Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional pa...Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.展开更多
The climate warming is mainly due to the increase in concentrations of anthropogenic greenhouse gases, of which CO_2 is the most important one responsible for radiative forcing of the climate. In order to reduce the g...The climate warming is mainly due to the increase in concentrations of anthropogenic greenhouse gases, of which CO_2 is the most important one responsible for radiative forcing of the climate. In order to reduce the great estimation uncertainty of atmospheric CO_2 concentrations, several CO_2-related satellites have been successfully launched and many future greenhouse gas monitoring missions are planned. In this paper, we review the development of CO_2 retrieval algorithms, spatial interpolation methods and ground observations. The main findings include: 1) current CO_2 retrieval algorithms only partially account for atmospheric scattering effects; 2) the accurate estimation of the vertical profile of greenhouse gas concentrations is a long-term challenge for remote sensing techniques; 3) ground-based observations are too sparse to accurately infer CO_2 concentrations on regional scales; and 4) accuracy is the primary challenge of satellite estimation of CO_2 concentrations. These findings, taken as a whole, point to the need to develop a high accuracy method for simulation of carbon sources and sinks on the basis of the fundamental theorem of Earth's surface modelling, which is able to efficiently fuse space- and ground-based measurements on the one hand and work with atmospheric transport models on the other hand.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11071278,111471004the Fundamental Research Funds for the Central Universities of GK201302026 and GK201102007
文摘Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
基金supported by the National Natural Science Foundation of China (Grant Nos. 91325204, 41421001)the National High-tech R&D Program (Grant No. 2013AA122003)the National Key Technologies R&D Program (Grant No. 2013BACO3B05)
文摘The climate warming is mainly due to the increase in concentrations of anthropogenic greenhouse gases, of which CO_2 is the most important one responsible for radiative forcing of the climate. In order to reduce the great estimation uncertainty of atmospheric CO_2 concentrations, several CO_2-related satellites have been successfully launched and many future greenhouse gas monitoring missions are planned. In this paper, we review the development of CO_2 retrieval algorithms, spatial interpolation methods and ground observations. The main findings include: 1) current CO_2 retrieval algorithms only partially account for atmospheric scattering effects; 2) the accurate estimation of the vertical profile of greenhouse gas concentrations is a long-term challenge for remote sensing techniques; 3) ground-based observations are too sparse to accurately infer CO_2 concentrations on regional scales; and 4) accuracy is the primary challenge of satellite estimation of CO_2 concentrations. These findings, taken as a whole, point to the need to develop a high accuracy method for simulation of carbon sources and sinks on the basis of the fundamental theorem of Earth's surface modelling, which is able to efficiently fuse space- and ground-based measurements on the one hand and work with atmospheric transport models on the other hand.
