We consider the cloud observatory configuration on board HALO . From this, we use and introduce below two instrument packages providing remote sensing and in situ measurements to derive the moisture budget components. First, we use measurements of the HALO Microwave Package (HAMP, ), which consists of two nadir instruments: a Ka-band cloud radar measuring at 35 GHz and a suite of passive microwave radiometers with 26 frequencies from the K-band (22.24 to 31.4 GHz), the V-band (50.3 to 58 GHz), the W-band window (90 GHz), the F-band (118.75 ± 8.5 GHz), and the G-band (183.31 ± 7.5 GHz). The 195.81 GHz channel was not operated during HALO-(AC)3. Here, we utilise the unified HAMP dataset published by , which is based on the unification by . The data of the two instruments were synchronised to a collocated 1 s temporal resolution. The time series of brightness temperatures (TBs) from the radiometer channels were synchronised with the equivalent radar reflectivity factor and linear depolarisation ratio. The nadir radar range gates were interpolated onto a vertical grid of 30 m resolution. The radar reflectivities and the radiometer brightness temperatures were post-calibrated, quality checked, and supplemented with a corresponding surface mask that distinguishes between land, sea, and sea ice cover .

Second, vertical profiles of moisture and wind were measured by dropsondes, from which we derived the moisture transport. The sondes deployed from HALO are of the Vaisala RD-41 type (; ). During their descent, the sondes simultaneously measured relative humidity and wind speed with an accuracy of 1 % and 0.1 ms-1, respectively . In our analysis, we include the sonde measurements in a processing state equivalent to the Level 2 data in , which have undergone quality checks after processing with the Atmospheric Sounding Processing ENvironment . A large part of the sonde measurements were transferred to the Global Telecommunication System for inclusion in the model assimilation of operational numerical weather prediction (NWP).

We consider two model configurations to compare the airborne observations with model results. First, the global ECMWF Reanalysis v5 (ERA5; ) is used to investigate Arctic AR conditions. ERA5 data fields have a vertical resolution of 137 model levels and a horizontal grid spacing of 0.25° × 0.25°. For the Fram Strait and the Greenland Sea, the ERA5 latitude–longitude grid results in zonal and meridional spacings of about 30 km. find that ERA5 outperforms other global reanalyses regarding AR characteristics. Furthermore, recent studies emphasise the high performance of ERA5 for Arctic conditions (e.g. ; ). This justifies the extended use of ERA5 to study AR conditions, especially in the Arctic (; ; ). The dropsonde data could not be included in the assimilation phase of ERA5 during the AR event of this study , and thus it is appropriate to compare ERA5 data with the independent dropsonde measurements.

Second, we include the AR representation by forecasts from the ICOsahedral Nonhydrostatic numerical weather prediction model (ICON; ). The modelling system of ICON is suitable for global and limited-area applications . We consider a modified and non-operational ICON limited area mode with a nominal horizontal resolution of about 2.4 km, similar to , which we refer to as ICON-2km. The ICON-2km domain extends from 70 to 85° N and from -20 to 30° E. ICON-2km was initialised at 00:00 UTC of every day. The lateral boundary conditions in ICON-2km were obtained by one-way nesting using the output of the operational ICON global model at a horizontal resolution of 13 km . ICON-2km was run for a forecast time of 48 h, with the atmospheric state saved every 30 min. The cloud microphysics were represented by five hydrometeor classes in a one-moment bulk scheme similar to . Vertical data in ICON-2km were given for 150 terrain-following height levels. In a similar model configuration, reported on the skilful ability of high-resolution ICON limited-area modes in the AR representation at decametre to kilometre scales against ERA5. The 30 min output of ICON-2km captured the displacement of AR filaments better than the hourly ERA5 output. Following , we interpolated ERA5 and ICON-2km onto the flight track in space and time to compare their representation with the airborne values and among each other.

The meteorological conditions during the first week of HALO-(AC)3 (middle of March 2022) were characterised by a sequence of warm and moist air intrusions, some of which met the criteria for ARs in terms of the intensity of moisture transport and geometric extent. showed that these ARs were notably strong in terms of IVT for common Arctic ARs and entered the Arctic via typical paths along the North Atlantic, steering towards the Fram Strait and Barents Sea before partially reaching the Arctic Ocean.

In this case study, we focus on the strongest AR event of HALO-(AC)3, which entered our region of interest (Greenland Sea and Fram Strait) on 15 March 2022, sampled during research flight 05 (RF05, Fig. ). classified this AR as a very strong event for Arctic conditions. Here, we describe the synoptic conditions causing the AR and its temporal evolution towards the following day, when the AR was observed by a subsequent research flight (RF06).

