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Local and External Moisture Sources for the Arctic Warming over the Barents–Kara Seas LINHAO ZHONG Chinese Academy of Sciences Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, and Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, Qingdao, China

LIJUAN HUA Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing, China

DEHAI LUO Chinese Academy of Sciences Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China (Manuscript received 30 March 2017, in final form 13 November 2017) ABSTRACT Water vapor is critical to Arctic sea ice loss and surface air warming, particularly in winter. Whether the local process or poleward transport from lower latitudes can explain the Arctic warming is still a controversial issue. In this work, a hydrological tool, a dynamical recycling model (DRM) based on time-backward Lagrangian moisture tracking, is applied to quantitatively evaluate the relative contributions of local evaporation and external sources to Barents–Kara Seas (BKS) moisture in winter during 1979–2015. On average, the local and external moistures explain 35.4% and 57.3% of BKS moisture, respectively. The BKS, Norwegian Sea, and midlatitude North Atlantic are the three major sources and show significant increasing trends of moisture contribution. The local moisture contribution correlates weakly to downward infrared radiation (IR) but significantly to sea ice variation, which suggests that the recent-decade increase of local moisture contribution is only a manifestation of sea ice melting. In contrast, the external moisture contribution significantly correlates to both downward IR and sea ice variation, thus suggesting that meridional moisture transport mainly explains the recent BKS warming. The moisture contributions due to different sources are governed by distinct circulation patterns. The negative Arctic Oscillation–like pattern suppresses external moisture but favors local evaporation. In the case of dominant external moisture, a well-organized wave train spanning from across the midlatitude Atlantic to mid–high-latitude Eurasia has the mid–high-latitude components similar to a positive-phase North Atlantic Oscillation with a Ural blocking to the east. Moreover, the meridional shift of the wave train pathway and the spatial scale of the wave train anomalies determine the transport passage and strength of the major external moisture sources.

1. Introduction In the Arctic, the pronounced warming that exceeds the global average, known as Arctic amplification, with the concurrent acceleration of sea ice melting, has been observed over recent decades (Serreze et al. 2009; Screen and Simmonds 2010a; Cohen et al. 2014). Although the Arctic sea ice extent shows the largest downward trend in the warm season, especially in Corresponding author: Linhao Zhong, [email protected]

September (Stroeve et al. 2012), the greatest Arctic amplification is found in the cold season [from October to January (ONDJ)], when the solar radiation is low or completely absent (Screen and Simmonds 2010b; Woods et al. 2013; Woods and Caballero 2016). It has also been shown that the winter sea ice melt has more influence on the sea ice extent in the following summer than the other way around (Lee 2014). In winter, the enhancement of downward infrared radiation (IR) caused by the poleward transport of moist and warm air has been proven to be one of the important drivers for both of the

DOI: 10.1175/JCLI-D-17-0203.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

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wintertime and summertime sea ice declines (Park et al. 2015; Park et al. 2015a,b). Thus, the mechanism of the winter warming is a key to understanding the recent Arctic amplification. The surface energy budget over the Arctic suggests that the wintertime warming of surface air temperature (SAT) is mainly dominated by the downward IR increase rather than the enhancement of turbulent heat flux from the ocean below (Gong et al. 2017) because the surface sensible and latent fluxes are greatly inhibited by the high static stability in winter (Lesins et al. 2012). Although the surface albedo feedback (SAF) was proposed to be the mechanism driving the winter warming through releasing the energy stored in the ocean to surface air because of preseason sea ice melting (Screen and Simmonds 2010a,b; Stroeve et al. 2012), the climate model experiments only support modest Arctic warming by SAF (Alexeev et al. 2005; Winton 2006), whereas the greenhouse effect due to the increase of water vapor and cloud cover explains a considerable part of Arctic amplification (Graversen and Wang 2009). Over past decades, warming and wetting trends have been observed in the Arctic (Wang and Key 2003; Boisvert and Stroeve 2015). Because the downward IR highly correlates to water vapor content in the atmosphere (Francis and Hunter 2007a; Doyle et al. 2011; Ghatak and Miller 2013), the increased poleward moisture transport to the Arctic has been observed to enhance the downward IR and sea ice melt in both the warm season (Persson 2012; Mortin et al. 2016) and winter (Park et al. 2015a; Park et al. 2015). It has been recognized that the atmospheric water vapor content over the Arctic comes mainly from two sources, that is, the local evaporation from the Arctic itself (Screen and Simmonds 2010a,b) and the moisture transport from remote regions (Groves and Francis 2002; Doyle et al. 2011; Yoo et al. 2012a,b; Woods et al. 2013). The change of the former is more strongly driven by local processes such as the positive feedback processes associated with local sea ice melt and sea surface temperature (SST) change (Screen et al. 2012). But for the moisture from remote regions, although it interacts with local feedback processes, the associated poleward moisture transport from lower latitudes is mainly dominated by the mid–high-latitude large-scale circulation (Groves and Francis 2002; Yoo et al. 2012a,b; Woods et al. 2013; Simmonds and Govekar 2014; Park et al. 2015; Park et al. 2015a; Gong and Luo 2017; B. Luo et al. 2017). Thus, to some degree, disentangling the source regions of the local and external moistures of the Arctic water vapor and their relative contributions could provide us a breakthrough point to investigate the relative importance of local feedback processes and large-scale

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circulations. Although the relative importance of the Arctic evaporation and remote moisture transport has been qualitatively or in part quantitatively estimated in previous studies (Woods et al. 2013; Park et al. 2015b; Baggett et al. 2016; Kopec et al. 2016; Woods and Caballero 2016), the remote moisture transport pathways and the proportion between locally and externally sourced moisture are still not comprehensively quantified because of the lack of water vapor conservation constraint in the previous analyses. Therefore, the first objective of the present work is to quantitatively identify the moisture sources and their contributions to the Arctic water vapor from the Lagrangian perspective of the water cycle over the Arctic and based on the moisture budget equation. Furthermore, considering the extreme importance of the poleward moisture transport for the winter Arctic warming, several possible mechanisms have been proposed to establish the connection between the Arctic warming and lower-latitude circulation. A series of works have indicated that the strong moisture intrusion and downward IR enhancement events are preceded several days earlier by the poleward-propagating planetary-scale Rossby waves triggered by tropical convection (Lee et al. 2011; Yoo et al. 2011; Ding et al. 2014; Park et al. 2015; Park et al. 2015a; Yoo et al. 2012a,b). Based on the linkage between localized tropical convective heating and Arctic warming, the tropically excited Arctic warming mechanism (TEAM) was proposed by Lee et al. (2011) and Lee (2012). This theory emphasizes that the winter Arctic warming is caused by the tropically originated wave train, which enhances the poleward moist static energy transport (Lee 2014). On the other hand, Woods et al. (2013) focused on the strong moisture intrusion events and the role of the mid– high-latitude circulation. They noted that in winter, the moisture intrusion events in the Arctic are concentrated in the Atlantic and Pacific sectors and are likely associated with a large-scale blocking pattern to the east of each basin. Luo et al. (2016a,b), Gong and Luo (2017), and B. Luo et al. (2017) further found that the mid–highlatitude circulation systems, that is, the Ural blocking (UB) with the positive NAO (NAO1) acting as a warming amplifier, could induce the strong winter Arctic warming and sea ice decline in the Barents–Kara Seas (BKS) because of the optimal intrusion of warm and moist air to the BKS from the Gulf Stream extension region through the Norwegian Sea by the relay between the UB and NAO1 (B. Luo et al. 2017). The above understandings about the large-scale circulations further motivate us to achieve the second objective of this work. Based on the quantitative estimate of moisture sources for the Arctic region, the additional effort to extract the typical circulation patterns that are

