Residual Layer Ozone, Mixing, and the Nocturnal Jet in California's San Joaquin Valley

The San Joaquin valley is known for excessive secondary air pollution owing to local production combined with terrain-induced flow patterns that channel air in from the highly populated San Francisco Bay area 50 and stagnate it against the surrounding mountains. During the summer, ozone violations of the National Ambient Air Quality Standards (NAAQS) are notoriously common, with the San Joaquin Valley having an average of 115 violations of the recent 70 ppb standard each year between 2012 and 2016. The nocturnal dynamics that contribute to these summertime high ozone events have yet to be fully elucidated. Here we investigate the hypothesis that on nights with a strong low-level jet (LLJ) ozone in the residual layer is more effectively mixed down into the stable 55 boundary layer where it is subject to dry deposition to the surface, the rate of which is itself enhanced by the strength of the LLJ, resulting in lower ozone levels the following day. Conversely, nights with a weaker jet will sustain residual layers that are more decoupled from the surface and thus lead to stronger fumigation of ozone in the mornings giving rise to higher ozone concentrations the following afternoon. We analyse aircraft data from a study sponsored by the California Air Resources Board (CARB) aimed at quantifying the role of residual layer ozone in 60 the high ozone episode events in this area. By formulating nocturnal scalar budgets based on flights around midnight and just after sunrise the following days, we estimate the rate of vertical mixing between the residual layer (RL) and the nocturnal boundary layer (NBL), and thereby measure eddy diffusion coefficients in the top half of the NBL. The average depth of the NBL observed on the 12 pairs of flights was 210 (± 50) m. Of the average -1.3 ppb h loss of the Ox family (here [Ox]  [O3] + [NO2]) in the NBL during the overnight hours from midnight to 06:00 PST, -0.2 65 ppb h was found to be due to horizontal advection, -1.2 ppb h due to dry deposition, -2.7 ppb h to chemical loss via nitrate production, and +2.8 ppb h from mixing into the NBL from the residual layer overnight. Based on the observed gradients of Ox in the top half of the NBL these mixing rates yield eddy diffusivity estimates ranging from 1.1 – 3.5 m s that are found to inversely correlate with the following afternoon's ozone levels, and provide support for our hypothesis. The diffusivity values are approximately an order of magnitude larger than the few others 70 reported in the extant literature for the NBL, which further suggests that the vigorous nature of nocturnal mixing in this region due to the LLJ has an important control on ozone. Additionally, we investigate the synoptic conditions that occasion strong nocturnal jets and find that on average, deeper troughs along the California coastline are associated with stronger jets. The LLJ had an average height of 340 m, an average speed of 9.9 m s (SD = 3.1 m s ) and a typical peak timing around 23:00 PST. Seven years of 915 MHz radio-acoustic sounding system and surface 75 air quality network data show an inverse correlation between the jet strength and ozone the following day, suggesting that air quality models need to forecast the strength of this nocturnal feature in order to more accurately predict ozone violations.


Introduction 80
Under typical fair weather conditions over the continents, thermals are generated near the surface beginning shortly after sunrise, forcing a convectively mixed layer, known more generally as the convective atmospheric boundary layer.
As solar heating of the Earth's surface increases throughout the day, this layer reaches its maximum height by late afternoon, typically between 700 and 900 m in California's central valley during summer months (Bianco et al., 2011;Trousdell et al., in preparation).Around sunset, when the solar heating of the surface ends, the convective thermals 85 are cut off and can no longer power turbulent mixing in the boundary layer.The result of the radiative cooling of the ground throughout the night forms a stable, nocturnal boundary layer (NBL) near the surface, typically extending between 100 and 500 m (Stull, 1988).The convective layer from the daytime, after spinning down and no longer actively mixing, functions as a residual reservoir for pollutants and other trace gases from daytime emissions and photochemical production.This layer overlying the NBL is known as the residual layer (RL).

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During both daytime and nighttime, mixing can occur between the boundary layer and the layer of air above.In the daytime, this process of entrainment is driven by convective thermals that penetrate into the laminar free troposphere, which then sink back into the convective layer, and may be augmented by wind shear near the top of the boundary layer (Conzemius and Fedorovich, 2006).Entrainment has been shown to be a significant factor for surface pollution, and more generally scalar budgets, as the two interacting layers usually have different trace gas concentrations 95 Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.(Lehning et al., 1998;Trousdell et al., 2016;Vilà-Guerau de Arellano et al., 2011).At night, another type of gas exchange can occur between the aforementioned stable boundary layer and the residual layer by shear-induced mixing.
Extensive observations of the structure of the NBL indicate that a localized wind maximum near the top of the stable layer, known as a low level jet (LLJ), is often present (Banta et al., 2002;Garratt, 1985;Kraus et al., 1985).This low level jet is able to drive sheer production of turbulence in an intermittent, cyclical manner, powering the mixing 100 between these layers.In stable air, wind sheers are able to build in the presence of dynamic forcing due to a lack of vertical momentum transport.Once the wind shear is great enough to produce turbulence, the momentum is mixed out vertically, which reduces the shear, and the cycle restarts (Van de Wiel et al., 2002).
California's complex terrain amplifies the challenge of both studying and managing air pollution in this area.The main source of air for California's Southern San Joaquin Valley (SSJV) is incoming maritime flow from the San 105 Francisco Bay area, which gets accelerated toward the southern end of the valley as a consequence of the valleymountain circulation (Rampanelli et al., 2004;Schmidli et al., 2010).The local sources of ozone are scattered along this primary inflow path to the SSJV.The ozone buildup in the SSJV results from both the large amount of local upwind sources and the Tehachapi Mountains to the south which block the flow, preventing advection out of the region (Dabdub et al., 1999;Pun et al., 2000).Because of this tendency for the air to stagnate, both daytime and 110 nocturnal vertical mixing is important in the phenomenology of ozone pollution in this area.
The LLJ in the SSJV is known to contribute to the formation of a commonly observed late night and early morning mesoscale wind feature known as the Fresno Eddy, which can drive both vertical mixing and regional horizontal advection.The aforementioned daytime northwesterly valley wind continues into the late evening, decoupling from the surface and forming a nocturnal jet (Davies 2000).The Tehachapi Mountains act as a barrier to the jet if the Froude 115 number is lower than about 0.2 (Lin and Jao, 1995).The eddy feature is formed during the hours before dawn when this northwesterly flow interacts with southeasterly nocturnal downslope flow coming from the high southern Sierra Nevada Mountains, although there is some question as to the extent to which the southeasterly flow observed in the morning hours is merely the result of a topographic deflection and recirculation of the nocturnal jet.The Coriolis force helps to circulate this flow; however, a mesoscale low is not thought to develop (Bao et al. 2007, Lin andJao, 1995).

