The gained source–receptor matrices represent the main results of the created dataset. Table 2 specifies the different matrix types, the allocation of source and receptor regions to columns and rows, and the numbers of matrices.

Particularly important is the provision of type 1 matrices within the dataset, as they represent the raw data on a grid cell basis from which any further aggregation to larger land areas of interest could potentially take place. Together with the type 2 (country to grid) and type 3 (basin to grid) matrices, they enable the plotting of evaporationsheds over the whole area of the considered grid. The matrices of type 4 and 5, on the other hand, allow for the generation of self-explanatory source–receptor tables between countries and basins, respectively.

Besides the relevant source–receptor matrices, mismatches within the water balance (Δclosure), as well as all other terms of Eq. (2), are provided within the dataset. Identified mismatches are in general negligibly small for the annual averages (on average 0.03 % for land grid cells) but reach higher values on a monthly basis (on average 12.6 % for land grid cells). Unassigned fractions of moisture were exclusively allocated to losses via the northern and southern boundaries of the model. Thus, system losses due to storage limits play no role at all.

Figures 1 to 3 display the yearly average evaporationsheds for three chosen land grid cells, countries and basins. Based on sample scripts provided within the dataset, these types of figures can be plotted for any land grid cell, country or basin of interest. An additional online viewer can be used to directly look up the plots for any land grid cell. Reprecipitation of evaporated water takes place over the whole considered grid and is expressed as a percentage of the evaporated water from the source region. The threshold for the plotting of reprecipitation within different grid cells lies at 0.02 % from the total amount of the assigned water. Additional information with regard to the location, the total evaporation input into the system (Einput), the unassigned fractions of water and the total share of reprecipitation displayed via the plot are provided separately via the image captions. Monthly information on moisture transfers for the chosen examples are available within the Supplement (Figs. S1 to S36).

Figure 1 shows the evaporationsheds for land grid cells located at Kansas City, USA (Fig. 1a), Delhi, India (Fig. 1b), and Kampala, Uganda (Fig. 1c). It exemplifies different possible shapes and geographical extents of evaporationsheds. The evaporationshed for the source cell at Kansas City sprawls, for instance, over large distances and still does not cover more than 70.0 % of the assigned reprecipitation. The evaporationsheds for the source cells at Kampala and Delhi, on the other hand, cover considerably higher shares of the assigned reprecipitation (79.0 % for Fig. 1b and 88.8 % for Fig. 1c). With regard to the source cell at Kampala, huge amounts of moisture reprecipitate close to the source of evaporation and, thereof, more than 5 % within the source cell itself. Reprecipitation of evaporated water occurs here mainly westwards from the source cell along the equatorial belt and covers huge areas of central Africa. For the other source cells, moisture recycling takes place mainly eastwards (Kansas City) and southeastwards (Delhi) with lower shares of reprecipitation close to the source of evaporation. The tracking of atmospheric moisture for the source cell at Kansas City led to slight boundary losses due to its location near the northern boundary of the model. With regard to Delhi and Kampala, unassigned fractions of moisture due to losses of tagged moisture via the northern or southern boundaries are negligible.

Figure 2 displays evaporationsheds for the example countries Brazil (Fig. 2a), Egypt (Fig. 2b) and Laos (Fig. 2c). Brazil shows a non-fragmented evaporationshed with a huge amount of moisture recycling occurring within the country itself. Egypt's evaporationshed is fragmented, with moisture recycling taking place close to the equatorial belt, over the Mediterranean, and in the southeast of Europe and Asia. However, hardly any reprecipitation occurs within the country. The evaporationshed of Laos is again non-fragmented, with the main areas of moisture recycling in Southeast Asia, over the surrounding sea or in China.

Figure 3 presents the example evaporationsheds for basins referring to parts of the Rio Grande (Fig. 3a), the Danube (Fig. 3b) and the Murray–Darling (Fig. 3c) basin. Core areas of moisture recycling are Central and North America (Fig. 3a), the equatorial belt and huge parts of Eurasia (Fig. 3b), and northern and eastern Australia and the South Pacific Ocean (Fig. 3c). Displayed evaporationsheds are large while covering only 59.4 % to 70.1 % of the assigned moisture recycling.

