Regional tropical cyclone impact functions for globally consistent risk assessments

Assessing the adverse impacts caused by tropical cyclones has become increasingly important, as both climate change and human coastal development increase the damage potential. In order to assess tropical cyclone risk, direct economic damage 10 is frequently modelled based on hazard intensity, asset exposure and vulnerability, the latter represented by impact functions. In this study, we show that assessing tropical cyclone risk on a global level with one single impact function calibrated for the USA – which is a typical approach in many recent studies – is problematic, biasing the simulated damages by as much as a factor of 36 in the North West Pacific. Thus, tropical cyclone risk assessments should always consider regional differences in vulnerability, too. This study proposes a calibrated model to adequately assess tropical cyclone risk in different regions by 15 fitting regional impact functions based on reported damage data. Applying regional calibrated impact functions within the risk modelling framework CLIMADA at a resolution of 10 km worldwide, we find global annual average direct damage caused by tropical cyclones to range from 51 up to 121 billion USD (current value of 2014, 1980-2017), with the largest uncertainties in the West Pacific basin, where the calibration results are the least robust. To better understand the challenges in the West Pacific and to complement the global perspective of this study, we explore uncertainties and limitations entailed 20 in the modelling setup for the case of the Philippines. While using wind as a proxy for tropical cyclone hazard proves to be a valid approach in general, the case of the Philippines reveals limitations of the model and calibration due to the lack of an explicit representation of sub-perils such as storm surge, torrential rainfall, and landslides. The globally consistent methodology and calibrated regional impact functions are available online as a Python package, ready for application in practical contexts like physical risk disclosure and providing more credible information for climate adaptation studies.


Introduction
Tropical cyclones (TCs) are highly destructive natural hazards affecting millions of people each year (Geiger et al., 2018; and causing annual average direct damages in the order of 29 to 89 US$ billions Gettelman et al., 2017;. Climate change and coastal development could significantly increase the impact of TCs in the future (Gettelman et al., 2017;Mendelsohn et al., 2012). Increasing risks from TCs and other extreme weather 30 events pose a challenge to exposed population and assets, but also to governments and investors as actors in globally connected economies. Governments, companies, and investors increasingly express the need to understand their physical risk under current and future climatic conditions (TCFD, 2017). Thus, quantitative risk assessments require a globally consistent representation of the economic impact of TCs and other natural hazards.

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Probabilistic risk models can provide the quantitative basis for risk assessments and adaptation studies. Since the mid-2000s, there have been increasing scientific efforts in developing and improving global scale natural hazard risk assessments https://doi.org/10.5194/nhess-2020-229 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. Gettelman et al., 2017;Ward et al., 2020). Natural risk is frequently modelled as a function of severity and occurrence frequency, which can be computed by combining information on hazard, exposure, and vulnerability (IPCC, 2014). Global and regional scale TC risk models often represent hazard as the spatial distribution of the maximum sustained 40 surface wind speed per TC event Ward et al., 2020). In past studies, wind fields modelled from historical TC tracks were used to assess economic risk in the Global Assessment Report (GAR) 2013 UNDRR, 2013) and to quantify affected population (Geiger et al., 2018), among others. For the assessment of future risk, historical TC records can be complemented with events simulated in downscaling experiments based on the output of global climate models (Gettelman et al., 2017;Korty et al., 2017), or synthetic resampling algorithms (Bloemendaal et al., 45 2020). The exposure component can be represented by the spatial distribution of people, assets or economic values potentially affected by TCs (Geiger et al., 2018;Ward et al., 2020). For the modelling of direct economic damage, exposure is usually derived from building inventories for local risk assessments (Sealy and Strobl, 2017), or estimated by spatially disaggregating national asset value estimates (De Bono and Mora, 2014;Eberenz et al., 2020;Gettelman et al., 2017).

