Main

Snowmelt is a major component of streamflow (Q) in cold regions and serves as an important supply of freshwater resources locally and downstream2,10, with broad implications for ecosystem functioning11, food security4 and natural hazards12,13. Observations indicate a substantial warming trend in global cold regions over the past several decades, at a rate much faster than the global average14, inducing an evident shift of winter precipitation from snowfall towards rainfall1,15. This phase change in precipitation is expected to alter the amount, timing and rate of snowpack accumulation and melt16,17, with profound consequent impacts on the amount and seasonal distribution of Q (refs. 9,18,19). For example, studies in some regions have shown that the annual Q amount may be reduced with declining snowfall fraction (fs) (ref. 3), possibly owing to more gradual melting of the snowpack and/or higher absorbed net radiation that increases evaporative water loss as a result of snow-albedo feedbacks16,20.

Compared with the total Q volume, the seasonality of Q is more directly relevant to seasonal water availability2,4, geomorphology processes21, reservoir operation2,10 and flood/drought risks22,23. Nonetheless, the responses of Q seasonality to declines in fs are not yet well understood9. In regions where precipitation falls as snow, the discharge of that precipitation as Q can be delayed until the accumulated snow melts in subsequent warmer seasons4. It follows that a shift from snowfall towards rainfall is expected to lead to an earlier Q timing, which is supported by earlier snowmelt widely observed across snow-affected regions5,24,25 and/or by numerical modelling experiments26,27. However, direct assessments of Q observations do not always support this expectation5,6,7,8. Although most existing efforts are made in western North America where the observed Q generally occurs earlier under warming28,29,30,31, relatively less emphasis has been given to other snow-affected regions with limited observational evidence showing diverse trends in Q timing6,8 (Extended Data Table 1). Moreover, how seasonal variation of Q magnitude responds to declining fs also remains largely unexplored. Although a few studies have assessed changes in Q seasonal variation in response to climate warming32, their findings vary considerably among catchments/regions and observational evidence of the direct linkage between fs and Q seasonal variation remains lacking.

Here we conduct observational analyses to comprehensively assess the impacts of changes in fs on Q seasonality by using an extensive dataset of long-term (nominally 1950–2020) Q measurements from 3,049 unimpaired, snow-affected (mean annual snowfall fraction higher than 10%) catchments across the Northern Hemisphere (Methods; Extended Data Fig. 1). A fixed water-year from October through to the following September was used for all catchments33. Two characteristics of Q seasonality are considered: (1) the timing of Q, represented by the centre of mass of streamflow34 (CTQ), which denotes the time of year when 50% of the annual Q occurs, and (2) seasonal variation in Q magnitude, characterized by the streamflow concentration index35 (QCI), whereby a larger QCI value signifies a more pronounced seasonal variation. We also seek to understand how changes in fs would affect the interannual variability of these two Q seasonality characteristics.

Spatial and temporal patterns

To investigate the impacts of changes in fs on Q seasonality, we first examine the spatial and temporal patterns of fs and the two Q seasonality indices (CTQ and QCI) for the 3,049 catchments over 1950–2020 (Fig. 1). As shown in Fig. 1a, higher mean annual fs (\(\bar{{f}_{{\rm{s}}}}\)) are generally found in high-mountain regions (for example, the Rocky Mountains and the Alps) and high-latitude areas (for example, northern Europe) (Extended Data Fig. 2). The spatial distributions of mean annual CTQ and QCI broadly follow that of \(\bar{{f}_{{\rm{s}}}}\), with higher \(\bar{{f}_{{\rm{s}}}}\) generally associated with later CTQ and larger QCI, despite a more complex pattern found for QCI (Fig. 1b,c). It is noteworthy that most catchments also exhibit clear precipitation seasonality, with the centre of mass of precipitation (CTP) generally occurring earlier than CTQ in most catchments and more closely matching CTQ in catchments with a lower \(\bar{{f}_{{\rm{s}}}}\) (Fig. 1b and Extended Data Fig. 3). Temporally, widespread declines in fs are observed over the entire mid-to-high latitude Northern Hemisphere during the past 70 years, with negative annual fs trends registered in about 85% of the catchments and nearly half of them are statistically significant (P < 0.1, t-test) (Fig. 1d). Larger declines in fs are generally found in catchments with a high \(\bar{{f}_{{\rm{s}}}}\), except for northern Europe where trends in fs are mostly insignificant. In comparison, trends in annual CTQ show a more diverse pattern with advancing and delaying CTQ trends, respectively, found in about two-thirds and one-third of the catchments (Fig. 1e), suggesting a more intricate response of CTQ to the diminishing fs over time. Notably, the spatial distribution of CTQ trends does not consistently follow that of CTP either, except for certain regions such as a few catchments in the western United States (Fig. 1e and Extended Data Fig. 3). As for QCI, about 75% of the catchments experienced a decreasing QCI trend, of which about 40% exhibit statistical significance (P < 0.1, t-test) (Fig. 1f), implying that historical declines in fs may have resulted in smaller seasonal Q variation in these catchments.

