High-Resolution Large-Eddy Simulations of Scalar Transport ...

High-Resolution Large-Eddy Simulations of Scalar Transport in AtmosphericBoundary Layer Flow over Complex Terrain

TAKENOBU MICHIOKA

Environmental Science Research Laboratory, Central Research Institute of Electric Power Industry, Chiba, Japan

FOTINI KATOPODES CHOW

Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California

(Manuscript received 8 January 2008, in final form 28 April 2008)

ABSTRACT

This paper presents high-resolution numerical simulations of the atmospheric flow and concentrationfields accompanying scalar transport and diffusion from a point source in complex terrain. Scalar dispersionis affected not only by mean flow, but also by turbulent fluxes that affect scalar mixing, meaning thatpredictions of scalar transport require greater attention to the choice of numerical simulation parametersthan is typically needed for mean wind field predictions. Large-eddy simulation is used in a mesoscalesetting, providing modeling advantages through the use of robust turbulence models combined with theinfluence of synoptic flow forcing and heterogeneous land surface forcing. An Eulerian model for scalartransport and diffusion is implemented in the Advanced Regional Prediction System mesoscale code tocompare scalar concentrations with data collected during field experiments conducted at Mount Tsukuba,Japan, in 1989. The simulations use horizontal grid resolution as fine as 25 m with up to eight grid nestinglevels to incorporate time-dependent meteorological forcing. The results show that simulated ground con-centration values contain significant errors relative to measured values because the mesoscale wind typicallycontains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observationsof arc maximum concentrations, however, lie within acceptable error bounds. In addition, this paperinvestigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, whichhave received little attention in the literature—in particular, for high-resolution applications. The choice oflateral boundary condition update interval is found not to affect time-averaged quantities but to affectthe scalar transport strongly. More frequent updates improve the simulated ground concentration values. Inaddition, results show that the computational mixing coefficient must be set to as small a value as possibleto improve scalar dispersion predictions. The predicted concentration fields are compared as the horizontalgrid resolution is increased from 190 m to as fine as 25 m. The difference observed in the results at theselevels of grid refinement is found to be small relative to the effects of computational mixing and lateralboundary updates.

1. Introduction

With the increasing availability of powerful super-computers, numerical simulation has become a very at-tractive tool for simulating transport and dispersion ofairborne materials in atmospheric flows. Many previouscomputational studies have focused on the prediction

of concentration downwind of a scalar release point, aproblem of great importance because of increasing en-vironmental pollution and other hazardous material re-leases (Kemp and Thomson 1996; Sykes et al. 1992;Meeder and Nieuwstadt 2000). The models and ap-proaches used vary greatly with the length and timescales of interest, though modeling choices are oftenlimited by computational resources. Two broad classesof models can be described. The first includes what arecommonly referred to as computational fluid dynamics(CFD) applications, using either large-eddy simulation(LES) or Reynolds-averaged Navier–Stokes (RANS)approaches for turbulence, and focusing on small-scale

Corresponding author address: Takenobu Michioka, Environ-mental Science Research Laboratory, Central Research Instituteof Electric Power Industry, 1646 Abiko, Abiko-shi, 270-1194Chiba-ken, Japan.E-mail: [email protected]

3150 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 47

DOI: 10.1175/2008JAMC1941.1

© 2008 American Meteorological Society

JAMC1941

plume behavior. These models might be used, for ex-ample, to predict detailed plume dispersion in an urbanarea, but they have limited ability to incorporate effectsof meteorological conditions. The second class of mod-els includes mesoscale models (typically using a RANSturbulence closure), which are applied at regionalscales to predict plume dispersion without giving muchattention to small-scale fluctuations because of coarsespace and time resolution and the inability to representhighly complex terrain (e.g., building geometries). Bothsmall-scale CFD and mesoscale models use a range ofeither Lagrangian or Eulerian approaches to representscalar transport.

