General concept and used datasets

The general idea of this investigation is to measure the composition of air parcels at different altitudes above the ABL in a Lagrangian concept before and after crossing the Alps. The windward sample A is considered as a background sample, showing smaller humidity and air pollutant concentrations than the ABL. Changes in the leeside sample B are then attributed to vertical lifting that transports pollutants and humidity upward over the mountainous terrain.

Water vapor is the only atmospheric constituent that originates from the earth’s surface and is measured on climatological time scales throughout the whole troposphere. Therefore, observed changes in the vertical profiles of specific humidity in the windward and the leeward side of a mountainous region are the only adequate means to climatologically describe the lifting effect caused by thermally driven flow.

Two datasets were used in this study. Surface measurements of wind speed and direction, temperature, humidity, sunshine duration, global radiation, and lightning activity were taken from the automated MeteoSwiss (Swiss national weather service) surface station network (ANETZ). Measurements were used with a temporal resolution of 1 h for the period from January 1991 to December 2002. A total of 72 surface stations were available within this dataset with an altitude range from 197 to 3580 m MSL. The second dataset of upper-air measurements of wind speed and direction, temperature, pressure and humidity included two sounding sites, Payerne, Switzerland (46.82°N, 6.95°E; 491 m MSL), situated on the Swiss plateau north of the Alps, and Milan, Italy, within the Po basin (45.43°N, 9.28°E; 102 m MSL) south of the Alps (Fig. 2). The data were taken from the quality-checked Comprehensive Alpine Radiosonde Data Set (CALRAS) (Haberli 2002) database. At Payerne two radio soundings per day [0000 and 1200 UTC (LT = UTC + 1)] for temperature, pressure, and humidity, and four soundings per day (0000, 0600, 1200, and 1800 UTC) for wind speed and direction, were available for the period from January 1991 to December 2002. At Milan four radio soundings per day (0000, 0600, 1200, and 1800 UTC) for temperature, pressure, humidity, and wind speed and direction were available for the same period.

The analysis was done for fair-weather days within a 12-yr period to derive a climatological estimation of mountain venting over the Alps. Different criteria to select fair-weather days are described in section 2f.

The vector-averaged wind speed ff and direction dd for a 12-h period were calculated at every altitude from all of the available soundings during this period and from both sounding stations. This usually resulted in six considered soundings.

Cross-Alpine flow on fair-weather days

On fair-weather days an air parcel that travels from point A to B across the mountains with the synoptically driven wind is influenced by vertical transport in the form of thermal injections over the mountains (Fig. 1). When the air parcel arrives at point B in the lee of the mountains its composition (e.g., specific humidity) might be modified (vertical profile on right side, windward profile indicated by a solid line, modified profile indicated by a dotted line). Fair-weather days are usually connected with subsiding air within high pressure systems. Over mountainous terrain this subsidence is counteracted by upward motion within the mountain heat low. Therefore, the altitude of a certain air parcel advected across the mountain is not expected to be altered considerably from the windward to the lee side (see section 3c for further discussion).

In our case points A and B are represented by Payerne and Milan, respectively. The distance between both stations is 237 km. An air parcel would need to travel with an average speed of 5.5 m s⁻¹ to start from one station and arrive at the other within 12 h. If we consider an individual sounding being representative for ±50 km along the wind direction, average traveling speeds between 4.4 and 6.6 m s⁻¹ would be adequate to fit into the Lagrangian concept.

Figure 3 shows the median terrain height in a 50-km strip connecting Payerne and Milan. The median terrain height is about 2500 m MSL in the central Alpine region, with up to 25% of the surface being higher than 3000 m MSL. The upper x axis provides the time for an air parcel that travels with 5.5 m s⁻¹ arriving in Milan at 0000 UTC. Because thermally driven flow lasts at least until 1700 UTC and all terrain above 1500 m MSL might contribute to the lifting processes, the air parcel might receive injections of ABL air between 1330 and 1700 UTC. For altitudes lower than 2500 m MSL the results should not be interpreted in a Lagrangian perspective, because direct flow could be blocked by the mountain barrier.

