LP-DOAS measurements are based on the identification and quantification of narrow-band trace gas absorption features in the open atmosphere . During ALPACA a 120 cm focal length, 30 cm diameter fiber telescope was used to send a collimated beam of light from a laser-driven Xe light source (Energetiq LDLS 99X) onto arrays of quartz corner-cube retro-reflectors. The reflected light was captured by the telescope and transferred through a mode mixer to a thermally stabilized 300 mm focal length Czerny-Turner spectrometer (ACTON Pro 300 at 20 °C) and a CCD detector array cooled to -70 °C (Teledyne PIXIS). The LP-DOAS telescope was located on the top floor of the Lacey-Street Parking Garage (64.844° N, -147.716° E) in downtown Fairbanks at an altitude of 17 m above ground level (m a.g.l.). To measure the vertical trace gas profile, four reflector arrays were mounted at different altitudes northeast of the telescope (Fig. ). The lowest path averaged trace gas concentrations along an 1154 m long path over an height interval of 12–17 m a.g.l. Three other reflectors were mounted along Birch Hill at 73, 115, and 191 m altitude at a distance of 3.6 to 4 km (Fig. ). The telescope was aimed sequentially at each reflector array using automated stepper motors for rotation in azimuth and elevation, providing a complete vertical scan every 30–60 min.

Trace gas mixing ratios were retrieved from LP-DOAS absorption spectra using established DOAS retrievals in various wavelength windows between 280–380 nm. This procedure also calculates the error of the measurements. Accuracy of the LP-DOAS path averaged trace gas concentrations are determined by the uncertainty in the absorption cross section and are in the range of 3 %–8 %. Details on the retrieval procedure and detection limits are given in Sect. S1 in the Supplement.

In-situ instruments were located near the University of Alaska Fairbanks Community and Technical College field site (CTC, 64.841° N, -147.727° E) (Fig. ). SO2 was measured in-situ at 3 m a.g.l. with a Thermo Scientific 43C instrument located in a stationary trailer parked next to the CTC building. Ozone and NOx were measured at the same location and height using a Thermo Scientific 49C and 42C instruments, respectively. A second ozone monitor (Teledyne 400E) was deployed at Birch Hill at an altitude of 158 m above the valley floor. Details on these observations can be found in the Supplement.

Temperatures were measured with aspirated thermometers at 3, 6, and 11 m on a small tower in an parking lot adjacent to the CTC building, and at 23 m a.g.l. above the roof of the buildings elevator shaft house . The temperature measurement had a precision better than 0.15 °C, allowing the derivation of vertical temperature gradients. Wind speed and direction were also measured at 23 m a.g.l. on the CTC roof using an RM Young 1005 monitor. A comparison of the 11 m and 10 m to 3 m temperature gradients show that the CTC gradients are ∼14 % lower than those at the the Alaska National Core Multi-Pollutant Monitoring Station site (NCORE), which is about 500 m north of the CTC building . Comparison of 23 m wind speeds on the CTC roof with 10 m wind speeds at the nearby NCORE site yields good agreement (Fig. S8 in the Supplement).

Interpretation of vertical profiles of LP-DOAS path-averaged concentrations is challenging due to overlapping altitude intervals. While a sequential difference approach has been used , we developed a different approach here that is better suited to study the polluted surface layer. Our approach is also able to incorporate in-situ observations, when available. The basic idea of our retrieval is the assumption that the shape of the trace gas concentration profile, C(z), can be described by a sigmoid function: 1C(z)=Ca+Cb×1-11+exp⁡(-(z-H)/M)