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responsible for different moisture sources, as well as their transport pathways to the Arctic, could thus extend our knowledge about the Arctic amplification from the perspective of atmospheric circulation. With consideration of the above issues, this paper is organized as follows: Section 2 briefly describes the data and hydrological method used in this paper. A dynamical recycling model (DRM) based on a Lagrangian time-backward moisture tracking is introduced to trace the Arctic moisture sources and quantitatively estimate their contributions. Section 3 presents the characteristics of the Arctic and remote moisture and their connections with downward IR and sea ice variation. Some quantitative estimates are also presented in this section. In section 4, the linkage between Arctic moisture sources and large-scale circulation is emphasized. The results are synthesized in section 5.

2. Data and methodology a. Data sources and study region The main datasets used in this work are the gridded data taken from ERA-Interim (hereafter ERAI) and the sea ice concentration (SIC) data from the National Snow and Ice Data Center (NSIDC). The ERAI has been widely used in the studies of Arctic warming (Screen and Simmonds 2010a; Serreze et al. 2012; Simmons and Poli 2015) and hydrologic cycle (Martinez and Dominguez 2014; Dufour et al. 2016). When compared to its predecessor (ERA-40), ERAI has made many improvements, including four-dimensional variational data assimilation with variational data bias correction, higher resolution, improved model physics, and a better hydrologic cycle (Dee and Uppala 2009; Dee et al. 2011; Screen and Simmonds 2011). More realistic representations of radiance and hydrologic processes make ERAI particularly applicable for this study because of the scarcity of direct radiance and evaporation measurements over the Arctic Ocean. In this work, we use the daily mean fields of precipitation, evaporation, precipitable water (PW) defined by vertical integral of water vapor, vertically integrated water vapor flux, downward IR, SAT (defined by temperature at 2 m), and 500-hPa geopotential height. These fields are produced based on the 3-h forecast fields or 6-h analysis fields (Berrisford et al. 2011). All the selected fields are at 18 latitude 3 18 longitude grid ranging from 1979 to 2015, in which only those in early winter (ONDJ) are analyzed, this being the period of low solar radiation but greatest Arctic amplification. The sea ice data used in this work are the NSIDC SIC product generated by using the NASA team algorithm developed by the Oceans

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and Ice Branch, Laboratory for Hydrospheric Processes at NASA Goddard Space Flight Center (GSFC) (Cavalieri et al. 1996), which provides a consistent time series of SIC (the fraction, or percentage, of ocean area covered by sea ice) spanning the coverage of several passive microwave instruments. The daily SIC data temporally cover the time period from 26 October 1978 to 31 December 2015 in the polar stereographic projection at a grid cell size of 25 km 3 25 km (http://nsidc. org/data/NSIDC-0717). Because the original daily SIC is provided every other day before 20 August 1987, a simple linear temporal interpolation is used to fill the missing data. Additionally, the NSIDC data had a dropout for the period from December 1987 to January 1988. According to the approach presented by Simmonds (2015), this monthly data gap is filled by a linear interpolation between the monthly anomalies of November 1987 and February 1988. For convenience, the field of SIC in ONDJ is further spatially interpolated on the regular longitude–latitude grid of ERAI. In the subsequent analysis, the monthly and yearly means of all the atmospheric fields and SIC are computed from daily data except for the dropout months of SIC mentioned above. The monthly anomalous fields are deseasonalized through removing the monthly calendar means. In the Arctic Ocean, the BKS have the strongest warming amplification and sea ice loss (Cohen et al. 2014). The sea ice cover in BKS has been demonstrated to be sensitive to both the local and remote factors, such as the moisture transport due to cyclone activity and large-scale circulation (Fang and Wallace 1994; Groves and Francis 2002; Zhang et al. 2004; Sorteberg and Kvingedal 2006; Francis and Hunter 2007b; Woods et al. 2013; Park et al. 2015; Kopec et al. 2016; Woods and Caballero 2016). Therefore, this work takes the BKS as an example to disentangle the moisture contributions from different origins in boreal winter. As shown by Fig. 1a, the irregular region bounded by the thick black line is the BKS studied here essentially according to the geographical definitions. For the horizontal spatial resolution of 18 3 18, the BKS contain 823 grid cells, whose moisture sources are quantitatively estimated in the following analysis.

b. DRM Aiming at quantitative estimates, a hydrological tool, the DRM (Dominguez et al. 2006), is applied to identifying the moisture sources for the BKS. The so-called recycling is the process of local evaporated water refalling to ground (Zangvil et al. 2004). The ‘‘recycled precipitation’’ thus means the precipitation resulting from local evaporation (Brubaker et al. 1993; Trenberth 1999; Zangvil et al. 2004). The ratio between recycled and total

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FIG. 1. (a) The standard deviation of Arctic SIC in early winter through the months ONDJ in 1979–2015 and the correlations between ONDJ SIC and (b) SAT, (c) PW, and (d) downward IR. The seasonal cycles have been removed from all the time series involved in the correlation analysis. The region bounded by the thick black line is the BKS. The color shaded contours in (b)–(d) display the significant correlations satisfying p , 0.05.