Excluded situations

To ensure that vertical transport is not dominated by processes other than thermally driven flow systems, different criteria were used to exclude these situations to the greatest possible extent.

Large wind speeds, in combination with a stably stratified atmosphere, are able to force gravity waves (mountain waves), followed by possible wave breaking and, hence, vertical mixing (Durran 1990). Therefore, cases with ff larger than 10 m s⁻¹ at any investigated altitude were excluded from the study.

Vertical exchange processes previous to the “background” sounding A might result in elevated moisture layers at A. These layers might mask the process of further vertical exchange when upper-air concentrations were already as large as in the ABL. Soundings that showed a secondary maximum in specific humidity in the “background” sounding at an altitude higher than 2000 MSL with a thickness of at least 500 m were excluded from the analysis.

Investigated days were divided into days with and without deep moist convection by using close-range (distance <5 km)-recorded lightning activity from the Swiss ANETZ surface station network. Days that showed lightning activity during the investigated transalpine transport at any ANETZ station between Payerne and Milan (circles in Fig. 2) were summarized as “lightning” cases, and days without lightning were “no lightning” cases.

Days with more than 1-mm precipitation during the investigated transalpine transport at any of the same stations were excluded from the no-lightning cases. If precipitation occurred in combination with lightning the case was still investigated in the lightning category.

The exclusion criteria are summarized in Table 1.

Evapotranspiration

An additional source of humidity in the leeside soundings at B might result from surface evapotranspiration from elevated terrain during the transalpine transport. Evapotranspiration ET (mm h⁻¹) for an air parcel crossing the Alps was estimated by applying an empirical formula that needs solar radiation R_s, temperature T, and relative humidity RH as input parameters, and was actually developed for adequately watered crop fields (Alexandris and Kerkides 2003):

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For every investigated category (see section 2f) these input parameters were calculated on an hourly basis for every investigated altitude. Incoming solar radiation was assumed to be rather constant with height and was taken from ANETZ stations between Payerne and Milan (circles in Fig. 2). Initial vertical profiles of temperature and relative humidity were taken from the average windward radio soundings. Evapotranspiration derived by (1) was assumed to be dispersed homogeneously within a vertical layer Δz = 100 m. The hourly (Δt = 1 h) increase of specific humidity Δq (g kg⁻¹) was derived by

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where f_a is the surface fraction at every investigated altitude, ρ_H2O is the density of liquid water, and ρ is the air density at every investigated altitude. Surface fractions were calculated using a 250 m × 250 m digitized topography model. This calculation also accounted for nonhorizontal surfaces, so that the sum of all surface fractions was larger than 1. Evapotranspiration was iteratively calculated for 12 h. Because the mountainous terrain above 2000 m is covered to a large percentage by rocks, we assume that the calculated evapotranspiration is an overestimation of the real value.

Averaging method

Two different approaches were designed to investigate the average differences between the windward and leeside soundings; the first took separate layers into account (layer method hereinafter), and the second used the entire vertical profiles (profile method). For both methods the sampled profiles were divided into equidistant layers with a vertical extension of 100 m. The layer method analyzed the vector mean wind direction dd (see section 2a) at every individual altitude. If dd was within ±35° from the connecting line between stations A and B, the case was added to the averaging process. This was done for all selected days. The catchment sectors for Milan and Payerne can be seen in Fig. 2. The selected wind range implies that the windward sounding is representative for ±160 km on a circular arc through the windward station, which is reasonable for advection from Payerne to Milan because of the terrain-height homogeneity in this direction.

In contrast to the layer method, the profile method used the whole profile of an individual day. If the vector mean of dd within the layer between 2000 and 5000 m MSL matched the connection line between stations A and B by ±35°, the whole profile was added to the average profile.

Categories to select fair-weather days

To investigate the effect of thermally driven flow systems on the leeside profiles of specific humidity, five different selection criteria for fair-weather days were used.