Fig. 1: Spatiotemporal patterns of snowfall fraction and streamflow seasonality across 3,049 catchments over 1950–2020.
figure 1

a, Spatial distribution of mean annual snowfall fraction. b, Spatial distribution of mean annual streamflow timing (represented by CTQ). c, Spatial distribution of mean annual seasonal streamflow variation (represented by QCI). d, Trends in annual snowfall fraction. e, Trends in annual CTQ. f, Trends in annual QCI. For d–f, grey dots indicate that the trends are not statistically significant (P > 0.1, t-test).

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Snowfall effects on Q seasonality

We subsequently examine the statistical relationships between \(\bar{{f}_{{\rm{s}}}}\) and the two Q seasonality indices across 3,049 catchments to quantify the impact of changes in fs on Q seasonality. It is found that both CTQ and QCI show a significant (P < 0.01, t-test) positive relationship with \(\bar{{f}_{{\rm{s}}}}\), demonstrating that Q in catchments with a higher \(\bar{{f}_{{\rm{s}}}}\) generally occurs later in the year and exhibits a larger seasonal variation (Fig. 2a,b). For catchments with a relatively high \(\bar{{f}_{{\rm{s}}}}\) (\(\bar{{f}_{{\rm{s}}}}\) > 0.5), the mean CTQ occurs in around late-April and the mean peak monthly Q occurs in June (Fig. 2c). Moreover, these high-\(\bar{{f}_{{\rm{s}}}}\) catchments are also accompanied by a large seasonal variation in Q (mean QCI > 15), owing to a large contrast between high flows in warmer seasons (the peak monthly Q accounts for more than 22% of annual Q) and low flows in colder seasons (the minimum monthly Q accounts for less than 3% of annual Q). In comparison, catchments characterized by low \(\bar{{f}_{{\rm{s}}}}\) (0.1 < \(\bar{{f}_{{\rm{s}}}}\) < 0.2) manifest both the mean CTQ and peak monthly Q in March. The mean QCI for these low-\(\bar{{f}_{{\rm{s}}}}\) catchments decreased to less than 11, demonstrating a comparatively diminished amplitude of seasonal variations in Q due to the narrower disparity between high- and low-flow during different periods of the year.

Fig. 2: Relationship between mean annual snowfall fraction and streamflow seasonality.
figure 2

a, Relationship between mean annual snowfall fraction (\(\bar{{f}_{{\rm{s}}}}\)) and mean annual streamflow timing (represented by CTQ) across the 3,049 catchments. b, Relationship between mean annual fs and mean annual streamflow seasonal variation (represented by QCI) across the 3,049 catchments. In a and b, whiskers represent the 1st and 99th percentile, the top and bottom of the box are the 25th and 75th percentile and the median is represented by the horizontal line internal to the coloured box. The red solid lines show the best linear fit across the 3,049 catchments. c, Seasonal course of streamflow for catchments with different \(\bar{{f}_{{\rm{s}}}}\) across the water-year. The 3,049 catchments are stratified into six groups according to their \(\bar{{f}_{{\rm{s}}}}\) (as used in a and b) and the solid curves represent the mean monthly streamflow series for each group and the vertical dotted lines indicate the mean CTQ in each group. The values of mean QCI for each group are also shown on the right-hand side of this subplot. The number of catchments in each of the six groups is provided at the bottom of a.

