High-resolution stable isotope signature of a land-falling Atmospheric River in southern Norway

Heavy precipitation at the west coast of Norway is often connected to elongated meridional structures of high integrated water vapour transport known as Atmospheric Rivers (AR). Here we present high-resolution measurements of stable isotopes in near-surface water vapour and precipitation during a land-falling AR in southwestern Norway on 07 December 2016. In our analysis, we aim to identify the influences of moisture source conditions, weather system characteristics, and post-condensation processes on the isotope signal in near-surface water vapour and precipitation. 5 A total of 71 precipitation samples were collected during the 24-h sampling period, mostly taken at sampling intervals of 10–20 min. The isotope composition of near-surface vapour was continuously monitored in-situ with a cavity ring-down spectrometer. Local meteorological conditions were in addition observed from a vertical pointing rain radar, a laser disdrometer, and automatic weather stations. We observe a stretched, "W"-shaped evolution of isotope composition during the event. Combining paired precipitation and 10 vapour isotopes with meteorological observations, we define four different stages of the event. The two most depleted periods in the isotope δ values are associated with frontal transitions, namely a combination of two warm fronts that follow each other within a few hours, and an upper-level cold front. The d-excess shows a single maximum, and a step-wise decline in precipitation and a gradual decrease in near-surface vapour. Thereby, the isotopic evolution of the near-surface vapour closely follows that of the precipitation with a time delay of about 30 min, except for the first stage of the event. Analysis using an 15 isotopic below-cloud exchange framework shows that the initial period of low and even negative d-excess in precipitation was caused by evaporation below cloud base. The isotope signal from the cloud level became apparent at ground level after a transition period that lasted up to several hours. Moisture source diagnostics for the periods when the cloud signal dominates show that the moisture source conditions are then partly reflected in surface precipitation and water vapour isotopes. In our study, the isotope signal in surface precipitation during the AR event reflects a combination of atmospheric dynamics, 20 moisture sources and atmospheric distillation, as well as cloud microphysics and below-cloud processes. Based on this finding, we recommend careful interpretation of results obtained from Rayleigh distillation models in such events, in particular for the interpretation of surface vapour and precipitation from stratiform clouds.


Introduction
Precipitation can be considered as the end product of the atmospheric hydrological cycle. Weather systems lead to sequences of ocean evaporation, horizontal and vertical transport and mixing of atmospheric water vapour, microphysical processes within clouds on characteristic time scales (Läderach and Sodemann, 2016). The stable isotope composition of precipitation is, therefore, an integrated result of the isotopic fractionation, that occurs during phase changes in the atmosphere (Gat, 1996). In 5 addition, post-condensation processes can influence the isotope composition below cloud base (Graf et al., 2019). Therefore, observations of stable water isotopes in precipitation hold the promise of allowing to extract information about moisture transport and moisture sources for individual weather events. Besides, detailed measurements of water isotopes provide the potential to constrain parameterisations in atmospheric models and thereby to improve weather prediction and climate models (Bony et al., 2008;Pfahl et al., 2012;Yoshimura et al., 2014).
The vapour data are post-processed and calibrated according to the following steps. (1) The raw data are corrected for isotope ratio-mixing ratio dependency using the correction function in Weng et al. (2020), which was determined for the same analyser used here.
(2) For each calendar month, SDM calibration periods are identified. Then, the median value of mixing ratio, δ 18 O and δD are obtained for each calibration period. The values that deviate from the median value by more than 0.5 ‰ in δ 18 O 10 or 4.0 ‰ in δD are discarded to remove variations due to bursting bubbles and other instabilities. The remaining data for each period are then averaged and the standard deviation calculated. Calibrations were retained if at least 60 % of the calibration period were kept after quality control. (3) The vapour measurements were calibrated to SLAP2-VSMOW2 scale following IAEA recommendations (IAEA, 2009). To this end, the two nearest bounding calibrations of sufficient quality were identified for each calendar day and each standard. Finally, the calibrated vapour data are averaged at a 10-minute interval using centred 15 averaging.

Precipitation isotope sampling and analysis
Liquid precipitation was sampled at the GFI rooftop observatory at high temporal resolution with a manual rainfall collector, similar to the setup used in Graf et al. (2019). The collector consists of a PE funnel of 10 cm diameter, which directs the collected water into a 20 mL open-top glass bottle. A total of 71 precipitation samples were collected during the 24-h sampling 20 period between 00:00 UTC 07 December and 00:00 UTC 08 December 2016. The sampling interval was adjusted according to the precipitation intensity. Two samples were collected over a 105 min interval, 8 samples with 20-40 min intervals, and 61 samples with 10-20 min intervals (ref. supplementary material). The bottle and funnel were dried between each sample using a paper wipe. The sample was immediately transferred from the bottle to a 1.5 mL glass vial VWR,USA) and closed with an open-top screw cap with PTFE/rubber septum (part no. 548-0907, VWR, USA) to prevent evaporation until 25 sample analysis.
The samples were stored at 4 • C before being analysed for their isotope composition at FARLAB, University of Bergen, Norway. During the analysis, an autosampler (A0325, Picarro Inc.) transferred ca. 2 µL per injection into a high-precision vaporizer (A0211, Picarro Inc., USA) heated to 110 • C. After blending with N 2 (Nitrogen 5.0, purity >99.999 %, Praxair Norge AS), the gas mixture was directed into the measurement cavity of a cavity ring-down spectrometer (L2140-i, Picarro 30 Inc., USA) for about 7 min with a typical mixing ratio of 20 000 ppmv. To reduce memory effects between sample, two so-called wet flushes consisting of 5 min of vapour mixture at 50 000 ppmv were applied to the analyzer at the beginning of each new sample vial. Three standards (12 injections each, plus wet flush) were measured at the beginning and end of each batch, consisting typically of 20 samples (6 injections each, plus wet flush). The averages of the last 4 injections were used for 6 https://doi.org /10.5194/wcd-2020-58 Preprint. Discussion started: 9 December 2020 c Author(s) 2020. CC BY 4.0 License. further processing. The measurement data were first corrected for isotope-humidity dependency using a linear correction for the analyzer obtained over a humidity range of 15 000-23 000 ppmv. Then, data were calibrated to the SLAP2-VSMOW2 scale following IAEA recommendations (IAEA, 2009)