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The vulnerability of an exposed value to a given hazard can be represented by impact functions, also called damage functions or vulnerability curves, relating hazard intensity to impact. Impact functions for the assessment of direct economic damage caused by TCs usually relate wind speed to relative damage (Emanuel, 2011). For the USA, TC impact functions are available specific to different building types (Federal Emergency Management Authority [FEMA], 2010;Yamin et al., 2014), as well as on an aggregate level (Emanuel, 2011).  found a lack of sensitivity of simulated TC 55 damage to the exact shape of the impact function for the USA. However, due to global heterogeneities in the tropical cyclone climatology (Schreck et al., 2014), building codes, and other socioeconomic vulnerability factors (Yamin et al., 2014), one universal impact function might be inappropriate for global TC risk assessments. Bakkensen et al. (2018b) used reported damage data to calibrate TC impact functions for China, highlighting both the potential of this approach and the considerable uncertainties related to the quality of reported damage data. Still, there is a lack of globally consistent and regionally 60 calibrated impact functions. Due to this lack, impact functions calibrated for the USA have been used in a variety of local and regional studies outside the USA, i.e. the Caribbean (Aznar-Siguan and Bertinelli et al., 2016;Ishizawa et al., 2019;Sealy and Strobl, 2017), China (Elliott et al., 2015), and the Philippines (Strobl, 2019). A similar impact function has also been applied for modelling TC damages on a global level (Gettelman et al., 2017).
For the GAR 2013, building type specific impact functions from FEMA were assigned to exposure points based on global 65 data based on development level, complexity of urban areas, and regional hazard level at each location (De Bono and Mora, 2014;Yamin et al., 2014). However, the impact functions were not calibrated regionally against reported damage data.
Furthermore, the required complexity in exposure data exceeds the scope of many risk assessments.
Can globally consistent TC impact modelling be improved by calibrating the vulnerability component on a regional level? 70 This article addresses this question by calibrating regional TC impact functions in a globally consistent TC impact modelling framework, as implemented within the open-source weather and climate risk assessment platform CLIMADA (Aznar-Siguan and . This study contributes to reaching the goal of consistent global TC risk modelling and a better connection of global and regional impact studies. The objectives of this study are to (1) calibrate a global TC impact model by regionalizing the impact function; (2) assess the annual average damage per region and compare the results to past studies; 75 and (3) evaluate the robustness of the calibration and discuss the limitations and uncertainties of both the model setup and the calibration. To inform the discussion of uncertainties, we complement aggregated calibration results (Sect. 3) with an event level case study for the Philippines (Sect. 4). https://doi.org/10.5194/nhess-2020-229 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.

Data and Method
To regionally calibrate TC impact functions, simulated damages are compared to reported damages, as illustrated in Figure   80 1: In a first step, direct economic damage caused by TCs are simulated in the impact modelling framework CLIMADA

CLIMADA -spatially explicit TC risk modelling
The CLIMADA (CLIMate ADAptation) impact modelling framework has been developed at ETH Zurich as a free, opensource software package . It is written in Python 3.7 and made available online both on GitHub (Bresch et al., 2019a) and the ETH Data Archive (Bresch et al., 2019b). We use CLIMADA for the pre-processing 100 of hazard and exposure data, and for the spatially explicit computation of direct damage on a global grid at 10 km resolution.
The setup does work equally well at higher resolutions, but given uncertainties especially in calibration data and computational constraints justify the chose resolution. Simulated damage per TC event and country is computed as following: (1) For each grid cell and event, the mean damage ratio (0 to 100%) is determined by plugging the maximum sustained wind speed (hazard intensity) into an impact function. (2) Absolute damage per grid cell is computed by 105 multiplying the mean damage ratio with the value of exposed assets at the grid cell. (3) The total damage per country and https://doi.org/10.5194/nhess-2020-229 Preprint.

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TCs typically inflict damage due to strong sustained surface winds, storm surge inundation, and torrential rain (Bakkensen et al., 2018a;Baradaranshoraka et al., 2017;Park et al., 2013). Next to maximum wind speed, storm size is an important factor controlling TC impacts (Czajkowski and Done, 2013). Since the severity of surge and rain are to a certain extend correlated to wind speed and storm size (Czajkowski and Done, 2013), the latter are often taken as a proxy hazard intensity (Emanuel, 2011;Gettelman et al., 2017).

