A model on changes in 210Pbex depth distribution for abandoned farmland
Authors: Yuan Yong , Donghong Xiong , Yunqi Zhang , Baojun Zhang , Xinbao Zhang 
Published: March 2022

&lt;p&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; Fallout radionuclides such as &lt;sup&gt;137&lt;/sup&gt;Cs and &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; have been successfully used to quantify rates of soil and sediment redistribution in many areas of the world in recent years. However, little attention has been given to the assessment of soil erosion rate in the abandoned farmland using the &lt;sup&gt;137&lt;/sup&gt;Cs and &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; tracer techniques. The artificial derived &lt;sup&gt;137&lt;/sup&gt;Cs is still basically uniformly distributed in the soil after farmland abandonment, while the depth distribution of the natural derived &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; in the soil of the abandoned farmland will be continuously changed by the combined effects of its continuous atmospheric deposition, infiltration and radioactive decay within 100 years after farmland abandonment. At present, there is no model to represent this change of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; distribution after the farmland abandonment, and the existing steady-state &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; model is not suitable for soil erosion assessment in the abandoned farmland. It is necessary to develop a model on the changes of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; depth distribution in the soil of abandoned farmland. In this study, the redistribution process of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; in the soil after farmland abandonment was decomposed and theoretically deduced on basis of analyzing the physical mechanisms of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; infiltration and decay in soil. The expression of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; decay in the plough layer on the initial abandoned farmland and the expression of infiltration of the new fallout &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; in soil after farmland abandonment were incorporated to develop the model on changes in &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; depth distribution for the abandoned farmland. The parameters such as the plow depth and the diffusion coefficient required for the model were obtained according to the measured &lt;sup&gt;137&lt;/sup&gt;Cs and &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; depth distributions from the typical abandoned farmlands in Sichuan Province, southwest China. The result showed that the modeled curves of &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; depth distribution in the farmland abandoned for 19, 15 and 8 years matched each other with the measured curves. In addition, the Nash-Sutcliffe efficiency coefficient (&lt;em&gt;E&lt;sub&gt;NS&lt;/sub&gt;&lt;/em&gt;) test showed that the &lt;em&gt;E&lt;sub&gt;NS&lt;/sub&gt;&lt;/em&gt; of the three abandoned farmland were 0.975, 0.961 and 0.889, respectively, indicating the modeled results are reliable. The present study has an important theoretical significance for the development of the models for calculating the soil erosion amount from &lt;sup&gt;210&lt;/sup&gt;Pb&lt;sub&gt;ex&lt;/sub&gt; measurements on the abandoned farmland, and further provides an effective method for the evaluation of the soil erosion response driven by abandonment.&lt;/p&gt;