Multiple Parameter Regularization: Numerical Solutions and Applications to the Determination of Geopotential from Precise Satellite Orbits

Kaula’s rule of thumb has been used in producing geopotential models from space geodetic measurements, including the most recent models from satellite gravity missions CHAMP. Although Xu and Rummel (Manuscr Geod 20 8–20, 1994b) suggested an alternative regularization method by introducing a number of regularization parameters, no numerical tests have ever been conducted. We have compared four methods of regularization for the determination of geopotential from precise orbits of COSMIC satellites through simulations, which include Kaula’s rule of thumb, one parameter regularization and its iterative version, and multiple parameter regularization. The simulation results show that the four methods can indeed produce good gravitational models from the precise orbits of centimetre level. The three regularization methods perform much better than Kaula’s rule of thumb by a factor of 6.4 on average beyond spherical harmonic degree 5 and by a factor of 10.2 for the spherical harmonic degrees from 8 to 14 in terms of degree variations of root mean squared errors. The maximum componentwise improvement in the root mean squared error can be up to a factor of 60. The simplest version of regularization by multiplying a positive scalar with a unit matrix is sufficient to better determine the geopotential model. Although multiple parameter regularization is theoretically attractive and can indeed eliminate unnecessary regularization for some of the harmonic coefficients, we found that it only improved its one parameter version marginally in this COSMIC example in terms of the mean squared error.     

Scattering of Rayleigh waves by a shallow circular alluvial valley： High-frequency solution

Introduction The effect of local site conditions on wave propagation is one of the most attractive topics in engineering seismology. It may be resolved by either a numerical method or an analytical method. Numerical methods include the finite difference, finite element, boundary element method, etc. The analytical method is the wave function expansion method. The advantage of these numerical methods is that they can be applied to local inhomogeneity of arbitrary shapes, but analytical method …     

Characteristics of coda wave attenuation in Yunnan area

The characteristic of seismic coda wave attenuation in Yunnan area in 7 frequency-bands range from 1 Hz to 20 Hz was estimated by using the local earthquake's waveform data recorded from 22 Yunnan digital seismic stations.Coda attenuation Q-c1 of each station was firstly calculated by single scattering method. Then, mean free path Le and seismic albedo Bo of each station were calculated, and scattering attenuation Q-1s and intrinsic attenuation Q-1i were separated from total attenuation Q-1t by multiple lapse time window analysis based on the multiple scattering model in uniform random isotropic scattering medium. The attenuating characteristics in Yunnan show that most value of Le are in 10～30 km, with maximal within 2～6 Hz;Bo are about 0.5 at 1～2 Hz, but less than 0.5at other frequency-bands, which means Q-1i is comparable with Q-1s at 1～2 Hz, and after 1～2 Hz, Q-1i is greater than Q-1s and dominates the attenuation process. Q-1c is close to Q-1i at other frequency bands except 1～2 Hz.Results show that Q-1 especially Qs-1 varies spatially, Q-1 in eastern Yunnan zone is a bit higher than in northwestern Yunnan zone;northwestern Yunnan zone higher than southwestern Yunnan zone. Comparing with other results in global, Qs-1 in Yunnan is lower than the global average value among these results, Q-1i is higher than the global average value, and Q-1t lies the middle among these results.     

Surface motion of a semi-cylindrical hill for incident plane SV waves： Analytical solution

Introduction Scattering of incident waves by local topographies is one of the most attractive topics in the field of engineering seismology. They can be resolved by either a numerical method or an analyti-cal method. The numerical methods include finite difference method, finite element method, boundary element method, etc. The analytical method is the wave function expansion method. Al-though numerical methods can be used for arbitrary-shaped topographies, the analytical solutions are still …     

Correlation of atmospheric visibility with chemical composition of Kaohsiung aerosols

