We first collected country-based information on desalination production for nine countries with the largest seawater desalination capacity in the world from the AQUASTAT database: United Arab Emirates (UAE), Saudi Arabia, Kuwait, Spain, Qatar, Libya, Bahrain, Israel, and Oman (hereafter “major countries”). We selected the year 2005 as the base year mainly due to the availability of socioeconomic data as discussed below. In addition, we collected municipality-based information for Saudi Arabia (KICP, 2011) and the UAE (RSB, 2013). In spite of our efforts, subnational information for other countries was not found.

To obtain spatially detailed data, we used DesalData (http://www.desaldata.com/). As of 2014, DesalData included data for 17 335 individual desalination plants around the world. The total capacity of desalination reached 31.4 km3 yr-1 globally from all water sources. Individual records contain data such as plant status, source water type, user category, plant size, and geographical location (longitude and latitude). Note that plant size shows the capacity of plants, not the actual production. The ratio between the capacity and production varies by project.

Since the objective of this study was to develop a model that would be applicable to the global domain for long-term water scarcity projections, we focused on information regarding active major plants using seawater as source water. Currently, seawater is the primary source of desalination, amounting to 19.2 km3 yr-1, followed by brackish water, saline inland and river water, and others. First, we selected the major desalination plants to be included in our analyses. The detailed selection criteria and the rationale are shown in Table S1 and the Supplement. Next, we selected 613 large plants using seawater as the water source. We examined the list of plants and excluded records if necessary. For example, DesalData contain some records indicating that plants in inland regions use seawater as the source, which is erroneous. A total of 54 plants were excluded from this study. These are listed in Table S2 with the reasons for their exclusion. Finally, we used a total of 559 large plants using seawater as the water source (hereafter “major plants”). Although this is less than 4 % of total records (559 out of 17 335), as shown in Table S3, these plants account for 81 % of the total capacity of active seawater desalination plants (12.7 km3 out of 15.7 km3). The number of plants and their total capacity are summarized in Table S3.

To determine the distances between desalination plants and major cities of selected countries, the geographical data of major cities were collected. We referred to the GeoNames database (http://www.geonames.org), which reports the geographical locations and populations of major cities around the world. We selected cities with populations larger than 100 000 (hereafter “major cities”).

At present, major plants are located mostly in arid regions. This makes sense because alternative water sources are limited in such conditions and costly seawater desalination becomes a practical option. To express aridity, the ratio of precipitation to potential evapotranspiration (hereafter aridity index, AI) was calculated globally. We used the WATCH Forcing Dataset (Weedon et al., 2011) as a global meteorological dataset for the historical period in question. This dataset covers the whole globe at a spatial resolution of 0.5∘ × 0.5∘ and includes basic meteorological variables at 6 h intervals, i.e., precipitation, air temperature, specific humidity, wind speed, air pressure, and shortwave and longwave downward radiation. Using the data from 1971 to 2000, we calculated the mean annual precipitation and potential evapotranspiration for each grid globally. The latter was calculated using the H08 global hydrological model (Hanasaki et al., 2008a, b).

For the future period, we used the climate projections obtained with a global climate model (GCM), namely MIROC4-ESM-CHEM. The selection and combination of the GCM and climate scenarios and the methods of downscaling and bias correction were identical to those reported previously (Hanasaki et al., 2013a, b).

For population and GDP, we referred to the shared socioeconomic pathways (SSPs) database provided by IIASA (https://secure.iiasa.ac.at/web-apps/ene/SspDb), which covers both the historical (1980–2005) and future periods (2005–2100) for 203 nations. The data for future periods came from model-based projections under five distinct socioeconomic views, i.e., SSP1 (sustainability), SSP2 (middle of the road), SSP3 (fragmentation), SSP4 (inequality), and SSP5 (conventional development; O'Neill et al., 2014). GDP is shown in purchasing power parity (PPP) in 2005 US dollars (USD). This means that both monetary inflation over time and differences in price among nations or regions are removed from the GDP projections in this study.

