MLCD: A SHORT-RANGE ATMOSPHERIC DISPERSION MODEL FOR EMERGENCY RESPONSE CONTRACT REPORT. Thomas Flesch, John Wilson, and Brian Crenna

Transcription

1 MLCD: A SHORT-RANGE ATMOSPHERIC DISPERSION MODEL FOR EMERGENCY RESPONSE CONTRACT REPORT Thomas Flesch, John Wilson, and Brian Crenna Department of Earth and Atmospheric Sciences University of Alberta Edmonton, Alberta 31 March 2002

2 EXECUTIVE SUMMARY Our objective, in cooperation with the Canadian Meteorological Centre, was to develop an atmospheric dispersion model suitable for short-range emergency response problems. This new model is called MLCD (Modèle Lagrangien Courte Distance), and represents a substantial increase in sophistication over traditional Gaussian models of short-range dispersion. The random trajectories of a large sample of particles are tracked downwind from a source, for durations up to 12 hours and distances up to about 150 km from release. The model runs on a desktop computer, offering speed and simplicity at the cost of neglecting horizontal variability of the atmosphere, a step that eliminates the necessity of coupling to a weather model. An important aspect of MLCD is its flexible use of windspeed and wind direction observations as the basis for the simulation of atmospheric transport. A (new) wind model is introduced, as a means to optimally interpret available wind observations to construct a complete vertical wind profile (we assume a two-layer model that matches a surface layer to a modified Ekman layer). This fitting also gives estimates of the depth of the boundary layer h, the friction velocity u*, and atmospheric stability L -- crucial properties for calculating dispersion. In a test with 30 wind profiles the two-layer model returned accurate wind profiles and accurate estimates of u*, h, and L in the large majority of cases. This two-layer wind model is a parsimonious approach (few assumptions, few degrees of freedom) to constructing a best guess wind field from partial information, and usually creates realistic wind profiles, a factor crucial for the accurate simulation of cloud dispersion. If appropriate the wind and turbulence profiles are updated in time, during the dispersion simulation. After MLCD has calculated realistic wind profiles from observed winds, thousands of model particles are released from a tracer source and followed downwind. Particle trajectories are calculated using a Langevin model for particle velocity, which updates velocities at a model timestep of order one second. Particle velocity responds in accordance with the average horizontal winds and the amount of atmospheric turbulence at their location. Each model particle has a mass that can be reduced by radioactive decay and wet and dry deposition (tracer i

3 properties provided by the user). Downwind concentrations are predicted by collecting the particles in receptor volumes. MLCD also has the option of including mesoscale velocity fluctuations when calculating particle velocities. These horizontal velocity fluctuations, at scales above the microscale turbulence, can be important in dispersing material in the atmosphere. The meso-fluctuations were calculated with a second set of Langevin equations, whose coefficients were estimated by analysis of a single time-series of surface wind observations from Europe. This option should be used with care, as the applicability of this analysis to other situations is uncertain. Three field experiments were used to examine the performance of MLCD. These experiments focussed on dispersion 10 to 500 km downwind of a tracer release (the accuracy of the MLCD Lagrangian approach over shorter ranges has been well documented in the scientific literature). From these we conclude that: 1) When provided a set of wind observations through the boundary layer, MLCD will simulate dispersion accurately in the large majority of situations. 2) In a minority of cases the two-layer wind model will fail, and return obviously inaccurate estimates of boundary layer conditions (which if uncorrected would result in unrealistic dispersion predictions). We recommend that MLCD be supervised to ensure realistic results. Usually a slight adjustment of the input winds will lead to realistic results. 3) Good predictions of dispersion are expected for downwind distances less than 100 km. 4) At distances beyond 100 km the model will be less accurate, due to the assumption of horizontally homogenous winds across the simulation domain. 5) The importance of including meso-fluctuations was not conclusively shown. Overall we judged the MLCD model successful. When the model is supplied a set of wind observations through the boundary layer, it will in most cases accurately simulate dispersion. ii

4 A. CONTRACT OBJECTIVE The objective of this project was to develop, in cooperation with the Canadian Meteorological Centre, an atmospheric dispersion model suitable for short-range emergency response problems. This new model is to be called MLCD (Modèle Lagrangien Courte Distance), and to use the advanced Lagrangian stochastic approach to mimicking turbulent dispersion. It is to run quickly on a desktop computer, and simulate dispersion from zero to 12 hours after a hazardous release. B. BACKGROUND Gaussian puff or plume models have for many years been the de facto standard for modelling atmospheric dispersion. They give simple formula for predicting concentration downwind of an emission source, and they claim to handle arbitrary source characteristics (continuous line source, moving source, etc.), effluent characteristics (buoyancy, stack downwash, etc.), and varying meteorological conditions. Despite their apparent sophistication the Gaussian framework is primitive. From a scientific standpoint there is good reason to move away from Gaussian models toward more accurate models. Here we briefly critique the Gaussian approach and introduce the Lagrangian stochastic approach. Gaussian models trace their origin to the mass-conservation equation, which describes the evolving concentration field: (1) This employs Reynolds' decomposition, where the instantaneous velocity and concentration fields (u, v, w, c) are written as the sum of a time average (U, V, W, C) plus the instantaneous fluctuation from the average (u, v, w, c ), e.g., (2) Thus u represents the unresolved turbulent velocity field, while U is supposed known. The ensemble mean concentration C is the quantity predicted by dispersion models. Even if U, V, W 1

5 are known the above equation does not determine C, because of the unknown turbulent fluxes, e.g., <w c > the mean vertical flux of tracer due to turbulent motion. These turbulent fluxes are modelled in Gaussian models by the gradient-diffusion hypothesis where K z is a vertical diffusivity. If we make further assumptions -- the diffusivities K are independent of position and time; the horizontal velocities U, V are independent of x, y, z, t; and the average vertical velocity W is zero -- the Gaussian solution results. For example, the average concentration field due to a dispersing puff released at (0,0,0,0) is given by: (3) (4) where x, y, zare standard deviations of particle spread in each direction, which are given by the diffusivities (e.g., (t) = 2K t). This type of equation forms the basis of Gaussian models. 2 x x The problem with Gaussian models is that the underlying assumptions are obviously false. If the wind field is dependent on time and space, as it clearly is in the atmosphere, then the Gaussian solution is no longer valid. In practice Gaussian models can provide useful predictions of dispersion. This requires treating the sigmas ( x, y, z) as empirical fitting parameters, determined from dispersion experiments. These are usually simple functions of atmospheric thermal stability and downwind distance or travel time. They have limited generality outside the experimental situation in which they were derived. In reality there should be different functions depending on downwind distance, the height of the release, the height of the C predictions, the height at which U and V are defined, the magnitude of the vertical wind shear, the depth of the boundary layer, etc. It is impossible that the dispersive state of the atmosphere can be universally described with a simple parameter like x. Therefore the usefulness of Gaussian models hinges on the acceptance of very large uncertainties in model predictions. There are more accurate alternatives to Gaussian models. Better solutions to the conservation equation exist, such as allowing the diffusivities K to vary with height. Yet this greater realism leads to much more complex solutions (numerical) which may not be suited to a practical PC based model. Lagrangian stochastic (LS) models seem to offer the most promising 2

6 treatment of dispersion, for both theoretical and practical reasons (Wilson and Sawford, 1996). These models mimic dispersion by numerically tracking particle trajectories. Thousands of independent trajectories are typically created, using a Langevin model that calculates the evolving particle velocity in response to the average windspeed and the level of atmospheric turbulence. These models have a theoretically rigorous foundation, and unlike other types of models are correct at all downwind distances. They also offer great flexibility (e.g., droplets evaporating in flight), and easily incorporate the complexities of the real atmosphere (e.g., they allow arbitrary vertical wind profiles). In the past these models were too slow for operational use: thousands of trajectories need to be created, each created using a timestep of order one second, typically lasting for several hours. However, increased computing capability has made it possible to apply these advanced models to real-time problems. C. MLCD MODEL DETAILS 1. Lagrangian Stochastic Model a) Stochastic Model Details MLCD is based on a first-order Lagrangian stochastic (LS) particle model, where thousands of particles are moved independently in the atmosphere by modelling their velocity. Particle position (x = x, y, z) and velocity (u = u, v, w) are incremented over a timestep dt. i i Velocity is split into an average Eulerian velocity U (U = U, V, W), which varies with position in the atmosphere, and a small-scale fluctuating velocity u (u = u, v, w ): i i i i (5) The change in particle position over dt is simply, (6) In MLCD the velocities U i are provided by a wind model described in Section C2. The change in ui over dt is calculated with a generalized Langevin equation: (7) 3

