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The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC), consisting of six Low Earth Orbit (LEO) Global Position System (GPS) receivers, on board the Formosat Satellite 3 (FORMOSAT-3) is providing dense observations of density, refractivity, temperature and water vapor profiles of the neutral atmosphere since middle of July 2006. Special radiosonde (Väisälä) campaign was conducted at Gadanki (13.48°N, 79.18°E), a tropical site in India, during July 2006 to March 2007 to validate these meteorological parameters. Co-located Nd: YAG Rayleigh lidar was also operated during the overpass of COSMIC and is utilized to validate the temperatures in the height range of 30 to 40 km. Atotal of 142 overpasses occurred during the above mentioned period within 300 km distance from Gadanki out of which 41 overpasses occurred within a time difference of ±4 hours of radiosonde launch. In addition, 18 overpasses occurred within the time difference of ±4 hours of lidar operation. A detailed comparison has been made with all these overpasses for the refractivity, temperature and water vapor obtained from COSMIC. The water vapor comparison has shown generally a good agreement with a mean difference of 5 - 10% below 6 - 7 km. Although there is a colder bias between COSMIC and radiosonde, a very good comparison in temperature is also found between 10 and 27 km with a mean difference of less than 1 K (RMS difference is only 0.64 K). There exists a large difference in temperature of about 8 K between 30 and 40 km (between COSMIC and lidar). Possible reasons for these large differences are given. There was one event that occurred just over Gadanki for which a detailed comparison has been made with special emphasis on water vapor retrievals. Sensitivity test is also done on the fractional difference in N for the event that occurred on 24 July 2006 between COSMIC (1D-var) and radiosonde and found that pressure plays a key role than temperature in determining the refractivity.

Accurate, consistent, and stable observations from different satellite missions are crucial for climate change detection. In this study, we use Global Positioning System (GPS) Radio Occultation (RO) data from the early phase of the FORMOSAT-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) mission, which was successfully launched on 15 April 2006, to inter-calibrate Temperature in the Lower Stratosphere (TLS) taken from Advanced Microwave Sounding Unit (AMSU) microwave measurements from different satellites for potential improvements of stratospheric temperature trend analysis. Because of the limited number of COSMIC soundings in the early phase of the mission, these results are considered preliminary. In this study, we use COSMIC RO data to simulate microwave brightness temperatures for comparison with AMSU Ch9 measurements (e.g., TLS) on board NOAA15, 16, and 18. Excellent correlation was found between synthetic COSMIC brightness temperatures (Tbs) and Tbs from NOAA15, NOAA16, and NOAA18, respectively. However, systematic differences on the order of 0.7 to 2 K were found between COSMIC and AMSU observations over Antarctica. Our results demonstrate that synthetic COSMIC Tbs are very useful in identifying inter-satellite offsets among AMSU measurements from different satellites. To demonstrate the long-term stability of GPS RO data, we compare COSMIC dry temperature profiles to those from collocated CHAMP profiles, where CHAMP was launched in 2001. The fact that the CHAMPand COSMIC dry temperature difference between 500 and 10 hPa ranges from -0.35 K (at 10 hPa) to 0.25 K (at 30 hPa) and their mean difference is about -0.034 K demonstrates the long-term stability of GPS RO signals. In order to demonstrate the potential usage of the GPS RO calibrated AMSU Tbs to inter-calibrate other overlapping AMSU Tbs, we examine the uncertainty of the calibration coefficients derived from AMSU-GPS RO pairs. We found the difference between COSMIC calibrated AMSU Tbs and those from CHAMP to be in the range of __0.07 K with a 0.1 K standard deviation. This demonstrates the robustness of the calibration coefficients found from AMSU-GPS RO pairs and shows the potential to use the calibrated AMSU Tbs to calibrate other overlapping AMSU Tbs where no coincident GPS RO data are available.