The first two criteria used data that were taken from the surface station network. Stations on both sides of the Alps—representative for the northern (10 stations) and southern (4 stations) Alpine forelands (diamonds in Fig. 2)—were selected. These stations covered the whole Swiss plateau in the west–east direction and the Ticino area south of the Alps. On fair-weather days it is very likely that cumulus clouds develop in the Alps. These might very locally change the amount of incoming solar radiation at the surface. Therefore, only stations outside of the Alps were selected. To avoid local influence, radiation data were used from more than one individual station.

If the total sunshine duration per day ΣS was larger than 9 h for at least 50% of the stations in the north and 50% of the stations in the south, a day was categorized as being a “sun day” (SND). A similar criterion is used to investigate thermally driven flow in the Bavarian forelands in southern Germany (Lugauer and Winkler 2005).

If the total amount of incoming solar radiation per day to the earth’s surface ΣR_s was larger than 19 MJ m⁻² at more than 50% of the stations in the north and south, a day was categorized as being a “radiation day” (RAD).

The other three categories used parameter 33 of the Alpine Weather Statistics (AWS) (Schuepp 1979; Wanner et al. 1998). The so-called Schüepp classification system contains 40 weather situations for the western Alpine region. For our analysis we selected days within the main category (“convective”) that compromises days with weak horizontal wind speeds at 500 hPa. The convective category is further divided into the following categories: “anticyclonic” (ANT), “indifferent” (IND), and “cyclonic” (CYC). To focus on days with a large potential for thermally driven flow, the selection was further confined to the months of March–September.

Figure 4 shows the average number of selected days per month for the 12-yr period. In addition, the number of selected days and the average values for ΣR_s, ΣS are summarized in Table 2. For the SND and RAD categories the selected days were mostly limited to the months from March to September, with a maximum in July and August. About 60% of all summer days fulfilled the RAD criterion. The number of days within the IND category was larger within the summer months, whereas the categories ANT and CYC showed no general dependence on the season. The average ΣR_s was largest for the days selected by the SND and RAD criteria, and was slightly lower for the ANT and IND categories, while it was much lower for the CYC category. Sunshine duration ΣS was largest for the days chosen by the SND criterion, followed by the ANT, RAD, and IND categories. Here, ΣS was much shorter for the CYC category.

In addition to these categories based on the current weather situation, days were categorized by season (SEA). Table 2 shows that ΣR_s and ΣS for the summer months [June–July–August (JJA)] compare to the IND category.

Further on, the categories were subdivided into a no-lightning and lightning category (see section 2c), indicated with the subscripts “nl” and “l,” respectively, as follows.

Relative increase and ABL export rate

For pollutant budget calculations it is important to quantify the export of ABL air to the FT. By knowing the specific humidity at the windward side of the mountains q_a, in the lee of the mountains q_b, and within the mountainous ABL q_abl, it is possible to calculate the relative increase (ri) (Prevot et al. 2000) in specific humidity at a certain altitude z above the ABL:

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Here, q_abl was taken as the average specific humidity during the thermally driven flow (0900–1700 UTC) at the surface stations (indicated with deltas in Fig. 2). These stations are all situated within the Alps at different altitudes between 580 and 1350 m MSL. The station-to-station variability was lowest for this selection. Including the stations at higher altitudes (<2000 m MSL) strongly increased the variability; ri varied about ±8% when including different numbers of ABL stations. Therefore, we think our selection is representative of the Alpine ABL. The calculation of ri, which gives the percentage of ABL air that was transported to a certain altitude, was done for every individual day.

Further, it was possible to estimate the fraction of air that leaves the ABL per hour. For this purpose the residence time t_r of an air parcel over mountainous terrain during active thermally driven flow was calculated for individual days. Thermally driven flow was assumed to persist from 0900 to 1700 UTC. Average wind speed and direction ff and dd (see section 2a) were used to calculate the residence period over mountainous terrain (a median altitude larger than 1500 m MSL) of an air parcel arriving at B for every investigated altitude. The intersection of both periods resulted in t_r.

