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The rate and depth of pedogenic carbonate accumulation in soils formed in Quaternary alluvium may be viewed as a theoretical problem that involves the mutual interaction of several independent and dependent soil-forming variables. We propose a model for carbonate accumulation in which the soil column is defined by a vertical sequence of 1-cm2-area compartments, each with a specified texture, bulk density, water-holding content, lithologic and mineralogic composition, soil-air pCO2, ionic strength, and temperature. On the basis of these data, rates of carbonate solubility and dissolution within a given compartment are determined. In arkosic to lithic arkosic sandy parent materials, high carbonate solubility (0.137 to 0.212 mg/ml) and the large reactive surface area of eolian calcareous dust result in rapid carbonate dissolution (0.79 to 9.92 × 10−10 g/cm2/sec) that promotes rapid translocation of carbonate by infiltrating water. We derive a group of equations and use them to calculate net carbonate depletion or accumulation in a soil compartment over an interval of time as a function of the independent variables temperature and precipitation. These two variables largely determine or strongly influence soil-water balance, the external carbonate influx rate, and carbonate solubility.

The carbonate distribution that our model predicts closely resembles the observed carbonate distribution in soils associated with Holocene deposits forming in arid, hyperthermic to xeric, thermic moisture-temperature regimes in southern California. This modeling indicates that with a mean carbonate influx rate of 1 × 10−4 g/cm2/yr and in a semiarid, thermic climate, the maximum depression of the top of the Cca horizon is attained within only a few thousand years. In contrast, given the same influx rate, our model predicts that a noncalcareous B horizon cannot form in an arid, hyperthermic climate, a conclusion supported by field and laboratory studies of calcic soils in this climate.

The influence of glacial-to-interglacial climatic changes on carbonate accumulation can be modeled by calculating latest Pleistocene soil-water balance with the aid of published estimates of full-glacial temperature and precipitation. On the basis of these modeling results, we propose that either of two types of glacial-to-interglacial climatic changes may account for the strongly bimodal, apparently polygenetic carbonate distribution that is observed in late Pleistocene soils of the eastern Mojave Desert of southern California. Such results of compartment-strategy modeling are encouraging and indicate the great potential of combined theoretical and empirical methods for considering pedological problems of interest to Quaternary geologists.

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