Does ERA5-land capture the changes in the terrestrial hydrological cycle across the globe?

Changes in the terrestrial hydrological cycle determine the future water availability across the globe with profound impacts in different facets of society. Precise estimation of such changes is vital for the effective implementation of water management policies. Among the numerous data products that describe the hydrological cycle components, ERA5-Land is one of the most increasingly used dataset. Still, there has been no assessment of its ability capacity to represent the water cycle shifts variability over land. This study endeavors to bridge this gap by comparing the magnitude and direction of change in precipitation minus evaporation (P—E) and runoff, as estimated globally by the ERA5-Land data product. Our findings reveal significant inconsistencies in the changes identified, with the climatological mean of P—E decreasing more substantially than runoff for numerous regions. Consequently, ERA5 presents a declining water availability for most of the regions, but the magnitude of change is incompatible to the change between P—E and runoff. To further validate, the estimates provided by the ERA5-Land product, two different hydrologic models (TerraClimate and Global Land Data Assimilation System, GLDAS-Noah) are also utilized. TerraClimate demonstrates a more reasonable alignment between changes in P—E and runoff, followed by GLDAS-Noah, particularly for the arid regions lying in the parts of Northern Africa and Southern Asia, the European continent, and the northern parts of Asia. Inconsistencies remain high for the tropical regions for both data products. Still, the estimates of change in water availability are better represented by the hydrologic model-based data sources for most parts of the globe, especially for the regions with low precipitation, such as the regions with arid and continental climates. Our results imply that ERA5-Land should be used with extreme caution when assessing the long-term changes in the terrestrial water cycle. Additionally, pinpointing the regions of the highest bias can help to improve the hydrological coupling of ERA5-Land in future versions of the reanalysis.


Introduction
Change in the terrestrial hydrological cycle, stemming from a warming climate, leads to changes in water availability and modifies the characteristics of hydrological events, especially the extreme events.Changes in the terrestrial hydrological cycle can be quantified by analyzing the changes in water availability which is a primary focus of the scientific community (Ohmura andWild 2002, Allan et al 2020).The nature of change (acceleration or dampening) depends on a plethora of hydrometeorological variables interacting in complex ways (Huntington 2006, Yeh andWu 2018).Given the complexity associated with such processes, significant uncertainties are observed in the quantification of such changes mainly arising from two sources.One is the methodological uncertainty from the descriptor used for the representation of change or the statistical framework used to analyze the observed change and the other is the observational uncertainty that lingers in the biases of the meteorological data sets.
Looking into the uncertainty that is manifesting from the descriptor of change; the metrics used for the change quantification are generally derived from the water and energy balance equations (Allan et al 2020).Hence, change in the terrestrial hydrological cycle can be assessed by analyzing the fluxes of the hydrological cycle components, also known as the net water fluxes.Ferguson et al (2018) suggested that change in water availability can be studied from three different perspectives namely, meteorological (precipitation and evaporation), hydrological (surface runoff and river discharge) and agricultural (precipitation minus evaporation).Studies have analyzed the long-term changes in various fluxes like precipitation, total evaporation (amount of water evaporated from the earth's surface including transpiration from vegetation), and runoff (including both surface and sub-surface runoff) to estimate the present and future water availability at different spatio-temporal scale (Milly et  Based on the spatial and temporal scale of analysis, each metric of water availability has its limitations and advantages (Barnett et al 2005, Zhou et al 2021), and significant changes in water availability have been observed in the water (net) fluxes at both regional and global scale (Sophocleous 2004).
The observational uncertainty has also been extensively studied.Different data sets can be employed to study the change in water availability based on the descriptors used for analysis, the spatial and temporal scale of analysis and the perspective of change to be emphasized.At global scale, especially while carrying out a gridded analysis, the more frequently used datasets include the simulations from climate models, satellite-based products, reanalysis products, or similar products derived from observed data (Oki andKanae 2006, van Beek et al 2011).It is also important to mention that sufficiently long series of observed datasets to carry out climatological studies for different fluxes are available for limited regions (Pradhan et al 2015, Dahal et al 2020).A commonly used, alternative data source are the reanalysis products, which combines model data with observations from across the world into a globally complete and consistent dataset using the laws of physics (Jourdier 2020, Tarek et al 2020, Jiang et al 2021, Jiao et al 2021).The most used reanalysis product is ERA5-Land due to its high resolution and long temporal coverage.The product developers claim that ERA5 family products provide a consistent view of the water and energy cycles at surface level during several decades (Hersbach et al 2020, Muñoz-Sabater et al 2021).Even through ERA5 outperforms other alternative data sources (Mahto and Mishra 2019, Jourdier 2020, Vargas Godoy and Markonis 2023b), the limitations associated with the product constrains its usage depending on the research question (Urraca et al 2018, Hou et al 2022).Therefore, it is vital to scrutinize the commonly used and highly recommended products for specific research questions, such as the quantification of the change in the terrestrial hydrological cycle under a warming climate.This forms the motivation for this study.
Our goal is to determine the discrepancies associated with ERA5-Land product in the estimation of the change in the terrestrial hydrological cycle at global scale.Based on the complexity associated with the climatology of a particular region, the performance of the reanalysis products may show high spatial variation in capturing the water availability.The regions showing highest uncertainty when using ERA5-Land product are identified based on the comparison of change in two water availability metrics, which reflect the meteorological (precipitation, total evaporation) and hydrological (runoff) perspective (Ferguson et al 2018).Then, to investigate if there is some systematic error stemming from the climatology/meteorology of the regions with higher inconsistencies, two additional data products are also investigated.