For nationwide water use data, including desalinated water production, we relied primarily on the AQUASTAT database for the historical period in question. This database includes municipal and industrial water use data for 200 nations from 1960 to 2010 at 5-year intervals. Data are available for most countries in 2000 or 2005 but are largely missing for other years. For the future period, we used the projections of Hanasaki et al. (2013a). They estimated water withdrawal for irrigation, industrial, and municipal use over three periods (2011–2040, 2041–2070, and 2071–2100, centered on 2025, 2055, and 2085, respectively). Projections of industrial and domestic water withdrawal were obtained with a semi-empirical model using electricity production and population as primary driving forces and scenario-based parameters of improvements in water use efficiency. The parameters were set to be compatible with the storylines of the SSPs (e.g., slow improvements in SSP3, rapid improvements in SSP1). Consequently, as shown in Figs. 12 and 14 of Hanasaki et al. (2013a), the projected future water withdrawal was largest in SSP3 and smallest in SSP1. Note that these projections are demand based without specifying water sources. The key socioeconomic factors are summarized in Table 1. In this study, we focused on three scenarios, i.e., SSP1, SSP2, and SSP3.

In this subsection, the collected data are analyzed to model seawater desalination around the world. We quantitatively investigate desalination production and usage at the national and subnational levels. Because seawater desalination is mainly used in coastal arid regions, aridity conditions and distances from the seashore to plants and cities are also examined.

Table 2 summarizes desalinated water capacity and production in the major countries. The countries accounted for 85 % of the seawater desalination plant capacity in 2005. UAE and Saudi Arabia produced the largest volumes of desalinated water, which accounted for more than half of the global total. The major countries share two characteristics. First, all are located in the Middle East or on the coast of the Mediterranean Sea and have arid or semi-arid climates. Second, their income is relatively high: GDP per person exceeds 14 000 USD PPP person-1 yr-1.

Next, we focused on water use in the major countries, as shown in Table 2. More than 3 times the volume of water was used by municipalities than by industry, except in Spain. Globally, 99 % of major plants were installed for combined municipal and industrial use, with 90 % for municipal water use. Seawater desalination was seldom used for agricultural water supply. The production to capacity ratio varied considerably among nations, ranging from 53 to 110 %; the ratio sometimes exceeded 100 %, probably due to inconsistencies in the data and the year of report.

Figure 1 shows the geographical distributions of major plants in the Mediterranean and Middle East regions where the majority of plants are concentrated. Note that the plants were aggregated into gridded data with a spatial resolution of 0.5∘ × 0.5∘ for consistency with the final simulation. As clearly shown in the figure, the major plants were mainly located on the seashore and near large cities.

Figure 2 shows the AI of the present climate. Among the major countries, countries located in the Arabian peninsula, namely UAE, Saudi Arabia, Kuwait, Qatar, Bahrain, and Oman, are located in a hyper-arid climate, where the AI is below 0.15. The countries on the coast of the Mediterranean Sea, namely Spain, Libya, and Israel, are located in more humid climates than the above-mentioned countries, with AIs typically between 0.15 and 0.5. Note that the desalination plants in Spain are only located on the southeastern coast and some islands where the AI is substantially lower than that in the remaining regions. The fraction of desalinated water production to total industrial and municipal water withdrawal is shown in Table 2. The fraction for the countries in the Arabian peninsula exceeds 50 % except for Saudi Arabia, while that for the Mediterranean countries falls below 20 %. This indicates that desalinated water is a major water source for industrial and municipal water in countries in the Arabian peninsula, while it is supplemental in the countries on the Mediterranean Sea.

We plotted the relationship between the AI and plant capacity in each grid cell (Fig. S2), which shows a remarkable difference in the distribution of capacity by AI. We applied the segmented regression method and estimated the break point at AI = 0.082.