Here, z is altitude, and Ca and Cb are two parameters that control the concentrations at the low and high end of the profiles. M is a parameter that broadly describes the slope of the transition. H is an altitude offset, which, for box-shaped profiles (M<1) can be interpreted as the half-point between Ca and Cb. It should be noted that Ca and Cb are only equivalent to surface and z=200 m concentrations when M is very small and H<∼200 m. Equation (), with its four free parameters, allows for the description of a broad set of profiles as illustrated in Fig. S3. Combination of the four parameters can describe many shapes from box-like, linear and curved decreasing, and constant profiles (Fig. S3). Most parameter combinations in Eq. () yield profiles that decrease with altitude, which matches the behavior of SO2, NO2, HONO, and HCHO, which typically have higher concentration at the ground. In contrast, ozone often has lower concentrations at the surface. Therefore, Eq. () has to be slightly modified to allow for the inverted ozone altitude profile: C(z)=Ca+Cb×1/(1+exp⁡(-(z-H)/M)). Because the four parameters in Eq. () do not represent direct physical measures we will not use them in our analysis, but rather interpret the resulting profiles C(z). We will justify the choice of a sigmoid function in Sect.  when we compare the retrieval results and with profiles from a 1D chemistry and transport model.

To derive the four parameters in Eq. (), we first interpolated the path-averaged LP-DOAS data from the upper three light paths onto the measurement time of the lowest light path, while propagating the measurement error to the interpolated data. Because path-averaged data varies slowly, a linear interpolation was chosen. Similarly, we averaged the in-situ data over the time interval of the lowest light path measurements. A non-linear Levenberg–Marquardt fit then optimized the model function describing the altitude averaged, time interpolated, LP-DOAS data and the concentration of in-situ observations. The function calculates Eq. () on a regular 1 m grid from the surface to 200 m altitude and then numerically integrates the concentration vector in the altitude intervals of the respective LP-DOAS light paths. In-situ data are taken from the grid cell closest to the exact measurement altitude. The non-linear fit then optimizes Ca, Cb, M and H to find the best agreement of the function output to the observations.

To quantify the impact of measurement errors on the retrieval results, we chose a Monte-Carlo approach. We performed the retrieval 250 times while randomly varying the input data to the retrieval using a Gaussian probability density function with the observation as the mean and the measurement error as the standard deviation. We then averaged the 250 retrieved profiles and used the standard deviation as our profile mixing ratio error. From these profiles, we determine the surface layer height (SLH) as the altitude in which the mixing ratio is the midpoint between C(0m) and C(200m), and the uncertainty of this value. Our retrieval assumes horizontal homogeneity within the extent of our light paths. The very good agreement of NO2 and SO2 on the lowest light path with the in-situ observations (Fig. ) confirms that this path is representative of surface mixing ratios in downtown Fairbanks. In the presence of a PSL, the volume probed by the upper three light paths is dominated by background air, which is typically well mixed vertically and horizontally. Our retrievals confirm that in most cases air above a well-developed PSL does not show a vertical profile within the uncertainties (see below). In the case of a well-mixed atmosphere, horizontal inhomogeneities are also reduced. In cases of intermediate mixing this assumption may, however, not strictly hold. Because horizontal inhomogeneities would distort vertical trace gas profiles, we can use the agreement of the retrieved point and altitude-averaged mixing ratios with the observations to assess whether horizontal inhomogeneities would prevent interpretation of our vertical profiles. Figures S4 and S5 show that the agreement of the retrieved and observed mixing ratios for O3 and NO2 is excellent. In particular, the agreement between the 3 m surface mixing ratios and the 158 m Birch Hill ozone in situ measurements with the retrieval results show that our retrievals are not noticeably impacted by horizontal inhomogeneities and that we can use the retrieved profiles to analyze the vertical structure of the Fairbanks atmosphere.

Path-averaged mixing ratios from the LP-DOAS instrument show large variability in time and altitude throughout the ALPACA experiments (Fig. ). Ozone mixing ratios were consistently highest on the upper light path (dark yellow in Fig. ) and lowest in the 12–17 m path (dark blue markers in Fig. ). The other paths were typically in between these two extremes. The smallest mixing ratio of ozone was observed by the in-situ instrument at 3 m a.g.l. (yellow line in Fig. ), where ozone often dropped to within measurement error of zero. For much of the experiment, the upper path reflected background levels of O3 of 30 to 35 ppb, which is also reflected in the in-situ ozone observations on Birch Hill (158 m altitude in Fig. ). Occasionally, ozone mixing ratios aloft dropped below 20 ppb.