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precipitation, called precipitation recycling ratio [(referred to as recycling ratio (RR)], is a good indicator of the relative importance of the local evaporation. As pointed out by Trenberth et al. (2003) and Zhang et al. (2012), the ratio of recycling precipitation is a useful diagnostic tool to measure interactions between land surface hydrology and regional climate as well as natural and anthropogenic contributions to the regional variations in hydrology. The DRM is constructed to compute RR based on time-backward Lagrangian moisture tracking (Dominguez et al. 2006). Although the RR means to what extent the local evaporation explains regional precipitation, it has also been extended to denote the contribution ratio of any place on the moisture Lagrangian trajectory (Martinez and Dominguez 2014). Unlike the regional DRM (Dominguez et al. 2006) adding a spatial boundary to terminate the Lagrangian tracking, the model used in this work terminates the backward moisture tracking by a time boundary (i.e., using fixed-length moisture trajectories in time). Further, through integrating the atmospheric water balance equation along the backward trajectory [Eqs. (A1)– (A3) in the appendix], we obtain two variables, that is, the trajectory count Ctraj and moisture contribution amount Wm, which describe the distributions of moisture transport pathways and the moisture sources, respectively. The trajectory count Ctraj [Eq. (A7)], or the equivalent of the trajectory density, is calculated through simply summing the trajectory number at each grid cell. So, the high-Ctraj distribution approximately reflects the main moisture transport pathway (Fig. 2d). Similarly, the Wm at a given place is calculated through accumulating the net water vapor gathered from all the trajectories passing that place [Eq. (A9)]. The high-valued areas in the map of Wm thus represent the main moisture sources (Fig. 2c). The detailed formulation of the DRM can be found in the appendix at the end of the paper. Tracing the motions of moisture ‘‘particles’’ in a fixed time length is the first step to carry out the DRM used here. On global average, the time scale of water vapor residing in the atmosphere is about 10 days (Numaguti 1999). But for the Antarctic precipitation, Sodemann and Stohl (2009) recommended to trace water vapor transport for 15–20 days backward in time to identify the moisture sources. They diagnosed the moisture origins for the Antarctic using 5-, 10-, 15-, and 20-day backward trajectories, respectively. It was found that 5-day water vapor tracing leads to significant biased results because only 50% of the total precipitation is attributed to a source region. In contrast, the time scale of 10 days is more acceptable because of ;80% of the attributable moisture is identified by backward trajectories. Whereas, for longer time scales, that is, 15 and 20 days (;90% attributed), the improvement becomes small.

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Therefore, for water vapor in polar regions (e.g., the Antarctic and Arctic), moisture tracing longer than 15 days has been sufficient to reduce the trajectory bias. Considering this, a 15-day backward moisture tracking is implemented in this study. For the BKS (Fig. 1a), most (more than 75%) 15-day moisture trajectories attribute more than 80% of BKS water vapor with a median of 84%, which suggests the reliable representation of the moisture state and variation of the study region. On the other hand, the circulation systems impacting the poleward moisture transport, such as the tropically originated wave train in the North Pacific (Lee 2012) and Ural blocking with NAO1 (Luo et al. 2016a,b; D. Luo et al. 2017), generally have a quasi-biweekly time scale. The 15-day time scale is long enough to resolve the influences on moisture transport because of these systems at the daily scale. For the water vapor in BKS (containing a total of 823 grid cells here), the DRM is carried out to produce 823 backward trajectories of 15-day length per day, thus having a total of more than 3 000 000 (823 grids 3 4459 days) 15-day moisture trajectories for the winters in 1979–2015. Along each trajectory, the spatially unbounded RR [Eq. (A3)], trajectory count Ctraj, and moisture contribution Wm [Eq. (A6)] are computed until reaching the time ‘‘boundary’’ (i.e., the 15th day prior to the given day).

3. Local and external moisture sources of the BKS During the 37 winters (1979–2015) studied here, the largest SIC variation occurs without exception in the marginal ice zone, as shown by Fig. 1a. Among those marginal regions, the BKS, which is bounded by black lines in Fig. 1a, has the largest SIC variation. The maximal SIC variation over the BKS exceeds 30% and the most variable sea ice cover concentrates in the northern and eastern parts, including the Kara Sea and the northern Barents Sea, where the strongest decline trend of sea ice extent is observed. The marginal ice zone is highly sensitive to the oceanic and atmospheric environment because sea ice melt may trigger the positive feedback processes through exposing the water beneath ice cover directly to much colder air above it. Therefore, high SIC variation generally causes strong resonance from other physical fields associated with air–sea interaction. From the correlation maps shown in Figs. 1b–d, the SAT, downward IR, and PW all show congruent variations with SIC, particularly over the northern and eastern BKS. The surface warming and SIC decrease in the BKS tightly link to the enhancement of water vapor (Fig. 1d), which is consistent with previous findings (Doyle et al. 2011; Woods et al. 2013; Park et al. 2015; Park et al. 2015a,b; Gong et al. 2017).

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FIG. 2. The results of time-reverse moisture tracking of water vapor over the BKS, i.e., the region bounded by thick black lines, on 30 Nov 2011: (a) moisture trajectory of the BKS, with color showing r; (b) as in (a), but for the trajectories colored according to Wm (mm day21); (c) the Eulerian-type map of Ctraj, which reflects the major moisture transport pathways; and (d) as in (c), but for Wm, which demonstrates the major moisture-source regions. The region bounded by the thick black line is the BKS.

Figure 2 presents the results of the DRM at a typical early winter day (30 November 2011). In Figs. 2a,b, the colors on each trajectory represent the values of accumulated recycling ratio r and moisture contribution

amount Wm, respectively. As the trajectories show in Fig. 2a, the BKS moisture can be attributed backward to the Mediterranean, North Atlantic, North America, and even east Pacific. The warm-colored/high-r trajectories