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Here, TC hazard intensity is represented by wind fields, i.e. the geographical distribution of the 1-min sustained wind speed per TC event, referred to as "wind speed" or "hazard intensity" in the following. We model wind speed at a horizontal resolution of 10 x 10 km from historical TC tracks as a function of time, location, radius of maximum winds, and central and environmental pressure, based on the revised hurricane pressure-wind model by Holland (2008). Please also refer to Geiger 120 et al. (2018) for a detailed description and illustration of the wind field model and its limitations.
Historical TC tracks were obtained from the International Best Track Archive for Climate Stewardship (IBTrACS) (Knapp et al., 2010). As data quality and global coverage improved after approximately 1980 (Geiger et al., 2018), we selected and processed 4'098 historical TC tracks from 1980 to 2017 based on data completeness criteria with regards to data fields 125 provided within IBTrACS, following the approach described by Geiger et al. (2018) and Aznar-Siguan and Bresch (2019).
Out of the 4'098 TCs, we identified 1'538 landfalling events with the potential of causing damage. Potential damage is given if at least one grid cell of a TCs wind field with an intensity of 25.7 ms -1 (~50 knots) or more coincides with an asset exposure value larger than zero. A worldmap showing the maximum intensity per grid cell for all tracks is shown in the Supplement (Fig. S1). 130

Asset exposure
Asset exposure for the assessment of direct economic risk is represented by the spatially explicit monetary value potentially impacted by a disaster. Here, we use gridded asset exposure value at a resolution of 10 km x 10 km. The dataset is based on the disaggregation of national estimates of total asset value (TAV , Table A3) proportional to the product of nightlight intensity and population count . Following the approach in GAR 2013 (De Bono and Mora, 2014), the 135 TAV per country is represented by produced capital stock of 2014 from the World Bank Wealth Accounting (World Bank, 2019a). Out of the 62 countries used for calibration, 32 come with produced capital estimates. For the remaining 30, an estimate of non-financial wealth is used as a fall back , based on GDP of 2014 from the World Bank Open Data portal (World Bank, 2019b) combined with an GDP-to-wealth factor from the Global Wealth Report (Credit Suisse Research Institute, 2017). The asset exposure dataset utilized here and a detailed overview over limitations and data 140 availability per country is documented in Eberenz et al. (2020).

Impact Function
In CLIMADA, vulnerability is represented by impact functions. They are used to compute damage for each TC event at each exposed location by relating hazard intensity to relative impact. Since no impact is expected for low wind speeds, TC impact functions for the spatial explicit modelling of direct damages can be constraint by a minimum threshold Vthresh for the 145 https://doi.org/10.5194/nhess-2020-229 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. occurrence of impacts and an upper bound of a 100% direct damage (Emanuel, 2011). Empirical studies suggest a high power-law function for the slope, i.e. the increase of damage with wind speed (Pielke, 2007). An idealized impact function satisfying these constraints was proposed by Emanuel (2011) Vthresh and Vhalf. A lower threshold Vthresh of 25.7 ms -1 (50 kn) was proposed for the USA by Emanuel (2011) and empirically supported for China (Elliott et al., 2015). The slope parameter Vhalf signifies the wind speed at which the function's slope is the steepest and a damage ratio of 50% is reached (Fig. 2). It should be noted that the effects of varying Vthresh and Vhalf on resulting impacts are not linearly independent.

