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Proficiency of probability distributions in unit hydrograph derivation 单位水文图推导中概率分布的熟练程度
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-03-08 DOI: 10.2166/nh.2024.151
Esmatullah Sangin, Pravin R. Patil, S. K. Mishra, Sumit Sen
The probability distribution function (PDF)-based unit hydrographs (UHs) are gaining momentum in an application for more accurate rainfall-runoff transformation. Employing seven statistical performance indices, R2, NSE, MSE, RMSE, MAE, MAPE, and SE in GRG-NLP optimization, 18 known and 12 adaptable UHs were assessed against UHs derived from 18 storms in 7 basins across the United States, Turkey, and India. To this end, 27 Maple codes were proposed for UH-application requiring only peak discharge (qp), time to peak (tp), and time base (tb) for derivation. The introduced PDFs, such as Dagum, Generalized Gamma, Log-Logistic, Gumbel Type-I, and Shifted Gompertz, replicated the observed data-derived UHs more closed than did the known PDFs, like Inverse Gaussian, 2-PGD, Log-Normal, Inverse-Gamma, and Nagakami. Among the three-parameter (6 nos.), two-parameter (21 nos.), and single-parameter (3 nos.) PDFs, the Dagum, Log-Logistic, and Poisson consistently outperformed their respective counterparts in replication.
基于概率分布函数(PDF)的单位水文图(UHs)在应用于更精确的降雨-径流转换方面势头正劲。在 GRG-NLP 优化过程中采用了 R2、NSE、MSE、RMSE、MAE、MAPE 和 SE 七种统计性能指标,根据美国、土耳其和印度 7 个流域 18 次暴雨得出的单位水文图,对 18 种已知单位水文图和 12 种可调整单位水文图进行了评估。为此,提出了 27 个 Maple 代码,用于 UH 应用,只要求推导峰值排水量(qp)、峰值时间(tp)和时基(tb)。引入的 PDF(如 Dagum、Generalized Gamma、Log-Logistic、Gumbel Type-I 和 Shifted Gompertz)比已知的 PDF(如 Inverse Gaussian、2-PGD、Log-Normal、Inverse-Gamma 和 Nagakami)更接近地复制了观测数据得出的 UH。在三参数(6 个)、二参数(21 个)和单参数(3 个)PDF 中,Dagum、Logistic 和 Poisson 在复制方面始终优于各自的对应参数。
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引用次数: 0
Temporal dynamics of water level and water sources analyses of karst tidal springs in Guilin, China 中国桂林岩溶潮汐泉的水位时空动态和水源分析
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-14 DOI: 10.2166/nh.2024.178
Jie Ma, Shilong Zhu, Xiaomei Wei, Yongli Guo, Jianhua Cao, Fen Huang
The hydrological dynamics and sources of karst tidal springs are difficult to capture and quantify due to fluctuations in their flow velocity. In this study, the Laolongshui (LLS) karst tidal spring in the Maocun underground river basin of Guilin City was taken as an example, with a 2-year continuous monitoring of the electrical conductivity, and water level,as well as water chemical analysis. The results showed the following: (1) discovered the variation pattern of LLS water level in different seasons, the water level fluctuates regularly on a daily scale, with a rise and fall time of 43.6 min after heavy rainfall in the rainy season, while in the dry season, it lasts for about 74–80 h. (2) Four peaks were extracted from the frequency distribution of electrical conductivity, representing the response of springwater under different rainfall conditions. (3) The annual average frequencies of the occurrence of P1, P2, P3, and P4 in terms of time are 53.82, 39.29, 6.18, and 0.72%, respectively. The results provide a new method for analyzing groundwater's source and dynamic changes in karst areas.
