To estimate sources of freshwater input into Greenland fjords, we combine different models and observational products (Table ). As a default for runoff, melt, sublimation, and precipitation, we used output from the polar regional atmospheric climate model RACMO2.3p2 (henceforth RACMO). The used run was forced at 3-hourly intervals (6-hourly before 1990) by the fifth-generation reanalysis (ERA5) of the European Centre for Medium-Range Weather Forecasts (ECMWF) and starts in 1958. Over Greenland, RACMO runs at a native spatial resolution of ∼ 5.5 × 5.5 km² . The output of this simulation is further statistically downscaled to a 1 × 1 km² polar stereographic grid . For comparison with RACMO precipitation, the Copernicus Arctic Regional Reanalysis (CARRA-West) (henceforth CARRA) is used, which has a 2.5 × 2.5 km² resolution and uses the HARMONIE-AROME model, cycle Cy40h1 . CARRA-West runoff is unrealistically small over land and ice (i.e. <10 % of the RACMO estimate) and is not used here.

For comparison with RACMO runoff, we use outputs from the Modèle Atmosphérique Régional (MAR) version 14 forced at 6-hourly intervals by ERA5 since 1940. MAR runs at 5 × 5 km² spatial resolution and is statistically downscaled to the same 1 × 1 km² grid as RACMO .

Basal melt on a 1 × 1 km² grid is taken from , who used a composite of estimates for basal melt from geothermal heat, friction, and heat from surface meltwater, with the latter contributing to seasonal variability. Monthly values represent 1991–2023 averages. Basal melt has a total uncertainty of 21 %.

The freshwater components presented here and discussed in detail in the following subsections are GrIS runoff, GIC runoff, tundra runoff, basal melt, GrIS solid ice discharge (which represents the flux of solid ice across the grounding line, i.e. combining calving and submarine melt), and direct precipitation spatially integrated over the fjord surfaces. These components are presented as yearly sums since 1940/1958 and monthly sums since 1990 and are aggregated regionally (see below for region definitions) unless specified otherwise. The differences between the default products (boldface in Table ) and other products are typically small. That is why the default values are being reported in the figures and main text, and the differences with other products are discussed in Sect. .

Because this study considers freshwater fluxes into fjords, which differs from most hydrological, glaciological, and oceanic applications, Greenland is divided into seven climatologically distinct regions (Fig. ): North (NO), North-East (NE), North-West (NW), Central East (CE), Central West (CW), South-West (SW), and South-East (SE). These are based on the seven land/ice basins from that in turn are based on the ice divides. We made one adjustment by moving the boundary between SE and CE northward, along the ice divide, to better follow hydrological catchments, as well as to make the regions more comparable in size. Place names used in this study follow the convention by Oqaasileriffik, which has a map available on their website .

For interpretation purposes (see Sect. ) the melt-over-accumulation (MoA) ratio is calculated using the following equation applied to the GrIS and GICs mask in the seven basins: MoA=(melt+rain)/(snowfall-sublimation).

All parameters have units of millimetres of water equivalent (mm w.e.) and are taken from RACMO downscaled to 1 × 1 km² on the ice-covered surfaces. Rain is defined as total precipitation minus snowfall.

Figure  shows a time series of the different components of the total annual freshwater input into Greenland's fjords, using six different data sources (see Methods). Combined, the annual total freshwater input into Greenland fjords averages 1144 (±170) Gt yr⁻¹ (0.035 Sv, sverdrup) between 1990 and 2023, where ± in this section represents uncertainty per source described in the Methods (Sect. ). The main contributor is solid ice discharge (462 ± 43 Gt yr⁻¹), accounting for 40 % of the total. On average, GrIS (meltwater) runoff is the second-largest source of freshwater into the fjords (31 %, 357 ± 53 Gt yr⁻¹), but in years with extreme surface melt, such as 2010, 2012, and 2019, GrIS runoff exceeds the contribution of solid ice discharge. The third-largest contributor is tundra runoff (15 %, 175 ± 17 Gt yr⁻¹), followed by GIC runoff (6 %, 71 ± 28 Gt yr⁻¹) and (fjord) precipitation (5 %, 54 ± 8 Gt yr⁻¹). Basal melt contributes 2 % (23 ± 5 Gt yr⁻¹).

