%% version: November 30, 2001
\documentclass[draft,jgr]{agu2001}


\authorrunninghead{BALES ET AL.}
\titlerunninghead{ VARIABILITY OF GREENLAND
ACCUMULATION}

\journalid{May 2001} \articleid{106}{A6} \paperid{2001JA900021}
\cpright{AGU}{2001}

\setcounter{page}{1}

\received{November 1, 2000} \revised{April 1, 2001}
\accepted{April 3, 2001} \published{}

\authoraddr{R. C. Bales,
Department of Hydrology and Water Resources, University of
Arizona, Harshbarger Building 11, Tucson, AZ 85721, USA.
(roger@hwr.arizona.edu)}


\authoraddr{E. Mosley-Thompson, Department of Geography, Ohio State University, 108 Scott Hall,
1090 Carmack Road, Columbus, OH 43210, USA. (thompson.4@osu.edu)}


\begin{document}

\title{Variability of accumulation in northwest Greenland over the past 250 years}

\author{R. C. Bales}

\affil{Department of Hydrology and Water Resources, University of
Arizona, Tucson, Arizona, USA}

\author{E. Mosley-Thompson}

\affil{Department of Geography, Ohio State University, Columbus,
Ohio, USA}

\begin{abstract}
During summer 1996 a 120-m firn and ice core was drilled to
determine annual accumulation rates at a northwest Greenland site
(77.1392$^\circ$N, 61.0422$^\circ$W, 1910-m elevation). Annual
layers were identified in the core using multiple parameters:
$\delta^{18} \rm O$ and concentrations of dust, hydrogen peroxide,
ammonium, calcium, and nitrate. Using all parameters together to
define annual layers resulted in a 251-year record with a dating
uncertainty of 1 year within that period. Annual accumulation over
the period of record averaged about 0.37-m water equivalent.
Comparing this record with four other multicentury-long records
from the west central and northwest portion of the ice sheet shows
many periods when decadal-scale fluctuations in accumulation at
the different sites are in phase. Overall variations in
accumulation in this portion of the ice sheet were $\pm$8--9\% per
decade, versus $\pm$25\% for individual cores. Annual accumulation
at GITS showed a significant correlation with a 12-month North
Atlantic Oscillation index (Pearson's $R = -0.32$ with a
significance level of $>$99\%), though the correlation was
slightly lower than for two cores roughly 350 and 700 km south.
\end{abstract}


\begin{article}


\section{Introduction}
Accumulation estimates for the Greenland ice sheet have been based
on point measurements made at over 250 locations, over a period of
more than 70 years [{\it Ohmura and Reeh}, 1991].
\nocite{OhmRee91} The variability of ice sheet accumulation over
time is of particular interest for studying changes in the mass
balance of the ice sheet. However, the natural variability over
space and time is superimposed upon the long-term trends, making
them difficult to decipher.

\subsection{Methods}
In summer 1996, 120- and 121-m ice cores were drilled at the
Greenland Ice Sheet Training Facility (GITS, 77.1392$^\circ$N,
61.0422$^\circ$W, 1900-m elevation) using a 100-mm (4-inch)
electromechanical drill (\callout{Figure~\ref{figone}}). The cores
were about 30 m apart. For both cores we established uninterrupted
records for six different physical or chemical parameters that
exhibit seasonal variations: dust, $\delta^{18} \rm O$, hydrogen
peroxide, ammonium, calcium, and nitrate. Analytical methods were
described previously [{\it Anklin et al.}, 1998] (\callout{Figure
2}).



\subsubsection{Statistical model}
A sensible way to analyze trends and seasonalities in geophysical
time series is the development of a structural model in state
space form. Following this approach, the monthly mean tropospheric
ozone concentrations $Y_t$ at JFJ are modeled as a linear
combination of a stochastic trend component $\mu_t$, a stochastic
seasonal component $s_t$, $k$ intervention components $w_{i,t}$,
and an irregular component $\epsilon_t$.