For the airborne derivation of all components of the moisture budget, i.e. our first research goal (G1, Sect. ), flight patterns must sample areas of the AR in a specific way. Flight tracks that enclose areas, such as circles, are often used to calculate the mesoscale horizontal divergence (e.g. ; ). However, if a single circle as large as the lateral extent of the AR is used, the internal heterogeneity of moisture and wind fields within the AR, particularly across the embedded cold front, would be smoothed out in the divergence calculations (; ). The high lateral variability in the moisture transport characteristics of ARs requires long flight legs across the AR. Therefore, and focused their enclosing flight patterns more on the AR transect to capture this cross-sectional variability. However, their patterns were too small to cover the lateral variability of the budget components identified by from reanalyses.

recommend full cross-sections of the AR. An internal flight leg shall connect two parallel cross-sections, resulting in a zigzag flight pattern. Figure  shows the realisation of the zigzag pattern for an AR flight corridor during RF05. The zigzag pattern samples the AR transverse to the IVT direction. The boundary cross-section legs perpendicular to the main flow (Fig. ) quantify the inflow and outflow of the flight corridor, i.e. ingoing and outgoing IVT across the lateral AR extension. Dropsondes densely sample both cross-sections to derive ∇ ⋅ IVT. The internal legs explore the precipitation rate, evaporation, and water load within the AR flight corridor. The radar reflectivities in Fig.  show very deep clouds in the AR for Arctic conditions. The cloud top height is up to 12 km. Significant radar echoes down to the surface were recorded in the AR core (middle of the cross-sections). The high reflectivity band at about 1–2 km high (Fig. ), a so-called bright band, indicates a melting layer. Bright bands result from snowflakes coated by liquid water, causing higher radar reflectivities . Below, liquid precipitation can be expected.

We divide sectors along the lateral AR cross-sections in Fig. , similar to the approach suggested by . This distinction considers the presence of a cold front embedded in ARs , whereby different thermodynamic conditions prevail on both sides of the front. calculate the moisture budget across the main AR axis and the embedded front and report on significant differences in the budget components across the AR (front). For our AR, the gradients of Θe (Fig. b) suggest remnants of a cold front. We thus divide the AR flight corridors into eastern and western parts. Concerning the approximate location of the cold front, we refer to the eastern (western) half as the pre-frontal (post-frontal) sector. This two-sector separation is shown in Fig.  by the orange sondes referring to the pre-frontal sector.

Recent studies (; ; ) categorise ARs into three sectors, with the AR core as a separate one between the pre- and post-frontal sectors, containing IVT values ≥80% of the maximum IVT. However, given the nature of the irregular sonde spacing and the purpose of including as many sondes as possible in the sector-based divergence calculations, we assign the sondes released in the eastern part of the AR core to our pre-frontal sector and those in the western part to the post-frontal sector. We restrict the extent of our sector to the actual positions of the outer sonde releases.

During RF05, ATC restrictions in Danish airspace extending over the western regions of the AR flight corridors did not allow sonde releases in the post-frontal sector for the northern cross-sections (Fig. ). This lack of data prevents reliable sonde-based divergence estimates for post-frontal sectors. Hence, the subsequent analysis is confined to pre-frontal AR sectors. Upcoming sections refer to the pre-frontal sector defined by the connection of the orange sonde locations in Fig. , henceforth denoted as S1. We consider S1 to demonstrate the derivation of each moisture budget component included in Eq. () using HALO.

The IWV is most accurately determined using dropsonde measurements of vertical moisture profiles. However, these dropsonde profiles have limited spatial coverage. The few internal profiles may thus lack spatial representativeness for estimating the local change in IWV within the pre-frontal AR sector. To address this issue, we use the quasi-continuous HAMP radiometer measurements of the channels from 22 to 190.81 GHz (Sect. ). Their 1 s measured TB values are very sensitive to the emitted radiation from water vapour across the microwave spectrum . In particular, the K-band channels of HAMP show rising TB with increasing IWV. Furthermore, continuum water vapour absorption influences the TB at window frequencies near 30 and 90 GHz.

From the observed TB values, the IWV can be estimated using appropriate retrieval methods. We build a linear regression model retrieval, as used in , which we describe in Appendix . As specified in Sect. , the regression coefficients between the two quantities (IWV and TB) are based on a training dataset containing meteorological fields from ECMWF Reanalysis v5 (ERA5), along with synthetic TBs generated from the forward simulator PAMTRA (Passive and Active Microwave TRAnsfer tool; ). Applying the emerging retrieval coefficients to the measured TB, the retrieved IWV data show a good agreement with the dropsonde-based IWV over a wide range from 6 to 18kgm-2. Furthermore, the comparison of the airborne-retrieved IWV values with the collocated and continuous ERA5-based representation confirms that the continuous HAMP representation reasonably replicates the IWV values (Sect. ; Fig. ).

To derive the local temporal changes in HAMP-retrieved IWV within the AR flight corridors, we consider the internal flight legs of the zigzag pattern (Fig. ). The derivation of δIWV/δt requires sampling a specific region at two distinct time steps. This requirement is met within the AR core at the crossing flight paths. However, the single intersection in Fig.  has limited representativeness for the entire sector, and the internal flight legs separate from each other in the pre-frontal sectors. Therefore, we opt to compare only segments of internal flight legs (of about 100 km) that lie close to each other, without considering single locations (Fig. ). Symmetrically around two sonde releases, we assess the “local” change in IWV over approximately 2 h.

While the dropsonde-based IWV values in Fig.  differ by less than 1 kg m⁻², the HAMP-based mean values of each leg differ by more than 2 kg m⁻². The IWV distributions along the leg segments (Fig. ) reveal a high spatial variability because we consider regions of strong IWV gradients. This variability leads to significant uncertainties in estimating local changes in IWV. To quantify these uncertainties, we subsequently extend the internal leg segments by a minute (starting from 1 and going up to 10 min) and calculate the standard deviation of the mean local IWV change across all segments. For the pre-frontal AR sector S1, we thus derive a value of local change in IWV of −0.79±0.19mmh-1. Because the resulting uncertainties are much larger than those based on the regression retrieval, we neglect retrieval uncertainties in the uncertainty assessment of δIWV/δt.

