Supplement to : Mo deling the Diurnal Variability of Agricultural Ammonia in Bakersfield , California during CalNex

Atmospheric and Environmental Research, Lexington, MA, USA Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, CO, USA Chemical Sciences Division, Earth System Research Lab, NOAA, Boulder, CO, USA Department of Chemistry, University of Toronto, Toronto, ON Canada Scripps Institution of Oceanography, University of California, San Diego, CA, USA Science Systems and Applications Inc., Hampton, Virginia, USA *Now at Aerodyne Research, Inc. Billerica, MA, USA **Now at Air Quality Research Division, Environment Canada, Toronto, ON, CA

Recent studies have recognized a diurnal pattern of NH 3 emissions from livestock attributed to potential differences in farm management practices, livestock housing outflow patterns, and variations in soil moisture, temperature and wind speed 5 (Hensen et al., 2009;Zhu et al., 2015a;Zhu et al., 2015b).To account for this, a diurnal variability scheme was implemented into global simulations using the global 3-dimensional chemical transport model, GEOS-Chem, and was shown to decrease NH 3 concentrations globally (Zhu et al., 2015a).That study also calculated the bi-directional exchange of ammonia, which decreased NH 3 concentrations in the US in the months of October through April and increased it in the month of July (Zhu et al., 2015a).Bash et al. (2013) also explored the sensitivity of modelled NH 3 concentrations to a bi-directional ammonia 10 scheme that used meteorological factors, including temperature, wind speed, agricultural crop flux values, and a nitrogen soil geochemistry parameterization in the CMAQ model.They found that over the continental US their model run with the bidirectional ammonia scheme decreased the total dry deposition of NH 3 by 45 %, thus increasing atmospheric NH 3 concentrations and NH x wet deposition by 10 % and 14 %, respectively.Wichink Kruit et al. (2012) use the DEPosition of Acidifying Compounds (DEPAC) surface-atmospheric exchange module in a CTM and saw an increase in atmospheric NH 3 15 almost everywhere in their model domain, including decreased NH 3 deposition with a remaining underestimation in agricultural areas.
Previous studies have also shown that errors in NH 3 emissions are a common contributing factor to modelled PM 2.5 and NH 3 bias (e.g., Schiferl et al., 2014).Skjøth et al., (2011) discuss their method for calculating dynamic NH 3 emissions that include distributions of agricultural ammonia in Europe.Their method is designed for use in chemical transport models and 20 their results show considerable improvements made in the agricultural ammonia sector, particularly areas with detailed records of agricultural practices.Inverse modelling studies have been used to reduce the uncertainty in NH 3 emissions as well, generally by assimilating surface observations of the wet deposition of ammonium (NH 4 + ) in precipitation.Gilliland et al. (2003) used the CMAQ model to determine that the 1990 version of the US EPA National Emissions Inventory (NEI), which is based on emission estimates and model inputs from State, Local and Tribal agencies (US EPA, 2015), 25 overestimated total emissions of NH 3 by 20 %.Gilliland et al. (2006) performed a similar study for the 2001 NEI and found that this updated inventory represented the total emissions of NH 3 well, but that NH 3 emissions needed to be increased in summer and reduced in winter.Henze et al. (2009) used the adjoint of the global chemical transport model GEOS-Chem to assimilate IMPROVE observations and found that the high nitrate concentrations in the model implied that total US NH 3 emissions for 1998 were overestimated.30 More recently, satellite observations of NH 3 have been incorporated into inverse studies.By assimilating satellite retrievals of NH 3 concentrations from TES (Beer et al., 2008;Shephard et al., 2011) aboard the NASA Aura satellite, it has been found that NH 3 emission sources in GEOS-Chem are broadly underestimated (Zhu et al., 2013).Heald et al. (2012) and Walker et al. (2012) used the Inter Agency Monitoring of Protected Visual Environments (IMPROVE) network data and satellite Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.retrievals of NH 3 from the Infrared Atmospheric Sounding Instrument (IASI, Van Damme et al., 2014)  Investigating the formation, transport, and fate of NH 3(g) and NH 4(p) in California was one of the major goals of the NOAA CalNex field campaign performed in May and June 2010, which provided measurements from flights and surface sites.10 Nowak et al. (2012) used this data to demonstrate the importance of ammonium nitrate formation downwind of the Los Angeles urban core and dairy facilities further east.They found that NH 3 emissions from these dairy farms were underestimated by a factor of 3 or more, thus indicating the need for better representation in this emission sector. Kelly et al. (2014) in general saw well-correlated comparisons of CMAQ model estimates to measurements from the EPA's Chemical Speciation Network.Their model tended to under-predict NH x (NH x = NH 3(g) + NH 4(p) ) during the day at the Bakersfield, CA 15 site and significantly over-predict NH 3(g) at night.They suggest that this model bias may be due to emissions from livestock and dairy farms being too low and lacking in variability in this region or to errors in crustal cation predictions and the missing effects of organic acids and amines on inorganic aerosol thermodynamics (Kelly et al., 2014).
Model estimates of the planetary boundary layer (PBL) height are essential in correctly quantifying atmospheric pollutant concentrations, especially for short-lived pollutants like NH 3 .Such estimates are difficult at fine spatial and temporal scales, 20 especially in the complex terrain of the SJV.Scarino et al. (2014) studied the PBL and mixed layer heights during CalNex using WRF and high spectral resolution lidar (HSRL) data taken during the campaign.They found that, in general, there is good agreement between the WRF modelled output and measured values; however, in the Central Valley there is a WRF mixed-layer height over-prediction and an inability to represent the diurnal growth of the mixed layer in the early part of the day.Additionally they suggest that future improvements will require a focus on mixing layer characteristics and soil 25 moisture and temperature.Baker et al. (2013) explored how well the WRF model configuration used to drive the CMAQ simulations of Kelly et al. (2014) simulates PBL height during CalNex, using two versions of WRF.The study shows that both WRF versions simulate the PBL and mixing layers well within the SJV, as well as other large scale flow patterns, but under-predict local wind speed and temperature.A strong aerosol gradient is used to identify the top of the PBL in HSRL measurements, which may also be present in a night-time residual layer.Baker et al. (2013) take this into account by 30 identifying the surface-attached mixed layer, which they assume as the lowest significant gradient in such a circumstance.
In this study, we use the CalNex observations of NH 3(g) and aerosol ammonium (NH 4(p) ) and the CMAQ model to evaluate the estimates of NH 3 emissions in the SJV contained in the California Air Resources Board (CARB) inventory (Figure 1a).
While previous NH 3 model evaluation efforts using CalNex data have focused on the NEI inventory (Kelly et al., 2014;Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.Heald et al., 2012;Walker et al., 2012), the CARB inventory is used in the development of California's State Implementation Plans (SIPs) under the Clean Air Act, and so ensuring the accuracy of this emission inventory is important to the design of air quality policy for the SJV and California in general.In addition, previous studies have not taken advantage of the high-resolution observations of NH 3(g) made by the TES satellite instrument over Bakersfield during the CalNex campaign.Here we evaluate the consistency of the satellite, aircraft, and surface observations of NH 3(g) and NH 4(p) during the 5 CalNex campaign and then use these observations, along with lidar retrievals of PBL height, to investigate the biases in the magnitude and diurnal cycle of emissions of NH 3(g) and NH 4(p) from the CARB inventory in the SJV.We also explore the sensitivity of modelled ammonia concentrations to bi-directional ammonia exchange using the bi-directional NH 3 flux scheme in CMAQv5.0.2.
Section 2 briefly describes the data sources used in this study, while Section 3 describes the CARB emission inventory and 10 the configurations used for the WRF, HYSPLIT and CMAQ model runs in this study.The performance of the CARB inventory used in our CMAQ simulations, along with model sensitivity studies, is presented in Section 4. Section 5 discusses our suggested improvements to the CARB NH 3 inventory and summarizes our conclusions.

