On the Rivers in the Euro-Atlantic Sky

We study and revisit the Atmospheric Rivers (AR) over Euro-Atlantic sky using long term reanalysis datasets and widely used methods and parameters. The atmospheric winds, temperature and specic humidity at different pressure levels during 1979-2018 were used to study the spatiotemporal variability of water vapour transport integrated between 1000-300 hPa (IVT300) as a proxy to ARs. The standard deviation (200 kgm-1s-1) of ARs is around 60% of the climatology (>300 kgm-1s-1) in all reanalysis datasets in the North Atlantic. High frequency of ARs over western Europe in winter half-year (WHY) has 6% lower intensity compared to the low frequency of ARs in summer half-year (SHY) with 3% higher intensity than the annual mean. The intensity of ARs in the North Atlantic has been increasing in recent times with large decadal variability and poleward shift in landfalling. The magnitude of atmospheric parameters in the lower atmosphere below 750 hPa dominates the total column water vapour and intensity of ARs. There is a signicant impact of the North Atlantic Oscillation and Scandinavian blocking on the location of landfalling of ARs and latitudinal dependence of the source of moisture ux in the open ocean contributing to the formation and enhancing ARs strength.


Introduction
Tropospheric atmospheric dynamics are guided by water vapour in the lower atmosphere (Schneider et al., 1999). Particularly, heat and momentum in the lower troposphere have strong coupling with the movement of moisture in the troposphere. Hence, it is essential to study the tropospheric moisture transport to better understand the global water cycle, synoptic weather patterns and climate change due to enhanced evaporation in recent decades due to global warming (Trenberth, 2011). Also, the ocean and atmosphere play a key role in transporting heat and water vapour poleward, respectively. Atmospheric general circulation plays a vital role in circulating water vapour in the lower troposphere. The large-scale land-ocean atmospheric exchange of water demonstrates the coupling of the atmospheric branch of the hydrological cycle (Hack et al., 2006). The global and continental-scale transport of water vapour has important implications for climate variability and hydrology (Brubaker et al., 1994). Hence, atmospheric scientists must consider studying climatological, meteorological and hydrological aspects of the transport of moisture in the lower atmosphere (Gimeno 2013; Gimeno et al., 2012). It is particularly important to understand the conceptual models of moisture transport to aid research into the origin of continental precipitation (Gimeno 2014). Also, moisture transport in mid-latitudes plays a key role in guiding the global atmosphere and climate dynamics in various temporal and spatial scales.
Most of the meridional water vapour transported across the midlatitudes (90% of the total mid-latitude vertically integrated water vapour ux) takes place through narrow corridors in less than 10% of the zonal circumference called atmospheric rivers (ARs) (Yong and Newell 1998; Ralph et al. 2004). These transient lamentary regions occur within the warm conveyor belt of extratropical cyclones in a maritime environment and are characterized by high water vapour content and strong low-level winds (Ralph et al. 2004(Ralph et al. , 2005(Ralph et al. , 2006. Thus, these corridors tend to be quite narrow (<1000 km wide) relative to their length scale (>2000 km) (Neiman et al., 2008). The warm conveyor belt transports both sensible and latent heat, particularly the later contributes to the poleward heat transport that occurs in the form of water vapour ux from the warm sea surface over oceanic regions serving as a major moisture source. Most of the water vapour transport within these rivers occurs in the lowest 2.5 km of the atmosphere due to moistneutral strati cation (Ralph et al. 2005). Hence, these are also called tropospheric rivers due to their occurrence in the lower troposphere Newell 1994, 1998). The combination of lowertropospheric moist neutrality, strong horizontal winds, large and concentrated water vapour content yields occurrence of heavy orographic precipitation and winds on elevated terrain lead to heavy ooding (Ralph  These datasets are produced by assimilating meteorological/oceanic observations into numerical weather prediction model output. In this work, we aim to study the characteristics of ARs over the north Atlantic by revisiting the widely used methods and parameters. The objective of this study is also to look at the variability of ARs in the north Atlantic in relation to the different ocean and atmospheric parameters. We also focus on the resolution dependence of ARs over the north Atlantic. The paper is organized as follows. Section 2 describes the data and methods, followed by results and discussions in section 3 and conclusions in section 4.

