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The grid-level present and future wealth maps that represent economic exposure for the loss calculations are based on present and future population grids from ref. 25 which were obtained by dasymetric mapping using the urban area maps in ref. 8. A cellular automata-based urban growth model called SLEUTH26 was used in ref. 8 to the urban area (30 m grids for Jakarta and Metro Manila, and 90 m grids for Istanbul due to size of the administrative area) in 2030. SLEUTH model leverages on the mapped urban area extracted from satellite images and several other predictors of change (ie, slope, transportation, and excluded area) which affect urbanization trends. It uses brute force calibration to generate a set of best-fit growth coefficients, namely slope, breed, difffusion, spread and road gravity. The growth coefficients define four growth rules in SLEUTH which are namely the spontaneous growth, new spreading center growth, edge growth, and road-influenced growth. During the calibration, a shape index called Lee-Sallee index is utilized for the selection of best-fit coefficients. Lee-Sallee index shows the spatial match, and it is defined as the ratio of intersection to the union of the ground truth urban area and simulated urban area8.
In each urban growth model, four urban area inputs and two road network inputs were used as suggested by SLEUTH, and only business-as-usual scenario was considered for the prediction of future urban area in ref. 8. The water bodies were used to define the excluded area. After obtaining the set of best-fit growth coefficients in ref. 8, it was observed that the dominant growth type is Edge Growth in Jakarta and Metro Manila while it is a combination of Edge Growth and New Spreading Center Growth in Istanbul. The predicted urbanization probabilities in 2030 were used in ref. 25 to disaggregate the extrapolated population of each megacity by following several assumptions. The details of these assumptions can be found in ref. 25 along with the present and future population density maps.
We obtained the grid-level wealth maps (Supplementary Figs. 1–3) following the economic exposure definition proposed by Jaiswal and Wald18 as given in Eq. 1:
$${{{{{{rm{Economic}}}}};{{{{{rm{Exposure}}}}}}}_{{{{{rm{grid}} }}}}}}=alpha times {{{{rm{per}}}}},{{{{{{rm{capita}}}}}}{{{{{{}}}}}} {rm{GDP}}}}}}_{{{{{{rm{country}}}}}}times {{{{{{rm{population}}}}}}}_ {{{{{rm{grid}}}}}}$$
(1)
Therefore, present and future economic exposure grids were derived by multiplying present (ie, 2016 for Metro Manila and 2018 for Jakarta and Istanbul due to data availability) and future (ie, 2030) GDP per capita with the corresponding population grids and the exposure correction factor α (ie, wealth per capita/GDP per capita) proposed in ref. 18. This correction factor accounts for the disparity between national wealth and economic value of assets that are exposed. Present country-level nominal GDP per capita values were obtained from World Bank Data (available at https://data.worldbank.org/), and the real GDP per capita predictions in 2030 (in 2010 prices) were collected from the United States Department of Agriculture (USDA), International Macroeconomic Data Sets (available at www.ers.usda.gov). Then, the real GDP per capita in 2030 was converted from 2010 prices to 2016/2018 prices leveraging the price index (ie, current GDP/real GDP) using 2010 as the base year from World Bank Data. Supplementary Table 2 summarizes the present and future GDP per capita values and exposure correction factors from ref. 18 for the selected countries in our study, namely Indonesia, the Philippines, and Turkey.
To assess the dynamics of spatio-temporal change in wealth exposed to seismic hazard, we overlaid present and future wealth maps with the 10 and 2% probability of exceedance seismic hazard maps in ref. 8. We used classical PSHA to generate grid-based hazard maps and hazard curves by utilizing the OpenQuake Engine (available at www.globalquakemodel.org)32,33 along with the Earthquake Model of Continental Southeast Asia (2018)34 for Jakarta and Metro Manila, and the Earthquake Model of the Middle East (EMME14)35 for Istanbul. The main reason of selecting the classical PSHA-based risk assessment instead of a probabilistic event-based approach in this study is to have a grid-based comparison between present and future urban grids following the urban expansion analysis rather than evaluating a portfolio of assets36, 37. It is also worth noting that the classical PSHA-based risk assessment is computationally more efficient36. Therefore, the loss exceedance curves were calculated site by site based on the hazard curves, and the spatial correlation in the ground motion residuals were not considered. The slope-based shear wave velocities, Vs30, by USGS were also taken into consideration for soil amplification during the analysis38. The Peak Ground Acceleration (PGA) values were then converted to Modified Mercalli Intensities (MMIs) using Ground Motion to Intensity Conversion Equations (GMICEs) proposed by Worden et al.39. It is worth noting here that the spatial resolution of the seismic hazard maps is same with the spatial resolution of the wealth maps (ie, 30 m for Jakarta and Metro Manila, and 90 m for Istanbul). For the grid-level hazard curves and loss estimation, we aggregated smaller grids to 270 m grids to decrease computation time.
