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\title{Lidar observation of the 2011 Puyehue-Cord\'{o}n Caulle volcanic aerosols at Lauder, New Zealand}

\author[1]{K. Nakamae}
\author[1]{O. Uchino}
\author[1]{I. Morino}
\author[2]{B. Liley}
\author[3]{T. Sakai}
\author[3]{T. Nagai}
\author[1]{T. Yokota}

\affil[1]{National Institute for Environmental Studies, Tsukuba,
Ibaraki, Japan}
\affil[2]{National Institute of Water and Atmospheric Research, Lauder, New Zeal
and}
\affil[3]{Meteorological Research Institute, Tsukuba, Ibaraki, Japan}

\runningtitle{Lidar observation of the 2011 Puyehue volcano}
\runningauthor{K.~Nakamae et~al.}
\correspondence{K.~Nakamae (nakamae.kumi@nies.go.jp)}

\received{}
\accepted{}
\published{}

\firstpage{1}

\maketitle

\begin{abstract}
  On 4 June~2011, the Puyehue-Cord\'{o}n Caulle volcanic complex
 (40.6{\degree}\,S, 72.1{\degree}\,W) in Chile erupted violently and
 injected volcanic aerosols into the atmosphere.  For the safety of
 civil aviation, continuous lidar observations were made at Lauder, New
 Zealand (45.0{\degree}\,S, 169.7{\degree}\,E), from 11 June through 6
 July~2011. The purpose of our study is to quantify the influence of the
 volcanic ejections from large eruption, and we use the data from the
 ground-based lidar observation.  We analyzed lidar data at a wavelength
 of 532\,\unit{nm} and derived the backscattering ratio and
 depolarization ratio profiles. During June and July, within the
 altitude range of \text{10--15}\,\unit{km}, the volcanic aerosols had
 high depolarization ratios (20--35\,{\%}), an indication of
 non-spherical volcanic ash particles. The time series of the
 backscattering ratio during continuous observations had three peaks
 occurring at about 12\,day intervals:  26.7 at 11.2\,\unit{km} on 11
 June, 18.1 at 12.0\,\unit{km} on 23 June, and 5.3 at 11.1\,\unit{km} on
 6 July. The optical depth of the volcanic aerosols was 0.45 on 11 June,
 when the continuous lidar observation started, 0.31 on 23 June, and
 0.12 on 6 July. The depolarization ratio values remained high up to a
 month after the eruption and the small wavelength exponent calculated
 from the backscattering coefficients at 532\,\unit{nm} and
 1064\,\unit{nm} suggest that a major constituent of the volcanic
 aerosols was large, non-spherical particles.  The presence of volcanic
  ash in the stratosphere might affect the error in  Greenhouse gases
 Observing SATellite (GOSAT) X\chem{CO_2} retrieval using the
 1.6\,\unit{{\mu}m} band. We briefly discuss the influence of the
 increased aerosols on  GOSAT products. 
\end{abstract}

\introduction

Eruptions with a volcanic explosivity index (VEI) larger than 4 to 5 are 
 generally expected to inject volcanic aerosols into the stratosphere
  \citep{newhall1982, deshler2008, vernier2011, trickl2013}. 
The VEI was developed as a simple and semi-quantitative scheme for
 estimating the magnitude of historic eruptions by
 \citet{newhall1982}. Eruptions are assigned to a VEI on a scale of 0 to
 8, using the criteria such as the volume of ejecta, column height and
 qualitative of the eruption. Especially, the volume of ejecta and the
 column height are important. 
Volcanic aerosol particles larger than 10\,\unit{{\mu}m} injected into
 the stratosphere settle rapidly, so their climatic effects can
 generally be neglected \citep{robock2000}. Volcanic ash is known to
 affect tropospheric cloud phases by acting as ice nuclei
 \citep{durant2008, lathem2011}.  
In contrast, when a large amount of sulfur dioxide is injected into the
 stratosphere, it is converted to sulfuric acid particles within several
 weeks \citep{zhao1995}. 
 The Mt. Pinatubo volcano (Philippines, 15.1{\degree}\,N;
 120.4{\degree}\,E) erupted on 15 June 1991 and stratospheric injection
 of about 20\,\unit{Mt} of \chem{SO_2} was detected by the Total Ozone
 Mapping Spectrometer \citep{bluth1992}. 
The \chem{SO_2} is oxidized to sulfuric acid vapor from  which
 sulfuric acid particles are produced by homogeneous nucleation
 \citep{wu1994}. These particles are long-lived in the stratosphere
\citep{uchino1995,nagai2010}, depending on the latitude and altitude of
 injection, and significantly affect the global climate and radiation
 budget and the ozone layer \citep{minnis1993, mccormick1995,
 alados-arboledas1997,robock2000, solomon2011}. 