Besides the visualization of evaporationsheds, the dataset enables a direct quantification of average moisture transfers between countries or basins within source–receptor tables. This aspect refers to the latter two matrix types (type 4 and 5). At this point, type 4 matrices (countries) are used to demonstrate the usage of both types of matrices. Table 3 shows the fate of evaporated water and the sources of precipitation for the selected countries. For comparative purposes, the same countries are displayed as for the plotting examples in Fig. 2. The presented information is in each case limited to the top 10 sites of reprecipitation and the top 10 sources of precipitation. Values are provided in percent and are related to the total amount of the evaporation or the precipitation input.

The presented shares with regard to the fate of evaporation are in line with the visualization of evaporationsheds in Fig. 2. For Brazil, the highest share of reprecipitation takes place within the country (43.6 %). With regard to Egypt and Laos, the highest share of evaporated water reprecipitates over the sea (Egypt: 31.3 %; Laos: 44.5 %). Concerning additional information on the origin of precipitation, Table 3 highlights the following: in all cases the sea is the biggest source of precipitation with values ranging from 63.3 % (Brazil) to 76.6 % (Egypt). With regard to Brazil and Egypt, the most important terrestrial source of precipitation is the country itself (Brazil: 28.9 %, Egypt: 2.7 %). The most relevant terrestrial evaporative source for the precipitation in Laos is Thailand, which supplies on average 6.4 % of the local precipitation.

The introduction already provided a broad overview on various uses of numerical moisture tracking. In the following, which of the named applications our created dataset could be particularly suitable for will be summarized. The first presented application referred to an increased knowledge on how regions of interest are dependent on the moisture supply from other regions. The provided dataset could provide valuable information to answer those questions but shows the following limitation: while the dataset includes comprehensive information on the fate of evaporation, information regarding the sources of precipitation is limited to land areas and cannot displayed across the whole grid of land and sea cells. The reason for this is the chosen tracking direction (forward in time) and the focus on land grid cells for the tracking in order to reduce to computational efforts. Nevertheless, the dataset quantifies the amount of precipitation originating from the sea without knowing the exact non-terrestrial source locations. Examples for this were given in Table 3.

The second presented application was related to predictions of potential impacts of human-induced land cover changes on the water cycle. The created dataset could serve as an estimate for the question how land cover changes and altered amounts of land evaporation would potentially affect the supply of water via reprecipitation elsewhere (Keys et al., 2012). Van der Ent et al. (2010) stated within this context that decreasing evaporation (e.g., via deforestation) for areas with high shares of moisture recycling over land “would enhance droughts in downwind areas where overall precipitation amounts are low”. The opposing statement to that would also be conceivable – namely that increased land evaporation in these areas could also result in positive water supply effects. Such first-order estimates are relevant in the context of socio-hydrology (Keys and Wang-Erlandsson, 2018; Sivapalan et al., 2012), but we highlight at this point that the dataset can generally not provide more than rough estimates regarding this topic. An exception could be the inspection of interannual data for sites where major land cover changes occurred within the covered time period. However, for more comprehensive information on this subject it is advised to apply atmospheric moisture tracking directly to different land cover scenarios.

With regard to the third stated application, sustainability studies and water footprinting, the provided dataset also shows promising usage possibilities. Knowledge of the fate of evaporation was firstly integrated within the method of water footprinting by Berger et al. (2014, 2018) via an enhanced water accounting method. This considered atmospheric moisture recycling ratios within drainage basins, which could reduce water consumption patterns significantly (Berger et al., 2014, 2018). Aspects of moisture recycling across basin boundaries have not yet been considered. Comprehensive information about the fate of land evaporation in the dataset could be used for research regarding this topic.

The fourth possible application was related to research on the variability of precipitation and included seasonal and interannual variabilities. As the dataset provides both monthly data averaged over the considered time period and interannual data, it shows a high suitability for this kind of usage. Limitations with regard to the usage of seasonal data could be related to possible mismatches in the water balance, which should be verified before usage. However, for the yearly averages those mismatches become negligibly small. The application of studying interannual variability, on the other hand, is limited to the covered time period (years 2001 to 2018).

