For this study, we used station-based discharge (Q) data from the following sources: the Global Streamflow Indices and Metadata Archive (GSIM; ), the Australian edition of the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS-AUS) dataset , the LArge-SaMple DAta for Hydrology and Environmental Sciences for Central Europe (LamaH-CE; ), and the Italian Hydrological Portal . We used annual mean discharge (Q‾) for the catchment-specific available time period. For the 1981–2010 period, we obtained the catchment average daily precipitation (P) and daily mean temperature (Ta) from the Global Soil Wetness Project Phase 3 (GSWP3; ) and daily potential evaporation (Ep) from the Global Land Evaporation Amsterdam Model version 3.5a (GLEAMv3.5a), which is based on the Priestley–Taylor approach . We selected 4856 catchments based on the following criteria: (1) at least 10 years of Q data during the 1981–2010 period; (2) catchment area < 10 000 km2 to limit the heterogeneity within catchments; (3) annual mean discharge (Q‾) smaller than annual mean precipitation (P‾) for the specific catchment.

For each catchment, we obtained irrigation estimates from two different data sources. Firstly, we used the average irrigated area fraction Ia (–), which is the areal fraction of land equipped with infrastructure for irrigation. Ia was obtained from the “AEI_HYDE_FINAL_IR” dataset developed by , which is representative of the irrigation extent in the year 2005 (Fig. a). This dataset was based on subnational irrigation statistics and the History Database of the Global Environment (HYDE), version 3.1, land use data . Secondly, we used estimates of annual mean irrigation water use representative of the 2011–2018 period (Iw‾ (mm yr-1)) from , who developed an algorithm to estimate irrigation from multiple satellite-based products and the Priestley–Taylor Jet Propulsion Laboratory (PT-JPL) model (Fig. b).

To identify the effects of irrigation for different regions, we used the Köppen–Geiger climate classes as a climate indicator. For each catchment, we selected the predominant Köppen–Geiger climate class based on a global map at a 1 km resolution representing the 1980–2016 period . The gridded data products for P, Ep, Ia, and Iw‾ were converted to catchment estimates using area-weighted averages of the grid cells with more than 50 % of their area located inside the catchment. Before area weighting, the gridded products were resampled to a spatial resolution of 0.05° using nearest-neighbor interpolation. This way, all gridded products were treated similarly and problems with small catchments with no matching grid cells were avoided.

Figure a shows a conceptualization of the memory method based on four storage components (mm): interception storage (Si), snow storage (Ssn), “surplus” storage (Ss), and storage deficit (Sd). Sd is initially conceptualized as an infinite deficit storage volume and its temporal evolution can be described by 1Sd(t)=∫t0τPe-Et+I-Psdt, where Pe represents effective precipitation (mm d-1), Et is transpiration (mm d-1), I is irrigation (mm d-1), and Ps is surplus precipitation (mm d-1) (Fig. a). In Eq. (), t0 corresponds to the first day of the first hydrological year and τ corresponds to the daily time steps ending on the last day of the last hydrological year. Our hydrological year starts the first day of the month after the wettest month, which is defined as the month with the largest positive difference between monthly mean P and Ep on average. At t0, the starting point of the analysis, Sd=0. In Eq. (), Pe (mm d-1) is calculated from the water balance of the interception storage Si (Fig. a), and Et (mm d-1) is described as a fraction of daily potential evaporation Ep (mm d-1) based on the catchment water balance. We used a simple snow model based on the degree-day method e.g., to account for the delay in liquid water input to the soil by describing liquid precipitation (Pl, mm d-1), precipitation falling as snow (Psn, mm d-1), and snowmelt (Pm, mm d-1). The equations for the interception storage, snow storage, and transpiration calculation are described in Appendix .

Surplus precipitation Ps (mm d-1) in Eq. () is described by Eq. (), in which we used the following notation for the sum of the fluxes between two time steps: Ft=∫t-1tFdt, where F is either Pe, Et, I, or Ps. Thus Ps,t is described by 2Ps,t=max0,Sd+Pe,t-Et,t+It, with Sd and It approaching zero during periods of abundant precipitation. Hence, it then holds that Ps,t≈Pe,t-Et,t.