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It is worth noting that the valley flow peaks shortly after sunset, while the katabatic drainage flow peaks shortly before dawn, so these two components of the Fresno eddy are not time-coherent.The initial northwesterly wind and a low Froude number are both critical for determining whether or not the eddy will form on a given night (Lin and Jao, 1995).Monthly averaged wind speeds from June through August of the low level jet near the Fresno eddy up to 12 m s -1 have been reported (Bianco et al., 2011).Beaver and Palazoglu (2009) found that ozone pollution potential in the 125 central San Joaquin Valley is particularly high on days where the preceding nocturnal Fresno Eddy is strong, even when strong ventilation is occurring.They also found that the early morning downslope flow through the Tehachapi pass is a strong predictor of ozone pollution potential in the SSJV.
At the core of our observational method, we acknowledge that most scalar budgets are driven by horizontal advection, vertical mixing (primarily entrainment), and local emissions/uptake and net production (including chemical gains 130 and/or losses).Conley et al. (2011) andFaloona et al. (2009) have shown that on any given day, advection can be a relatively large and significant term in the daytime scalar budget.However, when averaged over numerous flight days, the advection is often close to zero.Similarly, for ozone budgets in particular, net photochemical (production minus destruction) of the species has been shown to be a major component of the terms in the budget equation (Conley et al., 2011;Lehning et al., 1998;Lenschow et al., 1981;Trousdell et al., 2016).The nocturnal ozone chemistry is driven 135 primarily by its reaction with NO2 forming the nitrate radical.The nitrate radical can equilibrate with N2O5, react with VOCs, and rapidly react with NO (Brown et al., 2006(Brown et al., , 2007;;Wood et al., 2004).As we will attempt to show, the fate of the nitrate radical is highly uncertain and this plays an important role in the net overnight chemical loss of ozone.
Additionally, dry deposition of the chemical species of interest cannot be ignored (Conley et al., 2011;Faloona et al., 2009).

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While the aforementioned studies focused on daytime scalar budgets, to our knowledge, no attempts have been made at nocturnal scalar budgets using aircraft data.One central goal of this paper is to introduce a method for nocturnal scalar budgets, applied to flight data, in a similar manner to that of the daytime scalar budgets.The application of the results of this method will test a hypothesis that more nighttime mixing between the residual layer and stable boundary layer, induced by wind-shear turbulence beneath a strong low level jet, will effectively "deplete" ozone in the residual 145 layer, making less available to fumigate the following morning and seed further photochemical production.
It has been previously shown that residual layer ozone can have a substantial correlation with ground-level ozone the following day (Aneja et al. 2000;Zhang and Rao, 1999).Neu et al. (1995) estimated that about 75 % of the contribution to the difference in afternoon ozone concentrations from one day to the next is from residual layer depletion.This study was done in complex terrain of Switzerland and primarily used SODAR data.They also found a strong 150 correlation (r 2 = 0.74) between weaker turbulence in the RL, inferred from the amount of time the wind maximum at night was below 150 m, and this ozone difference.Coupling of the RL and NBL via intermittent turbulence has also been shown to correlate with ozone spikes at ground-level monitoring stations (Salmond and McKendry, 2005).
Because of the complexity of intermittent nocturnal turbulence, the spatial and temporal distributions of these spikes are unknown, and thus it is not known the extent to which these ozone spikes help to deplete the residual layer ozone 155 or contribute to the following day's ozone.One advantage of our study is that we are using airborne data to sample a large area, which overcomes the limitations of studies using ground monitoring stations that may be influenced by the intermittent bursts of turbulence and confounded by uncertain horizontal advection.
A study from southern Taiwan also found that residual layer ozone plays an important role in the following day's ozone concentrations, with fumigation of this ozone into the developing daytime boundary layer accounting for 19 % 160 of the variance (Lin 2012).As the ozone problems in this area are not heavily driven by local sources, a more extensively mixed daytime boundary layer can in fact contribute to a buildup, rather than ventilation, of ozone, because the daytime intrusion into the formal residual layer outcompetes the local production.This, and the fact that many ozone forecasts currently made only take into account local daytime boundary layer dynamics, highlights the need for studying the effects of residual layer ozone in more areas that have ozone problems.Winds are measured using a Duel-Hemisphere Global Positioning System combined with direct airspeed measurements, as described in Conley et al. (2014).The winds are measured at 1 Hz, and the power spectra is observed to fit the Kolmogorov Scaling Law within the inertial subrange (approximately from 0.12 -0.5 Hz in the daytime 190 convective boundary layer corresponding to roughly 150 -600 m spatial scales).At night, the -5/3 slope is observed from 0.02 -0.5 Hz (Fig. 1), corresponding to length scales of 150 -3700 m, the largest of which are likely contributions from buoyancy waves.This is evident by the calculated Brunt-Väisälä frequencies (Fig. 2), which have an average value of 0.023 Hz in the NBL.For simplicity sake, we consider anything smaller than this buoyancy frequency to be "turbulence", and use 1/NBV ~ 50 seconds to be the sampling time to observe wind variances, though 195 we recognize that this cutoff is somewhat arbitrary.The turbulent kinetic energy (TKE) is estimated by correcting the observed wind variance of a given detrended 50-second signal with the integrated nocturnal power spectra beyond the Nyquist frequency (0.5 Hz) using a -5/3 extrapolation, which indicates that approximately 11 % of the total variance is not directly captured by the system.Only horizontal winds are measured, thus similarity assumptions are required to estimate vertical wind variance (σw 2 ).While some similarity relationships have been reported for the stable 200 boundary layer (Nieuwstadt, 1984), we were not able to measure the governing parameters.However, Banta et al. (2006) reported a meta-analysis of stable boundary layer studies with an average σw 2 /σu 2 of 0.39, where σu 2 is the streamwise variance.We applied this correction to our TKE measurements to account for the missing vertical wind variance.
205    Here we aim to test the importance of the aforementioned nocturnal mixing on the ozone budget in this region by applying a scalar budgeting technique to the aircraft data in order to estimate an eddy diffusivity between the stable boundary layer and the residual layer.This objective aims to use a similar method that has been presented with daytime scalar budgets (Conley et al., 2011;Faloona et al., 2009;Trousdell et al., 2016) to further demonstrate the overall 240 practicality of this methodology.Analyzing such budgets allows one to answer the critical questions regarding what is ultimately giving rise to the observed pollutant levels in a fixed area.
The nocturnal budget equation is formulated by the Reynolds-averaged conservation equation for a scalarin this case Oxin a turbulent medium.Ox is defined here as NO2+O3 in order to avoid the effects of titration of O3 by NO.
If not depleted by chemical oxidation to NO3 and further reaction products, NO2 will photolyze the following day to 245 reproduce ozone in photostationary state, so it can act as an overnight reservoir of ozone.The chemical loss of Ox is then tracked by the reaction between O3 and NO2 to form nitrate, but its ultimate fate will affect the overall Ox loss.
In the stable nighttime environment we will treat the mixing between the RL and NBL by using an eddy diffusivity.
The NBL Ox budget can thus be represented as:

