The arid weather experienced throughout most of California during the summer is under the weight of the prevailing Pacific High, centered near 35∘ N some 2000 km offshore (Fig. 1, bottom right), which blocks storm systems from hitting the state instead shunting them northward towards Canada. The domineering anticyclone also drives synoptic scale subsidence on its downwind flank over the region. A strong thermodynamic “lid” or temperature inversion is set up by the synoptic subsidence, which resists convective motions throughout the lower atmosphere, leading to the collaboration of stagnant horizontal winds, sunny skies, and reduced vertical mixing that is emblematic of ozone pollution episodes. The zonal pressure gradient and surface friction impel a degree of onshore flow (atmospheric Ekman transport) that is principally blocked by the coastal mountains. The low-level summertime airflow into the interior of the state is therefore restricted to the main break in the Coast Range near the San Francisco Bay area and is strengthened by the land–ocean thermal contrast, with air entering the Carquinez Strait just beyond the San Francisco Bay and diverging into the conjoined Sacramento and San Joaquin valleys that together make up the great Central Valley of California (Schultz et al., 1961; Frenzel, 1962; Hays et al., 1984; Moore el al., 1987; Zaremba and Carroll, 1999). This restricted airflow is the feedstock of the Central Valley air and is diverted north-northwest into the Sacramento Valley and southeast into the San Joaquin Valley as it abuts the tall Sierra Nevada. The SJV is flanked by three mountain ranges: the southern Sierra Nevada to the east, the Tehachapi Mountains to the south, and to the west the Pacific Coast Ranges, all limiting outflow and ventilation and leading to orographic stagnation and uplift towards the southern end of the valley. However, airflow at higher elevations over the valley air and surrounding mountains is entrained down into the valley boundary layer due to convective turbulent mixing during the daytime. It is precisely this mixing mechanism that is critical to understanding the setup and evolution of air pollution events in the valley, and what we set out to quantify in this study.

In the SJV a nonlinear superposition of flows dictates the observed winds. In addition to the synoptic forcing discussed above, there is a direct thermal forcing of the mountain–valley circulation with consequent up-slope flows inducing mesoscale subsidence over the central valley floor (Rampanelli et al., 2004; Schmidl and Rotunno, 2010). In the far southern end of the San Joaquin up-valley air is forced to converge as it runs into the steep topography of the Tehachapi Mountains. This low-level orographic convergence, which was shown in ABL wind data by Bianco et al. (2011), gives rise to mesoscale uplift especially pronounced at the cul-de-sac of the valley. Monthly composites of vertical velocity (omega) from the National Center of Environmental Prediction North American Regional Reanalysis (NCEP NARR) data set, averaged over the decade from 2004 to 2013, are depicted in Fig. 1. Upward motion is present across large swathes of the Central Valley during summer, likely due to orographic lift on the windward side of the Sierra Nevada range, but it appears especially strong in the southern end of the valley (Fig. 1) where the thermal valley wind and southern mountains augment the effect.

The complex mesoscale terrain plays a very important role in the valley atmosphere. The influence of topography on the thermally driven flow pattern arising from land–ocean contrast in the Californian Central Valley during the summer is discussed in Zhong et al. (2004). Their study employed the use of 22 wind profilers with radio acoustic sounding systems (RASS) to vertically probe the atmosphere. The authors suggest, based on temperature profiles in the lowest 800 m, that the mixed-layer height, which probably exceeds 1000 m a.g.l., slopes up-valley in the San Joaquin. Additionally, the thermally driven flow pattern frequently extends upward to 800–1000 m a.g.l. Bianco et al. (2011), investigating various factors influencing ABL height in the Central Valley, reported low-level convergence in the southern end of the valley, leading to increased ABL heights. They did so by looking at the difference in up-valley wind between two sites in the SJV: Chowchilla and Lost Hills. This is in contrast to sites to the north in the SJV which see a shoaling in the summer months, likely due to cold air advection from the coast, or subsidence induced from the valley flow (far from the valley's terminus at the Tehachapi Mountains), or possibly other causes such as land use, wherein different irrigation patterns may lead to a different partitioning of latent and sensible heat fluxes (Bianco et al., 2011). Our study corroborates the convergence in the southern end of the valley in that the NCEP NARR data set shows strong uplift at the southern extremity of the SJV, and that there is often an unmistakable decrease in wind speeds approaching the southern mountains observed by the aircraft winds (data not shown).