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Figure 2: Idealized TC impact function based on Emanuel (2011). Vhalf is the hazard intensity (i.e. maximum sustained wind speed) at which the relative impact reaches 50% of the exposed asset value. No impact occurs for an intensity below Vthresh.
Based on the reference data provided by FEMA (2010), Vhalf for damage to buildings can range from 52 to 89 ms -1 160 depending on building type and surface roughness (Elliott et al., 2015). Applying FEMA impact functions that were verified with reported damage data for US Hurricanes Andrew [1992], Eric [1995], andFran [1996], Sealy and Strobl (2017) estimated Vhalf to range from 71.7 to 77.8 ms -1 , depending on building type, with a mean value of 74.7 ms -1 .
We define a default impact function with Vthresh = 25.7 ms -1 and Vhalf = 74.7 ms -1 that is used for a first, uncalibrated, 165 simulation of global TC damages, and as a starting point for calibration. While Vhalf is fitted during the calibration process, we keep the lower threshold Vthresh constant throughout the study.
Since we are not looking at single buildings but at a grid with a resolution of 10 km by 10 km, we don't necessarily expect full damage to occur to all buildings in a grid cell. However, the wind-speed dependent impact function is also implicitly 170 accounting for the damage caused by storm surge and torrential rain, when calibrated against reported damage data. For these two reasons, we allow for values of 089: lower and larger than the literature range for pure wind induced building damage in the calibration. By varying 089: with 089: > /01230 , we are looking for the functional slope best fit to simulate the direct economic damage of TCs in regional clusters of countries for a regional calibration of the impact function (Sect. EM-DAT provides one entry per country and event. Therefore, one meteorological TC can be listed in EM-DAT several times, with one entry for each country affected. In the following, each of these entries per storm and country will be referred We found that GDP scaling removes the significant positive trend from the yearly impacts in the USA (p-values of 0.04 before and 0.14 after normalization). This is in agreement with the findings of existing normalization studies for past TC 205 impacts in the USA (Pielke et al., 2008;Weinkle et al., 2018).

Event Matching: Assigning reported damage data to simulated TC events
For the comparison of simulated and reported TC damage, reported events from EM-DAT per TC and country need to be assigned to TC tracks from IBTrACS. Tracks were matched based on the country affected and timestamps (Lüthi, 2019): (1) 210 In a first step, the impacted countries per TC track is determined, i.e. in which countries a storm does make landfall. (2) Subsequently, the best fitting tracks are assigned to the reported events, based on an iterative comparison of start dates provided in the datasets. Given that countries are hit by several TCs in a relatively short time, the assignment certainty varies. Finally, (3) tracks with a low assignment certainty are double checked manually for removal or re-assigning.
In total, we matched 848 EM-DAT events to their respective tracks. These events account for 913 billion USD reported 215 economic damages out of the total 959 billion USD from the 991 EM-DAT events (95%). For 534 of the 848 assigned events, there is an economic damage larger than zero simulated in CLIMADA with the respective TC track. Generally, we found the difference between simulated and reported damage per matched event to span several orders of magnitude.
Extreme outliers are likely to be associated either to a mismatch or flawed values of reported damage. Therefore, we exclude 61 extreme outliers from calibration, i.e. all events that come with a deviation of more than factor 1'000 between normalized 220 reported damage and damage simulated with the default impact function.
Eventually, a total of 473 assigned events remain for analysis, referred to as 'matched events' in the following. These

Damage Ratios: EDR and TDR
For the analysis of regional differences in TC vulnerability, To compare the aggregated damage on a global or regional level, we use total damage ratio (TDR) defined as the sum of 235 simulated damages divided by the sum of normalized reported damages: Where N is the number of matched events E in a region R.

Calibration of regional impact functions
As a first step towards regional calibration of the TC impact model, distinct calibration regions were defined based on three 240 criteria regarding (1) geography, (2) data availability, and (3) Table  A1.

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Regional impact functions are calibrated following two complementary approaches, based on (1)  reported values and vice versa. Therefore, TDR is optimized by identifying the impact function associated to a TDR as close to 1 as possible. As TDR is a ratio of damage aggregated over several events, the TDR approach is biased towards better representing events with large absolute damage values. In both calibration approaches, the slope of the generic impact function (Fig. 2)

Damage ratio with default impact function
The comparison of TC damage simulated globally with a default impact function (Eq. 1 with Vhalf = 74.7 ms -1 ) reveals (1) inter-regional differences and (2) considerable uncertainties in CLIMADA's ability to reproduce the reported damage values 285 per event. EDR per matched event is shown in Figure A1, the distribution of EDR per country is shown in Figure S2 in the Supplement.