The period with data availability for all default components spans from 1990 through 2023, allowing for the calculation of absolute and relative changes in annual freshwater sources over time. Total average freshwater input since 2010 is 1239 (±180) Gt yr⁻¹, calculated to compare to other studies in Sect. . The freshwater sources that have been increasing most rapidly since 1990 are GrIS and GIC runoff, whose relative contribution to the total fjord freshwater input increased by 0.17 % yr⁻¹ (p=0.04) and 0.05 % yr⁻¹ (p=0.002), respectively. Tundra runoff is also increasing in absolute terms but slower than the other components, resulting in a decrease in its relative contribution of 0.08 % yr⁻¹ (p=0.002). Precipitation in fjords is changing very slowly in an absolute sense; i.e. its relative contribution is decreasing by 0.03 % yr⁻¹ (p=0.01).

For the period when monthly resolution is available for all components (2009–2023), Fig.  shows the average seasonal cycle of the Greenland total freshwater input into fjords based on monthly sums using (a) absolute linear, (b) absolute logarithmic, and (c) relative scales. Figure c is based on the default datasets (Table ), and values are presented in Tables  and . Most freshwater input occurs during July at the peak of the melt season (296 ± 57 Gt), and least occurs during March in late winter (48 ± 4 Gt). Freshwater input during winter months is primarily driven by solid ice discharge (82 ± 0.4 %, 41 ± 1 Gt per month, in DJF, December–January–February), whereas summer freshwater input is dominated by GrIS runoff (up to 68 ± 3.5 %, 172 ± 28 Gt per month, in July). Greenland tundra runoff peaks in early summer, when the seasonal snow melts (Fig. a) with a maximum of 36 ± 3 % of the total freshwater input occurring in May (Fig. c). While direct precipitation in fjords contributes little on average, when examined at a monthly scale, it can account for up to 11 ± 2 % of the total in January (Fig. c). Basal melt accounts for a maximum of 3 ± 0.6 % (March). There is an increase in summer GrIS runoff in the latter half of the period (2005–2023) compared to the first half (1990–2004), along with a rise in monthly solid ice discharge (Fig. a).

In order to study how the sources of freshwater are influenced by different climatic conditions across Greenland, surface types, (sea) ice conditions, and fjord geometry, Greenland is divided into seven different regions (Fig. ). First, we discuss the time series of annual totals per region (Fig. ) and then the seasonal cycle focusing on the relative contributions of the freshwater sources (Fig. ). In the following paragraphs, we will report 1990–2023 annual means of datasets indicated in boldface in Table , with a standard deviation of the annual values (±), unless reported differently. The absolute and relative average values can be found in Tables  and , respectively. These results will be put into a climatological context in the Discussion (Sect. ).

Annual freshwater input shows large variations between the regions, but on average freshwater input per sector is 251 Gt yr⁻¹ for SE, 178 Gt yr⁻¹ for SW, 179 Gt yr⁻¹ for CE, and 183 Gt yr⁻¹ for CW, and for the northern regions it is 119 Gt yr⁻¹ for NE, 146 Gt yr⁻¹ for NW, and 88 Gt yr⁻¹ for NO between 1990 through 2023 (Fig. ). In NO (Fig. a), which in an absolute sense provides the least freshwater to fjords of all basins, all freshwater sources except (fjord) precipitation increase over time. Other regions did not have a significant trend in precipitation. This region typically has large interannual variability in all runoff sources. At the start of the period, solid ice discharge was dominant (24 ± 2 Gt yr⁻¹, 1990–2004), but later in the period GrIS runoff took over as the dominant freshwater input in NO fjords (36 ± 11 Gt yr⁻¹, 2005–2023). In NO, tundra runoff has a relatively large share in the total regional freshwater input (17 ± 3 Gt yr⁻¹) compared to other regions, which is associated with the relatively large tundra area in this dry part of Greenland, where the ice sheet is mainly land-terminating (Fig. b). The pattern for NE (Fig. b) is similar to the pattern for NO, with the exception of a relatively smaller role of GIC runoff (12 ± 4 Gt yr⁻¹) and even more tundra runoff (30 ± 5 Gt yr⁻¹), making the latter occasionally the largest freshwater contribution in this region. In contrast, the wetter NW (Fig. c) has glaciers that are mainly marine-terminating, with a relatively narrow tundra and a small fjord area (Fig. b). Here, the freshwater input into fjords is clearly dominated by solid ice discharge (100 ± 8 Gt yr⁻¹), which is greater than the combined contributions of all other sources. GrIS runoff accounts for approximately 30 % of the input, while the other sources are relatively small. The NW solid ice discharge has been increasing since the early 2000s, in line with earlier work that diagnosed the cause to be increasing ocean temperatures .