Precipitation changes and trends represented the fifth application focus. The dataset can be used in this context to understand changes and trends of moisture recycling for the considered time period, whereas predictions into the future are not possible. The sixth and seventh application were related to impacts of climate change on the hydrological cycle and the understanding of extreme weather events. The usage of the dataset for the determination of impacts related to climate change is limited to changes in climate which are reflected by the reanalysis data considered for this study. However, for a deeper analysis of the relationship between global temperature increases and resulting changes in moisture supply patterns, models including scenario analyses would be more suitable. With regard to the understanding of extreme weather events, the dataset could be used in order to gain an increased knowledge of the causes for past droughts. This could be achieved via investigations into anomalies of moisture supply patterns for relevant locations and time periods covered by the model. Investigations into extreme weather events such as floods, on the other hand, are not possible with this dataset as those would require a modeling with higher spatial and temporal resolutions.

The following section deals with the critical reflection on the ERA-I data (Berrisford et al., 2011; Dee et al., 2011), which were used as input for the creation of the dataset. ERA-I, which has been updated during the process of the preparation of this article to ERA5 (Hersbach et al., 2020), “showed both a comparatively reasonable closure of the terrestrial and atmospheric water balance as well as a reasonable agreement with observation datasets” (Lorenz and Kunstmann, 2012). It has been frequently used to study the hydrological cycle (Li et al., 2019) and ranks among the best representations of the hydrological processes within the atmosphere (Gao et al., 2014; Lorenz and Kunstmann, 2012). However, within the past some biases were also reported, especially with regard to the variables of evaporation and precipitation (Bumke, 2016; Fu et al., 2016). Plots for these two variables are presented as daily averages in Fig. S37 of the Supplement. Moreover, we provide a grid-cell-based comparison between ERA-I and its successor version ERA5 in Fig. S38 of the Supplement. This revealed that the variations in evaporation (Fig. S38, part a) and precipitation (Fig. S38, part b) between the two data sources are relatively small in most regions (≪1 mm). The differences in precipitation (Fig. S38, part b), however, can also take higher values of up to 2, 3 or even more than 4 mm d-1 for a few connected regions. Those can mainly be found within the high-precipitation areas of the tropics and along the western coast of North and South America. Considering that ERA5 claims in particular an improved performance over land in the deep tropics (ECMWF, 2020; Hersbach et al., 2020), precipitation in ERA-I might be slightly overestimated (e.g., in Central Africa) or underestimated (e.g., on Borneo) for some of the tropical regions.

Next to the grid-cell-based comparison of ERA-I to ERA5, we provide an additional analysis on continental scales. This compares the average continental evaporation and precipitation of ERA-I to ERA5 and a study by Rodell et al. (2015). The latter combined a variety of data sources, such as GPCP v2.2 (Adler et al., 2003), SeaFlux v1.0 (Clayson et al., 2012), MERRA (Bosilovich et al., 2011), MERRA-Land (Reichle, 2012) and GLDAS (Rodell et al., 2004), to derive an observed state of the water cycle in the early 21st century. Methodological details regarding the comparison can be reviewed in the Supplement. Table 4 presents the derived results, which cover all continents except Antarctica plus the overall global land, global ocean and the Earth as a whole. We stress that a final conclusion on which dataset is closest to reality is regarded as out of the scope of this paper. We can, however, conclude that repeating our analysis with ERA5 would overall not lead to major differences. This is due to the fact that both the continental comparison (Table 4) and the grid-cell-based comparison (Fig. S38) between ERA-I and ERA5 revealed generally high similarities for most regions. The comparison to Rodell et al. (2015), on the other hand, led to more significant differences. Table 4 demonstrates that the intensity of evaporation over land in both ERA-I and ERA5 seems overestimated compared to Rodell et al. (2015), especially in Australia (up to +52.7 %) and Eurasia (up to +21.6 %). A similar trend can be observed regarding the variable precipitation, where, except for North America and Australia, ERA-I and ERA5 show consistently higher values. With regard to precipitation over Australia, however, an opposing trend is visible. Here, ERA-I and ERA5 might underestimate precipitation over land, which would be in line with findings made by Fu et al. (2016) for this region.