NOAA CalNex campaign 15
The NOAA WP-3 aircraft completed 18 research flights during the CalNex campaign, which included measurements of NH 3(g) and NH 4(p) .NH 3(g) was measured at 1 s (~100 m) intervals using chemical ionization mass spectrometry (CIMS) with an uncertainty of +/-30 % as described in detail in Nowak et al. (2010).Submicron NH 4(p) was measured at 10 s (~ 1 km) intervals with an uncertainty of ~ 30 % using a compact time-of-flight aerosol mass spectrometer from Aerodyne (c-TOF AMS, Bahreini et al., 2009).In this study we focused on the flights of 7 and 24 of May and 16 and 18 of June when the WP-20 3 was sampling air in the SJV (Figure 1a).The quality-controlled flight data were reported at a merged time resolution of 1 s, which we averaged to 1 minute values (the approximate time it takes the WP-3 to cross a 4 km CMAQ grid box) and then matched the sample times and locations to the corresponding time and location of the CMAQ hourly concentration output.

Bakersfield surface observations
Bakersfield, California is located on the southern part of the SJV and there is a general north-to-south orographic air-flow in 25 this region, with a tendency for emissions to get trapped in the valley due to the nearby mountains (seen in Figure 1a) (Baker et al., 2014).At the Bakersfield site the Ambient Ion Monitor Ion Chromatograph (AIM-IC, Ellis et al., 2010, Markovic et al., 2012) was used to measure NH 3(g) at a frequency of 1 Hz and an uncertainty of +/-20 %.In addition, size-resolved, submicron non-refractory NH 4(p) measurements were taken at 5 minute intervals using an Aerodyne Aerosol Mass Spectrometer (AMS) (Ryerson et al., 2013).We averaged these data to 1 h time resolution in order to compare to the hourly CMAQ model 30 output, which allowed for the evaluation of the ability of CMAQ to simulate the diurnal cycle of NH 3 concentrations.When Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.particulate ammonium (NH 4(p) ) measurements are available we compare model results to NH x to reduce our sensitivity to gas-to-particle partitioning errors in the model, otherwise we compare to NH 3(g) .

