Abstract
Abstract. Upcoming spaceborne imaging spectrometers will retrieve clear-sky total column water vapour (TCWV) over land at a horizontal resolution of 30–80 m. Here we show how to obtain, from these retrievals, exponents describing the power-law scaling of sub-kilometre horizontal variability in clear-sky bulk planetary boundary layer (PBL) water vapour (q) accounting for realistic non-vertical sunlight paths. We trace direct solar beam paths through large eddy simulations (LES) of shallow convective PBLs and show that retrieved 2-D water vapour fields are “smeared” in the direction of the solar azimuth. This changes the horizontal spatial scaling of the field primarily in that direction, and we address this by calculating exponents perpendicular to the solar azimuth, that is to say flying “across” the sunlight path rather than “towards” or “away” from the Sun. Across 23 LES snapshots, at solar zenith angle SZA = 60∘ the mean bias in calculated exponent is 38 ± 12 % (95 % range) along the solar azimuth, while following our strategy it is 3 ± 9 % and no longer significant. Both bias and root-mean-square error decrease with lower SZA. We include retrieval errors from several sources, including (1) the Earth Surface Mineral Dust Source Investigation (EMIT) instrument noise model, (2) requisite assumptions about the atmospheric thermodynamic profile, and (3) spatially nonuniform aerosol distributions. By only considering the direct beam, we neglect 3-D radiative effects such as light scattered into the field of view by nearby clouds. However, our proposed technique is necessary to counteract the direct-path effect of solar geometries and obtain unique information about sub-kilometre PBL q scaling from upcoming spaceborne spectrometer missions.
Highlights
Spatial scaling in the variability of atmospheric properties such as water vapour (q) can be characterised via structure functions, with the nth-order structure function of a field f (x), Sn defined asSn(r) = E (f (x) − f (x + r))n, (1)where E[] is the expected value, x a location, and r a separation between points
We can confirm that our derived values are representative of ζ2 derived from PCWVPBL, but further work is needed to determine the precise utility of statistics of PCWVPBL and, we note that corresponding estimates of planetary boundary layer (PBL) height from other sources may be necessary to help interpret measurements of PCWVPBL scaling
4 Discussion and conclusions We have shown that for the q fields simulated in five large eddy simulations (LES) runs of shallow convective PBLs, a novel strategy accounting for solar azimuth eliminates the SZA-induced bias in calculated ζ2 over r of 0.5–1 km from high-spatial-resolution visible and shortwave infrared (VSWIR) retrievals
Summary
Fields of temperature (T ), q, and wind speed are commonly well modelled by a power law: Sn (r) ∝ rζn , (2) Such that ζn is the log–log gradient of Sn as a function of r. There is strong motivation to quantify and understand these exponents and the ranges r within which they are valid, and here we specify second-order structure functions S2 with exponent ζ2, describing variance scaling. This is related to the commonly referenced Fourier power spectrum exponent β: β = − (ζ2 + 1) . Richardson et al.: Solar-aware sub-km vapour scaling be tuned for each model set-up, but scale-aware variance relationships allow a smooth and consistent transition between low-resolution (order ∼ hundreds of kilometres) and highresolution (order ∼ km) models (Arakawa et al, 2011; Schemann et al, 2013)
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