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over the Atlantic sector suggest the DRM identifies the most water vapor contribution for the BKS PW until the trajectories arrive in the Norwegian Sea, midlatitude Atlantic, Labrador Sea, and Baffin Bay. In contrast, the drier (cool colored) trajectories are basically found over land, such as northwestern Europe. The counterclockwiserotating trajectories over the North Atlantic suggest cyclonic circulation therein. To the south of this cyclonic circulation, the dense trajectories spanning across the Atlantic represent strong eastward water vapor transport from the Atlantic to Europe. Such a strong moisture transport is related to the cyclone–anticyclone pair over the Canadian Arctic Archipelago–Greenland and its east (Park et al. 2015; Park et al. 2015a; Gong et al. 2017), which is also associated with the circulation pattern combining NAO1 and Ural blocking (Luo et al. 2016a,b; Gong and Luo 2017; B. Luo et al. 2017). Figure 2b more clearly demonstrates the main moisture sources (warm-colored area/high Wm) of the BKS, which include the BKS, the Norwegian and North Seas, and the eastern Atlantic. For convenience, the Lagrangian trajectory together with the moisture contribution along it can be projected to the regular grid cells according to Eqs. (A7) and (A8). Figures 2c and 2d show the trajectory count Ctraj and water vapor contribution Wm over the ERAI grid, respectively. Similar to the Lagrangian-type map (Figs. 2a,b), the Eulerian-type maps also well reflect the main moisture transport pathways (Fig. 2c) and moisture-source distribution (Fig. 2d). Particularly in Fig. 2d, the high-valued region in the east part of the midlatitude North Atlantic represents the most dominant moisture sources at the given day. In the subsequent sections, based on the daily moisture-tracking information, these two kinds of daily Eulerian-type maps (Figs. 2c,d) will be used to produce the monthly hydrologic characteristics for the BKS. Through respectively summing the local (BKS) and external moisture contributions, we can quantitatively estimate the relative importance between local water vapor processes and poleward moisture transport. Figure 3 presents the monthly averaged trajectory count and moisture contribution as well as their linear trends. Because all of the backward trajectories originated from the sink region, it is natural that the BKS and the area near it have the densest trajectories/highest Ctraj, as shown by Fig. 3a. In addition, the climatology of moisture transport displays a comma-shaped distribution (Fig. 3a) concentrating on the pathway originating from the western Atlantic, through the eastern Atlantic and western Europe, and finally to the BKS. This distribution reflects the mean conveyor belt to the BKS. Although the moisture trajectories frequently visit land areas, such as western Europe, as shown by Fig. 3a, the main moisture contributions are all from oceans

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(Fig. 3b), including the BKS; the Norwegian, North, and Baltic Seas; and the east midlatitude Atlantic. One of the biggest moisture sources is the BKS itself, providing 35.4% of BKS water vapor. That is the equivalent of saying that 64.6% of winter PW over the BKS comes from external sources (the regions outside the BKS). This implies that the water vapor supply over the BKS should not be locally self-sustained solely through local processes. As the region partition shown by Fig. 3b, the region of Norwegian–North Seas–Scandinavia–Baltic Sea (NSB) explains 23.3% of BKS water vapor, midlatitude Atlantic (MA) 16.6%, Baffin Bay–Greenland– Iceland (BGI) 11%, and Mediterranean–Black–Caspian Seas (MBC) 6.4%. If we further partition the moisture sources into Arctic and non-Arctic parts by the 708N latitude circle just as Woods et al. (2013), the Arctic sources contribute to 47.3% of BKS PW, and those outside the Arctic region contribute to 52.7%. As mentioned in the introduction, the downward IR in the Arctic is mostly induced by moist air intrusion into the region (Doyle et al. 2011; Woods et al. 2013; Park et al. 2015). But the previous studies are mainly confined in the Arctic area and thus cannot tell us how much the sources outside the Arctic contribute and how the remote-sourced moisture is transported into the Arctic. This is just what the DRM can do. Figures 3c and 3d present the linear trends of the trajectory count and moisture contribution, respectively. For the trend of moisture pathway (Fig. 3c), the most prominent feature is the significant increasing trend over the Atlantic sector and western Europe but decreasing trend over most Arctic regions. The region NSB has the most significant increasing trend, and the MA comes second, followed by the BGI. On the contrary, a decreasing trend is found over most areas in the BKS. That means, in recent decades, the moisture conveyor belt tends to originate from the subtropical Atlantic and intrude on the BKS mainly through the Norwegian Sea. Figure 3d also shows significant increasing trends of moisture contribution from the non-Arctic sources, particularly over the three regions of NSB, MA, and BGI. For the local contribution, a significant trend of Wm is also found in the BKS, where all the parts except for the southwestern BKS show increasing contribution trends. From Fig. 1a, the places having increasing moisture contribution just correspond to those having strong SIC variation. That implies the local evaporation increase might be attributed to the sea ice melt. Figure 4 further demonstrates the spatiotemporal variations of moisture sources on the time–latitude and time–longitude planes through summing the moisture contribution Wm anomalies along meridional and latitude circles, respectively. In Fig. 4, the contributions due to local sources (shaded contours with lines) can also be

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FIG. 3. The (top) climatological means and (bottom) linear trends of (a),(c) Ctraj and (b),(d) Wm in ONDJ during 1979–2015. In (b), the regions bounded by the black-lined areas are the major moisture-source regions for the BKS, among which the NSB, BGI, MA, and MBC are the major external moisture-source regions. The percentage shown in each area in (b) is the regional contribution rate for the BKS water vapor. In (c) and (d), the significant trends (passing the p , 0.05 F test) are marked by black dots. The region bounded by the thick black line is the BKS.

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FIG. 4. Spatiotemporal variation of moisture sources for the BKS: (a) the time–latitude distribution of the moisture contribution Wm anomaly and (b) standard deviation of zonal-mean Wm; (c),(d) as in (a) and (b), but for the time–longitude distribution of Wm. The abscissas in (a) and (c) are time; in (a) and (b) the ordinates are latitude, and in (c) and (d) the ordinates are longitude. For contrast, the shaded contours and contour lines in (a) and (c) represent the moisture contribution due to external sources and the local/BKS sources, respectively. In (b) and (d), the local and external moisture contributions are represented by blue and red lines, respectively. In each plot, the red dashed lines mark the latitudinal [in (a) and (b)] or longitudinal [in (c) and (d)] locations of the main external source regions that have been shown in Fig. 3b. The spatial range of the BKS is also marked by thick blue ticks on the right ordinates of (b) and (d).

distinguished from those due to external sources (shaded contours without lines). From Fig. 4a, the increasing positive-valued areas occur in latitudes lower than 708N after 1999, especially in the period of 2003–12, when the largest sea ice decline has been observed (Fig. 5). It suggests that the non-Arctic sources tend to dominate the BKS water vapor during that period. It is also found that the local moisture contribution of the BKS seems not the change consistently with external moisture sources. The sign of the local moisture contribution anomaly is often

opposite to that of the external one, such as that during 2013/14, when an enhanced positive local contribution but inhibited external contribution are found. This ‘‘opposite sign’’ relation between local and external moisture sources can be found throughout the whole study period. One of the possible explanations for this feature might be that the evaporation from BKS surface (latent heat flux) is proportional to the difference between the surface specific humidity and the atmospheric specific humidity. With the import of midlatitude vapor, the atmospheric

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FIG. 5. The temporal variations of SIC, downward IR, SAT, Wall, WBKS, and WEXT. The series of Wall, WBKS, and WEXT are the regional total quantities for the BKS, and those of SIC, IR, and SAT are normalized spatial means in the BKS. The seasonal cycles have been removed from all the time series. A 7-point smoothing is used to filter the high-frequency variations.