Large amounts of volcanic ash in the atmosphere can damage aircraft
engines and raise flight safety concerns; as a result they can have
significant consequences for air traffic. The volcanic hazards for
aircraft have been recognized that are the stop of aviation engines,
reduction of visibility and the damage to windshield due to volcanic ash
\citep{bernard1990}. For example, the ash plume from the eruption of the
Eyjafjallaj{\"o}kull volcano (63.63{\degree}\,N, 19.62{\degree}\,W,
Iceland) on 14 April 2010 disrupted air traffic over Europe. 
The small particles and trace gases such as {\chem{SO_2}} from this
eruption were transported over long distances
\citep{tesche2010,ansmann2010, wiegner2012}. 

On 4 June 2011, the Puyehue-Cord\'{o}n Caulle Volcanic Complex
(hereafter PCCVC; 40.59{\degree}\,S, {72.11{\degree}\,W)} in Chile
erupted and injected large amounts of volcanic ash particles into the 
atmosphere (VEI=3) \citep{zierma2012}. This volcanic complex had
previously erupted in May 1960 \citep{lara2004, raga2013}. 
The volcanic aerosol plumes travelled eastward from Chile via the
prevailing westerlies and passed over New Zealand \citep{kluser2013}. 
Because the Volcanic Ash Advisory Center (VAAC) in Wellington had
forecast that a large volcanic aerosol plume would reach New Zealand, we
performed continuous observations of volcanic aerosols with lidar at
Lauder (45.04{\degree}\,S, 169.68{\degree}\,E), New Zealand, and
provided the observational data to the VAAC for the safety of civil
aviation. The aerosol lidar system at Lauder is a two-wavelength
polarization lidar. In this study, we used continuous lidar
observational data observed at Lauder from 11 June through 6 July 2011. 

 We retrieved the backscattering ratios at 532\,\unit{nm} and
 1064\,\unit{nm} and the depolarization ratio at 532\,\unit{nm}, and we
 calculated the ratio of the backscattering coefficients at
 532\,\unit{nm} and 1064\,\unit{nm}.  For meteorological data and
 derivation of the tropopause height required for the lidar data
 analysis, we used the twice-daily radiosonde data observed at  
Invercargill (46.42{\degree}\,S, 168.33{\degree}\,W), 186\,\unit{km}
 south-west of Lauder. We use the tropopause height as the lowest level
 at which the temperature lapse rate is less than 2 K/km for higher
 levels within 2 km defined by the WMO \citep{wmo1957}. 

In the next section, we describe the lidar system at Lauder. In Sect. 3,
we present the analysis and results and we discuss the backscatter
wavelength dependence in Sect. 4.


\section{Lidar system and data analysis}

Lidar measurement of stratospheric aerosols at Lauder was started in
November 1992, owing to interest in the then-recent eruption of
Mt. Pinatubo \citep{uchino1995} and as a component of the nascent
Network for the Detection of Stratospheric Change, subsequently the
Network for the Detection of Atmospheric Composition Change. Though that
system had only a single detector (532\,\unit{nm}), some depolarization
measurements were made starting in November 1995. 
The system operated reliably for 17 years and recorded the decline of
the Pinatubo aerosol to a minimum in the late 1990s \citep{nagai2010},
followed by an increase in stratospheric aerosols by other volcanoes
\citep{vernier2011, uchino2012}.  In February 2009 this lidar system was
updated for both daytime and night-time observations of aerosols and
clouds for Greenhouse gases Observing SATellite (GOSAT) product
validation \citep{nagai2009}. The updated system is a two-wavelength
polarization lidar. In this study, we use lidar data obtained by
continuous measurements from 11 June 2011 to 4 July 2011, with
measurements made before and after this period for GOSAT
productvalidation. The main lidar specifications are summarized in 
Table 1. The light source of the lidar system is a Nd:YAG laser with
a second-harmonic generator: the laser thus operates at two wavelengths,
532\,\unit{nm} and 1064\,\unit{nm}. The pulse repetition rate is
10\,\unit{Hz}, and the transmitted energy is 150 mJ per pulse. The
receiving telescope has a diameter of 30.5\,\unit{cm}. The signal at
1064\,\unit{nm} is detected with an analogue-mode avalanche photo diode
(APD), and two polarization components of the signals at 532\,\unit{nm}
are detected with three photomultiplier tubes (PMTs) from the near
surface to the to a high altitude of $\sim 40$\,\unit{km}.