We considered an air parcel with constant volume that receives injections of ABL air at a constant mass flux density μ with the concentration q_abl (Fig. 1). These injections can be regarded as thermal plumes that start within the ABL and reach certain altitudes; further vertical exchange between different elevated altitudes is not considered in this simplified model. At the same time because of continuity the same flux leaves the air parcel horizontally with the concentration q(t). The change of q with time is then given by

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The concentration at time t = 0 was given by the sounding at A, q(t = 0) = q_a. Solving the differential equation (4) for q(t) yields

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Here, μ can be written in terms of the fraction f_e of the ABL mass per surface area ρ_ablh_ablthat is vented from the ABL to a certain height per unit time

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where f_υ is the volume correction factor that considers the reduced volume of the ABL due to elevated terrain. We will refer to f_e as the ABL export rate hereinafter. Because calculations are done with a vertical resolution of Δz = 100 m, values for the ABL export rate (s m)⁻¹ will be given as f_e Δz (h⁻¹). Inserting q_b for t = t_r and (6) in (5) and solving for f_e yield

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Here, h_ablwas calculated as an average of both 1200 UTC soundings (Payerne and Milan) with a simple parcel method that assumes h_ablto be the altitude where the temperature of a parcel with the initial surface temperature that is lifted dry adiabatically from the surface intersects with the temperature of the current sounding. Under strong irradiation, but otherwise stable conditions, this method is in good agreement with more complex methods of determining h_abl (Seibert et al. 2000). Here, ρ(z) was taken from the soundings, ρ_ablwas taken as the average ρ for altitudes lower h_abl, f_υ was calculated using topographic information in a 250 m × 250 m grid of a strip of a 50-km width connecting Payerne and Milan, and f_e was calculated for every altitude each day. The total fraction of ABL air that is exported per unit time (s⁻¹) f_t was derived by the integration of f_e for the altitude range 2500–6000 m MSL,

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The lower limit of this altitude range was chosen because it remained unclear if the method is applicable underneath. An estimation of h_abl was made over the forelands. It is not straightforward to determine the actual ABL height within the Alps. It is likely that the ABL is higher in the Alps than over flat terrain. Therefore, f_e presents an upper limit of the export rate. On the other hand, the integration of f_e to derive f_t does not account for altitudes lower than 2500 m MSL. Therefore, f_t might be underestimated. Because the possible errors have opposite signs, the calculation of f_t should be reasonable.

Because fewer assumptions are necessary to calculate ri as compared with f_t, the analysis of ri is more robust. On the other hand f_e and f_t should be independent from the synoptic wind speed and, therefore, offer a more general conclusion.

Payerne–Milan

Figure 5 shows vertical profiles of q as calculated by the layer method for the soundings at Payerne at 1200 UTC and Milan at 0000 UTC of the following day for the SND category, with no lightning (SND_nl) (wind direction from Payerne toward Milan). Average specific humidity decreased from 1000 to 2500 m MSL for Payerne at 1200 UTC (thick solid line); farther up the decrease lessened. Up to 4100 m MSL the average specific humidity was larger in the 0000 UTC Milan profile (thick dashed line) in comparison with the 1200 UTC Payerne profile, above which the differences were small. In addition to the average profiles, median values are given for altitudes that show a significant difference between both stations [we used a Mann–Whitney test (Mann and Whitney 1947) and stated a significant difference if the probability of error was lower than 0.01, and at least 25 samples were included at a certain altitude]. The median profiles and the average profiles were similar. A layer ranging from 2400 to 4100 m MSL showed significant increases in q, which almost doubled in this layer. We will refer to such layers as “elevated layers” in the following and assume that they show a significant difference to the windward sounding, if not stated otherwise. In addition, the average profile for the 0000 UTC Payerne soundings is shown in Fig. 5 (thin dashed line). Throughout the whole lower troposphere, and especially at about 2000 m MSL, q increased, but the general structure of the profile did not change relative to the 1200 UTC Payerne profile. This increase might be related to synoptic-scale advection or larger-scale vertical motions due to atmospheric tides (Dai et al. 2002; Whiteman and Bian 1996), or vertical mixing over flat terrain or the Jura Mountains that are northwest of Payerne (see Fig. 2).