Methodology and data used
The uncertainty associated with using ERA5-Land reanalysis to assess the change in the terrestrial hydrological cycle at global scale is determined by using two metrics of water availability.The principle of water balance states that water entering a system (via precipitation), must be transferred into either evaporation, transpiration, surface runoff, or stored in the ground.Based on this basic principle the net water flux precipitation minus evaporation (P-E) is compared with runoff (R).These fluxes are defined based on the simplified form of the water balance equation (P − E = R) where the change in storage is considered negligible (Pradhan et al 2015, Zhang et al 2016, Greve et al 2018).The nature of change, in terms of direction and magnitude at the climatological scale, in the two metrics is analyzed for the period of 1960-2019.The period of analysis is divided into two 30 year intervals (T1: 1960-1989 and T2: 1990-2019) and the statistical parameters of the data for the two intervals are compared to assess the change in water availability.All the statistical analyses were performed in R (Vargas Godoy and Markonis 2023a), and for the basin aggregations, as well as the global precipitation data preprocessing, the pRecipe package was employed (R Core Team 2022).

Performance of the ERA5-land product
The ERA5-Land product is available in gridded format with a spatial resolution of 0.1 • × 0.1 • for the period of 1950-present (Muñoz-Sabater et al 2021).The long-term mean, also referred to as the climatological mean, for the period of 30 years is evaluated at each grid point considering both the metrics (P-E and R).The percentage change in the climatological mean between the two-time intervals is estimated with respect to T1.It may be hypothesized that the direction and magnitude of change in the climatological mean of the two metrics should be similar for each grid point.For instance, increase in long-term mean of P-E at a particular location can be interpreted as increase in water availability.Thereby, there should be similar increase in the long-term mean of runoff and ground storage following the principle of water balance.To test the above-mentioned hypothesis, the direction and magnitude of change in the two metrics is compared.Based on the direction of percentage change in the two metrics the grids are divided into five different categories (details provided in table 1).The grids lying in the first four categories need to be studied more closely to interpret the difference in the behavior of P-E and R. The analysis is extended further to determine the climate regions, based on the Koppen-Geiger (KG) climate classification (Beck et al 2018), showing higher inconsistencies.The percentage of grids falling under the abovementioned categories and five main climate groups (A: tropical, B: arid, C: temperate, D: continental, E: polar) is estimated.Lastly, for closer observation some specific regions and basins are selected that consist of grids falling in different categories (Z1, Z2, Z3, Z4 and Z5).In addition to the percentage change in the climatological mean of the two metrics, the lower (0.10 and 0.25) and higher (0.75 and 0.90) quantile values are also examined to further partition the uncertainty in representing the change of the terrestrial hydrological cycle.

