Research on Hour-scale Groundwater Evapotranspiration Based on Modified Method of Diurnal Water Table Fluctuation
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摘要:
基于水位昼夜波动计算潜水蒸散发（ETG）的方法应用广泛，但已有的水位昼夜波动法忽略了夜间地下水对毛细水的补给，低估了地下水侧向补给量，从而低估了ETG。本次研究提出考虑夜间毛细水恢复速率的改进方法，并结合一维饱和非饱和水流模型（HYDRUS-1D）和野外实测数据对改进方法进行了验证。结果显示：基于模型的不同土质条件下，Loheide方法的相对误差均大于45%，且误差随实际ETG与水位埋深的增大而增大；而改进方法的计算精度明显提高，相对误差均小于4%。结合实测数据的验证中，改进方法计算的小时尺度ETG与潜在蒸散发具有更好的相关性。上述结果表明，改进方法显著提升了小时尺度ETG的计算精度，可有效应用于半干旱地区小时尺度潜水蒸散发计算，为定量研究地下水与植物生态的相互关系提供了技术支撑。
Abstract:Groundwater evapotranspiration (ETG) is widely estimated using methods based on diurnal water table fluctuations. However, these methods fail to account for the recharge of capillary water by groundwater at night, which results in an underestimation of ETG due to the underestimated lateral recharge of groundwater. This study proposes a modified method that takes into account the capillary water recovery rate at night. HYDRUS-1D, a one-dimensional saturated unsaturated flow model, and field measurements are used to evaluate the modified method. Results demonstrate that the relative errors of the Loheide method are all larger than 45% under various soil conditions based on the model. The errors rise as the water table depth and real ETG both rise. The modified method significantly improves estimation accuracy, with an error of less than 4%. The hour-scale ETG estimated by the modified method shows a stronger association with potential evapotranspiration in the validation of the measured data. According to the above results, the modified method considerably raises the hour-scale ETG calculation accuracy. It can also be applied successfully to hour-scale ETG calculations in semi-arid areas, offering technical support for quantitative studies on the connection between groundwater and plant ecology.
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图 1 概念模型示意图（a），模型中小时尺度潜在蒸散发（ETP）（b）和模型根系垂向分布率（c）
Figure 1. A schematic of the conceptual model (a), the hourly variations of potential ET (ETp) (b) and the vertical root distributions in the model (c)
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图 2 模型中不同土质的水位埋深变化（a）和模型中砂质壤土剖面不同深度的土壤含水率变化（b）
Figure 2. Water table hydrographs in different soil textures (a) and soil moisture at various depths for sandy loam in the model (b)
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图 3 砂质壤土中25～29天不同方法计算的地下水恢复速率（a）和毛细水亏缺量变化速率与地下水恢复速率的低估值（Er）（b）
Figure 3. The groundwater recovery rate estimated by different methods (a) and the variation rate of capillary water deficit and Er during days 25-29 for sandy loam (b)
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图 4 砂质壤土中第28～30天不同方法计算结果与实际蒸散发的对比（a）和不同方法计算结果的日平均误差随水位埋深的变化（b）
Figure 4. Comparison of actual ETG and the ETG estimated by different methods during days 28-30 (a) and the variation of the daily mean error with the DWT estimated by different methods for sandy loam (b)
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图 6 实测水位埋深与不同深度的土壤含水率（a），毛细水亏缺量恢复速率与地下水恢复速率的低估值（Er）（b），气温与露点（c）和Loheide方法、改进方法的ETG与ETP的对比（d）
Figure 6. Measured DWT and soil moistures (a); the variation rate of capillary water deficit and Er (b); air temperature and dew point (c); Comparison of potential ET and the ETG estimated by the Loheide method and modified method (d)
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图 7 Loheide方法、改进方法的计算结果分别与潜在蒸散发的相关性分析
Figure 7. The correlation between potential ET and the ETG estimated by the Loheide method and modified method, respectively
表 1 模型中各类土质的水力参数
Table 1 Hydraulic parameters of each soil used in the model
土质类型 $ {\mathrm{\theta }}_{\mathrm{s}} $ $ {\mathrm{\theta }}_{\mathrm{r}} $ $ \mathrm{\Phi } $ （1/cm） n Ks （cm/h） 砂土 0.43 0.045 0.145 2.68 29.70 壤质砂土 0.41 0.057 0.124 2.28 14.59 砂质壤土 0.41 0.065 0.075 1.89 4.42 壤土 0.43 0.078 0.036 1.56 1.04 粉质黏土 0.36 0.07 0.005 1.09 0.02 
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表 2 不同方法计算结果与实际值的均方根误差（RMSE）和纳什系数（NSE）
Table 2 The RMSE and NSE of ETG-A and ETG-L estimated by different methods for each soil
ETG-L与ETG-A ETG-M与ETG-A RMSE （mm/h） NSE RMSE （mm/h） NSE 砂土 0.05 0.56 0.02 0.93 壤质砂土 0.08 0.46 0.01 0.98 砂质壤土 0.16 0.17 0.02 0.99 壤土 0.28 −0.14 0.04 0.98
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表 3 研究场地平均土壤水力参数
Table 3 Hydraulic parameters of the soil in the field site
$ {\theta }_{s} $ $ {\theta }_{r} $ $ \Phi $ （1/cm） n Ks （cm/h） 0.360 0.054 0.028 2.68 29.4
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