TES NH 3 retrievals
During CalNex, TES made special observations (transects) near the Bakersfield, CA surface site with a horizontal separation of 12 km on six different afternoons.TES is a nadir-viewing Fourier-transform infrared (FTIR) spectrometer with a high 5 spectral resolution of 0.06 cm -1 and a nadir footprint of 5.3 km x 8.3 km.TES flies aboard the NASA Aura spacecraft, which is in a sun-synchronous orbit with an equator crossing time around 01:30 and 13:30 local solar time.Beer et al. (2008) reported the first satellite observations of boundary layer NH 3(g) using the TES instrument.Shephard et al. (2011) developed and tested a full NH 3(g) retrieval algorithm.The retrieval is based on an optimal estimation approach that minimizes the differences between the TES Level 1B spectra and a radiative transfer calculation that uses absorption coefficients calculated 10 with the AER line-by-line radiative transfer model LBLRTM (Clough et al., 2006).The a priori profiles and covariance matrices for TES NH 3 retrievals are derived from GEOS-Chem model simulations of the 2005 global distribution of NH 3 .
The TES NH 3(g) retrievals generally have a region of maximum sensitivity between 700 hPa and the surface.While the retrieval is performed on 14 pressure levels, the number of degrees of freedom for signal (DOFS) is generally not greater than one.Therefore at any given single profile level the retrieved volume-mixing ratio (VMR) of NH 3 is highly influenced 15 by the a priori profile.Rather than attempting to analyse data from individual retrieval levels, it is often desirable to express the retrieved information in a representation where the influence of the a priori is reduced and the information available is collapsed to a single point.To address this issue, Shephard et al. (2011) developed a Representative Volume Mixing Ratio (RVMR) metric for NH 3(g) based on similar techniques used previously for CH 4 (e.g., Payne et al., 2009;Wecht et al., 2012;Alvarado et al., 2015) and CH 3 OH (e.g., Beer et al., 2008).This RVMR represents a TES sensitivity weighted average value 20 where the influence of the a priori profile is reduced as much as possible; it generally ranges from 20 % to 60 % of the retrieved surface value for NH 3(g) .The minimum detection level for TES NH 3(g) retrievals is an RVMR of approximately 0.4 ppbv, corresponding to a profile with a surface-mixing ratio of about 1-2 ppbv (Shephard et al., 2011).Pinder et al. (2011) showed that the TES NH 3 retrievals were able to capture the spatial and seasonal variability of NH 3 over eastern North Carolina and that the retrievals compared well with in situ surface observations of NH 3 , while Alvarado et al. 25 (2011) showed that TES NH 3 retrievals can also capture the higher concentrations of NH 3 in forest fires in Canada.Sun et al. (2015) demonstrated that under optimal conditions (i.e., good thermal contrast and NH 3 amounts significantly above the TES  and Connor, 2003).Thus, in order to use these TES observations to evaluate CMAQ model predictions of the concentrations of NH 3(g) , we first interpolate the hourly CMAQ NH 3 profile predicted for 13:00 local solar time (expressed as the natural logarithm of the mixing ratio) to the TES pressure grid.We then apply the TES observation operator to the interpolated CMAQ NH 3 profile to derive a model TES profile (x TES ).Finally, we apply the sensitivity weighting to calculate the model 5 RVMR ( !"#! ).This value represents the RVMR that would have been retrieved if (a) TES had sampled a profile identical to the CMAQ-simulated profile and (b) the retrieval errors due to jointly retrieved parameters, other model parameters, and instrument noise were negligible.The observation operator equation is where x a is a vector of the TES a priori NH 3 concentrations, A is the averaging kernel matrix, x CMAQ is a vector of the interpolated CMAQ NH 3 values, and W is a weighting matrix (Rodgers and Connor, 2003;Payne et al., 2009).

PBL heights
Several studies have used lidar observations of aerosol profiles to determine the height of the planetary boundary layer (PBL) by identifying regions of large gradients in aerosol concentrations with height (e.g., Tucker et al., 2009;Lewis et al., 15 2013;Scarino et al., 2014;Hegarty et al., 2015).Scarino et al. (2014) and Tucker et al. (2009) define the mixed layer measured by the HSRL as 'the volume of atmosphere in which aerosol chemical species emitted within the boundary layer are mixed and dispersed'.The NASA Langley Research Center (LaRC) airborne HSRL measured mixed layer heights during May and June 2010 for the CalNex campaign and the Carbonaceous Aerosol and Radiative Effects Study (Scarino et al., 2014), both of which we used in this study.20

WRF-ARW
CMAQ v5.0.2 was driven with meteorology provided by WRF ARW Version 3.5 (Skamarock and Klemp, 2008) that was configured with 3 nested domains of 36, 12, and 4 km horizontal grid spacing and 41 vertical layers.Shortwave and longwave radiation were calculated using the RRTMG radiative transfer code (Mlawer et al., 1997;Iacono et al., 2008).The 25YonSie University (YSU, Hong et al., 2006) non-local turbulent PBL scheme and the Noah land surface scheme (Chen and Dudhia, 2001) were used.Initial and boundary conditions for WRF were provided by the North American Regional Reanalysis (NARR, Mesinger et al., 2006), which is recognized as state-of-the-science for North America (Bukovsky and Karoly, 2007).The WRF runs were 32-hour simulations initialized every 24 hours at 0000 UTC with analysis nudging of winds, temperature and humidity above the PBL on the inner 10 km domain as well as winds in the PBL as in Nehrkorn et  2013).The WRF outputs for UTC hours 09:00 to 32:00 from each consecutive simulation were combined to form a continuous time series and the initial 8 hours of each simulation were discarded as spin-up time.The 8-h spin-up time and 32-h simulation length is longer than the 6-h spin-up time and 30-h simulation length used by Nehrkorn et al. (2013), but were necessary to perform 24-hour daily CMAQ runs using the 24-h daily CARB emissions files that started at 8:00 UTC.
The WRF output was then converted to CMAQ-model-ready files using the Meteorology-Chemistry Interface Processor 5 version 4.2 (MCIP).