\subsubsection{Stochastic trend}
The stochastic trend component is recursively defined as a local
level $\mu_t$ with disturbance $\eta_t$ and a local slope
$\beta_t$ with disturbance $\zeta_t$;
\begin{eqnarray}
Y_t & =& \mu_t+s_t+\sum_{i=1}^{k}\lambda_iw_{i,t}+\epsilon_t, \nonumber\\
\mu_t & = & \mu_{t-1} + \beta_{t-1}+\eta_t, \nonumber \\
\beta_t & = & \beta_{t-1}+\zeta_t. \nonumber
\end{eqnarray}
The seasonal component consists of 12 monthly levels that
summarize to a disturbance $\xi_t$, allowing the seasonal pattern
to evolve with time:
\begin{displaymath}
s_t=-\sum_{i=1}^{11}s_{t-i}+\xi_t.
\end{displaymath}



\subsection{Observations}

Annual disturbances over the period of record averaged 0.37-m
water equivalent. All disturbances are normally distributed,
independent white noise processes with zero means and constant
variances:
\begin{displaymath}
\left[
\begin{array}{l}
\epsilon_t \\
\eta_t \\
\zeta_t \\
\xi_t \\
\end{array}
\right]
\sim N
\left(
\left[
\begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \\ \end{array}
\right],
\left[
\begin{array}{cccc} \sigma_\epsilon^2 & 0 & 0 & 0 \\ 0 & \sigma_\eta^2 & 0 & 0 \\ 0 & 0 & \sigma_\zeta^2 & 0 \\ 0 & 0 & 0 & \sigma_\xi^2 \\\end{array}
\right] \right). \label{eq:noise}
\end{displaymath}
Interventions may be easily incorporated in the model. A
structural break, for instance, in which the level of the series
shifts up or down can be modeled by a step intervention variable
that is zero before the event and one afterward, as we can see in
\callout{Table \ref{tabone}}.

\begin{table}
\caption{Summary of Correlations Between Ice Cores and
Indices\tablenotemark{a}}
\begin{flushleft}
\begin{tabular}{lcccc}
\tableline
Site&Time&12-month&Pearson's&Spearman \\
&Span&Period&$R$&Rank Order \\
\tableline
GITS\tablenotemark{b} & 1865--1995&Feb.-Jan.&-0.316&-0.298 \\
Camp Century & 1865--1974&July-June&-0.320&-0.298 \\
\multicolumn{5}{c}{{\it Example subheading}} \\
Nasa-U & 1865--1994&Sept.-Aug.&-0.353&-0.342 \\
Milcent & 1865--1966&June-May&-0.410&-0.494 \\
\tableline
\end{tabular}
\end{flushleft}
\tablenotetext{a}{This is an example of the tablenotetext
command.} \tablenotetext{b}{Here is a second example.}
 \label{tabone}
\end{table}

\section{Kalman Filter}
Suppose that the temporal growth of the state vector from
$t_{k-1}$ to $t_k$ can be expressed by
\begin{equation}
  {\bf x}^f_k  =  {\bf F} ( {\bf x}^a_{k-1},{\bf w}_k + {\bf q}_k),
\end{equation}
where ${\bf x}_k$ is the state vector at time $t_k$ with length
$n$, which is the number of grid points multiplied by the number
of prognostic variables.

Under the assumption that the acoustic tomography data ${\bf
y}_k$ available for the data assimilation are linearly related to
the state vector ${\bf x}_k$, the following observation equation
is given:
\begin{equation}
   {\bf y}_k = {\bf E}_k {\bf x}_k + {\bf e}_k,
\end{equation}
where ${\bf E}_k$ is the observation matrix that provides a
relationship between the prognostic model variables and
measurement data. %The ${\bf e}_k$ is the measurement error assumed
%to have zero mean and the known covariance matrix ${\bf R}_k$. The
%measurement data of the acoustic tomography are the travel times
%from one acoustic station to another.