For the computation of applied irrigation (I), we split the time series into surplus and deficit periods (Fig. b). For each hydrological year, we defined one deficit period, which is the longest deficit period with the largest Sd in the hydrological year. Surplus periods were defined as the periods in between the deficit periods. For each surplus period, the surplus precipitation Ps (Eq. ) accumulates in the surplus store Ss: 3Ss(t)=max0,∫ts0ts1Ps-Idt, where ts0 is the first day of the surplus period and ts1 is the last day of the surplus period (Fig. b). Ss does not have a maximum storage capacity, but it is reset to zero each year, after each deficit period. This storage conceptualizes any water buffers that can be used for irrigation in the consecutive deficit period and may encompass ditches, lakes, and aquifers. This method assumes that irrigated water only originates from water inside the catchment boundaries and that it is sustainably extracted so that the long-term water balance is closed. During a deficit period, the fraction of Ss that is used for irrigation is defined by irrigation factor f (–), which determines how much of the surplus water stored during the surplus period is used for irrigation during the consecutive deficit period. f represents both the water evaporated or discharged during the irrigation process before recharging the soil and the spatial extent of the irrigation. It is assumed that daily irrigation I is equally distributed over the deficit period (Fig. b), so that I (mm d-1) is defined as follows: 4I(t)=fSsts1Δtd, where Δtd is the length of the deficit period (td1-td0) in days (Fig. b). Here, based on the two irrigation data sources used (Sect. ), we have developed two methods to estimate f in Eq. ():

The first of these techniques is the “irrigation water use” method (IWU), in which fd,IWU (–) is defined for each deficit period d for each catchment by5fd,IWU=max1,Iw‾dtSsts,1,sothatI(t)=Iw‾dtΔtdifsufficientwaterisavailableinSs.Here, Iw‾ (mm yr-1) is the catchment annual mean irrigation water use, dt=1 yr, and Ss(ts,1) (mm) is the surplus storage at the end of the surplus storage accumulation period, i.e., the amount of water stored in Ss at the start of the deficit period. In this method, fd,IWU is different for each deficit period d, as Ss also varies. For each catchment, fIWU is defined as the average fd,IWU.

To evaluate the effect of these methods on estimated Sr, we tested a third case, referred to as “no irrigation” (NI), in which fNI=0. A priori, we cannot and do not consider either of the two methods, i.e., the IWU or the IAF method, to be more representative than the other. While the IWU method uses the irrigation data more directly than the IAF method, the latter directly takes the interannual variability in surplus water into account.

Globally, the Sr estimates without accounting for irrigation ranged from 0 to 800 mm, with larger values in semiarid regions with high rainfall seasonality, such as northeastern Brazil (median Sr≈250 mm), or monsoon regions, such as northeastern Indian (median Sr≈450 mm), than in regions with temperate climates with year-round rainfall, such as western Europe (median Sr≈70 mm), or continental, colder, climates, such as Canada (median Sr≈40 mm) (Fig. ).

The storage deficits Sd (Eq. ) generally decreased when accounting for irrigation effects according to the IWU and IAF cases compared with the case without irrigation (NI). These overall effects of the method are illustrated by four selected example catchments in Fig. . More pronounced effects of irrigation on Sd are visible for the example catchments in Europe (Fig. e and f) and Asia (Fig. g and h), with larger Iw‾ and Ia, than in the example catchments in South America (Fig. a and b) and North America (Fig. c and d). As Sd decreased, the annual maximum storage deficits Sd,M, as determined by Eq. (), decreased as well. Consequently, the estimated Sr decreased for the IWU and IAF cases compared with NI, with more pronounced effects in the example catchments with larger Iw‾ and Ia (Fig. ). Globally, Sr consistently decreased for IWU and IAF (Fig. ), although the magnitudes varied to a considerable extent. Nevertheless, relatively clear regional patterns of the effects of irrigation on Sr emerged. The most pronounced effects cluster in catchments in regions that are characterized by widespread and intense crop cultivation, and thus high irrigation water use, such as northern Spain, France, and parts of India (Fig. ).