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The above results in Fig. 2 demonstrate that Q in catchments with a lower \(\bar{{f}_{{\rm{s}}}}\) generally occur earlier and exhibit a smaller seasonal variation. To scrutinize the temporal response of Q seasonality to shifts in fs, we compared the two streamflow seasonality indices between two 10-year periods with the highest and lowest fs for individual catchments. The findings show a concordance between the temporal and spatial analyses in terms of the influence of fs on seasonal Q variation; specifically, the QCI shows greater values during high-fs periods and comparatively lower values during low-fs periods (Fig. 3a). This relationship is further illustrated by a positive correlation between trends in QCI and fs across the 3,049 catchments over 1950–2020 (Extended Data Fig. 4). Notably, the decreased QCI in response to fs reduction over time is caused primarily by large declines in high flows during warm seasons, whereas the low flows during cold seasons remain essentially unchanged (Fig. 3a and Extended Data Fig. 4).

Fig. 3: Impacts of temporal changes in snowfall fraction on streamflow seasonality.
figure 3

a, Comparison of mean monthly streamflow over the water-year between the two 10-year periods with the highest (blue) and lowest (red) snowfall fractions for each six groups of catchments. The 3,049 catchments are first divided into six groups according to their mean annual snow fraction (\(\bar{{f}_{{\rm{s}}}}\)). Then for each catchment in each group, the two extreme fs 10-year periods are identified which are then averaged for each group. Solid curves represent the mean of all catchments and shadow areas represent the range of individual catchments in each group. The vertical lines indicate the streamflow timing (represented by CTQ) and the seasonal variation of streamflow (represented by QCI) is also shown. b, Sensitivities of CTQ to precipitation timing (εCTQ_CTP) and melt onset date (εCTQ_MOD), which, respectively, quantify the impact of one-day change in CTP and MOD on CTQ, as a function of \(\bar{{f}_{{\rm{s}}}}\) for the 3,049 catchments. c, Histogram of slopes in the linear regressions between precipitation timing (melt onset date) and snowfall fraction (εCTP_fs and εMOD_fs), which, respectively, quantify changes in CTP and MOD in relation to increases in fs by 0.01, for the 3,049 catchments.

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However, the temporal response of Q timing to changes in fs does not consistently align with its spatial response and the trends in CTQ do not exhibit a clear relationship with trends in fs (Extended Data Fig. 4). Nonetheless, the temporal response of Q timing to declines in fs exhibits a distinct disparity between delayed CTQ in low-\(\bar{{f}_{{\rm{s}}}}\) catchments (\(\bar{{f}_{s}}\) < 0.4) and advanced CTQ in high-\(\bar{{f}_{{\rm{s}}}}\) catchments (\(\bar{{f}_{{\rm{s}}}}\) > 0.5) (Fig. 3a). This contrast is further manifested by a clear gradient in the CTQ difference between low- and high-fs periods: the difference in CTQ between low- and high-fs periods is mostly positive (indicating a postponed Q timing as fs decreases) in catchments with a \(\bar{{f}_{{\rm{s}}}}\) < 0.2 and becomes increasingly smaller until \(\bar{{f}_{{\rm{s}}}}\) reaches approximately 0.4 to 0.5. After that, a reversal occurs, with the CTQ difference between low- and high-fs periods turning negative (indicating an earlier Q timing as fs decreases) and becoming increasingly larger as \(\bar{{f}_{{\rm{s}}}}\) increases (Fig. 3a and Extended Data Fig. 5).