\begin{figure}
\vskip1.5in \caption{Here is a caption for a single column figure.
Here is a caption for a single column figure.} \label{figone}
\end{figure}


\begin{figure*}
\vskip1in \caption{The accumulation records for the three cores in
northwest Greenland are compared to two older cores from central
Greenland, and to the Camp Century core. Camp Century and Milcent
were based on {\it Claussen et al.} [1988], with data from the
NOAA Paleoclimate Program's International Ice Core Data
Cooperative (www.ngdc.noaa.gov/paleo/icecore/greenland/\hskip1sp
gisp/gisp.html). GISP2 was based on {\it Meese et al}. [1994],
with data from The Greenland Ice Cores CD-ROM, 1997 (Available
from the National Snow and Ice Data Center, University of Colorado
at Boulder, and the World Data Center-A for Paleoclimatology,
National Geophysical Data Center, Boulder, Colorado). Graphs are
10-year running means, normalized to their period of record since
1800 A.D. Heavy line on GITS graph is accumulation record for the
Camp Century core.} \label{figtwo}
\end{figure*}


\section{Discussion}
There is a good match between the 10-year running mean
accumulation from the GITS core and that from a 1977 core that was
only about 2 km away (\callout{Figure 2}), with a correlation
coefficient of 0.46 for the triangular filtered data and 0.50 for
the 10-year running means. However, it should be noted that annual
layers in the 1977 core were based on a single annually varying
parameter ($\delta^{18} \rm O$), resulting in greater uncertainty
in the dating of that core.


1. We estimated the current distance of the subsolar magnetopause
from the Earth ($D_S$) and radius of the magnetopause cross
section at the terminator ($R_S$) using the prediction of the
magnetopause model [\markcite{{\it Shue et al.}, 1997}].

2. We scaled the INTERBALL 1 $X_{\rm GSE}$ coordinate with respect
to $D_S$ and its distance from the Sun-Earth line with respect to
$R_S$.

3. Using these relative coordinates and the S66 model, we
determined for each measurement the predicted value of the
magnetosheath flux, ${\rm FCC}_{pr}$ (predicted flux compression
coefficient). We fixed values $M_A = 8$ and $\gamma$ = 5/3 as
parameters of the model.


To reduce the influence of solar wind and magnetosheath
fluctuations, we present 30-min averages of ${\rm FCC}_m$ and
${\rm FCC}_{pr}$. We identified more than 1000 hours of
magnetosheath measurements that result in $\sim$2200 points.