Methods
In the present study, we have used six-hourly winds, temperature, and speci c humidity data at different pressure levels from six reanalysis products available until 2018. ), we also included temperature of corresponding layers in these algorithms to normalize the computed IVT (nIVT, Equation 2) and IWV (nIWV, Equation 4) and study the difference from the normal approach using different reanalysis products and compared these two methods in the Atlantic.
Integrated Vapor Transport (IVT): Normalized IVT: Integrated Water Vapor (IWV): Normalized IWV: Where Q is speci c humidity in kgkg -1 , U and V are zonal and meridional components of winds at different pressure levels measured in ms -1 , P is the desired pressure (hPa) up to which the atmospheric parameters are integrated; g is the acceleration due to gravity, which is a constant and is given as 9.8 ms -2 . Normalization with temperature is done by dividing the two terms inside the square brackets with the temperature at a corresponding pressure level. Table 2 shows the details of the variables and their units.
Thus, time-integrated (4 time-steps) daily ARs data has been generated from six-hourly reanalysis datasets using IVT (kgm -1 s -1 ), normalized IVT (kgm -1 s -1 K -1 ); IWV (mm) and normalized IWV (mmK -1 ) from the surface to 750 hPa, 500 hPa and 300 hPa. Temperature normalization is done to understand the change in the thermodynamic component of IVT and IWV using the Clausius-Clapeyron equation (3), which states that the water-vapour content of saturated air, q*, increases nearly exponentially with temperature T (Payne et al., 2020).
where L is the latent heat of vaporization and R v is the gas constant of water vapour. Within the saturated environment at the core of an AR where q≈q * , a small change in the surface warming would cause speci c humidity to further enhance. Thus, speci c humidity in the upper layers of the atmosphere strongly depends on the increase in layer's temperature with respect to surface temperature and the Clausius-Clapeyron scaling factor, α(T) and is approximately 6.6% K −1 for surface temperatures causing The time-integrated (6-hourly) daily AR data has been used in further analysis to study the temporal and spatial variability of ARs over the north Atlantic both in climatic and decadal timescales. In addition to studying the biases in different atmospheric parameters, the annual and seasonal climatology and strength of the ARs at different layers were studied. For the intercomparing of reanalysis datasets, we consider ERA5 as the reference dataset. Furthermore, the study focuses on the variability of ARs intensities in different products including major categories of ARs and their frequencies in the north Atlantic. Regression analysis done helps to understand the spatial trend in the ARs, followed by studying the state of the atmosphere using major atmospheric parameters describing the characteristics of the occurrence of ARs.

