Estimating numerical errors due to operator splitting in global atmospheric chemistry models: Transport and chemistry

We present upper bounds for the numerical errors introduced when using operator splitting methods to integrate transport and non-linear chemistry processes in global chemical transport models (CTM). We show that (a) operator splitting strategies that evaluate the stiff non-linear chemistry operator at the end of the time step are more accurate, and (b) the results of numerical simulations that use different operator splitting strategies differ by at most 10 percent, in a prototype one-dimensional non-linear chemistry-transport model. We find similar upper bounds in operator splitting numerical errors in global CTM simulations

Analysis of operator splitting for advection–diffusion–reaction problems from air pollution modelling

AbstractOperator or time splitting is often used in the numerical solution of initial boundary value problems for differential equations. It is, for example, standard practice in computational air pollution modelling where we encounter systems of three-dimensional, time-dependent partial differential equations of the advection–diffusion–reaction type. For such systems little attention has been devoted to the analysis of splitting and to the question why splitting can work so well. From the theoretical point of view, the success of splitting is primarily determined by the splitting error. This paper presents an analysis of operator splitting aimed at providing insight into the splitting error. Using the Lie operator formalism, a general expression is derived for a three-term Strang splitting in the pure initial value case. For a class of advection–diffusion–reaction problems the splitting error is analyzed in greater detail. A special case is discussed in which the splitting error can be reduced. Also some attention is paid to the use of operator splitting in initial boundary value problems

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

The HPx software for multicomponent reactive transport during variably-saturated flow: Recent developments and applications

Abstract HPx is a multicomponent reactive transport model which uses HYDRUS as the flow and transport solver and PHREEQC-3 as the biogeochemical solver. Some recent adaptations have significantly increased the flexibility of the software for different environmental and engineering applications. This paper gives an overview of the most significant changes of HPx, such as coupling transport properties to geochemical state variables, gas diffusion, and transport in two and three dimensions. OpenMP allows for parallel computing using shared memory. Enhancements for scripting may eventually simplify input definitions and create possibilities for defining templates for generic (sub)problems. We included a discussion of root solute uptake and colloid-affected solute transport to show that most or all of the comprehensive features of HYDRUS can be extended with geochemical information. Finally, an example is used to demonstrate how HPx, and similar reactive transport models, can be helpful in implementing different factors relevant for soil organic matter dynamics in soils. HPx offers a unique framework to couple spatial-temporal variations in water contents, temperatures, and water fluxes, with dissolved organic matter and CO2 transport, as well as bioturbation processes

Modelling of Mercury in the Arctic with the Danish Eulerian Hemispheric Model

International audienceA new 3-D mercury model has been developed within the Danish Arctic Monitoring and Assessment Programme (AMAP). The model is based on the Danish Eulerian Hemispheric Model, which in the original version has been used to study the transport of SO2, SO42- and Pb into the Arctic. It was developed for sulphur in 1990 and in 1999 also lead was included. For the current study a chemical scheme for mercury has been included and the model is now applied to the mercury transport problem. Some experiments with the formulation of the mercury chemistry during the Polar Sunrise are carried out in order to investigate the observed depletion. Some of the main conclusions of the work described in this paper are that atmospheric transport of mercury is a very important pathway into the Arctic and that mercury depletion in the Arctic troposphere during the Polar Sunrise contributes considerably to the deposition of mercury in the Arctic

“Offline” povezivanje unificiranog EMEP modela i WorkETA modela

In this paper the offline coupling of the Unified EMEP (European Monitoring and Evaluation Programme) model and WorkETA model was presented. For that purpose the meteorological driver was developed to supply the Unified EMEP model with input data from WorkETA model. To examine the use of the new driver, the Unified EMEP model was run from April to December 2005. The monthly and daily concentration of NO2, SO2 and SO42- obtained by using WorkETA driver was compared to measured values and to those obtained from the input data from parallel version of HIRLAM (High Resolution Limited Area Model), PARLAM-PS model. The analysis shows that the use of the new meteorological driver has more influence on the concentration of SO42- than on the concentration of NO2 and SO2.U ovom radu je predstavljeno tzv. “offline” povezivanje unificiranog EMEP modela i WorkETA modela. Kako bi se omogućilo korištenje rezultata WorkETA modela kao ulaz u unificirani EMEP model, razvijen je meteorološki preprocesor. Preprocesor je testiran simulacijom unificiranog EMEP modela, pomoću meteoroloških polja iz WorkETA modela, za razdoblje od travnja do prosinca 2005. Dobivene mjesečne i dnevne koncentracije NO2, SO2 i SO42- su uspoređene s izmjerenim koncentracijama kao i koncentracijama dobivenim iz paralelne verzije HIRLAM, PARLAM-PS modela. Analiza je pokazala da korištenje novog preprocesora ima veći utjecaj na koncentraciju SO42- nego na koncentraciju NO2 i SO2