7 where a i and b i,j are coefficients that depend upon particle velocity and position, and d j is Gaussian random number with zero average and variance dt. Thomson (1987) described two criteria for selecting a and b : consistency with Kolmogorov s similarity theory, and the well-mixed condition. The choice for b i,j is viewed as straightforward: i i,j (8) where i,j is the Dirac delta function (one when i = j, otherwise zero), C 0 is a universal constant (between 3 and 7), and is the turbulent kinetic energy dissipation rate. The two criteria outlined by Thomson do not uniquely define a i for atmospheric turbulence. Thomson gave a particular solution for Gaussian turbulence (i.e., turbulence in which the probability density functions for Eulerian velocities are Gaussian): (9) 2 where V is the Eulerian velocity covariance matrix (i.e., V 1,1 = u = the horizontal velocity -1 variance, V 1,3 = u w = the u-w velocity covariance, etc.), and V is the matrix inverse. The 1 conditional acceleration vector /g is : i a (10) Einstein summation rules apply to both Eq. (9) and (10). This solution for a i is the basis of MLCD. The fully expanded Langevin equations are complicated. We make important simplifying assumptions: we ignore covariance between the velocity components (e.g., u w = 0), we assume local stationarity (no time dependence), we ignore the horizontal inhomogeneity of the atmosphere, and we assume W = 0. Thomson s solution then reduces to: 1 This has been modified from Thomson s original solution for a Langevin model of total velocity u to a model for turbulent velocity u (by eliminating one of Thomson s original terms). i i 4

8 (11) where u, v, and w are the Eulerian velocity variances in the x, y, and z coordinates. In MLCD we assume (for the moment) that C 0 = 3.0. The Langevin model requires specification of the turbulence properties u, v, w and. b) Model Timestep and Particle Reflection The Langevin equation timestep dt should be less than the velocity decorrelation timescale of a tracer particle ( L). This timescale varies with position and the turbulent state of the atmosphere. In MLCD we use a traditional definition of L: (12) where b is the Langevin coefficient. We set dt = 0.05 L, which means the model timestep varies according to particle position and turbulence level. In MLCD particles are tracked in a vertical domain between a reflection height z r just above the ground, to the top of the boundary-layer h. When a particle crosses either boundary it is "bounced" back into the domain, and the sign of the particle velocity fluctuations are reversed (Wilson and Flesch, 1993). An exception is made if a particle moves above h because h is decreasing with time (when MLCD is operated in non-stationary conditions). Then the particle is allowed to remain above h. This particle is then moved with the appropriate average wind, but its fluctuating velocity is assumed zero (no Langevin equation calculations). 5

9 A particle that descends below z actually spends a time * before re-emerging above z, r and during this time it moves a distance *. This behaviour, which Wilson et al. (2001) call r surface waiting, is accounted for in MLCD. During reflection we add the average value of * to particle travel time using the formula given in Wilson et al.: where u* is the friction velocity in the surface layer. Then distance * is added to the alongwind particle displacement. According to Wilson et al. * is given by the product * and the average horizontal velocity below z r ( U zr ). We take U zr as the horizontal velocity at z = z r /2 (not precisely true). Increasing z r significantly reduces MLCD computation time. For example, in a neutrally stable atmosphere, with a roughness length z 0 = 0.1 m, increasing z rfrom 0.1 to 2.0 m decreases computation time by approximately 40%. The potential disadvantage of a large z r is inaccuracy in dispersion predictions near the ground. Since MLCD users are unlikely to be focussed on tracer concentrations immediately near ground we set z = 2 m (if the tracer source is below z the particle release height is set to z ). The value of z can be further increased if decreases in computation time are necessary. r r r r (13) 2. Wind Model An LS model is kinematic and requires knowledge of the wind statistics wherever dispersion is calculated. In MLCD we must provide profiles of the turbulence statistics (,, 2 2 u v 2 w, ) and the two components (U, V) of the mean wind, through the boundary layer (height h). We envision two ways of supplying these properties: internal algorithms and parameterisations, or importing numerical weather prediction (NWP) model fields. At this time MLCD uses only internal routines to give the needed statistics (NWP estimates of windspeed and direction can be externally provided to MLCD, which will then use these to fit a wind solution). 6

10 a) Parameterising the Turbulence MLCD requires four turbulent flow statistics: the velocity variances u, v, and w ; and the turbulent kinetic energy dissipation rate. These statistics vary strongly with height and thermal stratification (given by the Obukhov length L). We assume the horizontal variance components are equal ( = ), and follow the parameterisations of Rodean (1996): 2 2 u v (14) (15) (16) where u* is the friction velocity, h is the depth of the boundary layer, and k is von Karman s constant (0.4). Examples of turbulence profiles are shown in Figures 4-7. These turbulence parameterisations require knowledge of u*, L, and h. The surface-layer scales u* and L can be directly measured at the surface using 3-D sonic anemometers. But MLCD infers u* from average windspeed data provided by the user; and L is either specified by the user, or inferred from windspeed data (see Section C below). The boundary layer depth h is more difficult to know/provide. For our purposes h is the height of the mixed layer (with no mass exchange across h). The value of h is either assumed or calculated from the wind profile observations supplied by the user. When the user supplies four or fewer wind observations (at different heights) MLCD sets h based on stability: in stable stratification h = 300 m; in neutral conditions h = 1000 m; and in unstable conditions h = 1500 m. We suggest these values be 7

11 2 chosen based on local climatology. With more than four wind observations MLCD fits h as part of the average wind model (i.e., height where ground friction no longer influences the wind). b) Average Wind Model An analytical wind model is used to provide the complete vertical profiles of U i (though we anticipate an NWP model could provide these values in the future). The average wind speed (S) in the surface layer adjacent to the ground is well described by Monin-Obukhov (MO) similarity theory: (17) where u* is the friction velocity, k is von Karman's constant, and z 0 is the surface roughness length. The stability correction function depends on height and stratification (given by the Obukhov length L), (18) where x = (1-15 z/l) Above the surface layer the velocity profile is more complicated. An important distinction is the turning of the wind with height. This is idealized by the classic Ekman-spiral wind profile: with increasing height S increases toward its geostrophic value, and the wind is increasingly deflected in the clockwise direction. The Ekman solution gives simple analytical profiles of U and V. Unfortunately the conditions under which the Ekman equations are valid (steady state, barotropic, constant diffusivity, etc.) do not reflect the real atmosphere. In particular the Ekman solution cannot replicate the surface layer wind profile, and above the surface layer the thermal wind causes a departure from the idealised Ekman turning (the thermal wind is the departure of the actual wind from its geostrophic value due to baroclinicity). 2 An examination of mixed-layer heights in Edmonton (Sakiyama et al. 1991) would suggest h = 200 m (stable), 600 m (neutral), and 1000 m (unstable). 8

12 In MLCD we create a more realistic wind profile by matching the MO profile (Eq.17) with an Ekman profile containing a thermal wind component. Above the surface layer we assume a K-theory description of the atmosphere: (19) where U and V are the horizontal velocity components, U and V are the geostrophic wind components, U and V are the thermal wind components, f is the Coriolis parameter, and K is an T T eddy diffusivity (assumed constant). At the top of the surface layer (z s) the MO profile is matched to the Ekman profile, with K in the Ekman given by the MO value at z s (K = u 2 * /( U/ z)). We chose U to be aligned with the surface wind direction. A mathematical solution of Eq. (19) requires six boundary conditions. We chose: g g (20) where h is the depth of the boundary layer. These boundary conditions assure a continuous wind profile with height. The wind solution has the form: (21) 9