The concept of equilibrium vapour
Due to equilibrium and kinetic isotopic fractionation during phase transitions, the isotope ratios in water vapour and precipitation can not be directly compared to one another. Instead, we use the concept of equilibrium vapour to compare the state of both phases (e.g. Aemisegger et al., 2015). The equilibrium vapour from precipitation is the isotope composition of vapour 10 that is in equilibrium with precipitation at ambient air temperature T a . We calculate the equilibrium vapour of precipitation as where α l→v (T a ) is the temperature-dependent fractionation factor of the liquid to vapour phase transition following Majoube (1971). We quantify the difference between equilibrium vapour from precipitation samples and ambient vapour then as While a similar notation can be defined for ∆δ 18 O, we use the notation ∆δ to refer to ∆δD only. Using the above deviations from isotopic equilibrium, Graf et al. (2019) introduced a useful interpretative framework to quantify the effect of belowcloud processes on the isotope composition of ambient vapour and precipitation. This so-called ∆δ∆d-diagram quantifies the deviation of δD and d-excess in the liquid from the vapour phase at ambient temperatures from isotopic equilibrium 20 as indicators of evaporation and equilibration below cloud-base. We make use of this interpretative framework to quantify the below-cloud processes during the AR event studied here. In addition, we utilize a set of sensitivity studies with the Below-Cloud Interaction Model (BCIM, Graf et al., 2019) to identify the main influences during the case studied here in the ∆δ∆d-diagram.
The sensitivity experiments are described in more detail in Appendix B.

Reanalysis and weather forecast data 25
The large-scale meteorological situation is depicted using the global ERA-Interim reanalysis data from the European Centre for Medium-Range Weather Forecast (ECMWF) re-gridded to a 0.75×0.75 • regular grid. Moisture transport is quantified by the integrated water vapour transport (IVT; e.g. Nayak et al., 2014;Lavers et al., 2014Lavers et al., , 2016, whereas mean sea level pressure (SLP) is used to depicts the location of weather systems.
In addition, air temperature, solid and liquid precipitation, cloud water and cloud ice were extracted as profiles across all 30 model levels from ERA5 reanalysis data (Hersbach et al., 2020)

Lagrangian moisture source diagnostic
Moisture sources are a potential factor influencing the isotope composition in precipitation. Here we apply a quantitative 10 Lagrangian moisture source diagnostic WaterSip  to diagnose the moisture sources for evaporation contributing to the AR event on 07 Dec 2016. The WaterSip method identifies moisture source regions and transport conditions from a sequentially weighted specific humidity budget along backward trajectories of air parcels that arrive over the target area.
More specifically, the method assumes that the change in specific humidity in an air parcel during each 6 h time step exceeding a threshold value is due to either evapotranspiration or precipitation. A sequential moisture accounting then provides 15 the fractional contribution of each evaporation event to the specific humidity at an air parcel location, and by taking into account the sequence of moisture uptakes and losses, the final precipitation in the target area. For the AR event in this study, the thresholds are set to be 0.2 g kg −1 for ∆q c , with a 20-day backward trajectory length, and relative humidity >80 % to identify precipitation over the target region. These thresholds result in source attribution for over 98 %. Here, the moisture uptakes from both within and above the boundary layer (BL) have been taken into account Winschall 20 et al., 2014).
The basis of the WaterSip diagnostic applied here is the dataset of Läderach and Sodemann (2016), which we have extended over the entire ERA-Interim period. In that dataset, the global atmosphere is represented by 5 million air parcels of equal mass calculated using the Lagrangian particle dispersion model FLEXPART V8.2 (Stohl et al., 2005), with wind and humidity and other meteorological variables from the ERA-Interim reanalysis. For this study, the diagnostic was run with a target area of ca. 25 110 × 110 km centred over Bergen (59.9-60.9 • N and 4.3-6.3 • E), including both land and ocean regions. The precipitation event studied here was represented by in total 1100 trajectories arriving in the target area.
As with other methods to identify moisture source regions, the WaterSip diagnostic is associated with uncertainty due to threshold values, interpolation errors, and conceptual limitations Sodemann, 2020). To enable a comparison with stable isotope observations, the WaterSip method predicts the d-excess from the evaporation conditions at the 30 moisture sources using the empirical relation of Pfahl and Sodemann (2014). More specifically, the SST over ocean regions and the surface specific humidity from ERA-Interim are used to calculate RH with respect to SST, and then to calculate d-excess from the empirical relation d = 48.2 ‰ − 0.54 ‰/% · RH SST , using a weighted average of all contributing moisture sources.
On 7 of December 2016 a substantial amount of precipitation accumulated over southwestern Norway. The precipitation was related to the influx of moist air from an AR, whose structure appears as a band of high vertically integrated water vapour (IWV) in passive microwave satellite imagery (Fig. 1a). The AR reaches as a narrow band from the central North Atlantic to the study region, impacting the entire west coast of southern Norway. At 12 UTC on 07 Dec 2016, the head of the AR has 5 spread out broadly over the North Sea and the UK. The ERA-Interim reanalysis reproduces the observed structure of IWV faithfully, albeit with an apparent tendency to higher maximum values (Fig. 1b). While the IWV has commonly been used to define ARs, more relevant for the ensuing orographic precipitation is the associated water vapour flux, expressed as IVT (Lavers et al., , 2016. another over several days (not shown). We note that in the present case, the onshore water vapour flux is enhanced by the 15 pressure gradient between the Icelandic low and the high-pressure over Europe. Similar configurations have been observed earlier to be associated with AR events in coastal western Norway (Azad and Sorteberg, 2017).
At 06 UTC on 07 Dec 2016, the first front has passed over land, as seen by the 850 hPa temperature north of Ålesund (Fig. 2c) and the widespread precipitation above 2 mm h −1 (Fig. 2d) obtained from the control forecast of the AROME MEPS regional forecasting system. The trailing warm front is still at a distance from the coastline, but already causes intense precipitation near  10 https://doi.org/10.5194/wcd-2020-58 Preprint. Discussion started: 9 December 2020 c Author(s) 2020. CC BY 4.0 License.
the coast (Fig. 2d, green shading). At 18 UTC on 07 Dec 2016, the Icelandic cyclone has started to fill in, with the warm frontal system dissolving over southern Scandinavia. An upper-level cold front, trailed by a surface warm front approach the coast of southwestern Norway at this time (Fig. 2b). The temperature at 850 hPa shows the transition to a more cloud-free area with variable gradients as the upper-level cold air arrives over the North Sea (Fig. 2e). While there is still widespread precipitation over southern Norway, a more scattered precipitation regime sets in at this time (Fig. 2f). Precipitation already started forming before the increase of temperature, with precipitation rate from TPS-3100 (Fig. 3b, black line) below 1 mm h −1 between 00:00 and 03:30 UTC. Precipitation then steadily increased to 5.5 mm h −1 at 07:00 UTC, and varied thereafter on a generally high level throughout the rest of the day, with a brief intermission at 12:00 UTC, and ending on 23:30 UTC. Rainfall became in particular more variable after 14:30 UTC, reaching brief maxima above 7.0 mm h −1 .