The surface evaporation E can be estimated from bulk approaches, taking into account surface wind, temperature, and humidity. Our calculations are based on the aerodynamic bulk methods of , who derive the surface evaporation as: 5E=cdρa(qs-qa)⋅V, where qa is the near-surface specific humidity and qs is the saturation specific humidity for the current sea surface temperature (SST). ρa represents the air density near the sea surface. cd is the evaporation drag coefficient, where we follow and separate cd for two wind regimes, with cd=1.4×103 for winds ≤14ms-1 and cd=1.6×103 for higher wind speeds V. We obtain the near-surface values from the lowest dropsonde profile levels before reaching the sea surface (below 50 m). We filter out values from heights below 0 m, as the sondes sometimes transmit data just after they enter the sea. In other cases, erroneous GPS altitude data may prevent near-surface classification, so the corresponding sondes are omitted. We calculate qs for the SST extracted from the collocated ERA5 data. The air density is based on the near-surface sonde pressure, humidity, and temperature values. Uncertainties in the derived evaporation result from Gaussian error propagation of the sonde-based quantities given in .

Looking at the first complete zigzag pattern that contains S1, Fig. a shows that sonde-based deviations between qs and qa are quite small, except for the first sonde. This indicates near-saturated air, with some sondes even showing super-saturated air. Sondes in supersaturation reveal small negative values in evaporation (condensation). Overall, the evaporation is weak, with absolute values below 0.05 mmh-1 most of the time (Fig. b). The uncertainties in q are much smaller than the actual values of q but non-negligible (Fig. a). Based on the two sondes within the pre-frontal internal flight segment, we calculate a mean evaporation of 0.01 ± 0.06mmh-1.

Comparison with collocated ERA5 (Fig. b) verifies that the sonde-based bulk values of E are in a realistic order of magnitude. ERA5 confirms the very small contribution of evaporation to the moisture budget within the AR flight corridor. Note that suggest more detailed calculations of evaporation. However, given the overall agreement of our sonde-based results with model data (Fig. ), the simplified approach in Eq. () appears to be appropriate for Arctic ARs with small E.

We obtain the precipitation rates by using the cloud and precipitation radar measurements from the unified dataset (Sect. ; ). These radar reflectivities are offset-calibrated following . In addition, we correct the reflectivities for gaseous attenuation by water vapour, which we calculate from the model of using water vapour profiles from the ECMWF Integrated Forecast System (IFS) model. The conversion of radar reflectivity into precipitation rates is conventionally achieved by the application of empirically derived radar reflectivity to rain rate (Z-R) relationships e.g.. The Z-R relationships are provided by power laws in the form of Z=aRb; see Table . The parameters a and b account for variations in precipitation for a given reflectivity, arising from differences in the particle size distribution (PSD). However, the parameters vary greatly between radar frequencies, measurement viewing angles, and precipitation types . Using shipborne disdrometer data, mentioned the rapid spatiotemporal evolution of drop size distributions as an AR-specific caveat to using a single Z-R relationship.

This dilemma is exacerbated in Arctic ARs, where the coexistence of different precipitation phases (liquid and solid) is expected. The radar bright band shown in Fig.  provides evidence that melting of precipitation occurs in our AR event such that we observe rainfall and snowfall. The airborne estimation of precipitation rates along the internal legs for our moisture budget closure is thus 2-fold, based on . This estimation requires a precipitation type classification using a melting layer detection, followed by the application of a set of multiple Z-R and reflectivity-to-snow (Z-S) relationships (Table ).

For the precipitation type classification, we use the linear depolarisation ratio (LDR) included in . In the first internal flight leg, high reflectivity bands frequently occur (Fig. a), while the LDR represents a robust indicator for the melting layer (Fig. b). For the melting layer detection, propose an LDR threshold of -17 dB, which we apply to our radar data. The nearest-surface exceedance of the threshold marks the bright-band bottom BB_bottom.

However, such a pure threshold-based melting layer detection is subject to many artefacts and outliers. Therefore, we apply additional criteria. First, the maximum BB_bottom height is set to 2000 m, and then its spatial gradient is restricted. We consider variations of BB_bottom of up to 60 m per 200 m horizontal distance as realistic. Both vertical thresholds are checked for a rolling mean window of 5 s, which is applied to the initially pure LDR-based BB_bottom. While the gradient threshold is very suitable for most RF legs, it is too restrictive near front regions such as those that occur across ARs, where air mass transitions can cause vertical changes in the melting layer of several hundred metres in 1 km (e.g. Fig. b; 11:48). For this reason, we add gap-filling by linear interpolation, allowing for maximum gap lengths of ≈2.5km. These gap-filled periods are the ordinary BB_bottom. We declare precipitation below the presence of BB_bottom as rain and, if no bright band is found, as snowfall.

We account for a transition zone where mixed-phase precipitation is likely, as phase transitions do not occur immediately. We define periods of possible mixed-phase precipitation type by an additional interpolation over the remaining data gaps of BB_bottom up to ≈2km and by extrapolation of BB_bottom of ≈2km along the flight. Furthermore, mixed-phase precipitation becomes ubiquitous as the bright band descends to the surface. The near-surface BB reflectivities can then lead to an overestimation of precipitation rates. To prevent this, all corresponding precipitation periods with BBbottom<300m are treated as uncertain.