In this study, we used the Fernald method \citep{fernald1984}, in which
the lidar equation for retrieving vertical profiles of the aerosol
backscatter coefficients from lidar signal intensity is solved by
assuming an extinction-to-backscatter ratio (lidar ratio). We also
assumed that there was no aerosol in the upper atmosphere at around
30\,\unit{km}, and used the value from that altitude as a reference
value by which to normalize the rest of the profile. The lidar ratio is
an important parameter for obtaining profiles of the particle extinction
coefficient from lidar signals to use for iterative correction of the
backscatter profile.  The lidar ratio $S$ is defined as the ratio of the
extinction coefficient $\alpha$ to the backscattering coefficient
$\beta$: 
\begin{align}
&S=\frac{\alpha}{\beta}.
\end{align}
We assumed $S$ to be 50\,\unit{sr} at both 532 and 1064\,\unit{nm} in
this study. The lidar ratio depends on particle properties such as their
size distribution and shape. The backscattering ratio $R$ is defined as
follows:
\begin{align}
&R=\frac{(\beta_{\mathrm{A}}+\beta_{\mathrm{M}})}{\beta_{\mathrm{M}}},
\end{align}
where $\beta_{\mathrm{A}}$ is the aerosol backscattering coefficient and
$\beta_{\mathrm{M}}$ is the molecular backscattering coefficient. For a
pure Rayleigh atmosphere $R=1.0$, and the backscatter signal from
aerosols increases as $R$ becomes larger than 1.0. The molecular
backscattering coefficient $\beta_{\mathrm{M}}$ was calculated by using
the atmospheric density profiles obtained from 
radiosonde data launched at Invercargill (46.45{\degree}\,S,
168.33{\degree}\,W) \citep{bucholtz1995}.

The lidar transmits linearly polarized light at 532\,\unit{nm} and
records the backscattering intensity with parallel $P_{\parallel}$ and
perpendicular $P_{\perp}$ polarization to the transmitted
polarization. The total depolarization ratio $\delta$ is defined as 
\begin{align}
&\delta=\frac{P_{\perp}}{(P_{\perp}+P_{\parallel})}\times 100\,{\%}.
\label{eq3}
\end{align}

Because backscattering by spherical particles does not change the laser
polarization, $\delta=0$ for spherical particle. The depolarization
ratio is sensitive to the non-spherical particles.  When $\delta>0$,
the scattering by non-spherical particles is recognized
\citep{sassen1991}.



\section{Results}

\subsection{Comparisons of aerosol vertical profiles before and after
  the eruption}

Figure \ref{Fig.1} shows the vertical profiles of $R$ and $\delta$
before and after the PCCVC eruption.  The first aerosol plume from the
PCCVC eruption on 4 June 2011 was observed by lidar at Lauder at
midnight on 11/12 June.  The volcanic aerosol peak was located above the
tropopause (10.35\,\unit{km}) on 11~June. The peak $R$ value at
532\,\unit{nm} was 26.7 at 11.23\,\unit{km}, and the peak $\delta$ value
at 532\,\unit{nm} was 16.0\,{\%} at 10.3\,\unit{km}.  The maximum value
of $R$ on 28 May (before the eruption) around 7\,\unit{km} was due to
tropospheric aerosols; the maximum value of $R$ in the stratosphere was
1.09 at 16.03\,\unit{km}.

The integrated backscattering coefficient (IBC) is defined by Eq. (4)
\begin{align}
&{\text{IBC}}=\int^{Z_{\text{top}}}_{Z_{\text{tr}}} \beta_{\mathrm{A}} \mathrm{d}z.
\end{align}
We calculated IBC from the tropopause height $Z_{\text{tr}}$ to
$Z_{\text{top}}$, taking $Z_{\text{top}}=30$\,\unit{km}.
IBC represents the amount of stratospheric aerosol loading at a given
location. IBC was $2.2\times 10^{-4}$\,\unit{sr^{-1}} on 28 May; this
value is slightly larger than the stratospheric background value of
$1.42\times 10^{-4}$\,\unit{sr^{-1}} \citep{nagai2010}. 
On 11 June, after the eruption, IBC was $8.5\times
10^{-4}$\,\unit{sr^{-1}}; this value indicates that the PCCVC aerosols
had reached the stratosphere over Lauder. We calculated forward
trajectories to confirm that the observed profile peaks represented
layers of volcanic aerosols derived from the PCCVC eruption. We
calculated 10\,day isentropic forward trajectories of air parcels by
using the METEX (Meteorological Data Explorer) software package, which
is provided by the National Institute for Environmental Studies and
driven by NCEP/NCAR Reanalysis Data \citep{kalnay1996} 4 times daily
(Fig. \ref{Fig.2}).

