Dimensions of logarithmic quantities

Comment on the article by Philip Molyneux on "The Dimensions of Logarithmic Quantities" [J. Chem. Educ. 1991, 68, 467-4691].

The choice of names and symbols for quantities in chemistry

The importance of maintaining a clear distinction between the names and symbols for quantities and the names and symbols for units.

A unified titration formula

In a number of standard titrations, a volume of a monoprotic base MOH at a specific concentration is added to a volume of a monoprotic acid HA at a specific concentrations. Four different types of titration are possible, depending on whether the acid and base are strong or weak. A single unifying formula covering all four cases has been determined.

Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation

A cloud-resolving model is modified to implement the weak temperature gradient approximation in order to simulate the interactions between tropical convection and the large-scale tropical circulation. The instantaneous domain-mean potential temperature is relaxed toward a reference profile obtained from a radiative–convective equilibrium simulation of the cloud-resolving model. For homogeneous surface conditions, the model state at equilibrium is a large-scale circulation with its descending branch in the simulated column. This is similar to the equilibrium state found in some other studies, but not all. For this model, the development of such a circulation is insensitive to the relaxation profile and the initial conditions. Two columns of the cloud-resolving model are fully coupled by relaxing the instantaneous domain-mean potential temperature in both columns toward each other. This configuration is energetically closed in contrast to the reference-column configuration. No mean large-scale circulation develops over homogeneous surface conditions, regardless of the relative area of the two columns. The sensitivity to nonuniform surface conditions is similar to that obtained in the reference-column configuration if the two simulated columns have very different areas, but it is markedly weaker for columns of comparable area. The weaker sensitivity can be understood as being a consequence of a formulation for which the energy budget is closed. The reference-column configuration has been used to study the convection in a local region under the influence of a large-scale circulation. The extension to a two-column configuration is proposed as a methodology for studying the influence on local convection of changes in remote convection.

An earth-system prediction initiative for the twenty-first century

The necessity and benefits for establishing the international Earth-system Prediction Initiative (EPI) are discussed by scientists associated with the World Meteorological Organization (WMO) World Weather Research Programme (WWRP), World Climate Research Programme (WCRP), International Geosphere–Biosphere Programme (IGBP), Global Climate Observing System (GCOS), and natural-hazards and socioeconomic communities. The proposed initiative will provide research and services to accelerate advances in weather, climate, and Earth system prediction and the use of this information by global societies. It will build upon the WMO, the Group on Earth Observations (GEO), the Global Earth Observation System of Systems (GEOSS) and the International Council for Science (ICSU) to coordinate the effort across the weather, climate, Earth system, natural-hazards, and socioeconomic disciplines. It will require (i) advanced high-performance computing facilities, supporting a worldwide network of research and operational modeling centers, and early warning systems; (ii) science, technology, and education projects to enhance knowledge, awareness, and utilization of weather, climate, environmental, and socioeconomic information; (iii) investments in maintaining existing and developing new observational capabilities; and (iv) infrastructure to transition achievements into operational products and services.

Connections between concepts revealed by the electronic structure of carbon monoxide

Different models for the electronic structure of carbon monoxide are suggested in influential textbooks. Therefore, this electronic structure offers an interesting subject in teaching because it can be used as an example to relate seemingly conflicting concepts. Understanding the connections between ostensibly different methods and between different concepts, related or conflicting, is important in academic studies. The related reactivities of CO, O2, and N-2 and the notations of molecular orbitals are topics of interest and are discussed in detail.