An example of a typical small-scale CFD applicationcomes from Sykes and Henn (1992), who performedLES with a Lagrangian-based puff method to predictconcentration fluctuations emitted from elevated andground-level sources. In a similar way, Sada and Sato(2002) conducted LES with a mixed method, combiningan Eulerian method with a puff model to predict theinstantaneous concentration fluctuations of a plumefrom stack gas dispersion around a cubical building.These LES simulations captured not only the meanconcentration, but also the concentration fluctuationsand instantaneous high-concentration values, which areneeded to verify the behavior of detailed plume disper-sion. In a more realistic application, Sada et al. (2006)performed RANS simulations with Lagrangian particletracking to predict stack gas dispersion, considering thebuildings located near the stack and the complex ter-rain located relatively far from the stack. The simula-tion reproduced the ground concentration observed inwind-tunnel experiments, but the horizontal spread ofthe plume far from the stack was underestimated rela-tive to the expected plume spread in a real atmosphericboundary layer because the meandering effects of winddirection fluctuations were not represented by thesimulation. These CFD studies were able to representdetailed plume behavior and complex geometries in ur-ban areas and mountainous terrain, but they used ho-mogeneous surface conditions and simplified boundaryconditions (steady inflow) and did not allow for synop-tic flow forcing such as the influence of meanderingwinds.

In contrast to these small-scale CFD studies, meso-scale models have been used to predict contaminantdispersion on larger scales. Mesoscale models incorpo-rate heterogeneous land surface conditions and time-dependent synoptic boundary forcing but are typicallylimited by coarse resolution. Yamada (2000) performed5-km-resolution mesoscale simulations using a three-dimensional atmospheric modeling system with a

Lagrangian random puff dispersion model and com-pared results with observations from a tracer experi-ment in the complex terrain of the southwestern UnitedStates. Yamada found that the predicted surface con-centrations in the simulations agreed with actual mea-surements within a factor of 2, with a small standarddeviation. Koracin et al. (2007) used the fifth-genera-tion Pennsylvania State University–National Center forAtmospheric Research Mesoscale Model (MM5) withLagrangian particle tracking to investigate dispersionerror; model results were within a factor of 3 of eachother when using various turbulence schemes. Becausethese authors aimed to simulate relatively long distancetransport and diffusion, they used relatively coarseresolution simulations, with a horizontal grid spacing of3–5 km. Banta et al. (1996), however, showed thatsmall-scale, topographically forced winds of less than2 km in extent can have a strong influence on flow overcomplex terrain and thus can be important in the at-mospheric transport of hazardous materials over a rela-tively short distance. Other examples of the need forhigher grid resolution include Chen et al. (2004), whofound that increasing the horizontal resolution (to250-m spacing) improves wind and potential tempera-ture in simulations over the mountains in the Salt LakeCity, Utah, area. Chow et al. (2006) found that in-creased grid resolution (to 150-m spacing) also im-proved numerical simulation results in the Swiss Alps,though only when land surface conditions were prop-erly initialized. Brulfert et al. (2005) modeled flow intwo narrow valleys in the French Alps and also neededspacing as fine as 300 m to represent the complex to-pography; they used a photochemical model coupledwith a mesoscale model to predict air quality in thevalleys. High-resolution simulations with time-varyinglateral boundary forcing are particularly important foraccurately simulating the detailed concentration fieldresulting from atmospheric releases of toxic materialsover complex terrain.

Most simulations of scalar dispersion from a smallsource have been calculated using Lagrangian particledispersion models (LPDM) because the horizontalresolution is too coarse to resolve the region near thesource with an Eulerian-type scalar diffusion model(ESDM) (Weil et al. 2004; Kim et al. 2005). Nguyenet al. (1997) investigated the performance differencebetween LPDM and ESDM by simulating releasesfrom two elevated point sources in complex terrain withnonstationary flows. They showed that the LPDM ap-proach is a more natural way of describing the disper-sion process for coarse resolutions. There are diffi-culties in formulating an LPDM, however, because sev-

DECEMBER 2008 M I C H I O K A A N D C H O W 3151

eral empirical constants must be adequately chosen andthe choices have large effects on the predicted scalarfields (Sada et al. 2006). In contrast, an ESDM does notrequire empirical constants except for those in the sub-filter-scale turbulence closure model, and these areclosely linked to the coefficients to model turbulentmomentum transport.