The initial points of 15 air parcels at 11\,\unit{km} altitude were
located in a~$1{\degree} \times 1{\degree}$ latitude/longitude box
centered at the PCCVC eruption and released at 17:00\,UTC on 4 June. The
calculations showed that the air parcels leaving the volcano on 4
June~2011 reached Lauder in the early morning of 12 June.  The
calculations also showed that 43\,{\%} of all air parcels reached the
vicinity of Lauder, and the volcanic aerosol plume from the PCCVC
eruption remained near the tropopause level in the mid-latitudes of the
Southern Hemisphere.  These results agree with the findings of
\citet{kluser2013}, who used backward trajectory calculations and
observations of the Infrared Atmospheric Sounding Interferometer (IASI)
on board the MetOp satellite to determine the evolution of the ash plume
around the Southern Hemisphere.

\subsection{Vertical profiles of the backscattering ratio and the
  depolarization ratio}

Vertical and temporal cross sections of the backscattering ratio and
depolarization ratio at 532\,\unit{nm} over Lauder are presented in
Fig. \ref{Fig.3}.  Volcanic aerosol layers with a large backscattering
ratio above the tropopause heights were distinguished from the cirrus
clouds present at about 8--9\,\unit{km} altitude, simply by the
position of the tropopause except when we could calculate $R$ at
1064\,\unit{nm}, because we don't have enough signal-to-noise-ratio to
calculate $R$ at 1064 {nm} in most of the observation period.  In each
ratio, we observed three peaks above the tropopause height in the
analysis period, on 11~June, 23 June, and 4 July. 
This result suggests that the volcanic aerosol plume circled the
Southern Hemisphere three times, a finding that was confirmed by using
IASI, Ozone Monitoring Instrument (OMI), and Moderate Resolution Imaging
Spectroradiometer (MODIS) satellite data (not shown)
\citep{kluser2013}. To examine the three peaks of the aerosol vertical
profiles in greater detail, we calculated the particle depolarization
ratio $\delta_{\mathrm{p}}$, to estimate the non-sphericity of the
particles:
\begin{align}
&\delta_{\mathrm{p}}(z)=\frac{\delta(z) R(z)-\delta_\mathrm{m}}{R(z)-1} \times 100\,{\%},
\end{align}
where $\delta$ is the total (molecular plus particle) depolarization
ratio, calculated with Eq. (3), and $\delta_\mathrm{m}$ is the
depolarization ratio of atmospheric molecules.  We used
$\delta_\mathrm{m}=0.37$\,{\%} for this lidar system, {defined} from the
spectral transmission data of the interference filter at 532\,\unit{nm}
and the Rayleigh backscattering cross sections \citep{sakai2003}.
The measured $\delta$ was about 1.0-1.2\,{\%} at altitudes h
igher than about 15 km (see Figs. \ref{Fig.4}(a)-(c) and \ref{Fig.6}),
and this indicates that $\delta$ is sum of $\delta_\mathrm{m}$ (0.37
\,{\%}) and the lidar system error (about 0.65 \,{\%}) where there were
no aerosols. We estimated  δ_p taking into according of this lidar
system error \citep{sakai2003}. When $R$ is close to 1.0,
$\delta_{\mathrm{p}}$ has a lager error. For example, when $R=1.05$ and
$\delta_{\mathrm{p}}=8$ \,{\%}, the error of $\delta_{\mathrm{p}}$ is
larger than 20 \,{\%}.

We estimated the proportion of non-spherical particles in the volcanic
aerosol layers from the particle depolarization ratio over Lauder
measured by lidar.  On 11 June (Fig. \ref{Fig.4}a), the maximum values
of $R$, $\delta$ and $\delta_{\mathrm{p}}$ were 26.7 (11.2\,\unit{km}),
16\,{\%} (11.8\,\unit{km}) and 19\,{\%} (12.0\,\unit{km}), respectively;
{on} 23 June (Fig. \ref{Fig.4}b), they were 18.1 (12.0\,\unit{km}),
25\,{\%} (12.3\,\unit{km}) and 32\,{\%} (12.4\,\unit{km}), respectively;
and on 6 July (Fig. \ref{Fig.4}c), they were 5.3 (11.1\,\unit{km}),
20\,{\%} (11.4\,\unit{km}) and 29\,{\%} (11.7\,\unit{km}),
respectively. Values of $\delta_{\mathrm{p}}$ higher than 20\,{\%} in
the aerosol layer indicate a predominance of non-spherical particles
\citep{sakai2003}.
The $\delta_{\mathrm{p}}$ values of the PCCVC volcanic aerosol layer
were larger than 20\,{\%} even on the third overpass during the
continuous observation period. By comparison, the $\delta$ values of the
Eyjafjallaj\"{o}kull volcanic aerosol layers in April 2010 in Iceland
were 35--40\,{\%} \citep{ansmann2010, gasteiger2011}. According to the
analysis by \citet{grob2012}, the wavelength-independent
$\delta_{\mathrm{p}}$ values of the pure ash layer of the
Eyjafjallaj\"{o}kull volcano were between 35\,{\%} and 38\,{\%}. 