Results And Discussion
Climatology and standard deviation of ARs over the north Atlantic: Quanti cation of ARs over the north Atlantic was done using the climatology and standard deviation for different methods. This is essential to see the spatial variability including the magnitude of water vapour transport over the north Atlantic and into western Europe. The climatology from ERA5 daily data using IVT and nIVT methods shows highest AR intensity in the region enclosed between 30 o N-60 o N ( Figure 1). Though the intensity of AR varies from event to event, on average IVT300 (IVT between 1000-300 hPa) ( Figure 1a) over the north Atlantic is around 300 kgm -1 s -1 and is in line and directed along with the westerly wind over this region. The maximum nIVT300 (nIVT between 1000-300 hPa) over the north Atlantic is in coherence with the maximum IVT300 and along the same path with maximum values (>1 kgm -1 s -1 K -1 ) concentrated over central North Atlantic (Figure 1b). The nIVT300 is accounted for available IVT300 per unit temperature is a proxy to the fractional changes in available speci c humidity in the atmospheric column per degree of atmospheric warming. In the upper layers of the atmosphere, α varies with the varying temperature. Hence, α increases with the decreasing temperature with height and ampli es the changes in the speci c humidity aloft and is larger in the upper troposphere. On the other hand, increasing speci c humidity in the upper layers tends to release more latent heat ux with ascending air, and decrease the lapse rate with warming and thus increasing the temperature with height.
If the vertical column of the atmosphere is saturated and has moist-neutral conditions, the combination of these factors implies a rate increase in IVT that is substantially larger than that of near-surface water vapour (Payne et al., 2020). Hence, the fractional change in IVT is a reasonable approximation to the thermodynamic contribution to IVT change. Thus, on top of concentrated warm coastal surface waters due to Gulf stream over western North Atlantic causing higher evaporation; speci c humidity advecting from the tropics could be saturating the upper troposphere over the central north Atlantic and showing higher IVT300 and nIVT300.
Though AR mapping and characteristics study initially was started using IWV, the importance of tracking the AR made IVT as widely used method. However, using IWV would give estimation of concentration of total column condensable water vapour at a given instance ( In the north Atlantic, different reanalysis products used to map the ARs show variability in magnitudes ( Figure 3). The climatology (shaded) and standard deviation (contours) of ERA5 has lower IVT300 than any other reanalysis products used; while ERA-Interim has higher climatology and standard deviation. All reanalysis data sets are developed using numerical and statistical approaches integrated with observations with bias corrections. Thus, all these reanalysis datasets show a similar spatial pattern over the North Atlantic, but the difference in magnitudes could be attributed to the variability in the magnitudes of Q, U and V, which could be further due to bias in observations, discrepancies in product development. To illustrate it further, we compared the atmospheric parameters used (Q, U, and V) to map AR in 20CR (coarse resolution) with the ERA5 (high resolution data) ( Figure S3). A simple interpolation has been used to match grids points of parameters in ERA5 with 20CR data as these data sets have a different spatial resolution. The climatology of these individual parameters during 1979-2014 shows that 20CR overestimating the magnitude (Figures S3d-S3f) compared to the ERA5 (Figures S3a-S3c). Hence, the 20CR data has a negative bias of 0.5 gKg -1 in Q, 1 ms -1 in U and V components of wind in the north Atlantic ( Figures S3g-S3i). However, this would not be obvious for different seasons and different ARs in the Atlantic.
In the case of AR mapped on 6 th March 2002, different reanalysis products show signi cant bias in IVT300 compared to ERA5 (Figure 4). Both MERRA and ERA-Interim show positive bias at the head of the AR (AR path is marked as the grey arrow in Figure 4) and negative bias in the tail (Figure 4a, 4b). On the other hand, NCEP (NCAR, CFS) and 20CR have a strong negative bias on aggregate (Figures 4c-4e). Both these positive and negative biases are around 50 kgm -1 s -1 in magnitude and are of 10% of the total magnitude of AR (~500 kgm -1 s -1 ) (Figure 2). The variability in the magnitude of IVT300 in different products might lead to bias in the intensity estimation of precipitation and winds during landfall. Hence, we use ERA5 data as a standard dataset in our further analysis in the following sections.