The precipitation phase classification allows the derivation of precipitation rates to distinguish between snow and rain periods. This is essential because the Z-R and Z-S relationships are quite different due to the different scattering properties of the hydrometeors. We consider six reflectivity-rate relationships (Table ). Each of these relationships considers different aspects relevant for our Ka-band radar estimates of precipitation in Arctic ARs. In particular, the relationships weigh lower and higher reflectivity factor values differently. None of the relationships listed are optimal for our purposes. However, the variety of their different representativeness gives us a higher chance of reproducing the high PSD variability in AR conditions as found by . Therefore, we apply all relationships to our precipitation-phase-classified reflectivities and consider their spread to estimate our uncertainties.

We find different precipitation modes for the first internal leg (Fig. ). While the western post-frontal sector shows convective cells, there is very deep convection in the AR core and its eastern part belonging to S1, which contains two major precipitation fields (Fig. c). Further east in the pre-frontal sector (Fig. ; right side), precipitation becomes weaker and more stratiform. While the cell in the post-frontal (cold) sector is snow, the melting layer in the heavy precipitation core rises towards the warm pre-frontal sector (Fig. b, c). Within the pre-frontal half of the core, precipitation contains rain with mean rates greater than 0.5mmh-1, while the rates based on the relationship of exceed 1mmh-1. In particular, for more intense precipitation, the rates between the relationships increasingly diverge (Fig. c), leading to higher uncertainties in the precipitation estimate for the moisture budget closure. For the pre-frontal segment of the internal leg, we derive a mean precipitation rate of 0.05mmh-1, with an uncertainty range from 0.01 to 0.11mmh-1.

The Arctic precipitation rates we derive are much lower than the airborne precipitation rates in mid-latitude ARs by . Yet, our approach may underestimate precipitation because we neglect hydrometeor attenuation, which becomes relevant for estimates near the surface when the radar signal has to penetrate deep rain clouds with melting layers. Obtaining estimates of the magnitude of melting layer attenuation is complex. Approaches such as the path-integrated attenuation correction by are not feasible for our radar, as the receivers' high pulse power and high sensitivity lead to overdriven ground return.

For the dropsonde-based determination of the IVT divergence, we follow the methods of and . We derive both composites of the moisture transport divergence, namely, mass divergence (DIV_mass) and moisture advection (ADV_q) in Eq. (), using a regression approach applied to the respective sonde-based wind and moisture fields. In the case of linear variations, a time-stationary meteorological quantity Φ (e.g. wind speed) can be inferred as: 6Φ=Φo+δΦδx⋅Δx+δΦδy⋅Δy, where Φo is the area mean and Δx and Δy are zonal and meridional displacements from the area centre point. Using the values of Φ at sounding locations and minimising the least-squares errors in the linear regression fit of Eq. (), linear estimates of the zonal (x) and meridional (y) gradients are obtained. We calculate the divergence by summing the two gradients. The uncertainty in derived divergence is estimated by Gaussian error propagation from the uncertainty of the fitted regression coefficients.

We determine both the divergence of the wind vector field and the gradients of the moisture field to calculate the two components DIV_mass and ADV_q and finally, as the sum of the vertical integral of both composites, ∇ ⋅ IVT (Eq. ). Uncertainties of ∇ ⋅ IVT are non-trivial due to possible statistical dependence of the values along the vertical profile. While used a Monte Carlo approach to circumvent this limitation, we estimate the vertical decorrelation length by referring to a common low-level jet (LLJ) vertical extent of 400 m. We average the uncertainties for DIV_mass and ADV_q in vertical 400 m bins, with the bin size as our decorrelation length estimate. We assume that these values are statistically independent, so we can apply the Gaussian and central limit theorem. The uncertainty of the vertically integrated composites, IDIV_mass and IADV_q, is calculated from the standard deviation of the respective uncertainty values in the 400 m bins, multiplied by the vertical pressure range and the number of pressure levels.

For S1, Fig.  shows the vertical profiles of DIV_mass and ADV_q, as derived from the sonde-based regression. For both composites, the values remain in the range of ±1×10-4g kg-1s-1 and are rather low for Arctic AR conditions . Both composites contribute to the moisture budget through drying. Calculating the vertical integrals IDIV_mass and IADV_q, mass divergence causes a drying of 0.50 ± 0.06 mmh-1 and dry advection of 0.28 ± 0.14 mmh-1, respectively.

Both composites act differently at vertical levels. Mass divergence is most pronounced in the lower levels up to 4 km. Remarkably, the divergence is interrupted by a slight convergence at around 1 km (Fig. a). This is at the height of the LLJ , where the sondes measure wind speeds above 30ms-1. Mass convergence near the LLJ is typical for ARs and has also been identified in the Arctic ARs . At this height, mass convergence is associated with supergeostrophic winds, which enhance the moisture transport . Except for the LLJ, divergent winds dominate the mass divergence (Fig. a). While wind speeds remain similar along the mid-troposphere (≈25 ms-1 up to 6 km), horizontal wind divergence increases with height, mainly due to changes in wind direction. Still, the magnitude of moisture mass divergence (DIV_mass) decreases due to the superimposition of vertically decreasing moisture.

Moisture advection is low from the saturated boundary layer up to the LLJ (Fig. b). At these levels, all sondes indicate a very moist troposphere, with q around 4.5 gkg-1. While moisture in Arctic ARs can occasionally also exceed 5gkg-1 in early summer , such q values are exceptional for early spring conditions . Above the LLJ, dry advection is relevant from 1 to 2 km and above 4 km. Because the horizontal moisture gradients persist with height more than mean absolute moisture, advection decreases less with height than mass divergence. The sondes in the inflow legs partly show very dry mid-level conditions (not shown). The uncertainties increase significantly and are much higher than for mass divergence.

