) and integrating additional simplifications proposed in the subsequent paper (Emanuel, 1991) to simplify the expression, leads to the following framework summarized in Holland (1997).
where (x t , y t , t) are the coordinates of the eye defined in Equations (1) and (2), SST(x t , yt, t) and T tropo (x t , y t , t) are re-215 spectively the sea-surface and tropopause temperatures, R d = 287.058 J · kg −1 · K −1 is the specific gas constant for dry air, MSLP(x t , y t , t) is the mean local sea level pressure, RH(x t , y t , t) is the near surface relative humidity at 2 meters extracted from the monthly dataset of ERA-5 climate reanalysis or CMIP climate models. f (y t ) = 2ω sin(y t ) is a Coriolis parameter depending on the latitude, r env is the distance between the eye and the area under regular conditions (fixed at 500 km), q env and q * c respectively are the specific humidity at environmental conditions and at saturation, i.e. for RH = 100%, in the eye.

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∆S m is the difference of moist entropy between the environment and the storm center and L υ is the latent heat of vaporization.
The distributions of the variables computed from ERA-5 climate variables along IBTrACS involved in this step are shown in Figure 10. The distance to MPI is computed as the difference between the central pressure and the maximum potential intensity (MPI) defined in Equation (4).

Maximum pressure drop (MPD)
225 Several papers, including Bloemendaal et al. (2020), link the sea surface temperature directly to the pressure drop, or equivalently the wind speed, via a statistical relationship (DeMaria and Kaplan, 1994). Merrill (1987) suggests that this predictor alone does not provide a good indication whether a given storm will intensify. However, in line with Emanuel (1988) and De-Maria and Kaplan (1994) the sea surface temperature can be used to fix a limit for the pressure drop. More precisely, to prevent the pressure drop from diverging in the projection, we cap it by the maximum observed pressure drop for the corresponding 230 sea surface temperature:  where the maximum pressure drop function is given by the following equation:  ature value) shows a much weaker influence of sea surface temperature alone, even on a weekly basis (see Jien et al. (2017) and Figure A3 in the Appendix). However, this instrumental variable is essential to prevent CATHERINA from producing unrealistically low central pressure.

Depression dynamics (DD)
The evolution of the central pressure depending on local MPI is described by the following autoregressive stochastic depression 245 dynamics (James and Mason, 2005): where the distance to maximum potential, P c t − MPI t , enters as a non-linear term in the dynamic definition of the central pressure "providing an increasing tendency for ∆p to be positive as the central pressure approaches the mean MPI for the  cyclone's location " (James and Mason, 2005, p. 183). The parameters are fitted on historical tracks using ERA-5 reanalysis with nonlinear least squares (see Table 2). The confidence intervals show non-negligible variations, however, the coefficients remain statistically significant and of the expected sign. This relationship channels the effect of global warming, affecting the maximum potential intensity, on the cyclone intensity. In other words, the incremental variation of the central depression of the cyclone is linked to the difference between the central pressure at time t and the potential available in the environment.

Statistical decay relationship (SDR) over land
We model the evolution of the cyclone after landfall using an exponential decay function considering that "tropical cyclone intensity decreases as a function of the time and distance the tropical cyclone has covered whilst being over land" SYNT1998SI1 (1998) SYNT2000EP8 (2000) SYNT2004SI5 (2004) SYNT1990NI2 ( DeMaria, 1995). Similarly to Bloemendaal et al. (2020), after three steps on land we suppose that the wind at time t L follows: where D l is the distance to coast computed using natural earth coastlines 17 , V 0 is the wind at landfall and t L the time spent on land by the eye. This function was fitted on IBTrACS using nonlinear least squares. In our procedure, we use the global 18 parameters: R = 0.79, V b = 15 m.s −1 , α = 0.044 h −1 , and f 1 (t L ) =c 1 t L (t 0,L −t L ),c 1 = 3.35.10 −4 ms −1 h −2 , t 0,L = 172 h, Kaplan and DeMaria (1995) introduced this function to 265 model the decay of tropical cyclone over land in a simple way and showed that it provides an acceptable approximation for t L 12h. A more sophisticated description could integrate for instance, cyclone physics, kinetic energy, and non-meteorological parameters such as ground topology. The SDR puts a strong constraint on the cyclone evolution after three steps. However, in the context of national damage assessment we reiterate that reported damage costs are the combination of a series of various impacts including storm surge and not only extreme wind and that the most exposed area is at landfall. We consider therefore 270 that the hypothesis of a rapid decay is acceptable and in line with observations. 17 Available at https://www.naturalearthdata.com/downloads/10m-physical-vectors/. 18 The statistical parameters are stable and fitting this relationships with non-linear least square for each basin gives the parameters in Table A8 on page 43.

