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% Author names in capital letters:
\authorrunninghead{Coggon et al. 2013}

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\titlerunninghead{Biogenic Impacts on the Marine Atmosphere}

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\authoraddr{M.M. Coggon, J. S. Craven, R.C. Flagan, and J. H. Seinfeld, Divisions of Chemistry and Chemical Engineering and of Environmental Science and Engineering, California Institute of Technology, 1200 E. California Blvd., Mail Code 210-41, Pasadena, CA  91125, USA.  (seinfeld@caltech.edu)}

\authoraddr{A. Sorooshian and Z. Wang, Departments of Chemical and Environmental Engineering and Atmospheric Sciences, University of Arizona, PO Box 210158b, Tucson, Arizona 85721, USA}

\authoraddr{A.R Metcalf, Department of Mechanical Engineering, University of Minnesota, 111 Church St. , Minneapolis , MN 55455, USA}

\authoraddr{A. Nenes and J.J. Lin, Schools of Earth and Atmospheric Sciences and Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332, USA}

\authoraddr{H.H. Jonsson, Center for Interdisciplinary Remotely-Piloted Aircraft Studies, 3200 Imjin Road, Monterey, CA 93933, USA}
%
% Key Points:
% 1. We measure continental BOA above marine stratocumulus off the coast of California.
% 2. BOA was observed to mix into the marine boundary layer.
% 3. This source has a large area of impact off the coast of California.

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\title{Supplemental Information ``Observations of continental biogenic impacts on marine aerosol and clouds off the coast of California"}

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\authors{
M.M. Coggon           \altaffilmark{1},
A. Sorooshian            \altaffilmark{2,3},
Z. Wang         \altaffilmark{3},
J.S. Craven        \altaffilmark{1},
A.R. Metcalf           \altaffilmark{4},
J.J. Lin             \altaffilmark{5},
A. Nenes        \altaffilmark{5,6},
H.H. Jonsson            \altaffilmark{7},
R.C. Flagan             \altaffilmark{1,8},
J.H. Seinfeld           \altaffilmark{1,8}}


% Matthew Coggon, Jill Craven, John Seinfeld, and Rick Flagan
\altaffiltext{1}{Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California, USA}

% Armin Sorooshian, Zhen Wang
\altaffiltext{2}{Department of Chemical and Environmental Engineering, University of Arizona, Tucson, AZ, USA}

% Armin Sorooshian
\altaffiltext{3}{Department of Atmospheric Sciences, Tucson, University of Arizona, AZ, USA}

% Andrew R. Metcalf
\altaffiltext{4}{Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA}

% Jack Lin, Athanasios Nenes
\altaffiltext{5}{School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, USA}

% Athanasios Nenes
\altaffiltext{6}{School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA, USA}

% Haflidi Jonsson
\altaffiltext{7}{Naval Postgraduate School, Monterey, CA.}

% Richard Flagan and John Seinfeld
\altaffiltext{8}{Department of Environmental Science and Engineering, California Institute of Technology, Pasadena, CA, USA}


\newpage 

\begin{article}
\linenumbers*[1]

\clearpage

\section{Supplemental Movie}
\label{sec:supplementalmovie}

Included in the Supplemental Information is a movie illustrating the development of a continental plume during flight N10. This movie is a comprehensive illustration of the trends summarized in Fig. \ref{fig:N10_SummaryGraph} of the manuscript and is meant to illustrate the temporal influence of continental plumes on aerosol above marine stratocumulus. The movie is separated into two panels. On the left, satellite images from http://www.nrlmry.navy.mil/sat\_products.html are displayed with 24 hour back trajectories ending at the yellow stars 600 m above sea level (i.e., in the free troposphere above marine stratocumulus). The back trajectories update every 2 hours. We choose to show the development of back trajectories at this altitude because we are interested in illustrating the origins of aerosol above the marine temperature inversion with high Org/SO$_4$, which is identified in this study as continental organic aerosol impacted by biogenic sources (BOA). (see Sections \ref{sec:BOASource} and \ref{sec:BOAImpacts}). Air below cloud originated from the remote Pacific Ocean (Fig. \ref{fig:SI_BelowCloudBackTrajectories}). At the bottom left is a time stamp indicating the date and time that the satellite image was recorded. Note that the images begin on July 18, 2013, the day before flight N10. 

