Terms Of Root Mean Square Values Research Articles

An Improved Spatiotemporal Weighted Mean Temperature Model over Europe Based on the Nonlinear Least Squares Estimation Method

Weighted average temperature (Tm) plays a crucial role in global navigation satellite system (GNSS) precipitable water vapor (PWV) retrieval. Aiming at the poor applicability of the existing Tm models in Europe, in the article, we used observations from 48 radiosonde stations over Europe from 2014 to 2020 to establish a weighted average temperature model in Europe (ETm) by the nonlinear least squares estimation method. The ETm model takes into account factors such as ground temperature, water vapor pressure, latitude, and their annual variation, semiannual variation and diurnal variation. Taking the Tm obtained from the radiosonde data by the integration method in 2021 as the reference value, the accuracy of the ETm model was evaluated and compared with the commonly used Bevis model, ETmPoly model, and GPT2w model. The results of the 48 modeled stations showed that the mean bias and root mean square (RMS) values of the ETm model were 0.06 and 2.85 K, respectively, which were 21.7%, 11.5%, and 31.8% higher than the Bevis, ETmPoly, and GPT2w-1 (1° × 1° resolution) models, respectively. In addition, the radiosonde data of 12 non-modeling stations over Europe in 2021 were selected to participate in the model accuracy validation. The mean bias and RMS values of the ETm model were –0.07 and 2.87 K, respectively. Compared with the Bevis, ETmPoly, and GPT2w-1 models, the accuracy (in terms of RMS values) increased by 20.5%, 10.6%, and 35.2%, respectively. Finally, to further verify the superiority of the ETm model, the ETm model, and other Tm models were applied to the GNSS PWV calculation. The ETm model had mean RMSPWV and RMSPWV/PWV values of 0.17 mm and 1.03%, respectively, which were less than other Tm models. Therefore, the ETm model has essential applications in GNSS PWV over Europe.

Molecular and electronic structure and IR spectra of mononuclear dinitrosyl iron complex Fe(SC2H3N3)(SC2H2N3)(NO)2]: a theoretical study

The molecular and electronic structures of different isomers of a mononuclear dinitrosyl iron complex [Fe(SC2H3N3)(SC2H2N3)(NO)2] were calculated by the B3LYP and PBE density functional methods. Both theoretical approaches provide good agreement between the calculated and experimental geometry of the lowest-lying isomer (bond lengths differ by 0.02–0.04 A and bond angles differ by 2–3° in terms of root-mean square values). A feature of the complex is an intramolecular hydrogen bond N-H...N between the thiolate and thione ligands, which causes equalization of the Fe-S and S-C bond lengths. The ground state of the system has a spin of 1/2 and exists at antiparallel orientation of the spin (S = 3/2) of the Fe atom with formal electron configuration d7 and two local spins (S = 1/2) of the NO ligands. Although each NO group has a small negative charge, which is mainly localized on the O atom, the Fe-NO bond can be treated as similar to homeopolar one. This corresponds to the effective trivalent state of Fe with an oxidation state of 1+. Both theoretical methods correctly reproduce the experimental structure of the IR spectrum, but the PBE functional provides a better description of absolute positions of spectral lines, whereas the B3LYP functional gives a somewhat better description of the relative intensities of spectral components. In spite of similar geometric parameters of coordination of two NO groups, the splitting between the NO stretching bands is rather large (58 cm−1); this value is satisfactorily reproduced in theoretical calculations. A strong intramolecular hydrogen bond causes a large frequency shift of the N-H stretching vibrations corresponding to a broad absorption band in the region 2300–2600 cm−1.