Comparison of ERA5-land product and hydrologic model-based products
Comparison between the long-term means of P-E and R, is also carried out using two more data sources, namely TerraClimate (

Results
The change in the water availability metrics based on the difference in the climatological mean for the two intervals for ERA5-Land, TerraClimate, and GLDAS-Noah is presented in this section.

Performance of the ERA5-land product
The comparison of percentage change in the climatological mean of P-E and R for the two intervals (T1: 1960-1989 and T2: 1990-2019) indicate that more than half of the grids show some inconsistency even though, the global pattern of mean water availability in terms of net water flux and runoff and water cycle fluxes (precipitation and evapotranspiration) are well-represented by the ERA5-Land product (figures 1, S1, S2).For instance, for northern Africa the net water flux shows a 10%-25% increase whereas the runoff shows a decrease of more than 50% (figure 1; last row).For most of the regions in the temperate zone of Asia and North America, the decrease in net water flux (>40%) is much higher as compared to runoff (0%-20%).Similarly, in some parts of Central Asia, the increase/decrease in the net water flux is much higher compared to the runoff.The classification of the grids into five categories representing the change in fluxes (as described in section 2.1) shed light to the observed inconsistencies (figure 2).Most of the grids with the highest discrepancies can be found in the arid parts of Asia, Africa, and North America.About 11% of the total grids lie in the Z1 and Z2 categories over arid climate, violating the water mass balance.For the tropical, temperate, and continental regions, the highest fraction of grids lies in Z4 (the decrease in P-E is higher than the decrease in R) with a percentage of 8.5%, 8% and 15%, respectively.
To assess the inconsistencies more closely, four different regions are selected as shown in figure 2. These regions have unique climatological/meteorological characteristics based on their geographical location and different types of inconsistencies are observed for each region.The percentage change in the two metrics comparing the periods T1 and T2 for the four regions is shown in figure S3.Additionally, individual grid points are selected from each region and the variation in P-E and R over the period of 60 years along with the climatological mean for the two intervals are shown in figures S4-S7.These individual grid points are selected as examples and represent the overall climatology of the respective region.The monthly variation in the residual which is defined as (P-E-R) and the ratio of the residual to the water entering the land-surface system in terms of precipitation i.e. (P-E-R)/P are also shown in figures S8-S11.The first grid point examined (figures S4 and S8) lies in the eastern part of Africa and is classified as Z2 as the net water flux increased (∼49%) and the runoff decreased (∼11%).It is evident that very few precipitation events generate runoff, with most of them occurring in T2.The variation of the residual values is much higher in T1 as compared to T2.It is surprising that after 2010 the runoff remains close to zero, except for a single extreme event, even though there were numerous months with  E, but an increase in R. Similarly, Z2 category, there are the grids with an increase in P-E but a decrease in R. Z3 category involves the grids with an increase in the mean of both metrics but, the increase in R is higher than the increase in P-E.Likewise, Z4 category contains the grids where the decrease in P-E is larger than the decrease in R. All the other regions are represented by Z5 category.Four regions representing different climatology have been highlighted for further discussion.Additionally, the percentage of grid points per category and climate region (KG Classification) is also shown.
high positive values of net water flux.Similar inconsistencies can be observed for the dry, desert, and hot arid regions in Northern Africa and Southern Asia.A more realistic behavior is reported over a grid point of Z5 category found in the Indian subcontinent (figure S5).Here, both P-E and runoff increase with comparable magnitude (∼32% and ∼27%, respectively).However, multiple instances of unreasonably low values of (P-E-R)/P may be observed (figure S9).Mathematically such values will be attained only when the value of residual is very high whereas the value of P is very low.This region shows higher seasonality in rainfall and there are months that receive either zero or very low rainfall.Very high values of residual for such months shows inconsistencies in the estimation of the water cycle fluxes.Similar conditions in terms of net fluxes prevail over most of the regions in the Indian subcontinent, as well as the northern parts of South America and the eastern parts of North America (figure S6).Europe and Northern Asia are dominated by grid points belonging to the Z4 category, i.e.P-E declines more than runoff.A sample case in Central Europe can be seen in figure S6 with the decrease in the P-E being around 26% and the decline in runoff being almost half.The reason can be found in similar inconsistencies to the ones observed in figure S3.It is also interesting to note that unreasonably low values of (P-E-R)/P are observed for regions with comparatively high seasonality.To further investigate the abovementioned point, climatological mean and median of (P-E-R)/P and mean of (P-E-R) for the entire globe is shown in figures S12 and S13.Except for a small region in Africa, the frequency of zero/nearzero values are higher when considering (P-E-R)/P.Whereas, unreasonably high negative values of the mean may be observed for the regions lying in the tropical belt.In such cases, the value of P and P-E are very low, but a reasonably high runoff may be observed.Additionally, the mean value of (P-E-R) is almost negligible for most of the regions.In general, incompatibility is observed between the high/low values of P-E and runoff leading to difference in the climatological mean change between the two metrics.This implies that the primary reason for the difference in the direction and magnitude of change in P-E and runoff could be found in the high/low values of the water cycle fluxes.To further investigate this point, we also estimated the 0.1, 0.25, 0.75, and 0.9 quantiles for the four selected regions (figures S13 and S14).Results indicate that the primary reason for the difference in the direction and magnitude of climatological change in P-E and runoff could be explained by the inconsistencies in the higher/lower quartile values of the water cycle fluxes.
Grid-wise inconsistencies also raise questions about the ability of the model to represent the water balance at basin-scale.To further investigate this point, cumulative P-E-R monthly residuals from a representative river basin of each region are shown in figure 3. The systematic bias in ERA5-Land becomes even more evident, with totally unrealistic changes over time.The violation of the water budget results to a monotonous, extreme drying for Gulf of Mexico, Mahanadi, and Danube and wetting for Shebelli n Juba.Physical explanation of such abrupt increase/decrease in the value of the residuals is difficult following the principles of water balance.Thereby inconsistencies pertain at different spatial scales and having identified the regions with inconsistencies (Z1-Z4), scrutiny is suggested before assessing the change in net water fluxes using ERA5-Land product for these regions.