15
The total precipitation amount during this 24-h event was 55.3 mm. Other instruments for precipitation measurements provide a similar time series of precipitation intensity, and comparable precipitation totals (Appendix A).
Relative humidity changed markedly during the event. Before 04:30 UTC, RH varied between 77 and 80 %. As precipitation intensified, and before the temperature started to increase at 05:00 UTC, RH gradually increased to 92 % at 09:00 UTC, and remained between 92 and 95 % thereafter (Fig. 3b, blue line). 20 According to the time evolution of the meteorological parameters presented above, in particular the radar reflectivity, we separate the AR event into 4 distinct precipitation stages: pre-frontal Stage I before 03:30 UTC (purple bar), first frontal Stage II between 03:30 and 07:00 UTC (blue bar), a second frontal Stage III between 07:00 and 14:30 UTC (red bar), dominated by stratiform precipitation processes, and a post-frontal Stage IV after 14:30 UTC (yellow bar) that is dominated by convective precipitation. The four stages are indicated with corresponding colour bars at the top and bottom of Fig. 3. 25 The drop size distribution followed a similar evolution as the precipitation rate ( Fig. 3c) 4 Observed stable isotope signature in vapour and precipitation The measured isotope composition in the surface vapour and precipitation samples is now compared in relation to the four precipitation stages identified above. For the surface vapour, the 10 min averaged δD v initially showed a relatively stable value . The resulting stretched-out "W" shape of the water vapour isotopes resembles earlier observations made in precipitation samples (Muller et al., 2015). The amplitude of 72 ‰ is substantial but smaller than for example observed in rainfall by C08. The relative evolution of δ 18 O v closely follows that of δD v (not shown).
The equilibrium vapour from precipitation δD p,eq approximately follow the pattern of surface vapour (Fig. 3e, black seg-15 ments). There surface vapour isotope signal appears to lag the isotope signal in precipitation by about 30 min. Comparison of specific humidity from the isotope spectrometer with specific humidity calculated from the AWS shows no apparent time lag or offset at 1-min measuring frequency, indicating that atmospheric effects cause this time lag. Overall, the δD p,eq is more variable than the δD v time series. At Stage I, the isotope signal in δD p,eq is substantially less depleted than δD v . This reverses at the beginning Stage II (after 03:30 UTC), and during the transition to Stage III, δD p,eq reaches a minimum, before it again 20 is less depleted than δD v until about 08:30 UTC. Thereafter, differences between δD v and δD p,eq are small. An exception is the last hour of Stage III from 13:30 to 14:30 UTC, where δD p,eq is highly variable, and more depleted than δD v . Right at the beginning of Stage IV, the δD p,eq is again more enriched than δD v , before approaching equilibrium after about 18:00 UTC.
The time offset, and the relative enrichment and depletion characteristics of vapour and precipitation are further examined in Sect. 5. 25 We now investigate the time evolution of the secondary isotope parameter d-excess in vapour and precipitation. After a value of 11 ‰ during Stage I, the surface vapour d-excess (d v ) increases to 14 ‰ at Stage II, and stays around that level until the beginning of Stage III at 08:00 UTC, one hour after the second warm front arrives (Fig. 3f, dotted line). Then the d v gradually decreases throughout the rest of the event, with a more rapid decrease from about 10 ‰ as the upper-level cold front arrives at 14:30 UTC, to d v varying around 4 ‰ between 18:00 and 21:30 UTC and eventually reaching 0 ‰ at 23:00 UTC.

30
The d-excess of the equilibrium vapour from precipitation d p,eq shows a remarkable difference to d v at the beginning of the event (Fig. 3f, Stage I and II, black line segments). Here, d p,eq are substantially lower than the d v , with the lowest values even being negative (−7 and −9 ‰) during Stage I. This results in a large difference between d v and d p,eq of 18 and 20 ‰, respectively. During Stage II, d p,eq gradually approaches d v , remaining about 2-4 ‰ lower than d v . Similar to d v , d p,eq then shows a continuous decrease between 07:00 UTC and 16:30 UTC, then stabilising (with some variability) around 2 ‰. The original d-excess of precipitation, d p (Fig. 3f, blue line segments), should theoretically be equal to d p,eq . Small discrepancies at Stage I, Stage IV, and the two depletion minima, may at least partly arise from the definition of the d-excess (Dütsch et al., 2017).

5
As is evident from the results presented above, the precipitation and vapour isotope measurements, especially when combining δD and d-excess parameters, clearly provide signals that are not apparent in standard meteorological observations (such as air temperature and precipitation rate). Following our hypothesis that the isotope signature at each stage reflects the impact of several atmospheric processes, including moisture origin, processes during advection and mixing, condensation processes in clouds, as well as below cloud interaction, we now attempt to disentangle the individual contributions from these processes 10 on the observed isotope signature at the surface during the AR event.
5 Impacts on the stable water isotope signature The precipitation isotope signal during a weather event results from a convolution of different processes. We now proceed backwards from the last process, the below-cloud interaction, to weather system and transport influences, to the moisture source signal, to investigate how different processes contribute throughout the event.

