Status of component 4, “urbanLS”… testing the four optional configurations (forward/backward, 0 th /1 st order) John Wilson, 22 August/06 Context Random Displacement Model is it well-mixed? does it agree with standard dispersion data? Performance of variants (0f, 0b, 1f, 1b) of urbanLS relative to standard dispersion data Performance of urbanLS for Oklahoma City

Context: High resolution weather analysis/prediction: “Urban GEM-LAM” Building-resolving k-  turbulence model: “urbanSTREAM” (steady state, no thermodynamic equation, control volumes congruent with walls) Provides upwind and upper boundary conditions now offers four options 0f, 0b, 1f, 1b Lagrangian stochastic model “urbanLS” to compute ensemble of paths from source(s); now offers four options 0f, 0b, 1f, 1b Provides computational mesh over flow domain and these gridded fields:

A zeroth-order Lagrangian stochastic model, also called the “Random Displacement Model” (RDM), does not explicitly model particle velocity, and (by some criteria) is equivalent to an eddy-diffusion treatment… however it is a Lagrangian method, thus grid free It is far less demanding, computationally, than the 1 st - order LS model… and in the far field of a source, the RDM/eddy diffusion treatment is acceptable… as I will demonstrate here Why is the RDM of interest?

The complexity of a 1 st - order order LS algorithm… The T’s involve the mean velocity field, TKE dissipation rate , and the stress tensor R ij. They are computed and stored on the grid prior to computing the ensemble of paths. At each timestep, use T’s from gridpoint closest to particle (ie. no interpolation to particle position) ( G a standardized Gaussian random variate)

Relative simplicity of the 0 th - order LS algorithm and no requirement that where Attractive to use 0 th -order LS for its speed. Criteria: is the algorithm well-mixed? does it replicate standard experiments? Will address these questions in context of simplest real world (atmospheric) regime of flow, viz., neutral surface layer

Well-mixed “Well-mixed”? uniform initial density “p” t = 0 t > 0 Still uniform?

Reference dispersion data traceable back to Project Prairie Grass Ideal neutral surface layer (no horiz. gradients) z src = 0.46 m 100 m Detect crosswind- integrated concentration 9 min

universal function of x/z 0 z/z 0

Form of the RDM (0 th -order LS) for neutral surface layer Forward model m=1 Do we reverse this (m = -1) in a backward model?

Analytical and numerical tests for well-mixed property (nb! grid-free LS algorithm) Chapman-Kolmogorov equation: Upper and lower reflection boundaries Initial state (= 1 for present test) Final state “transition density”

Analytical and numerical tests for well-mixed property no reflection: path length reflection path has total length where 14.5 min

Upper reflection at L=4000 z 0 Lower reflection at z r =0 RDM with surface reflection is not a well-mixed model Flow regime: ideal neutral surface layer L = 

… but it (RDM) gives excellent simulation of reference dispersion “True” normalized, crosswind-integrated concentration at x/z 0 =2000 is 1.48 x 10 -3

And treatment of the drift term?.... “Truth”… do not reverse drift term

Now test actual code Now test actual code (urbanLS3.for) against reference dispersion by scaling PPG onto the urbanSTREAM grid for Oklahoma City: at its highest resolution,  z=3 m (  x,  y irrelevant since horizontal gradients vanish) urbanLS is not a grid-free Lagrangian model; unless the grid resolves the strong near-ground gradients of the ASL precise forward/backward 0/1-order consistency should not be expected; if one simulates (eg.) PPG57 with z0= m on this grid at full scale, then the velocity statistics in the lowest layer (k=2) represent the flow in the range therefore specify z 0 =zc(2)/2=0.75 m and a source-detector separation of 2000z 0 scales to 1500 m. Discretization error is greatly reduced, because the wind statistics in the plume layer are represented by more than 50 layers perfect reflection at z refl =z 0

Timestep 0 th -order simulations: 1 st -order simulations:  x (I)

forward-backward consistency of 1 st order simulations only modest sensitivity to timestep, but do need  t/T L smaller than 0.1 to attain agreement within one std error with reference dispersion data bigger impact of  t on backward than forward simulation 0th-order forward simulation excellent; backward very sensitive to  t

forward simulation good, and not very sensitive to whether one sets drift term to zero in lowest layer backward simulation very sensitive to whether drift term is reversed, to whether it is zeroed in lowest layer, and to  t Focus on 0 th -order simulations:

1 st -order forward and backward consistent, in good agreement with the reference dispersion data, only weakly sensitive to  t 0 th -order forward simulation in good agreement with the reference dispersion data, even with large  t, and only weakly sensitive to inclusion or neglect of drift term in lowest layer 0 th -order backward simulation demands drift term should not be reversed, but should be zeroed in lowest layer… else spurious vertical gradient arises remains to comprehend the 0 th -order backward simulations, which for the time being I distrust Recapitulate implications of tests of 0f, 0b, 1f, 1b against reference dispersion case: 26.5 min

Simulation of Gas Plume from a source in Oklahoma City continuous source 1.9 m above ground Intensive Observation Period 9, July 27, 2003: wind

200 forward paths, displayed only below 50 m height wind 350 m (Not to scale) #74

Mean ground-level concentration [parts per trillion] from forward LS simulation fully 3D, C 0 =4.8 fully 3D, C 0 =4.8 dt = 0.05 min (T L,  x/u ) dt = 0.05 min (T L,  x/u ) z refl =0.1 m z refl =0.1 m reset veloc. fluc if > 6  reset veloc. fluc if > 6  9 x 80,000 paths 9 x 80,000 paths detector half-widths 20 x 20 x 1.75 m detector half-widths 20 x 20 x 1.75 m execution time 44 hrs execution time 44 hrs (3.68 min per 1000 paths)

Paths displayed only below z = 25 m

Performance of (1f) Lagrangian model relative to experiment #74

Comparison of performance of (1f) Lagrangian and Eulerian solutions relative to experiment… Mean concentration [ppt]

Backward simulation… from detectors #54, 55, 56, 64

evidence suggests 0f option in urbanLS is fast and reliable puzzles remain relative to 0b option remains to repeat the 0f, 0b, 1f, 1b consistency tests in disturbed flow evidence suggests 0f, 1f, 1b options are all very satisfactory for realistic urban simulations however no evidence yet that implementing Lagrangian approach driven by urbanSTREAM wind statistics offers any greater (or lesser) accuracy than Eulerian approach available in urbanSTREAM Conclusion 31.5 min