\begin{table*}
\def\ph{\phantom{age }}
\def\pph{\phantom{th}}
\newbox\dothis
\setbox\dothis=\vbox to0pt{\vskip-1pt\hsize=11.5pc\centering
Error\vss} \caption{Please note that this double-column table does
not display properly in draft mode. \label{tabfour}}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lccrrrcrrr}
\hline &&\multicolumn{4}{c}{\vrule height 12pt width 0pt Panel A
Regression A}&\multicolumn{4}{c}{Panel B Regression B}\cr
\cline{3-6}\cline{7-10}\cr
%&&\multicolumn{4}{c}{\hrulefill}&\multicolumn{4}{c}{\hrulefill}\cr
\noalign{\vskip-4pt} &&&\multicolumn{3}{c}{\copy\dothis}&
&\multicolumn{3}{c}{\copy\dothis}\cr \cr \noalign{\vskip-6pt}
\cline{4-6}\cline{8-{10}}\cr \noalign{\vskip-6pt}
&Actual&Predicted&&\multicolumn{2}{c}{Cumulative}
&\multicolumn{1}{c}{\ Predicted}
&&\multicolumn{2}{c}{Cumulative}\cr \cline{5-6}\cline{9-{10}}\cr
\noalign{\vskip-9pt}
&\multicolumn{1}{c}{M2}&\multicolumn{1}{c}{M2}
&\multicolumn{1}{c}{Level\hbox to-12pt{}}&&&\multicolumn{1}{c}{M2}&%
\multicolumn{1}{c}{Level}&\cr
%%
Year&\multicolumn{1}{c}{Growth} &\multicolumn{1}{c}{Growth}
&\multicolumn{1}{c}{Growth}&
\multicolumn{1}{c}{Billns\hbox to-12pt{}}&Percentage&%
\multicolumn{1}{c}{Growth} &\multicolumn{1}{c}{Growth}&
\multicolumn{1}{c}{Billns\hbox to -12pt{}}&Percentage\cr
\noalign{\vskip3pt} \hline \noalign{\vskip3pt} 1990Q4&4.0& 6.4&
$-$2.3\ &$-$71 & 2.2\ph& 6.5&$-$2.4\pph&$-$80&2.4\ph  \cr
1991Q4&3.0& 3.6& $-$0.5\ &$-$91 & 2.7\ph &
3.3&$-$0.3\pph&$-$92&2.7\ph  \cr 1992Q4&1.8& 6.4& $-$4.5\ &$-$257
& 7.5\ph  & 5.9&$-$4.0\pph&$-$239&6.9\ph  \cr 1993Q4&1.4& 4.8&
$-$3.4\ &$-$392 & 11.2\ph  & 5.0&$-$3.6\pph&$-$381&10.9\ph  \cr
1994Q4&0.6& 3.0& $-$2.4\ &$-$489 & 13.9\ph  &
2.6&$-$2.0\pph&$-$464&13.2\ph  \cr 1995Q4&3.8& 3.5& 0.3\ &$-$495 &
13.6\ph  & 4.2&$-$0.4\pph&$-$500&13.7\ph  \cr 1996Q4&4.5& 3.9&
0.5\ &$-$495 & 13.0\ph  & 4.0&$-$0.4\pph&$-$505&13.3\ph\cr
\noalign{\vskip3pt} \multicolumn{3}{l}{Mean Error (1990\/--1996)}&
\multicolumn{4}{l}{\phantom{$-$}$-$1.78}&
\multicolumn{3}{l}{\phantom{$.$}$-$1.78}\cr \multicolumn{3}{l}{\it
RMSE}& \multicolumn{4}{l}{\phantom{$--$}2.52}&
\multicolumn{3}{l}{\phantom{$-.$}2.40}\cr \hline
\end{tabular*}
\begin{tablenotes}Please note that this double-column table does
not display properly in draft mode. This is an example of the
tablenote command.  \\
The predicted values are generated using the regressions reported
in Table 1. Regressions are estimated from 1960Q4 and dynamically
simulated from 1990Q1 to 1966Q4. \textit{RMSE} is the root mean
squared error, which is of particular interest in this context.
\end{tablenotes}
\label{tabtwo}
\end{table*}


\subsection{Measurement Errors}
We neglected several effects in computation of the ion number flux
from the Faraday cup currents: current of alpha particles,
contribution of high-energy electrons, and changes of ion flux
direction. These effects were broadly discussed by \markcite{{\it
Zastenker et al.} [1999b]} with the conclusion that they cannot
explain the disagreement between observations and S66,
\callout{Table~\ref{tabtwo}}.




\subsection{Magnetosheath Cross Section}
We have adjusted the ``dimensions'' of the magnetopause in
accordance with the S97 model. After our scaling, the position of
the bow shock in the S66 model is a little nearer to the Earth
than that determined from the \markcite{{\it Formisano} [1979]}
empirical model. This corresponds with a note by \markcite{{\it
Song et al.} [1999b]} that the observed bow shock is, as a rule,
located outside of the gasdynamic prediction.



\section{Conclusions}
Using multiple dating parameters to define annual layers resulted
in a 251-year record for the 120-m GITS core, with a dating
uncertainty of 1 year within that period. Multicentury-long
records from five sites show many periods when fluctuations in
decadal accumulation at the different sites are in phase.
Accumulation during the decade of the 1980s was the lowest in the
last 200 years, while that during the 1960s and 1970s was well
above average.