Spatio-temporal variability of IVT300
A general approach used to map the ARs is using IVT300 by considering pressure levels from surface compiled all the available methods including thresholds to map ARs globally as a part of describing Atmospheric River Tracking Method Intercomparison Project (ARTMIP). Hence, there is persisting ambiguity in using reference pressure levels to map ARs. Therefore, here we quantify the magnitude of annual and semi-annual IVT in different layers. For this purpose, the total column (1000-300 hPa) has been divided into sublayers consisting 500-300 hPa (IVT_Upper), 750-300 hPa (IVT_Middle), 750-500 (IVT_Lower) which lie above 750 hPa pressure level in addition to computing IVT500 (1000-500 hPa) and IVT750 (1000-750 hPa). This exercise helps to map the strength of IVT and spatial variability in these layers which is a function of exponentially decreasing water vapour pressure with height.
The annual, WHY and SHY mean IVT computed using ERA5 data in IVT_Upper ( Figures S4a, S4d, S4g), IVT_Middle ( Figure S4b, S4e, S4h) and IVT_Lower ( Figure S4c Figure S4g-S4i). Similarly, the low has become further less during WHY ( Figure S4d-S4f). Thus, IVT has maximum strength during SHY which could be due to increased evaporation over the warm waters in the North Atlantic. Figure 5 shows No signi cant difference was seen between IVT500 and IVT300 (~12 kgm -1 s -1 ) during the study period. But, IVT750 contributing ¾ of the total strength of IVT300 and IVT500. Thus, the strength of the IVT300 and IVT500 depends on the near-surface processes below 750 hPa. While there were no large changes in the strength of the IVT in the individual layers with seasons; IVT in SHY has 3% higher magnitude, whereas IVT in WHY shows 3% lower magnitude compared to the annual mean ( Figure 5). Hence, as the mean IVT is high up to 500 hPa irrespective of the season, and improved parameterization, in addition to accurate and high-resolution atmospheric data at least up to 500 hPa would be handy in better estimating the strength of the IVT in the north Atlantic.
Furthermore, we show hovmöller (Figure 6) of the monthly IVT300 in the central north Atlantic averaged between 30 o N-60 o N along 80 o W-0 during 2014-2018 to study the seasonal variability of peak IVT300 in more detail. IVT300 peaks in the western Atlantic (along the east coast of North America) during summer months. Due to large temperature and pressure gradients from south to north coupled with extratropical cyclone season, high IVT300 has been shifting towards the eastern Atlantic in winter as marked with arrows in Figure 6 and thus causing frequent ARs over western Europe during WHY. Yet, the extent, location and movement of the peak IVT300 were not constant and have large interannual variability with relatively low values during the spring season and hence the low AR activity during this time. This interannual and intraseasonal variability in IVT300 could be caused by the altering winds over this region.
To study this further, we explored the decadal variability and trend in IVT300 and related atmospheric components in the following section.