One interesting feature of the depolarization data warrants further
investigation. For each of the three overpass plume observations,
$\delta_{\mathrm{p}}$ had a~local minimum at the backscatter ratio
peak. If this is a~real physical effect and not an artifact of
measurement or retrieval, it suggests some vertical separation of the
volcanic plume, for which we have no ready explanation. The centroid
height of the volcanic aerosol plumes descended with time after the
Pinatubo eruption \citep{iwasaka1995} and after the 2008 Kasatochi
eruptions in the Aleutian Islands \citep{bitar2010}. However, because
our observation period was brief, we could not tell whether the height
of the aerosol plumes was descending. 

\subsection{Aerosol optical depth derived from the backscattering ratio}

Aerosol optical depth (AOD) was calculated as the product of the IBC and
$S$. The time series of the AOD at 532\,\unit{nm} showed three peaks:
0.45 on 11 June, 0.31 on 23 June, and 0.12 on 5 July
(Fig. \ref{Fig.5}). As discussed in Sect.~3.2, the presence of three
peaks, and the decrease of the peak value with time, is an indication
that the volcanic aerosol plume passed over Lauder three times.

Because the AOD as calculated in this study depends on the lidar ratio
value, the appropriateness of the value chosen for that ratio needs to
be considered. According to the analysis (Raman method) of
\citet{grob2012}, the lidar ratio at 532\,\unit{nm} for the
Eyjafjallaj\"{o}kull eruption was $49 \pm 5$\,\unit{sr} (Maisach,
Germany), and according to the analysis of \citet{ansmann2010}, it
ranged from $55 \pm 5$\,\unit{sr} (Maisach) to $60 \pm 5$\,\unit{sr}
(Leipzig, Germany). \citet{hoffmann2010} reported that the lidar ratio
at 532\,\unit{nm} for the Kasatochi eruption event was $65 \pm
10$\,\unit{sr}. We compared the AODs reported above with AODs calculated
by a method that does not use the lidar ratio \citep{uchino1983}.  In
this method, the transmission $\tau(z_1,z_2)$, between altitude $z_1$
and $z_2$ is 
\begin{align}
&\tau(z_1,z_2)=\frac{z_2}{z_1}\left[\frac{p(z_2)R(z_1)\beta_\mathrm{m}(z_1)}{p(z_1)R(z_2)\beta_\mathrm{m}(z_2)}\right]^{1/2},
\end{align}
where $p(z)$ is the total received signal photon count at altitude $z$,
$\beta_\mathrm{m}(z)$ is the atmospheric molecular backscattering
coefficient, and $R(z)$ is the backscattering ratio. The transmission
can be determined by choosing two altitudes, $z_1$ and $z_2$, where no
aerosols are assumed to exist; therefore, $R(z_1)=R(z_2)=1.0$. For
example, the AOD on 11 June as determined by this method was $0.52 \pm
0.08$ ($z_1=8.4$\,\unit{km} and $z_2=12.0$\,\unit{km}); this AOD value
is 13\,{\%} larger than the AOD derived from the IBC and $S$. The values
of AOD derived by Eq. (6) are 0.17 and 0.12 on 24 June and 6 June,
respectively. On average, the AOD derived by IBC was about 20\,{\%}
smaller than AOD derived by Eq. (6). If the lidar ratio is assumed to be
60\,\unit{sr}, AOD will be consistent each other. 


\section{Discussion}

The observed PCCVC particle depolarization ratios $\delta_{\mathrm{p}}$
were large. On 11 June, the maximum $\delta_{\mathrm{p}}$ was 23\,{\%};
on 23 June, it was 33\,{\%}; and on 6 July, it was 29\,{\%}. These large
values indicate that the aerosol particles were non-spherical. We then calculated the backscatter-related wavelength exponent $A_{\beta}$ as follows:
\begin{align}
&A_{\beta}= -\frac{\ln(\beta_{532}/\beta_{1064})}{\ln(532/1064)},
\end{align}
where $\beta_{532}$ and $\beta_{1064}$ are the backscattering
coefficients at 532\,\unit{nm} and 1064\,\unit{nm}. $A_{\beta}$ provides
information about the size distribution of both spherical and
non-spherical particles that takes account of the complex dependence of
backscatter on particle component size, wavelength, and
non-sphericity. $A_{\beta} > 2$ indicates relatively smaller particles
(radius $\le 0.5$\,\unit{\mu m}) and $A_{\beta}$ around zero indicates
larger particles (radius $\ge 0.5$\,\unit{\mu m}) \citep{kaufman1994,
schuster2006}.  For background stratospheric aerosols, $A_{\beta}$ is
about 2.0 \citep{shibata1984, hofmann2009}; for cloud layers $A_{\beta}$
is about $-$0.2 to 0.0 \citep{kamei2006, mona2012}, and for volcanic ash
$A_{\beta}$ is about 1.0 \citep{ansmann2012}.

