If the future amount of available water in a nation is reduced by climate change and falls below the requirements of production, then this production can no longer be sustained. On the other hand, the effect of increased water availability is much harder to predict, since production is not limited by water availability only. In many instances, the market demand for a product is the main limiting factor (Mankiw 2014). Since our focus is the compatibility of present-day water consumption and trades with future water availability within an otherwise unchanged setting, we restrict our analysis to the effects of reduced future water availability. Beneficial effects of the projected spatially redistributed and thereby in certain regions increased water availability are not taken into account, since these depend not only on climate but also on future economic and political choices. Despite this omission, our analysis allows us to investigate the sustainability of present-day water trades with regard to future patterns of water availability, as described below.

In the accounting scheme of figure 1, the left column shows that the water footprint within the nationʼs area, , consists of the water used for domestic production and consumed by the nationʼs population (internal water footprint of national consumption, ) as well as the virtual water in domestic products which are exported to other countries, . Similarly, the imports of virtual water (middle column), split into the external water footprint of national consumption , that is the virtual water which is imported for consumption by the nationʼs population, and the imported and re-exported virtual water, , where is a simple closing entry in the water budgeting (Mekonnen and Hoekstra 2011). Total national consumption (top row) consists of internal and external water footprints, .

We use the present-day (1996–2005) national water footprints and bi-lateral virtual water trades from Hoekstra and Mekonnen (2012) for blue and green water, which are partly available from the WaterStat database at www.waterfootprint.org (accessed December 2013). This database poses several challenges to our analysis.

First, it does not contain all components of the virtual water accounting for all countries, especially the footprints of consumption are not available for several countries.

Second, while for industrial products the national consumption footprint was derived as (top-down approach), for agricultural products (which account for the bulk of the water footprints globally, see figure S1 in the Supplementary Materials) the virtual water trades are determined for each product individually and summed up to obtain the national consumption (bottom-up approach, see Hoekstra and Mekonnen 2012 for details). As described in van Oel et al (2009), top-down accounting is sensitive to inaccuracies in trade data, especially for nations with large trade volumes relative to their domestic production, while bottom–up accounting relies directly on consumption data. Inconsistent data streams from incomplete or inaccurate reporting on production, consumption and international trade per country can lead to different footprints from top–down and bottom–up accounting, respectively. In particular, for the bottom–up accounting of agricultural products, the budget of the individual virtual water components can be unclosed, which is not the case for the top–down derived virtual water budget of industrial products. Different product categorisations in different data streams add to the accounting challenges and may lead to double counting of the virtual water in different products, although this has been eliminated as far as possible (see Hoekstra and Mekonnen 2012 and references therein). Inconsistent data bases lead for a few countries to violation of the required inequalities and see figure 1).

A further limitation of this database lies in the lack of temporal dynamics. We therefore cannot consider the temporal representativity of the 1996–2005 averages in our analysis, which might partly explain the detected inconsistencies. While earlier studies (e.g. Carr et al 2012) show that the network of virtual water flows has evolved substantially over time with many trade connections appearing and disappearing every year, one should keep in mind the challenges that already arise when computing the here used decadal averages. These challenges are even more relevant for shorter time scales and potentially compromise a thorough assessment of the temporal representativity. In our study we take the water footprint database as an 'average snapshot' of the present day situation and investigate whether this 'average snapshot' could as well exist under future water availability patterns.

Since our accounting requires knowledge of all components, we can only analyze the 173 countries with complete records. Removing the incomplete countries, however, introduces inconsistencies in the remaining countries, for example if the external consumption of a country depends substantially on the imports from one of the countries which are removed. This does not limit the investigation of local water demand versus local water availability, but affects the national water consumption through potentially inconsistent imports. For most countries, the differences between their imports from all nations and their imports from only these nations with complete records are below 10%. Countries with larger differences are listed in table 1. We do not exclude these countries from the analysis but highlight them by a stippling in the maps of section 4. Figure S2 in the Supplementary Materials provides histograms of the number of countries per class of relative adjustment and their respective shares of total imports and exports. Globally, the import/export adjustments range between 4% and 8%.

Table 1. Countries with differences between original and adjusted virtual imports (green or blue water). These countries are highlighted in the maps of section 4. Blue imports (Mm3 Green imports (Mm3 Country Complete Adjusted Complete Adjusted Australia 1181 1148 Brunei Darussalam 4470 15483 Burma Cambodia Eritrea Iran (Islamic Republic of) 1496 1330 16625 16509 Jordan Lebanon Maldives Pakistan 2797 2086 14521 14135 Seychelles Solomon Islands Suriname Syrian Arab Republic The former Yugoslav Republic of Macedonia Uganda Yemen 1615 19896

After calculating the adjusted imports and exports of each nation considering only the trades between nations with complete records, we recompute the blue and green water footprints of total national consumption as (the top–down approach). This ensures closed virtual water budgets.

We finally balance-adjust the internal and external footprints of national consumption ( and ) such that they balance the adjusted total footprints of national consumption while keeping their ratio unchanged. We further ensure that and do not exceed the within-area footprint and imports , respectively. Details and further discussion are provided in section S3, Supplementary Materials. We use only the adjusted footprints and therefore omit the 'adj'-superscripts.

The effects of all adjustments (for removal of incomplete countries, unclosed water balances, violated inequalities) on the water balance components are substantial for a number of countries, reflecting the inconsistencies of the data sources from which the water footprints are derived. Differences between adjusted and original consumption footprints are below 10% for less than a third of all countries and below 50% for approximately 80% of all countries (see table 2). In terms of volume, some 80% of most components of the global footprints are affected by adjustments below 25%. Figure S3 in the Supplementary Materials shows that adjustments are of both signs and globally correspond to volume adjustments of below 10% (except for blue water and , for which adjustments amount to 23%). Large relative adjustments concern mainly smaller volumes and do not affect the main water flows across the globe, which are concentrated between a limited number of trading nations (Konar et al 2011). See section S3 in the Supplementary Materials for details. Furthermore, since we are only interested in climate-induced changes of water consumption footprints, their absolute magnitude is less relevant for our purpose.