Estimated water vapor due to evapotranspiration during the 12-h transport time from Payerne to Milan accounted only for a small increase throughout the lower troposphere (thick dashed–dotted line). Only below 2200 m MSL evapotranspiration might explain the increase in specific humidity from Payerne to Milan. But, as mentioned above, the Lagrangian perspective might not be reasonable within this altitude range. As mentioned before, evapotranspiration was most likely overestimated. This fact further minimizes the impact of evapotranspiration as an additional water vapor source during advection. Therefore, all further comparisons focus on the differences between the original soundings at A and B, neglecting the estimated evapotranspiration.

Figure 6 gives the number of cases N that were used in the averaging and the average wind speed ff at every altitude for the SND_nl category. Direct flow from Payerne toward Milan was less frequent below 2500 m MSL. A broad maximum in frequency at about 4000 m MSL with up to 80 cases was observed. At higher altitudes the average wind speed was often too high to suit the selection criterion. The gray area in Fig. 6 marks the wind speed range from 4.4 to 6.6 m s⁻¹, which is favorable for the Lagrangian concept (see section 2b). Between 2500 and 4300 m MSL the wind speed lay within this range.

The results for the RAD_nl category were very similar to the SND_nlcategory. Figure 7 shows vertical profiles of specific humidity for the RAD_l category (the SND_l category is not shown because of the small number of cases in this category). Again, a strong increase in specific humidity was observed from Payerne at 1200 UTC to Milan at 0000 UTC. However, the “elevated layer” reached higher, up to 4800 m MSL, relative to the case without lightning. Even if the increase in specific humidity was large below 3200 m MSL, it was not considered to be significant because less than 25 cases were available at these altitudes. The observations suggest that thermally driven flow and moist convection act together in producing the resulting profile in Milan at 0000 UTC. Because moist convection is incorporated with cloud condensation and possible precipitation it remains unclear if specific humidity can be used as a conservative quantity in the context of thunderstorm activity.

Figure 8 shows the vertical profile of the relative increase ri (dashed line) and the ABL export rate f_e for the SND_nlcategory. Below 2400 m MSL a large scatter in ri was observed for individual samples and ri showed large values that should not be interpreted. A maximal ri value was reached within the elevated layer at ∼2700 m MSL of 0.3, meaning that 30% of the air in this layer originated from the ABL. Up to 3400 m MSL ri was larger than 0.2, and above 4000 m MSL ri decreased to values of about 0.01. The air between 2400 and 3800 m MSL, thus, contained more than 20% air that originated from the Alpine ABL. In addition to ri the vertical profile of the export rate f_e for the ABL between Payerne and Milan is shown. Because f_e incorporates the transport time, profiles of ri and f_e differ in shape. The lower wind speeds at lower altitudes tended to increase ri. Between 2400 and 3500 m MSL, f_e was rather constant for the significant layer (about 0.017 h⁻¹), meaning that the mass flux to this layer was relatively independent of height. Above 4000 m MSL f_e decreased to values lower than 0.004 h⁻¹. Integrating f_e for the altitude range of 2500–6000 m MSL yielded a total fractional ABL air export rate f_t of 0.31 h⁻¹. This means that about 31% of the Alpine boundary layer was injected per hour to altitudes above 2500 m MSL.

Table 3 summarizes the results on elevated specific humidity layers for different categories of days. The results for the selection SND_nl and RAD_l have already been discussed. For RAD_nl the characteristics of the elevated layer were similar to SND_nl, showing that the sunshine criterion can be relaxed to the radiation criterion, without loosing the general pattern in the results. RAD_nlincludes 133 cases, instead of 85 for SND_nl. The maximal observed ri within the elevated layer was somewhat higher in the SND_nlthan in the RAD_nl selection, 0.30 and 0.27, respectively. Both selections showed a similar maximal increase in specific humidity Δq_maxof 1.5 g kg⁻¹. For SND_l the significance of the elevated layer could not be assessed.

