Total Column Water Vapour Retrieval from S-5P/TROPOMI in the Visible Blue Spectral Range

<div> <p>Atmospheric water plays a key role for the Earth’s energy budget and temperature distribution via radiative effects (clouds and vapour) and latent heat transport. Thus, the distribution and transport of water vapour are closely linked to atmospheric dynamics on different spatio-temporal scales. In this context, global monitoring of the water vapour distribution is essential for numerical weather prediction, climate modeling and a better understanding of climate feedbacks.</p> </div><div> <p>Here, we present a total column water vapour (TCWV) retrieval using the absorption structures of water vapour in the visible blue spectral range. The retrieval consists of the common two-step DOAS approach: first the spectral analysis is performed within a linearized scheme. Then, the retrieved slant column densities are converted to vertical column densities (VCDs) using an iterative scheme for the water vapour a priori profile shape which is based on an empirical parameterization of the water vapour scale height.  </p> </div><div> <p>We apply this novel retrieval to measurements of the TROPOspheric Monitoring Instrument (TROPOMI) onboard ESA‘s Sentinel-5P satellite and compare our retrieved H<sub>2</sub>O VCDs to a variety of different reference data sets. Furthermore we present a detailed characterization of this retrieval including theoretical error estimations for different observation conditions. In addition we investigate the impact of different input data sets (e.g. surface albedo) on the retrieved H<sub>2</sub>O VCDs.  </p> </div>

A linear backward Euler scheme for a class of degenerate advection–diffusion equations: A mathematical analysis of the convergence in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω))

This paper concerns itself with establishing convergence estimates for a linearized scheme for solving numerically the saturation equation. In a previous paper, error estimates were obtained for the same scheme in L2(0, T0;L2(Ω)). In this work, we establish error estimates for the linear scheme in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω)) (in the discrete norms). Under certain realistic conditions, we show that, if the regularization parameter β and the spatial discretization parameter h are carefully chosen in terms of the time-stepping parameter Δt, the convergence, in these spaces, is at least of order O((Δt)α) for some determined α > 0, function of a parameter μ > 0 defined in the problem. Examples of possible choices of β and h in terms of Δt are given.

Linearization of a Simple Moist Convection Scheme for Large-Scale NWP Models

A simple Kuo-type convection scheme with an improved closure based on moist enthalpy accession (Kuo symmetric) has been linearized for the tangent-linear (TL) and adjoint (AD) versions of the Global Environmental Multiscale (GEM) model. The nonlinear scheme exhibits a reasonable behavior in terms of heating and moistening rates when evaluated in stand-alone mode over a set of deep convective profiles. A preliminary evaluation of a straightforward linearization in the global TL model has revealed the existence of noise that leads to an unacceptable solution after 12 h of integration. By neglecting several terms in the linearization (detrainment rate and cloud properties), the temporal evolution of humidity analysis increments is improved by including this simplified linearized convection scheme in the TL model. The behavior of the linearized scheme has also been compared favorably to the linearized version of the European Centre for Medium-Range Weather Forecasts (ECMWF) mass-flux convection scheme. When examining the validity of the TL approximation for surface precipitation, it appears that linearization errors are large for both stratiform and convective rainfall (rms errors are about twice the mean absolute perturbed precipitation). These errors are not reduced when considering accumulated rain rates instead of instantaneous quantities. However, the occurrence of “on–off” processes is reduced by a temporal integration of rain. This could make the variational assimilation of accumulated precipitation rates easier. Finally, errors coming from internal nonlinearities are slightly larger than those produced by discontinuities. This confirms the interest for improving the linearity of nonlinear convection schemes for applications in variational contexts.