To assess the temporal evolution of the AR moisture budget components (research goal G2, Sect. ), we analyse a series of four AR flight corridors encompassed by the two flights RF05 and RF06. Figure  illustrates how the two zigzag patterns per RF sample the AR to derive its budget components over a period exceeding 24 h. During both RFs, the outflow leg of the first zigzag pattern simultaneously serves as a leg in the zigzag pattern for the consecutive AR flight corridor (outflow in S2, inflow in S4). Aiming to derive the full moisture budget during the AR evolution from airborne observations, our analysis focuses on the pre-frontal AR sectors (Fig. ; orange areas) due to the ATC restrictions on western sonde releases during RF05.

The relevant sondes in the zigzag patterns cover four pre-frontal sectors (S1–S4, Fig. ). During RF05, the sectors S1 and S2 are located in the AR exit region, over the ice-free ocean southwest of Svalbard, while in RF06, they are located south of Svalbard. The outflow leg of the last AR sector (S4) approaches the southern coast of Svalbard, crossing the marginal sea ice zone. The number of sondes used to determine ∇ ⋅ IVT in each pre-frontal sector differs in S1 and S2 compared to S3 and S4 during RF06 (Fig. ). Eight sondes per sector are included in the divergence calculations for S1 and S2 (RF05). In turn, the pre-frontal flight legs in RF06 are shorter, resulting in only four to six sondes spanning the pre-frontal sectors. We account for the impact of the number of sondes on the accuracy of ∇ ⋅ IVT by quantifying the uncertainty in the regression coefficients.

The reanalysis IVT fields in Fig.  reveal a significant decay of the AR. The extended AR core, which maintained IVT ≥ 400 kg m⁻¹ s⁻¹ during RF05 (Fig. a, b), substantially decreased to below 300kgm-1s-1 (Fig. c, d) by the next day. For the airborne perspective, Fig.  illustrates the sonde-based distributions of IWV and IVT derived along each flight corridor corresponding to one of the AR pre-frontal sectors S1–S4 (Fig. ). Comparing the sonde-based integrated quantities of the 2 flight days, the IVT values decrease by approximately 50 %, while IWV decreases by 40 %, indicating a stronger decay in the moisture transport than in the moisture fields. The box heights in Fig.  show that the spatial variability along the AR flight corridors decreases from those including S1 and S2 to those of S3 and S4. Similar to the median values, the decrease in variability is more pronounced for IVT than for IWV. Reducing moisture transport (IVT) is primarily driven by decreasing wind speeds with a decay of the LLJ due to decreasing pressure gradients (not shown). Note that the sonde-based decay of IWV is similarly reproduced by the continuous along-track representation of the HAMP-based IWV retrieval (not shown).

The distributions in Fig.  between two flight corridors on the same day are almost similar. Nonetheless, the medians still suggest a decaying trend of the AR on these shorter timescales. With this consistent decay of the AR, it is worth investigating how this trend can be linked to the evolution of the moisture budget components.

We compare all airborne moisture budget components, derived as described in Sect. , over the series of pre-frontal AR sectors and determine to what extent each component contributes to the vertically integrated moisture budget (Eq. ). For all budget components and pre-frontal sectors, Fig.  shows that the individual components contribute to the moisture budget in a range of ±1mmh-1. The magnitude of these ranges is slightly lower than the reanalysis-based statistics of mid-latitude AR events in and nearly half the size of the airborne components derived in the mid-latitude case study conducted by . However, our AR flight corridors and pre-frontal sectors are substantially larger than those in . For Arctic conditions, the absolute magnitudes of IDIV_mass and IADV_q, which we derive in our AR, are comparable to distributions found in pre-frontal AR sectors in .

Figure  shows that the AR experiences rather weak surface interaction, characterised by small mean contributions from evaporation (E) and precipitation (P). Specifically, evaporation remains notably weak, with the highest value of E=0.15mmh-1 at the first sonde in Fig.  across both RFs. Moreover, the average pre-frontal precipitation based on the internal flight leg remains below 0.1mmh-1. Despite cloud systems' compact and deep nature within the AR core, the surface precipitation is very heterogeneous. While precipitation rates up to 1mmh-1 are derived for both rain and snow phases, they occur only for short periods. Rather, isolated moderate precipitation plumes often alternate with weak or no precipitation periods. Furthermore, stronger precipitation is partly found west of the pre-frontal budget regions.

The moisture transport divergence mainly controls the local change in water vapour for all sectors. Between advection and mass divergence, we identify mainly moisture (dry) advection aligned with the local water vapour change. This is consistent with mid-latitude ARs, where advection has been identified as being more correlated with local water vapour change . The convergence of mass governing the vertical motion that can trigger precipitation is very weak for this AR. Even more astonishing is the strong divergence of moisture mass during RF05, which is atypical for pre-frontal AR characteristics according to .