Figure 3 shows the distances of the major desalination plants from the seashore and the primary cities of the major countries. Desalination plants are typically located on the seashore supplying water to cities at close range. Therefore, we considered that the summation of the distance between the seashore and a plant, and that from the plant to the closest major city was the distance that seawater was transferred. We calculated the distance using the Clark Lab's IDRISI Taiga Release 16.05 GIS platform software (Eastman, 2009). Note that due to technical limitations of the software, the individual plants were first aggregated into 5 arcmin× 5 arcmin grid cells, and then the distance was estimated at intervals of 1 km. We analyzed seven of the major countries including cities larger than 100 000 persons. The results indicated that 90 % of the major desalination plants were located within 15 km from the seashore and 170 km from major cities. Taking the distance from the coastline and cities into account, the area using seawater desalination extended approximately 170–185 km (roughly corresponding to the edge (165 km) and diagonal (233 km) of 3 × 3 grid cells with a spatial resolution of 0.5∘ × 0.5∘) from the seashore.

For further geographical breakdown, Table 3 shows the water supply of the major cities in UAE and Saudi Arabia. The two largest cities in UAE, Abu Dhabi and Dubai, depend heavily on desalinated water. Municipal and industrial water for Abu Dhabi is supplied entirely by desalinated water (EAAD, 2012) and their plant capacity reaches 1.18 × 106 m3 day-1. Information on detailed water supply in Dubai was not available, but a news article suggested that 98.8 % of Dubai's water is supplied by desalination (Hackley, 2013). The total desalinated water production for the six cities in Saudi Arabia shown in Table 3 accounted for 80 % of the national desalinated water supply. For these cities, desalinated water accounted for as much as 69 % of the total supply. The sources of water varied between cities and regions. Jeddah, Makkah, Al Taif, and Al Madinah were largely dependent on desalinated water. Here, we note two exceptional cities. Although located 450 km from the seashore, Riyadh obtains about half of its water from seawater desalination transferred via pipeline. In contrast, although located on the seashore, Dammam depends on seawater desalination for less than 50 % of its water supply.

We developed a seawater desalination model (SDM) to estimate the areas where desalinated water is used and the volume of desalinated water production. As the model is intended to be incorporated into the global water resources model H08 (Hanasaki et al., 2008a, b), for consistency, its spatial resolution was set at 0.5∘ × 0.5∘.

SDM consists of a set of climatological, geographical, and socioeconomic conditions to estimate the spatial extent of where seawater desalination is likely to be used. SDM identifies the grid cells in which all of the conditions given below are met. We called these grid cells area utilizing seawater desalination (AUSD) cells. In the AUSD grid cells, fresh water is produced by seawater desalination technology and used to meet local water demands under several assumptions. By combining the gridded map of AUSD cells and requirements for water withdrawal (i.e., potential water demand), which is standard input/output data of global hydrological models, we can estimate the global production of seawater desalination. Note that AUSD cells indicate where desalinated water is used and, hence, they are not identical to the location of individual desalination plants. It is expected that the spatial extent of AUSD cells includes the locations of major seawater desalination plants, but desalination plants are not necessarily located at every AUSD grid cell because desalinated water can be transferred to surrounding grid cells through the pipeline network. The conditions and assumptions of SDM were determined based on analyses of the national and subnational statistics of desalinated water production and the geographical distribution of desalination plants, as described in Sect. 2.4.

In this study, we developed SDM and its variant (hereafter SDM2). SDM2 has an identical model structure to SDM, but it consists of different objectives and sets of conditions and assumptions. SDM estimates AUSD cells where industrial and municipal water are mostly dependent on seawater desalination. As seen in Sect. 2.4, countries such as UAE and Qatar are typical cases. SDM2 estimates AUSD cells where industrial and municipal water are at least partly dependent on seawater desalination. Countries on the Mediterranean Sea are typical cases.

SDM extracts AUSD cells or the grid cells meeting the following three conditions: Condition A

Nations are included whose GDP exceeds 14 000 USD PPP person-1 yr-1.

Four simulations were performed using SDM and SDM2. The first was a historical simulation for 2005, which was used for model validation. The results were used to validate the locations and production volumes of desalinated water. The remaining simulations were simulations of SSP1, SSP2, and SSP3 for three periods (2011–2040, 2041–2070, and 2071–2100), which were consistent with the projections of Hanasaki et al. (2013a, b). The results were used to assess future desalinated water use.