In this study, we use high-resolution numerical mod-eling to simulate the flow and concentration fields ac-companying scalar transport and diffusion from a pointsource near Mount Tsukuba in Japan. Our study useslarge-eddy simulation in a mesoscale setting, providingadvantages due to the use of robust turbulence modelscombined with the influence of meandering winds(synoptic flow forcing) and other meteorological forc-ing such as surface heating and soil moisture. Our simu-lation tool is the Advanced Regional Prediction System(ARPS)—a nonhydrostatic, compressible LES codewritten for mesoscale and small-scale atmosphericflows (Xue et al. 2000, 2001, 2003). An Eulerian modelof scalar transport and diffusion has been implementedin ARPS to compare scalar concentrations with datacollected during field campaigns conducted at MountTsukuba in 1989 (Hayashi et al. 1999). Chow et al.(2006) and Weigel et al. (2006, 2007) recently showedthat the complex thermal and dynamic structure of flowover complex terrain in the Swiss Alps could be accu-rately reproduced using ARPS. The current study fo-cuses on scalar transport over complex terrain usinghorizontal grid resolution as fine as 25 m with up toeight grid nesting levels to incorporate time-dependentmeteorological forcing.

The traditional concept of LES is typically associatedwith simulations in which most of the wavenumberrange is resolved. The method of LES, however, doesnot prohibit its application to high-Reynolds-numberflows, in which a large range of wavenumbers may re-main unresolved because of grid-resolution limitations(Wyngaard 2004). The coarser grids in our nested do-main setup are more typical of mesoscale simulationsbut can use the same LES equations. The differencesbetween LES and RANS become small when similarspace and time resolutions are used; often the only dif-ference in implementation is the formulation of the tur-bulence model. The LES formulation is preferred forstudies of turbulent flows because it is clear whichphysical features (length scales) are resolvable andwhich must be modeled. Several challenges associatedwith scalar transport predictions over complex terrainwill be described herein, together with recommenda-tions for numerical formulations that can improvesimulation comparisons with observations.

Scalar dispersion is affected not only by mean flow,but also by turbulent scalar fluxes that affect scalar mix-ing. This means that a focus on scalar transport in ad-dition to mean flow prediction requires greater atten-tion to the choice of numerical simulation parameters.This paper investigates the effects on scalar dispersionof computational mixing and lateral boundary condi-tions, which have received little attention in the litera-ture—in particular, for high-resolution applications.The importance of the computational mixing schemewas emphasized by Zängl et al. (2004), who found thatthe effect of the horizontal computational mixing waslarger than the effect of increased grid resolution, andthey implemented an improved computational mixingscheme in MM5. Their new scheme allowed the simu-lations to capture the essential features of the observedvalley wind. The authors did not suggest appropriatevalues for the computational mixing coefficient. Thechoice of the lateral boundary update interval has alsonot been thoroughly investigated. The standard or usu-ally acceptable update interval for lateral boundaries inmesoscale simulations is a few hours (see Nutter et al.2004; Chow et al. 2006). Nutter et al. (2004) suggestedthat the error introduced by aliasing of fields passingthrough the lateral boundaries becomes larger withlarger update intervals, but they found that the error isnegligible if the lateral boundary conditions are up-dated at least once per hour in their 25-km-grid-resolution simulations. They did not examine the ef-fects of the update interval at higher resolutions such asthose used in this study.

