考虑气候模式影响的径流模拟不确定性分析
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摘要
由于水文模型很难完整地描述现实中的水文过程,不确定性分析是径流模拟中不可缺少的部分。通常,径流模拟的不确定性来源于输入数据,水文模型参数和模型结构。但是,当以全球气候模式下的气象数据作为水文模型的输入数据时,气候模式、降尺度方法以及排放情景的不确定性,将直接影响输入数据,从而间接地影响径流模拟的效果。因此,本文除了对水文模型的参数和结构的不确定性进行分析,还考虑了不同气候模式影响下的输入不确定性,旨在全面地研究气候模式影响下的径流模拟不确定性。论文的主要研究内容和成果如下：
(1)采用GLUE方法对新安江模型,SMAR模型和SIMHYD模型的参数进行敏感性分析,旨在识别模型参数对模拟精度的影响程度,为流域水文模拟提供参考,从而为后面利用BMA对多个模型的加权平均提供可靠的参数。最后,通过对比三个水文模型参数在两个流域的敏感程度,将参数敏感性分为三类：不敏感参数、敏感参数和流域敏感参数。
(2)贝叶斯模型加权平均方法(BMA)不仅可以集合不同水文模型结果得到综合径流,而且还能推算出综合径流的不确定性区间,分析多个水文模型内和模型间误差。采用三个水文模型来研究两种BMA方案。在第一种BMA方案中,采用同一个目标函数(确定性系数)来率定三个模型,因而得到三组不同的预报值用来进行BMA综合。在第二种BMA方案中,采用除了确定性系数之外的三个分别在高、中、低水有较好模拟效果的目标函数,来逐一率定三个模型,从而每个模型都可以得到三组不同的优化参数值。由于同一个模型的不同优化参数值会导致不同的预报结果,因此有九组不同的预报值用来进行BMA综合。另外,对单个模型和两种BMA方法均采用蒙特卡洛组合的方法来得到预报不确定性区间。最后对单个模型和两种BMA综合方法得到的预报值的精度和不确定性区间进行分析和比较。
(3)对气候模式影响下的气象输入数据进行了不确定性分析。研究了三个全球气候模式(BCCR-BCM2.0,CSIRO-MK3.0和GFDL-CM2.0)在20C3M气候场景下的气候输出,并利用三种降尺度方法将全球尺度的降雨降尺度到流域尺度。最后利用BMA方法,分别研究了不同气候模式对降雨模拟的不确定性,以及不同降尺度方法对降雨模拟的不确定性。
(4)基于BMA方法,提出了两种BMA方案(即单层BMA和双层BMA)用于气候模式影响下径流模拟的不确定性研究。第一种BMA方案,首先将三个GCM和三种降尺度方法组合,然后将组合得到的九组降雨预报分别作为新安江模型的气候输入,最后得到的九组径流预报用BMA方法进行加权平均。由于第一种方案只用到一次BMA方法,称为“单层BMA"。第二种BMA方案,首先将三个GCM和三种降尺度方法组合得到的九组降雨预报用BMA方法进行加权平均,得到BMA(9)综合降雨。然后,将BMA(9)的综合降雨作为水文模型的气候输入,分别用新安江模型、SMAR和SIMHYD三个水文模型进行径流模拟,得到三组模型的径流模拟值。最后,再次利用BMA方法对三组径流值进行加权平均,得到BMA(3)综合径流。由于第二种方案用到了两次BMA方法,这里称为“双层BMA"。最后,将两种方案得到的综合径流与实测径流进行比较,选择最优的方案用于未来气候情景下的径流模拟。
(5)基于双层BMA方案,利用双层BMA方案得到的权重,对未来三种气候排放情景A1B、A2和B1下的多组降雨和多组径流进行加权平均,最后得到三种气候情景下的BMA(9)综合降雨和BMA(3)综合径流。然后利用对数正态分布,对三种气候情景下的BMA(9)综合降雨和BMA(3)综合径流的频率分布进行拟合,最后比较三种气候情景的降雨和径流预测的频率差异。
As hydrological model is the simplified description of the actual hydrological processes, it cannot capture every aspects of the real world. Uncertainty analysis of the runoff simulated by hydrological models has become a necessary component in runoff prediction. The sources of uncertainties usually arise from the input data, parameters of hydrological models and the model structure. When using climate data derived from GCMs as the input data, the input uncertainty is not only caused by the observation error, but also the uncertainties in climate models, downscaling methods and emission scenarios. These uncertainties will directly affect the precision of the input data, and thus affect the performance of simulated runoff. Therefore, besides the uncertainty analysis of parameters and the structure in hydrological models, the input uncertainties with respect to the climate models were taken into consideration as well. The main contents and results in this paper were summarized as follows:
(1) In order to check the sensitivities of the parameters in three hydrological models, i.e. Xinanjiang model, SMAR and SIMHYD, GLUE method was used to get the scatter plots of likelihood function. According to the results of scatter plots in two study basins, parameters of three models could be classified into three groups:non-sensitive parameters; sensitive parameters; regional sensitive parameters.
