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论文：水分胁迫条件下实际蒸散发量的计算方法与时间步长
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Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step（水分胁迫条件下实际蒸散发量的计算方法与时间步长）
Article first published online: 20 JAN 2012
DOI: 10.1002/hyp.8405
Copyright © 2011 John Wiley & Sons, Ltd.
Issue
Hydrological Processes
How to Cite: Shang, S. (2012), Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes. doi: 10.1002/hyp.8405
- Article first published online: 20 JAN 2012
- Accepted manuscript online: 13 NOV 2011 10:15PM EST
- Manuscript Accepted: 1 NOV 2011
- Manuscript Received: 30 APR 2011
Keywords（关键词）:
- evapotranspiration（蒸散发）;
- water stress（水分胁迫）;
- time step（时间步长）;
- explicit Euler method（显式欧拉法）;
- midpoint method（中点法）;
- Heun's third-order method（Heun三阶方法）
摘要：水分胁迫条件下实际蒸散发的计算是水文模拟与灌溉用水管理中的基本问题。实际蒸散发的计算取决于根据根系层含水量估算水分胁迫系数，其结果与采用的数值计算方法和时间步长。在无降水及灌溉的土壤水分消退期，实际蒸散发量可根据解析法及数值法计算。以解析法计算结果为基础，比较了几种常用数值计算方法（包括显式、隐式及修正欧拉法、中点法及Heun三阶方法）的计算精度。结果表明实际蒸散发量的一步计算相对误差与初始土壤含水量无关，且相对误差绝对值随数值计算方法的阶数而减小。相对误差绝对值也随着计算步数而减小，可以保证连续模拟过程中计算结果的稳定性。考虑不同时间步长及最大蒸散发量情况下的计算误差及计算复杂性，显式欧拉法可用于时间步长1d或2d（最大蒸散发量<5 mm/d）时的时间蒸散发量计算；中点法或修正欧拉法可用于时间步长7d或10d（最大蒸散发量<5 mm/d）的情况；而Heun三阶方法可用于时间步长15d的情况。
Abstract: Calculation of actual crop evapotranspiration under soil water stress conditions is crucial for hydrological modeling and irrigation water management. Results of actual evapotranspiration depend on the estimation of water stress coefficient from soil water storage in the root zone, which varies with numerical methods and time step used. During soil water depletion periods without irrigation or precipitation, the actual crop evapotranspiration can be calculated by an analytical method and various numerical methods. We compared the results from several commonly used numerical methods, including the explicit, implicit and modified Euler methods, the midpoint method, and the Heun's third-order method, with results of the analytical method as the bench mark. Results indicate that relative errors of actual crop evapotranspiration calculated with numerical methods in one time step are independent of the initial soil water storage in the range of soil water stress. Absolute values of relative error decrease with the order of numerical methods. They also decrease with the number of time step, which can ensure the numerical stability of successive simulation of soil water balance. Considering the calculation complexity and calculation errors caused by numerical approximation for different time step and maximum crop evapotranspiration, the explicit Euler method is recommended for the time step of 1 day (d) or 2 d for maximum crop evapotranspiration less than 5 mm/d, the midpoint method or the modified Euler method for the time step of up to one week or 10 d for maximum crop evapotranspiration less than 5 mm/d, and the Heun's third-order method for the time step of up to 15 d.
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