Historical simulations were performed to validate SDM and SDM2. First, we validated the geographical extent of the simulated AUSD cells. Validation was conducted in two steps. First, we checked whether AUSD cells existed in the major countries shown in Table 2. Next, we checked whether the AUSD cells included the grid cells with desalination plants shown in Fig. 1. The extent of AUSD cells is expected to be greater than the area of desalination plants, because desalinated water produced in a grid cell can be transferred to multiple cells through the pipeline system.

Figure 4a shows the AUSD cells derived from SDM. Recall that the objective of SDM was to identify the regions dependent, to a significant extent, on seawater desalination. The AUSD cells included the location of major plants in the Middle East (Fig. 1), spreading along the seashore in Kuwait, Saudi Arabia, UAE, Bahrain, Qatar, and Oman. Yemen was not included because it fell below the income threshold, which agreed well with Table 2 indicating that Yemen produces little desalinated water. Southern Oman was indicated as suitable for desalination, but this area had no desalination plants in 2005. This does not represent an overestimation of desalinated water production as the region is sparsely populated, and therefore water withdrawal is quite limited compared to the northeastern part of the country. Few AUSD cells are found in the Mediterranean except for a part of Libya, which is consistent with the findings in Sect. 2.4 that the fraction of desalination production to water withdrawal was relatively low in this region.

The simulated AUSD cells of SDM2 are shown in Figure 4b. AUSD cells were extensive not only in the Arabian peninsula but also in the Mediterranean region. These regions included the grid cells of the southeastern coast of Spain, western Mallorca, southern Sicily, and northwestern Libya, which agreed well with the actual distributions of major desalination plants (Fig. 1). In general, the AUSD cells of SDM2 were concentrated near the large cities, as compared to that of SDM. Although SDM2 performed well, particularly in the Mediterranean coastal regions, the AUSD cells of SDM2 differed from the actual situation in some cases. First, AUSD cells expand in large parts of the coastal regions of California in the USA (see Fig. S5a). Desalination plants exist in the region, but they produced marginal volume in 2005. Although the grid cells for California were categorized as a water-stressed area under the WWR index, in reality, water is effectively transferred long distances owing to California's long history of intensive water resource development. This implies that inter-grid water transfer should be taken into account when WWR is calculated. Another example is that, in reality, there are no plants at the southwestern edge of the Italian peninsula, but they do exist in the central northern coast of Algeria; however, the AUSD cells of SDM2 show the opposite. The geographical distributions of desalination plants reflect various local circumstances and it is difficult to estimate the AUSD grid by grid.

Because the stand-alone SDM2 model is unable to estimate the volume of production, the results from SDM are discussed hereafter. Table 2 includes the global and national volumes of desalinated water production for 2005 estimated by SDM. First, global total production and capacity of seawater desalination were estimated at 2.8 × 109 and 3.5–9.4 × 109 m3 yr-1, respectively. Note that the wide range in capacity reflects the production-to-capacity ratio included in Assumption C. The reported total global plant capacity in DesalData (5.5 × 109 m3 yr-1) was within the range of the latter. Next, the simulation results for national production agreed fairly well with AQUASTAT (Fig. S2 shows a scatter plot of the data in Table 2). For Saudi Arabia, Kuwait, Qatar, and Oman, the simulated and reported desalinated water production agreed well with AQUASTAT. The simulation for UAE underestimated the data from AQUASTAT. This was largely attributable to an inconsistency within AQUASTAT, in which desalination production exceeds the total of municipal and industrial water withdrawal. The severe underestimation in Spain and Israel was mainly due to lack of AUSD estimation; there were no AUSD cells in Spain, and only one grid cell in Israel. Note that we could not perform the calculations for Bahrain because the area of land could not be resolved in our model.