specific humidity will increase, and hence, all other things being equal, this would decrease the surface-toatmosphere difference of specific humidity and thus suppress the evaporation over the BKS. That is, the warm moist air from midlatitudes plays a role as the initial driver in the Arctic sea ice melt and moisture enhancement. On the other hand (as shown by Fig. 8), the moisture exchange between the Arctic and midlatitudes is enhanced when the external moisture sources dominate the moisture supply. While the warm moist air intrudes into the BKS, the local evaporation could also be transported away from the BKS because of the establishment of meridional flows. On the monthly time scale, this dynamical effect will further reduce the local evaporation with the accompanied increase of remote water vapor intrusion that is mainly dominated by quasi-biweekly circulation systems (B. Luo et al. 2017). Another prominent feature of the time variation of external sources is that (Fig. 4a), after about 2003, uniformly positive non-Arctic contribution anomalies more frequently cover the whole midlatitudes between 308 and 708N. That is to say, the external moisture sources of the BKS tend to shift southward during the recent decade. Figure 4b further shows that the variations of local and external sources are comparable and the zonal zone of 508–608N (mainly dominated by the NSB) has the largest moisture contribution. And the moisture variation of MA (Fig. 4b) mainly explains the moisture variation in the lower-latitude band of 308–508N, also particularly in the period of 2003–12.

In the time–longitude plane (Figs. 4c,d), there exists strong increasing moisture contribution from the 708W to 158E sector, which also approximately corresponds to the sources in NSB and MA (Fig. 4c). Therefore, from above spatiotemporal distributions (Figs. 4a,c), it can be simply concluded that the recent-decade BKS moisture enhancement can be attributed to the increasing of nonArctic moisture contribution through the water conveyor belt mainly along the midlatitude Atlantic; the North, Norwegian, and Baltic Seas; and finally to the BKS. To further compare the impacts of local and external moisture sources, Fig. 5 and Table 1 present the relationships between the Arctic warming-related fields, including spatially averaged SIC, SAT, downward IR, total water vapor Wall, local moisture contribution WBKS, and external moisture contribution WEXT. Here, the total water vapor over the BKS Wall is the sum of WBKS and WEXT (i.e., Wall 5 WBKS 1 WEXT). From Fig. 5, the monthly series of downward IR, SAT, and Wall all show highly consistent variations with WEXT but much less relevance to WBKS. So the variation of Wall is basically dominated by its externally sourced part (WEXT). Just as that shown in Table 1, the series Wall and WEXT have the extremely high linear correlation of 0.96 ( p , 0.01), but the local moisture contribution (WBKS) has much weaker correlation to Wall with r 5 20.27 ( p , 0.01). As the discussion of Fig. 4, significant negative correlation between WBKS and WEXT (r 5 20.49 with p , 0.01) suggests that external moisture intrusion

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TABLE 1. The cross correlations r between Wall, WBKS, WEXT, SIC, downward IR, and SAT. The correlations with one (two) asterisk(s) [i.e., r* (r**)] are significant, passing the p , 0.05 ( p , 0.01) test. The correlations without an asterisk are not statistically significant. The numbers in bold are relatively weak correlations.

Wall WBKS WEXT IR SIC

Wall

WBKS

WEXT

IR

SIC

SAT

— — — — —

20.27** — — — —

0.96** 20.49** — — —

0.91** 0.01 0.83** — —

20.57** 20.45** 20.40** 20.71** —

0.82** 0.20* 0.70** 0.96** 20.83**

seems not to trigger the positive feedback of the local moisture processes but rather inhibits the local evaporation. In the way of Arctic warming, the monthly series of downward IR, SAT, SIC, and Wall significantly correlate to each other (Table 1). Similar correlative relationships are also found for the external moisture contribution WEXT. However, the local moisture contribution WBKS only significantly correlates to SIC (r 5 20.45) but with statistically insignificant correlation with downward IR (r 5 0.01) and weak correlation with SAT (r 5 0.2 for p , 0.05). The above cross correlations suggest that the external moisture intrusion mainly explains the IR and SAT increase, as well as the sea ice loss. In contrast, relatively, a small part of surface warming and IR increase can be attributed to the local evaporation over the BKS. The high negative WBKS–SIC correlation (r 5 20.45) and WBKS–Wall correlation (r 5 20.27) further suggest that the local evaporation increase is associated with sea ice melt more frequently in low-Wall–dry and weak-IR–weak-warming status. The above analysis provides further quantitative proof for the major role of the water vapor intrusion in winter BKS warming and its inhibition effect on local evaporation (Park et al. 2015). The detailed connections between BKS warming and distributions of moisture passage and sources can be demonstrated by the correlative maps associated with trajectory count Ctraj and moisture contribution Wm, as shown by Fig. 6. From the Ctraj–SICBKS correlation map (Fig. 6a), the significant negative correlations are found mostly over the regions south of 708N, in particular, over MA and NSB. Thus, the sea ice loss over the BKS is primarily sensitive to the increase of moisture transport from these two nonArctic regions. On the contrary, the increase of moisture trajectories inside the Arctic area corresponds to the increase of the BKS sea ice cover, as shown by the positive Ctraj–SICBKS correlations in Arctic regions in Fig. 6a. These features also stand out in the Ctraj–IRBKS

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correlation map shown by Fig. 6c. Basically, a distinctive dipole correlation pattern in Fig. 6c emphasizes the positive effect from non-Arctic moisture transport on the downward IR increase over the BKS but negative effect from Arctic moisture transport. Accordingly, in Figs. 6b,d, the moisture contributions from the external sources over the North Atlantic and northwestern Europe highly correlate to the SIC decline and downward IR increase. On the other hand, the enhancement of local water vapor also shows high correlation to the sea ice loss but only weak correlation to IR increase mainly over the northeastern BKS, where the largest SIC variation is found (Fig. 1a). But in the southwestern part of the BKS, where there is low sea ice cover or even open water climatologically, the local evaporation only has weak negative correlations to SIC and the downward IR, which emphasizes the important role of sea ice change in the local processes associated with IR and water vapor.