Contribution from below-cloud interaction processes
Below-cloud interaction processes consist of the continuous exchange of falling precipitation below cloud base with the surrounding vapour in the atmospheric column. In near-saturated conditions, liquid precipitation will exchange with surrounding vapour in a near-equilibrium process. In undersaturated conditions, the vapour exchange will lead to a net mass loss of the droplets. Resulting from the same underlying process, both exchanges are strongly influenced by drop size, whereby smaller 20 droplets being affected more strongly (Graf, 2017).
We investigate the change in isotope composition due to below cloud processes using the ∆δ∆d-diagram (Graf et al., 2019). The ∆δ∆d-diagram uses the differences between equilibrium vapour from precipitation and ambient vapour in terms of both δD and d-excess (∆δ and ∆d, Sect. 2.3) as its axes (Fig. 5). The diagram is divided by the zero reference lines into four quadrants. The closer data points are located near the origin, the closer the equilibrium between the vapour and liquid  16 https://doi.org/10.5194/wcd-2020-58 Preprint. Discussion started: 9 December 2020 c Author(s) 2020. CC BY 4.0 License.
Towards Stage III (08:30 UTC), samples are close to equilibrium with surface vapour, with slightly negative ∆d values (0 to −4 ‰) and a relatively large spread of both positive and negative ∆δD values (12 to −12 ‰, letter C). An interesting phenomenon then occurs at the transition to Stage IV, when first a stronger cloud influence is apparent, with data points near −10 ‰ for ∆δ ( Fig. 5a, letter D), before directly jumping to +10 ‰ after 15:00 UTC (Fig. 5a, letter E). For the remainder of Stage IV, data points then progressively move closer to equilibrium conditions, corresponding to the origin of the coordinate axes (letter F).

5
Note that the samples from different stages are well separated in the diagram, indicating different dominating processes at each stage.
A key factor of influence for the below-cloud evaporation is RH below cloud base. When coloured by RH from the AWS, it is evident that the samples most affected by below-cloud evaporation coincide with below 90 % RH at the surface ( Fig. 5b) While RH is a key driver of below-cloud interaction, several other factors are also important, for example, precipitation rate. 15 The two samples with the lowest rain rates of about 0.5 mm h −1 (during Stage I) are located in the lower right quadrant of the ∆δ∆d-diagram (Fig. 5c). Several subsequent samples with slightly higher rain rate (∼ 0.9-2.2 mm h −1 ) are located in the left quadrant, ranging from about −15 to −6 ‰ in ∆d. As the rain rate of the sample further increases and the ambient air nearly saturates, the effect from below cloud evaporation weakens. Samples with relatively heavy rain rates (mostly between 3 and 5 mm h −1 ) are found during the rest period of the event; they are located close to the zero ∆d line, indicating weak 20 influences from below cloud interactions. A sensitivity analysis of the formation height parameter in the BCIM model shows weak sensitivity, that aligns horizontally along the ∆δ axis with increasing height. Interestingly, this agrees with data points at the transition to Stage III when the melting layer was among the highest (Fig. 3d).
The small precipitation rates are also a consequence of the below-cloud evaporation in an undersaturated environment. This below-cloud evaporation also leads to a reduced size of precipitation droplets, characterised by the droplet mean diameter. In 25 the ∆δ∆d-diagram, the samples with the lowest rain rates also have a small droplet mean diameter of below 0.9 mm (Fig. 5d).
There are further samples with mean diameters below 1 mm during Stage IV of the precipitation event. At these times, rather than being due to evaporation effects, the small drop sizes and the near-saturation conditions indicate that droplet growth may be taking place actively. An analysis of the sensitivity to the temperature profile with the BCIM shows a sloping of the sensitivity from a horizontal to a diagonal orientation with warmer temperatures. This is in qualitative agreement with the 30 observations during the event with surface warming continuing from Stage III through Stage IV.
In summary, we observe strong below cloud interaction at the beginning of the rainfall event. The period (Stage I and II) is characterised with the least saturated ambient air, the lowest rain rate, the smallest droplet size, and the lowest melting layer height. All these features except the melting layer height favour the occurrence of the below-cloud interaction. Transition phases between stages increase the disequilibrium between surface vapour and precipitation, with the precipitation signal leading the 35 17 https://doi.org/10.5194/wcd-2020-58 Preprint. Discussion started: 9 December 2020 c Author(s) 2020. CC BY 4.0 License. vapour in characteristic ways (Fig. 5a, letters A-F). The non-equilibrium fractionation during the evaporation causes the rain droplets to be more enriched in heavy isotopes (i.e., higher δ 18 O and δD values). At the same time, more HDO is transferred to the vapour phase, yielding to a low or even negative d-excess in the remaining rain droplet. These isotopic signatures match the precipitation samples taken during this period (Fig. 3e, f; Fig. 5). The variation during Stage III and IV, however, shows that these two stages are less affected by below-cloud interactions, and more related to a change in parameters related to the weather system, such as formation height and the temperature profiles. We, therefore, focus now on the potential contribution of weather-system related changes to the isotope composition of surface vapour and precipitation during the AR event.

Weather-system contribution
Now, we use the 4 stages, defined based on the surface meteorological observations (Fig. 3) to investigate the relationship between the observed isotope signatures and weather-system characteristics. The precipitation event was dominated by two 10 warm fronts, passing over Bergen in close sequence (Sect. 3). The fronts are apparent as marked gradients in air temperature at 850 hPa around 06 UTC (Fig. 2c).
A more continuous display of the frontal passage is provided by a time-height cross-section of equivalent potential temperature (θ e ), cloud water, and precipitation, using hourly ERA5 reanalysis data (Fig. 6). The cross-section depicts a constantly increasing temperature on the surface (below 850 hPa), consistent with the surface meteorological observations (shading), as The surface vapour and precipitation isotope composition during Stage I and II are initially dominated by below-cloud interaction. Both surface vapour and equilibrium vapour from precipitation exhibited relatively enriched δD (Fig. 3e), although probably for different reasons. The low depletion of −120 ‰ in δD for the surface vapour is probably related to the pre-frontal 25 boundary-layer airmass that originated from local evaporation, and had not undergone rain-out processes (e.g. a short distance moisture source). As identified in Sect. 5.1, the observed enrichment in the precipitation is probably the result of below-cloud evaporation, as reflected in the observed negative d-excess of −6 to −9 ‰ in the precipitation samples. With the precipitation signal leading the vapour isotope composition, the weather-system signal progressively becomes more dominant throughout Stage II, levelling at −180 ‰ between 05:00 and 06:00 UTC. We consider this the actual δD isotope signature of the first 30 frontal airmass.
From Stage I to Stage II, the d-excess of surface vapour increased from 12 to 15 ‰. We consider two possible influencing factors for this increase. First, the increase could reflect the gradual shift from the pre-frontal to the newly arriving warmfrontal airmass. However, there was a large distance between the d-excess of equilibrium vapour from precipitation and that of condensation level. The lowering here appears connected to the lower of cloud base height, allowing an increased contribution to falling raindrops that gain mass from, for example, the collision with droplets formed at low levels. Indeed, we observe a noticeable increase of radar reflectivity at the surface level below 1 km during Stage III ( Fig. 3d and 4b). The contribution of low-level vapour to surface precipitation is also consistent with the arguments by Yoshimura et al. (2010) based on a regional model study of an AR event that the precipitation isotope signal can be influenced by a deep section of the atmosphere.