At this stage, SDM has been validated mainly based on the spatial extent of areas and total volume of desalinated water production in 2005. Although a systematic validation of the temporal dynamics of desalinated water was hampered mainly by the lack of access to long-term data on socioeconomic conditions and water use, a simple validation was performed and is shown in Fig. 5. Conditions A–C and Assumptions A–C in SDM indicate that AUSD cells vary over time, due to changes in municipal and industrial water withdrawal, because the other factors are unchanged during the time frame of a few decades. Figure 5 shows the relationship between national desalination capacity and municipal and industrial water withdrawal in AUSD cells for different periods for 1980–2005 (the methods' summary is given in the Supplement). In general, the plots are located near the diagonal line. This supports Assumption B in SDM that the growth in municipal and industrial water in AUSD cells is sustained by seawater desalination. Exceptions are the cases of Spain and UAE. As we have mentioned several times above, AUSD cells in Spain are not well reproduced in this study. Although desalination capacity substantially increased in UAE during the period, AQUASTAT reported little increase in municipal and industrial water withdrawal. Taking into account the marked economic growth in UAE during the period, we inferred that water withdrawal would have grown more than reported in AQUASTAT.

In summary, SDM was validated from three perspectives: geographical extent of AUSD cells (Fig. 4a), total desalinated water production in 2005 (Table 2 and Fig. S2), and temporal change in production (Fig. 5). The simulated regions that rely largely on seawater desalination were well reproduced, as compared to earlier studies referred to in the Introduction section. The regions are typically hyper-arid coastal regions where it is difficult to find alternative water sources. SDM also reproduced the reported volume of desalination production fairly well in the major countries. Because such countries dominate global water desalination, SDM also captured the total global volume reasonably well. Although SDM and SDM2 advance our resources for modeling global desalination, the results conveyed uncertainties, which can mainly be attributed to the limited availability of data and the simplicity of the model structure, similar to the future simulations described below. SDM2 was validated only for the geographical extent of AUSD cells. The performance was promising because it reproduced reasonably well the present distribution of major plants.

For future simulation, we mainly report the results of SDM because it produced outputs of both AUSD cells and the volume of desalinated water production. Figure 6 shows the estimated spread of AUSD cells at present and in 2055 under SSP1, SSP2, and SSP3 scenarios together with the actual distribution of extra-large desalination plants (capacity ≥ 50 000 m3 d-1) that meet the criteria shown in Table S1 in 2005 and 2014. For all cases in 2055, AUSD cells have expanded considerably compared to the present. The change in AUSD cells can be largely explained by growth in income, with the change in AI due to climate change playing a marginal role. In the case of SSP1, AUSD cells showed marked expansion of grid cells including Baja California in Mexico, northern Chile, the coastline of northern Africa, and southwest Africa. Note that the coastlines on the Caspian Sea in central Asia became AUSD cells, as the inland lake is categorized as a sea. The expansions of SSP2 and SSP3 were somewhat limited compared to SSP1 because income levels in these scenarios were lower than in SSP1 (see Fig. S3). For example, the AUSD cells of SSP1 exclusively include Mauritania, Sudan, and Pakistan. The AUSD cells of SSP2 show no AUSD cells in Australia, which is attributed to wet climate under this scenario. As all SSP scenarios project considerable income growth with national income exceeding 14 000 USD PPP person-1 yr-1 for most countries in the world (Table 1 and Fig. S3), AUSD cells are expected to expand into most of the arid areas in the world by 2055 (compare Figs. 2 and 6).

It is difficult to assess the validity of future projections, but comparing AUSD projections with the present distribution of desalination plants (shown in Fig. 6e, f) can provide some insights. Interestingly, although production in 2005 was not significant, several desalination plants were actually operational in southern Africa and northern Chile, which is consistent with our AUSD expansion. In contrast, although at least one extra-large plant was located in Algeria, Angola, northern China, southeastern India, Japan, Korea, Singapore, Thailand, Florida in the USA, and Venezuela in 2014, AUSD cells did not cover these regions in any scenarios. This was primarily attributable to Condition B in SDM, which excluded non-hyper-arid regions. (As mentioned above, AUSD projections using SDM2 are shown in Fig. S5.) AUSD cells of SDM2 expanded into Algeria, northern China, and southeastern India, which was consistent with the distribution in 2014. AUSD cells did not expand into other east and southeast Asian countries because their AI was too high.