Overall, NO2 exhibits the opposite behavior from ozone, with highest mixing ratios close to the surface and lowest mixing ratio aloft. The lower path NO2 agrees well with the in-situ observations at nearby CTC. The rapid NO+O3 reaction in combination with weak vertical mixing explains the inverse behavior of O3 and NO2. Since background ozone is around 35 ppb, this reaction initially only forms 35 ppb of NO2. Additional NO2 comes from direct emissions. Further formation of NO2 from continued emissions of NO is inhibited by the lack of ozone. NO emissions under these conditions can lead to large spikes in NOx that are not reflected in NO2. The strongest pollution events are thus not easily visible (Fig. S6). The different sources and chemical formation likely smooths out the NO2 variability. We discuss this phenomenon more quantitatively in Sect. .

SO2 mixing ratios also decrease with altitude, and the general temporal and altitude trend follows that of NO2. However, the in-situ SO2 data shows much higher temporal variability, likely due to different sources of these species. SO2 is directly emitted, predominantly by residential heating, while NO2 is mostly formed by the NO+O3 reaction from traffic-related emission of NO, with direct NO2 emission playing a smaller role.

HONO mixing ratios and their vertical profile show a similar, but not identical, behavior to NO2 and SO2. While it is beyond the scope of this study to determine the source of HONO, we can speculate that HONO is directly emitted, but we cannot rule out a contribution from secondary chemical formation. HCHO mixing ratios seem to follow those of the other trace gases, but have a larger variability. The similar (inverted for ozone) behavior of these trace gases shows the strong impact of PSL formation on the accumulation of surface emissions.

To provide more details on the PSL and the vertical and temporal distribution of pollutants, we rely on the retrieved NO2 mixing ratio profiles (Sect. ). NO2 was selected due to its small measurement error and because it has the largest dynamic range, i.e. the difference between mixing ratios at the surface and aloft, of all the observed trace gases. In addition, the 3 m in-situ observations as well as the lower light path mixing ratios have a smoother temporal variability than SO2 (see Fig. ), making the profile retrievals, and thus the interpretation of the PSL height, more reliable. Retrieval results of the other trace gases are discussed in Sect. .

The NO2 profiles (Fig. a) show the frequent presence of a shallow PSL with NO2 mixing ratios above 10 ppb and a thickness between 20–80 m. The period from 28 January to 4 February stands out as the PSL is persistent and only 20–40 m thick, with NO2 mixing ratios in the range of 30–55 ppb. Noteworthy are also the abrupt transition from the PSL to periods with mixing ratios close to background levels below 1 ppb and the absence of strong vertical profiles.

The presence of the PSL is associated with low wind speeds (Fig. d) and strong temperature gradients (Fig. b). Times with increased wind speeds lead to negligible temperature and trace gas gradients, for example on 28 January and 4 February. The increased vertical mixing and wind-driven export during these time periods is responsible for low pollutant levels throughout the lowest 200 m of the atmosphere and the absence of a PSL. During the second half of ALPACA wind speeds were more variable and often reached above 2 ms-1, thus the presence of a PSL becomes less persistent.

To better understand how the SLH retrieved from the NO2 profiles are related to surface temperature inversions in Fairbanks, we performed a statistical analysis of the relationship of SLH and temperature gradients, dT, between 3 and 23 m altitude (Fig. a). Lower SLH are clearly associated with larger dT (Fig. a). At dT=0.0125 °Cm-1 a median SLH of 56 m is found, indicating that even relatively weak temperature gradients can be associated with SLH in the 50 to 60 m range. However, this dT bin also includes conditions where no well-defined PSL is formed. SLH decreases steadily from dT=0.0125 to dT=0.1375 °Cm-1 and levels off around 25 m. The variability of the SLH also decreases, implying that strong temperature inversions are always associated with low SLH. It should be noted here that the formation of surface temperature inversions and a PSL are not completely synchronous, as emissions take time to accumulate. We thus expect a certain amount of variability from this effect in our analysis. Nevertheless, it is clear that the SLH is closely related to surface temperature inversions, a result that we will use later when developing a parameterization for surface mixing for PACT-1D.

Wind speed also impacts the PSL height. SLH below 50 m are only observed when wind speeds are lower than 3 ms-1. For larger wind speeds, no clear surface inversion or inversions above 200 m are found (Fig. b).