The right panel is an expanded view of the area sampled by the Twin Otter. On July, 19, 2013 (N10), the aircraft begins its trajectory. At the top of the panel is a time-series trace of the Twin Otter's altitude with a dotted line indicating the base of the marine temperature inversion. Both the altitude and spatial traces are colored by the Org/SO$_4$ ratio. The highest color displayed is Org/SO$_4$= 20, however Org/SO$_4$ upwards of 50 are observed. 

As discussed in the manuscript (Section \ref{sec:BOAImpacts}), plume events developed over the course of the day on July 18 and 19, 2013. The formation of these plumes is induced by the flow of dry, offshore air \citep{Kloesel:1992}, which is illustrated by back trajectories. During flight N10, samples outside of fresh plume influence (below $\sim$ 39$\degree$) show moderate Org/SO$_4$ which is likely due to a plume event from the previous day. Spirals performed above 39$\degree$ were conducted within the plume and show enhancement of Org/SO$_4$, which appears to be due to fresh transport of continental BOA.

\section{Analysis of Mass Spectra by Positive Matrix Factorization}

The PMF solution described below is for the combined E-PEACE dataset. As discussed in Section 3.2, PMF solutions are utilized with the intention of identifying the source of organic aerosol measured above the marine temperature inversion during E-PEACE and NiCE (Fig. \ref{fig:SummaryGraph}). The two factors that are resolved are identified as continental (Factor 1) and marine (Factor 2), respectively. Justification for factor qualifiers is provided in Sections \ref{ContinentalOA} and \ref{sec:BOASource}. The discussion below is aimed at determining the size of the solution space and the uncertainty associated with Factor 1, which corresponds to the highly organic aerosol measured above the marine temperature inversion. 

\subsection{PMF Preparation}
The inputs to PMF (organic mass matrices and corresponding error matrices) were generated using AMS software (SQUIRREL v 1.51H) driven by IGOR Pro v 6.3 (Wave Metrics Inc., Lake Oswego, Oregon). Only masses less than \textit{m/z} 100 were considered in this analysis. Measurements of total organic mass less than the detection limit calculated by \citet{Coggon:2012} (organic mass $<$ 0.18 $\mu$g m$^{-3}$) were removed from the analysis. \citet{Ulbrich:2009vy} prescribes adjusting error matrices based on the signal-to-noise ratio (SNR) such that masses with SNR $<$ 0.2 are removed from the PMF analysis while masses with 0.2 $<$ SNR $<$ 2 are down-weighted via increasing corresponding error estimates by a factor of 2-3. In this analysis, most masses exhibit low SNR with a max at \textit{m/z} 43 (SNR = 4.75, Fig. \ref{fig:SI_PMFDiagnostics}B.). A low SNR is not uncommon in the marine environment; therefore, we forgo down-weighting masses with SNR $<$ 2 so as not to overestimate error. Masses that are calculated based on the signal of \textit{m/z} 44 are down-weighted (\textit{m/z} 16, 17, 18, and 44) since these provide redundant information to the PMF algorithm. The error associated with these factors was multiplied by a factor of $\sqrt{4}$, as prescribed by \citet{Ulbrich:2009vy}. Corrected data were analyzed using the PMF2 algorithm \citep{PMF2:2007} with factor spaces consisting of 10 seeds and FPEAK varying between -1 and 1. Model output were analyzed using the PMF Evaluation Tool (v 2) developed by \citet{Ulbrich:2009vy}.

Initially, all data were included in this analysis; however, preliminary PMF evaluations indicated the presence of a cloud-processed ship emission factor that was limited in space and time. E-PEACE measurements of aerosol and clouds impacted by cloud-processed ship emissions exhibit a high fraction of organic mass at \textit{m/z} 42 and 99 \citep{Coggon:2012}. The factor resolved from these preliminary evaluations exhibited organic fractions of \textit{m/z} 42 and 99 of 0.17 and 0.02, respectively, which is consistent with a moderate to heavy impact by cloud-processed ship emissions. At no other time during flight were there indications of cloud-processed ship emissions. Removal of these brief periods of ship-impacted aerosol had no influence on subsequently resolved factors.