Theoretically, in snow-affected catchments, the timing of Q can be jointly determined by the timing of precipitation and the timing of snowmelt7,28. To understand the contrast in the response of CTQ to changes in fs between low- and high-\(\bar{{f}_{{\rm{s}}}}\) catchments, we explore the responses of CTQ to the timing of precipitation (indicated by CTP) and the initiation of snowmelt (indicated by the melt onset date (MOD)). Two sensitivities, estimated by the slope in the linear regression between CTQ and CTP (εCTQ_CTP) and between CTQ and MOD (εCTQ_MOD) for each catchment, are used to quantify the responses of CTQ to CTP and MOD, respectively. We find that εCTQ_CTP is consistently higher than εCTQ_MOD in low-\(\bar{{f}_{{\rm{s}}}}\) catchments (\(\bar{{f}_{{\rm{s}}}}\) < 0.4) (Fig. 3b and Extended Data Fig. 6), suggesting that the timing of Q in these catchments is controlled primarily by the timing of precipitation. With the increases of \(\bar{{f}_{{\rm{s}}}}\), εCTQ_CTP decreases whereas εCTQ_MOD increases and generally surpasses εCTQ_CTP in high-\(\bar{{f}_{{\rm{s}}}}\) catchments (for example, \(\bar{{f}_{{\rm{s}}}}\) > 0.5), indicating the predominant influence of snowmelt on the timing of Q in these high-\(\bar{{f}_{{\rm{s}}}}\) catchments. With this, we further calculate the slope in the linear regression between CTP (MOD) and fs (that is, εCTP_fs and εMOD_fs) to examine the associations of CTP (MOD) with fs for each catchment (Fig. 3c and Extended Data Fig. 6). As expected, most (about 96%) of catchments exhibit a positive εMOD_fs, aligning with previous findings that decreased fs is generally associated with earlier snowmelt5,23. The positive MOD–fs relationship and a higher εCTQ_MOD jointly led to an advancement in CTQ as fs diminished in high-\(\bar{{f}_{{\rm{s}}}}\) catchments. As for CTP, a negative εCTP_fs is found in nearly all catchments (about 98%), indicating that a decline in fs is also commonly associated with, or more likely contributed by, a delay in seasonal precipitation (due to reduced cold season precipitation; Extended Data Fig. 7). This negative CTP–fs relationship, along with a higher εCTQ_CTP, collectively contributed to a delayed CTQ following decreases in fs in low-\(\bar{{f}_{{\rm{s}}}}\) catchments (\(\bar{{f}_{{\rm{s}}}}\) less than about 0.4).

Variability of Q seasonality

To demonstrate how changes in fs alter the interannual variability of Q seasonality, we first calculate the coefficient of variation of annual CTQ (CVCTQ) and QCI (CVQCI) over the entire data period for each catchment. Moreover, because the interannual variability of Q can be considerably influenced by that of precipitation, we also calculate the corresponding indices for precipitation (CVCTP and CVPCI). We then classify the 3,049 catchments into three groups based on CVCTP (or CVPCI) and examine how CVCTQ and CVQCI vary with \(\bar{{f}_{{\rm{s}}}}\) across catchments in each group. Results show that for the same \(\bar{{f}_{{\rm{s}}}}\), catchments with higher CVCTP (CVPCI) generally show higher CVCTQ (CVQCI), confirming a critical role of precipitation in governing the interannual variability of Q seasonality (Fig. 4a,b). Meanwhile, we find that both CVCTQ and CVQCI exhibit a significant (P < 0.01, t-test) negative relationship with \(\bar{{f}_{{\rm{s}}}}\) for all three catchment groups, indicating larger interannual variability of Q timing and seasonal variation in catchments with lower \(\bar{{f}_{{\rm{s}}}}\) for a given CVCTP and CVPCI.

Fig. 4: Impacts of declines in snowfall fraction on the interannual variability of streamflow seasonality.
figure 4

a, Relationship between interannual variability of streamflow timing (CVCTQ) and mean annual snowfall fraction (\(\bar{{f}_{{\rm{s}}}}\)) across the 3,049 catchments. b, Relationship between interannual variability of seasonal streamflow variation (CVQCI) and \(\bar{{f}_{{\rm{s}}}}\) across the 3,049 catchments. In a and b, whiskers represent the 1st and 99th percentile, the top and bottom of the box are the 25th and 75th percentile and the median is represented by the horizontal line internal to the coloured box. The solid lines show the best linear fit across the 3,049 catchments with the slope and probability level (calculated by means of a t-test) shown in the legend for the three groups. c, Relationship of relative change in interannual variability of streamflow timing (ΔCVCTQ/CVCTQ) and that of precipitation timing (ΔCVCTP/CVCTP) between two 20-year periods with the highest and lowest fs. d, Relationship of relative change in interannual variability of streamflow seasonal variation (ΔCVQCI/CVQCI) and that of precipitation seasonal variation (ΔCVPCI/CVPCI) between two 20-year periods with the highest and lowest fs. In c and d, catchments are divided into six groups on the basis of their \(\bar{{f}_{{\rm{s}}}}\), and lines are the best linear fit across catchments in each group. The slopes of the linear regression models are presented in the inset, denoted by asterisks * and ** to signify statistical significance at the 95% and 99% confidence levels (t-test), respectively.

