Dissertation Proposal




Studies on the Nature of Seasonal to Interannual Variability of Sea Ice Trends Utilizing Satellite Derived Data and Information


A Dissertation Proposal by Harold A. Geller (with academic advisor Dr. Menas Kafatos)


Climate variability and prediction is a key research area within the global change research community. The global circulation models have predicted that the polar regions will undergo greater changes in the immediate future than other areas of the globe, if these models are correct [IPCC, 1990 and IPCC, 1995]. One way to monitor the state of our polar regions is to monitor the extent of sea ice in the polar regions. Sea ice in the polar regions has an effect on the exchange of heat between the sun and earth, as well as an effect on the heat, mass and momentum exchanges between the ocean and atmosphere. Thus, satellite monitoring of sea ice may be a key indicator and predictor of global change.


The present work concerns itself with carrying out a series of sophisticated analyses on long term time series sea ice data to explore the nature of sea ice variability and its possible use in prediction of seasonal to interannual climatic events. The data that we will use will be predominantly satellite derived data, especially from the Scanning Multichannel Microwave Radiometer (SMMR) and the Special Sensor Microwave Imager (SSMI) [Gloersen et al., 1991 and Parkinson et al., 1987]. Other datasets include in situ measurements, such as those from NOAA National Weather Service for the Southern Oscillation Index (SOI).


We propose not only to perform standard time series analyses on these data, but also apply chaos data analyses to these data. Thus we hope to uncover causal relationships between different interannual cycles, as well as evidence for the possible chaotic nature of the data. This will aid in determining the utility of these data in forecasting and prediction of interannual events.




Remote sensing has long been used to monitor the cryosphere due the difficulties associated with access to these regions. For example, remote sensing has been used to monitor the variability of seasonal snow cover for the dual purpose of assisting the commercial ski resorts as well as city water planners [Duguay and Hurtubise, 1992]. Remote sensing has also been used to monitor the periodic movement of glaciers, known as glacier surge, to assist global change researchers and the merchant marine [Molnia, 1993]. Remote sensing has also advanced the understanding of ice drifts, polynya evolution, effects of storms, stresses of winds and wind direction, and standard sea ice mechanisms [Kozo et al., 1992].


The polar regions also play a large role in the comprehension and prediction of global climate change. Global circulation modelers have deduced that warming in the polar regions "would not only be higher than at lower latitudes, but also seasonally dependent" [Maxwell, 1987]. This is due in part to the fact that in the polar regions, "feedback between radiation and highly reflective ice and snow surfaces, as well as the presence of a strong surface-based temperature inversion, cause energy to be trapped near the surface" [Maxwell, 1987].


On seasonal to interannual scales, it has been reported [Gloersen, 1995] that some correlations may be traced to specific El Niño events. The last warm event of 1997-1998, the strongest recorded this century, makes the question of whether sea ice in polar regions responds to global climate events particularly relevant to the global change community.


The Center for Earth Observing and Space Research (CEOSR) at George Mason University (GMU) serves to unify earth observing, space sciences, and remote sensing and associated data research to address fundamental problems in these areas. Demonstrating its expertise to the earth system science community, GMU recently was awarded by NASA an ESIP named the Seasonal-Interannual Earth System Information Partnership (SIESIP).


Seasonal to interannual variability and prediction of cryospheric processes is a crucial portion of the modeling and analysis in support of the U.S. Global Change Research Program (USGCRP). Since late 1978, satellites have played an important role in monitoring the sea ice extent and coverage demonstrating the utility of remote sensing in polar regions, difficult and costly to access otherwise. The research proposed herewith fits within the research areas of CEOSR and concerns itself with carrying out a series of sophisticated analyses on long term time series sea ice data, to explore sea ice variability utilizing remote sensing data.




The data for this research will be derived from satellite data and some in-situ data. The satellite data is predominantly the microwave radiometer data collected by the Defense Meteorology Satellite Program (DMSP). The sensors used include both the Scanning Multichannel Microwave Radiometer (SMMR) and the Special Sensor Microwave Imager (SSMI) [Gloersen et al., 1991 and Parkinson et al., 1987].


An example of the data, averaged for each month by Geller, is provided in Figure 1 below. This is Arctic data as provided by Gloersen et al. The data was satellite derived on a bi-daily basis and averaged to monthly by the submitting student. There were some four satellite data sets employed in the forming of these data, including, Nimbus 7 SMMR (from October 25, 1978 through August 20, 1987), DMSP-F8 SSM/I (from July 9, 1987 through December 18, 1991), DMSP-F11 (from December 3, 1991 through September 30, 1995) and DMSP-F13 (from October 1995 through December 1996).