CMAQ
We ran CMAQ on the inner 4 km WRF domain using the SAPRC07 chemical mechanism (Hutzell et al., 2012, Carter et al., 2010ab), which corresponds to the model-ready emission files for CalNex provided by CARB, and with the CMAQ AERO6 aerosol module with aqueous chemistry.Biogenic emissions, photolysis rates, and deposition velocities were all calculated 10 inline.There were few clouds in California during this study period and thus lightning NO X emissions were negligible; however, lightning NO x emissions were also calculated inline in CMAQ.Initial and horizontal boundary conditions for CMAQ were provided by GEOS-Chem simulations on a 2° x 2.5° latitude-longitude grid for May and June 2010 following the approach of Lapina et al. (2014).
CMAQ emissions inputs for the state of California were provided as model-ready files by CARB, which prepared them 15 using the Modeling Emissions Data System on a 4 km x 4 km grid-scale (available at http://orthus.arb.ca.gov/calnex/data/calnex2010.html, last accessed January, 2016).The emission change log is provided at ftp://orthus.arb.ca.gov/pub/outgoing/CalNex/2010/modelready/ChangeLog for Posted Inventories.pdf(last accessed January, 2016).In this inventory, the NH 3 emissions in SJV are assumed to be constant throughout the day (i.e., no diurnal cycle), and are constant day-to-day in a given month.NH 3 emissions in the SoCAB did have a strong diurnal cycle, as about 20 75 % of the NH 3 emissions were coded as "industrial" and only emitted between 8 AM and 4 PM local time.As these emissions were mainly due to sewage treatment, this diurnal cycle assumption is likely incorrect.However, evenly distributing these SoCAB emissions across the day had little impact on NH 3 in the SJV.As the CARB model-ready files had no out-of-state emission sources, our initial simulations were run using the CARB emissions for California, the GEOS-Chem boundary conditions, and no out-of-state emissions.We quantified the potential error in gas-phase NH 3(g) , Aitken and 25 Accumulation mode aerosol NH 4(p) , and NH x in the SJV from neglecting out-of-state agricultural NH 3 emissions by using the agricultural NH 3 emissions from the NEI2011 platform, which we re-gridded from 12 km to our model's 4 km scale while keeping California state emissions constant.We performed this sensitivity test for a 7-day case study between 25-31 May with a 4-day spin up in order to correspond to in situ measurements and two of the TES transects.Adding these out-of-state emissions had a negligible impact on the modelled NH 3 concentrations in the SJV (less than 0.001 % change), as the 30 prevailing winds are mostly out of the north and northwest.Additionally, we tested the effect that errors in the boundary Finally, we also ran CMAQv5.0.2 using the bi-directional exchange scheme for ammonia developed by Bash et al. (2013) with results discussed in Section 4.4.This tool uses the U. S. Department of Agriculture's Environmental Policy and Integrated Climate (EPIC) model (Bash et al., 2013), which uses fertilizer application data, crop type, soil type, and 5 meteorology from MCIP output to calculate soil emissions potential and NH 4 .

HYSPLIT
In order to explore the sources influencing the Bakersfield concentrations we ran the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model.Using meteorological inputs from the WRF 4 km domain discussed in Section 3.1, we generated 36-hour back trajectories with Version 4 of the HYSPLIT model (Draxler and Hess, 1998) initiated from 100 10 m above ground level (agl) at Bakersfield at 17:00 PDT on June 18 th back to 20:00 PDT on June 17 th .Results from these runs are discussed in Section 4.3.

Evaluation of modelled boundary layer NH 3(g) with TES NH 3 retrievals
Figure 2a shows the RVMR retrieved from the TES spectra (TES RVMR ) for one overpass on 12 May 2010. Figure 2b shows 15 the equivalent modelled NH 3 RVMR (CMAQ RVMR ) (see Equation 1 and 2 in Section 2.2), and Figure 2c shows the difference between the two.We can see that CMAQ with the CARB emission inventory does a good job of representing the locations of different sources of NH 3 and the resulting relative changes in NH 3 along the transect, but that the NH 3 RVMRs are underestimated, particularly at higher NH 3 RVMRs.Figure 3 is a scatterplot of the modelled and measured RVMR for all six transects near Bakersfield, with the footprints closest to Bakersfield marked in green.The modelled and measured 20 RVMRs are reasonably well correlated (r 2 of 0.54 and mean bias of -2.68 ppbv), again suggesting that CMAQ with the CARB inventory does a good job of capturing the spatial distribution of NH 3 emissions near Bakersfield.However the slope of the linear regression of modelled to measured NH 3 RVMR suggests that CMAQ underestimates high NH 3 concentrations by a factor of 2.4.