In CW (Fig. d), the contribution of GrIS runoff (63 ± 18 Gt yr⁻¹) has been increasing but with high interannual variability. In recent years, it has been occasionally larger than solid ice discharge, which remains the overall main contributor (83 ± 9 Gt yr⁻¹). In contrast to most other regions, solid ice discharge decreased between 2013 and 2018 (Fig. d). Tundra runoff is relatively large in this region (21 ± 3 Gt yr⁻¹). Basal melt, (fjord) precipitation, and GIC runoff are of a similar small magnitude, with each contributing 3 % to the annual total. In CE (Fig. e), the largest input source is solid ice discharge (77 ± 6 Gt yr⁻¹), closely followed by GrIS runoff. Tundra runoff is approximately twice as large as GIC runoff (11 ± 2 Gt yr⁻¹) or (fjord) precipitation (14 ± 3 Gt yr⁻¹). This is the region where (fjord) precipitation has the largest relative contribution (up to 20 %), partly due to the relatively large fjord area (Fig. c). The largest and an increasing contributor in the SW (Fig. f) is GrIS runoff (80 ± 23 Gt yr⁻¹). Especially before 2006, tundra runoff (55 ± 9 Gt yr⁻¹) incidentally exceeded GrIS runoff during cold summers. Finally, the wet SE (Fig. g) has a narrow ablation zone, and the freshwater input into SE fjords is dominated by solid ice discharge (138 ± 7 Gt yr⁻¹). Similar to NW, solid ice discharge in SE has been gradually increasing since the early 2000s (Fig. g).

This study uses regional climate model data and observations of solid ice discharge to estimate the freshwater input from different sources entering Greenland's fjords. We find an average total annual Greenland freshwater input into fjords of 1.14 × 103 Gt yr⁻¹ for 1990–2023 (1.24 × 103 Gt yr⁻¹ since 2010). We estimate uncertainty to be 20 %, based on lower estimates for Greenland-wide surface mass balance. The average annual rates are compared for 2010–2016, a period with a relatively smaller trend than the preceding years and covered by all studies in this comparison. The annual rate in this study is slightly smaller than the total Arctic freshwater input found by (1300 Gt yr⁻¹ since 2010), which included non-Greenland ice caps. The region we study is a subset of the broader Arctic region analysed by , making their estimate useful for context and as an upper bound for our values. GrIS runoff between 2010–2016 is higher in and than estimated in this study. Before 2000, GrIS runoff was significantly higher in than in this study (∼ 350 vs. ∼ 250 Gt yr⁻¹).

We find higher tundra runoff than (150 vs. 80 Gt yr⁻¹) and than (100–130 Gt yr⁻¹). estimated a total tundra runoff based on MAR of between 140–160 Gt yr⁻¹ (1950–2021), similar to values found in this study using RACMO output (Sect. ). Observational studies show that tundra and GrIS and GIC runoff estimates are very sensitive to the selected region and are easily underestimated in regional climate models, with differences of up to 30 %–50 % between point measurements and regional climate models when specifically matching regions or even more than 100 % for smaller catchments . Yet, there are very few observational studies of total Greenland runoff and even less on tundra runoff, making estimates of the latter the least certain factor in the total freshwater input in its surrounding fjords and seas in this study.