13 This requires specification of u*, z 0, L, z s, h, U T, and V T, and then the values of r, i, r, i, U g, and V g are calculated (mathematical details are not given here). Bergstrom (1986) used a combination wind profile similar to this model (although less flexible), and found good agreement with wind observations up to at least z = 1000 m (when U = V = 0). There is a great deal of flexibility in this model: the eight degrees of freedom (when wind direction is added as a parameter) can be used to generate a variety of wind profile shapes. Of course this model, being an idealization, makes no attempt to describe disturbed wind profiles that might be seen over inhomogeneous terrain or near fronts, etc. T T c) Using Observed Winds to Drive MLCD Our average wind model requires specification of u*, z 0, L, z s, h, U T, and V T (and surface wind direction to describe the wind field fully). The turbulence parameterisation requires u*, L, and h. How do we know these eight parameters? Our approach in MLCD is to use actual wind observations at the time of interest to guide us in a fitting exercise. We search through a wide range of the parameter space (i.e., millions of parameter combinations), and for each parameter combination calculate a statistical error between the resulting model wind velocity and the observed winds. The combination that yields the lowest error is used. We note that u*, L, and h values have implications on the turbulence parameterisations in MLCD, and care must be taken not to accept unrealistic values. A wind observation consists of windspeed S and direction at a specific height (giving the velocities U and V). With eight input parameters we can theoretically fit four observations perfectly (within limits imposed by the form of our model). Usually there will not be exactly four observations. A fitting hierarchy is necessary to handle an arbitrary number of observations (from one to 20 heights). We assume the surface roughness (z 0) is known to the user, and do not fit its value. We also require atmospheric stability (L) be an input, although with more than four wind observations we find a best-fit L. i. One wind observation (i.e., S & at one height). This must be within the surface layer, as this observation defines the surface wind direction. The z 0 and L are provided by the user. 10

14 Set: - h is set to 300m (0 < L < 100), 1500 m (-100 < L < 0), or 1000 m ( L 100). - surface layer depth z s is set to 0.1 h - thermal wind components U and V are set to zero. T T Search:- for u* that minimizes error between model and observation. ii. Two wind observations (S & at two heights). One observation must be a surface layer wind. The z 0 and L are provided by user. Set: - h is set to 300m (0 < L < 100), 1500 m (-100 < L < 0), or 1000 m ( L 100). Search - - surface layer depth z s is set to 0.1 h for u* that minimizes error between model and observations. - for thermal wind components U and V that minimize error. iii. Three wind observations (S & at three heights). One observation must be a surface layer wind. The z 0 and L are provided by user. T Set - h is set to 300m (0 < L < 100), 1500 m (-100 < L < 0), or 1000 m ( L 100). Search - for u* that minimizes error between model and observations. - for thermal wind components U and V that minimize error. - for surface layer depth z s that minimizes error. iv. Four wind observations (S & at four heights). One observation must be a surface layer wind. The z 0 and L are provided by user. Search - for u* that minimizes error between model and observations. - for thermal wind components U and V that minimize error. - for surface layer depth z s that minimizes error. - for boundary layer depth h that minimizes error. v. Five or more observations (S & at five or more heights). One observation must be a surface layer wind. The z 0 is provided by user. T T T T T Search - for u* that minimizes error between model and observations. 11

15 - for thermal wind components U and V that minimize error. - for surface layer depth z s that minimizes error. - for boundary layer depth h that minimizes error. T - for Obukhov length L that minimizes error (overriding the input value). T Profile fitting with one, three, and five observations are shown in Figures 4, 5, and 6. d) Time Changing Winds MLCD allows for changing wind conditions over time. The user may supply up to 12 sets of wind observations, each at a different time during the simulation period (or before or after). Average wind profiles (and u*, L, and h) are then calculated for each observation time. MLCD then interpolates between the fitted profiles to get profiles at intermediate times (e.g., input profiles separated by three hours are interpolated to intermediate five minute profiles). The result is a stepwise change in winds between observation times, and between these shorter intervals the winds are assumed stationary. The interval length can be set by the user. A shorter interval more closely mimics a continuous change, while a longer interval gives slightly greater computational efficiency. We suggest five minutes as a good interval length. To create the intermediate profiles we linearly interpolate U and V between observation times. The u*, L, and h are also linearly interpolated over time, and used to create intermediate turbulence profiles. 3. Deposition and Radioactive Decay a) Dry Deposition Dry deposition to the ground results from the chemical and physical interaction of the tracer species with the surface. In MLCD dry deposition is parameterised in standard fashion using a dry deposition velocity (W ). The W is not really a velocity, but an empirical ratio of the d surface deposition rate (D) to the tracer concentration just above the surface (C sfc). d (22) 12

16 The W d is a difficult to measure interaction between the atmospheric flow and the physical, chemical, and biological characteristics of the tracer and deposition surface. We use W d to specify a reflection probability (R): the probability that a particle that impacts the ground is reflected upward (so that 1 - R is the absorption probability). Wilson et al. (1989) showed that: (23) In MLCD we reduced the mass M of each particle at reflection so that: (24) where M 0 is the mass before reflection. Over time the mass of each particle which impacts the ground becomes reduced. Each particle is therefore interpreted as representing an ensemble of real particles, with some of the ensemble deposited upon reflection. The value of W d is an input to MLCD. It typically varies with tracer chemical species, and is estimated from field experiments or models. b) Wet Deposition Wet deposition occurs when a tracer is removed from the air by absorption or collection by water drops (or snow flakes). Each model particle is followed for a timestep T follow (e.g. 300 seconds), and its mass M is reduced according to a wet deposition timescale w: (25) where M 0 is the particle mass at the beginning of the timestep. The deposition timescale depends on the moisture in the atmosphere and the tracer species. We define w (seconds) as: (26) 13

17 -1 where P is the precipitation rate (mm hr ), and S is a dimensionless scavenging coefficient r which varies depending on the chemical species (Draxler and Heffter, 1981). The above formula -1 predicts that an hour of moderate rainfall (P r = 5 mm hr ) will remove approximately 40% of an 5 SO 2 plume (S w = 4.2 x 10 ). Both S w and P r are inputs to MLCD. Each model particle is interpreted as representing an ensemble of real particles, with some of the ensemble washed out during precipitation. w c) Radioactive Decay The radioactive decay of tracer mass is handled similarly to wet deposition. Each model particle is followed for a timestep T follow (e.g., 300 seconds), and at the end of this timestep the particle mass M is reduced according to the radioactive decay law: (27) where M 0 is the particle mass at the beginning of the timestep, and r is the radioactive half-life. 4. Mesoscale Velocity Fluctuations MLCD uses Langevin equations (Eq. 7) to mimic the effect of small-scale turbulence. The magnitude of this microscale turbulence is defined by u, v, and w, and this turbulence covers the spectral range from timescales of less than a second out to the order of 10 minutes. But horizontal velocity fluctuations also occur at larger timescales. Consider a hypothetical record of surface windspeed S and direction, averaged to give a 30 minute interval timeseries. Even under seemingly stationary conditions there would be variability in S and from one 30 minute period to the next. These can be labelled mesoscale fluctuations, and their importance on dispersion is described by Gupta et al. (1997) and Maryon (1998). In some situations it can be important to account for meso-fluctuations. If a single wind observation is used to model several hours of dispersion, then taking into account the dispersion 14

18 caused by these fluctuations may be necessary. In MLCD we have added the option of m m introducing additional fluctuating particle velocities u and v to mimic meso-fluctuations. The total particle velocity is then: (28) m m The changes in u and v over the MLCD timestep dt are modelled with simple Langevin equations: (29) 2 where m is the velocity variance, T m the timescale for meso-fluctuations, and i are random Gaussian numbers (with variance dt). Defining and T is difficult. The extra Langevin equations could be considered as m m accounting for unresolved temporal variation in the wind (as we have done), or the unresolved spatial variation in the wind field, or a combination of both (it is not clear to what extent the two types of variability are related). If we consider and T as representing temporal variability in the wind, then they can be investigated by a timeseries analysis of the winds at an observation site. One such set of observations comes from the ETEX experiment (described in Section D4). A time series of the average velocities U and V, with an averaging interval of 10 minutes, was collected at the release site. We then re-averaged this 10 minute data into time intervals from 0.5 to four hours. Within each of these re-sampled timeseries there will be variability in the underlying 10 minute U and V data, from which we can calculate a and T. m The calculation of m from the re-sampled timeseries was straightforward. First we calculate a standard deviation in the underlying 10 min average U and V observations. We then subtract the variability caused by a time trend in the wind (we want fluctuations about the mean, and not variability caused by a time trend). A composite m is given by summing the squares of the individual standard deviations of U and V. The T m was calculated in a standard way: integrating the autocorrelation function of the individual U and V timeseries within an averaging interval (integrate to the first zero crossing). We also subtract the linear trend in U and V during this calculation. This gives an Eulerian timescale, while we really want a Lagrangian timescale. 15 m m m