4. Circulations associated with different moisture sources of the BKS Before we expand further discussion about the atmospheric circulations associated with the major moisture sources, the results, shown in Fig. 7, present the normalized series of moisture contributions Wm due to the five major source regions that have been defined in Fig. 3b. From Fig. 7e, it is found that positive-anomaly events are more frequently observed in the recent decade for all the five main source regions. For the local/ BKS sources (Fig. 7a), the most persistent positive moisture contribution occurs during 2012–15, when the sea ice cover tended to recover from its record low at 2012 (Fig. 5). However, the spatially averaged PW, IR, and SAT over the BKS, showing declines in the same period (Fig. 5), are not in phase of WBKS. All of these characteristics suggest that the increase of local moisture contribution after 2012 is a result of the sea ice melt but not the cause of it. The four external sources, shown in Figs. 7b–e, all show temporal variations well consistent with IR, SIC, and SAT. Among these external sources, the NSB and MA regions show better correlations with BKS warming than the other two regions, which can also be observed in the Wm–SICBKS correlation map in Fig. 6b. Considering the mean contribution distribution (Fig. 3b) and the significant increasing trends in these two regions (Fig. 3d), we can conclude that the NSB and MA are the most important external moisture-source regions for BKS water vapor supply. As a relatively minor external source, the water sourced from MBC (Fig. 7e) also shows significant increase (above one standard deviation) after about 1999. But before that

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FIG. 6. Correlation maps between moisture trajectory count Ctraj/moisture contribution Wm and SIC (SICBKS) and downward IR (IRBKS) over the BKS: correlation between (a) Ctraj and SICBKS, (b) Wm and SICBKS, (c) Ctraj and IRBKS, and (d) Wm and IRBKS. Only the correlations passing p , 0.05 significance test are shown in each plot.

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FIG. 7. Normalized time series of moisture contributions for BKS water vapor from different source regions: (a) BKS, (b) BGI, (c) NSB, (d) MA, and (e) MBC. The spatial ranges of the source regions have the same definitions as Fig. 3b. Their correlations r with spatially averaged downward IR, SIC, and SAT over the BKS are also shown in each plot. The superscript of the correlation coefficients represents the statistical significance level: two asterisks for p , 0.01, one asterisk for p , 0.05, and no asterisk for p $ 0.05 (nonsignificant). The level of one positive/negative standard deviation is represented by the dashed line in each plot.

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year, MBC contributed much less than the other three external sources (Figs. 7b–d). Considering the mean moisture transport pathway of the BKS (Fig. 3a), we speculate that MBC might be a key region to connect the moisture sources in MA and NSB during recent enhancement of poleward moisture transport to the BKS. To further extract the characteristics of the largescale atmospheric circulation, Fig. 8 composites the associated physical fields with respect to the contribution variation of each source region illustrated in Fig. 7. To highlight the features due to each source, the months with anomalies above one standard deviation are selected for the composite mean. A p , 0.05 t test is used to evaluate the significance of each field of the composite mean. Each row of Fig. 8 shows the composite means for one of the five main moisture-source regions. For the event with high local (BKS) moisture contribution (Figs. 8a–e), it is consistent with the correlative analysis presented above that a high BKS contribution corresponds to a low external contribution, which shows negative anomalies in the non-Arctic area in Figs. 8a and 8b. When compared with SIC anomalies during different events (Figs. 8c,h,m,r,w), the high-BKS-contribution event, on average, shows the strongest sea ice decline in the BKS (27.39%) (Fig. 8c). But this does not mean that the local evaporation contributes the most significantly to the BKS sea ice melting and warming because there is almost no concurrent downward IR increase found (Fig. 8c), which again suggests that the high local moisture contribution is only a manifestation of the sea ice melting. Corresponding to high local moisture contribution, the circulation (Fig. 8d) has a negative-phase Arctic Oscillation (AO2)-like pattern with an eastward-displaced positive anomaly that partly covers the BKS and with two negative anomalies located in the North Atlantic and East Asia. Under this kind of circulation pattern, less moisture transport from midlatitudes to the BKS is seen. The resulting warming is relatively weaker and only occurs over the northern BKS (Fig. 8e). For the high-contribution events due to the four external sources (i.e., BGI, NSB, MA, and MBC), one of the common features is the reverse-sign anomalies between the Arctic region and midlatitudes in trajectory count Ctraj (Figs. 8f,k,p,u) and moisture contribution Wm (Figs. 8g,l,q,v). It is distinguished from the high-BKScontribution event (Figs. 8a–e) by all the four external sources inducing significant sea ice loss, downward IR increase, and strong warming over the BKS. The common feature of these circulation patterns is that all have a wave train–like structure spanning the Atlantic

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and Eurasia from midlatitudes to high latitudes seemingly induced by the anomalous SST in the midlatitude Atlantic near the Gulf Stream Extension (Luo et al. 2016b). The mid–high-latitude components of this wave train pattern seem to be composed of NAO1 over the North Atlantic and a Ural blocking over the BKS–Ural Mountains region (Luo et al. 2016a,b; B. Luo et al. 2017; D. Luo et al. 2017; Gong and Luo 2017; Yao et al. 2017). As a physical explanation presented by B. Luo et al. (2017), the Ural blocking with an NAO1 is shown to be an optimal circulation pattern that promotes the moisture transport from North Atlantic midlatitudes near the Gulf Stream Extension to the BKS. In the Pacific sector, some previous findings (Lee et al. 2011; Yoo et al. 2011, 2012a,b; Lee 2012; Ding et al. 2014; Park et al. 2015a) have also shown that the Rossby wave train triggered by the enhanced convection in the warm pool (i.e., tropical Indian and western Pacific Oceans) or the tropical eastern Pacific Ocean can propagate through the North Pacific and northeastern Canada to the Arctic. This tropically originating wave train mainly contributes to the surface warming in Greenland; the Canadian Arctic Archipelago; the Chukchi and East Siberian Seas (Ding et al. 2014; Yoo et al. 2011); and also to the BKS (Park et al. 2015a). However, below, we will further see that the direction and strength of the wave train from the North Atlantic to Eurasia can steer the pathway of moisture in the North Atlantic and its adjacent region into the BKS and enhance the BKS warming. In fact, the four external sources can be further combined into two groups, here named the west type, including BGI and MA, and the east type, including NSB and MBC. As shown by plots in the fourth column, the circulation pattern is dominated by a wave train structure that is composed of the NAO1 and Ural blocking (Luo et al. 2016a,b) from midlatitude North Atlantic to the BKS and East Asia through Greenland in a highlatitude pathway (Figs. 8i,s) or Europe in a midlatitude pathway (Figs. 8n,x). Below, we present a new finding that the propagation direction of the wave train can also affect the pathway and strength of moisture transport to the BKS. This result is different from the finding of Gong and Luo (2017). Inside the two west-type moisture sources, that is, BGI (Fig. 8i) and MA (Fig. 8s), there only exists a nuance in the meridional scale of the circulation anomaly over the Atlantic and Europe. A relatively larger meridional scale for MA events (Fig. 8s) corresponds to the more southward-extended Iceland low and blocking over Europe and, thus, a more southward water moisture source. But for the east-type moisture sources, that is, NSB (Fig. 8n) and MBC (Fig. 8x), the wave train structure has a midlatitude pathway through Europe rather than the high-latitude