Performance of the hydrologic model-based products
As the question about ERA5-Land ability to adequately represent the terrestrial water cycle fluxes remains open, we compared our findings with two data products based on hydrological modeling.TerraClimate appears to perform better as there are almost double number of grid points (∼45%) fully consistent with the water budget closure (Z5; figure S18).Additionally, approximately 10% are classified within the unrealistic categories Z1 and Z2, which is less than half of the ones in ERA5-Land.Similar observations are made for GLDAS-Noah where ∼10% of the grids fall in the unrealistic categories even though the number of grids falling in Z5 remains the same as ERA5-Land.It is easy to observe that the range and the spatial pattern of P-E are similar for all three products (figures S1, S16, and S21).Comparing the precipitation and evapotranspiration fluxes obtained using the ERA5-Land and GLDAS-Noah it was observed that the climatological mean of both the fluxes is on the lower side using the latter for the period of 1960-1989 (figures S2, S17, and S22).This is leading to a drastic difference in the values of percentage change in the climatological mean between the two periods, especially for the northern hemisphere.Using TerraClimate the values of climatological mean of both the fluxes are on the lower side as compared to ERA5-Land.Even though all the three models show similar spatial patterns of change in precipitation with increase in climatological mean over the Northern parts of Asia and Northwestern parts of North America and decrease in most parts of Africa and Eastern part of Asia.A drastic difference in the magnitude of change is observed which is also reflected in the change of water availability index P-E (figure 4).Substantial differences are also observed in runoff between ERA5-Land products and Hydrologic model-based Products mostly in the northern part of Asia, parts of North America, and the tropical regions.In most of these regions, the runoff is higher in the ERA5-Land compared to the TerraClimate and GLDAS-Noah.Furthermore, there are discrepancies in the direction and magnitude of change, with the highest differences observed in the regions with arid climate, the central parts of Asia and some temperate regions of Asia and North America.It is interesting to note that the inconsistencies observed using the ERA5-Land product were also highest in the abovementioned regions.
These results are also evident within the KG classification of the grid points (figures 2, S18, and S23).The high inconsistencies that were observed in ERA5-Land over dry, desert, and hot arid regions of Northern Africa and Southern Asia, Southern Europe, and Northern Asia are absent in TerraClimate.Similar observations were made for GLDAS-Noah except for the European region where the inconsistencies are like ERA5-Land.It is also worthwhile to mention that although most of the regions of North and South America show low/negligible inconsistency when using the TerraClimate product, when considering the Indian subcontinent ERA5-Land and GLDAS-Noah show better performance.These results are further supported by the fraction of grid points falling under the five categories and the five main KG classes.The fraction of grid points in the first two categories and KG Class B decreased from 11% (ERA5-Land Product) to 4%-5% (Hydrologic model-based Products) of the total amount of grid points.Additionally, the climatological mean and median of (P-E-R)/P and (P-E-R) for the entire globe using TerraClimate and GLDAS-Noah data gives more acceptable results as compared to the ERA5-Land product (figures S19, S20, S24 and S25).At basin scale also, the residual values are more plausible as compared to ERA5-Land product for all the four river basins.In general, the regions showing higher inconsistency is the same, but the magnitude of the values is at least 10 times lower.In general, TerraClimate and GLDAS-Noah show lower inconsistencies in the arid and continental regions.

