Spring Seminar Series - February 21, 2003
University of Minnesota
School of Statistics
College of Liberal Arts

An Assessment of Climate Change in the Ocean

Michael Lavine
Institute of Statistics and Decision Sciences
Duke University

Friday, February 21, 2003
4:00 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300 Ford Hall

Abstract

  Note: This is a nontechnical talk, designed to introduce statisticians to some problems in physical oceanography and how statistics can play a role in their investigation.

Calculations based on the amount of anthropogenically released carbon suggest that the earth's atmosphere should have warmed by an amount greater than what has been observed. Are the calculations wrong, or has the excess heat gone somewhere not accounted for? One possibility is that the excess heat has gone into the ocean. This possibility is being explored by climate modelers, physical oceanographers and others.

The phenomenon of interest is temporal change over large spatial scales. Traditionally, physical oceanographers estimate such temporal change by examining the data from repeated occupations of a transect. That is, they look for instances where data-collecting ships have sampled the same latitude or longitude line in different decades. Two examples are the line of 24 degrees N latitude in the North Atlantic which was occupied in 1957, 1981 and 1992 and the line of 53 degrees W longitude, also in the North Atlantic, which was occupied in 1956, 1983 and 1997. Their method is to look at the three possible pair-wise comparisons of years. We will describe a spatio-temporal model that accounts not only for data from the three occupations, but also for data from other cruises that passed through or near the area of interest and in years other than those of the occupations. Our model allows us to view the temperature in the target region as a time series, and to see the three occupation years as part of that time series, leading to a more complete picture of temporal change.

In addition, we describe the importance of distinguishing property changes on isobars from that on isopycnals. An isobar is a surface of constant pressure, and hence approximately at a constant depth. An isopycnal is a surface of constant density. Because an isopycnal is gravitationally-neutral, properties such as temperature and salinity can flow or diffuse much more easily on an isopycnal than an isobar. When properties change temporally at a given location it is useful to decompose the change into two parts: one part due to the meandering or heaving of an isopycnal past a given depth, which can happen on relatively short time scales such as months, and one part due to changes on a given isopycnal, which typically represents structural change in the ocean occurring on a longer time scale.

The second way we look for temporal change is through the so-called mixed layer. The upper ocean (approximately 50-200 meters depending on season and location) is well mixed vertically through convection, so temperature and density are roughly constant. The mixing is biologically important because it brings nutrients to the surface where there is also light, thus promoting the production of phytoplankton, the primary component of ocean ecosystems. Again, this is significant for global warming because primary production is a sink for carbon. Below the mixed layer, temperature decreases and density increases rapidly and convection is inhibited. The depth and temperature of the mixed layer are subject to a solar-driven annual cycle. The second part of our research focuses on long-term changes in depth and temperature of the mixed layer. Because measurements are almost never taken at the same location we employ a statistical model with components for spatial, annual and long-term trends. Interest centers on the long-term; the spatial and annual must be modeled in order to handle the long-term accurately.