Using SDM, the projected levels of desalinated water production in 2025 and 2055 are 1.4–2.1 and 6.7–17.3 times greater than present, respectively (Table 4). The earlier estimates show a considerable range, but our results are within the range of spread for the reported period of 2015–2025. Only one earlier report was found with projections for the year 2050. Fichtner GmbH (2011) reported that total desalination production would be as high as 96 800 × 106 m3 yr-1, which is more than double our estimate under SSP3. Their projection is based on the assumption that concentrating solar power (CSP) desalination, which is an emerging technology for producing desalinated water without fuel consumption, would extend widely throughout MENA. Although the technical problems are substantial for large-scale installation of CSP desalination plants, the development of new technology may lead to further increases in desalination production. Among the three SSPs, the volume of desalination is greatest in SSP3. This is primarily due to the higher water demand in SSP3, which is accompanied by higher population and lower efficiency (Hanasaki et al., 2013a). The considerable growth in desalination in SSP3 may be perceived as contradictory to its narrative scenario: SSP3 depicts a world of low income and inefficiency; i.e., one in which it will be difficult to adapt to and mitigate climate change. It is also true, however, that the country-based GDPPC grows steadily and considerably in all SSP scenarios. The world in SSP3 is poorer and more fragmented than in other SSPs, but that does not mean poorer than the present day.

Further regional breakdown is illustrated in Table 5. We followed the regional classification of the SSP scenarios, which subdivides the world into 11 regions (see Table S4 for the list of countries). In 2005, 85 % of the production was concentrated in MENA (including all major countries except Spain). The second largest region of production was North America, which requires caution in its interpretation. A total of 409 × 106 m3 yr-1 of seawater desalination in this region was attributed to the AUSD cells of seven grid cells in southern California, USA. In particular, two grid cells including the suburbs of Palm Springs and El Centro were responsible for most of the production. In reality, there was no seawater desalination in these regions as of 2005, and SDM failed to reproduce the real situation for these cases. This does not necessarily mean that SDM is completely unreliable; in fact, several very large desalination plants are under planning in surrounding areas (e.g., the Carlsbad desalination plant in San Diego started operating in 2015). MENA was projected to continue producing the largest volume of seawater desalination in 2025. Several new regions appear in the table, notably Latin America and the Caribbean. The emergence of these countries is mainly due to the GDP per person of Mexico, Chile, and Peru exceeding the threshold of 14 000 USD PPP person-1 yr-1. In 2055, in SSP1, GDP per person will exceed the threshold in two densely populated countries, Egypt and Pakistan, which caused a marked increase in seawater desalination in MENA and southern Asia (ibid). Again, interpretation of these results requires caution. The AUSD cells in Egypt and Pakistan included grid cells through which the Nile and Indus rivers flow, respectively. Although these grid cells are located in extremely dry conditions, it is likely that water is supplied from these rivers to the cells. Assumption B would be not valid for these grid cells; hence, the AUSD cells may be overestimated. To improve the reliability of the projections, the availability of alternative water resources should be evaluated at each grid cell. Such simulations should be implemented when the SDM is fully integrated into global hydrological models with detailed water use submodels, such as the H08 model (Hanasaki et al., 2008a, b).

The economic cost of seawater desalination was estimated for each case (Table 4 for worldwide, Tables S5 and S6 for regions). Adopting the method of Lamei et al. (2008), we estimated the unit production costs at 0.40–3.78 USD m-3 based on the data available for 186 plants globally (see the Supplement for details). As shown in Table 4, the volume of seawater desalination was estimated at 2.8 × 109 m3 yr-1, with a cost of USD 1.1–10.6 × 106, equivalent to 0.002–0.019 % of total global GDP. This number is much higher in MENA, with values of 0.032–0.306 %. Among the scenarios, SSP3 in 2055 showed the highest numbers at 0.011–0.100 % globally and 0.121–1.147 % for MENA. This was mainly attributable to large water use and low GDP growth in SSP3.