For all other selections only the cases without lightning are discussed. On ANT_nl an elevated layer was observed in the leeside sounding in the range from 2700 to 3900 m MSL. The characteristics of this layer were similar to the categories RAD_nl and SND_nl. Within IND_nl, a narrower elevated layer was observed, reaching from 2900 to 4100 m MSL and showing smaller values for ri and Δq than the previous categories. For CYC_nl, no significant increase was observed. The seasonal analysis revealed a broad elevated layer (2600–4200 m MSL) for the JJA_nlperiod, with a maximal ri of 0.33 and Δq of 1.7 g kg⁻¹. For the no-lightning March–April–May (MAM_nl), no-lightning September–October–November (SON_nl), and no-lightning December–January–February (DJF_nl) seasons, no elevated layers were observed. Because radiative input was already large in MAM, we expected to observe an elevated layer for this time period. But the larger snow cover in the Alps in MAM might have caused a larger albedo. Therefore, less sensible heat was available to heat the atmospheric surface layer and the development of thermally driven flow systems might have been reduced. On the other hand, atmospheric stability is lower in spring because the upper atmosphere is still relatively cool. This results in enhanced cloud formation, thunderstorms, and, therefore, reduced incoming global radiation.

The total ABL export rate f_t was similar for the SND_nl, RAD_nl, ANT_nl, and JJA_nlselection (Table 3). The IND_nlcategory showed a somewhat lower value. It is interesting to note that also for selections that did not show an elevated layer, f_t was positive. For the MAM_nl season f_t was 0.14 h⁻¹, showing that vertical export could already be strong in spring, even if the increase in specific humidity was not significant for the whole period. Further analysis of the individual months showed that elevated layers were present for the months of May–August but not for March, April, or September.

In addition to the layer characteristics, PW was calculated from the average q profiles (together with average profiles of temperature and atmospheric pressure). Differences from the background profile are presented for the altitude range from 2500 to 3500 m MSL [injection layer (IL, subscript il) here following] (Table 3). This altitude range was chosen because the largest absolute changes in specific humidity were observed within this range. The difference between the 0000 UTC Milan and 1200 UTC Payerne soundings is ΔPW_il. In this context, the subscript “e” refers to the increase due to evapotranspiration, and the subscript “l” refers to the local change and was calculated from the 1200 and the following 0000 UTC Payerne profiles. For all of the selections that show elevated layers, the largest change in PW was observed between the 0000 UTC Milan and the 1200 UTC Payerne soundings, with ΔPW_ilbeing as large as 1.4 mm. The change due to evapotranspiration ΔPW_il,e was 1/5–1/7 the size. Because evapotranspiration was rather overestimated, it can be regarded as a minor additional source of humidity at elevated levels. The local change ΔPW_il,l was 1/3–1/4 times ΔPW_il. The local change itself might be influenced by vertical mixing over the Jura Mountains upstream of Payerne.

For selections including lightning ΔPW_ilwas even larger (∼2 mm). The cyclonic weather type showed a small increase in ΔPW_ilthat was similar to the local change, indicating that this change was rather synoptically influenced than being due to thermally driven flow. Within the MAM_nlseason PW_il increased as much as 0.25 mm from Payerne to Milan, which was about twice as much as the local change, but less than the local change and the change due to evapotranspiration together.

From Payerne to Milan PW_ildecreased during SON, and especially during the DJF_nl season, while the local change was rather small. Because days with rain were excluded from the study it is likely that subsidence dominated the lower layers of the Alpine atmosphere during the cold season and was responsible for this decrease.

The average ABL height at Payerne and Milan was much lower than the lower limit of any observed elevated layer for all investigated categories (see Table 3). By leaving the Alpine region these elevated layers, therefore, became part of the lower FT.

Figure 9 shows profiles of q for nighttime advection from Payerne at 0000 UTC to Milan at 1200 UTC for the SND_nl category. During this period a horizontally advected air parcel is not expected to be influenced by daytime thermally driven flow, which starts after the air parcel leaves the Alps (cf. Fig. 3). In contrast to increasing q during the daytime and the predicted slight increase due to evapotranspiration (dashed–dotted line), q decreased at the lee side throughout the whole lower troposphere, relative to the windward side. This might be related to a large-scale subsidence in high pressure systems dominating the sample. Especially below 2500 m MSL q strongly decreased in the leeside soundings. The decrease in q at Payerne itself was about the same as in Milan at 1200 UTC.