由于岩溶潮汐泉的流速波动较大,其水文动态和水源难以捕捉和量化。本研究以桂林市茅村地下河流域的老龙水岩溶潮汐泉为例,对其电导率、水位以及水化学分析进行了为期两年的连续监测。结果表明(1)发现了 LLS 水位在不同季节的变化规律,水位每天有规律地波动,雨季大雨后水位升降时间为 43.6 min,旱季则持续约 74-80 h;(2)从电导率的频率分布中提取了四个峰值,代表了泉水在不同降雨条件下的响应。(3) 从时间上看,P1、P2、P3 和 P4 的年平均出现频率分别为 53.82%、39.29%、6.18% 和 0.72%。这些结果为分析岩溶地区地下水的来源和动态变化提供了一种新的方法。
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引用次数: 0
Temporal dynamics of water level and water sources analyses of karst tidal springs in Guilin, China 中国桂林岩溶潮汐泉的水位时空动态和水源分析
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-14 DOI: 10.2166/nh.2024.178
Jie Ma, Shilong Zhu, Xiaomei Wei, Yongli Guo, Jianhua Cao, Fen Huang
The hydrological dynamics and sources of karst tidal springs are difficult to capture and quantify due to fluctuations in their flow velocity. In this study, the Laolongshui (LLS) karst tidal spring in the Maocun underground river basin of Guilin City was taken as an example, with a 2-year continuous monitoring of the electrical conductivity, and water level,as well as water chemical analysis. The results showed the following: (1) discovered the variation pattern of LLS water level in different seasons, the water level fluctuates regularly on a daily scale, with a rise and fall time of 43.6 min after heavy rainfall in the rainy season, while in the dry season, it lasts for about 74–80 h. (2) Four peaks were extracted from the frequency distribution of electrical conductivity, representing the response of springwater under different rainfall conditions. (3) The annual average frequencies of the occurrence of P1, P2, P3, and P4 in terms of time are 53.82, 39.29, 6.18, and 0.72%, respectively. The results provide a new method for analyzing groundwater's source and dynamic changes in karst areas.
由于岩溶潮汐泉的流速波动较大,其水文动态和水源难以捕捉和量化。本研究以桂林市茅村地下河流域的老龙水岩溶潮汐泉为例,对其电导率、水位以及水化学分析进行了为期两年的连续监测。结果表明(1)发现了 LLS 水位在不同季节的变化规律,水位每天有规律地波动,雨季大雨后水位升降时间为 43.6 min,旱季则持续约 74-80 h;(2)从电导率的频率分布中提取了四个峰值,代表了泉水在不同降雨条件下的响应。(3) 从时间上看,P1、P2、P3 和 P4 的年平均出现频率分别为 53.82%、39.29%、6.18% 和 0.72%。这些结果为分析岩溶地区地下水的来源和动态变化提供了一种新的方法。
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引用次数: 0
Bivariate regional drought frequency analysis using multivariate approaches: a case study in southwestern Iran 利用多变量方法进行二元区域干旱频率分析:伊朗西南部案例研究
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.160
Hanie Pashaie, S. S. M. Nadoushani, Ali Moridi, Ali Ahani
Bivariate approaches in Regional Frequency Analysis (RFA) address two issues: first, to evaluate the homogeneity of regions, and second, to estimate the joint return periods. This study was conducted to investigate the joint return period of a severe historical drought in southwestern Iran. Fifty-nine rain gauges were first clustered into three, four, and five regions using the fuzzy c-means clustering (FCM) algorithm. Then bivariate discordancy and homogeneity tests were applied to adjust the initial clusters. The results showed that only in the case of three clusters all the regions were homogeneous. Therefore, it can be inferred that combining clustering analysis and discordancy test is insufficient to form homogeneous regions. Finally, the joint return period, by choosing Generalized Logistic and Wakeby as marginal distributions and Clayton as a copula, was estimated for all the sites in the three regions. Since no three-parameter distribution function fitted well to the variable severity, the bivariate homogeneity index does not necessarily attest to region homogeneity regarding the marginal distribution functions. it is also deduced that sites with higher mean annual precipiataion (MAP) and, correspondingly, higher elevation are more likely to experience shorter return periods of same drought events, in contrast to sites with lower MAP or lower elevation.