(2) Since the BMA is a method that can combine the forecasts of different models together to generate a new forecast expected to be better than any individual model's forecast, and also has the ability to provide a uncertainty interval of the quantity to be forecasted, three hydrological models were employed in the investigation of two BMA schemes in this research to see if the BMA could improve the prediction reliability. The first BMA scheme was to calibrate each of the three models under the same Nash-Sutcliffe efficiency objective function, thus providing three different forecasts for the BMA combination. In the second BMA scheme, three different objective functions other than Nash-Sutcliffe efficiency were adopted, each of which is targeted for simulating different parts of flows, i.e. low flow, medium flow, and high flow. All three models were respectively calibrated for each of three objective functions to obtain the optimized parameter sets. As the same model with the different optimized parameter sets would give rise to different forecasts, thus in the second BMA scheme, there were nine different forecasts used for the BMA combination. For each of individual member model as well as both BMA combination schemes, the Monte Carlo method was used to infer the probability distribution of the quantity to be forecasted and determine prediction uncertainty intervals. Then, the model efficiency and uncertainty of each member model and two BMA combination schemes were assessed and compared.
(3) The uncertainties in rainfall simulation when considering the impact of climate models were analyzed. The output data of three GCMs, i.e. BCCR-BCM2.0, CSIRO-MK3.0and GFDL-CM2.0under the scenario of20C3M was firstly prepared. For each GCM, three downscaling methods were employed to downscale the rainfall data from the global scale to the regional scale. At last, based on BMA method, the uncertainty from climate models and the uncertainty from downscaling methods were discussed respectively.
(4) For the comprehensive uncertainty analysis of simulated runoff considering the input data uncertainty arose from climate models and downscaling methods, two BMA programs were firstly proposed in this paper. In the first BMA program, three GCMs and three downscaling methods were combined to construct nine sets of rainfall as input data. Therefore, nine sets of simulated runoff were obtained by Xinanjiang model for BMA combination. Because BMA method was only used once in the process of runoff averaging, the first BMA program was named "One-level BMA". In the second BMA program, the first step of constructing nine sets of rainfall was the same as the first BMA program. Secondly, nine-set rainfall were weighted averaged by BMA method to get a set rainfall called BMA(9) rainfall. Thirdly, BMA(9) rainfall was taken as input data respectively for three hydrological models to derive three sets of simulated runoff. At last, BMA method was used for the second time in the process of runoff averaging. As BMA method was used twice in the second BMA program, the second program was named "Two-level BMA". The BMA program which has a better performance in runoff simulation was chosen to be used in the future prediction.
(5) Based on the BMA weights calculated by Two-level BMA, both averaged rainfall and averaged runoff under three climate scenarios in the future could be computed easily. Using log-normal distribution to fit the frequencies of averaged rainfall and averaged runoff of three scenarios, the differences of three climate scenarios in predicting the future rainfall and runoff were distinguished.
(1)采用GLUE方法对新安江模型,SMAR模型和SIMHYD模型的参数进行敏感性分析,旨在识别模型参数对模拟精度的影响程度,为流域水文模拟提供参考,从而为后面利用BMA对多个模型的加权平均提供可靠的参数。最后,通过对比三个水文模型参数在两个流域的敏感程度,将参数敏感性分为三类：不敏感参数、敏感参数和流域敏感参数。
(2)贝叶斯模型加权平均方法(BMA)不仅可以集合不同水文模型结果得到综合径流,而且还能推算出综合径流的不确定性区间,分析多个水文模型内和模型间误差。采用三个水文模型来研究两种BMA方案。在第一种BMA方案中,采用同一个目标函数(确定性系数)来率定三个模型,因而得到三组不同的预报值用来进行BMA综合。在第二种BMA方案中,采用除了确定性系数之外的三个分别在高、中、低水有较好模拟效果的目标函数,来逐一率定三个模型,从而每个模型都可以得到三组不同的优化参数值。由于同一个模型的不同优化参数值会导致不同的预报结果,因此有九组不同的预报值用来进行BMA综合。另外,对单个模型和两种BMA方法均采用蒙特卡洛组合的方法来得到预报不确定性区间。最后对单个模型和两种BMA综合方法得到的预报值的精度和不确定性区间进行分析和比较。
(3)对气候模式影响下的气象输入数据进行了不确定性分析。研究了三个全球气候模式(BCCR-BCM2.0,CSIRO-MK3.0和GFDL-CM2.0)在20C3M气候场景下的气候输出,并利用三种降尺度方法将全球尺度的降雨降尺度到流域尺度。最后利用BMA方法,分别研究了不同气候模式对降雨模拟的不确定性,以及不同降尺度方法对降雨模拟的不确定性。
(4)基于BMA方法,提出了两种BMA方案(即单层BMA和双层BMA)用于气候模式影响下径流模拟的不确定性研究。第一种BMA方案,首先将三个GCM和三种降尺度方法组合,然后将组合得到的九组降雨预报分别作为新安江模型的气候输入,最后得到的九组径流预报用BMA方法进行加权平均。由于第一种方案只用到一次BMA方法,称为“单层BMA"。第二种BMA方案,首先将三个GCM和三种降尺度方法组合得到的九组降雨预报用BMA方法进行加权平均,得到BMA(9)综合降雨。然后,将BMA(9)的综合降雨作为水文模型的气候输入,分别用新安江模型、SMAR和SIMHYD三个水文模型进行径流模拟,得到三组模型的径流模拟值。最后,再次利用BMA方法对三组径流值进行加权平均,得到BMA(3)综合径流。由于第二种方案用到了两次BMA方法,这里称为“双层BMA"。最后,将两种方案得到的综合径流与实测径流进行比较,选择最优的方案用于未来气候情景下的径流模拟。
(5)基于双层BMA方案,利用双层BMA方案得到的权重,对未来三种气候排放情景A1B、A2和B1下的多组降雨和多组径流进行加权平均,最后得到三种气候情景下的BMA(9)综合降雨和BMA(3)综合径流。然后利用对数正态分布,对三种气候情景下的BMA(9)综合降雨和BMA(3)综合径流的频率分布进行拟合,最后比较三种气候情景的降雨和径流预测的频率差异。