Evaluation of modelled NHx diurnal cycle and vertical distribution 25
Figure 4a shows the average hourly ratio of modelled versus measured NH x concentrations for the Bakersfield ground site, averaged over all days of the CalNex campaign, which is derived from the boxplots shown in Figure 4b.We are plotting NH x here so as to include the effects of gas-to-particle partitioning, discussed later in this section.The CMAQ model runs with the CARB emission inventory generally underestimate NH x during the daytime by about a factor of 2.5, consistent with the average TES RVMR observations near Bakersfield at about 13:30 local solar time plotted as the green dot in Figure 4a.(2008) also found that NH 3 emissions from livestock feed lots show a strong diurnal cycle, peaking at mid-day.This also demonstrates the importance of using highly time-resolved observations of NH 3 to determine the diurnal cycle of NH 3 before using polar-orbiting satellite retrievals of NH 3 to improve the spatial and seasonal distribution of the emissions, as noted in Zhu et al. (2013).In other words, if we had relied on the TES observations at 13:30 local solar time to evaluate the CMAQ runs with the constant CARB diurnal profile of NH 3 emissions, we would have incorrectly assumed that the CARB 10 inventory was a factor of 2.4 too low for total NH 3 emissions, whereas the surface data demonstrate that the problem is primarily in the diurnal cycle of the emissions.
Besides errors in emissions another contributing factor to misrepresentation of modelled NH 3(g) could be errors in the gas-toparticle partitioning of NH 3(g) to NH 4(p) .Figure 4a also shows an average hourly plot of the ratio of measured to modelled fraction of the total NH 3(g) is being converted into NH 4(p) in this region, consistent with Baker et al. (2013).Thus, errors in gas-particle partitioning of NH 3 in CMAQ, while important for accurately estimating PM 2.5 concentrations, cannot account for the diurnal errors in NH x we have observed.
The aircraft observations in the SJV also indicate a large underestimate (range of 1.4 to 7.1) in NH x concentrations, as shown in Table 1 (all flights in SJV) and Figure 5 (two flights).The variation in model concentrations in the background of the plot 20 are due to the aircraft flying in and out of horizontal and vertical grid boxes.The May 24 th flight shows a strong CMAQ NH x underestimate of about a factor of 5 when considering the entire flight with an r 2 value of 0.4 and mean bias of -1.95 ppbv.This significant underestimate could partly be due to the underestimate of vertical mixing at night (discussed below); when only data before 18:00 PDT is considered (assuming this is before the collapse of the convective boundary layer) the underestimate is only a factor of ~1.5 and the r 2 is 0.77, a considerably better result.However, model comparisons to flight 25 data on 16 and 18 of June before 18:00 PDT, likely before the boundary layer collapse on these days, show a significant model underestimate and low r 2 values; thus there may be other contributing factors to this bias.When looking at NH 3(g) and NH 4(p) separately, NH 4(p) has a large absolute mean bias for all flights, but its low magnitude has a negligible effect on NH x concentrations (see Table 1).
Early afternoon (Figure 5a) and evening (Figure 5b) model runs and flight measurements show a clear difference in vertical 30 distribution of NH x .At night (May 24 th flight), the model contains most of the NH x in the lowest model grid, whereas during the day (June 16 th flight) it vertically mixes NH x .The aircraft measurements suggest 1) vertical mixing is happening during both flights, based on the higher NH x concentrations that the aircraft is measuring at higher altitudes, 2) or that there is a residual layer of NH x at night that is not captured by the model or 3) there is a non-local source that is also not well captured Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Finally, diurnal errors in the PBL height estimates could potentially be responsible for the diurnal pattern in the CMAQ NH x concentrations at Bakersfield discussed above.We used daytime HSRL measurements taken in the SJV during CalNex to evaluate our WRF simulated PBL heights.Figure 7 shows the WRF PBL plotted against the HSRL calculated mixed layer, which contains PBL heights both manually chosen based on the aerosol profile and using the Brooks algorithm (Scarino et 20 al., 2014).Results for the three daytime flights that passed over the SJV had a slope of 0.91, r 2 of 0.45 and mean bias of 45 m, and thus errors in daytime ML height cannot account for the underestimate in modelled daytime NH x .Scarino et al. (2014), when comparing all CalNex HSRL flight measurements to their configuration of the WRF-Chem model, obtained a similar result with a slope of 0.58 and r 2 of 0.3; however, this result was for all flights, not just those in the SJV region.
In summary, gas-to-particle partitioning and PBL height errors are likely not responsible for the diurnally-varying 25 measurement to model biases.The daytime high bias is most likely due to an underestimation of daytime emissions.
However, the aircraft observations of NH x in the SJV suggest that the vertical mixing in CMAQ at night is too low to reasonably simulate night-time surface concentrations of NH x .This suggests that the observed CMAQ overestimate of NH x at night is due to a combination of an overestimate of the night-time emissions, an underestimate of night-time deposition and an underestimate in vertical mixing at night.30