There are two possible explanations for the influence of wind speed on surface pollution. Larger wind speeds can cause shear-induced turbulence leading to weakening or breaking up of the surface inversion. In fact, non-zero surface temperature gradients are only found for wind speeds below 3 ms-1 in Fairbanks (Fig. c), supporting the idea that low wind speeds are a requirement for the formation of the PSL.

Wind also horizontally advects pollution out of and clean air into the Fairbanks urban area, thus lowering pollutant levels. To investigate this, we calculated the 3–200 m column density of NO2 and SO2 by integrating our trace gas profiles with altitude. A statistical analysis shows that trace gas columns, i.e. the vertically integrated concentrations, decay with increasing wind speed and reach values close to zero around 3 ms-1 (Fig. d), illustrating the effect of advection on air pollution in Fairbanks.

In summary, our analysis seems to indicate that PSL formation only occurs at wind speeds below 3 ms-1, while shear induced turbulence and advection remove surface pollution effectively above wind speeds of 3 ms-1.

To provide a more quantitative analysis of the processes leading to vertical trace gas profiles in Fairbanks, we set up UCLA's 1D vertical chemistry and transport model PACT-1D to represent the 4km×4km area of downtown Fairbanks. PACT-1D is an observation-driven one-dimensional model designed for the interpretation of field observations and mechanistic studies. The model simulates the temporal evolution of trace gas concentrations based on a set of boundary conditions, such as emissions, turbulent diffusivities, wind speed, photolysis rates, and temperature, many of which are constrained by field observations. The model does not constrain trace gas concentrations. The chemical scheme in PACT-1D is based on the RACM2 mechanism . The model considers molecular uptake of trace gases on the ground, which, in combination with the transport scheme, leads to deposition (see , for details). We ran the model for the entire ALPACA period using photolysis frequencies measurements by the Univ. of Houston's spectroradiometer and temperatures and RH from observations at the CTC site .

For Fairbanks we use the model with 39 vertical grid cells, of which 32 are in the lowest 200 m and 11 in the lowest 20 m of the atmosphere. Grid spacing decreases towards the surface to capture the fine structure of the PSL. Emissions, vertical eddy diffusivities and horizontal advection are central to accurately describing pollutant concentrations in the PSL. They are also supplied externally to the model, which will be discussed in the following sections.

The results of the statistical analysis (Sect. ) can be used to develop a conceptual model of the lower atmosphere in Fairbanks (Fig. ), which can be translated into a parameterization for inclusion in a one-dimensional model. Our observations show that under conditions of weak surface winds and the formation of a surface temperature inversion, surface emissions accumulate in a shallow PSL (Fig. ). Dilution of surface layer air with background air thus appears strongly reduced. However, the fact that trace gas concentrations in the surface layer do not continuously increase, often reaching a plateau (Fig. ), indicates the presence of some residual mixing across the top of the PSL. The small trace gas concentrations above the PSL and the strong gradient at the top of the PSL (Fig. ) imply that trace gases leaving the PSL are efficiently removed. We attribute this removal to advection by horizontal wind, which is typically stronger above the PSL.

Overall, a picture emerges where, at low wind speeds, emissions accumulate in a shallow surface layer, while slowly being mixed out of the top of the PSL where they are removed by advection (Fig. ). A pseudo steady state, PSS, between emissions and this loss is often established in the PSL. We will discuss the impact of this PSS and the associated residence times in Sect. . We can now use this conceptual model to develop a parameterization for vertical mixing and advection loss in our one dimensional model.

One of the advantages of using a detailed 1D model is the ability to archive all relevant chemical reaction rates and trace gas fluxes. Because one of our goals is to understand how trace gas fluxes, J(z), at altitude z impact chemistry, we will use transport rates, i.e. the rate at which transport contributes to a change in concentration at a certain altitude: dCtransport(z)dt=Jnet(z)/h in units of molec.cm-3s-1, where Jnet is the net flux into or out of the model grid box and h is the box height. When appropriate, we distinguish between vertical transport and advection terms.