\subsection{Choosing the number of factors}
\label{sec:FactorDecision}

In general, the PMF solution weakly varies as a function of the number of factors fit to the data. This is best illustrated by the variation of the quality of fit parameter, Q, which is the minimization function that drives a PMF solution. Q is defined as \citep{Paatero:1994,Ulbrich:2009vy}

$Q = \sum\limits_{i=1}^{m}\sum\limits_{j=1}^{n} (e_{ij}/\sigma_{ij})$

Where $e_{ij}$ and $\sigma_{ij}$ are the residuals and errors of an element in a $m\,x\,n$ matrix. A well-resolved solution implies that residuals are fit to within the respective error of a given mass, and thus the ratio of $e_{ij}/\sigma_{ij}$ should equal one. When normalized by the expected Q (Q$_{expected}$, equal to the number of elements in the organic matrix), a well-resolved solution should have Q/Q$_{expected}$ = 1. As illustrated in Fig. \ref{fig:SI_PMFDiagnostics}A, Q/Q$_{expected}$ is near unity for even a single factor solution and shows small decreases with increasing factors.  While these lower values of Q/Q$_{expected}$ could be due to overestimation of the error matrix \citep{Ulbrich:2009vy}, it is likely that this behavior is due to persistently low concentrations of organic aerosol (typically $\leq$ 1 $\mu$g m$^{-3}$) with low SNR (Fig. \ref{fig:SI_PMFDiagnostics}B) and relatively homogeneous composition.

Figure \ref{fig:SI_PMFDiagnostics}A also shows how Q/Q$_{expected}$ varies as a function of FPEAK. FPEAK is a parameter that allows one to explore the rotational ambiguity of a PMF solution. For any given number of factors, there could be multiple solutions that yield an equal fit. While there is a minimum Q/Q$_{expected}$ at FPEAK = 0, non-zero values of FPEAK may yield good solutions if Q/Q$_{expected}$ varies only slightly from its minimum ($\leq$ 10\%, \citet{Ulbrich:2009vy}). From Fig. \ref{fig:SI_PMFDiagnostics}A, we find that solutions greater than 2 factors exhibit large spread in Q/Q$_{expected}$ with varying FPEAK. Values of -0.6 $<$ FPEAK $<$ 0.6 show the least deviation from FPEAK = 0, which may imply that the best solution is within this range of FPEAK values. However, we note that Q/Q$_{expected}$ is low regardless of the value of FPEAK, and thus the best solution will rely on correlation with external tracers (discussed below and in Sections \ref{ContinentalOA} and \ref{sec:BOASource} of the manuscript). 

We can further investigate the variation of Q/Q$_{expected}$ by studying the scaled residuals for one, two, and three-factor solutions. Figure \ref{fig:SI_ScaledResiduals} shows that even for a one-factor solution, most masses are fit to within their respective error. The only mass that shows deviation is \textit{m/z} 43. For a two-factor solution, \textit{m/z} 43 is fit appropriately and we observe minor improvements in the scaled time-series residuals. Scaled residuals for solution spaces greater than two factors do not show significant improvements. This behavior is consistent with our inference that low Q/Q$_{expected}$ is due to relatively homogeneous organic aerosol composition since the only major difference between a one and two-factor solution is the improvement of fit to \textit{m/z} 43.

Despite small improvements in residuals, we find that increasing towards additional factors lends meaningful results. This is to be expected given that aerosol measured above the marine temperature inversion (organic $>$ 85\% by mass) exhibits different bulk properties than that measured below the inversion (sulfate $\simeq$ 50\% by mass , see text Fig. \ref{fig:SummaryGraph}). Likewise, the organic mass spectra measured at either altitude exhibits sufficient variation to warrant the presence of multiple factors. Figure \ref{fig:SI_TrianglePlot} shows that within the $f_{44}$ vs. $f_{43}$ triangular space \citep{Ng:2010}, aerosol measured above the inversion exhibits higher fractions of \textit{m/z} 43 ($f_{43}$) than that measured below. A multiple-factor solution would capture this difference, which is consistent with the improved fit to \textit{m/z} 43 for multiple factors (Fig. \ref{fig:SI_ScaledResiduals}).

%Note that only measurements with organic content greater than 5x the detection limit are shown ( $>$ 0.45 $\mu$g m$^{-3}$) in Fig. \ref{fig:SI_TrianglePlot}. }

