J3.4 LAGRANGIAN MODELING OF DISPERSION IN THE STABLE BOUNDARY LAYER Jeffrey C. Weil 1∗ , Edward G. Patton 2 , and Peter P. Sullivan 2 1 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 2 National Center for Atmospheric Research, Boulder, CO 1. INTRODUCTION Current knowledge of dispersion in the stable bound- ary layer (SBL) is far from complete and indeed much less so than for its convective counterpart. For the SBL, dispersion from surface releases is the most well- understood and documented case thanks to theoretical work (e.g., Horst, 1979; van Ulden, 1978) and field observations, most notably the Prairie Grass experi- ment (Barad, 1958). However, for sources above the surface, the situation is less clear due to insufficient observations and information on the turbulence struc- ture. Theories exist for the vertical dispersion of ele- vated plumes—standard statistical theory (Taylor, 1921; Venkatram et al., 1984), an alternative statistical model for stable environments (Pearson et al., 1983), and eddy- diffusion (K) theory (Nieuwstadt, 1984a). The main challenge is knowing the conditions under which they apply and having the required turbulence information. Large-eddy simulation (LES) is a promising tool for investigating turbulence and dispersion in the SBL. A number of LESs have been conducted (e.g., Beare et al., 2005; Brown et al., 1994; Kosovic and Curry, 2000), but they have been restricted to a weakly stable boundary layer (WSBL), which is characterized by moderate-to- strong winds, weak surface cooling, and a continuously turbulent layer. The key restriction is to continuous (i.e., non-intermittent) turbulence. The above LESs and the one used here (Moeng and Sullivan, 1994; Sullivan et al., 1994) have reproduced several SBL features including a low-level jet, a triple-layer potential temperature struc- ture, and realistic turbulence profiles. We investigate dispersion in the SBL using a La- grangian particle model driven by velocity fields from LES. In this approach, one follows passive particles in a turbulent flow given the random velocity field and finds the ensemble-mean concentration by simulating thou- sands of particle trajectories; the mean concentration is proportional to the probability density function (PDF) of particle position. The approach has been applied suc- ∗ corresponding author address: Jeffrey C. Weil, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307-3000; email: weil@ucar.edu cessfully to the convective boundary layer (CBL) (e.g., Lamb, 1978; Weil et al., 2004) and informative SBL results were presented earlier by Kemp and Thomson (1996). Here, we report on dispersion for a range of source heights in the SBL. 2. NUMERICAL MODELS 2.1 Large-eddy simulations The velocity fields used here were obtained using the Moeng and Sullivan (1994) and Sullivan et al. (1994) models but modified to address an SBL. They were gen- erated originally as part of the GABLS (Global En- ergy and Water Cycle Experiment Atmospheric Bound- ary Layer Study) initiative (Beare et al., 2005). The sim- ulations were conducted with a 400 m × 400 m × 400 m domain, 200 × 200 × 192 grid points, with a grid resolu- tion of ∼ 2 m; the geostrophic wind speed was 8 ms −1 , the surface cooling rate was 0.25 ◦ Khr −1 , and the sur- face friction velocity u ∗ was ∼ 0.28 ms −1 . The stabil- ity index z i /L was 1.6, where z i (= 200 m) and L are the SBL height and M-O length, respectively; the po- tential temperature gradient in the bulk of the layer was ∂Θ/∂z ≃ 0.006 ◦ Cm −1 , but it was greater near the sur- face and SBL top, thus producing a triple-layer structure of the mean potential temperature Θ. 2.2 Lagrangian particle model In Lagrangian dispersion models, passive “particles” released in a turbulent flow are assumed to behave as fluid elements and to travel with the local fluid velocity with molecular diffusion ignored. The mean concentra- tion C is found from C(x, t )= Q Z t −∞ p 1 (x, t ; x s , t ′ )dt ′ (1) where Q is the source strength, x is the position vector (indicated by a boldface symbol), and p 1 (x, t ; x s , t ′ ) is the position PDF of material released at the source position x s at time t ′ being found at x at time t . p 1 is computed from the numerically-calculated particle trajectories.