Evaluation of Landsat-8 and Sentinel-2A Aerosol Optical Depth Retrievals Across Chinese Cities and Implications for Medium Spatial Resolution Urban Aerosol Monitoring

In urban environments, aerosol distributions may change rapidly due to building and transport infrastructure and human population density variations. The recent availability of medium resolution Landsat-8 and Sentinel-2 satellite data provide the opportunity for aerosol optical depth (AOD) estimation at higher spatial resolution than provided by other satellites. AOD retrieved from 30 m Landsat-8 and 10 m Sentinel-2A data using the Land Surface Reflectance Code (LaSRC) were compared with coincident ground-based Aerosol Robotic Network (AERONET) Version 3 AOD data for 20 Chinese cities in 2016. Stringent selection criteria were used to select contemporaneous data; only satellite and AERONET data acquired within 10 min were considered. The average satellite retrieved AOD over a 1470 m1470 m window centered on each AERONET site was derived to capture fine scale urban AOD variations. AERONET Level 1.5 (cloud-screened) and Level 2.0 (cloud-screened and also quality assured) data were considered. For the 20 urban AERONET sites in 2016 there were 106 (Level 1.5) and 67 (Level 2.0) Landsat-8 AERONET AOD contemporaneous data pairs, and 118 (Level 1.5) and 89 (Level 2.0) Sentinel-2A AOD data pairs. The greatest AOD values (>1.5) occurred in Beijing, suggesting that the Chinese capital was one of the most polluted cities in China in 2016. The LaSRC Landsat-8 and Sentinel-2A AOD retrievals agreed well with the AERONET AOD data (linear regression slopes > 0.96; coefficient of determination r(exp 2) > 0.90; root mean square deviation < 0.175) and demonstrate that the LaSRC is an effective and applicable medium resolution AOD retrieval algorithm over urban environments. The Sentinel-2A AOD retrievals had better accuracy than the Landsat-8 AOD retrievals, which is consistent with previously published research.The implications of the research and the potential for urban aerosol monitoring by combining the freely available Landsat-8 and Sentinel-2 satellite data are discussed

Continuations of Hermitian indefinite functions and corresponding canonical systems : an example

M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators. In this note we study such a connection for the function f(t) = 1 − |t|, t - R, which is not positive definite on R: its restrictions fa := f|(−2a,2a) are positive definite if a ≤ 1 and have one negative square if a > 1. We show that with f a canonical differential equation or a Sturm-Liouville equation can be associated which have a singularity

Quantum R2R^2 Gravity in Two Dimensions

Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32\pi$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.Comment: 12 pages, latex KEK-TH-355, KEK preprint 92-212, UT-63

Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model

We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors.Comment: 53 pages, 11 figures (26 eps files

Variable coordination of amine functionalised N-heterocyclic carbene ligands to Ru, Rh and Rr: C-H and N-H activation and catalytic transfer hydrogenation

Chelating amine and amido complexes of late transition metals are highly valuable bifunctional catalysts in organic synthesis, but complexes of bidentate amine–NHC and amido–NHC ligands are scarce. Hence, we report the reactions of a secondary-amine functionalised imidazolium salt 2a and a primary-amine functionalised imidazolium salt 2b with [( p -cymene)RuCl 2 ] 2 and [Cp*MCl 2 ] 2 (M = Rh, Ir). Treating 2a with [Cp*MCl 2 ] 2 and NaOAc gave the cyclometallated compounds Cp*M(C,C)I (M = Rh, 3 ;M = Ir, 4 ), resulting from aromatic C–H activation. In contrast, treating 2b with [( p -cymene)RuCl 2 ] 2 ,Ag 2 O and KI gave the amine–NHC complex [( p -cymene)Ru(C,NH 2 )I]I ( 5 ). The reaction of 2b with [Cp*MCl 2 ] 2 (M = Rh, Ir), NaO t Bu and KI gave the amine–NHC complex [Cp*Rh(NH 2 )I]I ( 6 ) or the amido–NHC complex Cp*Ir(C,NH)I ( 7 ); both protonation states of the Ir complex could be accessed: treating 7 with trifluoroacetic acid gave the amine–NHC complex [Cp*Ir(C,NH 2 )I][CF 3 CO 2 ]( 8 ). These are the first primary amine– or amido–NHC complexes of Rh and Ir. Solid-state structures of the complexes 3–8 have been determined by single crystal X-ray diffraction. Complexes 5 , 6 and 7 are pre-catalysts for the catalytic transfer hydrogenation of acetophenone to 1-phenylethanol, with ruthenium complex 5 demonstrating especially high reactivity