IVT300 decadal variability and trend
It is evident that recent climate change during post-industrial era causing global warming and altering the global water cycle. On this note, it important to look for the changes in the IVT variability and trend in the recent times due to warming surface and enhanced evaporation as the changing Clausius-Clapeyron scaling factor α(T) could increase the total water vapour content in the individual atmospheric layers. In This increasing annual IVT300 trend in each decade is in coherence with the increasing IVT below 750 hPa and IVT_Lower (750-500 hPa) (Figure 7b). Particularly IVT750 has contributed more to the large increase in second (1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998) and fourth decades (2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018). As the IVT is proportional to Q, U and V; the changes in these parameters would impact these trends. Thus, the large trend of IVT300 in the second decade is dominated by the availability of Q in the near-surface layer (1000-750 hPa) which has an annual increasing trend of 2.5 gkg -1 and is largest in all decades (Figure 7c). However, the negative trend in the zonal and meridional components of wind (Figures 7d, 7e) in all layers during the same time, guiding the total trend in the second decade. Though Q has a positive trend in the rst and third decades, the negative trend in wind components in different layers caused the IVT annual trend to be moderate in these decades. On the other hand, the annual trend of both Q and wind components (U and V) were positive in the fourth decade (Figure 7c-7e) and thus led to a strong increase in the annual IVT300 in all layers (Figure 7b).
The spatial trend analysis signi cant at 95% during annual, WHY and SHY using daily IVT300 data from ERA5 is shown in Figure 8. While the annual trend shows a rapid increase (3000 kgm -1 yr -1 ) of IVT300 at 20 o N in the Atlantic and along the western Atlantic extended into central Atlantic with mean annual IVT300 increase of 2000 kgm -1 yr -1 , there was no signi cant increase in IVT300 over southwestern Europe during the study period (Figure 8c). Both WHY and SHY show opposite spatial trends. IVT300 was increased in the central Atlantic and the southwestern United Kingdom during SHY, which could be triggered by the large IVT300 available over the western Atlantic during this time (Figure 8b, Figure 6). Though the WHY show the opposite patterns with a negative trend in IVT300, the low is in the northern United Kingdom. There was a moderate increase in the IVT300 trend along southwestern Europe and the region below 20 o N has large positive trend during WHY (Figure 8a). IVT300 has been increasing poleward in the recent times with a strong positive trend along 45 o W during all the seasons, which could further guide intense AR towards the north.
Categories and frequency of ARs over the north Atlantic Furthermore, we study the spatial variability of frequency of ARs over North Atlantic using different categories of IVT300 as shown in table 3. We distinguish the daily IVT300 based on the magnitude of the intensity at each grid point or location in the selected region without consciousness on the duration of the event. The spatial frequency has been computed using the percentage of the ratio of the number of days of IVT300 of a category to the total number of days in the study period (14610). Thus, the cat 1 events are more frequent in the north Atlantic which occurs at 50% of the time (Figure 9a) along the southwest coast of Europe and in the central Atlantic. Other categories such as cat 2 (Figure 9b), cat 3 ( Figure 9c) and cat 4 ( Figure 9d) are less frequent (<15%) over the Euro-Atlantic sky. The source of this intense IVT300 is along the western Atlantic and a few events are reaching the west coast of Europe. Thus, the frequency of the intense ARs over Europe is less with cat 2 IVT300 being at 8%, cat 3 and cat 4 are at below 1% of the time. Nonetheless, the rare intense events which occur at less than 1% of the time could cause large damage over land when they come inland. To investigate the same along western Europe, we draw the frequency histogram ( Figure 10a) and compute the probability density function (Figure 10b  While most of the IVT300 values along the west coast during the study period are below 300 kgm -1 s -1 (Figure 10a), the values reaching 800 kgm -1 s -1 in a few instances could lead to extreme ARs. Similarly, the probability density function computed along the same boundary (Figure 10b) shows the IVT300 could reach up to 1400 kgm -1 s -1 and cat 1 IVT300 has the higher probability of occurrence (0.06) over western Europe than other categories. The decadal analysis along the same longitude ( Figure 11 is associated with blocking mainly over the European continent and Scandinavia. The occurrence of IVT300 (ARs) and their associated precipitation in the north between 55°N-70°N is related to Scandinavian blocking with the dipole of positive anomalies near the British Isles and negative anomalies over Greenland and Iceland (Figure 12e-12g). Although both NAO and Scandinavian patterns have strong relation with IVT300 occurrence in Europe, it is not obvious that each IVT300 (AR) landfall would follow the same synoptic weather patterns as the spatial pattern of the atmospheric state would vary signi cantly with time over a region.
Southernmost IVT300 events are drawing water vapour from both western and eastern North Atlantic as the SLHF anomalies show a dipole pattern with positive anomalies on either side (Figure 13a, 13b). Thus, these regions act as source to moisture entraining into ARs and impact the intensity of IVT300. The northcentral Atlantic is the source of moisture for the IVT300 in the 45°N-55°N latitude band (Figure 13c, 13d).
Further, a dipole pattern with positive SLHF anomaly in the west and negative in the east fueling IVT300 in the far north. Though the positive anomalies over the North Atlantic could lead to intensifying IVT300 in the north, the cold sea surface and associated negative SLHF anomalies over the Scandinavia could control the total moisture ux into the IVT300 and hence the intensity of ARs over this region.