19 We treat the two as roughly equivalent, thought the Lagrangian timescale should be larger than the equivalent Eulerian timescale. We expect and T to depend on observation intervals. If a single wind observation m m will represent 30 minutes, then and T will be relatively small (i.e., wind fluctuations at scales m m above the microscale will be of small magnitude, and must be of a timescale less than 30 minutes). But if a single wind observation is to represent a four-hour period, then and T should be larger. Figure 1 shows the calculated m during 36 hours of ETEX. Three averaging periods are displayed (1 hr, 2 hr, and 4 hr), with arbitrarily scaled on u*. As expected and T m did increase as averaging time increased (see Table below). Using this analysis we selected values of and T for use in MLCD, as indicated in the Table below (when only one wind input m m time is used, the 3.5 to 4.5 hour values of and T are used). m m m m m m ETEX data MLCD definitions Averaging Period m/u* T m (min) Input wind interval m/u* T m (min) 1 hour min < 1.5 hours min 2 hour min hours 1 60 min 3 hour min hours min 4 hour min > 3.5 hours min The use of the meso-fluctuations in MLCD can dramatically increase dispersion. In some cases the meso-fluctuations are much more dispersive than the microscale fluctuations (i.e., u, v, w). There is no reason to expect the ETEX values of m and T m to have generality to other situations. Therefore we recommend the meso-fluctuation option be used with caution. 5. Application Details a) Particle Release In MLCD tracer particles are released in a vertical cylinder. The user specifies the bottom and top heights of the column (above ground), and a the horizontal radius. Particles are released 16

20 randomly (uniformly) within the column, and given a random release velocity consistent with the average horizontal velocity and turbulence at the release point. Release times are evenly distributed between the time when the source begins to the end of the emissions. b) Model Input The MLCD inputs are supplied via two datafiles (see Table 1). An example file we call input.dat specifies tracer properties and source details. A second file called winddata.dat shows how atmospheric information is input. In this example the winds at two times are used by the model (at each time there can be up to ten wind observation heights). Table 1. Example of input.dat and winddata.dat file structure. input.dat Definitions FRIEBURG location name H not used emission duration (s), simulation time(s), meso-fluctuations (0=no, 1=yes) N, total tracer mass, W d (m/s), r (days), Sw longitude, latitiude of emission source initial emission column: bottom (m), top (m), radius (m) year, month, day, hour, minute (of initial emission) N = number of model particles; W d = dry deposition velocity = radioactive half life; S = scavenging coefficient r w winddata.dat Definitions FRIEBURG location name 2 number of wind observation times year, month, day, hour, minute (of wind observation) roughness z 0 (m), Obukhov length L (m), precip (mm/hr), no. observ. heights wind observation 1: z, windspeed (m/s), wind direction (deg) wind observation 2: z, windspeed (m/s), wind direction (deg) wind observation 3: z, windspeed (m/s), wind direction (deg) year, month, day, hour, minute (of wind observation) roughness z 0 (m), Obukhov length L (m), precip (mm/hr), no. observ. heights wind observation 1: z, windspeed (m/s), wind direction (deg) wind observation 2: z, windspeed (m/s), wind direction (deg) wind observation 3: z, windspeed (m/s), wind direction (deg) 17

21 c) Model Output MLCD outputs particle position and mass at user defined timesteps (e.g., 30 minutes). At each output time a new output file is created. The file name is based on the calendar time. For example, if the output time corresponds to 2230 on 7 November 2001, and the output timestep is 30 minutes, the output file name is pos _2030" (the prefix pos is supplied by the user). The file format is ASCII. A Cartesian coordinate system is used, with positive x to the east, positive y to the north, and positive z up. Distances are in meters and particle mass is consistent with the units given for tracer mass in the input file. An example output file is given in Table 2. Table 2. Example of the output file structure pos _2030 Definitions particle 1: x, y, z (all in meters), particle mass particle 2: x, y, z (all in meters), particle mass d) Computation Time The computation (CPU) speed of MLCD depends on the simulation duration (e.g., 3 or 12 hours), atmospheric stability, surface roughness, and the speed of the computer. The number of wind observations used to fit the two-layer average wind model also influences CPU time (the greater the number of wind observations the larger the parameter space searched in the fitting routine). Table 3 shows an example of CPU time for different conditions. We tracked 10,000 particles for 12 hours, released instantaneously 10 m above ground. CPU time was separated into the two main components: fitting the average wind model, and particle tracking. A PC with a 1.8 GHz Pentium 4 processor was used for this test. The CPU times in Table 3 should serve only as a rough guide. Different code compilers may create a more or less efficient model, and there is sensitivity to the release conditions and details of the atmospheric state. The code has not been optimized for speed. 18

22 Table 3. The CPU time for the two main components of MLCD for different conditions (10,000-1 particles, z 0 = 0.1 m, S = 2.6 m s at z = 10 m). Particles are tracked for 12 hours. Average Wind Model Particle Tracking Model No. wind observations CPU Time Stability CPU Time s Neutral (L = ) 47.5 s (= 0.8 min) s Unstable (L = -10m) 74.6 s (= 1.2 min) 5* 233 s Stable (L = 10m) 682 s (= 11.4 min) * there is little increase in CPU time for more than five observations D. EXAMPLE SIMULATIONS 1. Accuracy of the Average Wind Model: A Case Study We examined the accuracy of our two-layer model by looking at a set of wind observations from an NWP model. The Global Environmental Multiscale (GEM) model predicts profiles of S and, and u*, L, and h at model gridpoint locations. These observations can be used to test MLCD. While these observations are not real winds, they should be realistic. We extracted 29 GEM datasets over North America and Africa for one model run (7 October 2001). They represent a wide range of atmospheric conditions. The S and observations were taken from the eight lowest model layers (the roughness length z 0 was also known). Two different results are important: 1) how accurately does the MLCD profiles of S and reflect the observations ; and 2) how well does the model deduce h, L, and u*? We conclude that MLCD usually does a good job replicating S and when provided with detailed wind observations. Figure 2 shows three example profiles: a poor fit, and two good fits. The poor fit was unique: in all other cases MLCD was judged to do acceptably well. Figure 3 compares the MLCD predictions of u*, L, and h against the GEM values for all cases. It is not surprising that MLCD correctly infers u*, given the strong relationship between u* and S. The model is less skillful at predicting L, although the predictions (shown as 1/L in Fig. 3) generally 19

23 follow the GEM values except for a couple of outliers. In the most extreme case MLCD infers a very unstable atmosphere while the actual atmosphere is neutrally stable (although the MLCD wind profile is reasonably accurate in that case). The role of L is to provide stability corrections to the wind and turbulence, and it is not to be thought that a 50% error in L would imply a 50% error in dispersion predictions: for example in very short range dispersion (say, 100 m) from a near ground source, dispersion may be almost completely insensitive to L. No simple and general rule can be given regarding uncertainty or error in L, but we regard errors in u * as liable to be more serious. The h predictions from MLCD are less skillful than either u* or L. While there is strong correlation between the two, the values from MLCD are lower. In several cases MLCD gave h < 100 m, while GEM had just one such case. Some disagreement was expected for two reasons. First, the depth of the mixed layer is not thought to be well related to features in the wind profile (MLCD places h at a perceived discontinuity in the wind profile). It is better predicted from the temperature profile. But there is also the likelihood of poor GEM estimates of h. Boundary layer depth is not an important prediction from GEM, and is not an important internal variable. Therefore the quality of the GEM values is uncertain. An indication of this is the suspicious number of cases where GEM predicts h = 1000 m. We conclude that MLCD skillfully replicates the atmosphere in the majority of occasions. In almost all cases the model returns a wind profile that matches the user observations, and returns an accurate prediction of u* and L. The greatest uncertainty is the prediction of h. It is not clear how good the MLCD predictions are. It is worth noting in general that h is a difficult quantity to know. We reiterate that our two-layer wind model does not attempt to accommodate the potential complexity of the real world wind profile, due to surface changes, fronts, etc.: it is no more than a rational, science-based interpolator (and if necessary, extrapolator), from given information. 2. Example Dispersion Predictions We give four examples of simulations using the MLCD model. Three are for stationary conditions (no time variation), and the remaining example is a case of non-stationary winds. In 20