The dominant components are those with the highest absolute uncertainties. Uncertainties in δIWV/δt can reach up to ± 0.25mmh-1 (e.g. S2; Fig. ). A comparison of the two composites of ∇ ⋅ IVT shows that the uncertainties in advection are greater than those in mass divergence. This difference is due to higher spatial variability in the moisture field than in the wind field, which influences the uncertainty of the regression fits (Sect. ) and thus affects the accuracy of the resulting budget components. Higher moisture variability has also been found in other Arctic ARs . In addition, the components show the dependence of the moisture transport representation on the sampling frequency (; ). The sampling of S1 and S2 involved eight sondes along both cross-sections, while only six (four) were used for S3 (S4), as shown in Fig. . The sectors S3 and S4 exhibit much larger uncertainties in sonde-based integrated moisture transport divergence. Particularly, the uncertainties in S4 highlight that coverage by four sondes in a frontal sector may be insufficient.

During the decaying evolution, the magnitudes of the moisture budget components remain rather constant. However, the values change in their sign. The pre-frontal AR sectors exhibit a drying of more than 0.5 mmh-1 during RF05 (S1 and S2), in contrast to a surprising moistening of more than 0.5 mmh-1 during RF06. Throughout this transition, the balance of local change in water vapour and moisture transport divergence and the weak precipitation and evaporation persist across all sectors. The moisture transport divergence primarily contributes to the drying of the air masses during RF05 and the moistening during RF06. Both composites of ∇ ⋅ IVT shift from divergence to convergence, while advection emerges as the predominant component over the mass divergence. Because the trends in local moisture are mainly determined by moisture transport divergence, we examine the vertical profiles of moisture advection ADV_q and mass divergence DIV_mass for all pre-frontal AR sectors in more detail. This analysis enables a specification of the evolution of the moist air masses within the AR by identifying the dominant heights of moisture transformation. We further examine how the cloud and precipitation fields respond.

Figure  offers insights into the evolution of moisture advection and mass divergence during the AR decay across the sectors S1–S4, illustrating the dominant terms at different heights. During S1 and S2, almost the entire profile of DIV_mass exhibits positive values, apart from the convergence peak at the LLJ at around 1.25 km (Fig. a). Compared to the first flight day during S1 and S2 (Fig. a), S3 and S4 show lower amplitudes of DIV_mass along the vertical profile (Fig. c). DIV_mass shifts towards more convergence, although with reduced amplitudes. The convergence peak at the LLJ widens, and another convergence zone appears at about 2.5 km. Although a broader low-level convergence zone arises, the sondes indicate that the LLJ dissipates from RF05 towards RF06 (not shown). Wind speeds at the previous LLJ altitude decrease from 30ms-1 in S1 to less than 20ms-1 in S4. This suggests that friction at the edges of the LLJ induces the entrainment of slower currents, widening the LLJ but slowing its overall speed. From the lower mid-levels upwards, RF06 generally shows a significant decrease in mass divergence (Fig. a, c), such that mass divergence almost ceases to contribute to the moisture budget above 2.5 km.

For ADV_q, the dropsondes imply that the vertical characteristics undergo significant changes as well, though to a lesser extent within the marine boundary layer (<1 km). Despite the high moisture content, the marine boundary layer is well mixed, making advection a less dominant mechanism. During RF05 (Fig. b), dry advection prevails throughout the vertical profile on average, except for minor moisture advection around 2.5 km and in the marine boundary layer. Dry advection in mid-levels (3–7 km) intensifies notably from S1 to S2 but disappears during the second flight day (S3 and S4). In S3, moisture advection peaks in lower levels (-1×10-4gkg-1s-1 at about 2 km), while being negligible in the mid- and upper levels (Fig. b, d). S4 shows significant moisture advection in the upper mid-levels (-0.5×10-4gkg-1s-1 at 5 km), above dry advection around 2.5 km. However, all derived ADV_q values are subject to larger uncertainties than those of DIV_mass due to spatial moisture variability, and they increase with larger sonde spacing during RF06. Particularly, in S4 just below 2.5 km, the limited number of sondes (four) leads to an uncertainty range of approximately ±1.5×10-4gkg-1s-1 between dry and moisture advection. This variance contributes to the large uncertainty range in the integrated budget contribution of IADV_q (Fig. ). Dropsondes from both flights indicate a very moist troposphere (not shown). Notably, the lower levels of the inflow cross-sections (up to 3 km) in S3 and S4 are much moister than S1 and S2. The highest q values are found in the marine boundary layer with 5gkg-1 for RF06, attributed to moisture accumulation from intensified IVT in the AR remnants west of the Norwegian coast (Fig. d). The trends in moisture transport divergence raise the question of how the cloud and precipitation fields respond.

Radar observations of the AR sectors indicate substantial changes in surface precipitation characteristics and cloud fields across the sectors (Fig. ). Although precipitation overall contributes little to the moisture budget for all pre-frontal sectors in Fig. , it exhibits high spatial variability and differences between the sectors (Fig. ). S1 shows moderate local precipitation rates of over 1mmh-1, mostly falling as rain with a melting layer at about 1 km. While the second pre-frontal sector (S2) has much weaker precipitation, S3 exhibits higher rates, again with a more heterogeneous convective structure. Convection triggering is consistent with the sonde-based mass convergence in S3 (Fig. c). Despite similar low-level mass convergence in S4, substantial advection of dry and unsaturated air at a height of 2 km (Fig. d) here appears to hinder cloud formation and precipitation. The full internal legs reveal that precipitation in the post-frontal (cold) sector is mainly snow.

