The most significant part of the Wade Area Augmentation System (WAAS) integrity data consists of the User Differential Range Error (UDRE) and the Grid Ionospheric Vertical Error (GIVE). WAAS solutions are not completely appropriate to determine the GIVE term within the entire wade area coverage zone taking in account real irregular structure of the ionosphere. It leads to the larger confidence bounding terms and lower expected positioning availability in comparison to the reality under geomagnetic storm conditions and system outages. Thus a question arises: is the basic WAAS concept appropriate to provide the same efficiency of the integrity monitoring for both “global differential correction (i.e. clock, ephemeris etc)” and “local differential correction (i.e. ionoshrere, troposhpere and multipath)”? The aim of this paper is to compare official WAAS integrity monitoring reports and real positioning quality in US coverage zone (CONUS) and Canada area under geomagnetic storm conditions and system outages. In this research we are interested in comparison between real GPS positioning quality based on one-frequency C/A ranging mode and HAL (VAL) values which correspond to the LP, LPV and LPV200 requirements. Significant mismatch of the information between WAAS integrity data and real positioning quality was unfolded as a result of this comparison under geomagnetic storms and system outages on February, 2011 and June 22, 2015. Based on this result we think that in order to achieve high confidence of WAAS positioning availability alerts real ionospheric measurements within the wide area coverage zone must be involved instead of the WAAS GIVE values. The better way to realize this idea is to combine WAAS solutions to derive “global differential corrections” and LAAS solutions to derive “local differential corrections”.

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A jammed state is a common phenomenon in complex granular systems, in which the relationship between the mechanical properties and the geometric structures is very complicated. The critical jammed state in a two-dimensional particle system is studied by numerical simulation. The system is composed of 2050 particles with two different radii, whose distribution is random. Initially the particles with a smaller radius are of a looser distribution in the given space. When the radius increases, a transition from the looser state to the jammed state happens. The particle dimension-radius ratio and the percentage of large particles kB play primary roles in this system, which are discussed in detail based on the statistical analysis of the average contact number, packing fraction, and contact type. By analyzing the relationship between pressure and packing fraction of the granular system, the critical jammed point for the applied pressure to the boundary can be found. Numerical simulation result shows that no obvious connection exists between the average contact number and the percentage of large particles for the case that the particle dimension-radius ratio is less than 1.4. The average contact number approximate to 4 when = 1.4, which is consistent with previous conclusions. The average contact number first decreases and then increases when the percentage of large particles become larger in the case 1.4. A minimum value C = 0.84 is obtained when kB = 0.5. When the percentage of large particles increases, the critical packing fraction decreases first and then increases in the case 1.8, but it almost keeps constant for 1.8. When the percentage of large particles is close to either 0% or 100%, the granular system is approximately mono-disperse. In this case, the average contact number and packing fraction become constant. When the percentage is close to 50%, the critical average contact number decreases all the time with larger particles-radius ratio, while the critical packing fraction decreases first and then increases. The percentage of large-small contact type is also discussed. The value varies following a quadratic function with the increase of the percentage of large particles, while the particles-radius ratio has slight impact on this variation. Specifically, we have calculated the percentage of large-small contact type based on probabilistic method, and the result agrees well with the simulation results. We give the reason why previous researchers studied the case of = 1.4 :1 and kB = 0.5 on the basis of results in this paper, and find that the values of and kB have no influence on the power-law relation around the critical jammed state.