24 each case a different atmospheric stratification is used (neutral stability, stable, unstable), with a different number of wind observations used to drive the model. a) Neutral Atmosphere In this example a single wind observation (z = 10 m) is used to drive the MLCD simulation. The user specifies a roughness length z 0 = 0.1 m, and estimates the atmosphere is in a state of near-neutral stability (e.g., L = 1000 m). Figure 4 shows how MLCD has fit wind profiles to this observation. Without upper air wind observations the model assumes a classic Ekman layer turning with height. We then simulated a near-surface point source that emits tracer for one hour in this atmosphere. Figure 4 gives the position of 1000 particles at 0.5, 2, 3.5, and 6 hours after emissions began. Notice how the tracer cloud initially moves with the surface wind to the northeast. But as time increases there is a more easterly motion: as the plume expands in height it becomes advected by the more westerly upper winds. From the vertical cross section we see the plume does not become vertically well-mixed until after 3.5 hours. This rather long mixing time is due to the weak turbulence (i.e., u* is small). Notice the plume is tilted toward the east with increasing height. This is the result of strong wind shear and slow vertical mixing. We can use this example to see if the MLCD dispersion predictions are reasonable. The standard deviations of particle position in each coordinate ( x, y, z) are calculated at different times. These sigmas can be compared with Gaussian model algorithms. We instantaneously released 1000 model particles into the neutral atmosphere at z = 500 m, and calculated a horizontal puff sigma r as: Many Gaussian models convert plume-size-with-distance to puff-size-with-time by defining an 3 "equivalent distance" x for travel time (x = S t). We cite below the Pasquill-Gifford (P-G) equiv equiv (30) 3 Although there is in reality no such convenient equivalence between time and distance of travel in the atmosphere, owing to shear in the advecting velocity components. In calculating x we use S at z = 0.5 h. equiv 21

25 sigma (Green et al., 1980) for neutral stability (31) as well as the following formulation (from Batchelor): (32) where is the turbulent kinetic energy dissipation rate (Hanna et al. (1982) suggest puff models use this latter formulation). Comparisons of r from MLCD with these empirical formulae are shown in Table 4, and indicate that MLCD is plausible (by this criterion: consistency with empirical formulae for puff size), and the magnitude of computed horizontal dispersion is within the range of typically accepted values. We note however, that the Gaussian values of r should not be taken as truth. Table 4. Comparison of puff sigmas from MLCD and two Gaussian predictions. travel time MLCD Pasquill-Gifford Hanna et al. 1 hour 1,556 m 1,033 m 1,278 m 3 hour 3,896 m 2,679 m 6,640 m 6 hour 6,530 m 4,883 m 12,779 m r b) Unstable Atmosphere In this example three hypothetical wind observations are used to drive MLCD. These are from an unstable atmosphere (e.g., L = -10 m). Figure 5 shows the wind profiles created by MLCD, which accurately fits the observations. The wind at the surface is from the northwest and exhibits a turning with height opposite to the Ekman spiral (requiring a non-zero U and V ). In this atmosphere we simulated a near-surface instantaneous point source. Figure 5 gives the position of 1,000 particles at 0.5, 2, 3.5, and 6 hours after emission. The location and shape T T 22

26 of the dispersing plume are reasonable. Near-surface particles move slowly to the southeast, while higher particles move quickly in a more easterly direction. This stretches the plume along an east-west axis, while the plume centre moves to the east-southeast. The plume becomes vertically well-mixed by 0.5 hours. This rapid vertical growth is due to the strong turbulence. Notice that the plume is not tilted with height, because of the strong vertical mixing. c) Stable Atmosphere In this example five hypothetical observations are used in an MLCD simulation. The atmosphere is very stable (L = 10 m). Figure 6 shows the wind profiles created in MLCD. The model does a reasonable job of fitting the observations: is off by about 5 degrees at two points, but S is well reproduced. Because there were five wind observations the MLCD model determined a best-fit L different from observed (25 m). The wind exhibits strong Ekman turning with height. We used MLCD to simulate dispersion in this atmosphere due to a near-surface point source having a duration of two hours. Figure 6 gives the position of 1000 particles at 0.5, 2, 3.5, and 6 hours after emission. The appearance of the plume is much like the neutral case illustrated earlier. The plume initially moves northeast with the surface wind, then later arcs toward the east following the wind aloft. Surprisingly the plume is more horizontally dispersed in this stable atmosphere than the neutral example. This is due to the larger wind shear in the stable case: horizontal dispersion is dominated by differential advection rather than turbulence intensity. The strong shear, plus weak turbulence, leads to a plume that is very tilted with height. Vertical mixing is slow, and by six hours the plume is still far from well-mixed. d) Non-Stationary Conditions Figure 7 shows wind profiles from an atmosphere in transition from stable southwesterly flow to unstable northwesterly flow. These four profiles, each consisting of four observation heights, were supplied to MLCD. The model does a very good job of fitting these observations. Estimated boundary layer depth h increases from 100 to 700 m over the period. 23

27 The MLCD model was then used to simulate dispersion during this transition period. A near-surface point source emitted tracer shortly after the first observation time, for a duration of one hour. Figure 7 shows particle positions 0.5, 2, 3.5, and 6 hours after emissions began. After 0.5 hours the tracer particles have travelled in a stable environment, moving near the ground in low turbulence. The result is a narrow plume moving northeast. As time elapses the atmosphere becomes less stable, and the winds become more westerly. The strong wind shear begins to smear the plume toward the east. Later the atmosphere is very unstable with lots of turbulence and little wind shear. This creates a more circular plume, which moves to the southeast with the now northwesterly flow. Qualitatively this plume behaviour seems reasonable. E. VALIDATION STUDIES 1. Very Short Range The MLCD model is built from the same LS framework used by many others to successfully simulate dispersion at distances less than 1 km (e.g., Wilson et al. 1981). A feature of LS models is their superiority at simulating dispersion at short ranges, where the application of Gaussian models is less accurate. The Langevin model upon which MLCD is based was first calibrated on the Project Prairie Grass data short-range data. MLCD should therefore 4 unquestionably be valid when used at very short-range (say, up to a distance of 1 km). 2. Hawaii LROD Experiment The Long-Range Overwater Diffusion (LROD) experiment was designed to provide information on alongwind diffusion at intermediate to long ranges. This experiment was 4 However we must note the proviso that MLCD assumes an undisturbed wind field, and so should not be used to simulate short-range spread from a source in the immediate wake of a building, or a hill, etc. Neglect of mild terrain complexity can be expected to be less serious for longer range dispersion ( km), due to the fact that the puff or plume is largely travelling remote from the ground, where disturbances are most severe. The case of mountainous terrain is a different story, and not addressed by MLCD. 24

28 conducted over the ocean near Hawaii in July 1993 (Bowers et al., 1994). Over several days there were 13 instantaneous crosswind line releases of sulfur hexafluoride (SF 6) gas, made from an aircraft 90 m above the ocean. The 100 km crosswind tracer line was tracked beyond 100 km from release using an aircraft-mounted SF 6 analyzer. Concentration was measured in alongwind transects near the midpoint of the tracer cloud, unaffected by diffusion from either end of the cloud. The LROD data set includes more than 230 observations of the downwind center of mass of the tracer cloud (x 0) and the standard deviation of the alongwind concentration distribution ( x). Meteorological measurements were made from ship and aircraft. The z 0, u*, and L were estimated from empirical formulae based on windspeed and air-ocean temperature differences. Boundary layer depth h was determined from aircraft measurements of SF 6 concentration far downwind of release. MLCD was used to simulate seven of the LROD releases (all of the releases having a windspeed observation from a ship). For each simulation we released 5000 model particles at the height of the aircraft release. The average downwind distance and the standard deviation of particle position along the sampling transect line was calculated. Particles between z = 50 to 250 m were sampled to correspond to the 150 m height of the aircraft transect. Wind profiles (S and ) were measured for each run using the ship and balloon observations. Eight observation heights were used as input to MLCD. The balloon observations give a surface S and, and this was taken to represent a height z = 25 m above the ocean. Surface roughness (z 0) was given in the LROD report. The LROD experiment presents a test not only of the MLCD dispersion predictions, but of the MLCD predictions of u*, L, and h. Figure 8 shows these predictions versus the LROD estimates. The most noticeable result was 30% overprediction of u*. Further examination revealed an inconsistency in the LROD data: S at z = 10 m (from ship) was not reconcilable with the reported u*, z 0, and L. A reduction in z 0 by a factor of 10 is needed to give agreement. In the LROD experiment z 0 was calculated from formula given in Hosker (1974), which relates z 0 to S. But because z 0 is an empirical parameter whose purpose is simply to give an accurate S profile, it makes sense for us to use a z 0 that agrees with the observed S. Hereafter our results apply to the LROD data with the reported z 0 reduced by