Figure  shows that the effects of irrigation on Sr increased with increasing irrigated area fraction Ia for both the IWU and IAF cases. We found the largest effects in catchments with Ia>0.1, such as the example catchment in Asia (Fig. g). For these catchments, the median ΔSr was 19 mm (IQR of 10–31 mm) for IWU and 23 mm (IQR of 11–42 mm) for IAF (Fig. ), corresponding to decreases of 12 % and 15 %, respectively (Table ). These effects were considerably larger than the effects of irrigation in catchments with 0.05<Ia≤0.1, which reached a median ΔrSr of 6 %, corresponding to ΔSr≈9 mm (Fig. , Table ). Although the median effects of irrigation on Sr for catchments with Ia≤0.05 were relatively small, the effects can be considerable for specific individual catchments, as shown by the outliers in Fig. .

The strongest irrigation influence on Sr for catchments with Ia>0.05 was found in Asia, followed by South America, North America, and Europe, for both IWU and IAF (Fig. a). For the catchments in Asia, we found median ΔSr values of 21 mm (IQR of 13–41 mm) and 27 mm (IQR of 12–56 mm) for IWU and IAF, respectively . However, the relative differences in Sr (ΔrSr=9 %–10 %) were smaller in Asia than in other regions, reaching up to 14 % in South America, because the initial Sr without accounting for irrigation was considerably larger in Asia than in other regions (Fig. , Table ). Figure b shows that Sr decreased the most in tropical catchments, with a median ΔSr of 19 mm for IWU and 24 mm for IAF. These findings are in line with the results presented in Fig. a, as most of the tropical catchments that we evaluated were located in Asia (Fig. S3). For catchments in the arid, Mediterranean, temperate, and continental climate zones, the median ΔSr was smaller and varied between 5 and 15 mm. However, catchments in temperate climates exhibited the largest relative influence of irrigation on Sr: median ΔrSr=14 % for IWU and 15 % for IAF (Table ).

Figure  shows similar spatial patterns of ΔrSr for IWU and IAF, but the magnitudes differ. For most groups of catchments, IAF had a more pronounced effect on Sr than IWU (Table ; Fig. S4). The different results for IWU and IAF can be explained by the different methodologies (Table ). The IWU method directly used annual mean irrigation water use (Iw‾) from as an estimate for I (if sufficient water was available in the surplus store Ss). On the other hand, in the IAF method I was defined as a fraction of Ss based on the irrigated area fraction (Ia) and the constant β. Therefore, the estimated I in IAF directly reflected the interannual variability in surplus water. Another cause of the different results for IWU and IAF lies in the estimation of β in IAF, which was based on minimization of the differences between fi,IWU and fi,IAF (Sect. ; Fig. ). In spite of this optimization, differences between fi,IWU and fi,IAF remained, which partially explain the differences in ΔSr between the two methods.

Our results show that the effect of irrigation on Sr is discernible in all regions, but the magnitude of the effect depends on the amount of irrigation applied (Figs. –). For many parts of the world, the integration of irrigation in the Sr estimation did not have a large influence (Fig. ). However, Sr considerably decreased for catchments with irrigated area fractions Ia>0.05, and ignoring irrigation in these regions would lead to biased estimates of Sr and, as a consequence, inadequate modeling of vegetation transpiration (Fig. ). The reduction in Sr in catchments with irrigation was expected based on the fact that the memory method is founded on the theory that vegetation will invest less in roots if sufficient water is available . Here, the observed changes in Sr are attributed to changes in the roots of vegetation, as they are directly related to the size of Sr. Additionally, adaptations at the plant scale associated with irrigation, such as adjustments in stomatal aperture and root hydraulic conductance , are also implicitly related to changes in Sr. The influence of irrigation on Sr estimates, as presented in Fig. , resembles the spatial pattern found in global assessments of irrigation water withdrawal and the extent of irrigation activities . This was expected because we used similar underlying irrigation data in the irrigation methods developed here. Given the ongoing irrigation expansion as presented by , it is expected that larger irrigation water volumes will lead to further reductions in Sr at catchment scales in the near-future compared with the reductions reported in this study. At the same time, irrigation efficiency is also improving , but this effect on Sr is less straightforward. Improved irrigation efficiency (i.e., reduced soil evaporation) reduces the irrigation water volumes needed, which, at the catchment scale, leads to increased long-term mean discharge, and thus reduced long-term mean evaporation. This would result in reduced Sr in the memory method compared with a situation with lower irrigation efficiency. However, it has been shown that increased efficiency does not necessarily lead to reduced irrigation water use, as the saved water due to increasing irrigation efficiency is often applied elsewhere .

