On the importance of horizontal trblent transport in high resoltion mesoscale simlations over cities. A. Martilli (CIEMAT, Spain), B. R. Rotnno, P. Sllivan, E. G. Patton, M. LeMone (NCAR, USA)
In an rban area, srface hetereogeneitis have a spatial scale of few kilometers
To resolve them we need a resoltion of the order of several hndreds of meters
When resoltion becomes of the same order of the integral scale of trblence (or less), the conditions where volme and ensemble averages can be considered eqal are not flfilled anymore. A choice mst be done. We choose to consider the mean as an ensemble average.
However, we have shown in that when the resoltion is of the same order or less than the integral scale of trblence sprios circlations form over flat and homogensos terrain (even if they shold not). The cases of this problem are: The fact that the standard PBL schemes are not efficient enogh to transport heat in the vertical to redce the speradiabaticty The lack of a proper parameterization of the horizontal trblent fles.
Traditionally, only the vertical component of the trblent fl is sally parameterized w, w With PBL closres that are based on ensemble averages. Little attention has been given to the horizontal components of the trblent fles, which in general is : neglected, modelled with an horizontal diffsion coefficient that can be: Constant and ad hoc Based on the deformation of the flow and the model grid size (similar to Smagorinsky, which is the approach sed in LES volme averaged models).
Is the divergence of the horizontal trblent fles important over regions with high variability in srface fles? How can we parameterize them? y v y v,,,
Tool to investigate this problem: y Large Eddy Simlations (Sllivan and Patton, 011) applied to a case with strong horizontal hetereogeneity in srface fles. 180m 560m 180m Horizontal resoltion is 0m, and vertical resoltion is 8m. 56 X 56 X 56 grid points. Heat fl of 0.1 K m/s, roghness length of 0.1m ( rral ) Heat fl of 0.36 K m/s, roghness length of 1m ( city )
Techniqe to recover the mean De to the horizontal homogeneity in the y direction, averages over y and over time are performed to get the mean. Istantaneos vales are stored every 30 seconds, for a period of approimately.5 hors (300 otpts). For each otpt, horizontal averages (y direction) are performed and trblent fles are calclated ( i, iz, n) 1 NY iy 1, NY ( i, iy, iz, n) Reslts are averaged over the 300 otpts ( i, iz) tend 1 tstart ntstart, tend ( i, iz, n)
Potential Temperatre U W TKE
Horizontal section of the for terms of the fl divergence of potential temperatre at three different heights K s -1 w z w z K s -1 Smoothed over 60m. K s -1
The divergence of the horizontal trblent transport is at least as significant as the one for the vertical. Wyngaard (004) proposed an approach to parameterize the horizontal trblent fles that in D reads like ( for temperatre a similar formlation can be derived for momentm): w z w z w w w T w z w z w T T is a time scale of the order of tke l And it arises from the assmption that the pressre correlation term can be modelled as T p i i
Two relevant qestions: How good is the assmption on T? p i i T Can we find a way to parameterize T? Is it the same for all the variables? Are all the terms important?
Horizontal section of the for terms for w z w z
Horizontal section of the for terms for w w w w z w z w
Gidance, possible simple approach for a parameterization: z w T w z w T Downgradient term Different coefficients for the horizontal and the vertical Similar approach can be developped for momentm
Conclsions LES simlations over srfaces with hetereogeneos fles can give gidance for the development of a physically based parameterization of the horizontal trblent fles. These reslts sggest that a first attempt can be to represent the heat horizontal fles by mean of a downgradeint term (bt with a coefficient different than the one sed for the vertical), and a term fnction of the vertical heat fl and gradient of wind. This new develpment is epected to: Improve the repsentation of srface fl hetereogenities in mesoscale models Improve the reslts of mesoscale models at sbkilometer resoltion, (Ching et al. MWR, 014).
Thank yo
The presence of hetereogenities in the srface fles has two important conseqences: Horizontal homogeneity is broken Needs for high resoltion models The conditions where volme and ensemble averages can be considered eqal are not flfilled anymore. A choice mst be done. We choose to consider the mean as an ensemble average.
Basic eqations solved in a mesoscale model (in fl form) j j j j o o i i j j i j j i i t g p t 3 Overbar represents mean. Traditionally, mean has been intended as ensemble average or as volme average over the grid cell (or a volme of the size of the spatial filter). 3 1 / / / / / / 3 3 1 1,, d d d t U t U dv t v f t v t U t U t U N N,,,,, lim, 1 Where f is the p.d.f.
Wyngaard (004) jstified this confsion saying that for resoltions of several kilometrs (typical of mesoscale models till some years ago), the integral scale of trblence is in general smaller than the grid size, so within one grid cell there are several large eddies the volme average can be considered eqivalent to the ensemble average. Strictly speaking this is tre only when trblence is (qasi-)horizontally homogeneos, which implies horizontally homogeneos srface fles of heat and momentm.
Horizontal section of the for terms of the fl divergence of U at three different heights K s -1 w z w z K s -1 Smoothed over 60m K s -1