Figure \ref{fig:SI_FactorSolnSpace} summarizes the PMF results for a two and three-factor solution with FPEAK = -0.4. We choose a solution with FPEAK = -0.4 due to improved correlation with external factors relative to a solution at FPEAK = 0 (see Section \ref{sec:FPEAK}). In a two-factor solution, Factor 1 is dominated by mass at \textit{m/z} 44 (f$_{44}$ = 0.125) and 43 (f$_{43}$ = 0.11). Factor 2 is dominated by mass at \textit{m/z} 44 (f$_{44}$ = 0.125) and \textit{m/z} 29 (f$_{29}$ = 0.09) with little contribution by \textit{m/z} 43 (f$_{43}$ = 0.02). Factors 1 and 2 have f$_{44}$/f$_{43}$ that scatter within regions of the triangle space consistent with aerosol measured above and below cloud, respectively. In addition, Factor 2 shows positive variation with sulfate (R = 0.58), which is predominantly present below the marine temperature inversion (Fig. \ref{fig:SI_ExternalData}). Factor 1 is anti-correlated with sulfate (R = -0.2) and is dominant above the marine temperature inversion. Thus, a two-factor solution resolves the mass spectra of aerosol with high (Factor 1) and low (Factor 2) Org/SO$_4$ ratio, consistent with our inferences that aerosol measured above and below cloud differ in both bulk aerosol composition and organic mass spectra. 

When the PMF solution is increased to three factors, the mass spectral profiles for Factors 1 and 2 change very little, however we are left with a third factor composed largely of \textit{m/z} 29. The mass attributed to this factor is low and appears to only affect the time series trend for Factor 2. Figure \ref{fig:SI_Factor1And2Comparisons} compares the time series for Factors 1 and 2 from a two-factor solution with the time series of these factors resolved from a three, four, or five-factor solution. In general, the mass concentration for Factor 1 changes very little regardless of how many factors we choose to fit, implying that this factor is robustly resolved. The mass concentration of Factor 2, however, is lowered with additional factors. Factor 3 has no meaningful correlation with other external data, therefore we suspect that larger factor spaces result in Factor 2 splitting. Given that higher factors yield no meaningful results and that a two-factor solution space shows consistent variation with bulk aerosol composition, we conclude that a two-factor solution is sufficient to describe the variation in organic composition. 

\subsection{Variation with FPEAK and uncertainty.}
\label{sec:FPEAK}

As mentioned in Section \ref{sec:FactorDecision}, we evaluate our PMF solution with FPEAK = -0.4 due to improved correlation with external data. Solutions with FPEAK $\geq$ 0 exhibit correlation between Factors 1 and 2 (R $>$ 0.6), implying that a two-factor solution in this range of FPEAK can be equivalently described as a one-factor solution (Figure \ref{fig:SI_FPEAKCorrelations} ). However, aerosol above and below the marine inversion exhibit different organic composition (Fig. \ref{fig:SI_TrianglePlot}) and so a multiple-factor solution is anticipated. Thus, we neglect solutions with FPEAK $>$ 0. 

At lower values of FPEAK, we find that that Factor 2 correlates more strongly with sulfate. FPEAK = -0.2 yields a 10\% improvement in correlation over FPEAK = 0  while FPEAK = -0.4 yields a 4\% improvement in correlation over FPEAK =  -0.2. Thus, we choose FPEAK =  -0.4 since correlation between sulfate and Factor 2 does not improve dramatically after this value of FPEAK.

Given these variations with respect to FPEAK, there is uncertainty in our solution. However, our intention in using PMF is to evaluate the source of the highly organic aerosol measured above the marine temperature inversion, and thus we are concerned with how robustly this factor is resolved. As discussed in Section \ref{sec:FactorDecision}, Factor 1, which corresponds to this highly organic aerosol, has a profile that weakly varies as a function of how many factors we choose to fit. This is true for most values of FPEAK $<$ 0. Figure \ref{fig:SI_FPEAKUncertainty} shows that for -0.6 $<$ FPEAK $<$ -0.2, the Factor 1 profile varies little regardless of how many factors we choose to fit. For FPEAK = -0.8, the Factor 1 profile shows significant deviation with increased factors, however this is likely a reflection of inadequate fits with factors greater than 2 (see Q/Q$_{expected}$ for FPEAK = -0.8, Fig. \ref{fig:SI_PMFDiagnostics}). Thus, for well-fit solutions, the Factor 1 profile is consistently resolved to that of a two-factor solution with FPEAK = -0.4.

\subsection{PMF Summary}

Positive matrix factorization analysis shows that a two-factor solution is sufficient to describe the variation in organic mass for measurements made during E-PEACE. The two factors that are resolved correspond with aerosol measured above (Factor 1, high Org/SO$_4$ ratio) and below (Factor 2, low Org/SO4$_4$ ratio) the marine temperature inversion. Factor 1 has a profile that is robustly resolved regardless of the number of factors we choose to fit. In Section \ref{ContinentalOA}, we show that these factors best correspond to continental (Factor 1) and marine boundary layer (Factor 2) sources, respectively.