The future projection is sensitive to Condition A (threshold of 14 000 USD PPP person-1 yr-1), Condition B (aridity index of 0.08), and Condition C (three grid cells of seashore). Here, we conducted a sensitivity test on these thresholds. We examined thresholds of 0, 7000, and 24 000 USD PPP person-1 yr-1 for Condition A. A threshold of 7000 USD PPP person-1 yr-1 implies further reduction in cost due to technological change, while 0 implies that seawater desalination economically outperforms traditional water resource development in arid regions. The threshold of 24 000 USD PPP person-1 yr-1 was taken from the GDP per capita of Israel, one of the non-oil-producing nations in Table 2. Present Condition A was taken from the GDP per capita of Libya, which is an oil-producing nation. We considered that the threshold for oil-producing nations may be lower than for other countries due to massive consumption of fossil fuels for desalination. Similarly, we tested thresholds of 0.15 and 0.2 for Condition B, which expanded the potential area for AUSD cells (see Fig. 2), and two and four grid cells of seashore for Condition C.

The results of the sensitivity tests are shown in Fig. 7. First, a higher threshold of GDP per capita decreases the total desalination production due to reduction in AUSD cells. For the base year (2005), there is a gap between 0 and 7000 USD PPP person-1 yr-1. In contrast, there is no change in SSP1 between 0 and 14 000 USD PPP person-1 yr-1, as GDP per capita exceeds 14 000 for most countries (see Fig. S4). The large drop between USD 14 000 and 24 000 for SSP3 indicates that in this scenario a large number of countries cannot exceed a GDP per capita of 24 000 by 2055 (i.e., the growth in GDP per capita in SSP3 is considerably slower than in the other scenarios). The discrepancies among SSPs are attributable to differences in water use. Hanasaki et al. (2013a) projected the lowest water use for SSP1 due to rapid decreases in municipal and industrial water use intensity, with the opposite being true for SSP3. The sensitivity test of AI showed a linear response (only the results of SSP1 are shown in Fig. 7) due to gradual changes in AI (see also Fig. 2) and grid cells of seashore. Desalination production expands by increases in AI and the grid cells of seashore. The expansion was not proportional to the change in AI and the number of grid cells reflecting the complex geographical distribution of AI and shape of the coastline.

In 2005, the global total for industrial and domestic water withdrawal was reported to be 1170 km3 yr-1(AQUASTAT). In this study, desalination production was estimated at 2.8 km3 yr-1 for these two purposes, accounting for 0.24 % of the total. As shown in Table 1, water withdrawal will change considerably in the future. In the case of SSP1, which depicts a sustainable world, the projected water withdrawal is 1142 km3 yr-1 in 2055, showing almost no change from the present. However, in SSP3, which depicts a fragmented world, withdrawal will be more than double and reach 2831 km3 yr-1. The estimated seawater desalination production levels are 18.7 and 48.6 km3 yr-1 for these scenarios, accounting for 1.6 and 1.7 % of the global requirement, respectively. Although this portion appears small, desalinated water plays a critical role in AUSD cells. The population in the AUSD cells is estimated at 12.8 million in 2005, but by 2055, it is expected to increase to 138 million in SSP1, and 170 million in SSP3. The substantial increase in number was mainly attributable to AUSD cells extending into densely populated northern Africa and part of south Asia. As the AUSD cells are located in extremely dry regions, vulnerable to water scarcity, it is crucial to secure municipal and industrial water for water security and human well-being in AUSD regions. Moreover, the estimated geographical extent of present and future AUSD cells largely overlap with regions where water resources are projected to decrease due to climate change, typically in the Mediterranean (Jiménez Cisneros et al., 2014).

The SDM model estimates AUSD cells and the volume of desalinated seawater based on three conditions and three assumptions. The results demonstrate that these conditions and assumptions allow us to successfully simulate seawater desalination in accordance with the purpose of this study. Here, each condition and assumption is revisited and key uncertainties are discussed.

Conditions A and B, which set thresholds on national average income and aridity, explain the present distribution of major desalination plants and regions that are dependent on seawater desalination. It should be noted that countries meeting these conditions include major oil-producing countries. Seawater desalination has high energy consumption costs, even with the application of the latest technology. Hence, the price of energy is an important factor in the installation of desalination plants. Although we confirmed that non-oil-producing countries such as Spain and Israel had considerable desalination capacity, attention should be paid to the projected newly emerging AUSD cells in non-oil-producing countries under the SSP scenarios, such as Chile, Namibia, etc. The income threshold may differ for these nations compared to major oil-producing countries because of differences in energy prices. These regional biases cannot be completely eliminated from our model simulations and validation because the majority of desalination plants have, so far, been constructed in the Middle East. It should also be noted that we fixed the thresholds for income and aridity according to Conditions A and B throughout the study period. This corresponds to the assumption that technology and costs of production are essentially fixed at present. Advances in technology would likely further lower the production costs, which would alter the threshold for plant installation (e.g., Ghaffour et al., 2013; Ziolkowska et al., 2015).