Cyclone generation algorithm
The full cyclone generation procedure is presented in Algorithm 1. The cyclone wind speed is initiated at 20 m.s −1 and the initial pressure is determined from the WPR (Equation (3)). While the cyclone is over sea, the pressure evolution ∆P c is entirely determined from Equation (11) based on the local MPI. To prevent the model from producing unrealistically low 275 central pressure, we cap the maximum pressure drop (MPD) using Equation (10). With this truncation the lower bound for the pressure is given by the observed low pressure values in similar sea-surface temperature conditions. While the cyclone is over sea, the wind is defined with the WPR (Equation (3)). When the cyclone arrives on land the MPI is computed from the last known climate variables for the first three steps and the pressure still follows the relationship (11). After three steps (9h) on land, we start applying the decay relationship (Equation (13)) to define the wind. The variations of longitude and latitude are 280 always defined using Equation (1) and Equation (2). We force cyclones to remain in their genesis basins in this exercise. Wind speed (m/s) Fraction lost (%) Figure 13. Fraction of property value lost as a function of wind speed, obtained using Equation (14) with v j h = 50 (red), 74.4 (dark blue) and 100 m.s −1 (light blue) 4.3 ... to a regional damage calibration Using the reported damage estimates from the International Disaster Database (EM-DAT) crossed with cyclone tracks (IB-TrACS), and geographical and socio-economic information along these tracks, Lüthi (2019) refined the damage function approach using machine learning techniques introducing region-specific damage functions.
We recall the main steps of the methodology presented in (Lüthi, 2019;Eberenz et al., 2020a) to define the regional damage functions. The authors first defined the event damage ratio (EDR) as a ratio of simulated damage (SED) to normalized reported damage (NRD) for each cyclone: The total damage ratio (TDR) is then defined in each region summing over events: .
For each event, there is a value for v h allowing to optimally calibrate the explicit damage function given in Equation (14). The 305 relatively wide distribution of v h for the same country shows that there is a large uncertainty in the relationship between the wind speed and the corresponding fraction of losses 19 .
The authors propose two alternative optimization methodologies to find the value of v h maximizing the prediction quality of the regional damages: root mean square fraction (RMSF), minimizing the spread of the event damage ratios (EDR); and total damage ratio (TDR), finding the value of v h , such that the ratio of total simulated damage -obtained summing over event 310 damages -and total reported damage tends to 1. The values of v h obtained with the two methods are given in Table 3. For most regions the optimized curves are similar for the two optimization techniques, but the results diverge for the Philippines (WP2) and to a lesser extend for China Mainland (WP3) events. The case of the Philippines, discussed in Eberenz et al. (2020a), 19 In the Appendix, Figure A4 shows the uncertainty in regional damage functions depending on the optimization technique used and Figure A5 allows us to appreciate, for countries where more than 5 cyclones were reported, the spread of plausible damage functions. Coefficient from version 1.5 of the CLIMADA environment. Figure A4 also illustrate the shapes of the functions for the different optimization problems (RMSF vs. TDR) and version (1.0 vs 1.5).
is explained by the large number of parameters involved in the damage estimation, and emphasizes two main limitations of the model: first, this framework lacks an explicit representation of sub-perils which disrupt and damage several sectors and 315 services, and second, differences in exposure and vulnerability between urban and rural areas exposed to TCs are likely to contribute to the large spread in EDR.

Simplified estimation along tracks
In the context of our national level assessment, we propose a simplified damage module. The simulated damage for a given cyclone -in both IBTrACS and our synthetic tracks -is computed using the following procedure for each individual cyclone.

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First, a uniform grid with step given by the average cyclone radius is defined on the map of affected area. The cyclone track is linearly interpolated, and the tiles affected by the cyclone (containing a part of the interpolated path) are identified (see Figure   14). Second, for each tile identified in the previous step, we retrieve the maximum wind speed V , and compute the proportion of wealth lost f (V, v j h ) using the relation (14) with the total damage ratio parameter given in Eberenz et al. (2020a). Then, we compute the total simulated damage by aggregating the physical asset exposure multiplied by the proportion of wealth lost on 325 each tile over all tiles affected by the cyclone.
As a result of this procedure, we obtain the total simulated damage SED i (j, t) caused by the i-th cyclone in region j, simulated with climate variables for year t.
The damage functions used in the second step are retrieved directly from the CLIMADA environment. These functions were fitted with the same physical asset value, however, in our case we project these values on a coarser grid (first step), in such 330 a way that the extraction is simplified for a large number of synthetic tracks. Figure  over realised ratio in each region is acceptable, slightly overestimated for high income non-EOCD countries (in particular for Taiwan), using the total reported damage from EM-DAT.
Finally, the cyclone damage cost in region j and year t is simulated as follows: where the sum is taken over all cyclones occurring in a given year. This procedure can then be repeated many times to obtain the distribution of annual cyclone damages and compute other statistics such as the mean and quantiles of this distribution.
5 Application to damage assessment in representative concentration pathways (RCP) 5.1 Climate simulation debiaising for climate change application

