William Fyfe (1978) once remarked that the dominant cooling process of the Earth involves convective circulation of cold seawater. He added that it could hardly be otherwise when magmas are introduced at 1200°C under a thin layer of their own volcanic cover -the oceanic basalts. Convecting water acts as a cooling fluid, carrying thermal energy away from the hot areas of the Earth's crust toward the relatively cold surface. Convective processes dramatically increase the transfer of heat in the Earth's crust towards the surface in comparison with purely diffusive processes. Fluid movement occurs at relatively high velocities within the solid crustal matrix, and the more heat there is to be transferred the faster and more intense circulation has to be. Hydrothermal circulation is likely to have been more intense in the distant past of Earth's history. Probably the best argument for this assumption is that the total heat production of the Earth, based on concentrations of heat-producing radioactive elements, had to be much higher in the Hadean and the Archean than it is at present (see Chapter 1, Table I for the ages of the Earth). For example, assuming the Earth at steady state, the current radioactive heat production for the bulk of the planet corresponds to approximately one half of the observed heat flux (McKenzie and Richter, 1981). In the Hadean and the Archean, heat production by radioactive elements would have been more than 4 times higher (extrapolation based on present concentrations and radioactive decay rates), and therefore the heat flux must have been significantly higher (Davies, 1980; O'Connell and Hager, 1980) and the associated hydrothermal circulation more intense. In addition, other sources may also have contributed significantly to heat production on the early Earth. Among these are accretional energy resulting from planetesimal and meteoritic fragment impacts, and differentiation energy resulting from exothermic chemical reactions, partitioning and ffactionation in the interior of the planet (Jeanloz and Morris, 1986). The discovery of Archean komatiites (Viljoen and Viljoen, 1969) is in agreement with a hotter Earth's upper mantle and lower crust, but the existence of high pressure mineral assemblages in Archean metamorphic rocks (Boak and Dymek, 1982) also indicates that horizontal variations of temperature existed in the Archean crust and that temperature anomalies in the mantleOrigins of Life and Evolution of the Biosphere 22:15-3 I, 1992.
Radium activity measurements in water samples are encumbered by relatively large error bars, including for activity values near the regulatory drinking water maximum contaminant level of 5 pCi/L. The large error bars create uncertainty in the evaluation of temporal trends. This uncertainty is often the object of debate and disagreement in regulatory determinations, the design of remedial actions, and/or in litigation. The Mann‐Kendall nonparametric test is perhaps the most commonly used test for trend evaluation in environmental sciences. The test is simple and easy to apply by nonstatisticians and is recommended in several regulations and guidance documents. As typically applied, the Mann‐Kendall test does not consider the uncertainty related to error bars for individual data values. Ignoring this uncertainty can result in misleading conclusions on the presence or absence of trends. In this article, a procedure for trend analysis that accounts for error bars is described. For each data series analyzed, the procedure creates 1000 new data series by randomly assigning values that fall within the error bar around each data point. Trend analysis is then performed on the randomly created data series. The approach is applied to the evaluation of a radium data base containing analytical results from 137 locations (407 water samples) in Escambia County, Florida. The evaluation of the radium data base using the Mann‐Kendall test without accounting for the uncertainty reveals 10 significant trends at the 90% confidence level. Only two of these trends are supported by the data when the uncertainty from analytical error is accounted for.
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