Sensitivity to diurnal variability in emissions
The solid blue line in Figure 8a shows that the CARB NH 3 emissions in the SJV are mostly constant, both diurnally and dayto-day, with an hourly flux of around 0.23 moles s -1 for the Bakersfield 16 km 2 grid box.The Bakersfield ground Atmos.Chem.Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.measurements, however, indicate there should be a diurnal pattern of lower emissions at night and higher emissions during the day, as has been previously reported of NH 3 emissions from livestock (e.g., Bash et al., 2013;Zhu et al., 2015) and based on more detailed information regarding agricultural ammonia sectors (Skjøth et al., 2011) which the current CARB emissions inventory does not have.In order to test this hypothesis, we applied a scaling factor to all NH 3 area sources per grid box in the SJV, based on the CMAQ bias relative to the ground observations at Bakersfield (see Figure 4) and consistent 5 with measured temperature patterns.To do this, we first calculated the total NH 3 area source emissions for each grid box, based on additional information on the emissions breakdown from the CARB inventory.We then calculated the emissions for each hour based on the hourly average ground measurements.Note that the adjusted maximum emissions vary by about a factor of 5 from the minimum at night to the mid-day peak, as can be seen in Figure 8a (solid red line) which is more modest than the factor of 10 variation seen in feedlots (Bash et al., 2013;J. Bash, personal communication, Oct. 6, 2015).We then 10 reran CMAQ for a 7-day period during the CalNex campaign (May 25-31, with a previous 4-day spin-up) to assess the impact that this diurnal cycle had on the model bias.The overall diurnal cycle of this 7-day period was similar to the full campaign average, with a peak around mid-day; however the maximum concentration was less, with only about a 14 ppbv average compared to the 20 ppbv average of the full campaign.Unlike the data averaged over the full CalNex campaign that was used to derive the diurnal scaling factors, during this 7-day period the baseline CMAQ simulation described above was 15 in reasonable agreement with the surface observations between 12:00 and 18:00 PDT (mean bias of 2.1 ppbv), but showed significant overestimates of NH x (up to 50 ppbv) at all other times.Despite applying the scaling factor to all emissions instead of solely to the feedlots as in Bash et al. (2013), the CMAQ predictions using the adjusted emission scenario shown as the red lines in Figure 8b (for NH 4(p) ) and Figure 8c (for NH x ) match the measurements (black line) better than the original CARB inventory (blue line) over the day and night, consistent 20 with Bash et al. (2013), with the mean night-time bias reduced by about a factor of 2. As the NH x concentrations are dominated by NH 3(g) , NH 4(p) has little impact on total NH x results, as can be seen in the small amount of NH 4(p) in Figure 8b (< 1 ppbv).Furthermore, model errors in NH 4(p) reflect not only model errors in total NH x , but also errors in the formation of HNO 3 and H 2 SO 4 in the model.However, NH 4(p) do not show similar improvement to NH x when the improved diurnal cycle is used, with mixing ratios decreasing between the unadjusted and adjusted scenarios at night by 0.4 ppbv and remaining 25 relatively unchanged during the day.The remaining night-time NH x errors are significant, and may be due to the underestimate of vertical mixing at night in the model (see Section 4.2) or an underestimate of deposition (see Section 4.4) rather than a further overestimate of night-time emissions.Between 12:00 and 18:00 PDT there is a small increase in the model bias (1.2 ppbv) when the adjusted emissions are used, which is to be expected as we are increasing NH 3 emissions in this period.However, the changes are relatively small, and may reflect a slight overestimate of the total monthly NH 3 30 emissions in the CARB inventory during this period.
Two TES transects on 28 and 30 of May occurred during our case study time period.The changes in the model predicted NH x values were small at the TES overpass time (less than 10 %), thus there was a correspondingly small change in the ratio of modelled RVMR and TES RVMR, changing from a factor of 2.4 to a factor of 2.1.Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.

Evaluation of bi-directional ammonia in CMAQ
Gas-phase NH 3 can either be deposited to or emitted from the surface depending on the land-type, land-use, and ambient concentrations (Bash et al., 2015;Fowler et al., 2009).The maximum and minimum points in NH 3 concentrations in the ground measurements (Figure 8c) correspond to the maximum and minimum wind speeds and temperatures measured.These highs and lows do not, however, line up in the model, suggesting there may be a need to better represent the vertical NH 3 5 fluxes, which can be done by utilizing the bi-directional NH 3 flux exchange scheme in CMAQ.Using the initial CARB emissions inventory we ran CMAQv5.0.2 with the inclusion of the calculation of the bi-directional NH 3 exchange to test the scheme's prediction of NH 3 concentrations in the SJV.We can see in Figures 8b and 8c that the run including bi-directional NH 3 flux (green line) increases NH 3 during the daytime, as expected due to the decrease in deposition during this time frame.
At night, however, concentrations decreased compared to the initial run with the CARB emissions inventory due to an 10 increase in modelled NH 3 deposition, leading to a reduction in net vertical flux of NH 3 at night.Bi-directional ammonia calculations also reduce the CMAQ RVMR to TES RVMR bias to a factor of 1.7 for the two over-passes during the casestudy (from a factor of 2.4), consistent with Zhu et al. (2015a) who also looked at the impact of bidirectional exchange on RVMR in the SJV.These results are similar to the adjusted emissions case study discussed in Section 4.3, however the remaining over-estimate at night indicates a need for both a reduction in emissions at night and an inclusion of bi-directional 15 ammonia calculations in the model, which is further investigated in the next section.