Conclusions
We study the spatio-temporal variability of water vapour transport as a proxy to ARs in the Euro-Atlantic sky using six-hourly data from six reanalysis data sets available from NOAA, NASA, ECMWF and NCEP during 1979-2018. We use IVT and IWV methods to map the water vapour transport in different atmospheric layers the North Atlantic and normalized with temperature to study the water vapour variability with temperature. Both IVT and nIVT proved to accurate enough to map ARs. Though the IVT shows seasonal and semi-annual variability; the mean annual climatology of IVT300 is 300 kgm -1 s -1 , and the standard deviation is at 60% of the climatology in the north Atlantic. On the other hand, both these values vary in different reanalysis products with recently released ERA5 showing lower climatology and standard deviation whereas ERA-Interim has higher values compared to other reanalysis datasets.
However, the average bias in other datasets is around 60 kgm -1 s -1 as compared to ERA5 which amounts to 22% of the total observed ux. The bias in the magnitude of IVT in different layers is directly proportional to the bias in the Q, U and V of respective layers.
While most of the water vapour ux located below 500 hPa due to rapidly decreasing saturated moisture ux with height, the upper layer winds are key to transport the ux poleward. Hence, the accurate and high-resolution atmospheric parameters at least up to 500 hPa could improve the detection and tracking of ARs in the north Atlantic. On the other hand, the variability and trend of Q, U and V below 750 hPa guide the strength of the total column IVT. Thus, Q, U, and V below 750 hPa control the magnitude of IVT in the north Atlantic which shows an increasing decal trend with seesaw decadal variability. The IVT in the north Atlantic shows interannual variability with the zonal movement of peak values from the western Atlantic in summer to the eastern Atlantic in winter. However, the strength of the IVT in the Atlantic is 3% higher in summer as compared to annual mean due to strong evaporation from the warm ocean than 3% low in winter. While the semi-annual spatial trend of IVT300 shows an opposite pattern, the annual trend of IVT300 shows an increasing water vapour ux over western Atlantic with a poleward movement of this ux. Thus, the higher latitudes encountering intense ARs in recent times.

Data availability
All the data used in the study are freely available online from the corresponding data sources cited in the article. However, the data that support the ndings of this study are available on request from the corresponding author.

Code availability
All codes used in this study are available on request from the corresponding author.
Author contributions V.T. conceived the research plan, performed data analysis, and prepared the rst draft, A.R. and E.S helped to improve the research plan and gures, and contributed to analyze the results. All authors contributed to write and review the paper.

Figure 1
Climatology of ARs computed from daily ERA5 data using four different methods in the north Atlantic One example of an AR from 6th March 2002 mapped using four different methods in Figure 2 has IVT300 higher than 500 kgm-1s-1 (Figure 2a). This event was one of the intense ARs occurred over northern Europe and caused excess rainfall over Britain and southern Scandinavia. While the IVT300 is narrow and short, nIVT300 (Figure 2b) shows the adjacent regions saturated with water vapour. The advected moisture from these surrounding regions could enhance the intensity and lifetime of the AR over a given location. Thus, nIVT300 is a useful method in mapping the true characteristics and saturated water vapour content in AR. Similarly, IWV300 and nIWV300 (Figures 2c, 2d) for this event show origin of AR and the source of the advection, which is, in this case, occurred from the warm tropical region (20oN) enriched with high speci c humidity.  Bias in reanalysis products compared to ERA5 data in mapping AR on 2002 March 06 using IVT300 algorithm. Strength of annual, SHY and WHY mean IVT in different layers Decadal trend (signi cant at 95%) and variability of (a) IVT300 (b) IVT (c) speci c humidity (d) zonal wind (e) meridional wind of different layers in the central north Atlantic (30oN-60oN, 80oW-0).

Figure 9
Spatial frequency analysis of different categories of daily IVT300.   Frequency of daily IVT300 along 11oW.

Figure 12
Composite of geopotential anomaly along 11oW using different bins Figure 13 Composite of surface latent heat ux anomaly along 11oW using different bins

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