29 The MLCD model predicts a more unstable atmosphere than was observed (i.e., MLCD gives 1/L as more negative). This may be caused by the small magnitude of vertical wind shear ds/dz shear reported near the surface. In an MO profile a small wind shear is the result of an unstable atmosphere. The accuracy of h predicted with MLCD was deemed acceptable. On average MLCD underestimated h by only 5%, although the average magnitude of the difference was 39%. There was one outlier case, which if ignored gave an average magnitude of difference in MLCD predictions of 25%. Figure 9 shows the results of the MLCD simulation of Trial 2, which was a typical result. The model gives a reasonable reproduction of the actual wind field except very near the surface, where wind shear is overestimated. The model accurately calculates the downwind rate of cloud advection dx 0 /dt. Alongwind spread of the tracer cloud x is overpredicted by the model. In the standard configuration x is overpredicted by a factor of two. Figure 9 also illustrates MLCD results for two more trials, Trial 3 and Trial 6, the best and the worst of the LROD simulations. The overprediction of alongwind spread is the dominant feature of the LROD predictions. Figure 10 shows the ratio of predicted to observed x over all seven trials. In the standard configuration MLCD overestimated x by a factor of What is the cause of this overprediction? Inaccurate S and profiles may play a role (i.e., overestimation of ds/dz). Smith (1965) considered dispersion from a continuous point source in the presence of wind shear (U = z). Particle spread was due to three components: a) cross wind velocity fluctuations u, b) vertical velocity fluctuations in the presence of mean wind shear, and c) and u w velocity correlation. At large travel times (T >> L, the Lagrangian timescale): (15) The effect of wind shear (term b) quickly dominates (notice u w correlation, which must be opposite in sign to, acts to reduce dispersion). If MLCD overpredicts wind shear, x will be overpredicted. To see if inaccuracy in S and explains our overprediction of x, we substituted a more accurate wind model in MLCD. This model consists of a 20 m deep MO surface layer, with a linear interpolation between U and V observations above this (using reported L, u*, and h 26

30 to set the turbulence). This can more accurately describe the S and observations. The use of this wind model does improve MLCD predictions, but only slightly. The ratio of predicted to observed x now averages 2.09 (compared with the previous 2.36). Overprediction of x may also be partly due to overestimation of the horizontal velocity fluctuations u and v. If we set u = v = 0 we do reduce the overprediction of x from 2.36 to If we combine this with the linear-interpolation wind model, the overprediction is still a significant 1.8. Another possible explanation for model overdiffusion is the neglect of the velocity covariance u w in the Langevin model. Equation 15 demonstrates the effect of u w is to suppress x. But our experience has been that covariance effects are generally of secondary importance, and will not explain the large overprediction. From the LROD experiment we conclude that MLCD does well at calculating the average wind properties of the atmosphere (except very near the surface). The model also accurately predicts the downwind advection of the tracer cloud. Horizontal dispersion is less accurately predicted. It is not clear why this occurs. Overprediction of dispersion here is not unique to MLCD. In Fig. 9 we display predictions of x from the Pasquill-Gifford formulation for three LROD trials (Green et al., 1980). The P-G formula substantially overestimates x. 3. Great Plains Experiment The Great Plains mesoscale tracer experiment (GPEX) was carried out in July 1980 by the Air Resources Laboratory of the U.S. National Oceanic and Atmospheric Administration (Moran and Pielke, 1996). The experiment was conducted over the homogeneous, slightly sloping terrain of the south-central United States. Perfluoromonomethylcyclohexane (PMCH, C7F 4) was released near ground from an open field in Norman, Oklahoma, on 8 July Tracer release began at 1900 UTC (1300 local time) and lasted for 3 h, with a total of 192 kg of PMCH released. This took place under quasi-steady, anticyclonic, warm-season synoptic conditions (during a drought). Ground level concentration was measured along an arc 100 km to the north of NSSL (another arc was 600 km to the northeast). Seventeen PMCH samplers were placed along the arc at 4-5 km intervals. Each sampler collected ten consecutive 45-min samples beginning at 2100 UTC 8 July. 27

31 In the MLCD simulation of this experiment we used 500,000 particles to simulate the tracer release. Sampler concentrations were calculated in the model using receptor volumes with a radius of 2500 m, extending from the surface to a height of 100 m. Meteorological information was extracted Moran and Pielke (1996), with some additional assumptions about surface conditions: S -1 Surface winds at Norman were south-southwesterly at 4 m s, and the sky was clear -1 during the tracer release.... We set S = 4 m s, = 200 deg at z = 10 m. S The terrain in central Oklahoma is open and agricultural. We assume z = 5 cm, a typical value for open farmland in the summer (e.g., Stull, 1988). 0 S S S -2 We assumed a sensible heat flux of 500 W m (reasonable for midday, mid-summer, dryland conditions). This combined with the surface S translates to L ~ -10 m. Windspeed and direction at eight heights aloft were extracted from the nearby Oklahoma City radiosonde observations at 0 UTC on 9 July. These extended to z = 3000 m. Ferber et al. (1981) observed boundary layer depths h = m based on balloon measurements taken at Norman on 8 July. We assume h = 2300 m. The GPEX wind profile was surprisingly complicated. At midday during the release the winds were from the southwest at the surface, from the southeast at 200 m above ground, and back to southwest higher aloft. This turning of the wind caused problems for the MLCD two-layer wind model. Figure 11a shows the GPEX wind profile generated by MLCD. The model does a poor job of creating a realistic atmosphere. The model cannot mimic the profile of wind direction, missing the southeast swing that occurs at approximately z = 200 m. In trying to match this profile MLCD returns a stable atmosphere with the boundary layer depth h = 25 m. This is not believable, and does not agree with meteorological observations. When MLCD simulates dispersion with this unrealistic atmosphere the result is predictably poor. The plume moves off to the northeast, is very narrow, with high surface concentrations within the plume. This does not reflect the actual observations, which show the plume moved slightly west of north (as is shown later), with surface concentrations less than a 28

32 tenth that predicted by MLCD. GPEX provides an example where the unsupervised use of MLCD does not produce realistic results. To focus on the dispersion routine of MLCD (as opposed to the micro-meteorological pre-processor algorithm, which establishes the model atmosphere from given data), we turned to a linear-interpolation strategy that more accurately reflected the observations. As described earlier, this strategy combines a shallow MO surface layer (here 150 m deep) with simple linear interpolation (of U and V) between observations above 150m (using the assumed L, u*, and h to set the turbulence). This simple-minded procedure (whose theoretical content is null!) more accurately reflects the observations (Fig. 11b). Figure 12a shows the simulated tracer plume using this more accurate wind profile. The model accurately shows the plume moving slightly west of north, crossing the sampling transect along the western edge of the sampling line. Predicted versus observed sampler concentrations are shown in Figure 13. The following results are observed: 1) The model plume arrives at the sampling line earlier than observed (during the 21:00-21:45 UTC period). Given the sampling intervals it is not possible to know whether the model plume arrived one minute before the actual plume, or 90 minutes before. 2) The simulated plume moves further west than the actual plume. Better model agreement occurs if we shift the sampler predictions east by 5 km. 3) The simulated tracer mass passing the sensor line (time integrated, cross-wind integrated concentration, Stations 11-21) was 86% of observed (Stations 12-22). -1 4) The maximum predicted sampler concentration was 3500 fl L at Station 12. Maximum -1 observed concentration was 5900 fl L at Station ) The maximum predicted ground level exposure (GLE) was fl h L (at Station 12), while the maximum observed GLE was 7800 fl L-1 (at Station 13). 6) The standard deviation of particle position across the transect line ( y) at the time of maximum concentration was 5880 m. The actual y calculated by Moran and Pielke (1996) was 8200 m. 29

33 7) The model plume departs the sampling line too late. Given the sampling intervals it is not possible to know whether the model plume departed one minute after the actual plume, or 90 minutes after. Overall the MLCD simulations are reasonably good. The model places the plume centerline within 5 km of its true position (at 100 km distant), and gives surface concentrations, exposures and mass predictions near their proper magnitude. The most important deficiency was that MLCD was not dispersive enough in the cross-wind direction: the model plume was too narrow compared with the observations (although the model plume was overly dispersed in the alongwind direction!). An explanation for this may be the neglected mesoscale velocity fluctuations. Figure 12b illustrates the simulated GPEX plume when meso-fluctuations are added to MLCD (as described in Section C4). The crosswind dimensions of the plume are noticeably wider, with y at the transect line increased from 72% to 93% of observed (during the time of maximum concentrations). This improves MLCD accuracy in several predicted quantities. Figure 14 shows the crosswind integrated concentration (CWIC) and the total ground level exposure (GLE) for the standard MLCD results, and the results with meso-fluctuations added (model plumes shifted 5 km to place the plume centerline better). The addition of mesofluctuations leads to impressive improvements in the GLE estimates. For example, the maximum predicted exposure at the transect line is within 10% of observed. The addition of mesofluctuations did not alter the fact that the simulated plume is shifted too far to the west ( by 5 km), and that the plume arrives at the sampling location too early and leaves too late. The MLCD model accurately predicted GPEX dispersion when supplied with a realistic wind field. However, the failure of the MLCD wind model to mimic the actual wind is a concern. It shows limits to the flexibility of the two-layer model, and suggests that MLCD requires intelligent supervision to guarantee accurate simulation. What should the user do when confronted with a failure of the wind model? Ideally the user would recognize the complex turning of wind from SW to SE to SW was causing problems, and would modify the input profile. In this particular situation, where we are interested in long range transport, details of the surface layer winds are not so important as winds higher in the boundary layer. Therefore we 30