Seven flights from 16 January to 4 February 2013 were deployed across the San Joaquin Valley transverse to its axis with extensive vertical profiling of the ABL and the FT above it, in conjunction with the NASA DISCOVER-AQ California campaign (flight region 1, see Fig. 2). In each vertical profile up and down through the ABL we monitored the inversion height in addition to a suite of scalar measurements (ozone, water vapor, methane, horizontal winds, carbon dioxide, and temperature). In addition, on each profile we fly up through the ABL top in order to characterize the composition and thermodynamic properties of the FT. The second set of deployments was focused at the southern end of the SJV during the summer months, employing a slightly different flight strategy (flight region 2, see Fig. 2). Although vertical probing up and out of the ABL was similarly performed during this second experiment, a much greater emphasis was placed on the horizontal extent of the measurements in the direction of the mean ABL wind. The main focus of this campaign was to better understand the cause of the large number of ozone NAAQS exceedances in this region surrounding the small town of Arvin. To do so required a thorough quantification of the horizontal advection as well the entrainment flux of O3 (directly related to entrainment rates). Flights were targeted at O3 exceedance episodes with each of four deployments lasting 2–3 days spanning two summers (2013–2014) between June and September.

Our flight data were collected aboard a single-engine Mooney TLS, operated by Scientific Aviation, Inc. (http://www.scientificaviation.com), and piloted by one of the authors (Stephen A. Conley). The Mooney is outfitted with a 2B Technologies O3 monitor, a Vaisala HMP60 temperature and relative humidity probe, a modified Picarro 2301f Cavity Ring-Down Spectrometer (CRDS) to measure CO2, CH4, and H2O, and an Aspen Avionics PFD1000 flight display delivering pressure, altitude, true air speed, etc. Measurement of the horizontal wind is accomplished using a novel technique developed for easy and inexpensive deployment on a single-engine aircraft. Utilizing a dual GPS antenna to provide accurate airplane heading and a ground velocity by vector subtraction from true air speed (TAS), the horizontal wind is calculated – a technique outlined in Conley et al. (2014).

In order to support the objectives of the DISCOVER-AQ campaign by probing the boundary-layer dynamics near the northern edge of the domain, the aircraft was flown back and forth perpendicular to the valley axis approximately between the NASA profile stations at Fresno and Tranquility (Fig. 2). In the absence of making fast vertical wind measurements, we derive entrainment rates in a novel way using a complete scalar budget of the ABL height throughout each flight targeted from midday to late afternoon hours (usually 11:00–16:00 PST). The flight hours are specifically chosen to focus on the ABL dynamics after its initial, rapid growth through the residual layer in the mid-morning. The inferred entrainment rates derived from the ABL height-budget, are then used in all of the scalar budgets to reveal O3 photochemical production rates, surface latent heat fluxes, and regional methane emissions as residuals.

To study the processes that govern the evolution of the surface concentration of O3 during the summer months in the southern SJV in more depth, we performed an airborne experiment in collaboration with Scientific Aviation, Inc., targeting the vicinity of Arvin, California, during the summers of 2013 and 2014. Flying around and upwind of Arvin 3–7 h per day during each of the four 3 day campaigns, observations of wind, temperature, methane, water vapor, and ozone were used to measure the principal dynamical components of the total ozone budget: namely, advective up-valley transport within the ABL and entrainment mixing from above. By comparing these measured dynamical terms with the observed O3 rise throughout the region during the afternoon, and using a reasonable parameterization of dry deposition, the net photochemical production rate can be inferred. Consequently, the relative contributions of these processes to the resulting surface O3 concentration can be estimated for midday conditions, which are most important in determining whether an ozone exceedance of the NAAQS is reached. On one of the flights during the second deployment (15 August 2013) we additionally made NO2 measurements with a Los Gatos Research cavity enhanced absorption spectrometer. All flights, for both campaigns, targeted days with weak horizontal winds in the ABL because stagnation tends to accompany both wintertime PM2.5 and summertime O3 episodes.

Because it is not currently possible to accurately measure mean vertical wind speeds by aircraft, we resort to the NCEP NARR data set to estimate the mean vertical wind speed at the top of the ABL during each flight. NARR is an extension of the NCEP global reanalysis, and was created to provide long-term consistent climate data focused over the US at a regional scale. The model runs at 32 km resolution with 45 vertical layers providing data eight times a day with a reanalysis period from 1979 to 2015. More information about this reanalysis data set can be found at http://www.esrl.noaa.gov/psd/data/gridded/data.narr.html.