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FIG. 8. Composite fields according to different moisture sources for BKS water vapor. The rows of the plots are arranged by moisturesource regions, i.e., corresponding to composites in terms of the moisture contribution dominated by (a)–(e) BKS, (f)–(j) BGI, (k)–(o) NSB, (p)–(t) MA, and (u)–(y) MBC. These five source regions have the same definitions as those in Fig. 3b. The composites are obtained through averaging the monthly deseasonalized fields over the high-contribution months, when a certain source region has moisture contribution above one standard deviation, which is shown in Fig. 7. The first to fifth columns correspond to the composite means of Ctraj, Wm (mm day21), SIC (color shaded contours) and downward IR (green and red contours), geopotential height at 500 hPa (m), and SAT (K). The shaded/line areas in the first three columns and the dotted areas in the last two columns pass the p , 0.05 t test. The dashed green lines in the plots of the fourth column approximately represent the propagation pathways of the wave train–like patterns.

pathway for the west-type sources (Figs. 8i,s). And the east-type event has a more eastward-shifting blockinglike anomaly over Eurasia, in contrast with the west type. In short, the wave train propagating along the

high-latitude pathway tends to strengthen the moisture contribution from the west source regions, but that with the midlatitude pathway favors the east source regions. The transition between the above two types of

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circulation patterns thus can determine the main external moisture sources for the BKS.

5. Conclusions and discussion The Arctic water vapor is a key factor in the downward infrared radiation (IR) processes that are associated with the sea ice loss in winter. To evaluate the relative importance of local processes and poleward moisture transport in the Arctic warming, a hydrological tool, the dynamical recycling model (DRM), is used to quantitatively estimate the local and external moisture contributions to the water vapor over the Barents–Kara Seas (BKS) in the early winter [October to January (ONDJ)] during 1979–2015 based on the ERA-Interim. The DRM is constructed based upon the time-reverse Lagrangian moisture-tracking method. Therefore, it can provide a useful tool for tracking the moisture trajectories and identifying the moisture contribution from different moisture-source regions. In the meaning of the climatological mean, the results of DRM demonstrate that the local evaporation explains 35.4% of BKS water vapor, and the external moisture contribution from the North Atlantic and Europe sectors explains about 57.3%. Therefore, the ONDJ-mean water vapor over the BKS is mainly dominated by the external water vapor transport. On average, the Arctic and nonArctic moisture sources contribute to 47.3% and 52.7% of BKS water vapor, respectively. The major Arctic sources are in the BKS and Norwegian Sea, whereas the non-Arctic moisture contribution is dominated by the sources in the midlatitude North Atlantic and North and Baltic Seas. Thus, it is concluded from the perspective of water vapor sources that local/Arctic and external/nonArctic moisture contributions are both important for the water vapor supply over the BKS in the early winter. For the time variations during the period 1979–2015, the main external moisture sources for the BKS tend to shift westward and southward, which is followed by the enhancement of local moisture contribution, particularly after 2003. The BKS water vapor, downward IR, and SAT (SIC) are found to exhibit significant positive (negative) correlation with the external moisture. However, the local moisture contribution shows weak correlations with downward IR and SAT but significant negative correlations with the BKS water vapor, external moisture contribution, and SIC. That is to say, the increase of remote moisture transport tends to weaken the local moisture contribution. These results suggest that the external moisture transport should be responsible for the enhanced downward IR and sea ice decline over the BKS. But the increase of the local moisture contribution is more likely a result of the local sea ice melting.

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Because of the dominant role of external moisture transport in the variation of BKS water vapor, the winter warming over the BKS can be mainly attributed to the variation of the large-scale atmospheric circulation. Through compositing the circulations according to different moisture sources, it is found that a negative-phase AO (AO2)-like pattern tends to strengthen local moisture contribution through inhibiting the meridional moisture transport from lower latitudes. But in the case of dominant external moisture sources, the mid–high-latitude circulation pattern behaving as a wave train seems to partly consist of the NAO1 and downstream Ural blocking, which tends to enhance the water vapor transport from the midlatitude North Atlantic to Europe and then steer moisture passage northward into the BKS (Gong and Luo 2017; B. Luo et al. 2017). However, the propagation direction of the wave train affects the pathway and strength of the remote moisture transport. When the wave train propagates in a high-latitude pathway from North Atlantic midlatitudes to the BKS–East Asia along Greenland, the external moisture contribution mainly comes from west sources in the mid–high-latitude North Atlantic. But when the wave train propagates in a midlatitude pathway from the midlatitude North Atlantic to Europe and then to the BKS–East Asia, the moisture transport comes mainly from east sources including the Norwegian, North, Baltic, and Mediterranean Seas. These results are partly different from the previous findings (Gong and Luo 2017; B. Luo et al. 2017). The present work focuses on the monthly hydrological features over the Arctic in order to disentangle the roles of the local processes and the meridional exchange from the perspective of the water cycle. However, at shorter time scales (e.g., daily), the relationship between local and external moisture contributions and the associated circulation characteristics is not examined in this paper, although it is important for our understanding of the physical cause of the BKS warming and associated sea ice decline. In the future work, we will focus on examining the relationship between the atmospheric transient circulation and local and external moisture contributions from a daily perspective. Acknowledgments. This work was jointly supported by National Key Research and Development Program (2016YFA0600403) and the National Natural Science Foundation of China (Grants 41790473, 41430533 and 41475072). The authors thank Professor Sukyoung Lee for providing constructive comments and suggestions. Two anonymous reviewers contributed to improve this paper.