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To further investigate how CVCTQ and CVQCI change with fs through time, we adopt a 20-year moving window and examine the relationships between relative changes in CVCTQ (CVQCI) and CVCTP (CVPCI) between the two 20-year periods with the highest and lowest fs for each catchment. The 20-year window was selected to ensure the sample size was long enough to account for interannual variability. Results show that the sensitivities of CVCTQ (CVQCI) to CVCTP (CVPCI) evidently increase as \(\bar{{f}_{{\rm{s}}}}\) decreases (Fig. 4c,d). This means that the interannual variability of precipitation seasonality exerted a stronger control on the interannual variability of Q seasonality as fs decreases. Comparison of the sensitivities of CVCTQ (CVQCI) to CVCTP (CVPCI) among catchments experiencing different fs changes also shows a similar finding (Extended Data Fig. 8), because changes in fs are largely related to the magnitude of fs (Fig. 1a,d). This result implies that when the interannual variability of precipitation seasonality remains unchanged, decreases in fs would increase the variability of Q timing and seasonal variation between years, consistent with findings from the spatial analyses (Fig. 4a,b).

Summary and discussion

Although it has long been recognized that warming-induced declines in snowfall will exert profound impacts on Q characteristics, the underlying mechanisms are complex and existing findings vary substantially across geographic locations5,8,9,26. Here, by using long-term Q observations across many catchments over the entire Northern Hemisphere, we present a comprehensive observation-based assessment of the impacts of changes in fs on Q seasonality. Three key conclusions are obtained.

First, seasonal Q variation decreases with the decline in fs. This response is consistent across both space and time and is caused by a decreased warm season fractional Q and an increased cold season fractional Q, consistent with previous findings36,37,38. However, when absolute Q changes are assessed, the warm season Q shows an evident reduction whereas the cold season Q remains relatively stable (Fig. 3a and Extended Data Fig. 7), implying that the annual total Q must decrease as fs declines3. Consequently, the increased cold season fractional Q is driven primarily by decreases in annual total Q rather than increases in cold season Q itself. The decreased warm season Q can be directly attributed to a reduced water supply from snowmelt30 and potentially amplified evaporation losses as a result of enhanced energy availability20. Mechanisms underlying changes in cold season Q are more complex. Although the intuitive notion is that rainfall directly generates runoff so that a shift from snow toward rain will increase cold season Q (ref. 2), our results show that a decline in fs is commonly associated with a delayed seasonal precipitation (Fig. 3c), which implies a decreased cold season precipitation (Extended Data Fig. 7). Additionally, enhanced evaporation and decreased snowmelt rate are also likely to reduce cold season Q (refs. 16,18). Collectively, these opposing effects seem to have substantially offset each other, yielding marginal net changes in cold season Q.

Second, declines in fs do not always lead to an earlier Q timing. Although most existing observational evidence indicates an earlier Q timing due to earlier snowmelt associated with declines in fs under warming, these previous findings are mostly concentrated in western North America where \(\bar{{f}_{{\rm{s}}}}\) is relatively high28,29,30,31,39. By extending existing analyses to the entire Northern Hemisphere, our results demonstrate that the lower fs to earlier Q relationship generally persists spatially but does not always hold over time. Specifically, advances in seasonal Q are found mostly in catchments with a relatively high \(\bar{{f}_{{\rm{s}}}}\), consistent with previous findings in western North America. By contrast, delays in seasonal Q are observed in catchments with relatively lower \(\bar{{f}_{{\rm{s}}}}\), which is driven primarily by delays in seasonal precipitation despite earlier snowmelt as fs decreases.

