%% 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. 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