Lagrangian detection of precipitation moisture sources for an arid region in northeast Greenland: relations to the North Atlantic Oscillation, sea ice cover and temporal trends from 1979 to 2017

Temperature in northeast Greenland is expected to rise at a faster rate than the global average as consequence of anthropogenic climate change. Associated with this temperature rise, precipitation is also expected to increase as a result of increased evaporation from a warmer and ice-free Arctic Ocean. In recent years, numerous palaeoclimate projects have begun working in the region with the aim of improving our understanding of how this highly-sensitive region responds to a warmer world. However, a lack of meteorological stations within the area makes it difficult to place the palaeoclimate records in the 5 context of present-day climate. This study aims to improve our understanding of precipitation and moisture source dynamics over a small arid region located at 80° N in northeast Greenland. The origin of water vapour for precipitation over the study region is detected by a Lagrangian moisture source diagnostic, which is applied to reanalysis data from the European Centre for Medium-Range Weather Forecasts (ERA-Interim) from 1979 to 2017. While precipitation amounts are relatively constant during the year, the regional moisture sources display a strong seasonality. The most dominant winter moisture sources are the 10 North Atlantic above 45° N and the ice-free Atlantic sector of the Arctic Ocean, while in summer the patterns shift towards local and north Eurasian continental sources. During the positive phases of the North Atlantic Oscillation (NAO), evaporation and moisture transport from the Norwegian Sea is stronger, resulting in larger and more variable precipitation amounts. Testing the hypothesis that retreating sea ice will lead to increase in moisture supply remains challenging based on our data. However, we found that moisture sources are increasing in case of retreating sea ice for some regions, in particular in October to December. 15 Although the annual mean surface temperature in the study region has increased by 0.7 ◦C dec−1 (95% confidence interval [0.4, 1.0] ◦C dec−1) according to ERA-Interim data, we do not detect any change in the amount of precipitation with the exception of autumn where precipitation increases by 8.2 [0.8, 15.5] mm dec−1 over the period. This increase is consistent with future predicted Arctic precipitation change. Moisture source trends for other months and regions were non-existent or small.

1 Introduction Figure 1. Average of yearly ERA-Interim precipitation (1979. The study region is depicted with the nine gridpoints located between 22.5°W and 21°W and between 79.5°N and 81°N. The exact location of the studied caves is (21.7419°W, 80.3745°N). Average precipitation in the study region is 207 mm year −1 (95 % confidence interval of [192,224] mm year −1 ). (see Sect. 2.2). ERA-Interim has a fully revised humidity scheme and higher spatial resolution (∼79 km) than ERA-40, that was used by Sodemann et al. (2008a) to compute Greenland winter precipitation sources. The even newer ERA5 reanalysis data was not yet available at the time we conducted these analyses. The study region (21°W-22.5°W, 79.5°N-81°N, Fig. 1) consists of nine gridpoints with a horizontal resolution of 0.75°, which are located around the caves in northeast Greenland. 90 Several gridpoints were chosen to smooth out local inhomogeneities. The ERA-Interim dataset is used in the time span of 3D-wind field, surface pressure, PBL height and two metre temperature were used. Moisture sources over land and ocean are distinguished by using the land/sea mask of ERA-Interim on the same 0.75°grid. For each gridpoint, the monthly sea ice area was computed by multiplying the ERA-Interim sea ice fraction (0-1) by the latitudinally-weighted gridpoint area. To classify gridpoints into land, ocean and sea ice, a threshold of 0.5 was set for the fractional land/sea mask and sea ice fraction.
In addition, relations between precipitation and its moisture sources to other ERA-Interim parameters were examined. These 100 are the sea ice area, the mean 500 hPa geopotential height, and the vertically integrated water vapour transport (sum of the integrated northward and eastward cloud liquid, cloud frozen, and water vapour transport). To relate precipitation and moisture source variability to large-scale teleconnection patterns, we computed correlations to the monthly NAO index data from the National Oceanic and Atmospheric Administration climate prediction centre (NOAA, 2020).