We make heavy use of the data collected by NOAA during 2008 from five 915 MHz radar wind profilers equipped with radio acoustic sounding systems distributed across the Central Valley and reported in Bianco et al. (2011). Briefly the radio signal backscatter is augmented in regions with strong fluctuations in temperature and water vapor as exists in the entrainment zone at the top of the ABL. The method of Bianco et al. (2008) uses not only the backscattered intensity, but further includes the vertical velocity variance and its spectral width to automatically select the ABL top throughout the day. The minimum gate height for these profilers is 120–140 m above ground, and their vertical resolution is 60 m. To evaluate the average ABL growth rates we simply subtract the mean height at 11:00 from the mean height at 15:00 and divide by the 5 h interval.

Quite often the growth rate of the boundary layer is interpreted as equivalent to the entrainment velocity, we, or volume flux of FT air into the ABL (Tennekes, 1973), assuming that there is no large-scale mean vertical wind. However, in most situations the ABL growth (dzidt) is actually determined by the difference of two distinct processes: the entrainment, which is considered to be driven by micrometeorological factors (viz. surface buoyancy flux, inversion strength, and possibly wind shear across the inversion), and the larger scale subsidence, W, in the lower FT just above the ABL, which is forced by synoptic flow patterns. we=dzidt-W. In a seminal paper on the effects of surface heating on the inversion height, Ball (1960) declared that there are several processes that counteract the tendency of entrainment to raise the inversion height. One is that “horizontal divergence in the lower layers, accompanied by subsidence at inversion level, may be sufficient to counteract the rise”, and the other is that the “inversion usually slopes upward along the trajectories and thus advection tends to lower the inversion at a fixed point”. To be even more precise then, we consider the total derivative of the ABL or mixed-layer height (zi) and expand it into the Eulerian derivative of ABL height and an advection term. The resultant zi budget equation leads to a relationship between the entrainment velocity, the observed local ABL growth rate, the mean advection of ABL depth, and the mean vertical velocity at the inversion height: we=∂zi∂t+U∂zi∂x-W. The first two terms on the right hand side of Eq. (2) are, in principle, easily observed by aircraft, while the last term has evaded careful measurement by aircraft or any other means (Lenschow et al., 1999, 2007; Angevine, 1997). While the sorties provided a sufficient number of ABL crossings to estimate the ABL growth rate with acceptable accuracy, there were generally not enough at different locations to capture an unbiased, two-dimensional gradient of the inversion height (second term on the right-hand side of Eq. 2). Consequently, we estimate the advection term using the gradient in ABL height as determined from the NCEP NARR data set in conjunction with the observed in situ mean wind (Fig. 3). The observations of zi indicate that the reanalysis data do not predict the absolute boundary-layer depth with great accuracy in the Central Valley. This is most likely due to the fact that the model does not treat the heavily irrigated agricultural land surface with any fidelity. Inspection of the surface latent heat fluxes in the model (data not shown) indicate unrealistically small values for a region with such fecund agricultural productivity. Nevertheless, we assume here that the reanalysis data do capture the gradients of ABL depth reasonably well. In fact, the gradients evinced in Fig. 3 are in rough accord with those reported in Bianco et al. (2011): for example, approximately 500 m difference across the lower ∼ 200 km of the southern SJV. The large-scale vertical mean wind, W, is derived from the NCEP NARR pressure velocity omega (ω=dpdt), and the surface pressure tendency neglecting horizontal pressure advection and assuming hydrostatic balance: W=1ρg×∂p∂t-ω. The pressure level from which to select the omega value was chosen using the hypsometric equation p2=p1×exp⁡-zi×gRd×T‾v, using an average observed ABL height, zi, an average ABL virtual temperature, T‾v, for the flight duration, the dry air gas constant Rd, and an estimated average surface pressure, p1, of 1010.5 mb for June–September, and 1020 mb for January–February.

The local pressure change is estimated by the surface pressure tendency using hourly data from several CARB (The California Air Resources Board: http://www.arb.ca.gov/aqmis2/metselect.php) meteorology stations in the area over the flight time. Throughout the afternoon during both seasons the valley experiences a fairly strong and consistent drop in surface pressure of approximately 0.6 mb h-1. Similar diurnal oscillations of surface pressure were found by Li et al. (2009) to be prevalent in deep mountain valleys of the western US. Although these pressure changes are large by synoptic standards, they are generally an order of magnitude smaller than the omega values.