The objective of this study was to investigate the correlation of visibility with chemical composition of Kaohsiung aerosols. Daytime visibility was observed around noon at two observation sites in metropolitan Kaohsiung, Taiwan in the years of 1999 and 2000. Both seasonal and diurnal variation patterns of visibility were observed in the region. Ambient aerosols were sampled and analyzed for 11 constituents, including water-soluble ionic species (Cl⁻, NO₃⁻, SO₄⁻², NH₄⁺, K⁺, Na⁺, Ca⁺², and Mg⁺²) and carbonaceous contents (OC, EC, and TC), to characterize the chemical composition of Kaohsiung aerosols. Furthermore, a stepwise multiple linear regression model was developed to elucidate the influence of aerosol species on visibility impairments. The results showed that sulfate was the dominant species that affected both light scattering coefficient and visibility. On average, the percentage contributions of visibility degrading species to light scattering coefficient were 29% for sulfate, 28% for nitrate, 22% for total carbon, and 21% for PM_2.5-remainder. An empirical regression model of visibility based on sulfate, nitrate, and relative humidity was also developed. The model showed that sulfate in PM_2.5 was the most sensitive species to visibility variation, suggesting that the reduction of sulfate in PM_2.5 could effectively improve the visibility of metropolitan Kaohsiung. During the investigation period, an event of Asian dusts intruded metropolitan Kaohsiung and dramatically increased the aerosol loadings, especially in the coarse particles. However, local visual air quality did not degrade accordingly during the Asian dust event because both visibility and light scattering coefficient are affected mainly by the fine particles. The results are discussed in detail in the paper.     

Multiple exposures and dynamic vulnerability: Evidence from the grape industry in the Okanagan Valley, Canada

This paper assesses the vulnerability of grape growers and winery operators in the Okanagan Valley, British Columbia to climate variability and change, in the context of other sources of risk. Through interviews and focus groups, producers identified the climatic and non-climatic risks relevant to them and the strategies employed to manage these risks. The results show that the presence of multiple exposures affects the way in which producers are vulnerable to climate change. Producers are vulnerable to conditions that not only affect crop yield, but also affect their ability to compete in or sell to the market. Their sensitivity to these conditions is influenced in part by institutional factors such as trade liberalization and a “markup-free delivery” policy. Producers’ ability to adapt or cope with these risks varies depending on such factors as the availability of resources and technology, and access to government programmes. Producers will likely face challenges associated with the supply of water for irrigation due to a combination of climatic changes and changing demographics in the Okanagan Valley, which in turn affect their ability to adapt to climatic conditions. Finally, adaptations made by producers can change the nature of the operation and its vulnerability, demonstrating the dynamic nature of vulnerability.     

半球形沉积谷场地对入射平面Rayleigh波的三维散射解析解

把半球形沉积谷和周围半空间场地分别用具有不同弹性模量和不同半径的球坐标描述。利用Fourier-Bessel级数展开法,在频域内给出了半空间中半球形沉积谷场地在平面Rayleigh波入射下三维散射问题的解析解。利用这一解析解计算分析了入射波频率、场地软硬对场地内地表位移幅值的影响。     

起伏地表条件下的声波散射数值模拟的积分方程法

从散射理论的角度来看,起伏地表可以看作是一种特殊的扰动介质,因此应用散射积分方程求解起伏地表条件下的散射场在理论上是可行的。从三维频率域声波方程出发,由格林函数定理,得出起伏地表条件下的散射积分方程。散射积分方程为关于起伏地表的面积分和与速度扰动体有关的体积分之和,同时给出了格林函数在奇异点的积分方法。由于数值离散求解积分方程存在着计算时间太长和存储内存不足的问题,采用电磁散射积分方程的拟解析近似的方法。在假设反射函数为缓变函数的基础上,最终得到其近似表达式,因此散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。这种方法避开了传统数值计算方法存在的问题,为地震散射波场快速正演模拟打下了基础。理论分析表明,这种方法适用于小扰动的问题。当扰动较大时,拟解析近似会产生较大的误差。     

On the solar cycle dependence of winds and planetary waves as seen from mid-latitude D1 LF mesopause region wind measurements

At the Collm Observatory of the University of Leipzig LF D1 low-frequency total reflection nighttime wind measurements have been carried out continuously for more than two decades. Using a multiple regression analysis to derive prevailing winds, tides and the quasi-2-day wave from the half-hourly mean values of the horizontal wind components, monthly mean values of mesopause wind parameters are obtained that can be analysed with respect to long-term trends and influences of solar variability. The response of the prevailing wind to the 11-year solar cycle differs throughout the year. While in winter no significant correlation between the zonal prevailing wind and solar activity is found, in spring and summer a negative correlation between the TWC can be seen from the measurements. This is connected with stronger vertical gradients of the zonal prevailing wind during solar maximum than during solar minimum. Since the amplitude of the quasi-2-day wave is dependent on the zonal mean wind vertical gradient, this is connected with a positive correlation between solar activity and quasi-two-day wave activity.Paper Presented at the Second IAGA/ICMA (IAMAS) Workshop on Solar Activity Forcing of the Middle Atmosphere, Prague, August 1997