区域频率分析 (RFA) 中的双变量方法解决了两个问题:第一,评估区域的同质性;第二,估算联合回归期。本研究旨在调查伊朗西南部历史上严重干旱的联合回归期。首先使用模糊 c-means 聚类(FCM)算法将 59 个雨量计聚类为 3、4 和 5 个区域。然后应用双变量不一致性和同质性检验来调整初始聚类。结果显示,只有在三个聚类的情况下,所有区域都是同质的。因此,可以推断将聚类分析和不一致性检验结合起来不足以形成同质区域。最后,通过选择广义 Logistic 分布和 Wakeby 分布作为边际分布,Clayton 分布作为协整 分布,对三个区域的所有地点进行了联合回归期估计。由于没有一个三参数分布函数能很好地拟合变量严重程度,因此二元同质性指数并不一定能证明区域在边际分布函数方面的同质性。此外,还推断出年平均降水量(MAP)较高、海拔也相应较高的地点更有可能经历较短的相同干旱事件回归期,而年平均降水量较低或海拔较低的地点则相反。
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引用次数: 0
Estimating groundwater recharge rates in the Upper Awash Basin, Ethiopia under different combinations of model complexity and objective functions 在不同的模型复杂性和目标函数组合下估算埃塞俄比亚上阿瓦士盆地的地下水补给率
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.059
Muauz Amare Redda, Behailu Birhanu, Bediru Hussien
Reliable quantification of groundwater recharge rate is crucial for the sustainable utilization of groundwater resources. However, little information is documented about the uncertainty associated with recharge rate estimation from the different combinations of model complexity and objective function perspectives. Therefore, this study aims to (i) analyze the sensitivity of the model parameters under different combinations of model complexities and objective functions and (ii) estimate the groundwater recharge rate in the Hombele catchment, Upper Awash Basin, Ethiopia, for different combinations of objective functions and model complexities. The effect of these model complexities in estimating groundwater recharge rate and parametrizing model parameters was quantified for the period 1986–2013. A total of 10 combinations of model complexities and objective functions were used for the analysis. The Kling–Gupta efficiency (Nash–Sutcliffe efficiency) values for calibration, validation, and the whole period are 0.89 (0.80), 0.80 (0.73), and 0.87 (0.77), respectively, when a semi-distributed HBV-light model was used. For all objective functions, we found that the average annual recharge rate of the study catchment ranges from 185.9 to 280.5 mm when the HBV-light model was considered as a semi-distributed model. In contrast, the average annual recharge rate ranges from 185.3 to 321.7 mm when applying the HBV-light model as a lumped model.
地下水补给率的可靠量化对于地下水资源的可持续利用至关重要。然而,有关从模型复杂性和目标函数的不同组合角度估算补给率的不确定性的资料很少。因此,本研究旨在:(i) 分析模型参数在模型复杂性和目标函数不同组合下的敏感性;(ii) 针对目标函数和模型复杂性的不同组合,估算埃塞俄比亚上阿瓦士盆地 Hombele 流域的地下水补给率。对 1986-2013 年期间这些模型复杂性在估算地下水补给率和参数化模型参数方面的影响进行了量化。分析共使用了 10 种模型复杂性和目标函数组合。当采用半分布式 HBVlight 模型时,校准、验证和整个期间的 Kling-Gupta 效率(Nash-Sutcliffe 效率)值分别为 0.89 (0.80)、0.80 (0.73) 和 0.87 (0.77)。对于所有目标函数,我们发现,当 HBV-light 模型被视为半分布模型时,研究流域的年平均补给率在 185.9 至 280.5 毫米之间。相比之下,将 HBV light 模型作为一个整体模型时,年平均补给率在 185.3 至 321.7 毫米之间。
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引用次数: 0
Hydrological effects of open ditch damming and controlled subsurface drainage in a Nordic agricultural field 北欧农田明沟筑坝和受控地下排水的水文影响
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.053
Kielo Isomäki, Aleksi Salla, H. Salo, H. Koivusalo
Controlled drainage (CRD) is an agricultural water management practice designed to adjust the capacity of a drainage system under varying hydrological conditions. This simulation study aimed to quantify the potential of combining a controlled subsurface drainage (CS) with open ditch damming (CD) to manage the water table depth (WTD) and field water balance in Nordic conditions. Simulations with and without controlled drainage were run using a hydrological model that had been set up for a flat loamy field in Northern Ostrobothnia, Finland, for the period 2010–2021. All CRD scenarios reduced the probability of deep WTDs during growing seasons (May–Sep). The impact of CS on WTDs was greater and more uniform than CD. The CRD effects on water balance were seen in water outflow pathways, as CS reduced drain discharge while CD had the opposite effect. When both methods were applied simultaneously, annual evapotranspiration increased 5–12% compared with the free drainage scenario. The effects of CRD on evapotranspiration were greatest during the dry years indicating that CRD has potential to reduce drought in food production areas. None of the CRD scenarios could maintain optimal WTDs during the entire growing season, highlighting the complexity of optimizing field water management using CRD alone.