For S1 and S2, the AR embedded precipitating deep clouds reach up to 12 km. While the internal leg belonging to S1 shows two major cloud filaments (Fig. a), these filaments have merged during S2. The high cloud tops during RF05 persist in a subsiding and drying environment, presumably causing the clouds to dissolve slightly towards RF06. For the second day, the deeper clouds do not reach above 8 km. The lowering of the clouds coincides with the decreasing depth of vertical mixing (Fig. d) when the higher troposphere (≥8km) exhibits a dynamical equilibrium. For S4, the cloud systems decouple from the boundary layer, with a cloud base height between 2 and 4 km and a low cloud fraction underneath.

Summarising the trends of the budget components, we conclude that the IVT decay is not dominated by drying in lower levels but by a weakening of the winds. This weakening implies less spatial variability, resulting in lower mass divergence amplitudes and a reduced depth of vertical mixing and shallower cloud fields. The moisture transport divergence during RF05 is consistent with the directional dispersion of the IVT fields over the flight pattern (Fig. ), leading to decreasing AR intensity and local drying. However, we neglected whether the components based on airborne observations robustly closed the moisture budget. If we aim to unravel air mass transformations within the AR by using the airborne budget components, we need to assess their plausibility by the magnitudes of emerging residuals in the budget closure of Eq. ().

We calculate the residuals from the difference between retrieved δIWV/δt, based on HAMP measurements (Sect. ), and the sum of all other airborne components contributing to δIWV/δt according to Eq. (). Figure  shows that the mean residual for each sector is in the range of 0 to 1mmh-1, indicating that the residuals are within the range of the main moisture budget components. Except for S2, the mean residual concerning HAMP-based δIWV/δt results from a possible underestimation of sonde-based moisture transport divergence (IADVq+IDIVmass). S2 is notable for its high sonde-based moisture transport divergence, which, together with precipitation and condensation, overcompensates for the HAMP-based weak temporal water vapour change (drying). S2 is the only sector where the residual, together with its uncertainty range, is completely non-zero. For all other sectors, the moisture budget can be closed when the uncertainties of the budget components are included.

Further investigation of the origins and causes of the residuals will improve the interpretation of the plausibility of the airborne budget components. The following analysis of the residuals compares our airborne budget components with those from the ICON-2km and ERA5 model grid data (Sect. ). The models serve as a valuable tool to examine factors influencing the airborne representation. By leveraging the models, we can test the sensitivity of the airborne budget components concerning sonde-based sampling frequency and the nonstationarity of the AR, and we can investigate the airborne representativeness for the entire enclosed AR area. We use S1 as an example to assess the extent to which the airborne derivation and perspective of the budget components may differ from the actual prevailing components.

While sonde-based IVT provides high accuracy at individual points, the sporadic release of sondes leads to undersampling of moisture transport fields along the cross-sections, impacting the derivation of moisture transport divergence (; ). We compare sonde-based moisture transport divergence (Fig. ; green) with the model-based values from ICON-2km, collocated along the flight path and analysed at the sonde locations (Fig. ; grey). For the along-track perspective, the model-observation comparison shows good agreement. The profiles generated by ICON at the sonde locations show similarity in moisture transport divergence (ADV_q and DIV_mass) with the actual sonde-based profiles. The vertical variability is higher in the sonde-based profiles. In particular, the significant mass convergence within the LLJ evident from the sondes is not adequately reflected by the ICON-2km mimicked sondes (Fig. a). Nonetheless, the ICON-2km mimicked sondes and the real dropsondes show similar means of the integrated budget contributions, especially for IADV_q (Fig. ).

Compared to the continuous along-track representation in ICON-2km (Fig. ; black-bold), undersampling from discrete soundings has little effect on the divergence values for both composites, namely, ADV_q and DIV_mass. Differences in the moisture transport divergence between ICON values based on the sonde locations and those based on the continuous representation along the flight path are overall small, barely exceeding 0.1 mmh-1 (Fig. ). The largest discrepancies occur in ICON-based dry advection (below 3 km), which is overestimated when considering only the sonde locations (Fig. b). The uncertainties at each height are slightly lower for the continuous ICON-2km (not shown). We find that the continuously collocated ERA5 (Fig. ; orange) has difficulties in representing the low-level moisture transport divergence below 3 km, as there are large deviations from ICON-2km and dropsondes. This confirms ICON-2km as a robust model-based IVT divergence along the flight track. The differences in ICON-based ∇ ⋅ IVT between the continuous and sporadic sonde release sampling strategies are too small to attribute the undersampling of moisture transport by sondes as the main cause for the residuals reaching up to 1 mmh-1.

As a second effect, emphasise the temporal evolution of the AR, e.g. by AR displacement during flight, causing nonstationarity that represents a relevant source of error for sonde-based estimates of moisture transport divergence. In our AR case, both models reproduce stronger advection of moisture in the instantaneous view compared to the non-instantaneous observations (not shown). This stronger advection would, in turn, increase the residuals.