34 would suggest that the wind direction in the lowest two levels be set to 180 degrees to agree with the winds aloft. If this were done, the MLCD two-layer wind model would return a more realistic profile of S and, give h = 1800 m in a moderately unstable atmosphere, and give a realistic simulation of dispersion. The result would be a simulated plume shifted only 5 km to the east of the observed plume, a maximum predicted concentration of 81% of observed, predicted exposures within a factor of two, and a plume width 80% of observed. 4. ETEX experiment The European Tracer EXperiment (ETEX) was a field study of dispersion over continental scales. There were two controlled releases of Perfluoromethylcyclohexane (PMCH) in western France, succeeded by the monitoring of surface PMCH concentration over Europe for many days after release (Van Dop et al., 1998). We use MLCD to stimulate the first of the ETEX releases, which occurred 35 km west of Rennes in northwest France, starting at 1600 UTC on 23-1 October 1994, and lasting for 12 h. The release rate was 7.95 g s. Three-hour average PMCH concentration was measured at 168 surface locations covering most of Europe, with sampling lasting until 96 hours after the start of the release. We focus on predicting concentration at five sampling locations within 500 km of the release site (F21, F02, F19, F03, and F20), during the 18 hours after emissions began. Only one station (F21) was within 100 km of the release site. In the MLCD simulation we used 250,000 particles to simulate the tracer release. Sampler concentrations were calculated in the model using receptor volumes with a radius of either 2500 m (F21) or m (all others), and extending from the surface to a height of 100 m. Meteorological information came from three sources: a sonic anemometer at the release site (z = 18 m); radiosonde profiles from balloons released at the release site; and sodar profiles taken at the release site. These data provided the height profiles of S and used with MLCD. We assumed a roughness length z 0 = 0.2 m. Our simulation lasted 18 hours. Weather conditions changed appreciably during this period, with both diurnal changes and larger scale synoptic changes. This was a more complex situation than in either GPEX or the LROD experiment. We used the MLCD capability to input a 31

35 timeseries of wind profiles, taken at 15, 19, 23, 03, and 07 UTC (on 23 and 24 October). These were created from a combination of sonic anemometer observations, the radiosonde data at 15, 19, 23, and 03 UTC, and sodar data at 07 UTC. Figure 15 shows these five input profiles, and the corresponding MLCD generated profiles. Wind variability during the simulation period is large, with changes in windspeed and wind direction. The MLCD two-layer wind model does a good job of fitting the observations. The simulated ETEX plume is shown in Figure 16. During 18 hours the plume moves initially northwest, then is advected southeast, then moves northwest again. When we compare predicted concentration with the ETEX observations we see mixed results (Figure 17): 1) MLCD properly passes the plume over the nearest station F21 (21 km from the release site), and at the appropriate times. The time integrated concentration (exposure) at F21 is roughly twice the observed, which we consider a good result. Both the predicted and measured concentration at F21 vary strongly between the three-hour observations, as the plume moves back and forth over the station. However the correlation between the predicted and observed concentration for these periods is weak. We conclude that at F21 the model does well at describing the big picture, but less well at the details. 2) The model is less accurate in predicting concentration at station F02 (160 km from the release site). Observations show tracer material at F02 throughout the simulation period, while the model plume does not arrive until after 14 hours. This behaviour is due to the changing wind direction. Initially MLCD moves material northeast toward F02, but just before reaching the site the plume is steered southeast. After 14 hours the plume finally passes over the station as the winds shift again. Because the model plume initially misses F02, the simulated exposure is underpredicted by a factor of ) Predictions at F19 (340 km from the release site) and F20 (470 km from release site) suffer from the same deficiencies observed at F02. The simulated plume never reaches F19 or F20 as it has been directed more southeast. 4) MLCD does well at predicting concentration at F03, which is surprising as it is 415 km from the release site. The simulated plume arrives only slightly late, the concentration 32

36 magnitudes are accurately predicted, and the simulated exposure is close to the observed. The position of F03, straight east of the release site, makes predictions less sensitive to the timing of the change in wind direction from southwest to northwest back to southwest. Can MLCD performance be improved by adding meso-fluctuations? Figure 16b shows the simulated plume with meso-fluctuations added. The change in plume appearance is dramatic, being much broader in the crosswind extent. This broader plume does improve the predictions at most of the stations (Fig. 17 and 18). While the improvement is not so apparent at F21 (modelled exposure is slightly more accurate), it is at F02 and F19. A more accurate simulation of plume arrival time at F03 is also the result of adding meso-fluctuations. Including meso-fluctuations is clearly beneficial in ETEX. This case illustrates the potential for MLCD inaccuracy at long ranges. In ETEX the tracer cloud moves northeast for a much longer distance than MLCD predicts. After release MLCD quickly changes the plume movement to southeast, as wind direction at the release site indicates. Because MLCD assumes horizontal homogeneity, this change in wind direction occurs everywhere. In reality it is more likely that the change proceeds as a wave across the region (as synoptic patterns are advected from west to east). In this situation the leading edge of the plume would move more persistently northeast, and not experience the wind direction change until after it occurs at the release site. This would explain why the actual plume quickly reaches F02, then F19, then F20, while the model plume does not. We conclude that MLCD inaccuracy in predicting tracer behaviour at the distant sites F02, F19, and F20 is due to a combination of the time-variability of the winds over the region (i.e., synoptic scale changes in the wind field), the MLCD assumption of horizontal homogeneity in the winds across the region, and the use of wind observations distant from the prediction locations. F. SUMMARY AND CONCLUSION The MLCD model represents a substantial improvement in sophistication over traditional Gaussian models of dispersion. The model uses the advanced Lagrangian stochastic approach to 33

37 mimic turbulent dispersion, and is designed for problems from zero to 12 hours after a hazardous release, and at distances up to 150 km from release. Test cases showed the model runs quickly on a desktop computer. The major advantage of the MLCD approach is large flexibility in calculating realistic average wind profiles, which when coupled with a particle model, allow for accurate simulation of the effect of wind shear in advecting and dispersing a tracer cloud. Three field experiments were used to examine the performance of MLCD, focussing on dispersion at distances from 10 to 500 km downwind of a release (the accuracy of the Lagrangian approach over shorter ranges has been well documented). Based on simulation of these experiments we conclude that: 1) In the large majority of cases MLCD will accurately depict the wind conditions in the boundary layer. 2) In a minority of cases the two-layer wind model in MLCD will fail, returning obviously inaccurate estimate of boundary layer conditions. We observed this in the GPEX experiment, and in one of the 30 trial profiles extracted from GEM. These failures were obvious, and led to unrealistic simulations of dispersion. We therefore recommend that MLCD be supervised to ensure realistic results. 3) Predictions of tracer dispersion should be good at distances below 100 km (when the twolayer model correctly predicts the atmospheric state). In both the LROD and GPEX experiments the model did well at predicting the movement of the plume centerline at this distance range. And in GPEX, and the nearest ETEX station, the surface concentration predictions were accurate. 4) At distances beyond 100 km the model will be less accurate in simulating the behaviour of a tracer cloud. This was observed in the ETEX experiment. We concluded that this inaccuracy was caused by the increasing departure from a horizontally homogeneous wind field as the MLCD domain size increased. 5) Two experiments show that MLCD overpredicted alongwind dispersion. In the LROD experiment the alongwind spread in the tracer cloud was overpredicted by roughly a factor 34