控制排水(CRD)是一种农业用水管理方法,旨在不同水文条件下调整排水系统的容量。本模拟研究旨在量化将控制性地下排水(CS)与开沟筑坝(CD)相结合的潜力,以管理北欧条件下的地下水位深度(WTD)和田间水平衡。在 2010-2021 年期间,利用为芬兰北奥斯特罗布尼亚的一块平壤土田建立的水文模型,对有控制排水和无控制排水进行了模拟。所有控制排水方案都降低了生长季节(5 月至 9 月)出现深度 WTD 的概率。与CD相比,CS对WTD的影响更大且更均匀。CRD 对水平衡的影响体现在出水途径上,CS 减少了排水量,而 CD 则产生了相反的影响。当两种方法同时应用时,与自由排水方案相比,年蒸散量增加了 5-12%。在干旱年份,中水回灌对蒸散量的影响最大,这表明中水回灌具有减少粮食生产地区干旱的潜力。没有一个 CRD 方案能在整个生长季节保持最佳 WTD,这凸显了仅使用 CRD 优化田间水管理的复杂性。
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引用次数: 0
Hydrological effects of open ditch damming and controlled subsurface drainage in a Nordic agricultural field 北欧农田明沟筑坝和受控地下排水的水文影响
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.053
Kielo Isomäki, Aleksi Salla, H. Salo, H. Koivusalo
Controlled drainage (CRD) is an agricultural water management practice designed to adjust the capacity of a drainage system under varying hydrological conditions. This simulation study aimed to quantify the potential of combining a controlled subsurface drainage (CS) with open ditch damming (CD) to manage the water table depth (WTD) and field water balance in Nordic conditions. Simulations with and without controlled drainage were run using a hydrological model that had been set up for a flat loamy field in Northern Ostrobothnia, Finland, for the period 2010–2021. All CRD scenarios reduced the probability of deep WTDs during growing seasons (May–Sep). The impact of CS on WTDs was greater and more uniform than CD. The CRD effects on water balance were seen in water outflow pathways, as CS reduced drain discharge while CD had the opposite effect. When both methods were applied simultaneously, annual evapotranspiration increased 5–12% compared with the free drainage scenario. The effects of CRD on evapotranspiration were greatest during the dry years indicating that CRD has potential to reduce drought in food production areas. None of the CRD scenarios could maintain optimal WTDs during the entire growing season, highlighting the complexity of optimizing field water management using CRD alone.