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Where the term on the left represents the change in concentration with respect to time within the flight volume.The leftmost term on the right side of Eq. 1 represents the net loss of Ox due to chemical reaction of the resultant NO3 and contains an unknown constant of proportionality, , which depends on the subsequent reaction pathway of NO3, and can range from 0 -3.For reasons later discussed,  is assumed to be ~ 1.5 for this analysis.The next two terms represent changes due to advection by the horizontal wind, followed by terms representing the dry deposition of ozone

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to the surface, and finally the vertical turbulent mixing term that uses the vertical gradient and the eddy diffusivity, Kz a number that encapsulates the strength of the overnight mixing.The storage term, chemical loss, advection, surface ozone, and stable boundary layer height can be calculated using the aircraft data.Combining those measurements with an estimated 0.2 cm s -1 dry deposition velocity of ozone (Padro, 1996), we can indirectly estimate Kz.Profiles of wind speed, potential temperature, NO2, and O3 from each night and morning flight were analyzed to make a best guess of the NBL height, h. Figure 4 shows the average scalar profiles from all 15 late night flights to illustrate the typical gradients in the lower portion of the atmosphere.One method of determining h is to observe the lowest 265 point where ∂θ/∂z becomes close to adiabatic, as the layer below that physically represents air that is in thermodynamic communication with the radiatively cooled surface (Stull, 1988).Another method is to use the level of wind maximum, or LLJ height, when one is present.The drop in momentum above the jet is similar to the jump in other scalars (humidity, methane, etc) often observed at the top of either the NBL or daytime atmospheric boundary layer.In our case, the vertical jump (or sharp gradient) of Ox in this height region should be considered, as this likely points to a 270 region of maximum mixing.A blend of these three methods was ultimately used for both the late night and corresponding morning flight to determine an average h for each night.All of the aforementioned factors lead to an estimated uncertainty of ± 100 m for all of the NBL heights obtained.The average conditions from the late night and morning flights are presented in Table 1.The height of the stable boundary layer for each night (h) was used as the upper altitude limit when averaging observations to obtain advection, chemical loss, and time rate of change (storage) terms for the budget equation, since the budget equation is meant to be applied to the NBL.

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Both NO2 and NO3 are able to regenerate ozone in the presence of sunlight and participate in the same sequence of reactions, which are grouped together into a family referred to as odd oxygen (Ox).Ox is usually defined as O3+NO2+2NO3+3N2O5 (Brown et al., 2006;Wood et al., 2004); however, since we were unable to measure the higher oxidation state NOy species, we will define Ox as O3+NO2, by far the dominant species.Considering Ox is useful in 290 this case because the family is conserved in the rapid oxidation of NO by O3 (R1), yielding NO2 that is quickly photolyzed back to O3 once the sun rises as part of the standard daytime photostationary state.
Aside from dry deposition to the Earth's surface, NOx chemistry is the main loss of ozone at night, counteracting its role in production during the daytime (Brown et al., 2006(Brown et al., , 2007)).The chemical loss of ozone at night begins with the production of the nitrate radical (R2): 295 NO3 photolyzes rapidly once the sun rises, so the ultimate net loss of ozone depends on the loss of nitrate in the dark.

