Statistical models for use of palaeosol magnetic properties as proxies of palaeorainfall

The magnetic properties of well-drained, near-neutral modern soils exhibit strong relationships with mean annual precipitation (MAP, conventional 30-year averages). The pedogenic magnetic susceptibility is low for low map values (≈ 300 mm/yr), increases with increasing map (up to ≈ 1500 mm/yr), and then flattens or declines for higher map values. These relationships have been amply documented, characterised quantitatively, and used for Quaternary palaeorainfall reconstructions. However, neither the fitting of climofunctions nor the evaluation of the associated uncertainty had yet been done recognizing the measurement errors that invariably affect the values of magnetic susceptibility and of map. Using published datasets - from the Great Plains of the United States, from the Chinese Loess Plateau and the Russian steppe, from arid and tropical areas of Mali, and from Mediterranean and Saharan regions of Morocco - we illustrate the development and calibration of statistical models that enable the use of magnetic properties of palaeosols as proxies for palaeorainfall. The methods we use (errors-in-variables regression) take into account the measurement errors that inevitably affect both the measurements of magnetic susceptibility, and of rainfall. We also characterise the uncertainty of the palaeoclimatic reconstructions that these models produce, and show that the uncertainty with which we can estimate the long-term (over hundreds of years) average values of map that truly characterise the prevailing climate, is sufficiently small to enable reliable palaeoclimate reconstructions. As an example, we provide an assessment of the uncertainty of the Holocene palaeorainfall reconstruction for Duowa, Qinghai Province, in the Chinese Loess Plateau, which corroborates the changes in the regimen of monsoons detected in previous studies.