Moreover, as \(\bar{{f}_{{\rm{s}}}}\) generally increases with elevation, discernible contrasts in the alterations of seasonal Q timing with declining fs are similarly observed along an elevation gradient, showing advanced (delayed) seasonal Q predominantly in catchments at higher (lower) elevations (Extended Data Fig. 5). This is expected and hints at an elevation dependence of changes in Q timing with declining fs. Previous studies reported that snowpack dynamics are more sensitive to temperature changes at lower elevations and more responsive to precipitation changes at higher elevations40,41,42. Here we observe that εCTP_fs becomes more negative whereas εMOD_fs becomes less positive as elevation increases (Extended Data Fig. 9). Because MOD is largely controlled by temperature (or more precisely energy availability24), this result indicates that changes in fs are more closely associated with changes in precipitation and less so with changes in temperature as elevation increases, consistent with previous findings on snowpack dynamics. Furthermore, by multiplying the changes in CTP and MOD (ΔCTP and ΔMOD) with the dependence of Q timing on CTP and MOD (εCTQ_CTP and εCTQ_CTP, as shown in Fig. 3b), we can approximately estimate the impact of ΔCTP and ΔMOD on ΔCTQ, respectively. Results show that ΔCTP-induced ΔCTQ becomes increasingly less positive, whereas ΔMOD-induced ΔCTQ becomes increasingly negative with rising elevation (Extended Data Fig. 9). These trends combine to result in the ΔCTQ gradient from advanced CTQ in high-\(\bar{{f}_{{\rm{s}}}}\) (high-elevation) catchments to delayed CTQ in low-\(\bar{{f}_{{\rm{s}}}}\) (low-elevation) catchments (Fig. 3a and Extended Data Fig. 5). Notably, a reversal in ΔCTQ (from advancing to delaying) between high- and low-fs periods generally occurs when \(\bar{{f}_{{\rm{s}}}}\) approximates 0.4, corresponding to an elevation of about 1,500 m. This suggests a critical \(\bar{{f}_{{\rm{s}}}}\) and elevation threshold influencing the composition of Q regimes, distinguishing between snowmelt-dominated and rainfall-dominated Q regimes41. Intriguingly, this critical elevation threshold on Q timing changes aligns reasonably well with previous findings about the critical elevation that distinguishes temperature-dominated from precipitation-dominated controls on snowpack dynamics (for example, about 1,560 m in the Central Rocky Mountains42 and about 1,400 m in the Alps43). With ongoing climatic warming, this critical elevation governing climatic controls of snowpack dynamics was projected to rise in the future44. In this context, it remains of interest to assess whether similar shifts would manifest in the \(\bar{{f}_{{\rm{s}}}}\) and elevation thresholds for changes in Q timing and runoff-generation regime under future warming.

Third, declines in fs increase the interannual variability of streamflow seasonality. We found that the interannual variability of CTQ and QCI become larger and are increasingly controlled by CTP and PCI as fs decreases across both space and time (Fig. 4 and Extended Data Fig. 8). Although the interannual variability of Q is widely recognized as being defined primarily by the interannual variability of precipitation45, we demonstrated that higher precipitation variability does not necessarily lead to a higher Q variability due to the presence of snow. When fs is high, the interannual variability of seasonal Q timing and variation are more controlled by that of snowmelt, which is determined primarily by the interannual variability of energy supply that is usually much smaller than the interannual variability of precipitation46. This pinpoints an important buffering role of snow in mediating the partitioning of precipitation variance into Q variance45, which, however, is weakening as fs diminishes with ongoing climate warming. Meanwhile, climate models project that the interannual variability of global mean land precipitation will increase at a rate of 4–5% per degree increase in temperature47, suggesting that the interannual variability of Q seasonality will be further amplified under future warming.

The above findings on the responses of streamflow seasonality to declines in fs have important hydrologic implications. Although previous studies concluded that earlier snowmelt would increase the risk of spring flood48, our results indicate that the frequency of spring flood might increase primarily in high-\(\bar{{f}_{{\rm{s}}}}\) catchments, whereas fewer spring floods may be expected in catchments where \(\bar{{f}_{{\rm{s}}}}\) is relatively lower. Furthermore, subtle changes in cold season Q coupled with substantial declines in warm season Q imply a decreased magnitude of snowmelt floods as fs declines—a phenomenon that has already been globally documented in the assessments of river flood changes49. By contrast, decreased warm season Q directly indicates a higher risk of summer and/or autumn drought, potentially exerting adverse effects on broad aspects of water/food security4, ecosystem health11 and hydropower generation2. Meanwhile, the increased interannual variability of Q seasonality implies a higher uncertainty in the seasonal Q regime, which results in larger difficulties in predicting seasonal Q changes thereby posing further challenges to seasonal and interannual water resources planning and management. In this light, adaptive measures, for example, seeking alternative water supplies (groundwater), increasing reservoir capacities and/or increasing the efficiency of water use, are imperative to enhance the resilience of the water system against dwindling fs to maintain ecosystem service functions in snow-affected and downstream regions under future warming.

