Vertical structure of stratospheric water vapour trends derived from merged satellite data

Stratospheric water vapour is a powerful greenhouse gas. The longest available record from balloon observations over Boulder, Colorado, USA shows increases in stratospheric water vapour concentrations that cannot be fully explained by observed changes in the main drivers, tropical tropopause temperatures and methane. Satellite observations could help resolve the issue, but constructing a reliable long-term data record from individual short satellite records is challenging. Here we present an approach to merge satellite data sets with the help of a chemistry–climate model nudged to observed meteorology. We use the models’ water vapour as a transfer function between data sets that overcomes issues arising from instrument drift and short overlap periods. In the lower stratosphere, our water vapour record extends back to 1988 and water vapour concentrations largely follow tropical tropopause temperatures. Lower and mid-stratospheric long-term trends are negative, and the trends from Boulder are shown not to be globally representative. In the upper stratosphere, our record extends back to 1986 and shows positive long-term trends. The altitudinal differences in the trends are explained by methane oxidation together with a strengthened lower-stratospheric and a weakened upper stratospheric circulation inferred by this analysis. Our results call into question previous estimates of surface radiative forcing based on presumed global long-term increases in water vapour concentrations in the lower stratosphere.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.