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The loss occurs mainly via three general channels.In one channel, dinitrogen pentoxide is formed (R3), which has a If the hydrolysis of N2O5 (R4) is the dominant NO3 sink, then the net reaction leads to a loss of 3 Ox molecules per nitrate produced (R2).However, if the dominant loss is reaction with VOC's (R5) then the net reaction leads to 2 Ox molecules lost per R2.And if there is sufficient NO, R6 will dominate the nitrate loss leading to no net Ox loss.
Reaction (R6) has often been ignored at night under the presumption that local sources of NO are sparse and reaction (R1) will outcompete reaction (R6) (Brown et al., 2007;Stutz et al., 2010); however, at 30 ppb of O3 and 20 ppt of

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NO3 the lifetimes of NO to (R1) and (R6) are nearly equivalent (~80s).Our measurements indicate ground-level NO of about 0.6 ppb at midnight (SD = 1 ppb), corroborated by the surface air quality network, increasing in the early morning hours to 2-4 ppb.However, these values may be biased high relative to the regional average because the aircraft flew low approaches near California Highway 99 and other urban centers (Fig. 3).Nevertheless, the rate of reaction (R6) is 2.6 x 10 -11 cm 3 s -1 molec -1 (Sander et al., 2006), extremely rapid relative to the others, such that even 325 60 ppt of NO, an order of magnitude lower than our measurements, results in an NO3 lifetime of only 25 seconds.
There is then a further question as to whether any VOCs would be able to compete with this channel of NO3 model, the expected lifetime of NO3 can be estimated using the second-order reaction rate for (R2) for the formation of the nitrate radical, and combining all of the loss channels into a single lifetime (τNO3): (2) Using the average NBL ozone and NO2 from Table 1, a NO3 concentration of 10 ppt would imply its lifetime to be about 25 seconds, which is about twice as large as our estimate from Table 2. Out of respect for these direct measurements of NO3, our lifetime calculations likely represent a lower bound and further illustrate the uncertainty

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given the sensitivity to the unconstrained VOCs and our NO measurements, which have an envelope of error that spans a large range of possible nitrate loss lifetimes.With longer lifetimes of nitrate loss with respect to the VOC and NO channels, we are faced with the possibility that hydrolysis of N2O5 is also an important loss channel, increasing the amount of Ox molecules lost per nitrate molecule formation in (R2).Smith et al. (1995) report that the lifetime of NO3 was found to be highly dependent on relative humidity, with lifetimes ranging from seconds to 10 minutes when 350 the relative humidity is above 45 % (presumably due to N2O5 hydrolysis), but between 10 and 60 minutes when below the 45 % threshold.Figure 5 shows the diurnal cycle of temperature and relative humidity observed at the airports in our flight region during the days of our campaign, compared with the 2015-2016 1 June -30 September averages.
The > 45 % relative humilities observed at FAT and VIS imply that the hydrolysis of N2O5 is an important sink for NO3.Given the obvious importance of the nitrate loss to VOCs and NO, but some importance of the N2O5 hydrolysis,

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we use a best estimate that each effective collision of NO2 and O3 will lead to the net loss of approximately 1.5 (0.5) molecules of Ox from the net effects of the entire series of reactions outlined above.This is a "center of the envelope" estimate for the possible range of 0 -3, and best accounts for the lack of certainty as to which (if any) nitrate loss channel is dominant.Although our measurements are unable to constrain this coefficient, the ultimate fate of the nitrate radical can be seen to have a very important role in quantifying the net loss of Ox overnight, and without a 360 greater understanding of the nitrate budget, predicting this loss rate is highly uncertain.(3) Where α can range from 0 -3, and per the discussion above, is estimated to be 1.5 ± 0.5.To estimate a value for the second order rate constant (kO3+NO2), we start with the temperature dependent function for this reaction (Sander et al., 2006): Where T is the temperature in Kelvin.For the domain being analyzed, an instantaneous value of kO3+NO2 is determined at each data point.These values of kO3+NO2 are then averaged to obtain a constant value for the given night.It should be noted that small errors in the value of k that would be within the order of our temperature fluctuations were found to not have a measurable impact on the chemical loss term.To estimate the chemical loss of Ox, the initial 20 m altitude bins for NO2 and O3 are taken from the late night and morning profiles.In each bin, the concentrations are

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linearly interpolated between the late night and morning values, so that there is an estimation of the current average concentration within that bin at every time during the night.

Horizontal Advection by Mean Wind
Advection is calculated by first collecting all 1-second Ox data points for the late night and morning flights separately.
A multiple linear regression is fit through the Ox data for latitude (y), longitude (x), and altitude (z), allowing Where u is the mean x-component (zonal) wind and v is the mean y-component (meridional) wind.The same procedure is repeated for the morning flights, and the advection terms from the late night and morning flights are averaged 395 together.

Dry deposition of Ox
Deposition of ozone is presumed to be the main sink of Ox at the surface, the flux of which can be parameterized as the product of the surface ozone values (measured directly from the aircraft) and the deposition velocity for ozone.
There are reports of ozone deposition in the area of this field campaign from a 1994 study using the eddy covariance 400 technique (Padro, 1996).The findings of their study suggest nocturnal ozone deposition velocities are a few times smaller than the daytime counterpart, but still important for the budgeting technique presented here.Results from a European field study in a similar environment corroborates this finding (Pio et al., 2000).We thus estimate a dry deposition velocity of 0.2 cm s -1 ± 0.1 cm s -1 for ozone at night in these agricultural regions based on these, as well as other (Pederson et al., 1995;Meszaros et al., 2009;Neirynck et al., 2012;Lin et al., 2010) We purposefully ignore NO2 deposition on the basis that crop canopies can be either a small source or sink of NO2 at the surface (Walton et al., 1997).The amount of Ox lost overnight due to deposition would be within our stated uncertainty (± 0.86 ppb h -1 ) as long as |vd NO2| < ~ 2.5 cm s -1 .

