Atmospheric black carbon (BC) warms Earth's climate, and its reduction has been targeted for near-term climate change mitigation. Models that include forcing by BC assume internal mixing with non-BC aerosol components that enhance BC absorption, often by a factor of similar to 2; such model estimates have yet to be clearly validated through atmospheric observations. Here, direct in situ measurements of BC absorption enhancements (E-abs) and mixing state are reported for two California regions. The observed E-abs is small-6% on average at 532 nm-and increases weakly with photochemical aging. The E-abs is less than predicted from observationally constrained theoretical calculations, suggesting that many climate models may overestimate warming by BC. These ambient observations stand in contrast to laboratory measurements that show substantial E-abs for BC are possible.
The Arctic is undergoing rapid environmental change, manifested most dramatically by reductions in sea ice extent and thickness. The changes are attributed to anthropogenic effects related to greenhouse warming, with secondary contributions from changing ocean and wind currents as well as from pollutants, especially “absorbing” black carbon. The warmer Arctic air temperatures and new patterns of wind and ocean circulation have also contributed to a younger ice cover [Maslanik et al., 2011]. Specific factors that determine the temporal distribution of sea ice are poorly understood because few observations of key variables have been made in the central Arctic. For example, the planetary boundary layer (PBL), the lowest part of the atmosphere governed by interaction with Earth's surface, plays a critical role involving the exchange of momentum, heat, water vapor, trace gases, and aerosol particles. Satellites can provide limited observations of sea ice properties, but so far, accurate measurements of ice thickness or boundary layer properties have not been easily obtained. Although satellite retrievals of geophysical variables might be an essential source of information, their reliability remains questionable owing to inadequate spatial and/or temporal resolution and to a need for further validation.
To set up the general framework for relativistic explicitly correlated wave function methods, the electron-electron coalescence conditions are derived for the wave functions of the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), Dirac-Coulomb-Breit (DCB), modified Dirac-Coulomb (MDC), and zeroth-order regularly approximated (ZORA) Hamiltonians. The manipulations make full use of the internal symmetries of the reduced two-electron Hamiltonians such that the asymptotic behaviors of the wave functions emerge naturally. The results show that, at the coalescence point of two electrons, the wave functions of the DCG Hamiltonian are regular, while those of the DC and DCB Hamiltonians have weak singularities of the type $r_{12}^{\nu}$ with $\nu$ being negative and of $\mathcal{O}(\alpha^2)$. The behaviors of the MDC wave functions are related to the original ones in a simple manner, while the spin-free counterparts are somewhat different due to the complicated electron-electron interaction. The behaviors of the ZORA wave functions depend on the chosen potential in the kinetic energy operator. In the case of the nuclear attraction, the behaviors of the ZORA wave functions are very similar to those of the nonrelativistic ones, just with an additional correction of $\mathcal{O}(\alpha^2)$ to the nonrelativistic cusp condition. However, if the Coulomb interaction is also included, the ZORA wave functions become close to the large-large components of the DC wave functions. Note that such asymptotic expansions of the relativistic wave functions are only valid within an extremely small convergence radius $R_c$ of $\mathcal{O}(\alpha^2)$. Beyond this radius, the behaviors of the relativistic wave functions are still dominated by the nonrelativistic limit, as can be seen in terms of direct perturbation theory (DPT) of relativity. However, as the two limits $\alpha\rightarrow0$ and $r_{12}\rightarrow0$ do not commute, DPT is doomed to fail due to incorrect descriptions of the small-small component $\Psi^{SS}$ of the DC wave function for $r_{12}<R_c$. Another deduction from the possible divergence of $\Psi^{SS}$ at $r_{12}=R_c$ is that the DC Hamiltonian has no bound electronic states, although the last word cannot be said. These findings enrich our understandings of relativistic wave functions. On the practical side, it is shown that, under the no-pair approximation, relativistic explicitly correlated wave function methods can be made completely parallel to the nonrelativistic counterparts, as demonstrated explicitly for MP2-F12. Yet, this can only be achieved by using an extended no-pair projector.