## Set Up: Large Eddy Simulations

Fig. 1 The suggested simulation domain for Large Eddy Modells centered around the EUREC4A circle

### Domain Period and resolution

Because of the higher computational costs a smaller domain and a shorter period has been selected for LEMs. The domain is is centered at 13.3º N and 57.7º W and comprises the HALO circle. It is elongated on the zonal (East-West ) direction for a total domain size of 250x400 km^{2}: from the centre, the domain spans 125km North and South, and 200 km East and West. For the vertical domain height of at least 6 km is advised as the heighest clouds can reach heights up to 4 km beyond with a sponge layer of a few km has to be added.

Participants are encouraged to use an horizontal resolutions as close as possible to 100 m, coarser resolutions up to 400 m are also accepted as alternative, or in addition. For the vertical resolution a resolution of 20m near the surface is advised. The grid may be stretched such as to have a resolution of 50m near cloud top height at 3 km.

The simulation period is from 00 UTC on February 1^{st }2020 to 00 UTC on February 12^{th} 2020. The first day is to be discarded because of the spin-up so that analysis will cover the 10 day period from February 2^{nd} to Februay 11^{th } 2020.

### Initial and Lateral Boundary Conditions

Originally, Large Eddy Models were used on rather small horizontal domains, which justified the use of periodic boundary conditions. In that case large scale forcings such as advection of heat, moisture and momentum into the model domain is usually taken into account by imposing the large scale forcings from a larger scale model as prescribed tendencies to all the grid cells of the Large Eddy Model. This approach becomes less attractive on larger domains such as in the present EUREC4A-MIP. It is also not possible to apply Pseudo Global Warming (PGW) perturbations to a Large Eddy Model that uses periodic boundary conditions. We therefore encourage submissions of Large Eddy Simulationsthe operate with open lateral boundary conditions. However also submissions of simulations that use periodic boundary conditions are welcome.

**LEM's using Open Lateral Boundary Conditions**

Initial and Lateral Boundary Conditions are provided on a hourly basis from simulations form the COSMO model on a resolution of 2 km and can be found __ here__. The lateral fields are provided at model levels and include ( T, u, v,, zg, q

_{v}, q

_{i}, , q

_{i}) ( Temperature, horizontal wind components, geopotential heights, water vapour specific humidity, liquid cloud water and cloud ice). Surface fields such as Sea Surface Temprature (SST) and surface pressure p

_{s}are also provided at an hourly frequency and at a resolution of 2 km and can be found

**here.**

It is our experience that direct nesting of the 100~200m LEM into the 2 km resolution COSMO model output can give rise to numerical issues such as spurious waves and long spin up patterns for turbulence. We therefore recommend a double nesting strategy by using a coarser 500m resolution simulayion on a domain as large as the common analysis domain as a first nesting. The results of this first nesting simulation can subsequently be used as a source in which the 100~200 m resolution large eddy simulation can be nested in.

**LEM's using Periodic Lateral Boundary Conditions**

In this case the same COSMO model output can be used for the initialisation and for the surface boundary conditions. The large scale forcings have been derived from simulation of the SRM Harmonie on a hourly basis and can be found** here**. These large scale forcings include tendencies for temperatue (T), specific humidity (q_{v}) , liquid water content (q_{l}) and for the horizontal velocity components ( u,v). Note that these tendencies only depend on time and height as they are averaged over the whole Large Eddy Model domain. This implies that allthe gridpoints of the Large Eddy Model that are at the same heigh will be feeded with the same large scale tendency.

No double nesting is required in the case of periodic lateral boundary conditions.

*Relaxation *

With periodic boundary conditions and forcings that only involve tendencies, runaway effects are easy to occur. For this reason participants are advised to use a nudging or relaxation towards the ERA5 mean profiles for temperature (T), total specific humidity (q_{t}), zonal and meridional winds (u, v). So for an arbitrary LES field c(x,y,z,t) this implies

dc(x,y,z,t)/dt = ( c(x,y,z,t) - c_{ERA}(z,t) ) / tau

where c_{ERA}(z,t) are hourly profiles from a reanalysis describing the evolving mean state of the field c. In order to give the LEM more freedom in the boundary layer we suggest to use longer relaxation times in the boundary layer and shorter ralaxation times higher up in the atmosphere. A relaxation profile can be found here ( and a image here).