Another diagnostic tool we use is the residence time of a trace gas in the PSL see also. A comparison between this residence time and the timescale of chemical reactions provide important insights into the behavior of the chemistry-transport system in the PSL. The residence time is commonly calculated using the assumption of a pseudo steady state, i.e. stationary atmospheric transport conditions. We calculate this instantaneous residence timescale τ⋆(t) from the modeled vertically integrated pollutant concentration c¯, and the transport-related removal rates of pollutants from the PSL (V† and H†, where V† includes deposition). The latter are calculated by integrating vertical and horizontal transport rate profiles, V and H, over the height of the PSL (hPSL): 4τ⋆=c¯H†+V†=∫0hPSLc(h)dz∫0hPSLHdz+∫0hPSLVdz However, the instantaneous residence timescale τ⋆ does not represent the true residence time of a gas within the surface layer. For example, if at a given time t, τ⋆ is 3 h but one hour later changes to 1 h, the effective residence time at t will be shorter than 3 h. The effective pollutant residence time τ(t) at a given time t therefore depends on the future value of τ⋆. The effective residence time is the upper bound of the following integral expression: 5∫tt+τ(t)1τ⋆(t′)dt′=1 We can solve this equation numerically for τ to thus determine the temporal evolution of the effective residence time τ of pollutants in the PSL (see Sect. ).

The model results for the entire ALPACA experiment (Fig. d–f) reproduce the presence of frequent PSLs observed by the LP-DOAS system (Fig. a–c). It accurately captured persistent PSLs, with increased concentrations of SO2 and NO2 and depleted ozone, interspersed with periods of efficient mixing and low SO2 and NO2, during the first third of the experiment. The model also reproduces the more variable PSL in the second half of the experiment, when increased solar heating leads to more mixing during the day. The height of the modeled PSL is slightly (∼10 m) higher than those observed, but considering the uncertainties in height retrievals and vertical mixing parameterization, the agreement is very good.

Over the entire experiment SO2, NO2 and O3 mixing ratio agree well between model and observations (see Sect. ). The opposite profiles of NO2 and O3 will be discussed in more detail in Sect. . During some instances of intermediate mixing, for example when ozone mixing ratios are low throughout the entire 200 m high domain on 26 January and 1 February, the model is unable to correctly reproduce the concentrations aloft. We attribute this to mixing in the model being too weak during these times, pointing to a need to improve our parameterization for these cases. In the following two sections we will provide a more detail look at the model-observation intercomparison of mixing ratios and profile shape.

An interesting observation during ALPACA was the rapid formation of the PSL. A close look into the morning hours of 4 February shows that before 02:15 AKST, in the absence of a temperature inversion (Fig. f) ozone was relatively well mixed in the lowest 200 m of the atmosphere, as shown by the agreement of the in-situ and LP-DOAS measurements (Fig. d). Similarly, SO2 showed a weak vertical profile, with 2 ppb at the surface and 0.3 ppb on the upper LP-DOAS light path. Once the temperature inversion starts to form, around 02:15–02:30 AKST, surface SO2 increases (Fig. e) and surface ozone decreases (Fig. d). SO2 in the 12–17 m height interval follows the 3 m in-situ data. In contrast, O3 in the 12–17 m interval showed a 20 min delay and ozone mixing ratios remained larger after 04:00 AKST when the 3 m data was close to zero. In-situ NO starts increasing considerably later than SO2 and only appears when ozone has been nearly completely depleted at the surface (Fig. d). The LP-DOAS observations of SO2 and O3 on the three light paths above 17 m, on the other hand, showed little change, indicating that the PSL was confined to the lowest 20 m of the atmosphere.

The model results (Fig. a–c) generally agree with the observations and clearly show that ozone depletion at the surface occurs from the ground upwards, as NO surface emissions first react with surface O3. As ozone is depleted at the surface and NO accumulates, vertical mixing of NO will cause ozone destruction higher up in the PSL. The non-zero 12–17 m ozone mixing ratios around 04:45 AKST indicate some residual ozone in the upper part of the PSL. This is supported by the model which shows ozone at the top of the PSL, albeit at a somewhat larger height than the observations. The high 12–17 m ozone mixing ratios after 05:00 AKST are not reproduced by the model and could indicate that the PSL height decreases below 12 m, or due to some mixing at the top of the PSL. Interestingly, the high ozone coincides with decreasing SO2 at the surface and at 12–17 m. Vertically more highly resolved measurements are required to study such cases in the future.