Milan–Payerne

For advection from Milan toward Payerne in the range of 2500–4000 m MSL only 9 days out of the 12-yr period met the SND_nl criterion (7 days for RAD_nl). A weather situation with advection from the southeast is rather infrequent for the Alpine region. The average specific humidity increased only slightly from Milan at 1200 UTC to Payerne at 0000 UTC for the SND_nl case. In addition, the 0000 UTC Milan soundings showed the same change as the 0000 UTC Payerne soundings. The same resulted for the RAD case with lightning and the AND, IND, and JJA cases with or without lightning.

Of all selected days with advection from Milan toward Payerne in the range of 2500–4000 m MSL only 1 day lay within the summer month—8 July 1995. All of the other days were within the spring or autumn season. Only for the case in July was a well-defined increase in specific humidity in the lee sample observed.

Specific humidity was generally larger up to 5000 m MSL in the leeside sounding in Payerne at 0000 UTC than in Milan at 1200 UTC. The windward sounding at 0000 UTC showed uniform specific humidity up to 1800 m MSL and a strong decrease above with generally lower values than on the lee side. In the IL PW increased by 2.8 mm from Milan to Payerne, while locally PW decreased in the IL by 0.1 mm at Milan.

This case underlines that elevated layers in the lee of the Alps are also formed during southeasterly advection. Unfortunately, statistical proof was not possible because of the rare occurrence of this situation.

Further considerations of the method

The layer method does not represent a real average over complete profiles, but only an average at every height level. Figure 10 presents the results for the profile method for the SND no-lightning case. Despite the fact that the profiles are somewhat smoothed in comparison with Fig. 5, no general difference between both methods was observed within the elevated layer that resulted from the layer method (2500–4100 m MSL). Below 2500 m MSL q increased more and was generally larger using the profile method than using the layer method. This might result from situations with wind shear in the lower troposphere and southern advection in the ABL at Milan and southwesterly advection at Payerne. These situations would contribute to the average of the profile method but not to the layer method.

Average potential temperatures θ (Fig. 11) increased during the daytime transport from Payerne to Milan by about 2 K in the elevated layer (SND, RAD, ANT, and IND categories). Because mixing and diabatic processes might be active in this altitude range, it was not possible to attribute the warming to adiabatic subsidence. Above 4500 m MSL θ increased less than 1 K. This corresponds to a downward motion of ∼200 m within 12 h if the warming was only caused by adiabatic subsidence. In addition, the top of the observed elevated layer (∼4000 m MSL) agrees well with observations from case studies within the Alps (Nyeki et al. 2000; Carnuth and Trickl 2000; Henne et al. 2004). Therefore, the assumption that an air parcel stays at about the same height during the advection process is justified.

For the same criteria and daytime advection average relative humidities (not shown) were lower than 40% on the windward side and between 50% and 60% on the lee side. This underlines that if condensation occurred it was only very localized. Clouds dissolved before they reached the sounding site in Milan.

Radiosondes with different humidity sensors were used at the two sounding sites. In general, the accuracy of humidity sensors of radiosondes is lower for low temperatures. Differences between the two stations might result from this lack of accuracy for individual soundings. No systematic difference could be observed for average specific humidities in an air mass that was advected from Payerne to Milan in situations without considerable vertical exchange (nighttime, Fig. 9 and above 4500 m MSL for all other no-lightning categories).

Because of humidity sensor changes at the Swiss sounding site in 1992 and 2001, calculations were carried out for two separate periods (1991 + 2001 + 2002, and 1992–2000). The general structure of the findings for the SND_nl and RAD_nl case did not change from the first period to the second. But specific humidity was larger in the first period than in the second, especially in the 0000 UTC Milan sounding, resulting in a somewhat larger increase in specific humidity in the first period. Whether this is due to the instrument changes or climatological variation could not be determined by this study.