Inter-regional differences
Both RMSF (Fig. 5b) and the ratios EDR (Fig. A1) and TDR (Fig. 5c), indicating the deviation of the damages simulated with the default impact function from reported damages, show inter-regional differences. For most regions, TDR is less than

Intra-regional uncertainties
The EDR values within regions show a large spread over several orders of magnitudes ( Fig A1). The largest spread, as expressed by the RMSF, can again be found in the regions WP4 and WP2 (Fig. 5c). The lowest RMSF was found for the regions NI, NA2, and NA1, i.e. the North Indian and North Atlantic basins. While the large inter-regional differences show 300 the need for a regional calibration of impact functions, the spread of EDR within some regions point towards uncertainties and limitations of the modelling setup that will not be removed by calibrating the impact function alone.

Regional impact functions
We calibrated regional impact functions to address inter-regional differences in TDR. The resulting impact functions 305 calibrated with two complementary approaches are shown in Figure 4. The resulting impact functions vary between the regions, both in slope and level of uncertainty, with Vhalf ranging from 46.8 to 190.5 ms -1 (Fig. 5a and Table A2). Additional to the regional impact functions, global impact functions were fitted based on all 473 data points combined, resulting in Vhalf ranging from 73.4 (RMSF optimization, i.e. RMSF=min.) to 110.1 ms -1 (TDR optimization, i.e. TDR=1). Applying the regional impact functions, TDR calculated for all regions combined is 4.7 for the default impact function and 2.2 for the 310 RMSF optimized impact functions (Fig. 5b). With the calibration based on TDR optimization, the bias in aggregated simulated damages can be removed, i.e. an impact function is fitted that leads to TDR=1. This does not mean that the fitted curves (Fig. 4). However, the difference between Vhalf for the two approaches ranges from 3 ms -1 (region NA2) to 104 ms -1 (WP2). The largest uncertainties were found in the fitting of Vhalf for regions WP2-4 in the North West Pacific. In these regions, the TDR optimization fits values of Vhalf that are much larger than for the RMSF optimization (Fig. 5a). This

Annual average damage AAD
Despite considerable interannual variability of TC occurrence and impacts, AAD is often used as a reference value for the mean risk per country or region. Here, we compare AAD computed with the regionalized TC impact model to values from 350 EM-DAT and literature (Table 1) Table A1). AAD in countries not attributed to any 355 region is calculated with impact functions calibrated globally. The resulting AAD for the calibration regions and the global aggregate are shown in Figure 5d and Table 1. The standard deviation of AAD is generally of the same order of magnitude as AAD (Table 1).
For the years 1980 to 2017, we find aggregated global AAD to range from 51 up to 121 billion USD (current value of 2014).

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In comparison, global AAD from EM-DAT is 46 billion USD. Values from GAR 2013 and Gettelman (2017)

Explorative case study: the Philippines
For a better understanding of the uncertainties involved in the TC impact function calibration, we exploratively examine 390 simulated and reported damages of matched events in the Philippines (region WP2). The Philippines is the region with the least robust calibration results, with a large spread in EDR and the largest discrepancy between the two calibration approaches: The difference in Vhalf between the two calibration approaches exceeds 100 ms -1 (Fig. 5a). Consequently, there is a large spread in simulated AAD, ranging from 0.8 to 14 billion USD (Table 1)

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(2) The simplified representation of the TC hazard intensity with wind speed alone is not capable to adequately model the impact of TCs with over-proportional damage caused by sub-perils like storm surge and torrential rainfall (Baradaranshoraka et al., 2017;Park et al., 2013). In the following, we explore these hypotheses by the example of 83 matched TC events in the Philippines, while keeping in mind that the model setup is not designed to represent single events perfectly, due to the large inherent stochastic uncertainty. To explore these hypotheses, we review reports and literature on TC impacts in the 405 Philippines, and examine the relationship between EDR per event with the spatial distribution of the wind field and subsequent simulated damages associated to each single event.