控制排水(CRD)是一种农业用水管理方法,旨在不同水文条件下调整排水系统的容量。本模拟研究旨在量化将控制性地下排水(CS)与开沟筑坝(CD)相结合的潜力,以管理北欧条件下的地下水位深度(WTD)和田间水平衡。在 2010-2021 年期间,利用为芬兰北奥斯特罗布尼亚的一块平壤土田建立的水文模型,对有控制排水和无控制排水进行了模拟。所有控制排水方案都降低了生长季节(5 月至 9 月)出现深度 WTD 的概率。与CD相比,CS对WTD的影响更大且更均匀。CRD 对水平衡的影响体现在出水途径上,CS 减少了排水量,而 CD 则产生了相反的影响。当两种方法同时应用时,与自由排水方案相比,年蒸散量增加了 5-12%。在干旱年份,中水回灌对蒸散量的影响最大,这表明中水回灌具有减少粮食生产地区干旱的潜力。没有一个 CRD 方案能在整个生长季节保持最佳 WTD,这凸显了仅使用 CRD 优化田间水管理的复杂性。
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引用次数: 0
Bivariate regional drought frequency analysis using multivariate approaches: a case study in southwestern Iran 利用多变量方法进行二元区域干旱频率分析:伊朗西南部案例研究
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.160
Hanie Pashaie, S. S. M. Nadoushani, Ali Moridi, Ali Ahani
Bivariate approaches in Regional Frequency Analysis (RFA) address two issues: first, to evaluate the homogeneity of regions, and second, to estimate the joint return periods. This study was conducted to investigate the joint return period of a severe historical drought in southwestern Iran. Fifty-nine rain gauges were first clustered into three, four, and five regions using the fuzzy c-means clustering (FCM) algorithm. Then bivariate discordancy and homogeneity tests were applied to adjust the initial clusters. The results showed that only in the case of three clusters all the regions were homogeneous. Therefore, it can be inferred that combining clustering analysis and discordancy test is insufficient to form homogeneous regions. Finally, the joint return period, by choosing Generalized Logistic and Wakeby as marginal distributions and Clayton as a copula, was estimated for all the sites in the three regions. Since no three-parameter distribution function fitted well to the variable severity, the bivariate homogeneity index does not necessarily attest to region homogeneity regarding the marginal distribution functions. it is also deduced that sites with higher mean annual precipiataion (MAP) and, correspondingly, higher elevation are more likely to experience shorter return periods of same drought events, in contrast to sites with lower MAP or lower elevation.
区域频率分析 (RFA) 中的双变量方法解决了两个问题:第一,评估区域的同质性;第二,估算联合回归期。本研究旨在调查伊朗西南部历史上严重干旱的联合回归期。首先使用模糊 c-means 聚类(FCM)算法将 59 个雨量计聚类为 3、4 和 5 个区域。然后应用双变量不一致性和同质性检验来调整初始聚类。结果显示,只有在三个聚类的情况下,所有区域都是同质的。因此,可以推断将聚类分析和不一致性检验结合起来不足以形成同质区域。最后,通过选择广义 Logistic 分布和 Wakeby 分布作为边际分布,Clayton 分布作为协整 分布,对三个区域的所有地点进行了联合回归期估计。由于没有一个三参数分布函数能很好地拟合变量严重程度,因此二元同质性指数并不一定能证明区域在边际分布函数方面的同质性。此外,还推断出年平均降水量(MAP)较高、海拔也相应较高的地点更有可能经历较短的相同干旱事件回归期,而年平均降水量较低或海拔较低的地点则相反。
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引用次数: 0
Estimating groundwater recharge rates in the Upper Awash Basin, Ethiopia under different combinations of model complexity and objective functions 在不同的模型复杂性和目标函数组合下估算埃塞俄比亚上阿瓦士盆地的地下水补给率
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-02-01 DOI: 10.2166/nh.2024.059
Muauz Amare Redda, Behailu Birhanu, Bediru Hussien
Reliable quantification of groundwater recharge rate is crucial for the sustainable utilization of groundwater resources. However, little information is documented about the uncertainty associated with recharge rate estimation from the different combinations of model complexity and objective function perspectives. Therefore, this study aims to (i) analyze the sensitivity of the model parameters under different combinations of model complexities and objective functions and (ii) estimate the groundwater recharge rate in the Hombele catchment, Upper Awash Basin, Ethiopia, for different combinations of objective functions and model complexities. The effect of these model complexities in estimating groundwater recharge rate and parametrizing model parameters was quantified for the period 1986–2013. A total of 10 combinations of model complexities and objective functions were used for the analysis. The Kling–Gupta efficiency (Nash–Sutcliffe efficiency) values for calibration, validation, and the whole period are 0.89 (0.80), 0.80 (0.73), and 0.87 (0.77), respectively, when a semi-distributed HBV-light model was used. For all objective functions, we found that the average annual recharge rate of the study catchment ranges from 185.9 to 280.5 mm when the HBV-light model was considered as a semi-distributed model. In contrast, the average annual recharge rate ranges from 185.3 to 321.7 mm when applying the HBV-light model as a lumped model.