Surface pollution in wintertime Fairbanks is associated with the formation of a PSL, as clearly illustrated by the direct profile observations shown in Fig. . Here we discuss this dependence by analyzing three distinct vertical trace gas profile scenarios.

The first scenario corresponds to a strongly polluted PSL. It is characterized by a shallow PSL with high concentrations of primary pollutants, such as SO2 and NOx=NO+NO2, and low ozone. Figure a, f, and k shows an example of such a profile from 08:13 AKST on 2 February 2022. The observed and modeled profiles of SO2 and NO2 show a remarkable near step-wise transition from a highly polluted surface layer with 28.4 ± 1.1 ppb of SO2 and 45 ± 0.7 ppb of NO2 to background air with low mixing ratios. Defining the height of the layer as the halfway point between surface and 200 m mixing ratio yields ≈34 ± 7 m for SO2 and 43 ± 5 m or NO2. The retrieved ozone profile shows a slightly smoother shape with 1 ± 5 ppb at the surface and 35.2 ± 5 ppb at 200 m altitude. While the shape is different from that of the other two trace gases, the height of the half-way-point is similar, at 34 ± 15 m. As the shaded areas representing the uncertainty (Fig. ) show, our profile retrieval can only identify the surface-layer height to within 5 to 10 m for SO2 and NO2 and is even less accurate for ozone.

The abrupt transition in the SO2 concentration profiles is a common phenomenon during PSL events (see also Fig. ). In our model this transition is caused by a drop of Kz to very low values at the transition height and increased advection above the transition. The modeled vertical transport and advection rates expressed as the rate of concentration change due to the respective transport process in each box in Fig. d and e (red curves) show a negative vertical transport rate below ∼20 m and a positive rate between 20–40 m, indicating that freshly emitted SO2 is transported into the upper part of the PSL. A small amount of SO2 is also advected out of the urban core. In the 20–40 m height interval upward transport and advection balance each other, making advection the main SO2 loss process. A similar picture emerges for NO2 (Fig. i and j, red curve). The region of loss due to vertical transport is lower in the PSL due to traffic emissions occurring closer to the ground. The vertical gradient of NO2 is less pronounced in the PSL than that of SO2, due to its chemical formation through the NO+O3 reaction. The loss of NO2 from the PSL thus occurs predominately at the top of the PSL as indicated by the small positive vertical transport rate peak (Fig. i). Advection of NO2 is similar to that of SO2.

Mixing ratio profile and transport rates for ozone are generally inverted from those of NO2, except for the surface peak which stems from NO2 emissions (Fig. n and o, red curve). The downward transport of ozone thus also occurs primarily at the upper part of the PSL, where there is a transition from a weakly positive to a negative peak of the transport rate.

Our second scenario is that of a well-mixed atmosphere, such as that encountered at 15:39 AKST on 7 February 2022 (Fig. b, g, and l). SO2 and NO2 mixing ratios are much smaller at the surface, at 3 and 12 ppb respectively, while they seem slightly higher aloft than in our first scenario. The reverse behavior is true for ozone with modeled mixing ratios of 25 ppb at the surface and 32 ppb aloft. The fact that ozone mixing ratios at 200 m are lower than the model background of 35 ppb and the presence of 0.5 ppb of NO aloft (Fig. s) indicates that ozone is titrated by NO emissions (which peak during that time of day) throughout the lower atmosphere. The vertical transport rate profiles reflect this behavior with negative values below ∼20 and ∼50 m for SO2 and NO2, respectively, and positive rates above (Fig. d and i, blue curve). Ozone vertical transport is the inverse of that of NO2 (Fig. n, blue curve). The transport rates are generally larger than in the polluted scenario due to enhanced turbulent mixing.