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APPENDIX

K

rr 5 Wm /W 5

å ri wi DAi

i51

= å w DA , K

i51

i

i

(A4)

DRM and Moisture-Source Identification The starting point of DRM is the atmospheric water balance equation (Schmitz and Mullen 1996). For grid cell i (i 5 1, 2, . . . , K) within a study region V, the moisture budget in this grid is governed by the equation ›wi 1 Vi  =wi 5 Ei 2 Pi , ›t

(A1)

dri E(1 2 ri ) . 52 w dt

(A2)

Ðp where w 5 0 0ðq/g) dp is the PW obtained from vertically integrating specific humidity q from the surface p0 to the model top (Dominguez etÐ al. 2006; Berrisford et al. p 2011) and V 5 (u, y) 5 0 0v(p)q/g dp is humidityweighted wind velocity of the whole air column, where v(p) is the wind velocity at pressure level p (Dominguez et al. 2006; Berrisford et al. 2011). On the right-hand side of Eq. (A1), E and P are evaporation and precipitation, respectively. Here, to distinguish from the recycling ratio (RR) for the whole region V, the RR at a specific grid cell i is referred to as local RR or ri. When the precipitation is partitioned into the part due to local evaporation Pi,m and that due to moisture advection Pi,a, that is, Pi 5 Pi,m,, ri can be expressed as ri 5 Pi,m/Pi. The DRM assumes that the moistures from different sources are well mixed, that is, wi,m/wi 5 Pi,m/Pi, where wi,m is the PW from local evaporation in grid cell i. Therefore, the RR indirectly reflects the ratio of PWs because of local evaporation and external moisture transport. Under the well-mixed assumption, Eq. (A1) can be written as an equation of ri (Dominguez et al. 2006). Through further transforming the local recycling ratio equation into the Lagrangian coordinate, that is, s 5 (x 2 ut, y 2 yt, t) we obtain

Now, the variables E and w in Eq. (A2) are, respectively, the evaporation and PW at any location on the timebackward Lagrangian moisture trajectory s originating from grid cell i. Through integrating Eq. (A2) along the trajectory si(t), the expression of ri at time t is obtained as (Dominguez et al. 2006) " ð # s i (t ) ri (t) 5 1 2 exp 2 E/w ds .

(A3)

s i (0 )

Based on Eq. (A3), it is easy to obtain the regional recycling ratio rr of the study region V (Eltahir and Bras 1994) through

where DAi is area of grid cell i in region V, Wm is the PW K due to the local evaporation over V, and W 5 åi51 wi is the total PW in V. The estimation of rr can thus tell us to what extent the regional PW or precipitation depends on the moisture supply from the evaporation of the study region itself. From the above description about DRM, one of the key points is the generation of the backward moisture trajectory. In this work, the moisture trajectory s is produced by a Lagrangian trajectory tracking method presented by Blanke and Raynaud (1997) and then developed by de Vries and Döös (2001). This method diagnoses the motion trajectory of a fluid particle through directly solving the finite-difference equation of fluid particle velocity by analytical or semi-analytical methods. Because of the pure physical basis of fluid motion, this tracking method has been widely applied to oceanic and atmospheric trajectory tracking (Döös and Engqvist 2007; Kjellsson and Döös 2012; Nilsson et al. 2013). With the consideration of computational efficiency, the daily averaged moisture-weighted velocity is used for trajectory generation in this work, and the analytical method is used. At any time, the independent scheme (de Vries and Döös 2001) is used to find the trajectory solution, which means the location of a water vapor ‘‘particle’’ at a given time is solved by using the velocity information at that time but not considering a solution change due to velocity change before or after the given time. This scheme provides strong solvability for the trajectory solution finding. More detailed descriptions of the trajectory-tracing scheme can refer to the work of Blanke and Raynaud (1997) and de Vries and Döös (2001), and references therein. For the regional DRM (Dominguez et al. 2006), the backward moisture tracking terminates until the trajectory reaches the boundary of the study region. As a result, the detected moisture contributions for the study region are all from the sources within the same region. Martinez and Dominguez (2014) extended the DRM to quantify the relative contributions from different sources free of the spatial restriction. For our present work here, we use the temporal boundary to replace the spatial boundary when carrying out the backward moisture tracking. Therefore, we can terminate the Lagrangian moisture tracking through setting a fixed termination time that is long enough to resolve most moisture contributions. Here, as mentioned in section 2, a 15-day backward moisture tracking is used to identify the moisture sources of the BKS.

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Returning to the study region V containing K grid cells, the backward moisture-tracking procedure will produce a K-member family of moisture trajectories for a given time t, which can be written as s(t) 5 [s1(t), s2(t), . . . , sK(t)]. At any discrete time level t 5 tn (n 5 0, 1, . . . , N) (N 5 15 days for this study), the accumulated moisture contribution rate rn 5 r(t n ) is computed through K

rn 5 Wm (tn )/W 5

å ri,n wi Ai

i51

= å w DA , K

i51

i

i

(A5)

where ri,n 5 r[si(tn)] is the local RR [Eq. (A3)] at trajectory location si(tn). On the right-hand side of Eq. (A5), the denominator represents the area-weighted regional PW of region V, which equals the denominator of the regional RR shown in Eq. (A4). But the numerator of Eq. (A5) represents the water vapor contribution along moisture transport pathway to anywhere the backward trajectory arrives. Therefore, for a given sink region, Eq. (A5) can quantitatively illustrate where the moisture comes from and how much water vapor the source contributes. On the other hand, if one assumes that the trajectory family s(t) arrives at a spatial location g(t) 5 [g 1 (t), g 2 (t), . . . , gK(t)] at time t, the local moisture contribution between the g(tn) and g(tn21) can be simply represented by the contribution difference between time tn and tn21, that is, Wm [g(tn )] 5 (rn 2 rn21 ) 3 W ,

(A6)

with Wm [g(tn)](n 5 0, 1, . . . , N) being the local moisture contribution over location g(tn). Based on the trajectory location information g(tn) and local moisture contribution Wm [g(tn)], we can obtain the moisture contribution and trajectory count over a given spatial location gc through simply summing trajectory counts and local moisture contribution over gc, that is, N

å dg(t ),g ,

(A7)

å dg(t ),g Wm [g(tn )] ,

(A8)

Ctraj (gc ) 5

n

n51

c

and N

Wm (gc ) 5

n51

n

c

where d is the Kronecker delta with dg(tn),gc 5 1 for g(tn) 5 gc and dg(tn),gc 5 0 for g(tn) 6¼ gc, and Ctraj(gc) and Wm(gc) are trajectory count and moisture contribution at the location gc, respectively. In practice, the same trajectory may visit the same place more than once

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throughout the whole N time levels. On the other hand, different trajectories may also visit the same place simultaneously. The Kronecker delta in Eqs. (A7) and (A8) means that the summation operation is executed for all these possibilities. In fact, the Eulerian-type distributions of Ctraj and Wm can be projected by Eqs. (A7) and (A8). For the study region V at a given time, the characteristics of the moisture transport pathways can be observed from the distribution of Ctraj, and the distribution of moisture sources as well as their quantitative contributions can be demonstrated by the map of Wm. Furthermore, the moisture contribution rate at any spatial location [r(gc)] can be simply computed by r(gc ) 5

Wm (gc ) . W

(A9)

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