An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields

Article excerpt

1. INTRODUCTION

There has been much interest recently in climatic change and potential global warming. Of central focus is the phenomenon popularly called the "greenhouse effect": the heating of the earth via the entrapment, by certain gases, of long-wave radiation emitted from the earth's surface. This effect produces a global mean temperature of about 59[degrees]F rather than an estimated -6[degrees]F in the absence of atmosphere (Mitchell 1989). Increasing concentrations of the gases thought to contribute to this effect have led to concern in the scientific community about temperature increases and the resulting climatic effects.

There appears to be no clear-cut consensus on the extent of global warming

over the last century; most estimates run from 0.5[degrees]F to 1.0[degrees]F. The difficulty is the lack of good long-term data over large regions. The global temperature constantly changes on time scales of tens of thousands of years. In fact there have been times in the past millennium when it has been much warmer than the temperatures discussed in most global warming scenarios. The objective here is the statistical validation of a postulated rapid change over the next century that will have enormous environmental impact.

Much of the evidence for a global warming effect has been based on large-scale general circulation models (GCM's), which use multilevel mathematical representations of the atmosphere for weather prediction. Given the complexity of the environment and the relative simplicity of the models, there is much controversy concerning their validity. Results from the four most widely cited GCM's from the National Center for Atmospheric Research (NCAR), Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanographic and Atmospheric Administration, the Goddard Institute of Space Studies (GISS), and the Hadley Center for Climate Prediction and Research at Bracknell, England, are still far from being in agreement, although all models predict higher winter temperatures at the higher northern altitudes as a function of increasing greenhouse gases.

Significant global warming would have an enormous effect on the environment and the world economy. Altering the world economy to reduce the production of the gases suspected of increasing the greenhouse effect would be very costly and/or drastically alter our way of life. Some argue that the political decision is best postponed until after the empirical evidence is in. This article sheds light on how long we would have to wait to detect a global warming with sufficiently high confidence to support such a decision.

In this paper we develop spatial-temporal models for temperature fields over a region in the northern United States covering eastern Montana through the Dakotas (90[degrees]-107[degrees] in longitude) and northern Nebraska up to the Canadian border (41[degrees] -49[degrees] in latitude) . We choose the winter months and this region as our study area because GCM predictions of climatic change (4[degrees]F-10[degrees]F) induced by increased greenhouse gases are expected to be at maximum for high latitudes during the winter months (IPCC 1990; Mitchell 1989). In addition, the relatively stable and simple topography of the region help ensure homogeneity and the minimization of localized effects. Data from the United States historical climatological network, reported by Quinlan, Karl, and Williams (1987) is used to explore long-term changes and potential effects of increased greenhouse gas concentrations.

There is much interest in empirical studies of climatic change. Jones et al. (1986) considered station data to investigate long-term variation in the surface temperature of the northern hemisphere. Karl (1984, 1985) considered climate variation and change in North America. These studies emphasized the dynamic nature of the climate system and the existence of abnormal winter temperatures within the climate system. …