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\providecommand{\natexlab}[1]{#1}
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 \bibitem[{\textit{Allan et~al.}(2004)}]{Allan:2004}
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\bibitem[{\textit{Coggon et~al.}(2012)}]{Coggon:2012}
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\bibitem[{\textit{Ng et~al.}(2010)}]{Ng:2010}
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\bibitem[{\textit{Paatero and Tapper}(1994)}]{Paatero:1994}
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Paatero, P. (2007), User's guide for positive matrix factorization programs PMF2.EXE and PMF3.EXE, University of Helsinki, Finland.

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\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=10cm]{SI_BelowCloudBackTrajectories.pdf}
\end{center}
\caption{Back trajectories illustrating the origin of air below cloud during flight N10. These back trajectories end 100 m above sea level at 23:00 UTC in the region described in Supplemental Information Section \ref{sec:supplementalmovie}.}\label{fig:SI_BelowCloudBackTrajectories}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_PMFDiagnostics.pdf}
\end{center}
\caption{A) Q/Q$_{expected}$ as a function of the number of factors for various values of FPEAK. FPEAK = 0, which gives the best mathematical fit, is shown as the thick black line. B) Signal-to-noise ratio (SNR) of the organic matrix input to the PMF analysis. Dotted lines indicate SNR = 2 and 0.2, respectively.}
\label{fig:SI_PMFDiagnostics}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_ScaledResiduals.pdf}
\end{center}
\caption{Time series (left column) and mass spectral (right column) residuals scaled to Q$_{expected}$ for 1 (black), 2 (red), and 3 (blue) factors with FPEAK = -0.4. }
\label{fig:SI_ScaledResiduals}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_TrianglePlot.pdf}
\end{center}
\caption{Triangle plot \citep{Ng:2010} showing the relative contributions of organic mass at \textit{m/z} 44 ($f_{44}$) and 43 ($f_{43}$) measured above and below cloud, respectively. Both sources fall within the semi-volatile region of the triangular space, where the above cloud aerosol exhibits a higher fraction of organic at \textit{m/z} 43 than that of aerosol below cloud. The square markers indicate $f_{44}/f_{43}$ for Factors 1 and 2, respectively.}
\label{fig:SI_TrianglePlot}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_FactorSolnSpace.pdf}
\end{center}
\caption{Summary of A) two and B) three factor solutions. Traces on the left are time series of a given factor. Mass spectra on the right indicate the organic signature for each factor.}
\label{fig:SI_FactorSolnSpace}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=18cm]{SI_ExternalData.pdf}
\end{center}
\caption{External data compared to A) Factor 1 and B) Factor 2. Shaded regions indicate measurements performed above the marine temperature inversion (determined based on temperature discontinuities with altitude). The NaCl trace is defined similarly to that from \citet{Allan:2004} and is the sum of mass at \textit{m/z}  23 (Na$^+$), 35 (Cl$^+$), 36 (HCl$^+$) and 58 (NaCl$^+$).  }
\label{fig:SI_ExternalData}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_Factor1And2Comparisons.pdf}
\end{center}
\caption{Comparison of Factor 1 (A) and 2 (B) time series for a two-factor solution to the Factor 1 and 2 time series resolved from a three, four, or five-factor solution. The one-to-one line indicates that a factor profile for $>$ 2 factor-solutions is identical to that of a two-factor solution. In general, the Factor 1 profile does not change as we choose to fit additional factors. The Factor 2 profile, however, is split as more factors are included in the solution.}
\label{fig:SI_Factor1And2Comparisons}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_FPEAKCorrelations.pdf}
\end{center}
\caption{Factor 2 correlations with Factor 1 and SO$_4$ as a function of FPEAK. }
\label{fig:SI_FPEAKCorrelations}
\end{figure}

\clearpage

\begin{figure}[p]
\vspace*{2mm}
\begin{center}
\includegraphics[width=15cm]{SI_FPEAKUncertainty.pdf}
\end{center}
\caption{ A) Comparison of Factor 1 time series for a two-factor solution to the time series resolved from a three of four-factor solution for various values of FPEAK. B) The relative location of Factor 1 in the triangle space under various conditions of FPEAK and solution-space size. The solution reported here (two factors, FPEAK = -0.4) is shown.}
\label{fig:SI_FPEAKUncertainty}
\end{figure}




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