Ultimately the estimation of the entrainment rate made by applying Eq. (2) to the aircraft measurements and reanalysis data is used to illumine the specifics of trace gas evolution by connecting it to their individual entrainment rates in each one's own budget equation. For example, the scalar budget of ozone in a well-mixed ABL can be mathematically represented as: ∂O3∂t=-U∂O3∂x+w′O3′s-w′O3′zizi+P. The first term on the left represents the observed temporal trend in a fixed region, the second term represents the advection (the influence of the mean wind, U, acting on the mesoscale gradient in the O3 field), zi is the ABL depth, the third term is the opposite of the vertical turbulent flux divergence, and P represents the net photochemical production (Conley et al., 2011). We use observations and/or estimates of the first four terms of Eq. (4) to solve for the net production rate of ozone. The surface flux, Fs, for a reactive species like ozone that is taken up in plant stomata is parameterized as the product of a deposition velocity, vdep and mean concentration, Fs≡w′O3′s≅-vdepO3. The entrainment flux, Fent, on the other hand, is due to the mixing in of free tropospheric air at the top of the ABL, and is commonly parameterized as the product of the entrainment velocity of Eqs. (1) and (2), and the concentration difference (or scalar jump) across the inversion interface at zi, Fent≡w′O3′zi≅-weΔO3FT-ABL. This relationship applies to all the scalars and thus the determination of we feeds into each budget equation.

The scalar jumps are diagnosed from vertical profiles made during each flight (see Fig. 8 for an example). From experience, we have found it best not to attempt its determination with an algorithm, and instead calculate the jump from each vertical profile directly by eye, comparing concentrations from approximately the top half of the ABL with the lowest ∼ 100 m of the FT, assuming that the scale of turbulent entrainment is limited by the stability of the temperature inversion (Faloona et al., 2005) to ∼ 50–100 m above zi. Errors in the jumps, estimated by the spread in the jumps and their approximate ambiguity, have been estimated to be ∼ 10-100 % of the observed jumps (Tables S2 and S3 in the Supplement). The scalar jump (ΔC(FT-ABL)) – with C representing a generic scalar such as ozone (O3), water vapor (q), or methane (CH4) – is usually negative for a compound with a surface source (e.g., water, methane, and ozone precursors), and a positive entrainment velocity holds for a turbulent boundary layer, which tends to grow at that rate in the absence of mean vertical wind (Eq. 1). Therefore, the sign of the entrainment flux is positive, and upward due to the entrainment dilution of FT air into the ABL – a downward flux of concentration deficit is equivalent to an upward flux.

In the absence of clouds and precipitation (in situ sources or sinks) the water vapor budget equation is even simpler than that for ozone (Eq. 4): ∂q∂t=-U∂q∂x+w′q′s+weΔqFT-ABLzi. During our flights the first, second, and fourth terms above are measured by the aircraft allowing for the observation of the surface flux of water vapor. And in an exactly analogous manner we can use the aircraft measurements of methane to infer the surface flux, or average emission rate, of methane in the region. The surface latent heat flux, LH, divided by the latent heat of vaporization, Lv, LHLv=w′q′s, was taken from the NCEP NARR data set, and found to significantly underestimate our estimates in the regions of interest. We then look to the reference evapotranspiration (ETo) at various sites throughout the Central Valley from the California Irrigation Management System (CIMIS). ETo comes from standardized grass or alfalfa over which the measurement stations are situated, and it includes loss of water from the soil and plant surfaces. Although agriculture is prevalent in the area of interest, it does not represent the entire land surface.