Logically, at the end of this discussion, the question arises as to what users of the dataset could do if they find the ERA-I evaporation or precipitation data unreliable while, at the same time, more representative data is available. In this case, we recommend to solely use the relative source–receptor relationships of our dataset while plugging in their own data regarding the absolute values of evaporation and precipitation. This assumption will likely be satisfactory in cases where all data are equally biased, but when only certain areas are considered biased a correction procedure would be more complicated.

At this point, a general comparison of our dataset to the existing one referring to the Lagrangian 3D quasi-isentropic back-trajectory (3D QIBT) method (DelSole and Dirmeyer, 2012; Dirmeyer et al., 2009) forced with the NCEP-DOE AMIP-II reanalysis (R-2) (Kanamitsu et al., 2002) and CMAP data (Xie and Arkin, 1997) is given. Next to a slightly higher spatial resolution (1.5∘ compared to 1.9∘ resolution), the results of our study are easier to access due to the publication of raw data and aggregated data in a public repository (ready-to-download data). An advantage of the dataset based on the 3D QIBT method, on the other hand, is a longer considered time period (25 to 18 years). A significant difference lies in the tracking direction of the two approaches. The 3D QIBT approach generally traces moisture backward in time, and its application led to comprehensive information on the sources of precipitation. By contrast, our study focus was on analyzing the fate of evaporation, which was realized through a forward tracking of atmospheric moisture. The different tracking directions led to different opportunities for the plotting of atmospheric watersheds. Our dataset enables the plotting of evaporationsheds over the whole considered grid of land and sea cells, whereas the plotting of precipitationsheds is limited to the areas of land. Vice versa, the dataset based on the QIBT method enables the plotting of precipitationsheds over the whole considered grid, whereas the plotting of evaporationsheds is limited to land cells. In order to exemplify differences of the study outputs, study results on a country level from Dirmeyer et al. (2009) were compared to the results of our dataset based on the following two data items:

terrestrial evaporative source (TES is the fraction of precipitation that originated as evaporation from terrestrial sources) according to Dirmeyer et al. (2009),

Next to general trends, different country compositions can be observed within the lists of the two datasets. Table 5 highlights that only 3 out of the 10 countries appear for both datasets within the list of the 10 highest TES values (Mongolia, the Central African Republic and Paraguay). In this context, in each case Mongolia represents the country with the highest share of precipitation originating from terrestrial sources (80.3 % – WAM-2layers and 95.7 % – 3D QIBT). Regarding the countries with the lowest TES values, both approaches list five countries in common (Chile, New Zealand, the Philippines, French Guiana and Portugal) while showing the lowest value for Chile (4.3 % – WAM-2layers and 8.1 % – 3D QIBT). Regarding the CIES (Table 6), high values appear in general for relatively large countries. At this point, 7 out of 10 countries are listed for both datasets within the top 10 (Brazil, Russia, China, DR Congo, Australia, United States and India). The highest value refers to Brazil (28.9 %) for the WAM-2layers method and to Russia (64.7 %) for the 3D QIBT approach. Small CIES values, on the other hand, appear for relatively small countries. Here we find five countries in common (Luxembourg, Qatar, Gambia, Israel and Djibouti), with Luxembourg showing the lowest value in each case (0.2 % – WAM-2layers and 0.4 % – 3D QIBT). The fact that different countries appear in the tables is most likely caused by spatial differences of evaporation, precipitation and wind speed in the underlying reanalysis input data. Differences regarding the tracking method itself, on the other hand, might play a less important role, as WAM-2layers was found to reach generally similar results to Lagrangian models (Van der Ent et al., 2013; Van der Ent and Tuinenburg, 2017). The overall comparison of the results for the TES and the CIES between the two methods including all countries can be gained from the Supplement (Table S2).

Larger overlaps between the two datasets could partly be identified while focusing on the top contributors for precipitation over individual countries. This is exemplified through Tables S3 to S5 of the Supplement, which provide an overview of the top 10 sources of precipitation for the sample countries Brazil, Egypt and Laos with regard to both datasets. The country of Laos in particular shows a relatively high match regarding the appearance of sources and their ranking to each other in this context. A more detailed direct interpretation of the differences in the results between individual countries is at this point regarded as out of scope for this paper but could be tackled by comparative studies in the future.