As hydrological model is the simplified description of the actual hydrological processes, it cannot capture every aspects of the real world. Uncertainty analysis of the runoff simulated by hydrological models has become a necessary component in runoff prediction. The sources of uncertainties usually arise from the input data, parameters of hydrological models and the model structure. When using climate data derived from GCMs as the input data, the input uncertainty is not only caused by the observation error, but also the uncertainties in climate models, downscaling methods and emission scenarios. These uncertainties will directly affect the precision of the input data, and thus affect the performance of simulated runoff. Therefore, besides the uncertainty analysis of parameters and the structure in hydrological models, the input uncertainties with respect to the climate models were taken into consideration as well. The main contents and results in this paper were summarized as follows:
(1) In order to check the sensitivities of the parameters in three hydrological models, i.e. Xinanjiang model, SMAR and SIMHYD, GLUE method was used to get the scatter plots of likelihood function. According to the results of scatter plots in two study basins, parameters of three models could be classified into three groups:non-sensitive parameters; sensitive parameters; regional sensitive parameters.
(2) Since the BMA is a method that can combine the forecasts of different models together to generate a new forecast expected to be better than any individual model's forecast, and also has the ability to provide a uncertainty interval of the quantity to be forecasted, three hydrological models were employed in the investigation of two BMA schemes in this research to see if the BMA could improve the prediction reliability. The first BMA scheme was to calibrate each of the three models under the same Nash-Sutcliffe efficiency objective function, thus providing three different forecasts for the BMA combination. In the second BMA scheme, three different objective functions other than Nash-Sutcliffe efficiency were adopted, each of which is targeted for simulating different parts of flows, i.e. low flow, medium flow, and high flow. All three models were respectively calibrated for each of three objective functions to obtain the optimized parameter sets. As the same model with the different optimized parameter sets would give rise to different forecasts, thus in the second BMA scheme, there were nine different forecasts used for the BMA combination. For each of individual member model as well as both BMA combination schemes, the Monte Carlo method was used to infer the probability distribution of the quantity to be forecasted and determine prediction uncertainty intervals. Then, the model efficiency and uncertainty of each member model and two BMA combination schemes were assessed and compared.
(3) The uncertainties in rainfall simulation when considering the impact of climate models were analyzed. The output data of three GCMs, i.e. BCCR-BCM2.0, CSIRO-MK3.0and GFDL-CM2.0under the scenario of20C3M was firstly prepared. For each GCM, three downscaling methods were employed to downscale the rainfall data from the global scale to the regional scale. At last, based on BMA method, the uncertainty from climate models and the uncertainty from downscaling methods were discussed respectively.
(4) For the comprehensive uncertainty analysis of simulated runoff considering the input data uncertainty arose from climate models and downscaling methods, two BMA programs were firstly proposed in this paper. In the first BMA program, three GCMs and three downscaling methods were combined to construct nine sets of rainfall as input data. Therefore, nine sets of simulated runoff were obtained by Xinanjiang model for BMA combination. Because BMA method was only used once in the process of runoff averaging, the first BMA program was named "One-level BMA". In the second BMA program, the first step of constructing nine sets of rainfall was the same as the first BMA program. Secondly, nine-set rainfall were weighted averaged by BMA method to get a set rainfall called BMA(9) rainfall. Thirdly, BMA(9) rainfall was taken as input data respectively for three hydrological models to derive three sets of simulated runoff. At last, BMA method was used for the second time in the process of runoff averaging. As BMA method was used twice in the second BMA program, the second program was named "Two-level BMA". The BMA program which has a better performance in runoff simulation was chosen to be used in the future prediction.
(5) Based on the BMA weights calculated by Two-level BMA, both averaged rainfall and averaged runoff under three climate scenarios in the future could be computed easily. Using log-normal distribution to fit the frequencies of averaged rainfall and averaged runoff of three scenarios, the differences of three climate scenarios in predicting the future rainfall and runoff were distinguished.
引文
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