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Estimation of soil moisture distribution in desert regions is challenged by the deep unsaturated zone and the extreme natural environment. In this study, an entropy-based method, consisting of information entropy, principle of maximum entropy (PME), solutions to PME with constraints, and the determination of parameters, is used to estimate the soil moisture distribution in the 10 m deep vadose zone of a desert region. Firstly, the soil moisture distribution is described as a scaled probability density function (PDF), which is solved by PME with the constraints of normalization, known arithmetic mean and geometric mean, and the solution is the general form of gamma distribution. A constant arithmetic mean is determined by considering the stable average recharge rate at thousand year scale, and an approximate constant geometric mean is determined by the low flow rate (about 1 cm a year). Followed, the parameters of the scaled PDF of gamma distribution are determined by local environmental factors like terrain and vegetation: the multivariate linear equations are established to qualify the relationship between the parameters and the environmental factors on the basis of nineteen random soil moisture profiles about depth through the application of fuzzy mathematics. Finally, the accuracy is tested using correlation coefficient (CC) and relative error. This method performs with CC larger than 0.9 in more than a half profiles and most larger than 0.8, the relative errors are less than 30% in most of soil moisture profiles and can be as low as less than 15% when parameters fitted appropriately. Therefore, this study provides an alternative method to estimate soil moisture distribution in top 0–10 m layers of the Badain Jaran Desert based on local terrain and vegetation factors instead of drilling sand samples, this method would be useful in desert regions with extreme natural conditions since these environmental factors can be obtained by remote sensing data. Meanwhile, we should bear in mind that this method is challenged in humid regions since more intensive and frequent precipitation, and more vegetation cover make the system much more complex

Entropy Base Estimation of Moisture Content of the Top 10-m Unsaturated Soil for the Badain Jaran Desert in Northwestern China