Nonstationarity becomes most effective in deviating the airborne results when there is a high subscale spatial variability. Not only did the zigzag pattern take quite a long time, especially in RF05, but it also aimed to represent the divergence in a very large AR flight corridor. To further investigate the spatial variability of IVT divergence within the AR flight corridor, we examine the ERA5 moisture transport divergence field product, which is sufficient to capture the internal large-scale variability that may be missed by the airborne measurements. Figure a illustrates a pronounced dipole structure in the ERA5-based ∇ ⋅ IVT field within the pre-frontal sector of the AR flight corridor. While the southern region and the inflow leg exhibit divergence with budget contributions of ∇ ⋅ IVT ≤ -1 mm h⁻¹, the northern region is characterised by convergence and positive moisture rates of about 1mmh-1. This dipole is averaged out when the divergence calculations are based solely on the two cross-sections, resulting in lower airborne estimated budget contributions. An important factor for the divergence pattern in Fig. a is the widening of fields of strong IVT north of the inflow cross-section induced by changes in the transport (wind) direction (Fig. a). This change in wind direction within the flight corridor is reflected in the sonde-based predominance of DIV_mass against ADV_q. Furthermore, the dipole structure can clarify the along-track discrepancies between ICON-2km and ERA5. While the models are confident about the widening of strong IVT fields north of the ingoing leg, slight variations in the dipole pattern result in differing characteristics from the airborne perspective on ∇ ⋅ IVT. Thus, although the divergence calculations based on sonde data and the models align reasonably well along the flight path, their representativeness for the entire budget region is limited. In RF06, such dipole structures are absent (Fig. b). Instead, a more distinct zone of overall IVT convergence is identified. This indicates that the sampling in the AR flight corridors during RF06 is more representative despite fewer sondes.

The high precipitation rates due to this AR observed at Svalbard, with more than 30 mm d⁻¹ as reported by , seem to contrast with the relatively low precipitation estimates along the AR flight corridor. However, the radar demonstrates the heterogeneity of precipitation within the AR, with local regions experiencing moderate precipitation (Fig. ). This raises concerns regarding the representativeness of the airborne-radar-derived estimates. In particular, the curtain-based perspective of the radar may not capture the considerable variability in cloud conditions . Additionally, the missing correction for hydrometeor radar attenuation is a limitation of the airborne estimates.

Therefore, we revisit the comparison of the airborne data with the model data, focusing initially on precipitation from the along-track perspective. We compare the radar observations with the collocated ICON-2km and ERA5. Figure  shows the radar and the model data precipitation rates along the first internal leg belonging to S1. For the pre-frontal part of the internal leg, the mean precipitation of the along-track ICON-2km closely aligns with the radar-based precipitation estimates. At the same time, ERA5 shows significantly higher values in a few regions. ICON-2km shows greater fluctuations than ERA5 due to its finer horizontal resolution (Sect. ), but it is much more homogeneous with lower spatial variability than the radar data. While ERA5 estimates a mean precipitation of 0.2mmh-1, its amplitude remains below 0.5mmh-1 and is even lower in ICON-2km. The two pre-frontal precipitation maxima seen in the radar data, with local rates exceeding 1mmh-1, are also found in ICON-2km, albeit with slight spatial shifts and smoothened with smaller local maxima.

The low radar-based precipitation mean could suggest an airborne underestimation, especially as the radar is uncorrected for hydrometeor attenuation. Specifically, the attenuation at the melting layer due to riming is mostly relevant. provide regression-based coefficients to quantify the attenuation by the melting layer and rain based on predetermined rain rates and reflectivities. We apply these coefficients to the rain rates in Fig.  and deduce a radar attenuation of up to 2 dBZ. To have a conservative estimate of the maximum underestimation of precipitation caused by attenuation, we thus increase all reflectivities by 2 dBZ. These elevated radar reflectivities increase the mean precipitation rate by 0.03mmh-1 (50 %) in Fig. . Radar-based precipitation estimates become more intense than that from ICON-2km, but ERA5 still indicates significantly stronger precipitation. also found that ERA5 tends to overestimate precipitation over the Arctic Ocean.

Irrespective of attenuation effects, the high spatial variability of precipitation from the radar – and, to some extent, from ICON-2km – underscores the complexity of accurately representing precipitation conditions in an entire budget flight corridor using data from a single along-track curtain. Therefore, we compare the along-track distribution of precipitation rates with the horizontal distribution across the AR using the 2D surface field data from ICON-2km (Fig. ). We average the radar reflectivities every 10 s to improve the comparability of the radar and ICON-2km data by achieving a similar horizontal resolution (≈2.5km). Along the flight track, ICON reveals dominance of moderate precipitation rates ranging from 0.15 to 0.35mmh-1, while the radar locally shows higher rates. However, these higher rates are hardly relevant for the kernel density estimate (KDE) in Fig. a, which is why the radar still has a lower mean.

When incorporating the horizontal ICON precipitation field, both the KDE and the spatial precipitation pattern (Fig. a, b) show that the flight path misses several precipitation regions within the AR flight corridor. The northern area of the AR corridor has stronger precipitation that is underrepresented by the airborne radar. Over the flight corridor area, the precipitation rate KDE (Fig. a; orange) more greatly resembles a Weibull distribution, but higher precipitation rates contribute more than in the radar (Fig. a). Note that the spatial shift of the precipitation rates along the track in Fig. b is attributed to the temporal variations in AR dynamics during the zigzag manoeuvre, contrasting with the instantaneous model depiction.

Concluding the plausibility analysis of Sect. , we find a considerable subscale variability in the budget components within the AR flight corridors. Combined with the curtain-based sampling, this variability largely accounts for the residuals in the airborne budget closure. Our airborne analysis reveals that precipitation within Arctic ARs is hard to quantify. Even if precipitation is rather weak over the ocean, there is considerable small-scale precipitation variability. Future research efforts can expand upon the comparison between model-derived and observed precipitation using the remaining AR flight segments of HALO-(AC)3 (; ).