Tropical cyclones in the Philippines
The Republic of the Philippines is one of the most TC-prone countries in the world (Blanc and Strobl, 2016). From 1951 to 410 2014, an annual average of 19.4 TCs entered the Philippine Area of Responsibility (Cinco et al., 2016), with six to nine TCs making landfall in the Philippines each year (Blanc and Strobl, 2016;Cinco et al., 2016). This is a relative high frequency compared to five to eight landfalls in China (Zhang et al., 2009), and an average of three landfalls per year in the North Indian Ocean region (Wahiduzzaman et al., 2017) as well as in the USA (Lyons, 2004). The north and east of the Philippines are the regions most exposed to TC landfalls, with most TCs crossing the Philippines from east to west (Cinco et al., 2016; 415 Espada, 2018). Rainfalls associated to TCs contribute around 35% of annual precipitation in the Philippines, with regional values ranging from 4 % to 50 % (Cinco et al., 2016).
In total, 83 matched TCs making landfall in the Philippines were used for calibration. For 11 of the 21 most damaging TC events, reports and scientific literature on associated sub-perils and impacts were reviewed (Table A4). In summary, TCs making landfall in the Philippines cause damage due to large wind speed, storm surge, as well as rain induced floods and 420 landslides. Most events inflict damage on several sectors, most costly on housing and agriculture, but also on schools and hospitals, power and water supply, roads, and bridges (Table A4). Single events were also reported to damage and disrupt airports and ports (Typhoon Haiyan), dikes (Pedring), and water supply (Bopha and Fengshen). This complexity of how and where TCs cause damage in the Philippines is in stark contrast to the relatively simple representation of hazard and exposure in our modelling setup. It is therefore not surprising, that our calibrated TC impact model is over-and underestimating the 425 damage of individual events, as illustrated for the Philippines by the wide spread of EDR. In the following, we will take a closer look at events with over-and underestimated simulated damage to explore the two hypotheses above.

Urban vs. rural exposure
Most of the asset exposure value of the Philippines is concentrated around the metropolitan area of Manila, located around 430 14.5°N, 121.0°E (Fig. 6a). The Typhoons Angela (1995), Xangsane (2006), and Rammasun (2014) are prominent TCs hitting the Manila region. In our analysis, they come with particularly large EDRs, i.e. an overestimation of simulated vs reported damages, even with calibrated impact functions (Table A4). All three typhoons show maximum sustained wind speeds in Manila larger than 50 ms -1 (Fig. 6b,e,f), corresponding to relative damage ranging from 6 up to 37 % of asset exposure value with the calibrated impact function. These large relative with an EDR>10 and zero occurrences of EDR<0.1 (Fig. 7). In contrast, only 9 of 64 TCs not affecting Manila directly come 440 with an EDR>10. In summary, we found simulated damage of an event more usual to substantially exceed normalized reported damage if the event hit Manila directly. This confirms hypothesis (1) that a special treatment of the impact functions for urban areas could improve the TC impact model.

Impact of storm surge and torrential rain
Tropical Storm Ondoy (2009) is an example with very low simulated damages: Ondoy's EDR is 0.002, i.e. its simulated damage is more than two orders of magnitude smaller than reported. The large reported damage (NRD=401 million USD) 460 was mainly due to floods and landslides: Torrential rainfall caused severe river flooding in the Manila metropolitan region and landslides around Baguio City resulting in severe damages NDCC, 2009a). These damages were not resolved by the wind-based impact model, with intensities well below 50 ms -1 and neither affecting Manila nor the northern Baguio City directly (Fig. 6d).

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For the most severe TC in the recent history of the Philippines, Typhoon Haiyan (2013), normalized reported damage and simulated damage are in the same order of magnitude resulting into an EDR of 0.17. Haiyan, with sustained 1-min surface wind speeds up to 87.5 m/s, caused thousands of casualties and around 10 billion USD of economic damage in the Philippines (Guha-Sapir, 2018;Mas et al., 2015). Devastating wind and storm surge associated to Haiyan caused damage to multiple sectors, including ports and an airport. It should be noted that these sector specific impacts are not resolved in the 470 impact model and Haiyan did not affect Manila directly. However, relatively large damages were simulated around the cities Iloilo and Cebu (Fig. 6c). The relatively good performance of the model in the case of Haiyan is thus not explained by a perfect location and representation of the impact in the model. It is rather based on overestimated urban wind damages partly balancing the lack of damages caused by storm surge.