5
The plateau in δD reached after about 09:00 UTC indicates that this likely is the actual isotopic signal of the second warm front. While both warmer temperatures and more contribution from lower atmospheric layers are consistent with the lower depletion, it is also possible that a different transport process has contributed to the different isotope signal of this airmass (see next section). The d-excess of both surface vapour and equilibrium vapour from precipitation during Stage III gradually decreased from 15 to 9 ‰ for the vapour, and from 13 to 6 ‰ for precipitation. A plateau reached in the precipitation d-excess 10 after 11:00 UTC indicates that the steady state in below cloud exchange has been reached thus the signal of the airmass is likely apparent at the surface level at this time.
In the ERA5 reanalysis, the middle and lower troposphere starts to become more unstable after 14:00 UTC, as indicated by θ e changing from about 320 K to about 305 K towards the end of the day. Noting the shift by 3 h in relation to observations, the transition to Stage IV is marked by the disappearance of ice-phase precipitation, with a tongue of cloud water reaching 15 above 600 hPa, and cold air overrunning the warm front at about 720 hPa at 18:00 UTC (Fig. 2b). The such created instability may explain the very intense precipitation lasting for a 1-h period at the end of Stage III, associated with strong deviations in the ∆δ∆d-diagram. The local δD minimum of −175 ‰ at the transition of Stage III to Stage IV would then represent a higher-elevation cloud signal, reflecting the isotopic gradients in the column.
The stable stratification weakens further during the remainder of Stage IV, leading to a change from stratiform to convective 20 precipitation. Precipitation formation shifts to the lower troposphere, mostly below the melting layer height, consistent with MRR2 measurements (Fig. 3d). The apparent lack of a melting layer implies condensation temperatures above 0 • C. The δD of both surface vapour and equilibrium vapour from precipitation gradually becomes less depleted, reaching −110 ‰ around 18:00 UTC and finally −100 ‰ after 21:00 UTC, even less depleted comparing with the values during Stage I (Fig. 3e). The To understand the isotope signals of surface precipitation with a rain out perspective, we modelled the observed δD of surface precipitation at different stages using the Rayleigh fractionation model of Jouzel and Merlivat (1984). The model assumes that conditions during airmass ascent. The condensation temperature of the precipitation is obtained when the modelled δD became equivalent to the observed δD in surface precipitation. The model results are shown in Table 1.   The modelled condensation temperature of Stage I reaches above 14 • C, substantially higher than the actual surface temperature (∼5 • C). With a condensation temperature well below ∼5 • C, the δD of formed precipitation is expected to be quite depleted. The modelled d-excess from the Rayleigh model is 11.7 ‰, in large contrast to the observed −3.2 ‰. The observed 5 enriched δD and negative d-excess indicates that the cloud signal of precipitation has been substantially modified by below cloud evaporation. At Stage II, the modelled condensation temperature dropped to 0.9 • C, which is in better agreement with the concurrent temperature profile (Fig. 6). The reduced difference between modelled and observed d-excess supports a lower influence from below cloud evaporation. However, cloud tops in ERA5 reach temperatures below −25 • C, which is not reflected in the Rayleigh model. In Stage III, the modelled condensation temperature increases to 2.4 • C, corresponding to the more in cloud (Jouzel and Merlivat, 1984) and should be considered with caution. Also in these two most depleted situations, the condensation temperature from the Rayleigh model is more consistent with a mass-weighted average of condensation, rather than cloud-top temperatures.
It is also worth to note that the precipitation amount collected during Stage I and II only contributes about 9.4 % of the total precipitation amount collected during the entire event. Hence the effect of below cloud evaporation will unlikely be detected 5 in a precipitation sample that is collected on an event basis, or daily and longer time scales.
Based on the isotope signals of the different airmasses during Stage II to IV, we now explore to what extent these reflect the moisture source and transport conditions.