Condition C, which sets the maximum distance from the seashore for AUSD cells, plays a crucial role in the simulated volume of desalinated water. Desalinated water can be used at large distances from the seashore if transportation costs are affordable. Assumption B, or 100 % dependence on desalination in AUSD cells, is probably the largest uncertainty in the SDM. Although surface water is unreliable under super-arid conditions in AUSD cells, the dependence is influenced by the availability of other water sources, typically rivers, groundwater, and sometimes long-distance water transfer (Lamei et al., 2008). Recycled water is another emerging source of freshwater in water-scarce regions. For example, Singapore has been strongly promoting recycled water usage, which is economically more efficient than seawater desalination due to Singapore's stringent waste water quality control and appropriate infrastructure (Tortajada, 2006). In contrast, major desalination plants are occasionally implemented in relatively wet regions, e.g., on islands that are characterized by relatively small catchment areas, limited storage capacities, and large temporal variations in water demand. Such regional details are beyond the capability of present global hydrological models, but may substantially affect the results in some places.

In this study, we used the future water use projection of Hanasaki et al. (2013a) based on empirical relationships between water use and population and electricity production excluding regional details, and therefore projections for individual nations include substantial uncertainty. The spatial distribution of water use is another source of uncertainty. Historical and future water use are obtained first at the national scale, and then converted into grid cells under various assumptions. This study adopted the assumption that the spatial distribution of municipal and industrial water use is proportional to that of population. We note that supply and demand are interconnected: seawater desalination relieves the availability of water constrained by hydrology. Increases in water availability may enhance water consumption. This may alter the future situation substantially from the historical past on which the water demand projections of Hanasaki et al. (2013a) were based. Water use projections substantially differ among models and a systematic model intercomparison is under way (Wada et al., 2016).

Finally, we summarize the limitations due to the preconditions of the SDM model. First, SDM was designed to be incorporated into GHMs, typically simulated at a spatial resolution of 0.5∘ × 0.5∘ (approximately 55 × 55 km at the equator). It is impossible to resolve individual plants with this spatial scale; hence, this is outside the scope of this model. Second, although the cost of desalination and its difference in cost to alternative sources play a crucial role in desalination projects in reality, this price mechanism is not included in the present formulation of SDM. Third, partly as a consequence of the previous factor, SDM is unable to analyze the effects of technological advances and subsequent cost reductions on the introduction of new desalination plants to regions with wetter climates and lower incomes. The results of the sensitivity test of changing the threshold of Condition A (minimum GDP per capita; Fig. 7) and Condition B (maximum AI) provided us with several useful insights, but further investigations are necessary to assess the combined effect. Fourth, the availability of alternative water resources cannot be estimated by the stand-alone SDM model. Such analyses would be feasible if we combined SDM2 with a global hydrological model that explicitly simulates renewable/fossil groundwater. Fifth, the thresholds in SDM were fixed throughout the simulation period. The above-mentioned factors, namely the relative cost of desalination relative to alternative water sources, technological advances in desalination, and availability of alternative water sources, might change the thresholds in the future. Sixth, the conditions and assumptions used for future simulations were independent of the narrative scenarios of the SSPs. Reflecting the conditions and assumptions in the narrative scenarios would enhance the consistency between our study and the SSPs (e.g., SSP1 depicts a world of sustainability; hence, conventional energy-intensive desalination plants would not be favored). Seventh, in general, the performance of SDM is highly dependent on the availability of data. In this study, we mainly used datasets with global coverage (DesalData and AQUASTAT), and reports published by academic and governmental institutions written in English. Reports published by the private sector and written in local languages were not collected due to limitations in capability and resources. International collaboration would be needed to enable systematic collection of further data.