Compatible finite element methods for numerical weather prediction

This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often referred to as compatible finite elements, mimetic finite elements, discrete differential forms or finite element exterior calculus. We provide an elementary introduction in the case of the one-dimensional wave equation, before summarising recent results in applications to the rotating shallow water equations on the sphere, before taking an outlook towards applications in three-dimensional compressible dynamical cores.Comment: To appear in ECMWF Seminar proceedings 201

Illustrations of reporting accounting changes: a survey of reporting under APB opinion no. 20; Financial report survey, 02

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Multiple Tunnels in Soil with Shotcrete Linings on Tren Urbano, San Juan, Puerto Rico

Tunnelling was part of the new Tren Urbano transit system in San Juan, Puerto Rico. Four tunnels in soil were designed and constructed with shotcrete linings using the sequential excavation method (SEM), which uses some aspects of the New Austrian Tunneling Method (NATM). Four 6-m-diameter tunnels of about 100 m in length were required to preserve two historic structures located above the subway alignment. Two of the four tunnels were constructed as part of a turnout to a future line. Cover over the SEM tunnels ranges from 20 to 5 m. Some of the tunnels are located less than 1 m from each other in the turnout section. Detailed analysis of the staged construction was undertaken to design shotcrete lining thickness, shotcrete strength, and reinforcing with welded wire fabric and lattice girders. Several variations in lining section were required, which depended on sequence of tunnel excavation and depth of cover. Further refinement of the lining design was possible by considering the initial lining as permanent since it had been constructed with final structure quality requirements. Compensation grouting effectively mitigated ground movements and building settlement was limited. Tunnel lining convergence measurements revealed the lining displacements due to excavation of adjacent or overlying tunnel construction to be within acceptable limits. Design and construction of the tunnels as sequentially excavated with shotcrete support (SEM) was unprecedented in Puerto Rico and not in widespread practice in the continental United States. Further, this was the first major United States underground transit construction project with design-build project delivery