Figure \ref{Fig.6}a displays the vertical profiles of $R$, $\delta$ and
$\delta_ {\mathrm{p}}$ at 532\,\unit{nm}, and Fig. \ref{Fig.6}b shows the
vertical profiles of $R$ at 532\,\unit{nm} and{1064\,\unit{nm}} and of
$A_{\beta}$ at 532\,\unit{nm}/1064\,\unit{nm}, on 13 June. The peak of
$R$ was below the tropopause, but we infer that this represents the
volcanic layer because its average $A_{\beta}$ at 11--13\,\unit{km}
altitude was 0.92, whereas that of the stratospheric background aerosols
at 13--15\,\unit{km} was 2.54, and the mean value of cirrus clouds at
8--9.5\,\unit{km} was $1.29 \times 10^{-2}$.  Although the stratospheric
aerosol $A_{\beta}$ value at 13--15\,\unit{km} is a~little larger than
the literature value, the $A_{\beta}$ values of the volcanic aerosols
and cirrus clouds are consistent with value reported by previous studies
\citep{kamei2006, mona2012, ansmann2012}.
This result indicates that it should be possible to distinguish between
a volcanic aerosol layer and underlying cirrus clouds by using the
vertical profile of $A_{\beta}$. Unfortunately, because there were
optically thick clouds under the volcanic aerosol layers and the
vertical backscattering coefficient at 1064\,\unit{nm} were very noisy,
we were not able to apply this method to distinguish the aerosols and
cirrus clouds on the other days.

It is possible to use $A_{\beta}$, $\delta$ and $\delta_{\mathrm{p}}$
derived from lidar measurement to determine approximately the
proportions of sulfur acid aerosols and the ash particles. However, it
is not possible to determine the absolute quantity of these
particles. Typically, non-spherical and larger particles are volcanic
ash, whereas spherical and smaller particles are sulfuric acid
aerosols. As mentioned in Sect. 3, the finding that the total and
particle depolarization ratios of the PCCVC volcanic aerosols were
larger than 20\,{\%} suggests that the volcanic plume included many
non-spherical and large particles. Therefore, we concluded that the
dominant component of the plume observed over Lauder was volcanic ash.

Similarly, for aerosols from the eruption of Eyjafjallaj\"{o}kull, the
total depolarization ratios were 35--40\,{\%} \citep{ansmann2010,
gasteiger2011}.  In contrast, the Kasatochi ratios were 1.5--5.0\,{\%}
\citep{hoffmann2010} and the ratios for aerosols from the eruption of
Nabro volcano in Eritrea in 2011 were $\delta= 1$--2\,{\%} and
$\delta_{\mathrm{p}}=4$--7\,{\%} \citep{uchino2012}.  In the case of the
eruption of Eyjafjallaj\"{o}kull, \text{\citet{ansmann2011}}
reported that sulfate aerosols originating from volcanic \chem{SO_2}
plumes contributed about 50\,{\%} of the particle
mass. \citet{miffre2011} used the volcanic ash particle depolarization
ratio $\delta= 40 \pm 0.2$\,{\%} obtained from laboratory measurements
performed by \citet{munoz2004} to determine the composition of the
Eyjafjallaj\"{o}kull plume.

Recent studies have provided estimates of \chem{SO_2} emission from
several eruption events. \citet{karagulian2010} estimated the total mass
of \chem{SO_2} ejected by the Kasatochi eruption to be 1.7\,\unit{Tg},
based on the IASI high-spectral-resolution infrared radiance
measurements. \citet{haywood2010} estimated that 1.2\,\unit{Tg} of
\chem{SO_2} was ejected by the Sarychev (Kuril Islands) eruption in
June~2009. \citet{clarisse2012}, using IASI data, reported that
1.5\,\unit{Tg} of \chem{SO_2} was ejected by the Nabro volcano, and
0.25\,\unit{Tg} by the PCCVC eruption.  Because less \chem{SO_2} was
ejected by the eruption of Puyehue-Cord\'{o}n Caulle compared with the
amounts ejected by the eruptions of Nabro and Kasatochi, the tephra
fraction of the PCCVC plume was greater, and its depolarization ratios
were larger.