Vertical Turbulent Mixing between the NBL and the RL
Finally, a vertical flux divergence for Ox must be estimated, which is represented by the last two terms in Equation 1.

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For the top part of the stable boundary layer, the flux of Ox can be interpreted as an eddy diffusivity (Kz) multiplied by the vertical gradient of Ox between the NBL and RL.A linear regression is used to determine the Ox gradient (∂[Ox]/∂z) in the upper portion of the NBL that appeared to contain the strongest gradient.The layers used for the regression fit were 100 -200 m thick and did not extend below 70 m AGL on any given night to avoid capturing the region where the Ox sink due to surface deposition is likely to account for the vertical gradient (Fig. 6).The eddy 415 diffusivity can now be solved for with all of the other terms estimated.Results of the scalar budget analysis for all 12 paired flights are presented in Table 3.An error propagation analysis is presented for each term in the budget, as well as for the ultimately calculated Kz values.

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Table 3. Results from the nocturnal scalar budget for all terms.Estimated error in parenthesis.
Of note is the fact that on average the chemical loss is expected to be a little more than twice as large as the physical loss from dry deposition.Another way to frame that is as competing timescales of ozone loss in the NBL: for dry deposition the average lifetime of ozone is 28 h (200 m / 0.002 m s -1 ), and for chemical loss it is 12 h.Further, both losses of Ox added together are about double the observed time rate of change, and thus the physical and chemical 435 losses are partially compensated by vertical mixing.Because the RL consistently contains more ozone than the stable NBL, turbulent mixing will result in a transfer of ozone into the NBL.While NO2 is observed to be higher in the NBL than in the RL (by about 3-5 ppbv), it is a much smaller contribution to the Ox (O3 is less by anywhere from 10-20 ppbv.)Thus, vertical mixing at the top of the stable boundary layer, influenced by the strength of the LLJ, is inherently a source term of Ox to the lower NBL.It is also worth noting that the chemical loss of Ox does not vary significantly 440 between the RL and NBL because the increase of NO2 in the NBL is compensated by the decrease of O3, although this assumes that there are not other chemical differences that alter the ultimate reaction fate of nitrate (altering the coefficient in Eq. 1.)

Error Analysis
The storage term error is computed by first taking the standard deviation of 1-second ozone measurements divided by for both the u and v components of wind.To compute the chemical loss error, the large uncertainty of the α coefficient 450 must be taken into consideration.Based on our analysis concluding that all channels of nitrate loss are probably nonnegligible, we infer that α is between 0.5 and 2.5 with a 95 % confidence interval.Thus, one standard error for the α coefficient is about 0.5.An error propagation is then carried out for each 20 m altitude bin, using the standard deviations of the O3 and NO2 measurements divided by the square root of the sample size.As previously stated, the estimated standard errors of the stable boundary layer height and surface deposition of ozone are conservatively taken 455 to be 100 m and 0.1 cm s -1 , respectively.The surface ozone standard error is computed as the standard deviation of the aircraft measurements divided by the square root of the sample size, and the vertical Ox gradient uncertainty is computed by the standard error of the regression slope.The uncertainties in the vertical mixing, deposition, and diffusivity values can then be computed by standard error propagation.The resultant relative error estimates of the nighttime diffusivities are about 50 %, and errors of this order seem reasonable based on a technique that assumes the 460 closure of 4 independently measured terms.Past studies using similar airborne budgeting methods have estimated relative uncertainties ranging from 15-75 % (Conley et al., 2011;Faloona et al., 2009;Kawa & Pearson, 1989;Trousdell et al., 2016).

The Fresno Eddy and Low-Level Jet
One complicating factor that remains for this particular analysis is the presence of the Fresno eddy and its influence 465 on our measurements of advection.If an eddy is recirculating a scalar quantity, using a simple linear fit model as we did to estimate advection would be questionable, especially if the flight area only covered a small portion of the larger mesoscale circulation.Figure 4 of Zhong et al. (2004) shows that at night, the northwesterly low level jet is formed in the San Joaquin Valley, and a weak katabatic southerly flow is observed in the foothills to the east at the Trimmer site.As the night progresses, the eddy becomes more coherent as the northwesterly jet relaxes while the southerly 470 flow strengthens and expands westward.After daybreak, the eddy appears to deform and disintegrate with much of the SSJV experiencing a strong southerly wind.
This pattern is roughly consistent with our aircraft observations.An analysis of the average wind vectors and their consistency for all nocturnal and morning flights in the approximate stable boundary layer (0-300 m AGL) and residual layer (300-700 m AGL) are shown in Figure 7.The wind consistency is defined as the ratio of the vector-averaged