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To compute the motion of air parcels, 15-day backward trajectory calculations by the Lagrangian Analysis tool LAGRANTO version 2.0 (Sprenger and Wernli, 2015), first version by Wernli and Davies (1997), were realised for every six hours from February 1979 to May 2017. Trajectories start at the node of the 0.75°regular grid of the study region (9 gridpoints, Fig. 1) on 11 vertical levels from the surface to a height of 500 hPa (∆p = 49.9 hPa). This corresponds to 99 trajectories per time step.
In the next step, the trajectories that aren't leading to precipitation in the study region were filtered out. The requirements for 110 the selected trajectories were that relative humidity exceeded 80 % and specific humidity (q) decreased in the last time step (Sodemann et al., 2008a).
Evaporation and precipitation of precipitation-trajectories are identified by temporal changes in specific humidity (∆q).
Using the assumption of a well-mixed PBL, the moisture content of air parcels increases within the PBL in case of a positive ∆q. Moisture uptakes that occur above the PBL, however, are detached from the surface and are explained by physical or 115 numerical processes, e.g., convection, evaporation of precipitating hydro-meteors, change of liquid water content, or ice water content, subgrid-scale turbulent fluxes, numerical diffusion, and errors, or physical inconsistencies (Sodemann et al., 2008a).
Along each trajectory, moisture uptake locations inside the PBL are weighted by their contribution to the total precipitation in the study region by taking en route precipitation into account. Each moisture uptake is interpolated on a 1 • grid and we calculate the monthly means on this basis.

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This Lagrangian approach of Sodemann et al. (2008a) is suitable for our study as it gives similar moisture source regions and needs lower computation cost than a more complex Eulerian approach (Winschall et al., 2014, for a case study in Europe).
The marine PBL height is often underestimated in numerical weather prediction models (Zeng et al., 2004). Therefore, the threshold for a moisture source location inside the PBL height is lifted by a factor of 1.5. Similar to Langhamer et al. (2018), the height of the PBL was converted in our study into pressure coordinates by applying the barometric formula with surface 125 pressure and temperature as free variables (and a constant temperature lapse rate of 0.0065 K m −1 ).
A measure for the performance of the method is shown in Fig. 3. The Lagrangian evaporation sum that contributed to precipitation in the study region correlates very well with the total precipitation over the study region from ERA-Interim, indicating that the method is able to reproduce the variability of precipitation. 48 % of the total moisture sources could be assigned to specific evaporation locations with the applied Lagrangian moisture source diagnostic. For comparison, similar 130 studies by Sodemann and Zubler (2010) in the European Alps and Langhamer et al. (2018) in Patagonia reached 50% and 71% attribution, respectively. The remaining moisture sources could not be identified to evaporation at the surface (moisture uptake above PBL) or were unidentifiable. There is no clear annual cycle visible in the attribution: the fraction ranges from a minimum of 41 % in August to a maximum of 57 % in June (Fig. 4). Specifically in summer, precipitation in the study region varies more than its attributed moisture sources. We discuss the possible implications of these uncertainties in Sect. 5.4.

Statistical methods
To compute confidence intervals of our trends and averages, we estimate the 95 % confidence intervals of the mean or median (significance level of 0.05) without assuming a parametric distribution by using the bootstrapping method (Wilks, 2011). This is done because some subsets of daily precipitation averaged over a month as well as other related parameters reject the null hypothesis that their distributions are drawn from a normal distribution using a Shapiro-Wilk normality test (Wilks, 2011). To Therefore, significant differences in e.g., the mean of two values occur at the 5 % significance level if the 95 % confidence intervals do not overlap.
May and June are slightly drier on average whereas September is wettest (Fig. 4). September is the wettest month for 9 of 40 years, June is the driest month for 6 of 40 years, and April is the driest month for 8 of 40 years. September (as the wettest 160 month) has the greatest variability (interquartile range of 0.30-1.24 mm day −1 ), whereas June (as the driest month) displays the least variability (interquartile range of 0.14-0.30 mm day −1 ). April also shows a large variability (interquartile range of 0.10-0.80 mm day −1 ) and is the month with the most positively skewed monthly precipitation distribution. Generally, precipitation over the Atlantic Arctic sector is stronger in winter months due to the enhanced North Atlantic cyclone track over the relatively warm open water and the moisture flux convergence specifically near to the Icelandic Low. For continental areas 165 above 60°N, however, most precipitation occurs in July, August and September (ERA-Interim and ASRv1, Bromwich et al., 2016). This can be explained by higher cyclone and frontal activity in summer because of heating contrasts between snow-free land and snow areas (Serreze and Barry, 2014).

