基于中国科学院自主研发的第二代地球系统模式CAS-ESM2.0,本研究通过在陆面分量模式CoLM(Common Land Model)中引入植被水力模型以替换原有的经验性方案,开展了两组34年(1981~2014年)的AMIP(Atmospheric Model Intercomparison Project...基于中国科学院自主研发的第二代地球系统模式CAS-ESM2.0,本研究通过在陆面分量模式CoLM(Common Land Model)中引入植被水力模型以替换原有的经验性方案,开展了两组34年(1981~2014年)的AMIP(Atmospheric Model Intercomparison Project)数值模拟试验,探讨了植被水力方案的引入对中国夏季降水模拟的影响。结果表明,植被水力方案的引入能够显著降低CAS-ESM2.0模式对中国夏季降水气候态的模拟偏差,特别是显著改进了中国东部、青藏高原降水的低估,青藏高原以东的川西地区降水高估的偏差,同时也改善了夏季降水年际变率和极端大雨日数的模拟性能。进一步分析显示,植被水力方案的改进显著减小了土壤湿度在长江流域偏干、青藏高原偏湿的模式模拟偏差,降低了我国中东部以及青藏高原地表感热通量和潜热通量的模拟偏差,改善了模式对陆气相互作用过程的模拟能力。陆气相互作用的改进显著提升了模式对东亚季风环流的模拟,改进后的模式模拟的西北太平洋海平面气压的负偏差显著降低,有利于西南季风以及西北太平洋向我国东部的水汽输送,同时在对流层低层出现反气旋异常响应,有效改善了中国东部南风偏弱及水汽辐合偏弱的模拟偏差,使得我国东部降水负偏差显著减小。以上结果表明,包括植被水力过程的陆气相互作用的合理表述是改善东亚夏季降水模拟的重要途径之一。展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
文摘基于中国科学院自主研发的第二代地球系统模式CAS-ESM2.0,本研究通过在陆面分量模式CoLM(Common Land Model)中引入植被水力模型以替换原有的经验性方案,开展了两组34年(1981~2014年)的AMIP(Atmospheric Model Intercomparison Project)数值模拟试验,探讨了植被水力方案的引入对中国夏季降水模拟的影响。结果表明,植被水力方案的引入能够显著降低CAS-ESM2.0模式对中国夏季降水气候态的模拟偏差,特别是显著改进了中国东部、青藏高原降水的低估,青藏高原以东的川西地区降水高估的偏差,同时也改善了夏季降水年际变率和极端大雨日数的模拟性能。进一步分析显示,植被水力方案的改进显著减小了土壤湿度在长江流域偏干、青藏高原偏湿的模式模拟偏差,降低了我国中东部以及青藏高原地表感热通量和潜热通量的模拟偏差,改善了模式对陆气相互作用过程的模拟能力。陆气相互作用的改进显著提升了模式对东亚季风环流的模拟,改进后的模式模拟的西北太平洋海平面气压的负偏差显著降低,有利于西南季风以及西北太平洋向我国东部的水汽输送,同时在对流层低层出现反气旋异常响应,有效改善了中国东部南风偏弱及水汽辐合偏弱的模拟偏差,使得我国东部降水负偏差显著减小。以上结果表明,包括植被水力过程的陆气相互作用的合理表述是改善东亚夏季降水模拟的重要途径之一。
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