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wind speed to the magnitude-averaged wind speed, with values close to 1 indicating a consistent wind direction (Stewart et al., 2002;Zhong et al., 2004).The nocturnal low-level jet can be seen clearly to fill most of the SSJV in both the NBL and RL.In the morning residual layer level, there is localized consistent southerly flow closest to the foothills, some of which may be regarded as surprisingly strong.The lower level winds in the morning are consistent with the deformed eddy.We note that caution should be exercised in directly comparing our flight data to the analysis 480 from Zhong et al. as our flights specifically targeted high ozone episode events, which we based primarily on high temperature stagnation conditions, so they may be subject to a meteorological bias (see Fig. 5).
From this analysis we conclude that it is likely that our dataset captures the bulk of the dominant flow (and thus advection) on both the late night and morning flights, which are averaged and interpolated.It is noted that the average advection term for the 12 nights presented is -0.24 ppb h -1 , which is nearly an order of magnitude smaller than the 485 chemical loss and storage terms.The small average contribution from advection is consistent with previous findings from daytime scalar budgets performed over the oceans (Conley et al., 2011;Faloona et al., 2009) and in the SJV (Trousdell et al., 2016) and what might be expected in the presence of a recirculating eddy.Lastly, it is noted that Since the low-level jet is hypothesized to contribute to the variability of ozone, we explored some of the possible contributing meteorological factors that are absent in the current literature.Seven years of data (2010-2016) from the 495 915 MHz sounder located in Visalia, CA, is compiled to obtain the low-level jet speed and the height at which it was observed.For this analysis we define the nocturnal low-level jet speed as the maximum hourly-averaged wind speed observed below 1000 m in 100 m bin space from 23 PST to 7 PST, specifically during the summer months (defined here as 1 June -30 September).The 1000 m cutoff is used to ensure that the wind maximum that is captured is related to the LLJ at the top of the NBL rather than free-tropospheric wind.Using this definition, the low-level jet had an 500 average height of 340 m, an average speed of 9.9 m s -1 (SD = 3.1 m s -1 ) and a typical peak timing around 07 UTC.
The 700 mb level corresponds to approximately 3000 m, well above the Pacific Coast Range but approximately in line with the top of the Southern Sierras.To analyze variability of the jet strength, daily average synoptic charts from the North American Regional Reanalysis (NARR) are created for days when the low-level jet strength was less than 7 m s -1 (N=147 nights), and greater than 12 m s -1 (N=165 nights).Both the strong and weak low-level jets show a climatological trough pattern, but it is situated about 100 km to the east for the strong cases.We also note that the pressure gradient is at least twice as strong for the stronger low-level jets, and that the synoptic pattern of the weak jets favors southerly geostrophic wind aloft, which directly opposes the up-valley northwesterly thermally driven flow.We also note the positive correlation found between the LLJ strength and the upwelling index (Fig. 10), which is primarily driven by the North Pacific High, which when strong, acts to 510 push the trough farther eastward as seen in Figure 8.These findings are consistent with the Lin and Jao (1995) modeling study where the Fresno Eddy did not form when the synoptic flow over the coastal range was westerly.Beaver and Palazoglu (2009) found that maximum daily 8-hour average ozone (MDA8) exceedances were more frequent in the central and southern San Joaquin Valley when an offshore ridge or onshore high were present, consistent with Figure 8 (right).The results of our study suggest that this may be at least partially explained by the 515 presence of a weaker LLJ under those conditions.It is important to note that the LLJ and Fresno Eddy are not exactly the same thing, rather, the LLJ is part of the northwesterly flow that is an important precursor to the Fresno Eddy.
When the eddy is present, the LLJ is essentially the strongest branch.Nevertheless, Beaver and Palazoglu (2009) conclude that recirculation from the Fresno Eddy contributes to a buildup of ozone, while we conclude that a strong jet may lead to lower ozone.Future research may attempt to further establish the degree to which the LLJ and Fresno

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Eddy are linked, as well as which of these two nocturnal mechanisms will dominate the ozone budget under different synoptic conditions.As a provisional compromise, we suggest that the Fresno Eddy, when present, will act to recirculate pollutants regardless of the strength of the LLJ.That is, a stronger eddy will not recirculate pollutants any more than a weaker eddy will.Thus, the optimal nighttime dynamics for ozone pollution the following day may consist of a Fresno Eddy just coherent enough to effectively recirculate pollutants, but without its strongest branch too strong 525 as to deplete the RL ozone by vertical mixing.
In addition to synoptic forcing, slightly lower surface temperatures across the entire region during stronger low-level jets are observed.This could either be a consequence of the synoptic flow (southerly geostrophic flow will generally result in warmer temperatures) or itself be an underlying precursor to the LLJ (a colder delta region will lead to more up-valley thermal forcing resulting in stronger winds that decouple from the surface at night).The higher temperatures    proposed that mixing induced by nocturnal jets may decrease ozone levels the following day (Hu et al., 2013;Neu et al., 1995).Greater coupling between the NBL and RL could reduce the amount stored in the RL reservoir rendering cleaner air the following day.The relationship between the eddy diffusivity values found in this study and surface

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ozone is analyzed, and serves as both an additional check on the relative validity of the calculated Kz values as well as a test of this proposed hypothesis.
The thermals generated by solar heating after sunrise initiate a fumigation process where as the daytime boundary layer develops, the ozone that was in the RL will be mixed downward.The change in surface ozone concentration troposphere, which is also a generally stable environment, and found a general range of 0.3 -3 m 2 s -1 .Pisso and Legras (2008) estimated diffusivities of about 0.5 in the lower stratosphere during Rossby wave-induced intrusions of midlatitude air into the subtropical region.A modeling study by Hegglin et al. (2005) reports diffusivities of 0.45 -1.1 630 m 2 s -1 in the lower stratosphere with an average Brunt-Väisälä frequency of 0.021 Hz, indicating a similar environment to ours.Finally, Lenschow et al. (1988) analyzed flight data in the NBL over rolling terrain in Oklahoma, and found eddy diffusivities for heat (Kh) of ~0.25 m 2 s -1 for the upper half of the NBL, and ~1 m 2 s -1 for the lower half.To our knowledge, this is the most comparable observational finding within the NBL to our range of diffusivities.
Nevertheless, the variability of these reports leads to the inevitable conclusion that vertical diffusivity in very stable 635 environments is poorly understood, and further research is necessary to illuminate its phenomenology.More specifically, while it is possible that the diffusivity measurements in this study are slightly large, it is also possible that the LLJ and other mesoscale wind features of the complex terrain account for stronger nocturnal mixing in the SSJV compared to other stable environments.
Lastly, we estimate the Bulk Richardson number (BRN) on each late night flight within the NBL, using 100 meter 640 bins to estimate wind shear.A range of Richardson numbers between 0.23 and 1.34 is obtained, and the estimates are seen to have a negative relationship with eddy diffusivities, as expected (Fig. 15).While the relationship is not strong, it is important to remember that both parameters are noisy estimates.The time series of all late night flights was scanned for any period where 1) the aircraft maintained an ascent (or descent) rate of at least 1.4 m s -1 , and 2) during a given elevation span of 100 m, a virtual potential temperature decrease with height was observed.The process was repeated for a thickness of 50 m.