We next estimated the influence of the PCCVC volcanic ash particles on
the column averaged dry air mole fraction of carbon dioxide
(X\chem{CO_2}) determined by GOSAT. When the GOSAT X\chem{CO_2} is
retrieved by using the 1.6\,\unit{{\mu}m} band without taking account of
volcanic ash particles in the upper troposphere and lower stratosphere,
the negative bias of X\chem{CO_2} is estimated to be 2\,{\%} for an AOT
of 0.4 at 532\,\unit{nm} and surface albedo of 0.2 at Lauder 0.28 (based
on MODIS band2).


\conclusions[Summary]
On 4 June~2011, the Puyehue-Cord\'{o}n Caulle Volcanic Complex
(40.59{\degree}\,S, 72.11{\degree}\,W) in Chile erupted and the volcanic
plume passed over Lauder in New Zealand. Because the VAAC at Wellington
had forecast that the aerosol plume would pass over New Zealand, we
started continuous lidar observations on 11 June. On the same day, we
detected the PCCVC volcanic aerosol layer from the profiles of the
backscattering ratio $R$ and the depolarization ratio $\delta$ at
532\,\unit{nm}. This observational result was confirmed by a forward
trajectory analysis done by using METEX and some satellite data (from
the MODIS, OMI and IASI instruments).  
We found that the volcanic aerosol layer peak passed over Lauder three
times from 11 June to 6 July at intervals of 10--12 days. The maximum
$R$ value on 11 June, immediately after the eruption, was 27 at
11.2\,\unit{km}, and the AOD was 0.45. This $R$ value is much larger
than the maximum $R$ value of 2.0--3.5 observed at Saga and Tsukuba,
Japan, for the Nabro volcano, which erupted on 12 June 2011
\citet{uchino2012}. On 11 June, when the continuous lidar observation
started, the maximum value of $\delta$ was 16\,{\%} and that of
$\delta_{\mathrm{p}}$ was 23\,{\%}.  On 6 July, at the end of the period
of continuous lidar observations, the maximum value of $\delta$ was
20\,{\%}, and that of $\delta_{\mathrm{p}}$ was 29\,{\%}. Thus,
$\delta_{\mathrm{p}}$ remained at 20--30\,{\%} over the entire
observation period, and even one month after the eruption the
depolarization ratio had not decreased. This result indicates that the
major component of the PCCVC volcanic aerosol layers was non-spherical
particles.

The backscatter-related wavelength exponent of the PCCVC volcanic
aerosols at 1064/532\,\unit{nm} was 0.9 at 11--13\,\unit{km} altitude;
this value indicates that the PCCVC volcanic aerosols were composed of
large particles. According to \citet{ansmann2012}, the wavelength
exponents of the Eyjafjallaj\"{o}kull volcanic aerosols were
1.12--1.19. The wavelength exponents of the Kasatochi eruption aerosols
were 0.5--1.5 \citep{tesche2010}.  The lidar observations at Lauder
showed that the PCCVC volcanic aerosol layers contained non-spherical
and larger particles. These results agree with the findings of previous
studies, which reported that the volcanic plume of the PCCVC eruption
contained less \chem{SO_2} than the plumes from the Kasatochi and Nabro
eruptions \citep{karagulian2010, clarisse2012}.

\Supplementary{zip}

\begin{acknowledgements}

This research was supported in part by the Environment Research and
Technology Development Fund (2A-1102) of the Ministry of the
Environment, Japan. 
The author wish to thank the editor.
\end{acknowledgements}


