| 摘要: |
| 【目的】进行灌域尺度的地下水多参数联合反演。【方法】利用集合卡尔曼滤波（EnKF）方法，基于二维潜水运动模型SWF2D，构建了地下水多参数联合反演模型SWF2D_DA。以内蒙古河套灌区永济灌域为研究对象对地下水参数进行了反演分析，该地区地下水运动共涉及8个参数，分别为给水度Sy，降雨入渗补给系数aP，两阶段的灌溉入渗补给系数aI1、aI2，两阶段的潜水蒸发参数aA1、aA2和两阶段的潜水蒸发极限埋深aS1、aS2，采用SWF2D_DA模型分别反演了2待定参数情况和8待定参数情况。【结果】模型对2参数反演平均相对误差MRE为0.124%，均方根误差RMSE为0.002 663，8参数反演MRE为0.376%，RMSE为0.003 283，反演结果均满足精度要求，同时反演8参数会增加得到理想参数所需的同化步。同时，还设置5种观测误差方差，分别为0.01、0.000 1、0.002 5、0.1、0.64 m2，讨论了不同观测误差方差对反演结果的影响。当观测误差方差大于0.1 m2时，随着观测误差增大，MRE、RMSE、Spread增长较快，即观测误差过大会影响数据同化的反演精度；当观测误差方差在0.000 1～0.01 m2之间时，随着观测误差减小，MRE、RMSE并无显著变化，即观测误差达到一定精度时，即使观测误差减小，模型也不能得到精度更高的解，反而增加了观测成本。【结论】模型SWF2D_DA可以实现大尺度复杂地区的多参数联合反演，且待求参数越少，得到可靠的结果所需同化步越少；增加参数个数，需增加同化步。在目前的观测条件下，在观测误差方差为0.01 m2、相对于地下水位最大变幅的相对观测误差在4.4%以内的情况下，反演得到的地下水参数可满足精度要求，同时观测成本较低。 |
| 关键词: 多参数联合反演； 数据同化； 观测误差； 集合卡尔曼滤波；地下水； 模型 |
| DOI：10.13522/j.cnki.ggps.2017.0637 |
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| Estimating Aquifer Parameters in Irrigation District Using Inverse Method Coupled with the Ensemble Kalman Filter |
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ZHANG Yuxue, ZHU Yan, YANG Jinzhong
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State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
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| Abstract: |
| 【Objective】 The objective of this paper is to present a coupling method to inversely estimate parameters of shallow aquifers at irrigation district scale. 【Method】 We proposed a multi-parameter inversion groundwater flow model, SWF2D_DA, based on the ensemble Kalman filter method to estimate aquifer parameters, and a two-dimensional groundwater flow model, SWF2D, to simulate water flow. We then applied SWF2D_DA to inversely estimate the parameters of a shallow aquifer in the Sub-Irrigation District of Yongji in Hetao Irrigation District. The model involved eight parameters, including the specific yield, infiltration coefficient of precipitation, two infiltration coefficients for two-stage irrigation, two evaporation parameters for two-stage evaporation, and two critical evaporation depths. We studied two cases: one was to determine all the eight parameters and the other one was to determine six of the eight parameters. 【Result】 The SWF2D_DA model worked well in multi-parameter inversion with the mean relative error, MRE, of 0.124%, and the root mean square error, RMSE, of 0.002 663 when six parameters needed to be determined; and MRE of 0.376% and RMSE of 0.003 283 when all the eight parameters needed to be determined. We also investigated the impact of measurement errors on inversion accuracy by artificially setting the error variance of five measurements to be 0.01, 0.000 1, 0.002 5, 0.1, 0.64 m2, respectively. When the measurement error variance was greater than 0.1 m2, MRE, RMSE and Spread increased steadily with the measurement errors. When the measurement error variance was from 0.000 1 to 0.01 m2, MRE and RMSE remained almost unchanged, indicating that, as long as the measurement errors were controlled to a certain range, the model can give accurate and robust results. 【Conclusion】 The SWF2D_DA model is able to inversely estimate aquifer parameters at regional scale, and that the less parameters needed to be calibrated, the less assimilation steps the model would take to give reliable results. Its was also found that the tolerable measurement error variance was 0.01 m2, which, for the aquifer we investigated, corresponded to a relative error of 4.4% in groundwater table measurement. The model yielded accurate results when the measured errors were in this range. |
| Key words: multi-parameter joint inversion; data assimilation; observation error; ensemble Kalman filter; ground water; model |