Mean and Annual cycle of moisture sources
While precipitation amounts are relatively constant during the year, the corresponding contributing moisture sources display 170 a strong seasonality in magnitude and location (Fig. 5). In winter, most moisture sources are located over the North Atlantic above 45°N and the ice-free Atlantic sector of the Arctic Ocean with a maximum between Scandinavia and Svalbard. This maximum is most pronounced in January and then gradually diminishes until May. Starting with May, local moisture sources begin to contribute to precipitation and peak in June. In July, moisture sources seem to come mostly from land areas over the north Eurasian continent. September has the minimum amount of sea and land ice and represents a transitional phase, where 175 there seems to be both land sources over Scandinavia and the majority of ocean sources over the North Atlantic. This could be a possible indicator why precipitation is strongest in September (Fig. 4). From October, the pronounced maximum over the Norwegian Sea appears again with minimal contributions from land.
The gradual transition from more North Atlantic, North Sea, Norwegian Sea and Barents Sea contributing moisture sources in winter to more local and continental Scandinavian and Eurasian contributions in summer can be partially explained by 180 changes in the geopotential height of the 500 hPa surface (Fig. 5). The zonal geostrophic flow south of Greenland is stronger in winter than in summer, as shown by the stronger gradient of the geopotential height. The westerly zonal flow weakens in summer, specifically in June, which could explain why June has the smallest and least variable precipitation.
Another way to describe moisture transport is to look at the integrated water vapour transport (IVT, mean annual cycle in This emphasises why the maximum of moisture source contribution is diagnosed over the Norwegian Sea for most months. Evaporation over the Arctic Ocean seems to be prevented by sea ice and in summer, a gradual transition occurs towards more IVT in the Arctic. In June, IVT is larger near to the study region, which is an indicator for the more local moisture sources found by the Lagrangian moisture source diagnostic (Fig. 5). Furthermore, from July till September there is generally larger 190 IVT over the Eurasian continent. This coincides with the large fraction of contributing moisture sources over the north Eurasian continent found by the Lagrangian diagnostic in these months.   Figure 5. Annual cycle of mean monthly attributed moisture sources contributing to precipitation in study region over the period February 1979-May 2017 (gridpoints coloured after their contribution). The mean sum of moisture sources over all gridpoints (i.e. accounted precipitation) is given for each month with its 95 % confidence interval and is only a part of the total precipitation (Fig. 4). The averaged mean 500 hPa geopotential height (grey lines) and the mean ice area cover (grey shaded area) are depicted as well.

K-means clustering of moisture contributions
To analyse regional contributions of moisture sources, different moisture source regions were defined by applying a classification algorithm (K-means clustering, e.g., Wilks, 2011). K-means clustering separates data in samples grouped after their 195 similarities. In our case, we estimated similarity by first selecting the gridpoints that have contributed moisture sources over the study period and then computing the percentage of each gridpoint's moisture source contribution to the total mean precipitation for each month of the year. Therefore, a table of 24051 gridpoints x 12 months (where gridpoints=100 %) was fed to the algorithm (here: sklearn, Pedregosa et al., 2011). The algorithm then separates the gridpoints in a user-chosen number of clusters, here based on the annual cycle of moisture source contribution to precipitation in the study region.

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The raw output of the K-means clustering is plotted in Fig. 7a. Although the gridpoints' locations were not included in the algorithm, the clusters mostly cover homogeneous areas, which means that gridpoints that are near to one another display a similar behaviour in the relative moisture source contribution throughout the year. The algorithm recognises the features of cluster formations from Fig. 5: the green coloured cluster corresponds to the area of a pronounced maximum in moisture sources for most months, and the cyan coloured cluster corresponds to the local sources in summer directly above the study 205 region. The K-means clustering algorithm separated the gridpoints into clusters displaying significantly different behaviour with respect to the 95 % confidence interval (Fig. 7b, c). The number of five distinct clusters shown here was chosen because it produced the best compromise between differentiating behaviour patterns and still having significantly different clusters.
In winter, moisture sources over land contribute minimally (in January ∼6 %), however, in summer, the majority of moisture 210 sources come from land regions (in July ∼62 %). The moisture source contribution of sea ice areas is relatively low, but highest in June (23 %, Fig. 7d). As June is the driest month with the highest contribution of local moisture sources (Fig. 7), there is an indication that evaporation over sea ice near to the study region is contributing to precipitation in the study region. However, if those gridpoints are chosen that are defined with a sea ice concentration equal or above 0.9 (instead of 0.5, see Sect. 2.1), the contributions in all months decrease to a maximum of 15 % in June and is in most other months around 3 % (not plotted).

