一种改进的时间序列重建方法及其在地下水埋深估计中的应用

A Modified Reconstruction Method of Time Series and Its Application in Estimation of Water Table Depth

带噪声传递函数(TFN)模型可通过相关性分析在输入输出序列时间上同步的情况下估计输出序列。基于TFN模型、Kalman滤波和复合型混合演化(SCE-UA)算法,发展一种新的时间序列重建方法,并将其用于地下水埋深估计。该方法将高阶TFN模型表述成状态空间,并用Kalman滤波进行状态估计,基于SCE-UA方法优化TFN模型参数,能够在输入输出序列异步的情况下率定TFN模型并用于时间序列重建。最后,利用已有降水和地下水观测资料验证该方法,并重建了中国东北部分地区40年地下水埋深序列,结果表明该方法有较好精度且能反映埋深变化对降水的响应,在各类时间序列重建中具有一定推广性。

Transfer function-noise （TFN） model could be used to estimate output series through correlation analysis when the input-output series were synchronous. A modified time series reconstruction method was presented, which was based on TFN model, Kalman filter and SCE-UA method. First, the TFN model was represented as state-space. Then the Kalman filter combined with SCE-UA method was applied to calibrate the model even if the input and output series were asynchronous. Finally, the method was validated by observed series of precipitation and water table depths, and 40-year series of water table depths over the northeast of China were reconstructed by precipitation series as well. The validation and application show that the method not only has good modeling accuracy, but also reflects how the water table fluctuation respond to the precipitation reasonably well. Therefore, the method could be extended to reconstruct other kinds of series in a similar way.