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The case of the Philippines reveals limitations of the model and calibration due to the lack of an explicit representation of subperils such as storm surge, torrential rainfall, and landslides (Sect. 4.3). Adding to the stochastic uncertainty, the magnitude of rainfall during a TC events in the Philippines is not only determined by the intensity of the TC event, but also by the coinciding monsoon season, as in the case of the Typhoons Fengshen and Haiyan (Espada, 2018;IFRC, 2009).
Next to a lack of representation of all components of hazard intensity, differences in exposure and vulnerability between urban 480 and rural areas exposed to TCs are likely to contribute to the large spread in EDR and subsequently uncertainty in the impact function calibration. This has been illustrated in Sect. 4.2: The large overestimation of simulated event damage of TCs affecting the Manila metropolitan area points towards relevant sources of epistemic uncertainty: On the one hand, a large share of exposed asset values in the model is concentrated in urban areas, while exposed agricultural assets in rural areas are neglected.
On the other hand, one single impact function might not be sufficient to represent both urban and rural building vulnerability.

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Another factor contributing to the high simulated damages in Manila could be the wind field model:

Relevance for TC risk assessments
In this study, we showed how the regionalization of impact functions improves the assessment of TC risk in numerous world regions, correcting a overestimation of aggregated TC damages by a factor of potentially up to 36 in the North West Pacific, https://doi.org/10.5194/nhess-2020-229 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. and an underestimation by the factor 5 in the South Indian Ocean. To complement the global perspective, we explored the 495 limitations of the TC impact modelling setup by the case study of TC events in the Philippines.
The calibration resulted in large regional differences in the slope of impact functions, with considerable consequences on the magnitude of simulated damages. In Sect. 3.2, we compared average damages simulated with regionalized impact functions to results from literature. While the comparison is limited by differences in the model setups, we found that regional damage 500 estimations relative to the exposed asset values generally agree well to the results of previous studies. However, the results for the North West Pacific region (WP4), consisting of Japan, South Korea, Macao, Hongkong, and Taiwan, deviate substantially from GAR 2013. Simulated relative AAD in the region ranges from 0.2-0.8 ‰ as compared to 3.1 ‰ in GAR 2013. This difference implies that, besides the use of building type specific impact functions, the TC impact model of GAR 2013 substantially overestimates TC damages in WP4 compared to reported data. Consistent with this finding, the uncalibrated 505 simulation showed the largest overestimation of aggregated damages in this region. Assuming that the order of magnitude of reported direct damages from EM-DAT is reasonable, the regionalization of impact functions presented here is an improvement for TC risk assessments in the region.
For calibration, two complementary approaches were employed: The optimization of aggregated simulated compared to 510 reported damages (TDR), and the minimization of the spread of damage ratios of single events (RMSF).
Annual average damage simulated based on the TDR optimized set of impact functions are generally closer to the values found in EM-DAT than the values based on RMSF optimization. This is not surprising, since TDR is designed to represent aggregated damage per region. For the assessment of TC risk on an aggregated level, it is therefore most appropriate to employ the more conservative TDR optimized model, even though single events can be massively underestimated with the 515 flatter impact functions. Complementary, impact functions based on RMSF optimization and the spread of individually event fitting can be included in risk assessments for sensitivity analysis.