Previous studies using the memory method have not considered irrigation in Sr estimates e.g.,, nor have they evaluated its effects . To put our results into perspective, we looked at the effects of snow accumulation and melt on Sr estimates from for the continental United States, as this process alters the Sd time series in a similar way to irrigation by temporally shifting liquid water input into the system. estimated that integrating snow accumulation and melt in the memory method led to an average reduction in Sr of 6 mm (2 %) for areas with >10 % winter snow coverage and of 28 mm (17 %) for areas with >80 % winter snow coverage . These magnitudes are broadly consistent with our findings for irrigation (Table ). Our results indicate that the effects of snow and irrigation on Sr are comparable. In our study, 27 catchments have both considerable snowfall (snow days >5 % of the total days) and irrigation (Ia>0.05). For these catchments, the snow model (Appendix ) led to an Sr reduction of 7 mm (7 %) on average for the NI case compared with a setup without the snow model. With irrigation, Sr further decreased by 6 mm (7 %) and 11 mm (12 %) for IAF in these catchments.

Both the results of IWU and IAF showed considerable effects of irrigation on Sr (Figs. –), and both are suitable for use in the memory method, keeping in mind the individual uncertainties related to data and methodological assumptions. We think that the IWU method is more suitable for regional applications for periods with available Iw data than IAF, as Iw was derived from water balances, which strongly depend on the evaluated period. However, for spatial and temporal extrapolation, the direct use of the Iw data in the IWU method is more uncertain than the simpler IAF method, as the irrigated area fraction (Ia) used in IAF is expected to be temporally less variable than the water used for irrigation (Iw). Therefore, we think that the simpler parameterized IAF method is more suitable for use in the memory method for global applications and varying time periods. Moreover, IAF has the potential to be integrated dynamically in hydrological or land surface models employed for global Earth system model studies and future predictions.

By using several data sources, we obtained a large sample of 4856 catchments on different continents, characterized by a wide spectrum of climates and, in particular, regions with various levels of irrigation activity. However, the global coverage is not entirely balanced because Africa and large parts of Asia were undersampled. A further limitation may arise from the assumption in the memory method with irrigation methods proposed here that catchments are hydrologically closed systems. However, inter-catchment lateral flows, such as groundwater and irrigation water, can significantly alter catchment water balances e.g.,. Moreover, the extraction of fossil groundwater for irrigation can violate the assumption of closing water balances for the irrigation methods in the memory method developed here. Our methodology, based on a sustainable water use assumption, provides a lower boundary of Sr reduction in irrigated catchments. It is expected that irrigation exceeding sustainable use would lead to larger Sr reductions than reported here, as more water is available to crops than derived from the water balance in this case. Furthermore, the methodology assumes single succession of excess and deficit periods within a year (Fig. b), which is not necessarily representative in regions with double-cropping systems or bimodal monsoons . Another limitation was the availability and quality of irrigation data (Sect. , Fig. ). The annual mean Iw‾ used in IWU was based on the 2011–2018 period, while the catchment time series varied between 1981 and 2010. Similarly, the Ia that we used represented the 2005 irrigated area fraction . The temporal mismatch between catchment hydrological time series and irrigation data may have led to an overestimation of I for the catchment-specific period, as irrigated area and irrigation techniques and efficiency have developed over the evaluated period . Although this inconsistency in the temporal data influences the catchment-specific outcomes, we believe that it did not have a major influence on the quantification of the general patterns of the effects of irrigation on Sr, which was the aim of this study.

An additional source of uncertainty in the application of the memory method, as used in this study, relates to the derivation of Sr from the Sd time series (Fig. ). Given that an ecosystem has developed its Sr such that it functions optimally and can overcome dry periods e.g.,, Sr for a specific time period would correspond to the maximum Sd value observed during that same time period (Sr=max(Sd)). However, it is important to note that the memory method represents a simplified approximation of real ecosystem behavior and has inherent limitations. The most important limitation is that our application of the memory method did not account for the feedback between Sd and Et/Ep, which likely led to an overestimation of Sd . In this study, we primarily focused on crops that do not exhibit a multiyear root adaptation for survival, as there is no remaining Sr after each year's harvest. However, the catchments used here are not entirely covered by crops in any of the cases; therefore, we used a return period of 2 years for the Sr estimation (following ).