Idealized Planar Array study for Quantifying Spatial heterogeneity (IPAQS) - Numerical Simulations

The Idealized Planar Array study for Quantifying Spatial heterogeneity (IPAQS) is the result of a National Science Foundation (US) funded project, that aims at studying the effect of surface thermal heterogeneities of different length-scale on the atmospheric boundary layer. This project consisted of a computational effort (dataset here included), and an experimental effort (dataset being prepared for publication). 

Overview of the numerical (Large Eddy) simulations:

The simulations are separated into two sets to study the differences between heterogeneous and homogeneous surfaces. In the first set, a total of seven configurations are considered, all with a homogeneous surface temperature fixed at a value of \(T_s\) = 290 K, and for which the geostrophic wind speed has been increased from 1 to 15 m s-1 (i.e., Ug = 1, 2, 3, 4, 6, 9, 15 m s−1 ). These homogeneous cases are referred to as Homog-X, where X indicates the geostrophic wind speed corresponding case (see Margairaz et al. 2020a). In the second set, the surface temperature is distributed amongst square patches, where the temperature of each patch is determined by sampling a Gaussian distribution with a mean temperature of 290 K and a standard deviation of 5 K. In this case, three different patch sizes were considered (i.e., lh = 800, 400, and 200 m). The sizes of the heterogeneities were chosen to be of similar size (lh /ld ≈ 1), half the size (lh /ld ≈ 1/2), and about a quarter of the size (lh /ld ≈ 1/4) of the largest flow motions within the represented thermal boundary layer, assuming that this is of the order of the boundary-layer height (ld ∼ z i ). These heterogeneities are typically not resolved in NWP models. These cases have been studied for the same geostrophic wind speeds indicated above, and hereafter are referred to as PYYY-X-, where X indicates the corresponding geostrophic wind speed, and YYY refers to the size of the patches (e.g., P800_Ug1_ would be the heterogeneous case with patches of 800 m, and forced with Ug = 1 m s−1 ). Additionally, for the case with larger patches, three different random distributions of the patches were considered to evaluate the potential effect of a given surface distribution for all geostrophic wind speeds. In this dataset we only include case v3. The LES imposed surface temperature distributions emulate the surface thermal conditions observed in Morrison et al. (2017 QJRMS, 2021 BLM, 2022 BLM), where measurements of the surface temperature were taken with a thermal camera at the SLTEST site of the US Army Dugway Proving Ground in Utah, USA. This is an ideal site with uniform roughness and a large unperturbed fetch, where surface thermal heterogeneities are naturally created by differences in surface salinity. In all studied cases, the surface roughness is assumed homogeneous, with z0 = 0.1 m, and representative of a surface with sparse forest or farmland with many hedges (Brutsaert 1982; Stull 1988). The initial boundary-layer height is set to zi = 1000 m. The temperature profile is initialized with a mean air temperature of 285 K. At the top of the initial boundary layer, a capping inversion of 1000 m is used to limit its growth. The strength of this inversion is fixed at Γ = 0.012 K m−1. The atmospheric boundary layer (ABL) is considered dry and the latent heat flux is neglected in all cases. Further, in all simulations, the surface heat flux is computed using MOST, as explained in Margairaz et al. 2020a, where the surface temperature is kept constant in time throughout the simulations. Thus, there is no feedback from the atmosphere to the surface as the surface temperature does not cool down or warm up with local changes in velocities. As a consequence, the ABL gradually warms up as the simulations progress, and hence becomes less convective over time. However, the runs are not long enough for this to be significant. In addition, to ensure a degree of homogeneity within each patch and a certain degree of validity of MOST, note that even for the heterogeneous cases with the fewest amount of grid points per patch, a minimum of eight grid points is granted in each horizontal direction. The domain size is set to (Lx, Ly, Lz) = (2π, 2π, 2) km at a grid size of (Nx , Ny , Nz ) = (256, 256, 256) resulting in a horizontal resolution of \(\Delta\)x = \(\Delta\)y = 24.5 m and a vertical grid spacing of \(\Delta\)z = 7.8 m. A timestep of \(\Delta\)t = 0.1 s is used to ensure the stability of the time integration. The two sets of simulations span a large range of geostrophic forcing conditions, allowing the study of the effect on the structure of the convective boundary layer (CBL) above a patchy surface compared to a homogeneous surface. The procedure used to spin up the simulations is the following: a spinup phase of four hours of real time is used to achieve converged turbulent statistics, which is then followed by an evaluation phase. During the latter, running averages are computed for the next hour of real time (dataset here published). Statistics have been computed for averaging times of 5 min to 1 h, showing statistical convergence at 30-min averages with negligible changes between the 30-min and the 60-min averages. The simulations cover a wide range of atmospheric stability regimes ranging from −zi/L < 5 to −zi/L > 700, and hence spanning from near neutral to highly convective scenarios.