The airborne data measuring ABL growth rates are used to diagnose the entrainment rate by budgeting of zi as expressed in Eq. (2). The average ABL heights (dashed lines) and their midday growth rates (slopes of dashed lines with shaded regions representing ±1σ of the observed growth rates) are shown for all the flights in Fig. 4 and compared with the corresponding RASS data presented in Bianco et al. (2011). The Chowchilla site is 50 km upwind from Fresno, and the Lost Hills site is just on the upwind edge of our sampling domain for the ArvinO3 study (Fig. 2). Both the boundary-layer depths and their growth rates measured in the airborne experiments appear to be slightly lower than the Bianco et al. (2011) seasonal averages. The discrepancy is probably attributable to both airborne experiments specifically targeting the stagnation, high-pressure synoptic settings that characterize both the wintertime PM2.5 and summertime ozone episodes, which in principle suppress ABL development due to subsidence. Table S1 in the Supplement summarizes the estimated entrainment velocities from the two experiments, but the average from the two missions can be viewed in Fig. 5, indicating a range from near zero (or below our detection limit of about 0.5 cm s-1) to 2.4 cm s-1 during the wintertime in the central SJV (average of 1.5 ± 0.9 cm s-1), and approximately 0.9 to 6.5 cm s-1 during the summertime over the southern SJV (average of 3.0 ± 2.1 cm s-1). Broadly comparable values have been observed in other continental studies: 4.3 cm s-1 during late July over grassland in the Netherlands in a study by Vilà-Guerau de Arellano et al. (2004), 1.4 ± 0.3, 5.5 ± 1, and 9.6 ± 1.5 cm s-1 over the foothills of the Sierra Nevada adjacent to the California's Central Valley using isoprene flux measurements during June by Karl et al. (2013), and 5 ± 1 cm s-1 over the Ozark mountains in the southeastern US during September by Wolfe et al. (2015). As far as we can tell, the data presented here are the first of their kind to estimate entrainment during the winter season, which, although observed to be smaller (as expected) because of weaker surface heating, are critical to understanding the meteorological influence on the valley's PM2.5 episodes.

The entrainment velocities estimated in the two studies show evidence that they are linked to physically relevant surface parameters present during the flights. For example, the summertime entrainment velocities correlate well with the average ABL potential temperature (r2=0.57, data not shown), insinuating that the forcing that heats the boundary layer (surface and consequent entrainment heat fluxes) is intimately linked to the entrainment rate. In a similar vein, the wintertime entrainment velocities correlate well with estimates of net surface radiation found in the NARR data set (r2=0.68, data not shown). A climatology of boundary-layer heights reported by Pal and Haeffelin (2015) near Paris showed that although surface heat fluxes should most directly control the boundary layer height, a better correlation was found, on diurnal to seasonal time scales, with the surface down-welling shortwave radiation. Although surface fluxes were not directly measured as part of the experimental setup, we turn to the surface solar radiation measured with pyranometers by the CIMIS network across the region. Figure 6 shows a very strong linear relationship with the surface pyranometer observations and the average boundary-layer height for each flight. In fact, the linear fits for each separate experiment seem to be the same within the uncertainties of the fits, and the slopes of 1.5 m (W m-2)-1 are similar to those reported in Pal and Haeffelin (2015) of 1.7 m (W m-2)-1.

Pal and Haeffelin (2015) further survey nearly a dozen past studies that reported ABL growth rates over different seasons ranging from 0.8 to 8.3 cm s-1. There are two main reasons that these growth rates are not exactly comparable to the entrainment velocities reported here. First, most of these studies do not explicitly take into account horizontal or vertical zi advection (the last two terms in Eq. 2). Second, the convention used by many is to report ABL growth rates for the interval from when the surface heat flux reverses sign shortly after sunrise to the time when the boundary-layer height is 90 % of its daily maximum. Such growth rates are thus a combination of the rapid growth through the nearly statically neutral residual layer in the morning and the slower growth near midday when the ABL is actively entraining air from the free troposphere. For the chemical budgets under consideration in this work, we contend that it is more important to quantify the late morning to early afternoon entrainment mixing between the ABL and FT, because entrainment of the residual layer in the early morning (sometimes called fumigation) represents merely a recycling of the previous day's boundary-layer air (albeit from sources an overnight advection scale of order 100 km away). For the purposes of estimating regional source strengths or regional in situ photochemistry, we suggest that the more pertinent mixing process is the dilution of the anthropogenically influenced ABL air mass by the more global “baseline” FT air, and we therefore exclude data from the morning period when the boundary layer is growing rapidly into the residual layer. Both of these differences lead to the realization that the ABL growth rates reported by Pal and Haeffelin (2015) and references therein, should be systematically larger than the entrainment velocities reported in this study, at least under fair weather conditions (subsidence). Our data from the DISCOVER-AQ wintertime study presented in Fig. 5 (and Table S1 in the Supplement) indicate that the advection and subsidence terms may not be first-order, especially for longer period averages, and therefore may be comparable to other ABL growth rate statistics reported in the literature. This conjecture is consistent with conclusions from previous budget studies indicating that while advection may make a significant contribution to the scalar budget on any specific day, it may average out when considered on longer intervals (Conley et al., 2009; Faloona et al., 2010). A similar argument can be made for the vertical velocity term in Eq. (2); namely, that it may average to near zero across periods of instability and uplift, and periods of fair weather and subsidence. In a similar vein, the average zi budgets for the southern SJV (ArvinO3 in Fig. 5 and Table S1) show a sizeable average orographic uplift and opposing horizontal advection of zi, which together may be in a quasi-steady state nearly canceling over long periods of weeks to months.

