In the photoionization of the diatomic molecule AB to yield AB++e− the photoelectron may be charatcterized by a partial wave expansion in terms of its orbital angular momentum quantum number l. For a given value of l, conservation of angular momentum implies that transitions can only occur for ΔJ=l+ (3)/(2) , l+ (1)/(2) , ... ,−l− (1)/(2) , −l− (3)/(2) , where ΔJ=J+−J is the change (half-integer) in the total angular momentum (excluding nuclear spin) of the AB+ ion rovibronic level and the AB neutral rovibronic level. Other selection rules are ΔΩ=−λ+ (3)/(2) , −λ+ (1)/(2) , ... , −λ− (3)/(2) , and ΔM=−ml+ (3)/(2) , −ml+ (1)/(2) , ... , −ml− (3)/(2) . In addition, for Hund’s case (a) and case (b) coupling, ΔS=S+−S=± (1)/(2) , ΔΣ=± (1)/(2) , and ΔΛ=−λ, −λ±1. Parity selection rules have been derived for transitions connecting levels described by one of the four coupling schemes, Hund’s case (a), case (b), case (c), and case (d). In particular, for a case (a)–case (a) transition, ΔJ−ΔS+Δp+Δs+l=odd, where the symbols have their traditional spectroscopic meanings. The parity label p=0,1 has been associated with the e, f label, from which it may be shown that (e/f )↔(e/f ) for ΔJ− (1)/(2) +l=odd and (e/f )↔( f/e) for ΔJ− (1)/(2) +l=even. It also follows that ±↔± for l odd and ±↔∓for l even. Moreover, Σ± is connected to Σ± in general, but Σ± is only connected to Σ∓ for l≥2 and λ=±1 (π wave). For homonuclear diatomics, the additional selection rules are (g/u)↔(g/u) for l=odd, (g/u)↔(u/g) for l=even, and (s/a)↔(s/a) but (s/a)↔/(a/s).

This paper introduces the Flexible Global Ocean‐Atmosphere‐Land System Model: Grid‐Point Version 3 (FGOALS‐g3) and evaluates its basic performance based on some of its participation in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) experiments. Our results show that many significant improvements have been achieved by FGOALS‐g3 in terms of climatological mean states, variabilities, and long‐term trends. For example, FGOALS‐g3 has a small (−0.015°C/100 yr) climate drift in 700‐yr preindustrial control (piControl) runs and smaller biases in climatological mean variables, such as the land/sea surface temperatures (SSTs) and seasonal soil moisture cycle, compared with its previous version FGOALS‐g2 during the historical period. The characteristics of climate variabilities, for example, Madden‐Julian oscillation (MJO) eastward/westward propagation ratios, spatial patterns of interannual variability of tropical SST anomalies, and relationship between the East Asian Summer Monsoon and El Niño–Southern Oscillation (ENSO), are well captured by FGOALS‐g3. In particular, the cooling trend of globally averaged surface temperature during 1940–1970, which is a challenge for most CMIP3 and CMIP5 models, is well reproduced by FGOALS‐g3 in historical runs. In addition to the external forcing factors recommended by CMIP6, anthropogenic groundwater forcing from 1965 to 2014 was incorporated into the FGOALS‐g3 historical runs.

Human water regulation, groundwater lateral flow, and the movement of frost and thaw fronts (FTFs) affect soil water and thermal processes, as well as energy and water exchanges between the land surface and atmosphere. Reasonable representation of these processes in land surface models is very important to improving the understanding of land‐atmosphere interactions. In this study, mathematical descriptions of groundwater lateral flow, human water regulation, and FTFs were synchronously incorporated into a high‐resolution community land model, which is then named the Land Surface Model for Chinese Academy of Sciences (CAS‐LSM). With a series of atmospheric forcings and high‐resolution land surface data from the Heihe Watershed Allied Telemetry Experimental Research (HiWATER) program, numerical simulations of the period 1981–2013 using CAS‐LSM with 1‐km resolution were conducted for an endorheic basin, the Heihe River Basin in China. Compared with observations, CAS‐LSM reproduced the distributions of groundwater, evapotranspiration, and permafrost reasonably and well matched the temporal changes in ground temperature, heat fluxes, and FTFs. Results illuminate the temporal and spatial characteristics of frozen soil and the changes in the land‐atmosphere exchange of carbon, water, and energy. The permafrost and seasonally frozen soil were distinguished. In the seasonally frozen areas, the maximum soil frost depth increased by 0.65 mm/year within natural areas and decreased by 2.12 mm/year in human‐dominated areas. The active layer thickness increased 8.63 mm/year for permafrost. In the permafrost zone evapotranspiration and latent heat flux increased, and the sensible heat flux declined. In the human‐dominated areas water use raised the latent heat flux and reduced the sensible heat flux, net ecosystem exchange, and streamflow recharging to the eco‐fragile region in the lower reaches. Results suggested that the land surface model CAS‐LSM is a potential tool for studying land surface processes, especially in cold and arid regions experiencing human interventions.