Our third scenario is an intermediate case when the atmosphere is stable but a distinct surface layer is not formed, such as at 13:48 AKST on 8 February 2022 (Fig. c, h, and m). This case shows pronounced vertical profiles and increased surface mixing ratios of SO2 and NO2 and low, but non-zero, ozone mixing ratios. These profiles are more similar to those previously observed in lower-latitude urban areas at night . The vertical transport rate profiles in this case are similar to our second scenario, but generally more pronounced (Fig. d, i, and n, orange curve).

One of the most visible consequences of the presence of the urban PSL are the low ozone mixing ratios at the surface and the extremely strong ozone vertical concentration gradient across the top of the PSL, which are accompanied by the inverse gradients of NO2. This phenomenon, and the generally inverted profiles of O3 and NO2, can be explained by the emission of NO, reaction of NO with ozone and the very slow entrainment of ozone rich air from the background atmosphere aloft and by advection. Modeled NO profiles (Fig. s) show very high surface mixing ratios during strong PSLs, in good agreement with the observations. Modeled NO mixing ratios above the PSL are very low in this case. NO profiles also show the same abrupt transition as the other PSL pollutants. As the Fairbanks atmosphere becomes more mixed the NO mixing ratios and the concentration gradients weaken.

We extracted the NO+O3→NO2+O2 reaction rates from the model to illustrate how ozone chemistry changes for the three stability regimes (Fig. p, q, and r). In the case with a strong PSL (Fig. p) the reaction rate increases in the PSL to a maximum of ∼3×108 molec.cm-3s-1 near the top of the PSL where NO and background ozone mix.

In scenarios with more mixing, and larger ozone surface mixing ratios, the NO+O3→NO2+O2 reaction rate increases from the ground upwards. Interestingly, small amounts of NO and therefore reaction rates can be found up to 200 m altitude in these cases (Fig. s). Our results show that increased mixing leads to more pronounced profiles of the reaction rate and more NO aloft.

The common view of the role of the PSL in air quality is that it “traps” pollution. To investigate this perspective more quantitatively, we calculated the effective residence time of pollutants, τ, using the model analytics of an inert tracer, which is emitted into the PSL and transported according to the turbulence-advection scheme (Sect. ).

The effective residence time in the lowest ∼20–50 m during ALPACA is between 0.2 h, when no PSL is present, to 4 h with a well-developed PSL (Fig. c). It is closely associated with surface temperature gradients and wind speed (Fig. b), confirming the role of surface inversions and advection in controlling PSL mixing with background air (see Sects.  and ). The effective residence time correlates well with SO2 mixing ratios (Fig. a). This is due to continuous SO2 emissions, predominantly from residential heating. An analysis of the SO2 budget reveals that turbulent mixing and advection are the dominant processes controlling SO2 (and other trace gas) concentrations, while chemical loss and deposition of SO2 account for less than 10 % of the total budget in our case and thus are of lesser significance. SO2 is indeed trapped in the PSL, however, in most cases only for 1–4 h.

The range of values of τ have important implications for PSL chemistry. Chemical reactions with a time scale much smaller than τ will proceed completely within the PSL. For example, the average ozone lifetime in a well developed PSL (29 January to 3 February) due to its reaction with surface emitted NO is less than 15 min. The chemical lifetime of NO in the PSL, which is dominated by the NO+O3 reaction, is somewhat larger but still smaller than τ. Processing of both trace gases therefore proceeds largely inside the PSL. On the other hand, chemical lifetimes of SO2 and NO2, for example due to their oxidation by OH radicals, are longer than 100 h. Their PSL concentrations are thus controlled by the efficiency of transport out of the PSL.

Residence times between 1 and 4 h for the extreme cold event shown in Fig.  reveal that the PSL is not a permanent trap for pollutants. Pollution is lost by continuous mixing with background air, albeit slowly, and replenished by emissions, even in very persistent PSLs such as those in Fairbanks. The short (1–4 h) pollutant residence times near the surface also limit the formation of secondary aerosol species through multiphase chemistry, because particulate matter is exported from the PSL by the same transport processes. The substantial influence of the short pollutant residence time on PSL oxidation and multiphase chemistry is analyzed and discussed in .