Uncertainties and limitations
The deviation between the results of the two calibration approaches indicates how robust the calibration is with regards to 520 the model's ability to represent the correct order of magnitude of single event damage. Whereas the model setup returns reasonable risk estimates and consistent calibration results for Central and North America, we found an extensive spread in EDR and calibration results for other regions, especially in East Asia. While the correlation between simulated and reported event damages is improved by the calibration, the simulated damage of single TC events can deviate several orders of magnitude from reported damages ( Fig. A1 and A2). In the regions of the North West Pacific (WP2-4), the fitted impact 525 functions are ambiguous, with large discrepancies between the two calibration approaches. The low robustness found for these regions stems from multiple causes, including the stochastic uncertainty in TCs as natural phenomena, as well as epistemic uncertainties located in the hazard, exposure, and vulnerability components of the impact model. An additional source of uncertainties is located in the reported damages used for reference. Future improvement of the TC impact model and a sound judgement of the limitations of the calibrated impact functions requires better understanding of the epistemic 530 uncertainties. In the following, we will discuss these uncertainties for the different components of the model.
The case of the Philippines provides insights into the uncertainties located in the model setup, both in the representation of hazard intensity and in differences between the structure and vulnerability of exposed assets in urban and rural areas (Sect. 4). The hazard is represented by wind fields modelled from TC track data and the same impact functions are applied in urban and rural areas. These are considerable simplifications of the actual interaction of cyclones with the natural and built environment. To reduce these uncertainties, the hazard component could be improved by considering topography (Done et al., 2019) and complementing wind speed with sub-perils like storm surge, torrential rain, and landslides. For a better representation of urban assets, building type specific impact functions, and a differentiation of urban and rural exposure as applied for GAR 2013 (De Bono and Mora, 2014) could be beneficial. Furthermore, geospatial agricultural yield data could 540 be added to the exposure data, albeit reported damage for calibration is mostly not available at such sectoral granularity.
Next to the model setup, the reported damage data obtained from EM-DAT are another relevant source of uncertainty.
Reported damage data are expected to come with considerable uncertainties, partly due the heterogeneity of data sources, the blending of direct and indirect economic damages, as well as political and structural reporting biases (Guha-Sapir and Below, 2002;Guha-Sapir and Checchi, 2018). Further uncertainty is introduces by the lack of international standards for 545 reported damage datasets, leading to inconsistencies between data providers (Bakkensen et al., 2018b). These uncertainties limit our understanding of the robustness of the calibration. For future calibration studies relying on reported damage data, calibration robustness could be increased by combining datasets from different sources in an ensemble of datasets (see Zumwald et al., 2020).

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In this study we did not explicitly quantify the uncertainties related to the model setup, the input data for hazard and exposure, as well as the reported data used as reference data for calibration. Rather, the robustness of the calibrated impact functions was judged based on the deviation between the two calibration approaches and the spread of impact functions fitted to the individual TC events. Based on the limitations discussed above, we conclude that the resulting array of regionalized impact functions should be applied with caution, being aware that the model setup is not suitable to represent 555 single TC events adequately. However, the calibrated impact functions mark an improvement for the modelling of aggregated risk estimates, such as the annual average damage. Impact functions sampled from the range of calibration results can be applied for a more probabilistic modelling of TC impacts. It should also be noted that the impact functions calibrated for the years 1980-2017 cannot be expected to be stable in the future. Applying these impact functions for the assessment of future TC risk requires a ceteris paribus assumption with regard to vulnerability.

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The regionalized impact functions presented here were calibrated for wind-based damage modelling on a spatially aggregated level. Model setups with an explicit representation of related sub-perils like storm surge or torrential rain require different (i.e. flatter) impact functions for the wind-induced share of TC damage, as well as additional impact functions for all sub-perils. Likewise, impact models with an explicit representation of building types and agricultural assets require a 565 more differentiated set of impact functions. Considering the irreducible stochastic uncertainties in the system, it remains to be shown to which degree the large inter-regional differences in calibrated impact functions found in this study can be explained by regional differences in building types and standards, physical TC characteristics, or other factors.

Conclusion and outlook
In this article, we improved global TC risk assessment by regionalizing the vulnerability component of the TC impact 570 assessment. To better account for regional differences, we calibrated a TC impact model by fitting regional impact functions.
The impact functions were calibrated within the CLIMADA risk modelling framework, using reported direct economic damage estimates from the EM-DAT dataset as reference data. For calibration, two complementary optimization approaches were applied, one aiming at minimizing the deviation of single event damages from the reported data and one aiming at minimizing the deviation for total damage aggregated over 38 years of data. By fitting impact functions, we were able to 575 reduce regional biases as compared to reported damage data, especially for countries in the North West Pacific and South       https://doi.org/10.5194/nhess-2020-229 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.