It follows that although not exactly equivalent to entrainment as described by Eq. (2), the range of ABL growth rates reported in the literature (from Pal and Haeffelin, 2015, and references therein) is nonetheless reasonably consistent with the data reported in Table S1. In the studies that report both winter and summer seasonal average ABL growth rates (Chen et al., 2001; van der Kamp and McKendry, 2010; Lewis et al., 2013; Schween et al., 2014; Korhonen et al., 2014; and Pal and Haeffelin, 2015), the summer to winter ratios tend to range from 1.4 to 3.0, with an average of 2.0. This is consistent with our results that indicate entrainment rates 80 % higher in the SJV during summer than winter.

Bianco et al. (2011) postulate that convergence at the southern end of the SJV in summer leads to deeper ABLs there than in other parts of the valley, closer to the delta inflow region, which are influenced by strong marine-layer inflow. A typical slope of ABL height up the SJV from Bianco et al. (2011) can be estimated from the Chowchilla and Lost Hills sites, which differ by about 750 m (from their Fig. 2) over a distance of approximately 175 km for the summer months. Applying to this gradient a calculated average along-valley wind at the top of the ABL of 2.5 m s-1 gives an advection term of -1.1 cm s-1. This estimate compares well to the -1.15 cm s-1 shown visually in Fig. 5, derived from the NARR data set from our flight region 2 during summer. In addition, Bianco et al. (2011) make a rough estimate of convergence in the southern SJV by simply taking the difference in the horizontal along-valley wind at the two sites (2.5 m s-1 between June and September), divided by the distance between them, leading to ABL flow convergence of 1.4 × 10-5 s-1. Such convergence would lead to an uplift of 1.4 cm s-1 at the top of a typical 1000 m boundary layer. This estimate is, again, right inline with our estimates from this study. From our findings it appears that the local-time rate of change of observed ABL height nearly matches the entrainment rate when both are averaged over all the flights. The convergent uplift and the advection of ABL height appear to balance on average in the southern SJV. This suggests that the radio acoustic wind profiler data in the SJV, reported by Bianco et al. (2011), could be used to estimate entrainment rates by simply measuring the boundary-layer growth during the midday.

This idea is explored in Fig. 7, where we show the monthly average ABL growth rates observed year-round by NOAA's wind profiler network operated across California's Central Valley during 2008 (Bianco et al., 2011). Additionally, the monthly average subsidence at boundary-layer height is shown as captured in the NARR data set. Assuming that the advection term does not dominate at any of the sites in a long-term average (other than at Lost Hills where it is possibly counterbalanced by the convergent uplift), we can get a sense of the general entrainment characteristics across the Central Valley throughout the year. For example, there appears to be stronger entrainment at lower latitudes in the valley (∼ 3 cm s-1 annual peaks in the Sacramento Valley vs. ∼ 4 cm s-1 peaks in the San Joaquin Valley), possibly due to greater shortwave forcing or generally weaker stratification in the lower FT. It further seems that at most sites there is a definite peak in entrainment during the spring but also a secondary maximum in the autumn with a minimum during the mid-summer. This corresponds to the lowest ABL depths observed in the middle of summer as discussed by Bianco et al. (2011). In their analysis the authors suggest that the lower inversion heights of mid-summer are due to greater cold air advection through the delta and/or possibly the peak in irrigation in the heavily agriculturally controlled landscape of the Central Valley. Both effects serve to cool the ABL, thereby increasing lower tropospheric stability (LTS) and suppressing entrainment. The lower right panel in Fig. 7 shows the LTS, as measured by the difference in potential temperatures between 750 and 900 hPa from NARR. The LTS minima in spring and autumn appear to not coincide exactly with the peaks in entrainment, but rather follow (spring) or presage (autumn) them by a month or two.

Once the entrainment rate has been calculated for each flight it can be used to close the other scalar budget equations and calculate any single residual term, assuming all the others have been characterized. The time derivative and gradient terms were all calculated by applying a simple multi-linear regression on all flight data collected below the (time varying) ABL height as described in Conley et al. (2009). The averaged budget terms for each respective mission can be viewed in Fig. 5, which serves as a visual aid to refer back to in the following sections. For more detailed breakdown see the Supplement, which includes the data for each individual flight.