The set of guidelines and recommendations for conventional loss estimation methodologies are primarily based on the method suggested by the Applied Technology Council (1985), which is designated as ATC-1340. The ATC-13 method contains two main components, namely, a seismic hazard analysis and a structural vulnerability function. Seismic hazard analysis takes the frequency distribution of earthquakes, intensity attenuation, and soil conditions into account, while the vulnerability analysis requires a detailed inventory of buildings and facilities in the region. The expected loss at a site is then determined by ATC-13 as shown in Eq. 2 below:
$${{{{{rm{Loss}}}}}}=mahop{sum} limits_{{B}_{k}}left[left{mathop{sum} limits_{{I}_{i}}Pleft({I}_{i}{{{{{rm{|}}}}}}{B}_{k}right)* left(mathop{sum} limits_{{{dr}}_{j}}Pleft({{dr}}_{j}{{{{{rm{|}}}}}}{I}_{i},{B}_{k}right)* left({{dr}}_{j}{{{{{rm{|}}}}}}{B}_{k}right)right)right}* {V}_{{B}_{k}}right]$$
(2)
where ({B}_{k}) is the building type k, ({I}_{i}) is the intensity level i, ({{dr}}_{j}) is the expected damage ratio j, and ({V}_{{B}_{k}}) is the value of all buildings of type ({B}_{k}).
To our knowledge, the first macro-level seismic loss estimation approach was proposed by Chen et al.19 as presented in Eq. 3:
$${{{{{rm{Loss}}}}}}_{{{{{rm{grid}}}}}}}=mahop{sum} limits_{{I} _{j}}Pleft({I}_{j}right),times, {{{{rm{MDF}}}}}}({I}_{j}) ,times, {g({{{{rm{GDP}}}}}),times, {{{{rm{GDP}}}}}}}_{{{ {{{rm{grid}}}}}}}$$
(3)
where (Pleft({I}_{j}right)) is the probability of intensity level j, ({{{{{rm{MDF}}}}}({I}_{ j})) is the Mean Damage Factor to represent hazard-exposure-loss relation given intensity ({I}_{j}), and (g({{{{rm{GDP}}}}) }})) is a function to correlate the total social wealth with the macroscopic indicator GDP. The summation over ({I}_{j}) represents the expected loss at each grid considering different probabilities of shaking intensities. (g({{{{{{rm{GDP}}}}})) is supposed to be 4 for low- and middle-income, 5 for high-income, and 3 for China, India and Japan. Due to the limitation of the earthquake data, ref. 19 Assume that the ({{{{rm{MDF}}}}}}({I}_{j})) is defined globally by the relation between intensity and loss ratio.
Jaiswal and Wald18 pointed out several limitations about previous macro-level forms such as the broad economic categories of vulnerability curves, and the use of GDP which is an indicator of economic activity (ie, flow) rather than the existing investment (ie, stock) . Therefore, through the US Geological Survey’s (USGS) Prompt Assessment of Global Earthquakes for Response (PAGER) system, they proposed using country-level vulnerability parameters and an exposure correction factor α (ie, wealth per capita/GDP per capita) to adjust GDP as represented in Eq. 1. PAGER system rapidly estimates the population exposed to different levels of shaking intensities along with the range of economic losses in the aftermath of a large earthquake by means of a deterministic approach. Total expected economic loss is estimated as described in Eq. 4 by summing the product of loss ratio (r(s)), and total economic exposure at each shaking intensity level, (s):
$${Eleft({{{{{rm{Loss}}}}}right)=rleft(sright),times, {{{{{rm{Economic}} }}}}};{{{{{rm{Exposure}}}}}}_{s}$$
(4)
The loss ratio (r(s)) is defined in ref. 18 as given below in Eq. 5:
$$r(s)=phi left[frac{1}{beta }{{{{{rm{ln}}}}}}(frac{s}{theta })right]$$
(5)
where (phi) is the standard normal cumulative distribution function, (theta) is the mean, and (beta) is the standard deviation of natural logarithm of shaking intensity (s).
By integrating the probabilistic approach of Chen et al.19 and the deterministic approach of Jaiswal and Wald18, here we propose a probabilistic wealth-based macro-level loss estimation approach. The main difference of our proposed approach from other approaches is the integration of the exposure correction factor α and the loss ratio definition given in ref. 18 into the probabilistic GDP-based framework of Chen at al.19 to calculate the present and future probabilistic risk metrics AAL and PML. The AAL results represent the amount that a country or a municipality would have to set aside each year to cover the cost of future disasters in the absence of insurance or other disaster risk financing mechanisms. They also provide a basis to calculate the premium of an insurance program. PML results are relevant to the maximum loss that could be expected within a given period of time. They represent the size of the reserves that insurance companies or the government should have available to buffer potential future losses. We then propose the following form shown in Eq. 6 to calculate AAL and PML based on economic exposure given in Eq. 1:
$${E({{{{{rm{Loss}}}}}})_{{{{{rm{grid}}}}}}=mahop{sum} limits_{ s}Pleft(sright),times, r(s),times, {{{{{{rm{Economic}}}}};{{{{{) rm{Exposure}}}}}}}_{{{{{{rm{grid}}}}}}}$$
(6)
where (s) is the shaking intensity, (Pleft(sright)) is the probability of occurrence of shaking intensity (s), and (r(s)) is the loss corresponding ratio to shaking intensity (s).
We obtained the country-level MMI-based vulnerability parameters (ie, (theta) and (beta)) corresponding to Indonesia, the Philippines, and Turkey from Jaiswal and Wald18 as summarized in Supplementary Table 3, and the vulnerability curves obtained by using these parameters are shown in Supplementary Fig. 5. Based on the wealth maps, hazard curves, and vulnerability curves, we obtained the grid-level AAL, and 475-year and 2475-year PML maps following our proposed approach. Subsequently, we aggregated the AAL values to obtain Admin Level 2, and then megacity-level AAL values for Jakarta, Metro Manila, and Istanbul.
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