Relation of moisture sources to meteorological evolution
We now consider the synoptic development over the three days proceeding the precipitation event, with a focus on how moisture 10 sources and moisture transport to Bergen are connected to the weather system configuration.
On 4 December 2016, two low-pressure systems are located south of Greenland and in the North Atlantic. Strong moisture transport takes place at the southern flank in the warm sector region, displayed as IVT above 800 kg (ms) −1 (Fig. 7a). This region is connected to widespread cloudiness at the northern edge of an airmass with high humidity (Fig. 7b, green shading).
Bergen (red cross) is under the influence of a weak pressure gradient, with an onshore flow from NE, and lower humidity. 15 Moisture uptakes contributing to precipitation in Bergen during the AR event are identified for the respective time periods.
The most substantial moisture uptake (thick blue contours) contributing to the precipitation on 07 Dec 2016 coincides with the boundary between the dry and cold air to the north (Fig. 7b, red and blue shades), and the moist airmass to the south (green shades) over the central and western North Atlantic. At this boundary, extensive cloud formation occurs, ranging from deep clouds (white) to low-level stratus clouds (light green). 20 On 5 December, the two low pressure systems have merged, with a core low below 975 hPa near Iceland (Fig. 7c,d). IVT and cloudiness in the frontal band have intensified. South of Norway and central Europe, high pressure is starting to form, with a 1030 hPa core pressure. The moisture uptake has moved further north and overlaps now with the IVT maximum. This warm frontal band coincides with the two warm fronts passing southern Norway during the event (Fig. 2a).
On 6 December at 12 UTC high wispy cirrus clouds mark the surface warm front over Bergen (Fig. 7f). The cyclone had 25 entirely separated from its frontal bands and started to fill in. High pressure over Europe increased to 1040 hPa, with the pressure gradient further accelerating the onshore flow, supporting an intense meridional IVT of above 800 kg (ms) −1 , which just straddled over Scotland. Moisture sources advanced substantially further to the northeast, with the IVT maximum and now concentrated south of the British Isles.
On 7 December, a small, secondary cyclone dominated the moisture flux in the north, while the southern part of the IVT 30 structure remained supported by yet another low-pressure system downstream (Fig. 7g). Moisture uptakes are identified over the North Sea near Scotland, contributing to precipitation in Bergen later that day (blue contours). The area over Scotland corresponded to relatively cold air with broken clouds intruding at the rear side, over the UK, belonging to the cold frontal air during Stage IV (Fig. 7h).
The most substantial moisture uptake was occurring in the vicinity of the IVT maximum, embedded in the fused warm frontal bands. As the time window to the precipitation event shortened, the moisture uptake moved substantially further northward over the North Sea. This change in moisture source distance corresponds at least qualitatively to progressively less depleted isotopic signature during the event. We now investigate more quantitatively how different the evaporation conditions at the 5 moisture sources were for Stages II, III and IV.

Moisture source contribution
The evaporation conditions at the moisture sources identified above determine the vapour isotope composition before the start of the condensation processes. Here we investigate if the stepwise decrease in precipitation d-excess observed during Stage II and Stage III can be related to changes in moisture source conditions. Moisture source conditions are quantified here in terms 10 of moisture source distance, surface temperature, relative humidity with respect to sea surface temperature (Fig. 8a-c).
The large majority of moisture uptakes took place within a distance of 8000 km (Fig. 8a). with a median of about 3 days. This timing corresponding to uptake locations from 04 to 07 Dec 2016, shown in Fig. 7. In earlier and later stages, lifetime distributions also peak at less than 5 days, while including more notable contributions with more than 5 days since evaporation. 20 Along with the shift in the moisture source location, evaporation conditions also changed. The most frequent temperature at the moisture sources was about 23 • C throughout the event, yet including a range of colder temperature conditions (Fig. 8b).
Colder temperatures contributed in particular during the beginning of the event, when the average moisture source temperature was 17.6 • C at 00 UTC on 07 Dec 2016 (green line), and moisture sources were more local. Overall, the range of moisture source temperature variations was relatively limited throughout the event (within 2 • C).

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The relative humidity with respect to the SST (RH SST ) is a key factor in kinetic fractionation during evaporation (Craig and Gordon, 1965). Throughout the event, mean RH SST is around 65-70 % (Fig. 8c). The peak at near 100 % is an artefact of the contribution from land regions where RH SST is not defined. The maximum RH SST shifts during the event, from above 60 % before the most intense precipitation period to 55 % at 12 UTC on 07 Dec 2016. It appears that the most intense precipitation stage was thus also associated with the most intense evaporation due to the strongest humidity gradient over the North Atlantic 30 moisture sources.
For comparison with the stable isotope measurements, we predict the d-excess at the moisture source from the empirical relation between RH SST and d-excess by Pfahl and Sodemann (2014) (Fig. 8d). The highest d-excess from the moisture sources is predicted during the peak of the precipitation event, with a maximum at 16 ‰ (grey shading). As for RH SST , land 25 https://doi.org/10.5194/wcd-2020-58 Preprint. Discussion started: 9 December 2020 c Author(s) 2020. CC BY 4.0 License.
sources produce an artefact for d-excess below −5 ‰. Both before and after the main precipitation period, the maximum in the d-excess distribution is shifted to lower values. This sequence from low to high to low d-excess throughout the event is qualitatively consistent with the observed d-excess signal. The initial low and even negative d-excess in precipitation during Stage I is thus likely a combination of the moisture source conditions, amplified by below-cloud evaporation. The source dexcess is more sensitive to RH SST than to SST (Merlivat and Jouzel, 1979;Aemisegger et al., 2014). Considering additionally 5 that the source temperatures only change slightly during the event, the humidity gradient above the moisture sources appears as the dominant driver of the d-excess changes observed here.
Considering a longer time period around the case investigated here, the Lagrangian diagnostic indicates a rather constant dexcess value during the whole precipitation event (Fig. C1d). The observed d-excess variation is not captured by the Lagrangian diagnostic. The detailed inspection of Fig. 8 indicates the lack of variability is likely due to averaging the complex histograms 10 to one value at the arrival location. The key characteristic of the histogram distribution is the maximum probability, but skewed and bimodal distributions make it difficult to provide more robust statistic measures. To represent the full variability of the moisture source conditions, detailed inspection of the moisture source properties throughout the event is therefore needed.

Discussion
We now return to the initially mentioned dispute in the literature regarding the interpretation of the precipitation isotope signal 15 from an AR case making landfall at the coast of California. From sampling precipitation at a 30 min time interval during the AR event, C08 found a remarkable variation in δD of 60 ‰, progressing from less depleted to depleted and back. Both the shape and amplitude of the stable isotope variation were similar to the case studied here. C08 based the interpretation of the variability primarily on changes in cloud height, i.e. the temperature of condensation (Scholl et al., 2007). Using a Rayleigh distillation model, C08 proposed that the initial phase precipitation would originate from low clouds with an average 20 condensation temperature (T c ) of 10.0 • C, followed by deeper clouds with an average T c of −4.2 • C, and again shallow clouds with T c of 9.7 • C.
Y10 then simulated the same AR event with a regional isotope-enabled model, leading them to propose a fundamentally different explanation for the isotope variation in surface precipitation observed by C08. According to that interpretation, the initial drop from less depleted to depleted precipitation would be caused by below-cloud evaporation. Furthermore, Y10 found 25 from their simulation that up to one-third of the condensate would be contributed from the lower troposphere (below 800 hPa), with an increasing tendency throughout the event. Notably, the contribution from the cloud top would decrease during the most depleted phase of the event. Despite uncertainties in some model parameters and parameterisations, Y10 concluded from their analysis that cloud microphysics, below-cloud exchange and advection all play a role for the observed isotope variation during different phases of the event. 30 Expanding the dataset to 43 events sampled with a network of automatic rain samplers across northern California, Coplen et al. (2015) (henceforth C15) confirmed the pronounced isotope variation during events as seen in the case discussed in C08.
C15 argue that if the below-cloud kinetic exchange were to explain the initial enrichment in C08 as proposed by Y10, kinetic effects due to evaporation should have led to characteristic deviations from the GMWL.
The above controversy revolves around two questions: (i) What is the contribution from below-cloud interaction, and in particular evaporation, to the precipitation isotope signal? (ii) Are Rayleigh-type models adequate to explain the surface precipitation signal during AR cases? Based on our highly detailed analysis of an AR event, with high-resolution precipitation 5 sampling and simultaneous water vapour measurements, we are in a situation to contribute constructively to both aspects of this scientific controversy.