This work examines the performance of highly re-solved large-eddy simulations for scalar dispersion in amesoscale setting over complex terrain. The experi-mental conditions and numerical setup are briefly de-scribed in the next section. This is followed by an evalu-ation of the simulated surface velocity and temperaturefields in section 3 and the simulated concentrationfields in section 4. We then perform sensitivity experi-ments to evaluate the influence of the computationalmixing, the update interval for lateral boundary forcingon the flow, and grid resolution on turbulent statisticsand surface concentration predictions in section 5.

2. Numerical simulation setup

ARPS was developed at the Center for Analysis andPrediction of Storms at the University of Oklahomaand is formulated as an LES code that solves the three-dimensional, compressible, nonhydrostatic, filteredequations. ARPS is described in detail by Xue et al.(1995, 2000, 2001, 2003). The major modification wemade to the original ARPS code (version 5.2.4) was to


add an ESDM. The advection–diffusion equation for apassive scalar is given by

��C �

�t�

��uiC �

�xi� Dc � Qc , �1�

where C is the concentration of the scalar, � is air den-sity, Dc is the turbulent mixing term, and Qc is thesource term.

ARPS solves equations for each velocity componentand for the perturbation pressure, potential tempera-ture, and moisture fields. Density is diagnosed from anequation of state. Fourth-order spatial differencingis used for the advection terms in the momentum,potential temperature, and pressure equations, and amultidimensional positive-definite central difference(MPDCD) scheme is used for the advection terms inthe scalar transport equations. The MPDCD is basedon flux correction/limiting on leapfrog-centered advec-tive fluxes (Lafore et al. 1998). Temporal discretizationis performed using a mode-splitting technique to ac-commodate high-frequency acoustic waves. The largetime steps use the leapfrog method. First-order for-ward–backward explicit time stepping is used for thesmall time steps, except for terms responsible for ver-tical acoustic propagation.

The 1.5-order turbulent kinetic energy closure (TKE-1.5) was used for the subfilter-scale turbulence modelfor all prognostic variables on all domains. The turbu-lent mixing coefficients for scalars are related to theone for momentum through the turbulent Prandtl num-ber, which is set to 1/3 (Xue et al. 2000). The TKE-1.5closure is consistent with an LES formulation becauseit uses a length scale proportional to the filter width(or grid spacing). LES separates resolved and subfilter-scale motions using a physical length scale, the width ofthe explicit spatial filter. RANS, on the other hand,applies a time average, usually with a very broad aver-aging period so that only very large scales are resolved.In addition to a turbulence model, computational mix-ing is applied to remove high-frequency oscillations. A

computational mixing coefficient of Cmix � 1.0 � 10�4

was used for all grid levels, as discussed further in sec-tion 5.

ARPS is used for simulations of seven tracer gas re-leases near Mount Tsukuba, where a field campaignwas conducted from 13 to 19 November 1989 (Hayashiet al. 1999). Mount Tsukuba is at 877 m MSL eleva-tion and is located in southeastern Japan, about 30 kminland from the Pacific Ocean. Trini Castelli et al.(2006) studied the Mount Tsukuba experiments usingthe Regional Atmospheric Modeling System meso-scale model with grid nesting down to 250-m horizontalspacing, but focused only on comparisons with surfacewind and temperature observations and the effect ofdifferent turbulence closure models and did not simu-late scalar dispersion. All of our simulations begin at2100 Japan standard time (JST; �UTC � 9 h) of theday prior to the passive scalar release. The simula-tion period details are given in Table 1. In each case,the tracer gas was released at a steady rate for 90 min,and ground surface concentration statistics were ob-tained by averaging over the last 30 min of the releaseperiod. The predominant wind direction was fromthe east in cases I–V and from the west in cases VI andVII. During each case, the atmospheric stability nearMount Tsukuba was neutral or slightly unstable be-cause of mostly cloudy conditions. Tracer gas [sulfurhexafluoride (SF6)] was released at 100-m elevation atsite A for cases I–V or at site B for cases VI and VII(see Table 1; Fig. 1c). Sixty-two concentration sensorsat about 1.5 m above the ground surface were distrib-uted downwind of the release point. The sensors weremoved to different optimal downwind locations foreach case.

