基于CA-Markov模型与ANUDEM内插法的崩岗侵蚀量预估

崩岗是中国南方最为严重的土壤侵蚀类型之一，产生的大量泥沙危害农业生产和生态环境，因此对其侵蚀量的预估是防治该现象的重要途径。崩岗面积较小且侵蚀剧烈，难以应用现有方法预估侵蚀量。该文应用CA-Markov模型和ANUDEM内插法对其高程级别模拟和空间内插，从而实现对崩岗侵蚀量的预估，并以福建省安溪县龙门镇的一处崩岗为例进行实证研究。结果表明：CA-Markov模型适用于对崩岗高程级别的模拟；ANUDEM内插法对崩岗地形的整体还原度较好，但对细节的刻画不够；以经过级别划分和内插处理的高程数据为基期底图计算得的崩岗侵蚀量较符合实际值，且实际侵蚀量越大，模拟精度越高；案例崩岗在一般年景、干旱年景和多雨年景中的年侵蚀量分别为：824.69、731.03和 924.57 m3，不同年景之间侵蚀量的最大差值为193.54 m3，因此在修建崩岗拦沙坝时需考虑不同降雨年景中侵蚀量的差异。研究结果不仅提供了预估崩岗侵蚀量的新思路，还可为崩岗侵蚀的防治工作提供参考依据。

Estimation of erosion amount in collapsed gully based on CA-Markov model and ANUDEM interpolation

Abstract: Collapsed gully is a kind of soil erosion in South China threating agriculture production and ecological environment due to its considerable sediment yield. Therefore, the prediction and estimation of erosion amount play a significant role in its prevention and control. However, collapsed gullies normally cover a relatively smaller area and eroded more severely than other kinds of soil erosion, which made existing methods and approaches hardly to apply on it. In this research, cellular automation-Markov (CA-Markov) model and Australian National University digital elevation model (ANUDEM) are employed to estimate and predict the erosion amount of collapsed gully. The former is taken to simulate the transition of collapsed gully elevation classes, and the latter is taken to spatial interpolate on the simulation results of collapsed gully elevation classes. Based on the two processes, the continuous elevation data of collapsed gully can be simulated and predicted. Then the erosion amount is computed according to the prediction result and base time data. To test this approach, a collapsed gully located in the Longmen Town, Anxi County, Fujian Province is chosen as the case study. And it contains two parts, which are the confirmation of simulating accuracy and the prediction under 3 types of scenes for annual erosion amount. The results show that the modified CA-Markov model performances well on the simulation of collapsed gully elevation classes, which resulted from a lower area error between simulation results and actual value (1.47%), and a higher Kappa coefficient of 0.958. The goodness of fit (R2) of the interpolation result using ANUDEM is 0.998 7 and its mean error (ME) is 0.27 m, which means ANUDEM is good at the integral restoration of collapsed gullies terrain but not sufficient at details. As a consequence, two types elevation at the base time are chosen to estimate the erosion amount, one is original DEM, and the other one is the elevation data through classes division and interpolated processing. The erosion amount calculated from the second type of base data performances difference rates of 17.55% and 8.66%, which are much lower than the one derived from the first type of base data. Thus, the second type of base data is accessible for computing collapsed gully erosion amount, and the huger the real erosion amount, the higher the accuracy. After the confirmation of modeling accuracy, 3 types of rainfall scenes were set based on the historical records of rainfall, which are normal years, drought years and rainy years. The annual erosion amounts of case collapsed gully under the 3 types of rainfall scenes are 824.69, 731.03 and 924.57 m3, and the difference of the two extreme rainfall scenes is 193.54 m3, which means that the difference of erosion amount between different rainfall scenes should be taken into account when building a sediment storage dam to control the damage of a collapsed gully. The methods proposed in this research can not only provide a novel way to study the erosion process and erosion amount of collapsed gully, but also supply a reasonable reference for the prevention and control of collapsed gully erosion.