Methods

Datasets

We use daily and/or monthly measurements of streamflow (Q) from 3,049 catchments (including their boundaries), sourced from four global/regional Q databases, including the following: (1) the Global Runoff Data Centre, Germany (https://www.bafg.de/GRDC/EN/01_GRDC/grdc_node.html); (2) the USGS National Water Information System (https://waterdata.usgs.gov/nwis/sw); (3) European Water Archive of EURO-FRIEND-Water (https://www.bafg.de/GRDC/EN/04_spcldtbss/42_EWA/ewa_node.html); and (4) the Water Survey of Canada Hydrometric Data (https://wateroffice.ec.gc.ca/). The selected 3,049 catchments all satisfy the following four criteria. First, the catchments had at least 30 years of continuous Q records over 1950–2020, with a maximum data gap of 10 days; the remaining gaps were then filled using linear interpolation. Second, to minimize the influence of human interventions, all catchments had irrigation areas smaller than 3% of the catchment area (based on the Global Map of Irrigation Areas‐GMIA50), urban areas smaller than 1% of the catchment area (based on the GlobCover v.2.3 map51) and reservoir capacities smaller than 3% of the mean annual Q (based on the Global Reservoir and Dam database52). Third, to focus on the snow impact, all catchments had a mean annual snowfall fraction (the ratio of snowfall over precipitation) higher than 10%. Fourth and finally, catchments in the Southern Hemisphere were excluded to ensure a consistent water-year for all analysed catchments. A fixed water-year (1 October through 30 September of the following calendar year53) was used for all catchments. It should be noted that the Q database is temporally heterogeneous. Despite that, the catchments collectively encompass about 45% of the snow-affected regions over the entire Northern Hemisphere with the lengths of Q records varying from 30 to 70 years (mean is about 55 years) (Extended Data Fig. 1).

Hourly precipitation, net radiation, snowfall and snow water equivalent (SWE) at 0.1o spatial resolution over 1950–2020 were obtained from the fifth generation of European ReAnalysis (ERA5-Land) dataset53. The gridded data were further spatially lumped for each catchment and temporally aggregated to daily and/or monthly scales. The ERA5-Land dataset features long temporal coverage and high spatial resolution and has undergone rigorous evaluation against observations, which confirms its accuracy and suitability for long-term hydrological investigations13,53.

Summary of calculations

To quantify the Q seasonality, we adopt two Q indices to, respectively, determine the timing and seasonal variation of Q. Specifically, CTQ34 is used to indicate the seasonal Q timing, which denotes the time of year when 50% of the annual streamflow occurs and is calculated as:

$${\rm{CTQ}}=\mathop{\sum }\limits_{i=1}^{12}(i\times {q}_{i})/\mathop{\sum }\limits_{i=1}^{12}({q}_{i})$$
(1)

where i is time in months from the beginning of the water-year and qi is monthly Q (mm month−1) for water-year month i.

The QCI35 is used to quantify the seasonal variation of Q and is calculated as:

$${\rm{QCI}}=\mathop{\sum }\limits_{i=1}^{12}{{q}_{i}}^{2}/{(\mathop{\sum }\limits_{i=1}^{12}{q}_{i})}^{2}\times 100$$
(2)

The two Q indices have been widely used in the literature to assess Q and/or P seasonality characteristics under global change30,54 (Extended Data Table 1). To account for the influence of changing precipitation, we similarly calculated the corresponding indices for precipitation (CTP and PCI) in the same way.

The MOD is determined as the first date in the water-year when SWE starts to drop after reaching the maximum SWE24. Adopting a different definition of SWE yields similar results (Extended Data Fig. 6). The period between MOD and the first date SWE starts to increase is defined as the warm season and the rest of the year is considered as the cold season. In the assessment of changes in seasonal precipitation and Q, the climatological warm season and cold season were used for each catchment, which are determined from the mean annual daily courses of SWE.