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The variables from climate model projections used by CATHERINA are subject to multiple biases. To reduce uncertainty caused by these biases, we use the Cumulative Distribution Function-transform (CDF-t) method developed in (Vrac et al., 2012;Michelangeli et al., 2009) to correct the distribution of each variable, in each basin.
Consider a generic climate variable (denoted by χ) at a fixed location, which is available both from ERA5 reanalysis and from a given CMIP5 model. We are interested in two time periods: the historical period (covered both by the climate model and the reanalysis) and a future time period (covered only by the climate model). Let F h ERA5 and F h CMIP be the distribution functions of χ under reanalysis and under climate model for the historical period, and F f CMIP5 be the distribution function of χ under climate model for the future period. The distribution function under the climate model is subject to much stronger biases than that under the reanalysis. The CDF-t method constructs the distribution function for χ with reduced bias for the future time period, denoted by F f CMIP and given by For a given value χ f CM IP of the variable χ obtained for the future period from the climate model, the corresponding unbiased valueχ f CM IP may then be computed via When the future period and the historical period coincide, the method reduces to the standard quantile transform: First, we use the method on the historical period to compare the description of the MPI and wind speed with and without 350 correction, so equation (16)  We apply the CDF-t correction technique along our historical synthetic tracks and compute the maximum potential intensity following section 3.3.3. The pressure follows the dynamic process introduced in section 3.3.4 and the corresponding wind is derived from the WPR (see section 3.3.1). We define the model error as the relative error ( χCMIP−χERA5 χERA5 ) between the value produced by the model and the one produced by the reanalysis ERA-5. Figure 18 displays the average relative errors and shows 365 that a 4% relative error in the description of the maximum potential intensity can lead to a 35% error in the description of the implied wind compared to the result obtained with ERA-5. On average the CDF-t correction technique clearly reduces the error between the MPI estimated with climate reanalysis and the one computed from modeled climate data as well as (more importantly) the error in the description of the maximum wind speed. In relative terms, the average relative error is reduced by more than 65% for the MPI and 74% for the wind. Wind Max (m/s) R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R C P 8 5 R C P 2 6 R C P 4 5 R

Results in CMIP5 projections
The international climate modeling community introduced shared-socioeconomic pathways (SSP) to translate varying narratives on the development of the society in the long-term. These projections impact the local physical asset value dynamics (Jones and O'Neill, 2020;Chen et al., 2020), and global macroeconomic variables (O'Neill et al., 2014(O'Neill et al., , 2017. Under the assumption of constant impact ratio (i.e. the damage functions remain the same), CATHERINA allows us to derive dam-375 age projections in varying climate and socio-economic scenarios. Using unbiased climate variable projections from the seven climate models over the period 2070-2100, we provide an example of application of the CATHERINA framework 22 .
For example, over 2070-2100, the RCP 2.6 scenario, which is in line with the Paris Agreement and keeps global warming below 2°C by 2100, involves an increase in annual financial losses of 27% on average compared to the last 40 years. In the case of RCP 4.5 (between 1.7 and 3.2°C warming by 2100) and RCP 8.5 (between 3.2 and 5.4°C warming by 2100), the average   SSP2  SSP3  SSP4  SSP5   USA  CHN  IND  BGD  MEX  VNM  JPN  PHL  PYF  BHS  USA  CHN  IND  BGD  MEX  VNM  JPN  PHL  PYF  USA  CHN  IND  BGD  MEX  VNM  JPN  PHL  PYF  USA  CHN  IND  BGD  MEX  VNM  JPN  PHL  PYF

Conclusions
This paper proposes a relatively simple structural framework to generate synthetic storms based on large-scale climate data. 390 We show that when used with reanalysis data and CMIP5 models, our method produces tracks consistent with historical observations.
The synthetic tracks generated with our model have several applications.
while the pressure is bellow normal, wind is above threshold and we are not on land, do: where ∆yt ∝ Equation (2) MPI ( Same functional for x and y but, compute distance to land D(s) from natural earth coastlines and do Note: This algorithm assumes step-wise extraction of climate data in the Monte-Carlo process. Another way, closer to the framework suggested in Bloemendaal et al. (2020) would be to (i) compute the tracks without properties, (ii) retrieve all climate variables, (iii) determine the properties using the extracted climate conditions in the last step.  Wind (m/s) Impact Figure A5. Country calibration of damage function (when the countries has been hit more than 5 times)    Figure A7. Bias correction (300 years with ERA-5). On the top grid, we compare Depression (hPa), landfall count and winds, on the full sample. We can see that the correction effectively centers the distribution of ERA-5 properties. The grid bellow focuses on a grouping on maximum wind and depressions. We note that the correction also allows us to reduce the dispersion between models, however, it tends to shift up extreme values.