Discussion and conclusions
The ability of various data products to represent the diverse components of the hydrological cycle depends on the nature and the spatio-temporal scale of analysis.In the scope of this study, we place emphasis on the reliability of ERA5-Land in estimating global changes in water availability over the past 60 years.Our results show a notable difference in the spatial pattern of change in water availability when compared to global hydrological model simulations.In accordance with the basic principles of water balance, a reduction in the value of P-E (net water fluxes) should correspond to a decrease in runoff, given that the residual (P-E-R) remains very low or negligible as compared to the total water input into the land-surface system (P) across most of the regions.Furthermore, it is expected that the magnitude of change in P-E and runoff should be comparable at regional scale.However, our analysis reveals substantial disparities when employing the ERA5-Land product across various regions and spatial scales worldwide.
The primary reason underlying these inconsistencies can be attributed to ERA5-Land inability to generate high runoff after high precipitation events (high values of P-E).When examining these fluxes individually, precipitation, evaporation, and runoff, it is evident based on the findings of previous studies the reliability of P and E is higher when compared to runoff (Lehmann et al 2021, Muñoz-Sabater et al 2021).This is also confirmed in our study for precipitation at global scale, where ERA5-Land performs quite well, although TerraClimate slightly outperforms it for most climate regions (figure S26).Still the observational uncertainties remain and becomes even more profound for runoff and evapotranspiration, where purely observational data with global coverage do not exist.Our alternative to overcome this challenge is to investigate instead how well ERA5-Land reproduces the water budget closure.Thus, despite the dataset uncertainties (precipitation) or lack of data (ET, runoff), it is possible to highlight the unrealistic behavior of ERA5-Land both at grid and river basin scale.
This study comes with certain limitation that can fuel future research.The examination of four grid cells and river basins is a simplification and should not be generalized.Although, they can be used for their explanatory value for the potential reasons for the inconsistencies in the ERA5-Land reanalysis, more research is needed to highlight the underlying reasons of the discrepancies.In addition, our study does not investigate ERA5-Land behavior in terms of groundwater or soil moisture storage.If a significant amount of water is infiltrated to the groundwater, then this could explain the different behavior, between runoff and P-E, as well as different land cover types.It would be interesting to further analyze the change in the water availability with respect to the storage component of the water cycle.
While the ERA5 family products are considered a valid proxy of observed data, it is important to note that various studies have identified their limitations in accurately capturing extreme events (Taszarek et al 2021, Bhattacharyya et al 2022, Lei et al 2022).Similar observations are made for other reanalysis products also (Bhattacharyya et al 2022).The tendency to overestimate higher quantile values and underestimate lower quantile values can have substantial impacts to the climatological mean.Consequently, interpretations based on such estimates might not represent the ground reality on water availability across all regions.In light of these findings, we propose the following recommendations for studies related to changes in the hydrological cycle and water availability: • Due to the substantial inconsistencies that have been identified, we do not recommend the use of ERA5-Land product for the study of hydroclimatic variability over dry, desert, and hot arid regions located in Northern Africa and Southern Asia, the European continent, and the northern parts of Asia.• Considering the superior performance of TerraClimate and GLDAS-Noah for the abovementioned regions, utilizing either the mentioned models or alternative hydrological modeling tool may yield improved estimates of shifts in water cycle fluxes.• Given that one of the key factors of change in the hydrological cycle is associated with extreme events, enhanced scrutiny is suggested before using the precipitation, evaporation, and runoff data provided by ERA5-Land.• The discrepancies in water budget closure tend to accumulate over time, which can produce unpragmatic hydroclimatic shifts, such as extreme drying or wetting.Estimating the cumulative budget residual can pinpoint this inconsistency.
Undoubtedly, ERA5-Land represents a significant development in the domain of reanalysis data products.Here, we show which aspects can be further enhanced to fully capture the changes in the terrestrial hydrological cycle, which can lead to a more consistent assessment of the prevailing dynamics of global water availability.We hope that these findings will be considered during the development of the forthcoming ERA6 version.However, in its current iteration, ERA5-Land falls short in reproducing mid-to long-term variations in water availability.This deficiency not only holds profound implications for studies investigating hydroclimatic variability or ecosystem functioning but also bears critical significance at an operational level for water resource management policies and planning.
al 2005, Oki and Kanae 2006, Greve and Seneviratne 2015, Dezsi et al 2018, Markonis et al 2019, Huang et al 2021).Other studies have focused on the net water fluxes like precipitation minus evaporation and runoff or runoff plus change in water storage to assess the water availability (Padowski and Jawitz 2012, Kumar et al 2014, Li et al 2014, Greve et al 2018, Ajjur and Al-Ghamdi 2021, Zhou et al 2021).