These data have undergone a complex data analysis process themselves, including application of the NASA Team Algorithm [Cavalieri et al., 1984] which uses three microwave channels in calculating sea ice concentration.


Figure 1. Arctic Sea Ice Data from Gloersen et al. Averaged Monthly by Geller


Trend Analysis Methodology


There are a number of analysis techniques to be applied to the satellite and in situ data for trend analysis purposes. (In situ data referring to, for example, point data derived from observations such as those developed by Newell [1990], for sea ice in the Labrador Sea which are available to the present work.) One technique is referred to as the ARMA Process, where ARMA stands for autoregressive moving average. This technique is extensively reviewed by Brockwell and Davis [1996]. In accordance to their definition, "the time series (Xt) is an ARMA(1,1) process if it is stationary and satisfies (for every t)

Xt fXt-1 = Zt + qZt-1

Where: {Zt} is a white noise sequence with mean of zero and variance of s2; and f and q are real valued constants where |q| < 1 and f + q does not equal q.


The ARMA approach assumes the "existence and uniqueness of stationary solutions of the defining equations and the concepts of causality and inevitability." Therefore, to justify the ARMA approach results, one must demonstrate the fulfillment of existence of solutions, uniqueness, causality, and inevitability. This technique was applied to the Arctic data illustrated in Figure 1, producing the following data plot, Figure 2.


Figure 2. Arctic Monthly Data De-seasonalized Using ARMA Technique of Brockwell and Davis


The need to demonstrate causality is equivalent to the need to prove the lack of presence of chaotic dynamic processes. Therefore, we will examine the presence of such processes in the time series of the satellite-derived data. There is "no one measurement or calculation that can establish the existence or absence of chaos" in any time series data. Cambel [1993] proposed a series of tests in order to determine the presence of chaotic dynamic processes. This is a six-fold approach that includes establishing that:

  1. the system is nonlinear and its time series is irregular;
  2. random components exist;
  3. the behavior of the system is sensitive to initial conditions;
  4. the system has fractal dimensions;
  5. the Kolmogorov entropy is positive; and,
  6. there exist positive Lyapunov coefficients.


To accomplish this approach, Cambel [1993] recommends a number of steps. The first step, of course is to obtain a time series of the events of interest, in this case, the sea ice extent. The plot of the time series data is studied and is examined for linearity or an absence of fluctuations. If there are no fluctuations in the time series plot and it can be shown to be linear, then there is no chaos. Clearly the analysis carried out so far indicates this is not the case.


Next the researcher is advised to search for random inputs to the system that can appear as chaotic output. Basically, chaos may be suspected if the amplitude of the output signal is considerably larger than that of the input signal. This is followed by a Fourier analysis leading to a power spectrum. Such a power spectrum has already been constructed for the example of the Arctic data. A sample Fourier analysis power spectrum is provided in Figure 3 below.


Figure 3. De-seasonalized Arctic Data Power Spectrum after FFT


Once Fourier analysis is performed, the autocorrelation function should be obtained. This compares the time series with a similar time series that has been delayed by a specified amount, which is a phase shifted time series of the same data set. Cambel [1993] points out that if the system is chaotic, the autocorrelation function will decay, tending to zero for large values of the time increment.


Next, a fractal dimension should be established for the system. If the fractal dimension is an integer, there is not likely to be chaos present in the system. Finally, the Lyapunov exponent for the system should be evaluated. If chaos is present in the system, the Lyapunov exponent should be a positive coefficient.


Search for Causal Linkages of Sea Ice Variability and Climate Change


Whether or not there are chaotic dynamical processes in effect within the trend analyses of the sea ice data, it would be instructive to examine correlation coefficients for certain parameters associated with the sea ice conditions. Gloersen and Yu [1997] examined the trends in Arctic sea ice concentration while Gloersen and Mernicky [1998] examined the trends in Antarctic sea ice concentration trends. Such trends can be correlated with other well known seasonal to interannual meteorological and climatic events such as El Niño Southern Oscillation (ENSO). Gloersen [1995] reported finding correlations in the regional waters around Antarctica with ENSO.


We have already done some preliminary examination of the correlation between ENSO and polar sea ice extent. Figure 4, depicts some of the preliminary correlation analysis graphically between sea ice variability and the climate related southern oscillation index, compiled by the NOAA National Weather Service.