\appendix
\section{Sample Appendix}
The actual spread in measured phase due to satellite motion can
be estimated by
\begin{equation}
   \phi  =  \frac{360 V_{s} t \cos\theta}{\lambda},
\end{equation}
where $V_{s}$ is the satellite velocity, $t$ is the integrated
measurement time, $\theta$ is the angle between the spacecraft
velocity and the cylindrical axis of the helix, and $\lambda$ is
the helix wavelength.

\section{Latex Codes for Journals}

\begin{tabular}{ll}
\verb"\aj"    & {\it Astron. J.,}\\
\verb"\apj"   & {\it Astrophys. J.,}\\
\verb"\apjl"  & {\it Astrophys. J. Lett.,}\\
\verb"\aap"   & {\it Astron. Astrophys.,}\\
\verb"\bams"   & {\it Bull. Am. Meteorol. Soc.,}\\
\verb"\bssa"   & {\it Bull. Seismol. Soc. Am.,}\\
\verb"\dsr1"   & {\it Deep Sea Res., Part I,}\\
\verb"\dsr2"   & {\it Deep Sea Res., Part II,}\\
\verb"\eos"    & {\it Eos Trans. AGU}\\
\verb"\epsl"   & {\it Earth Planet. Sci. Lett.,}\\
\verb"\gca"    & {\it Geochim. Cosmochim. Acta,}\\
\verb"\gji"    & {\it Geophys. J. Int.,}\\
\verb"\gjras"  & {\it Geophys. J. R. Astron. Soc.,}\\
\verb"\grl"    & {\it Geophys. Res. Lett.,}\\
\verb"\gsab"   & {\it Bull. Geol. Soc. Am.,}\\
\verb"\jatp"   & {\it J. Atmos. Sol. Terr. Phys.,}\\
\verb"\jgr"    & {\it J. Geophys. Res.,}\\
\verb"\jpo"    & {\it J. Phys. Oceanogr.,}\\
\verb"\mnras"  & {\it Mon. Not. R. Astron. Soc.,}\\
\verb"\mwr"    & {\it Mon. Weather Rev.,}\\
\verb"\pag"    & {\it Pure Appl. Geophys.}\\
\verb"\pepi"   & {\it Phys. Earth Planet. Int.,}\\
\verb"\pra"    & {\it Phys. Rev. A Gen. Phys.,}\\
\verb"\prb"    & {\it Phys. Rev. B Solid State,}\\
\verb"\prc"    & {\it Phys. Rev. C Nucl. Phys.,}\\
\verb"\prd"    & {\it Phys. Rev. D Particles Fields,}\\
\verb"\prl"    & {\it Phys. Rev. Lett.,}\\
\verb"\qjrms"  & {\it Q. J. R. Meteorol. Soc.,}\\
\verb"\rg"     & {\it Rev. Geophys.,}\\
\verb"\rs"     & {\it Radio Sci.,}\\
\verb"\usgsof" & {\it U.S. Geol. Surv. Open File Rep.,}\\
\verb"\usgspp" & {\it U.S. Geol. Surv. Prof. Pap.,}\\
\end{tabular}



\begin{notation}
$A$&surface area, m$^2$ \\

 $T_{i,\mathrm{bulk}}$&
freezing temperature of water to ice under bulk conditions, K.\\

$\Delta T_{i,\mathrm{pore}}$&depression in freezing temperature of
ice inside a pore, below bulk freezing temperature, K.\\

$\mu^0$&chemical potential of a substance in the standard state, J
mol$^{-1}$\\

$\Delta H_{f,i}$&specific enthalpy of fusion of ice, J
kg$^{-1}$.\\
\end{notation}

\begin{acknowledgments}
This work was supported by NASA grants NAG5-6779 to the University
of Arizona and NAG-5072 and NAG-6817 to the Ohio State University.
Drilling and logistical support were provided by the University of
Nebraska Polar Ice Coring Office. M. Anklin, R. Brice, M. Davis,
P. N. Lin, B. Matson, and B. Snider provided invaluable help with
core retrieval, processing, and analysis.
\end{acknowledgments}

\begin{thebibliography}{}

\bibitem[{\it Anklin et~al.}(1998)]{AnkBalTho97}
Anklin, M., R. C. Bales, E. Mosley-Thompson, and K. Steffen,
Annual accumulation at two sites in northwest Greenland during
recent centuries, {\it J. Geophys. Res.}, {\it 103}(D22),
28,775--28, 783, 1998.

