The weather research and forecasting（WRF） model is a new generation mesoscale numerical model with a fine grid resolution（2 km）, making it ideal to simulate the macro-and micro-physical processes and latent heatin...The weather research and forecasting（WRF） model is a new generation mesoscale numerical model with a fine grid resolution（2 km）, making it ideal to simulate the macro-and micro-physical processes and latent heating within Typhoon Molave（2009）. Simulations based on a single-moment, six-class microphysical scheme are shown to be reasonable, following verification of results for the typhoon track, wind intensity, precipitation pattern, as well as inner-core thermodynamic and dynamic structures. After calculating latent heating rate, it is concluded that the total latent heat is mainly derived from condensation below the zero degree isotherm, and from deposition above this isotherm. It is revealed that cloud microphysical processes related to graupel are the most important contributors to the total latent heat. Other important latent heat contributors in the simulated Typhoon Molave are condensation of cloud water, deposition of cloud ice, deposition of snow, initiation of cloud ice crystals, deposition of graupel, accretion of cloud water by graupel, evaporation of cloud water and rainwater,sublimation of snow, sublimation of graupel, melting of graupel, and sublimation of cloud ice. In essence, the simulated latent heat profile is similar to ones recorded by the Tropical Rainfall Measuring Mission, although specific values differ slightly.展开更多
LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives...LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.展开更多
基金The National Key Basic Research Program of China under contract No.2014CB953904the Natural Science Foundation of Guangdong Province under contract No.2015A030311026the National Natural Science Foundation of China under contract Nos 41275145 and 41275060
文摘The weather research and forecasting（WRF） model is a new generation mesoscale numerical model with a fine grid resolution（2 km）, making it ideal to simulate the macro-and micro-physical processes and latent heating within Typhoon Molave（2009）. Simulations based on a single-moment, six-class microphysical scheme are shown to be reasonable, following verification of results for the typhoon track, wind intensity, precipitation pattern, as well as inner-core thermodynamic and dynamic structures. After calculating latent heating rate, it is concluded that the total latent heat is mainly derived from condensation below the zero degree isotherm, and from deposition above this isotherm. It is revealed that cloud microphysical processes related to graupel are the most important contributors to the total latent heat. Other important latent heat contributors in the simulated Typhoon Molave are condensation of cloud water, deposition of cloud ice, deposition of snow, initiation of cloud ice crystals, deposition of graupel, accretion of cloud water by graupel, evaporation of cloud water and rainwater,sublimation of snow, sublimation of graupel, melting of graupel, and sublimation of cloud ice. In essence, the simulated latent heat profile is similar to ones recorded by the Tropical Rainfall Measuring Mission, although specific values differ slightly.
文摘LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.