Figure 4


Note the situation during the 1982-1983 very strong El Niño. While the SOI was decreasing steeply from mid-1982 through mid-1983, after a delay, the sea ice extent in the Antarctic also decreased. However, the Antarctic sea ice extent appears to have rebounded prior to the rebound of the SOI. Furthermore, a decrease in sea ice as extreme, occurred in 1980 without any similar decrease in the SOI.




  1. Brockwell, P.J. and Davis, R.A. (1996). Introduction to Time Series and Forecasting, Springer-Verlag, New York.
  2. Cambel, A.B. (1993). Applied Chaos Theory: A Paradigm for Complexity, Academic Press, Inc., San Diego.
  3. Cavalieri, D.J., P. Gloersen, and W.J. Campbell (1984) Determination of Sea Ice Parameters with the NIMBUS-7 SMMR, Journal of Geophysical Research, Vol. 89, (D4), p. 5355-5369.
  4. Duguay, C.R. and Hurtubise, P. (1992). Monitoring the Spatial and Spectral Variability of Seasonal Snow Cover with Landsat MSS and TM for Climate Studies, ASPRS/ACSM/RT 92 Technical Papers Volume 1 - Global Change and Education, August 1992, pp. 346-354.
  5. Gloersen, P. and J. Yu (1997). Oscillatory Behavior in Arctic Sea Ice Concentrations, Journal of Geophysical Research, Volume 101, pp. 6641-6650.
  6. Gloersen, P. and A. Mernicky. Oscillatory Behavior in Antarctic Sea Ice Concentrations, In Progress.
  7. Gloersen, P. (1995). Modulation of Hemispheric Sea-Ice Cover by ENSO Events, Nature, Vol. 373, pp. 503-506.
  8. Gloersen, P., W.J. Campbell, D.J. Calvalieri, J.C. Comiso, C.L. Pakinson, and H.J. Zwally, (1991). Arctic and Antarctic Sea Ice, 1978-1987: Satellite Passive Microwave Observations, NASA Special Publication.
  9. IPCC [Intergovernmental Panel on Climate Change] (1990). Climate Change: The IPCC Scientific Assessment, J.T. Houghton, G.J. Jenkins and J.J. Ephraums, eds., University Press, Cambridge, UK.
  10. IPCC (1995). Climate Change 1995: The Science of Climate Change, J.T. Houghton, L.G. Meira Filho, B.A. Callander, N. Harris, A. Kattenberg and K. Maskell eds., University Press, Cambridge.
  11. Kozo, T.L., Fett, R.W., Farmer, L.D. and Sodhi, D.S. (1992). Clues to Causes of Deformation Features in Coastal Sea Ice Eos, Transactions, American Geophysical Union, Volume 73, Number 36, September 8, 1992, pp. 385-389.
  12. Maxwell, B. (1987) Atmospheric and Climatic Change in the Canadian Arctic Northern Perspectives, Volume 15, Number 2, p. 4.
  13. Molnia, B.F. (1993) Major Glacier Surge Continues Eos, Transactions, American Geophysical Union, Volume 74, Number 45, November 9, 1993, pp. 521-524.
  14. Newell, J.P. (1990). Spring and Summer Sea Ice and Climate Conditions in the Labrador Sea, 1800-Present. Ph.D. dissertation, University of Colorado at Boulder, Roger Barry advisor.
  15. Parkinson, C.L., Comiso, J.C., Zwally, H.J., Cavalieri, D.J., Gloersen, P. and W.J. Campbell (1987). Arctic Sea Ice, 1973-1976: Satellite Passive Microwave Observations, NASA, Washington, DC., NASA SP-489.


Dissertation Schedule


Milestones for Dissertation Research


Activity Descriptor

Estimated Completion

Admitted to PhD Program at CSI

September 1992

Develop Dissertation Research Concentration

September 1996

Acquire Time Series Data for Sea Ice

December 1997

Develop Time Series Data Analysis Methodology

June 1998

Develop Chaos Data Analysis Methodology

June 1998

Oral Qualifying Examination

August 1999

Written Qualifying Examination

August 1999

Rise to doctoral candidacy

August 1999

Dissertation Literature Review

September 1999

Submit Poster to AGU Fall Meeting

September 1999

Software Applications Review

October 1999

Time Series Trend Analyses

November 1999

Correlation Analyses

November 1999

Preliminary Results Available for Review

November 1999

Develop First Draft of Dissertation

December 1999

Submit Paper to Nature

December 1999

Present Paper at AGU Fall Meeting

December 1999

Complete Dissertation

January 2000

Prepare for Oral Defense

January 2000

Modify Dissertation Based Upon Defense Issues

February 2000

Revise Paper for Nature Publication

March 2000

Degree Conferred

May 2000