On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the di...On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the direction of the unknown point. The requirement must be fulfilled: the distance from each point to an unknown point must be equal to the sum of the length of the segment outgoing from this point, and some increment, the same for all three segments. In the article, the conditions for the solvability of a geometric problem are established by the methods of spherical trigonometry and vector algebra. It is proved that when they are fulfilled, the problem is always solvable. The number of solutions is two, except in rare cases where there is only one solution. A solution method is presented. One of the practical applications is the problem of determining the time and location of a cloud-to-ground lightning discharge, which is directly reduced to this problem.展开更多
By using the cloud-to-ground(CG)lightning location data from the lightning detection network of He-nan Province,surface Doppler radar data and standard orbit data of PR,TMI and LIS on TRMM satellite,the spatial and te...By using the cloud-to-ground(CG)lightning location data from the lightning detection network of He-nan Province,surface Doppler radar data and standard orbit data of PR,TMI and LIS on TRMM satellite,the spatial and temporal characteristics of CG lightning flashes in 10 severe hailstorms are analyzed.The results show that the percentage of+CG lightning in these hailstorms is high with an average value of 45.5%.There is a distinct increase in CG flash rate during the rapid development stage of hailstorms.The hailstone falling corresponds to an active positive flash period,and the increase of+CG flash rate is generally accompanied with a decrease of–CG flash rate.The flash rate declines rapidly during the dissipating stage of hailstorms.The precipitation structure and lightning activity in two typical hail-storms are studied in detail.It is found that strong convective cells with reflectivity greater than 30dBZ mainly are situated in the front region of hailstorms,whereas the trailing stratiform region is in the rear part of the hailstorms.The maximum heights of echo top are higher than 14 km.Convective rain con-tributes much more rainfall to the total than stratiform rain,and the convective rain takes about 85%and 97%of the total in the two cases,respectively.Total lightning in the hailstorms is very active with the flash rate up to 183 fl/min and 55 fl/min,respectively.The results also indicate that most lightning flashes occurred in the echo region greater than 30 dBZ and its immediate periphery.The probability of lightning occurrence is 20 times higher in the convective region than in the stratiform region.The result suggests that the lightning information is helpful to the identification of convective rain region.The linear relationship between flash rate and ice water content is disclosed primarily.展开更多
文摘On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the direction of the unknown point. The requirement must be fulfilled: the distance from each point to an unknown point must be equal to the sum of the length of the segment outgoing from this point, and some increment, the same for all three segments. In the article, the conditions for the solvability of a geometric problem are established by the methods of spherical trigonometry and vector algebra. It is proved that when they are fulfilled, the problem is always solvable. The number of solutions is two, except in rare cases where there is only one solution. A solution method is presented. One of the practical applications is the problem of determining the time and location of a cloud-to-ground lightning discharge, which is directly reduced to this problem.
基金Supported by the National Natural Science Foundation of China(Grant Nos.40325013,40505001 and 40135010)
文摘By using the cloud-to-ground(CG)lightning location data from the lightning detection network of He-nan Province,surface Doppler radar data and standard orbit data of PR,TMI and LIS on TRMM satellite,the spatial and temporal characteristics of CG lightning flashes in 10 severe hailstorms are analyzed.The results show that the percentage of+CG lightning in these hailstorms is high with an average value of 45.5%.There is a distinct increase in CG flash rate during the rapid development stage of hailstorms.The hailstone falling corresponds to an active positive flash period,and the increase of+CG flash rate is generally accompanied with a decrease of–CG flash rate.The flash rate declines rapidly during the dissipating stage of hailstorms.The precipitation structure and lightning activity in two typical hail-storms are studied in detail.It is found that strong convective cells with reflectivity greater than 30dBZ mainly are situated in the front region of hailstorms,whereas the trailing stratiform region is in the rear part of the hailstorms.The maximum heights of echo top are higher than 14 km.Convective rain con-tributes much more rainfall to the total than stratiform rain,and the convective rain takes about 85%and 97%of the total in the two cases,respectively.Total lightning in the hailstorms is very active with the flash rate up to 183 fl/min and 55 fl/min,respectively.The results also indicate that most lightning flashes occurred in the echo region greater than 30 dBZ and its immediate periphery.The probability of lightning occurrence is 20 times higher in the convective region than in the stratiform region.The result suggests that the lightning information is helpful to the identification of convective rain region.The linear relationship between flash rate and ice water content is disclosed primarily.