Details of the ARPS simulation domains are given inTable 2. Six one-way nested grids were used to simulateflow and scalar dispersion around Mount Tsukuba athorizontal resolutions of 45, 15, 5, and 1.7 km and 570and 190 m (see Fig. 1). Two further grid nesting levelsat 65- and 25-m resolution are described later. The ver-tical resolution was also refined; Table 2 lists the num-

TABLE 1. Model simulation period.

CaseStarting time

(JST) SpinupTracer gas

release timeScalar statistics

(30-min avg)Turbulent statistics

(10-min avg)Release

point

I 2100 13 Nov 16 h 1300–1430 14 Nov 1400–1430 14 Nov 1350–1400 14 Nov AII 2100 14 Nov 13 h 1000–1130 15 Nov 1100–1130 15 Nov 1050–1100 15 Nov AIII 2100 14 Nov 17.5 h 1430–1600 15 Nov 1530–1600 15 Nov 1550–1600 15 Nov AIV 2100 15 Nov 16 h 1300–1430 16 Nov 1400–1430 16 Nov 1350–1400 16 Nov AV 2100 16 Nov 14 h 1100–1230 17 Nov 1200–1230 17 Nov 1150–1200 17 Nov AVI 2100 17 Nov 17.5 h 1430–1600 18 Nov 1530–1600 18 Nov 1550–1600 18 Nov BVII 2100 19 Nov 17.5 h 1430–1600 20 Nov 1530–1600 20 Nov 1550–1600 20 Nov B


ber of grid points below 1000 m for each grid level. Theratio of the coarser horizontal grid spacing to the finergrid was roughly a factor of 3 at each nesting level. Thelateral boundaries are placed as far as possible from ourregion of interest to minimize contamination by errorsgenerated at the lateral boundaries that are magnifiedwhen the boundaries cross through complex terrain(Warner et al. 1997). Topography for the 45-km through570-m grids was obtained using U.S. Geological Sur-vey (USGS) 30-arc-s topography datasets. The 190-m-resolution (and finer) terrain data were extracted froma Japanese Geographical Survey Institute 50-m dataset.The terrain is smoothed near the boundaries of eachnested subdomain to match the elevations from the sur-rounding coarser grid.

To obtain realistic initial and boundary conditions,data from the Japanese 25-yr reanalysis (JRA-25)dataset were used to force ARPS simulations on thecoarsest-resolution (45 km) grid. JRA-25 analyses aregiven at 6-h intervals with 1.125° (approximately 135km) horizontal spacing and 40 vertical levels (Onogi etal. 2007). The spinup time was 13–17.5 h for each case;using a spinup time of more than 18 h did not signifi-cantly affect the results. Update intervals on subse-quent nesting levels are between 1 h and 10 s. The effectof these choices is discussed in section 5.

Heterogeneous land surface forcing is providedthrough the ARPS land surface soil–vegetation model,which solves equations for soil temperature and mois-ture, as described in detail in Xue et al. (1995, 2001).

FIG. 1. The elevation contours (m MSL) for (a) the 45-km grid,(b) the 5-km grid, and (c) the 190-m grid. The locations of surfacestations defined in Table 3 are shown in (c).


Two soil layers of depths 0.01 and 0.99 m for the surfaceand deep soil, respectively, are used by the soil model.ARPS uses 13 soil types (including water and ice) and14 vegetation classes (following the U.S. Department ofAgriculture classifications). Land use, vegetation, andsoil-type data are obtained from USGS 30-s globaldata. Initial soil moisture and sea surface temperaturedata are provided by the JRA-25 analyses. Initial soiltemperature was chosen as an offset from surface airtemperature, as described further in section 3.