Contribution from below-cloud interaction to the isotope composition in surface precipitation
Y10 proposed that below-cloud processes can explain the isotopic enrichment in precipitation observed at the beginning of the C08 event, rather than cloud height. The joint observation of both surface vapour and precipitation in this study shows a 10 characteristic time lag of the vapour over the precipitation signal. One plausible explanation for this time lag is that diffusional interaction takes place between precipitation and the surrounding vapour over extended time periods. Even though the total column mass of precipitation in a column is typically only about 1/10 th of the IWV, precipitation persisting over longer periods will imprint on ambient vapour isotope composition, and vice versa. As more precipitation falls, the below-cloud air gradually saturates, reduce the vertical isotope gradient, and eventually reach isotopic equilibrium with the precipitation. At that point, 15 the time lag between precipitation and vapour isotopes would vanish. Here, we find this time lag to be on the order of 30 min.
As long as the surface air is unsaturated, net mass transfer is directed away from raindrops, thus below-cloud evaporation reduces drop sizes and rainfall amounts, causing characteristic deviations in the ∆δ∆D framework that reflect kinetic fractionation effects. The rainfall contributed during Stage I in this study was however too small to markedly influence the isotope composition of the rainfall total (Table 1). Concerning the scientific controversy introduced above, we note that below-cloud 20 processes can influence precipitation and surface vapour, but that the signal can be too small to detect if samples are too long, or due to sampling and analytical uncertainty. It is therefore not possible to confirm that the initial enrichment in C08 dataset was actually due to below-cloud evaporation, in particular without additional vapour measurements. Other factors, such as advection effects or progressive vapour/precipitation exchange could also have contributed to the initial enrichment.
6.2 Adequacy of the Rayleigh model to explain the isotope composition in surface precipitation 25 The majority of the precipitation in ARs is arriving with the strong onshore flow of the warm sector, led by the warm front and dominated by long-range transport. Large-scale ascent, enforced by orographic lifting and condensation heating during landfall leads to condensation and predominantly stratiform cloud formation. The warm conveyor belt (WCB) model is often used to describe the strongest precipitation-generating airflow in the warm sector of cyclones (Madonna, 2013). According to a common classification criterion, airmasses in the WCB airstream rise 300 hPa or more in 48 h, corresponding to vertical 30 ascent on the order of several cm s −1 . Precipitation from cold-sector airmasses, in contrast, has a more convective nature, characterized by an isolated ascent in updrafts, and dominated by vertical motions on the order of up to several m s −1 .
From the Rayleigh model simulation presented in Sect.5.2, we find that the condensation temperature of the surface precipitation is most consistent with the temperature profiles in the reanalysis data (Fig. 6, purple contours) when interpreted as a representation of the vapour-mass-weighted average in the column rather than the cloud base or cloud top temperatures. MRR2 reflectivity profiles for the four precipitation stages considered here confirm that lower levels contribute substantially to the surface precipitation.

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Variants of the Rayleigh distillation model are often used to represent the isotope fractionation during condensation processes (e.g. Jouzel and Merlivat, 1984). In nature, however, precipitation will enter from above into subsequent air parcels from below.
This process, as well as the isotopic exchange of the falling precipitation with air parcel vapour (in case of liquid phase), is not part of Rayleigh distillation model. Indeed, the Rayleigh model may thus only be adequate to simulate the vapour composition in a rising air parcel, and the precipitation falling directly from it, which can be adequate for some convective-type precipitation 10 processes. In the case of the more slowly ascending warm-sector airmasses, however, where clouds contribute to condensation at a range of atmospheric layers, a single air parcel appears insufficient to capture the actual precipitation process. Conceptually, it could be possible to consider instead an entire stack of Rayleigh-model air parcels as a better representation of stratiform cloud processes. Each air parcel in the column is at or near saturation, contains cloud droplets, and will receive input of hydrometeors from above. Each air parcel will thus contribute to the precipitation by condensation or deposition, riming, 15 scavenging, and partially equilibrate with the water vapour on passing through. The vertical connection of an entire stack of Rayleigh-type parcels creates a more efficient, coupled fractionation process than an isolated Rayleigh-type parcel as in the convective case. Given such a vertically coupled perspective, a single cloud top or condensation temperature from one Rayleigh process appears too limited to capture the influences on the fractionation process in the entire cloud. This is underlined by the fact that the Rayleigh model used in C08 only needed temperatures down to −4.2 • C to explain the observed precipitation 20 isotopes, which could not be reconciled by the range of temperatures throughout the entire column found by Y10. A similar observation was made here with the Rayleigh model of Jouzel and Merlivat (1984).
As the precipitating warm-frontal airmass is advected horizontally with the AR, it will produce a coherent isotopic signal at the surface, as noted by the displacement times in C15. C15 also noted that there is no immediate relation between the isotopic depletion and either the total amount or the intensity of precipitation during landfall. Both of these findings are consistent with 25 the interpretation that the isotope composition of the stratiform cloud can obtain a coherent, depleted isotope signature from a sustained lifting process. The isotopic signal of stratiform cloud then reflects a time-integrated condensation history of the airmasses, whereas surface precipitation is a combination of the airmass signature, the surface vapour, and the below-cloud interaction processes.
We conclude from this discussion that since the isotopic precipitation signal is intimately coupled to the cloud microphysics 30 and dynamics, the Rayleigh perspective can be adequate to represent the isotope composition near cloud top and in some convective situations. However, for surface precipitation, and precipitation from deep stratiform clouds in frontal systems, such as ARs, the Rayleigh model reaches conceptual limitations. Despite their own uncertainties, it, therefore, appears necessary to invoke more complex numerical tools in the interpretation, such as isotope-enabled numerical weather prediction models, or Rayleigh-type models adapted to stratiform clouds.
We have presented a high-resolution stable isotope signature of a land-falling atmospheric river event in southwestern Norway during winter 2016. Figure 9 provides a conceptual summary of the sequence of events, by providing a spatial depiction of the airmasses arriving at Bergen. In surface precipitation, we observe δD that develops in a stretched "W" shape (between −180 and −100 ‰ for equilibrium vapour of precipitation), and d-excess that increases from −9 to 13 ‰, followed by a gradual 5 decrease to 0 ‰. In surface vapour, δD exhibits the same "W" shape, following closely to the precipitation isotope variation, with a lag of about 30 min. The d-excess in vapour differs in the beginning markedly from precipitation signal, increasing from 10 to 16 ‰. As relative humidity below cloud base increases, the vapour d-excess follows the same trend as that of precipitation, reaching 0 ‰ at the end of the event.
Combining isotope and meteorological observations, we have identified four different precipitation stages during the event.