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Hence, large parts of contributing evaporation over a defined sea ice area occur over those gridpoints where the total area of the gridpoint is partially sea ice covered.
For more detailed analyses (and because the clustering algorithm cannot separate ocean from land sources), we now further refine the automated clusters with manual intervention. The blue coloured cluster in Fig. 7a does not differ between the Norwegian/Greenland and the Barents Sea moisture sources. To interpret the results in the context of NAO, we split the former 220 blue coloured region into two regions (2O and 4O) and distinguished between ocean (with sea ice) and land regions (compare Fig. 7a and Fig. 8a). Moreover, we divided the large former violet coloured cluster of Fig. 7a into two new groups: the 7O/7L cluster that contributed least (in total only 10 % of the former violet coloured cluster area) and into the 6O/6L cluster that contributed most (in total 90 % of the former violet coloured cluster area). This gives a better impression of areas contributing that are far away from the study region. Hence, the new separation results in seven ocean and four land clusters (Fig. 8a, the 225 small 4L cluster area is not a significant contributor and therefore neglected).
For the ocean clusters 2O, 3O, 4O & 5O, the relative maximum is in winter while the minimum is in summer (Fig. 8e). The Norwegian Sea (3O, Fig. 8) is one of the main moisture sources, specifically during winter. The Norwegian Sea is located below the North Atlantic storm track and is a main region for convective warming (Tsukernik et al., 2004) because of the relatively warm ice-free ocean and the relatively dry and cold air above resulting in the highest total column vapour (precipitable water) 230 in the Arctic. In addition, in the colder seasons, more evaporation occurs because of larger vertical humidity gradients and stronger moisture transport due to higher temperature gradients between the subtropics and the Arctic (Serreze and Barry, 2014).
All land clusters have their maximum contribution in July except for the local 1L cluster where the maximum occurs in June ( Fig. 8d, g). A large part of summer Arctic precipitation comes from evapotranspiration over nearby land regions by regional 235 recycling of water vapour that peaks in summer due to enhanced convection from stronger solar insolation (Serreze and Barry, 2014). The moist continental air masses from non-local regions over the north Eurasian continent are transported in summer towards northeast Greenland by a cyclone with a trough axis between Iceland and Svalbard (see 500 hPa geopotential height in Fig. 5 and IVT of Fig. 6). Large parts of these land clusters (1L, 5L, 6L, Fig. 8a) and the study region itself are located in the continuous permafrost zone (Brown et al., 1998). Thus, enhanced evapotranspiration in summer could also be explained by 240 thawing of the uppermost permafrost layers (Biskaborn et al., 2019).

Interannual variability from the North Atlantic Oscillation (NAO)
The NAO is one of the most important patterns of atmospheric circulation variability over the middle and high latitudes, specifically in the cold season (November-April; Hurrell et al., 2003). In its negative phase (NAO−), there is a weaker subpolar (h)   for ocean (e, g) and for land (g) would give the total land or ocean (with & without sea ice) contribution shown in Fig. 7d. In (h), the used cluster abbreviations and descriptions of approximate geographical regions of the K-means clusters of (a) are listed.
low over Iceland and a less pronounced subtropical high over the Azores, while in its positive phase (NAO+), a larger pressure gradient leads to stronger northeastward-oriented surface winds over the North Atlantic. In the following, we assess whether variability in the NAO affects the inter-annual variability of precipitation and moisture sources of the study region. ocean as well as the 5L and 6L land moisture source clusters contributed significantly more for NAO+ than for NAO− months 265 (Fig. 10). The larger NAO dependency of the 4O cluster, part of Barents Sea, compared to the 2O cluster, part of northeast Atlantic and western Norwegian Sea (Fig. 10), is another justification for the manual splitting of these areas that were clustered as one region by the K-means clustering (compare Fig. 7a and Fig. 8a). To conclude, there was an increased moisture uptake and transport to the study region for NAO+ months in January, April and September from the North Atlantic above 45°N and the ice-free Atlantic sector of the Arctic Ocean, specifically from the Norwegian Sea, which resulted in more precipitation over 270 the study region for these months in the NAO+ phase.

