Using an antidiffusive transport scheme for vertical transport: a promising path towards solving the long-standing problem of excessive vertical diffusion in Eulerian models
Authors: Mailler Sylvain , Lachatre Mathieu , Menut Laurent 
Published: March 2020

&lt;p&gt;A well-known drawback of Eulerian models is excessive numerical diffusion of the transported species. This applies to chemical species but also to water vapor. We present a new way of dealing with this problem in the vertical direction by using the Despr&amp;#233;s and Lagouti&amp;#232;re (1999) scheme &amp;#8211; hereinafter DL99, a simple 1&lt;sup&gt;st&lt;/sup&gt;-order advection scheme with antidiffusive properties. These authors have only studied this scheme in the context of 1d transport. Here we test the applicability of this scheme in atmospheric modelling by applying it to tracer transport in the vertical direction in idealized 2d (zonal-vertical) atmospheric circulations and quantify the gain compared to classical advection schemes. &lt;br&gt;&lt;br&gt;In this idealized framework, we have tested the efficiency of DL99 in two cases representative of important situations for atmospheric transport&amp;#160;: &lt;br&gt;- Formation of a thin plume from an initially thick column of tracer (e.g. volcanic plume, biomass burning plume etc.) under the effect of zonal wind shear in presence of large-scale variations in vertical wind &lt;br&gt;- Long-range advection of a thin polluted layer under the action of zonal wind in presence of large scale oscillations in the vertical wind. &lt;br&gt;&lt;br&gt;In these idealized case studies, we show that using DL99 in the vertical direction yields dramatically improved performance compared to any other scheme we have tested, including the 3&lt;sup&gt;rd&lt;/sup&gt;-Order Piecewise Parabolic Method (PPM). As an example, in a simulation with a vertical resolution of 500m and a zonal resolution of 25 km initialized by a 1000m-thick, zonally uniform layer of tracer, after being transported horizontally over 2000km over 48 hours by a uniform zonal wind ~11.5ms&lt;sup&gt;-1&lt;/sup&gt; together with an oscillating vertical wind of +-0.05ms&lt;sup&gt;-1&lt;/sup&gt;, maximal tracer concentration at the end of the simulation with DL99 is 94% of its initial value instead of 51% with PPM, l&lt;sup&gt;2&lt;/sup&gt; relative error is 10% instead of 61%, and 92% of the tracer mass is still confined in the correct 1000m-thick envelope instead of 50%.&lt;br&gt;&lt;br&gt;This and other numerical experiments shows that, by design, DL99 reduces numerical diffusion, but it also proves it to be able to preserve the areas of uniform tracer concentration even if these areas cover only a very small number of cells in the vertical direction. We argue that this unique set of properties, along with the simplicity of its formulation and its minimal computational cost make the DL99 an extremely attractive candidate for a robust and non-diffusive representation of vertical advection in Eulerian meteorological and chemistry-transport models. This scheme has been implemented in the state-of-the-art CHIMERE chemistry-transport model (Mailler et al., 2017), and we have shown that it brings a clear improvement in the representation of the structure of a volcanic plume from the Etna volcano (Lach&amp;#226;tre et al., 2020, Atmos. Chem. Phys.)&lt;/p&gt;&lt;p&gt;Main references:&lt;/p&gt;&lt;p&gt;Despr&amp;#233;s, B., and F. Lagouti&amp;#232;re, 1999, Un sch&amp;#233;ma non lin&amp;#233;aire anti-dissipatif pour l'&amp;#233;quation d'advection lin&amp;#233;aire, &lt;em&gt;Comptes Rendus de l&amp;#8217;Acad&amp;#233;mie des Sciences&lt;/em&gt;&lt;/p&gt;