To determine potential drivers behind these regional differences, freshwater components were correlated with the melt-over-accumulation (MoA) ratio (Sect. ), based on land-ice-integrated mass fluxes in each region (Fig. a, b). The MoA ratio has been used previously in firn studies to determine the climatic conditions under which melt would generate runoff in the accumulation zone. Previous work has identified a theoretical MoA ratio threshold between 0.6 and 0.7, indicating the onset of runoff . More recently, MoA has been used to predict when melt ponding starts on Antarctic ice shelves . In this study, MoA is used as a climatological indicator over the ice sheet, which we hypothesize is highly relevant to the partitioning between solid ice discharge and liquid water runoff into fjords. MoA does not directly depend on runoff but on melt as well as snowfall; the relative regional sizes of ablation and accumulation areas and the potential for meltwater buffering (through snowfall) also become important. We find that the fraction of total freshwater by solid ice discharge is strongly and negatively correlated with MoA (Fig. a), while tundra runoff fraction shows a strong and positive correlation (Fig. b). A somewhat weaker correlation exists between the fraction of total freshwater of GrIS runoff and MoA (r=0.78, p=0.04, not shown). Furthermore, the regional fractions to total freshwater input of both GrIS and tundra runoff decrease with an increasing fraction of solid ice discharge (Fig. c, d). Yet, no such relation is found for fraction of GIC runoff or precipitation. These results can be intuitively understood: in a region with a smaller MoA ratio, i.e. experiencing relatively low melt and/or high accumulation, the ice sheet extends further towards and into the ocean. This leads to relatively narrow tundra and ablation zones and a higher contribution of solid ice discharge at the expense of GrIS and tundra runoff. To our knowledge, no studies have identified a strong link between MoA and freshwater input fractions in Greenland fjords. In contrast, freshwater input fractions into fjords poorly correlate with temperature, melt, or snowfall. This novel result will facilitate the interpretation of e.g. future changes in the distribution of freshwater fluxes in terms of climate change. Higher temperatures increase melt, hence GrIS runoff, and allow for a higher exposed-land fraction, while more solid precipitation has the opposite effect. Both southern regions are relatively mild, but due to their different precipitation regimes, their freshwater fractions are different. Similarly, the NW sector is drier than the SW sector, but because of the lower temperatures, the freshwater fluxes in the NW are even more dominated by solid ice discharge than the SE sector.

Annual mean tundra runoff is on average 15 % of the total runoff (1990–2023), exceeding the relative contributions estimated in previous work (9 %–11 % estimated from Fig. 3 in ). Seasonal contributions from tundra runoff and fjord precipitation to Greenland-wide freshwater input can reach up to 35 % and 11 %, respectively. The south and east of Greenland have relatively high precipitation rates , which leads to the regions CE, SE, SW, and NE having a relatively high contribution of fjord precipitation to the total freshwater input (monthly percentages up to 22 %, 12 %, 20 %, and 22 %, respectively), especially from October until April, when runoff is small (Fig. ). This study also identifies an increase in summertime fjord precipitation in CE and SE, but no significant trends in annual totals are found. Although summertime fjord precipitation has a relatively low contribution to the total freshwater input, its impact differs from runoff as all precipitation enters the fjord surface waters directly in a relatively spatially homogeneously fashion, thereby increasing stratification. While the precipitation phase (liquid or solid) is unlikely to have a large impact on freshwater input, it has a large impact on the heat budget. For example, snowfall into fjords can have a cooling effect on the upper layers, decreasing stratification, but this is outside the scope of this study.

In CE, NE, NW, and SE we find an increase in (summer) tundra runoff. Compared to glacial runoff, tundra runoff brings a different type of nutrients to fjords, and its entry point is less concentrated than runoff and solid ice discharge from marine-terminating glaciers. This ultimately affects ecosystems , e.g. by shifting spring blooms to different communities. Despite the increase in absolute tundra runoff, its relative importance for the fjord freshwater balance is decreasing in time as freshwater sources from land ice are increasing more rapidly. An obvious reason is the limited water storage in the tundra seasonal snow cover compared to land ice.

The region covered by a fjord is hard to define, and some freshwater studies only considered land surface basins or included or excluded large bays such as Disko Bay and Kangertittivaq (formerly known as Scoresby Sund). To address the sensitivity of our results regarding how fjords are defined, we performed a fjord area sensitivity test. When being more lenient in the algorithm outlining fjords to include bays such as Disko Bay and by running the algorithm not only for the mainland but also for all barrier islands, the total fjord (and bay) area increases by up to 87 % (Fig. ). The largest relative increase in area is found in the NW (and NE) at +177 % (+160 %), while in CE, the fjord area only increases by 7 %. This results in up to 186 % (181 %) increases in (fjord) precipitation in NE (NW) and 15 % more in CE. In NE and NW, this increases the relative contribution of (fjord) precipitation from 5 % to 8 % and from 2 % to 3 % between 1990–2023. In CE, we find an increase from 8 % to 9 %.

In the previous sections, we used RACMO-based freshwater fluxes and solid ice discharge from . As discussed in this section, using alternative estimates does not considerably change the absolute and relative contribution of the freshwater input sources. CARRA gives slightly lower (fjord) precipitation values than RACMO (on average 7 Gt yr⁻¹ less or 15 %), but the temporal variability is comparable (Fig. ). The lower precipitation results in a decrease in the maximum (monthly) share of fjord precipitation from 12 % to 10 %. Regionally, the difference is largest in the SW in DJF (+3 %), which is true for most regions, except for NO, where the largest reduction in the total share is in May (-3 %) (Fig. ).

