Dear Krishnapriya ,

Eulerian models define specific reference points in a gridded system that monitors atmospheric properties, including temperature, pressure, chemical concentration of tracers, over time. Being the representative of the Eulerian model, the Unified Model divides the world up into fixed grid cells which allows for modelling the interactive chemistry within the atmosphere, regarded as a three-dimensional single fluid, and applying well-developed convection parameterisation scheme to represent convective motions.

Unlike Eulerian models, Lagrangian models take the perspective of a finite element or so-called ‘air parcel’. Over time both the position and properties of this air parcel are calculated according to the mean wind field data. The path along which air parcel travels is called its trajectory. It can be expressed as a differential equation. Advanced equation for the trajectory contains two components: mean winds and random turbulence.

Of the Eulerian models, the box model is the easiest to envision conceptually. Simply, the atmosphere over the modeling region is perceived as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and a changing mixing (or inversion-base) height.

Eulerian “grid” models are the most complex, but potentially the most powerful, air quality models, involving the least-restrictive assumptions, and are the most computationally intensive.

https://www.ncbi.nlm.nih.gov/books/NBK218138/

With my best regards

Prof. Bachir ACHOUR

Hi Sir,

Thank you for your valuable information.

But my doubt is that if some forest fire event happened in any area, whether an Eulerian model can predict the intensity of emission and track the emission pathway accurately.

With regards

Krishnapriya

In order to include the sub-grid scale sources such as forest fires it is quite common to apply the hybrid models. The small scale transport in such systems is calculated in the Lagrangian frame of reference. Considering the chaotic nature of atmospheric dispersion this approach is almost essential when analyzing any "special sources" in the large scale Eulerian transport models. This fact was often realized in the context of tracing the releases of radioactive material to the atmosphere (the high accuracy of the source description in such a cases is essential) but is also very useful in the case of the chemical tracers.

We have succesfully used STILT (Stochastic Time-Inverted Lagrangian Transport model) for GHG. In any case, Lagrangian or Eulerian, you'll need good meteorological fields and emission/absorption inventories.

The answer is that both models can be used, but the answer depends more on the process you want to investigate. Eulerain models use fix grid to calculate the concentrations in space and Lagragian use moving grid points where each concentration is calculated at those points alone. Each has their pros and cons. EU models tend to "diffuse" things but they calculate the properties of the whole grid, LA models are accurate, but while points move in space, they develops spatial gaps that you will need to figure out how to resolve. So once you define the question you want to answer, it will be much easier to decide which to use.

Prof. Bachir ACHOUR has clearly explained the topic. The remarks of Dr. Cristina Mihaela Balaceanu and Dr.Yaron Segal are also to be noted. The suggestion of Dr. Janusz Pudykiewicz is helpful for modeling a forest fire event . Thanks and regards to all

In order to complete this interesting debate it is quite relevant to mention the semi-Lagrangian models where the advection step is accomplished in the Lagrangian frame of reference with the trajectories originating at the fixed set of points usually coinciding with a grid system. The concentrations are then remapped after each time step back to the Eulerian frame of reference. There are numerous examples of semi-Lagrangian Chemical Transport Models (SL CTM). The main advantages of SL CTM include computational efficiency, natural incorporation of the sub-grid-scale sources and flexibility of including different parameterizations of physical processes and chemistry.

There are three available models. EPA has AERMOD is for distances under 50 Km and is a steady state Gaussian model. CALPUFF is a model for distance greater then 50 km and can use varying inputs over the travel distance. If you want a global model must of the easy models are mass balance (see books like Masters-introduction to envr engineer.