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At each stage, weather-system processes imprint on the isotope variations (Fig 9). Specifically, at the beginning of the event (Stage I), below-cloud evaporation is substantial, contributing to the low and even negative d-excess and relatively enriched δD in surface precipitation. At Stage II, the gradual weakening of below-cloud evaporation as ambient air becomes more saturated, and the involvement of hydrometeors from above the melting layer results in a gradual drop of δD and an increase in d-excess.
Regarding the controversial discussion of the isotopic signal during previous AR events in the literature (C08, Y10, C15), we emphasize from our results that the isotopic precipitation signal is intimately coupled to the cloud microphysics and dynamics. Idealized Rayleigh models may be adequate to represent the isotope composition of water vapour near cloud top during convective precipitation events. However, additional factors and more complex models should be considered to interpret the isotopic signal in surface precipitation, in particular for deep, stratiform clouds. A stack of Rayleigh models could be a more 5 adequate conceptual view for these cloud types (Fig 9).
Our case study provides a unique isotope dataset of an AR event in southwestern Norway. More cases should be performed in the future to test the more general validity of the results obtained in this case study. However, from one case already it is apparent that the isotopic information from combined (paired) water vapour and precipitation isotope sampling can be highly valuable for future data-model comparison studies with isotope-enabled weather prediction models.

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Data availability. Datasets are available in the supplement.

Appendix A: Comparison of precipitation rate measurement
The precipitation rate at the sampling site (45 m a.s.l.) is measured by two instruments, i.e. Total Precipitation Sensor (TPS-3100) and Parsivel 2 distrometer. Fig. A1 shows a comparison of hourly precipitation rate during the precipitation period between the measurements of these two instruments and that of the rain gauge measurement from the closest meteorological 15 station (70 m away, 12 m a.s.l.). The comparison shows that the TPS-3100 measures a slightly higher precipitation rate while the Parsivel 2 recorded a substantially lower precipitation rate, particularly in the situation of heavy precipitation. Since the TPS-3100 measurements agree well with the rain gauge measurements, we choose to use the precipitation rate from TPS-3100 for the analysis in this study. We did not choose to calibrate the TPS-3100 measurements against the rain gauge measurements because the small discrepancy can be due to the different locations and elevations of the two instruments. -The sensitivity to RH was evaluated by modifying the surface RH in steps of 2 % between 64 and 100 % while keeping all other parameters unchanged.
A dry period of one and a half day precedes the AR precipitation event. Following the AR precipitation, discontinuous, moderate precipitation occurs (Fig. C1a). The comparison of the precipitation time series shows a qualitative agreement, but with substantially lower precipitation intensities estimated by the Lagrangian diagnostic. The discrepancy in the precipitation intensity likely arises from the neglect of microphysical processes in the trajectory-based diagnostic, and from the limitation of comparing a regional estimate with a single-point ground observation. The Lagrangian moisture source diagnostic shows 5 that the dominating moisture source for the dry period pre the AR precipitation came from the north of Bergen (N of 65 • N; After the AR event, the moisture source gradually shifts back to the north, reaching 55 • N on 9 December, followed by another south-to-north variation. Closely following the source latitude, the moisture source distance reveals the airmass evolution from a local airmass pre AR event, to a substantial remote airmass during the AR event, and a moderate-distance airmass after 10 the AR event (Fig. C1b, blue dashed line). The estimated RH SST at moisture source indicates relatively intense evaporation condition at the moisture source before the AR event (RH SST reaching 62 %), more moderate evaporation condition during the AR event (RH SST ≈ 80 %), and varying evaporation conditions afterwards (RH SST varying between 72 and 85 %; Fig. C1c, black solid line). The local RH at the sampling site stays high (above 90 %) during the entire period, except at the beginning of the AR event and between UTC 00 and 12 on 9th December (Fig. C1c, blue dashed line). 15 Finally, we examine the d-excess of near-surface vapour, of equilibrium vapour from precipitation, and the d-excess estimation based on Lagrangian diagnostics (Fig. C1d). The d-excess of surface vapour exhibits a peak (above 8 ‰, with a maximum of about 16 ‰) during the first half-day of the AR event. Thereafter, the d-excess of surface vapour remains at low levels mostly between 0 and 8 ‰. The low d-excess can be due to the calm evaporation conditions at the moisture source or a contribution from land regions. The d-excess of equilibrium vapour from precipitation follows the overall variation of d-excess of surface 20 vapour. The lower d-excess values for the quasi-daily precipitation samples collected after the AR precipitation event can be due to below cloud evaporation, and cloud microphysical processes.
Author contributions. YW and HS designed the study jointly. Observation and data analysis was led by YW with contributions from AJ and HS. All authors contributed to the writing of the paper.