Figure 1 .
Figure 1.Comparison of the mean monthly P-E (mm) and runoff (mm) in ERA5-Land for the period of 1960-1989 and 1990-2019.The mean value for the two time periods is compared in terms of percentage change.

Figure 2 .
Figure 2. Comparison of the direction of change (positive/negative) for P-E and runoff.The colors represent five different classes.Z1 category contains the grids showing a decrease in P-E, but an increase in R. Similarly, Z2 category, there are the grids with an increase in P-E but a decrease in R. Z3 category involves the grids with an increase in the mean of both metrics but, the increase in R is higher than the increase in P-E.Likewise, Z4 category contains the grids where the decrease in P-E is larger than the decrease in R. All the other regions are represented by Z5 category.Four regions representing different climatology have been highlighted for further discussion.Additionally, the percentage of grid points per category and climate region (KG Classification) is also shown.

Figure 4 .
Figure 4. Comparison of the mean monthly P-E (mm) and runoff (mm) in (a) TerraClimate and ERA5-Land products and (b) GLDAS-Noah and ERA5-Land products for the period of 1960-1989 and 1990-2019.The deviation in the results of the two products is shown in terms of the difference in the percentage change in mean.

Table 1 .
Details on five categories used to study the inconsistency in the data products.The second and third columns provide the direction (magnitude wherever necessary) of change in the climatological mean of the respective water cycle flux.The first two categories strongly violate the conservation of mass, while the remaining two could also be explained by hydrological changes in water storage (e.g.gradual melting of the glaciers).All the other regions, that are consistent with the water budget closure, are represented by the fifth category (Z5).