Description of the Dataset as included in the NetCDF files:

Data for each study case is included in two files, one for momentum related variables, and one for temperature related variables. For example, the following files "P200_Ug1_Momentum.nc" and "P200_Ug1_Scalar.nc",  include the 1h averaged variables for momentum and temperature for the case of 200 m surface patches with 1 m/s geostrophic winds. 

Each corresponding momentum file "PXXX_UgX_Momentum.nc" includes the following variables in a Python Xarray structure:

'avgU' = mean streamwise wind speed; 'avgV' = mean spanwise wind speed; 'avgW' = mean vertical wind speed, 'avgP' = mean dynamic modified pressure field (\(p^*\), see Margairaz et al 2020a),

'avgU2', 'avgV2', 'avgW2' = correspond to \(\overline{UU}\), \(\overline{VV}\), and \(\overline{WW}\), where the capital indicates the LES filtered variable.

'avgUV', 'avgUW', 'avgVW' = correspond to \(\overline{UV}\), \(\overline{UW}\), and \(\overline{VW}\). These variables together with the ones above are used to compute the Reynolds stress components (e.g. \(R_{xz} = \overline{U}\overline{W} - \overline{UW}\)).

avgU3', 'avgV3', 'avgW3', 'avgU4', 'avgV4', 'avgW4' = correspond to the equivalent but instead of squared they are cubed and to the 4th power.

'avgtxx','avgtyy','avgtzz','avgtxy','avgtxz','avgtyz' = These represent the corresponding averaged subgrid scale (SGS) stress.

'avgdudz','avgdvdz','avgNut','avgCs' = Represent the averaged vertical derivatives, an averaged subgrid Nusselt number, and the Cs coefficient computed in the SGS model.

Overall, there are a total of 26 variables related to the momentum field. Alternatively, the temperature fields are included in the "PXXX_UgX_Scalar.nc" files. These files include 10 variables, 

'avgT' = mean Temperature field, 'avgT2' = corresponds to \(\overline{TT}\),  'avgUT' = correspond to \(\overline{UT}\), 'avgVT' = correspond to \(\overline{VT}\), 'avgWT' = correspond to \(\overline{WT}\); one can use these terms to compute the corresponding Reynolds averaged turbulent fluxes as is the case for momentum. 

'avgUT_sgs','avgVT_sgs','avgWT_sgs' = These represent the corresponding subgrid scale fluxes.

'avg_nus', avg_ds' = averaged subgrid Nusselt number, and the Ds coefficient computed in the scalar SGS model.

All variables output from the LES are normalized by Tscale = 290 [K] when it includes dimensions of temperature, u_scale = 0.45 [m/s], when it relates to velocity fields, and  zi = 1000 [m] for length scales.

The only output variables that are expressed in dimensional form are those for the surface temperature included in the files "SurfTemp_DXXX.nc"

Together with the data files we include a Python script that loads the data and includes it in two Xarray structures that one can then use to work with the datasets.