地下水补给率的可靠量化对于地下水资源的可持续利用至关重要。然而,有关从模型复杂性和目标函数的不同组合角度估算补给率的不确定性的资料很少。因此,本研究旨在:(i) 分析模型参数在模型复杂性和目标函数不同组合下的敏感性;(ii) 针对目标函数和模型复杂性的不同组合,估算埃塞俄比亚上阿瓦士盆地 Hombele 流域的地下水补给率。对 1986-2013 年期间这些模型复杂性在估算地下水补给率和参数化模型参数方面的影响进行了量化。分析共使用了 10 种模型复杂性和目标函数组合。当采用半分布式 HBVlight 模型时,校准、验证和整个期间的 Kling-Gupta 效率(Nash-Sutcliffe 效率)值分别为 0.89 (0.80)、0.80 (0.73) 和 0.87 (0.77)。对于所有目标函数,我们发现,当 HBV-light 模型被视为半分布模型时,研究流域的年平均补给率在 185.9 至 280.5 毫米之间。相比之下,将 HBV light 模型作为一个整体模型时,年平均补给率在 185.3 至 321.7 毫米之间。
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引用次数: 0
A deep learning-based hybrid approach for multi-time-ahead streamflow prediction in an arid region of Northwest China 基于深度学习的混合方法,用于中国西北干旱地区多时段河水流量预测
IF 2.7 4区 环境科学与生态学 Q2 Environmental Science Pub Date : 2024-01-10 DOI: 10.2166/nh.2024.124
J. J. Fang, Linshan Yang, Xiaohu Wen, Weide Li, Haijiao Yu, Ting Zhou
Accurate streamflow prediction is crucial for effective water resource management. However, reliable prediction remains a considerable challenge because of the highly complex, non-stationary, and non-linear processes that contribute to streamflow at various spatial and temporal scales. In this study, we utilized a convolutional neural network (CNN)–Transformer–Long short-term memory (LSTM) (CTL) model for streamflow prediction, which replaced the embedding layer with a CNN layer to extract partial hidden features, and added a LSTM layer to extract correlations on a temporal scale. The CTL model incorporated Transformer's ability to extract global information, CNN's ability to extract hidden features, and LSTM's ability to capture temporal correlations. To validate its effectiveness, we applied it for streamflow prediction in the Shule River basin in northwest China across 1-, 3-, and 6-month horizons and compared its performance with Transformer, CNN, LSTM, CNN–Transformer, and Transformer–LSTM. The results demonstrated that CTL outperformed all other models in terms of predictive accuracy with Nash–Sutcliffe coefficient (NSE) values of 0.964, 0.912, and 0.856 for 1-, 3-, 6-month ahead prediction. The best results among the five comparative models were 0.908, 0.824, and 0.778, respectively. This indicated that CTL is an outstanding alternative technique for streamflow prediction where surface data are limited.
准确的流量预测对于有效的水资源管理至关重要。然而,由于不同时空尺度的河水流量具有高度复杂性、非稳态性和非线性过程,因此可靠的预测仍然是一个相当大的挑战。在本研究中,我们利用卷积神经网络(CNN)-变换器-长短期记忆(LSTM)(CTL)模型进行了流量预测,该模型用 CNN 层取代了嵌入层以提取部分隐藏特征,并添加了一个 LSTM 层以提取时间尺度上的相关性。CTL 模型融合了 Transformer 提取全局信息的能力、CNN 提取隐藏特征的能力以及 LSTM 捕捉时间相关性的能力。为了验证 CTL 模型的有效性,我们将其应用于中国西北部疏勒河流域 1 个月、3 个月和 6 个月的流量预测,并将其与 Transformer、CNN、LSTM、CNN-Transformer 和 Transformer-LSTM 进行了性能比较。结果表明,CTL 的预测准确性优于所有其他模型,其 1 个月、3 个月、6 个月预测的纳什-萨特克利夫系数 (NSE) 值分别为 0.964、0.912 和 0.856。五个比较模型的最佳结果分别为 0.908、0.824 和 0.778。这表明,在地表数据有限的情况下,CTL 是一种出色的河水流量预测替代技术。
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引用次数: 0
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