Evaluation of adjusted emissions and bi-directional ammonia in CMAQ
Based on results from both the adjusted emissions scenario and bi-directional ammonia calculations it was clear that combining techniques could result in better agreement with measurements.Thus, Figure 8c also contains a model simulation showing the results from a CMAQ run (purple line) where we adjusted emissions with a diurnal pattern as in section 4.3, and 20 also ran CMAQ with the bi-directional NH 3 flux scheme as in section 4.4.This configuration produced lower mixing ratios at night when compared to ground measurements while maintaining reasonable mixing ratios during the day, but with slight overestimation of NH x between 3:00pm and 10:00pm.This resulted in an overall MB decrease from 14.91 ppb in the initial CARB run, to 3.99 ppb in these final simulations, over the 7-day period (Table 2).At the time of the TES overpass, measurement and satellite RVMR comparisons also improve, with a bias reduction from -2.55 ppb in the initial run to -1.24 25 ppb for the two overpasses during the 7 day period, lower than the other two model simulation comparisons (Table 2).

Conclusions
We used NH 3 retrievals from the NASA Tropospheric Emission Spectrometer, as well as surface and aircraft observations of remained, possibly due to remaining errors in vertical mixing at night.The model performance is slightly degraded during the afternoon (12:00 to 18:00 PDT) when the diurnal cycle is adjusted, but this may reflect relatively small (~20 %) errors in the total monthly NH 3 emissions in the CARB inventory rather than remaining errors in the diurnal cycle.We then ran a simulation with the original CARB inventory but utilizing the bi-directional ammonia scheme in CMAQ.This resulted in similar results as adjusting the emissions, with decreased overestimates at night and a slight overestimate during the day.15 When running CMAQ with both adjusted diurnal emissions and the bi-directional NH 3 flux scheme, the over-estimate at night is almost negligible, with a slight over-estimate during the day remaining, providing the best agreement with measurements overall.Our results indicate that both a diurnally-varying emissions and a bi-directional NH 3 flux scheme should be applied when modelling NH 3(g) and NH 4(p) in this region, with more research needed to improve the modelling of vertical mixing and the residual layer at night.20 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-44, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.
aboard the EUMETSAT MetOp-A satellite to show that NH 3 emissions are likely underestimated in GEOS-Chem for California, leading to a local underestimate of ammonium (NH 4(p) ) aerosol.Other infrared nadir sounders have also been used to provide satellite observations of NH 3 .For example, Shephard and Cady-Pereira (2015) demonstrated the ability of the Crosstrack Infrared Sounder (CrIS) aboard the joint NOAA-NASA Suomi National Polar-orbiting satellite to measure daily, spatially 5 distributed tropospheric NH 3 in California, and in preliminary results found it correlated well with Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality (DISCOVER-AQ) measurements in the SJV in January 2013.
level of detectability), TES NH 3 agreed very well with in situ aircraft and surface measurements taken in the California Central Valley during the Deriving Information on Surface Conditions from COlumn and VERtically Resolved Observations Relevant to Air Quality (DISCOVER-AQ) 2013 campaign.30 There are at least three issues that have to be considered when using NH 3 satellite profiles to evaluate model predictions: (a) the vertical resolution of the satellite profile is substantially coarser than that of the model profile; (b) the DOFS for NH 3 are Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-44,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.generally less than 1.0; and (c) the retrieved satellite profile reflects the influence of the choice of a priori profile (Rodgers Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-44,2016   Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.al.( conditions from GEOS-Chem might have on the model runs.Doubling NH 3 boundary conditions for the same 10-day case Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-44,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.study also had little impact on NH 3 concentrations in the SJV (less than 0.001 % change), which was expected based on the short lifetime of NH 3 .
Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-44,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.However, this model underestimate is not constant throughout the day.Instead it shows a clear diurnal cycle, with CMAQ significantly overestimating surface NH x concentrations at night by up to a factor of 4.5.The overall magnitude of measured concentrations generally increases from May to June (not shown), possibly due to increasing temperatures.This suggests that the constant daily emissions for agricultural NH 3 emissions in the CARB inventory may be misrepresenting the diurnal emission patterns seen in the measurements, which is consistent with previous work done in North Carolina: Wu et al. 5 Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.by the model.Model comparison to flight measurements are constrained by mismatch errors caused by the difference in temporal and spatial resolutions, since the model output is only every hour on a horizontal grid spacing of 4 km.Another potential source of diurnal errors in NH x concentrations are diurnal variations in meteorology, which could potentially alter the source regions to which the Bakersfield site was sensitive throughout the day.Differences in NH 3 emission errors at upwind sites would thus appear as diurnal errors in NH x .Figure 6 shows a case study for June 18 th , where 5 HYSPLIT back trajectories were run for eight different times during the day (only 4 shown).As on most days during the CalNex campaign, there is a general flow from the north/north-west during the day and night that is funnelled through the California Central Valley towards Bakersfield.In these simulations, as well as in other runs on different days (not shown), there is no significant change in meteorology with time of day, and thus diurnal changes in transport are not likely a contributing factor to the diurnal mismatch shown in modelling results.Back trajectories for other days (not shown) all 10 support this assessment and also indicate a consistent general flow from the north/north-west passing through the PBL of the California Central Valley in the previous 24 hours.The back trajectories arriving at Bakersfield on the 18 of June indicate that the air would have been funnelled into the valley through the gap in the coastal range adjacent to San Francisco Bay, with lighter winds occurring at night-time.These back trajectories, driven with our WRF model data, did not show a change in source attribution locations and are in general agreement with those generated with the NAM12 and EDA40 operational 15 analyses (not shown).
NH 3(g) and submicron NH 4(p) gathered during the CalNex campaign, to evaluate the ability of the CMAQ model run with the CARB emission inventory to simulate ambient NH 3(g) and NH 4(p) concentrations in the San Joaquin Valley.We find that 30 CMAQ simulations of NH 3 driven with the CARB inventory are qualitatively and spatially consistent with TES satellite Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-44,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 9 March 2016 c Author(s) 2016.CC-BY 3.0 License.observations, with a correlation coefficient (r 2 ) of 0.54.However, the surface observations at Bakersfield indicate a diurnal cycle in the model bias with CMAQ overestimating NH 3 at night by at times more than 50 ppbv and underestimating it during the day by up to 10 ppbv.The surface, satellite, and aircraft observations all suggest that the afternoon NH 3 emissions in the CARB inventory are underestimated by at least a factor of two, while the night-time overestimate of NH 3 is likely due to a combination of overestimated night-time NH 3 emissions, underestimated night-time deposition, and insufficient vertical 5 mixing in the WRF meteorological fields used to drive CMAQ thus indicating that the diurnally-constant NH 3 emissions used by CARB in the SJV likely misrepresent the diurnal emission cycle.We used the surface observations at Bakersfield to derive an empirical diurnal cycle of NH 3 emissions in the SJV in which nighttime and midday emissions differed by about a factor of 4.5.Adding this diurnal profile to the CMAQ simulations while keeping the daily NH 3 emissions constant at the CARB values significantly improved the model performance at night, but sizable errors (up to 20 ppbv) in nighttime NH 3 10 Figure 1a) Distribution of NH 3 emissions across the CMAQ domain for May 12, 2010 at 19:00 UTC.1b) Selected P3 flight 5 tracks (small circles), TES transect (green squares), Bakersfield site (red dot) and LA site (blue dot).

