Nudging

Usually, the LES model PALM is used to simulate the flow in the boundary layer which is a certain part of the atmosphere. Processes occurring on larger scales than those in the boundary layer including large scale advection of scalars, large scale pressure gradients or large scale subsidence have also to be considered in the model, especially when focusing on realistic situations observed during measurement campaigns.

One possibility to account for tendencies in the LES model resulting from larger scales is the usage of nudging. Nudging is a (Newtonian) relaxation technique which adjusts the large-eddy simulation to a given, larger scale flow situation (Anthes, 1974; Stauffer and Bao, 1993). It can be used to simulate less idealized flow situations and to adjust the simulation to an observed state when cyclic boundary conditions are used. In case that continuous measurement data over a longer time period (weeks to month to years) is available (for example from a meteorological super-site or intensive measurement campaigns), these periods can also be simulated with LES. The LES results could for example be used for the comparison with larger-scale models to test parameterizations. The simulation of longer time periods permits to calculate statistics and to identify situations in which the differences to the larger scale model are significant (Neggers et al., 2012).

Instead of taking nudging data from measurements it is also possible to use data from a larger scale model to drive PALM. Further information about nudging can for example be found in Yamada and Koike, 2011; Schlünzen et al., 2011 or Neggers et al., 2012.

Beginning with revision r1241 it is possible to use nudging. The nudging method in PALM which is based on implementations in the ​DALES and ​UCLA-LES model consists principally of the following steps for the prognostic variables

• Interpolation in time and height of large scale (LS) profiles provided by measurements or a larger scale model
• Calculation of domain-averaged profiles of the prognostic variables in the LES model
• Calculation of a tendency at each single grid point where is the nudging time scale

The strength of the nudging strongly depends on the nudging time scale used. Usually, this time scale should be in the order of several hours. By varying the nudging time scale with height it is possible to apply the nudging not everywhere but for example only above the boundary layer. In case this is wanted, the time scale should be set to a very large number (~10¹⁰) inside the boundary layer. By this way, the nudging tendency approaches zero.

A complete example for a PALM run with nudging is documented here.

References

• Anthes, R. A., 1974: Data assimilation and initialization of hurricane prediction models. J. Atmos. Sci, 31, 702-719.​doi
• Neggers, R. A. J., A. P. Siebesma and T. Heus, 2012: Continous single-column model evaluation at a permanent meteorological supersite. Bull. Amer. Meteor. Soc, 29, 91-115. ​doi
• Schlünzen, K. H., D. Grawe, S. I. Bohnenstengel, I. Schlüter and R. Koppmann, 2011: Joint modelling of obstacel induced and meoscale changes - Current limits and challenges. J. Wind Eng. Ind. Aerodyn., 99, 217-225. ​doi
• Stauffer, D. R. and J.-W. Bao, 1993: Optimal determination of nudging coefficients using adjoint equations. Tellus, 45A, 358-369. ​doi
• Yamada, T., and K. Koike, 2011: Downscaling mesoscale meteorological models for computational wind engineering applications. J. Wind Eng. Ind. Aerodyn., 99, 199-216. ​doi