Relationship to sea ice
A clear decreasing sea ice trend north of 30°N has been observed for the last 40 years. From ERA-Interim data, we compute 0.35 [0.26, 0.43] million km 2 decade −1 yearly minimum sea ice area decrease (mostly September) and 0.67 [0.54, 0.80] million km 2 decade −1 yearly maximum sea ice area decrease (mostly March). Bintanja and Selten (2014) showed that decreasing sea ice will enhance future evaporation in the Arctic, as open water at freezing point will replace ice at temperatures far below zero.
We now test the working hypothesis that reduced sea ice results in larger contributing moisture sources for our study region.
For total precipitation in the study region, no significant correlation to the Arctic sea ice area was found when looking at each month of the year separately. Adding a time lag between sea ice and resulting precipitation of plus one or two months also resulted in no significant correlation. When comparing the seasonal mean precipitation against the maximum sea ice area

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of that year, we found some significant but small relations in autumn and winter.
A clearer insight might emerge when looking at the relation of each ocean cluster's attributed moisture sources against the respective relative sea ice area. When considering the total attributed moisture sources for each ocean cluster across the whole year, no significant correlations (Spearman's rank correlation with p-value<0.05) between moisture sources and relative sea ice area are found (Fig. 12a). If individual months are considered for each ocean region, then few significant correlations are 285 observed. The main exception is for December, where the majority of regions display a significant correlation with relative sea ice area (Fig. 12a). Changes in the sea ice area can only poorly describe the variance in the moisture sources of entire ocean cluster areas (Fig. 12a) because large parts of them never had sea ice from 1980 till 2016 (for that month of the year or even not at all). Thus, the effect of sea ice in a given area on the attributed moisture source was further investigated by considering sub-regions of clusters with only those gridpoints that had once over the study period a sea ice concentration of above 0.5 290 (Fig. 12b). As this is different for each month of the year, for each month a different fraction of the ocean cluster was analysed.
Compared to Fig. 12a, Fig. 12b shows that the annual contribution from sea ice related fractions of the 4O, 5O and 6O clusters is significantly correlated to decreasing sea ice. In addition, some more correlations for individual months were found over those specific fractions of the clusters (strongest in autumn-winter months, Fig. 12b). However, moisture sources over the sea only at the area of those ocean gridpoints that had once a sea ice concentration of above 0.5 during the study period (effectively reducing each cluster's area to the sea ice relevant areas). The legend for the used cluster abbreviations is in Fig. 8a, h.
ice related sub-regions as defined in Fig. 12b contribute on average only 16 % to the entire diagnosed moisture sources. Hence, 295 the correlations of moisture sources against sea ice (Fig. 12b) describe only a very small fraction of the entire moisture sources for the study region, which also explains why we did not find correlations between Arctic sea ice area and precipitation in the study region.
When specifically considering moisture source regions, the 1O ocean cluster (closest to the study region) displays significant correlations for seven months (September till April) with increasing attributed moisture sources over 1O for decreasing relative 300 sea ice area (Fig. 12a, b). Changes in the sea ice amount in 1O change the general evaporation over the area, possibly directly influencing precipitation in the study region. For clusters located further away, changing sea ice might also directly effect the evaporation over that area. However, contributing moisture sources depend also on the moisture transport to the study region, which changes with decreasing sea ice as well. This might be one reason for the weak relations that we found. Looking at all ocean clusters together, we only found a correlation for June, which was positive: this is not expected and is likely a statistical 305 coincidence.

Temporal evolution
According to ERA-Interim, the study region has warmed by 2.8 [1.6, 4.0] • C (two metre temperature) in the 40-year period 1979-2018. We now test whether such a trend is also detectable for precipitation (or regional moisture sources) by looking at its temporal evolution (Fig. 13a). A possible trend was tested by computing the Pearson correlation coefficient through 310 a linear fit between time and precipitation or moisture sources. Linear regression analysis requires that residuals from the fitted regression line are normally distributed, which is not always the case for monthly data. Therefore, the more robust nonparametric Mann-Kendall trend test was also applied to detect whether a monotonic upward (downward) trend had occurred, which does not necessarily need to be linear (Wilks, 2011). The yearly, winter, spring and summer precipitation from 1979 to 2018 at the study region do not show a significant trend. There is a small increasing trend in autumn precipitation of 315