\begin{table}
\caption{Lidar system at Lauder, New Zealand.}
\scalebox{.98}[.98]{\begin{tabular}{l|c|c}
\tophline
 \multicolumn{3}{l}{System after update (after 18 Feb 2009)}\\
\middlehline
 \multicolumn{3}{c}{Transmitter}                                                   \\
\middlehline
{Laser}                      & \multicolumn{2}{c}{Nd:Yag}                          \\
{Wavelength}                 & 532\,\unit{nm}                   & \hack{\qquad\qquad}1064\,\unit{nm}\hack{\qquad\qquad}  \\
     Pulse Energy            & 150\,mJ                          & \hack{\qquad\qquad}150\,mJ\hack{\qquad\qquad}          \\
{Pulse Repetition}           & \multicolumn{2}{c}{10\,\unit{Hz} }                  \\
{Beam Divergence}            & \multicolumn{2}{c}{0.2\,\unit{mrad}}                \\
\middlehline
 \multicolumn{3}{c}{Receiver}                                                      \\
\middlehline
{Telescope Type}             & \multicolumn{2}{c}{Ritchey--Chr\'{e}tien (advanced)} \\
{Wavelength}                 & 532\,\unit{nm}                   & \hack{\qquad\qquad}1064\,\unit{nm}\hack{\qquad\qquad}  \\
{Telescope Diameter}         & \multicolumn{2}{c}{30.5\,\unit{cm} (12 inch) }      \\
{Field of View (full angle)} & \multicolumn{2}{c}{1.0\,\unit{mrad} }               \\
%{Band Width (FWHM)}          & \multicolumn{2}{c}{0.28\,\unit{nm}
                         %}                \\
{Band Width (FWHM)}          & 0.28\,\unit{nm}                  & \hack{\qquad\qquad}0.34\,\unit{nm}\hack{\qquad\qquad}   \\
 Polarization measurement    & Yes                              & \hack{\qquad\qquad}No\hack{\qquad\qquad}               \\
 Number of Receiving Channel & 3                                & \hack{\qquad\qquad}1\hack{\qquad\qquad}                \\
 Detector                    & PMT                              & \hack{\qquad\qquad}APD\hack{\qquad\qquad}              \\
 Signal Processing           & 12 bit A/D\,$+$\,Photon counting & \hack{\qquad\qquad}12 bit A/D\hack{\qquad\qquad}       \\
{Time Resolution}            & \multicolumn{2}{c}{10\,s (max), 5\,min (nominal)}   \\
{Altitude Resolution}        & \multicolumn{2}{c}{7.5\,\unit{m} }                  \\
\bottomhline
\end{tabular}}


\begin{figure}
\includegraphics[width=120mm]{acpd-2014-0014-f01}
\caption{Vertical profiles of backscattering (left) and depolarization
 (right) ratios before (28 May, blue line) and after (11 June, red line)
 the PCCVC eruption  on 4 June 2011. The horizontal dot-dash line in
 each panel shows the tropopause height derived from radiosonde data at
 Invercargill on 11 June 2011.} 
\label{Fig.1}
\end{figure}


\begin{figure}
\includegraphics[width=120mm]{acpd-2014-0014-f02}
\caption{Ten-day isentropic forward trajectories of air parcels (colored
 lines) determined by using  METEX. The starting position was the PCCVC
 (40.59{\degree}\,S, 72.11{\degree}\,W), at  11\,\unit{km} above the
 surface. Large black dots mark each 24\,h period in the simulation.}
\label{Fig.2}
\end{figure}

\begin{figure}
\includegraphics[width=60mm]{acpd-2014-0014-f03}
\caption{Vertical and temporal cross-section of the backscattering ratio
 \textbf{(a)} and the depolarization ratio \textbf{(b)} at
 532\,\unit{nm}. The light purple rectangles show tropopause height.}
\label{Fig.3}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{acpd-2014-0014-f04}
\caption{Vertical profiles of the backscattering ratio $R$ (blue line),
 the total depolarization ratio $\delta$ (red line) and the particle
 depolarization ratio $\delta_{\mathrm{p}}$ (green line) observed at on
 \textbf{(a)} 11 June at 18:00\,LT, \textbf{(b)} 23 June at 18:00\,LT,
 and \textbf{(c)} 6 July at 03:00\,LT. The horizontal dot-dash lines in
 each panel shows tropopause height; \textbf{(a)} 10.3\,\unit{km},
 \textbf{(b)} 10.6\,\unit{km} and \textbf{(c)}  9.4\,\unit{km}. The
 volcanic aerosol layers are indicated by the $R$, $\delta$ and
 $\delta_{\mathrm{p}}$ peaks above the tropopause height. 
The error bars are also show for $R$, $\delta$, and
 $\delta_{\mathrm{p}}$  profiles.}
\label{Fig.4}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{acpd-2014-0014-f05}
\caption{Temporal variation of the stratospheric AOD over Lauder from 11
 June to 6 July~2011. Three  AOD peaks occurred of 0.45 on 11 June, 0.31
 on 23 June and 0.12 on 6 July.}
\label{Fig.5}
\end{figure}


\begin{figure}
\includegraphics[width=120mm]{acpd-2014-0014-f06}
\caption{\textbf{(a)} Vertical profiles of the backscattering ratio $R$
 (blue line), the total  depolarization ratio $\delta$ (red line), and
 the particle depolarization ratio  $\delta_{\mathrm{p}}$ (green line)
 at 532\,\unit{nm} on 13 June. The horizontal dot-dash lines in each panel
 shows tropopause height. \textbf{(b)} Vertical profiles of  the
 backscattering ratio at 532\,\unit{nm} (blue line), the backscattering
 ratio at  1064\,\unit{nm} (orange line), and the wavelength exponent of
 the backscattering ratios  ($A_{\beta}$) at
 1064\,\unit{nm}/532\,\unit{nm} (red line) on 13 June.}
\label{Fig.6}
\end{figure}

\end{document}

\endinput