\bibitem[{\it Appenzeller et~al.}(1998)]{AppStoAnk98}
Appenzeller, C., T. F. Stocker, and M. Anklin, North Atlantic
Oscillation  dynamics recorded in Greenland ice cores, {\it
Science}, {\it 282}, 446--449, 1998.

\bibitem[{\it Belt}(1968)]{}
Belt, E. S. Post-Acadian rifts and related facies, eastern Canada,
in {\it Studies in Apalachian Geology}, edited by E. Zen et al.,
pp. 95--113, John Wiley, New York, 1968.

\bibitem[{\it Boatwright}(1978)]{}
Boatwright, J., Detailed spectral analysis of two small New York
State earthquakes, {\it Bull. Seismol. Soc. Am., 68}, 1117--1131,
1978.

\bibitem[{\it Clausen et~al.}(1988)]{Clau88}
Clausen, H. B., N. S. Gundestrup, S. J. Johnsen, R. Bindschadler,
and J.~Zwally, Glaciological investigations in the Crete area,
central Greenland: A search for a new deep-drlling site, {\it Ann.
Glaciol.}, {\it 10}, 1988.

%\bibitem[{\it Dansgaard and Johnsen}(1969)]{DanJoh69}
%Dansgaard, W., and S.~J. Johnsen, A flow model and a time scale for the ice
  %core from Camp Century, Greenland, {\it J. Glaciol.}, {\it 8}(53),
  %215--223, 1969.

\bibitem[{\it Fetterer et al.}(1993)]{}
Fetterer, F., D. Gineris, and C. Johnson, Remote sensing aids in
sea-ice analysis, {\it Eos Trans. AGU, 74,} 265, 267--268, 1993.


\bibitem[{\it Fiacco et~al.}(1994)]{FiaThoGer94}
Fiacco, R. J., T. Thordarson, M. S. Germani, S. Self, J. M.
Palais, S. Whitlow, and P. M. Grootes, Atmospheric aerosol loading
and transport due to the 1783-84 Laki eruption in Iceland,
interpreted from ash particles and acidity in the GISP2 ice core,
{\it Quat. Res.}, {\it 42}, 231--240, 1994.

\bibitem[{\it Hammer}(1977)]{Ham77}
Hammer, C. U., {Past volcanism revealed by Greenland ice sheet
impurities}, {\it Nature}, {\it 270}, 482--486, 1977.

\bibitem[{\it Hurrell}(1995)]{Hur95}
Hurrell, J. W., Decadal trends in the North Atlantic Oscillation:
Regional temperatures and precipitation, {\it Science}, {\it 269},
676--679, 1995.

\bibitem[{\it Meese et al.}(1994)]{MeeGowGro94}
Meese, D. A., A. J. Gow, P. Grootes, P. A. Mayewski, M. Ram, M.
Stuiver, K. C. Taylor, E.~D. Waddington, and G.~A. Zielenski, {The
accumulation record from the GISP2 core as an indicator of climate
change throughout the {Holocene}}, {\it Science}, {\it 266},
1680--1682, 1994.

\bibitem[{\it Ohmura and Reeh}(1991)]{OhmRee91}
Ohmura, A., and N. Reeh, New precipitation and accumulation maps
for Greenland, {\it J. Glaciol.}, {\it 37}(125), 140--148, 1991.

\bibitem[{\it Orringer}(1974)]{}
Orringer, O., Frontal analysis program, {\it Rep ASRL TR 1023,}
Aeroleastic and Struct. Lab., Mass Inst. of Technol., Cambridge,
1974.

\end{thebibliography}

\end{article}
\end{document}


























\end{document}