Instead of using lightning measurements taken at surface stations between Payerne and Milan, the convective available potential energy (CAPE) was estimated from the 1200 UTC soundings at both sites to partition between days with and without deep convection. The results for the low CAPE (<2500 J kg⁻¹) and the no-lightning categories are similar. The same is true for the high CAPE (>2500 J kg⁻¹) and lightning categories. The median CAPE for SND_nl and RAD_nl were 1300 and 1600 J kg⁻¹, respectively, while for the lightning categories (SND_l and RAD_l) the median CAPE was much larger (2900 and 2900 J kg⁻¹, respectively). Therefore, CAPE can be used in situations where no lightning measurements are available to distinguish between days with or without potential for deep convection.

Dependence on atmospheric parameters

This subsection addresses the question of whether it is possible to find a relationship between the export rate f_e and atmospheric parameters like the total solar radiation per day ΣR_s, ff, or static stability dθ/dz. For this analysis the whole dataset (12 yr) was selected. Days with lightning or rain were still excluded. The export rate f_e was rather independent of height within the altitude range of 2500–3500 m MSL (IL). For days with advection from Payerne at 1200 UTC toward Milan at 0000 UTC the average f_e in the IL was estimated. In contrast to f_e, f_t could not be calculated for individual days, because the direct advection was not detected at all altitudes above 2500 m MSL. In addition to f_e, different atmospheric parameters were derived for each individual day: ΣR_s, ΣS, q_ablfrom stations in the Alpine boundary layer below 1500 m MSL; ff_il, T_il, q_a,il from radio soundings within the IL; dθ/dz, dθ_e/dz, dθ/dz_max from radio soundings from the surface up to 5000 m MSL.

The highest correlation of f_e with any of the other parameters was determined for ΣR_s: r = 0.41. The correlation with ΣS and q_abl was 0.37 and 0.35, respectively. The latter is remarkable, because f_e is a quantity that was already normalized by q_abl. Larger specific humidity within the ABL might cause condensation when air is transported upward and, therefore, assists in vertical motion and ABL air export. Only a weak correlation was observed for the specific humidity in the IL on the windward side q_a,il (r = −0.14). The wind speed in the IL and f_e were not correlated (r = −0.03), supporting the residence time concept presented in section 2. Of the stability parameters dθ/dz showed the most negative correlation: r = −0.33.

Correlations of average ri within the IL with the specified atmospheric parameters showed generally lower absolute values for all parameters with the exception of wind speed ff_il (r = −0.16).

Figure 12 shows a box plot of average f_e within the IL for different categories of ΣR_s. The fraction of ABL air that was injected into a layer of 100-m thickness per hour is f_e. Multiplying f_e by 10 gives the fraction of ABL air that was injected into the IL (1000 m thickness) per hour. There is a considerable trend of larger median f_e for larger ΣR_s. Also visible is the large spread of the data within the different categories. Some outliers also influenced the mean (stars) of the category, increasing the trend for the mean relative to the median. Days with ΣR_s lower than 7.5 MJ m⁻² showed a negative median of f_e. Subsidence was dominating on these days. Days with R_s larger than 12.5 MJ m⁻² favored positive ABL export over the Alpine terrain between Payerne and Milan.

Figure 13 shows a box plot of average f_e within the IL for different categories of dθ/dz. In general, there was a trend to larger f_e for lower stabilities (lower dθ/dz). But, median and mean f_e showed maximal values for dθ/dz in the range of 3–4 K km⁻¹ and lower values for dθ/dz = 2 K km⁻¹. More cases with low stability would be necessary to prove this tendency. For large atmospheric stability (dθ/dz > 5 K km⁻¹) negative values of f_e dominated in these situations. Vertical transport was too weak to counteract the strong atmospheric stability. Too few cases with very strong atmospheric stability (dθ/dz = 7–8 K km⁻¹) were included in the analysis to determine if the mean and median for f_e were only due to some extreme events.