GrIS runoff from MAR is higher than RACMO (+3 %, 1990–2023), especially since 2010 (+5 %) (Fig. ). This is not the case for GICs, which is 3 % lower in MAR on average (1990–2023). The impact on the relative share of GrIS runoff to freshwater is only +1 % (1990–2023). Regionally, the differences between MAR and RACMO are most noticeable in NW (+8 Gt yr⁻¹), SW (+11 Gt yr⁻¹), and CE (-9 Gt yr⁻¹). The difference leads to a higher share of GrIS runoff when using MAR in NO, NW, and SW (+2.3 %, +3.6 %, and +3.4 %, respectively) and a lower share in CE (-3.4 %). For GIC runoff, the largest change is -3 Gt yr⁻¹ in MAR in NE, reducing the relative share of GIC runoff by 1.9 % in NE.

We find that tundra runoff in RACMO is 36 % higher than in MAR (175 vs. 128 Gt yr⁻¹, averaged over 1990–2023). Differences are especially large in NO and NE, where the difference is 8 Gt yr⁻¹ (47 %) and 13 Gt yr⁻¹ (43 %), respectively. Using MAR tundra runoff thus results in a decrease in the tundra runoff contribution to the total freshwater input in fjords of 9 % and 17 %, respectively. This shows that in MAR the contribution of tundra runoff remains significant, but the large model differences require further investigation.

Solid ice discharge in is only 0.9 % smaller than in the study by . For their common epoch of monthly values (2009–2018) (see Sect. ), the datasets agree on annual totals (Fig. ). The latter dataset shows larger seasonal variability, resulting in a small maximum mean increase of 1 Gt in July over the whole of Greenland (Fig. ) and a small relative change compared to the other components of 0.4 % in September (Fig. ). Regionally differences are larger, leading to relatively less solid ice discharge in NO, NW, and CE, decreasing the percentage share of solid ice discharge by 1.5 (±0.3) % on average (Fig. ). In the other regions (NE, CW, SW, SE) the relative share of solid ice discharge increases by 0.6 (±0.3) % on average. The changes are not uniform over the months but are still considered small. We conclude that uncertainty due to the use of different data sources is less than the interannual variability during the period 2009–2023.

Apart from the above-discussed uncertainties, this study covers freshwater input but not the freshwater budget of fjords. It moreover neglects (i) the storage effect of sea ice, i.e. collecting snow and rain accumulation; (ii) the advection of sea ice into and out of the fjords; and (iii) sea ice preventing precipitation from directly entering the fjord waters. The effect of sea ice on the fjord's freshwater budget varies per region and season. Most sea ice in Arctic fjords is landfast and thus will melt in the same fjord where it originally formed, temporarily storing freshwater rather than being a separate source . Large regional and temporal variability exists in sea ice presence and the timing of formation and melt. In SE Greenland, Arctic sea ice can originate offshore, importing freshwater, while fjords in the SW can remain largely ice-free throughout the year . The timing of seasonal sea ice break-up differs regionally: in SE Greenland, it occurs between May and August, while NO fjords can be ice-covered throughout most of the year . We hypothesize that the uncertainty resulting from neglected sea ice processes will be larger with increasing latitude, with more in the east than in the west and in winter months. Exploring the impact of sea ice on the freshwater budget is a potential avenue for future research.

Another process not considered is that the transformation from solid ice to freshwater may happen outside the fjord if icebergs leave the fjord . Finally, our study neglects freshwater storage effects in the fjord, as fjord circulation is outside the scope of this study. We excluded solid ice discharge from the GICs, as it is estimated to be only 2.3–3.2 Gt yr⁻¹ between 2000–2020 on average per decade , and the dataset does not specify discharge on a regional and monthly scale. Solid ice discharge is determined by applying fixed flux gates, which comes with the advantage that the solid ice discharge in this study is consistent with earlier work . However, the disadvantage is that we neglect solid ice discharge due to systematic glacier front retreat, which is estimated to have averaged 42 Gt yr⁻¹ since 2000 for the total ice sheet , i.e. similar to or larger in magnitude than basal melt over the studied period. Because the glacier front advances in winter and retreats in summer (63 ± 6 Gt seasonally; ), the use of fixed flux gates likely leads to an underestimation of solid ice discharge in summer and an overestimation in winter. This error is however less important for a study addressing freshwater input assuming fixed outlines of the fjord, like we do here, than one addressing the freshwater budget of fjords.