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The locations of the layers detected, along with their elevation and magnitude, is shown in Figure 16.One feature of note is that the layers appear to be more prominent over urban areas, such as Fresno, Visalia, and Bakersfield.This may lead one to suspect that some of these layers are driven by an urban heating effect, however, this seems unlikely as the unstable layers would have to extend upward beyond the NBL depth.It is perhaps more likely that this is an artifact of more flight time in those areas.Another feature worth noting is that more unstable layers are observed closer 660 to the Tehachapi pass.One possible explanation for this is that the katabatic flow down the mountain slopes detrain along the way and are carried over the valley by local advection before mixing with surrounding air.Given that these layers are found from near the bottom of the residual layer all the way up to 2.5 km, it is possible that they contribute to the overnight mixing of Ox from the RL to the NBL.Further research, both observational and modeling-based, is needed to explore this possibility.The unstable layers are not seen to have more TKE than the rest of the atmosphere, and this may reflect the limitations of the method used to estimate turbulence from this low-cost wind measurement system.However, this finding is consistent with the study by Cho et al. (2003) which found no relationship between turbulence and static stability in 670 the free troposphere.Since the aircraft is moving horizontally a lot faster than it is vertically, it is possible that our observations reflect an artifact of localized temperature gradients that are more prominent in the horizontal dimension.
To check this, we plotted the wind quivers in the unstable layers along with the direction of the colder air.The cooler air was not systematically detected in any one direction, which supports the hypothesis that these are true vertical temperature gradients.

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To analyze the stability, wind shear, and turbulence from a climatological standpoint, a July-August 2016 composite of the 915 MHz Visalia sounder data is presented in Figure 17.Even in the climatological averages, some nocturnal unstable layers are detectable between 500 and 1500 m.

Conclusions
We have demonstrated a method for performing a nocturnal scalar budget analysis using aircraft data, and applying it to estimate the effects of turbulence in the stable boundary layer which can be related to air quality problems.
Inherently, eddy diffusivity estimates for any given night will have a large uncertainty due to the indirect nature of the measurement and the limited flight durations.However, the overall between-flight consistency and the correlations 685 with both the Richardson number and surface ozone suggest that this method is informative.We obtain eddy diffusivity values between 1.1 and 3.5 m 2 s -1 , which are slightly larger but approximately within the same order of magnitude of values that have been obtained from other studies in the free troposphere, lower stratosphere, and nocturnal boundary layer.The obvious limitation in our study is the lack of sample size, with only 12 overnight flight pairs being conducted.However, we believe it demonstrates the importance of synoptic and mesoscale features at 690 night within the context of high ozone episodes, and the utility of this type of focused flight strategy.
The larger set of soundings and surface network data establishes a correlation between low level jet speed and the maximum 1-hour ozone the following afternoon for summertime months.Our limited aircraft dataset suggests a similar relationship, although in the former analysis, the low level jet is presumed to be predictive of mixing strength.
While the correlation is not very strong, explaining only about 17 % of the variance, it is an important link that may 695 have consequential implications for modeling studies and policy making.In particular, we note that 11 of 12 days where the Visalia ozone concentration exceeded 100 ppb was preceded by a low-level jet speed < 9 m/s.While we cannot infer a causal relationship between a strong low-level jet, stronger mixing, and reduced ozone pollution, we propose that a stronger LLJ leads to greater mixing, which helps depletes the ozone reservoir by bringing it into the stable boundary layer overnight, where it is subject to deposition to the surface, and that dry deposition rate may itself 700 Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.be partially modulated by the strength of the LLJ through reduced aerodynamic resistance.Subsequently, when thermals begin to form after sunrise the following morning, there is less ozone to fumigate downward.Of course, photochemical production of ozone as well as advection will play a major role in the ultimate daytime peak ozone levels observed.Other flights we performed in the Bakersfield area showed an average photochemical production as high as 6.8 ppb h -1 , with an average advection of -0.8 ppb h -1 , though on any given day advection tended to be more 705 comparable in magnitude to photochemical production (Trousdell et al., 2016).In that study we also have demonstrated that on days with very high ozone that pose hazards to human and agricultural health, the ozone abundance is dependent on elevated ozone in the mornings that serve to catalyze photochemical production through the afternoon.Future modeling studies may directly investigate these factors, which may help elucidate the causal mechanisms of high ozone events.

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We have also illustrated that the fate of the NO3 plays an important role in the nocturnal ozone budget, which consequently has impacts for the following days maximum ozone concentration.The loss of the nitrate radical at night can occur from N2O5 hydrolysis, reaction with VOCs, or a very rapid reaction with small NO concentrations.The lifetime of NO3 can range from seconds to several minutes depending on the dominant loss pathway, which affects the value of α.It is thus crucial to measure the lifetime of NO3 in future studies that analyze the NBL ozone or Ox 715 budget.

Figure 1 .
Figure 1.Power spectra for nighttime winds averaged over 309 5-minute samples.The average airspeed was 76.6 m s -1 .