Figure 2 .
Figure 2. NH 3 representative volume mixing ratios (RVMRs) on 12 May 2010 during the CALNEX campaign for (a) TES special observations, (b) modelled RVMR for CMAQ and (c) the difference between each RVMR near the Bakersfield, CA, surface site with the white diamond locating the Bakersfield measurement site.

Figure 3 .b
Figure 3. NH 3 representative volume mixing ratios for all TES special observation passes (TES RVMR ) during the CalNex campaign compared against modelled CMAQ RVMR (black dots).Green dots denote the overpasses closest to the Bakersfield measurement site.The statistics for the best-fit line, r 2 , MB and MNB are in provided for each.

Figure 5 .
Figure 5.The hourly output of modelled NH x is shown in the background with the measured 1 minute averaged NHx concentrations within the modelled hour shown as the dots.(a) The top plot is daytime flight over Bakersfield on June 16, 2010 between 10am and 6pm PDT and the (b) bottom plot is an evening flight on May 24, 2010 between 5pm and 9pm PDT.

Figure 6 .
Figure 6.HYSPLIT back trajectories initiated from Bakersfield, CA generated using WRF 4 km input data.The back trajectories are initiated on June 18 th at 17:00 PDT (red eastern-most in the top panel) and run backwards every 3 hours until June 17 th at 20:00 PDT.Only the first 4 outputs are shown.

Figure 7 .
Figure 7. WRF predicted planetary boundary layer heights and HSRL calculated mixed layer heights for 3 flights in the San Joaquin Valley (2 during CalNex and one during a CARES campaign).

Figure 8
Figure 8. a) The CARB NH 3 emissions (solid blue) and adjusted scenario emissions (solid red) based on ground measurements at the Bakersfield site.b) Fine NH 4(p) for the same time period to show the small concentrations relative to NH 3 (notice scale difference).c) NH x concentrations for the CalNex measurements (solid black), the initial CMAQ run 5 (dashed blue), an adjusted emissions CMAQ run (i.e., diurnally varying emissions, dashed red), a CMAQ run using the original emissions and the bi-directional NH3 flux scheme (dashed green), and a CMAQ run using both adjusted emissions and bi-directional flux (dashed purple) at the Bakersfield site averaged hourly from 25 to 31 of May, 2010.

Table 1 .
Summary statistics of the modelled to measured NH x concentration comparisons following the SJV flights, with mean bias (MB) and mean normalized bias (MNB) of NH 3(g) and NH 4(p) included.See Figures1 and 5.

Table 2 .
Summary statistics of the modelled to measured NH x concentration comparisons to the ground measurements and TES RVMR with 1) the original CARB emissions inventory runs and 2) the bi-directional ammonia scheme runs with adjusted emissions for our 7-day case study period.Note as TES only observes NH 3(g) there are no statistics for NH 4(p) and NH x from TES. 15