38 of two. In GPEX the model predicted a too-early arrival of the tracer plume at downwind locations, and a too-late departure. 6) The importance of including horizontal meso-fluctuations was not conclusively shown. In one experiment (LROD) the model predictions were worsened by including these fluctuations, while in the others (GPEX and ETEX) the predictions were improved. The difference may be due to the experiment location: vast horizontally homogenous ocean (LROD) versus the less homogenous and thermally unstable land surface (GPEX). One difficulty in assessing this issue is the likelihood that our simple estimates of mesofluctuation variance and timescale are not valid for all conditions (e.g., locations, heights, synoptic conditions, etc.). Overall we judge the MLCD model plausible. When the model is supplied a set of wind observations, it will most often accurately simulate dispersion in that atmosphere. And when the model does fail, due to failure of the two-layer wind model to return a realistic boundary layer profile, a simple alteration of the input wind profile will generally fix the problem and give realistic dispersion predictions. REFERENCES Bergstrom, H A simplified boundary layer wind model for practical application. J. Climate Appl. Meteor., 25: Bowers, J.F., G.E. Start, R.G. Carter, T.B. Watson, K.L. Clawson, and T.L. Crawford Experimental design and results for the long-range overwater diffusion (LROD) experiment. Report DPG/JCP-94/012, Joint Contact Point Directorate, U.S. Army Dugway Proving Ground, Dugway, Utah van Dop, H., Addis, R., Fraser, G., Giarardi, F., Graziani, G., Inoue, Y., Kelly, N., Klug, W., Kulmala, A., Nodop, K., Pretel, J., 1998, ETEX: A European tracer experiment; observations, dispersion modelling and emergency response. Atmos. Env., 32 :

39 Draxler, R.R., and J.L. Heffler (1981). Workbook for estimating the climatology of regionalcontinental scale atmospheric dispersion and deposition over the United States. NOAA Technical Memorandum ERL ARL-96, Air Resources Laboratories, Silver Spring, Maryland. Ferber, 0. J., K. Telegadas, J. L. Heffter, C. R. Dickson, R. N. Dietz, and P. W. Krey, 1981: Demonstration of a long-range atmospheric tracer system using perfluorocarbons. NOAA Tech. Memo. ERL ARL-101, Air Resources Laboratory, National Oceanic and Atmospheric Administration, Silver Spring, MD, 74pp. Green, A.E., R.P. Singhal, and R. Venkateswar, Analytic extensions of the Gaussian plume model. JAPCA, 30: Gupta, S., McNider, R.T., Trainer, M., Zamora, R.J., Knupp, K., and Singh, M.P., Nocturnal wind structure and plume growth rates due to inertial oscillations. J. of Appl. Meteor. 36: Hanna, S.R., G.A. Briggs, and R.P. Hosker (1982). Handbook on atmospheric dispersion. U.S. Department of Energy Document DOE/TIC 11223, Office of Heath and Environmental Research. Hosker, R. P., 1974: A comparison of estimation procedures for overwater plume dispersion. In Proceedings of the Symposium on Atmospheric Diffusion and Air Pollution. American Meteorological Society, Boston, MA, Maryon, R.H., Determining cross-wind variance for low frequency wind meander. Atmos. Environ. 32, Moran, M.D., and R. A. Pielke. Evaluation of a mesoscale atmospheric dispersion modeling system with observations from the 1980 Great Plains Mesoscale Tracer Field Experiment. Part I: Datasets and meteorological simulations. J. Appl. Meteor., 35: , Rodean, H.C., Stochastic Lagrangian Models of Turbulent Diffusion. Meteorological Monographs No. 48, American Meteorological Society. 84 pp Sakiyama, S.K., R.H. Myrick, R.P. Angle, and H.S. Sandhu (1991). Mixing heights and inversions from minisonde ascents at Edmonton/Ellerslie. Alberta Environment, Edmonton, Alberta, 59 p. Smith, F.B., The role of wind shear in horizontal diffusion of ambient particles. Quart. J. R. Meteor. Soc. 91:

40 Stull, R.B., An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, 666 pp. Thomson, D.J., Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech., 180: Wilson, J.D., F.J. Ferrandino, and G.W. Thurtell (1989). A relationship between deposition velocity and trajectory reflection probability for use in stochastic Lagrangian dispersion models. Agric. Forest Meteorol. 47: Wilson, J.D., and T.K. Flesch, Flow boundaries in random flight dispersion models: enforcing the well-mixed condition. Journal of Applied Meteorology 32: Wilson, J.D., T.K. Flesch, and R. D'Amours Surface delays for gases dispersing in the atmosphere. J. of Applied Meteorology. 40: Wilson, J.D., and B.L. Sawford (1996). Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere. Boundary-Layer Meteorol. 78: Wilson, J.D., Thurtell, G.W. and Kidd, G.E.: 1981, Numerical simulation of particle trajectories in inhomogeneous turbulence--iii. Comparison of predictions with experimental data for the atmospheric surface-layer. Boundary-Layer Meteorol. 21,

41 m Figure 1. Standard deviation of mesoscale velocity fluctuations (scaled on the friction velocity u*) at the ETEX release site during a 36 hour period. The data were collected during October 1994 from a sonic anemometer located in northwest France, at a height of z = 18 m. The different symbols represent different averaging intervals. 38

42 Figure 2. Three examples of profile fitting using the MLCD two-layer wind model. Windspeed (S) and wind direction (dir) data (extracted from GEM) are given by the symbols in the left 2 2 graphs. The best-fit MLCD profiles are given by the lines. MLCD velocity variance ( u and w ) profiles are given on the right. GEM values and MLCD predictions of friction velocity u*, Obukhov length L, and boundary layer depth h are given in the adjacent panels. 39

43 Figure 3. Comparison of GEM observations and MLCD estimates of friction velocity (u*), Obukhov length (L), and boundary layer depth (h). These are for 29 profiles extracted from GEM model gridpoints over North America and Africa, for a model run on 7 October The dashed line is a 1:1 line. 40

44 Observations: -1 z (m) S (m s ) Dir (deg) z 0 = 0.1 m, L = 1000 m Fitted Wind Model: u* = 0.2 m s -1 L = 1000 m h = 1000 m, z s = 100 m surface wind direction = 221 deg -1 U g, V g = 4.89, m s (Ug to sfc. wind) -1 U, V = 0, 0 s (U to sfc. wind) T T T Emission Source: Point source at z = 10 m Emission began at t = 0 Emission ended at t = 1 hr Figure 4. The top panel shows wind profiles generated by MLCD for a neutrally stable atmosphere. The average windspeed (S) and wind direction (dir) observations are given by symbols, and the MLCD best-fit profiles are given by lines. The MLCD profiles of velocity 2 2 variance ( u and w ) and dissipation rate ( ) are given beside. The lower panel gives the MLCD predictions of particle dispersion in this atmosphere at four times after tracer emission began. 41

45 Observations: z (m) -1 S (m s ) Dir (deg) z 0 = 0.1 m, L = -10 m Fitted Wind Model: u* = 0.45 m s -1 L = -10 m h = 1500 m, z s = 75 m surface wind direction = 326 deg -1 U g, V g = -0.69, m s (Ug to sfc. wind) -1 U, V = , s (U to sfc. wind ) T T T Emission Source: Point source at z = 10 m Emission began at t = 0 Emission ended at t = 0 hr Figure 5. The top panel shows wind profiles generated by MLCD for an unstable atmosphere. The average windspeed (S) and wind direction (dir) observations are given by symbols, and the 2 2 MLCD best-fit profiles are given by lines. The MLCD profiles of velocity variance ( u and w ) and dissipation rate ( ) are given beside. The lower panel gives the MLCD predictions of particle dispersion in this atmosphere at four times after tracer release. 42

46 Observations: z (m) -1 S (m s ) Dir (deg) z = 0.1 m, L = 10 m 0 Fitted Wind Model: u* = 0.2 m s -1 L = 25 m (overriding observation) h = 400 m, z s = 25 m surface wind direction = 207 deg -1 U g, V g = 10.37, m s (Ug to sfc. wind) -1 U, V = , 0 s (U to sfc. wind) T T T Emission Source: Point source at z = 10 m Emission began at t = 0 Emission ended at t = 2 hr Figure 6. The top panel shows wind profiles generated by MLCD for a stable atmosphere. The average windspeed (S) and wind direction (dir) observations are given by symbols, and the MLCD best-fit profiles are given by lines. The accompanying MLCD profiles of velocity variance ( 2 u 2 and w ) and dissipation rate ( ) are given beside. The lower panel gives the MLCD predictions of particle dispersion in this atmosphere at four times after tracer release began. 43

47 Figure 7. Top panel gives time series of four hypothetical wind profiles. The average windspeed (S) and wind direction (dir) observations are given by symbols, and the MLCD best-fit profiles are 2 2 given by lines. The accompanying MLCD profiles of velocity variance ( u and w ) and dissipation rate ( ) are given beneath. The lower panel gives the MLCD predictions of particle dispersion in this atmosphere at four times after a tracer release. 44