Figure 2 .
Figure 2. Mean and standard deviation profile of Brunt-Väisälä frequencies for all late night flights.The mean value within the stable boundary layers is 0.023 s -1 .

Figure 3 .
Figure 3. Ground tracks of all flights of the Residual Layer Ozone project.Airports with low approaches and ground ozone monitors are shown.The ground network stations (blue crosses) used were Bakersfield-5558 California Avenue, Bakersfield-Municipal Airport, Clovis-N Villa Avenue, Edison, Fresno-Drummond Street, Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 4 .
Figure 4. Mean and ±1 standard deviation (swatches) of potential temperature, ozone, NO, NO2, and wind speed from all late night flights.
Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.Table 1.NBL heights, ozone, NO2, Brunt-Väisälä (BV) frequencies, Bulk Richardson Number (BRN), Turbulent Kinetic Energy (TKE), and LLJ maximum wind speeds observed during the late night / morning flight pairs.Maximum daily 8-hour average ozone (MDA8) values are from the following day and are an average of the 11 ground networks in our flight region.For the domain of interest, all measured NO2 and O3 data was averaged for each 20 m altitude bin in order to generate 280 mean vertical profiles of Ox.Separate profiles were created for the late night flight and the subsequent morning flight.

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extrapolated from information in references indicated so values here may not exactly match literature.

Figure 5 .
Figure 5.Diurnal plots of temperature and relative humidity during flight days of the Residual Layer Ozone campaign (individual days = grey lines, campaign average = blue lines), compared to 1 June -30 September 2015

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estimations for ∂[Ox]/∂x and ∂[Ox]/∂y in the horizontal advection terms.The total advection term within the NBL on a given flight is:

Figure 6
Figure 6 shows an example of the observed profiles of Ox on the late night and morning flights, for the series performed on 2016-06-04.The height of the NBL is shown (green), and the lower bound of the layer used in the vertical gradient

445
the square root of the number of samples, then the standard error of the means for both the late night and morning profiles are combined.This analysis is carried out in 20 m altitude bins separately and then averaged together because there is more uncertainty at lower altitudes due to fewer measurements.The advection term error is computed from the standard error of the slopes of the regression fit, with errors propagating for each of the 4 advection components Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 7 .
Figure 7. Wind consistency for late night flights and morning flights in the NBL (0 -300 m) and the RL (300 -700 m).

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associated with the weak nocturnal jets may make for a twofold mechanism for high ozone: the high temperatures either causing increased photochemical production or resulting from increased meteorological stagnation, and a lack of mixing overnight induced by the low level jet causing less depletion of the RL ozone.It is worth noting that this relationship with temperature is only apparent with climatology, as ambient overnight low temperature at Visalia yields only a very weak relationship with the jet strength (r 2 = 0.035, p < 10 -5 ).535 Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 10 .
Figure 10.Upwelling index at 33° N as a function of low-level jet speed.Lastly, we present an analysis of the non-dimensional jet height climatology.It is seen that the jet is significantly lower during the summer.The cause of this is an active area of investigation, but here we speculate that this is due to

Figure 11 .
Figure 11.Seasonal variation of LLJ height in comparison with the previous daytime boundary layer height at Chowchilla.

Figure 12 .
Figure 12.Select scalar profiles and ±1 standard deviation from all late night flights.3.4.Vertical Turbulent Mixing and the LLJ The physical significance of mixing overnight in relation to the air pollution problem remains somewhat of an open

Figure 13 .Figure 14 .
Figure 13.Correlation between overnight eddy diffusivity and maximum daily 8 hour average ozone (MDA8) the following day.All values are averages of 11 CARB surface network stations that are within the flight region.In an effort to increase the sample size to better test this hypothesis, 7 years of low-level jet speeds obtained from the Visalia sounder is combined with the CARB surface network ozone monitoring site at Visalia N Church St (36.3325°N, 119.2908°W, 30 m elevation) for analysis.The low level jet, hypothesized to be the main contribution to the
During the late night flights in stable environments, the flight crew reported many patches of turbulence.While most of these subjective reports were during low approaches and thus likely attributable to wind shear between the LLJ and the surface, they noted that some patches corresponded with what appeared to be elevated mixed layers, i.e. layers of air where virtual potential temperature was observed to decrease with height.Understanding these anomalies may 650 guide future research toward a deeper phenomenological understanding of overnight mixing and turbulence in the SSJV.Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License. 665

Figure 16 .
Figure 16.Detected nocturnal elevated mixed layers with at least 50 meters thickness, with elevations shown.

Figure 17 .
Figure 17.Stability and wind quivers for Visalia 915 MHz sounder, 1 Jul 2016 -31 Aug 2016. 680 Gentner et al. (2014a)ction (R6) negligible for our study.An investigation into the faster VOC reactions with NO3 perAtkinson et al. (2006)andGentner et al. (2014a)is presented in Table2.The estimated lifetime of NO3 due to the VOC reactions in our analysis is 9.5 seconds, about four times the lifetime of NO3 with respect to the presence of 0.6 present DOAS measurements from 15 nights in July and August 1990 (their Figure6a) from a site 32 km southeast of Bakersfield suggesting that NO3 concentrations in the SSJV peak around 30 pptv within an hour or two after sunset 335 and plateau in the middle of the night around 10 ppt, then decline to zero by sunrise.The variability of NO3 reported in that study is high, with nocturnal values ranging from near zero to over 50 ppt.Under a simplified, steady-state Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-854Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 12 September 2018 c Author(s) 2018.CC BY 4.0 License.

Table 2 .
Estimations of VOC reactions with nitrate in the summertime nocturnal boundary layer for the SSJV.Reaction rates from Atkinson & Arey (1998), Table 2 & Atkinson (2006).Valley-averaged concentrations are