3. Evaluation of the simulated surface velocity andtemperature fields

To evaluate the performance of the numerical simu-lations in reproducing scalar transport and dispersion,we present a detailed comparison of results from ARPSwith observation data in this and the following sections.All results are from the 190-m-resolution grid unlessotherwise noted. The simulation nesting procedure,grid resolution, time steps, and land surface forcingwere chosen to minimize errors in the flow field. As afirst step, therefore, the velocity and temperature fieldswere examined to determine the accuracy of the under-lying flow field that drives the passive scalar transport.

Table 3 shows the root-mean-square errors (RMSE)and mean errors (bias) between the ARPS simula-

tions and surface observations at six sites. They aredefined as

bias �1L �

j�1

L 1M �

i�1

M

�Ai,jo � Ai,j

p � and �2�

RMSE � � 1L �

j�1

L 1M �

i�1

M

�Ai,jo � Ai,j

p �2�1�2

, �3�

where L is the total number of cases, M is the numberof time steps, Ao is the observed variable, and Ap is themodel-predicted variable. The data for the error calcu-lation were collected every 30 min in the last 90 min ofthe simulation (thus giving four time snapshots duringthe tracer gas release time) as listed in Table 1. Forexample, the overall bias and RMSE of the wind direc-tion at the release point A are 6.06° and 42.24°, respec-tively. It is difficult to determine the exact reason forthese errors because they are affected by complicatedfactors (e.g., the presence of complex topography, er-rors in the reanalysis or land surface data, and thechoice of microphysics and turbulence parameteriza-tions). These errors are not large, however, especiallywhen compared with the results of other typical simu-lations over complex terrain (Zängl et al. 2004; Zhongand Fast 2003; Chow et al. 2006). As discussed furtherbelow, the effects of mean wind direction errors on

TABLE 2. Nested grid configurations with dimensions.

Region Grid size Domain (km) x, y zmin

Update intervalTb

No. of grid levelsbelow 1000 m

1 83 � 83 � 53 3600 � 3600 � 25 45 km 50 m 6 h 142 83 � 83 � 53 1200 � 1200 � 25 15 km 50 m 1 h 143 83 � 83 � 53 400 � 400 � 25 5 km 50 m 30 min 144 83 � 83 � 53 136 � 136 � 20 1.7 km 50 m 10 min 155 83 � 83 � 53 45.6 � 45.6 � 17.5 570 m 30 m 5 min 196 83 � 83 � 83 15.2 � 15.2 � 16 190 m 20 m 5 min 326-H 153 � 153 � 83 28.5 � 28.5 � 26 190 m 20 m 5 min 327-H 253 � 253 � 93 16.25 � 16.25 � 15.5 65 m 10 m 1 min 368-H 411 � 411 � 103 10.2 � 10.2 � 15.0 25 m 5 m 10 s 41

TABLE 3. Root-mean-square errors and mean errors (bias) for wind speed, wind direction, and temperature.

SiteElev MSL

(m)Elev AGL

(m)

Wind velocity (m s�1) Wind direction (°) Temperature (K)

RMSE Bias RMSE Bias RMSE Bias

A 24 10.5 1.28 �0.48 42.24 6.06 — —BB 30 1.5 — — — — 1.86 �0.025W2 45 8 1.44 0.06 81.92 �10.74 — —W3 370 8.5 2.30 �1.53 35.93 �23.67 — —W4 530 17.5 1.70 0.64 35.91 6.51 — —W5 24 5.5 1.82 0.59 64.63 �7.03 — —


scalar transport, however, are significantly more pro-nounced, because the mean wind determines the maindirection of the scalar plume. Scalar concentrationcomparisons therefore show great sensitivity to drivingflow conditions.

To improve the accuracy of the wind direction, weattempted to apply data assimilation with incrementalanalysis updating (IAU) to harmonize the wind direc-tion with the observations (Bloom et al. 1996; Brewster2003a,b). The horizontal velocity and potential tem-perature from radiosonde observations were assimi-lated at every hour for the last 3 h at sites AA and BB,but the dispersion results did not improve. The mostlikely reason for this is errors in the lateral boundaryconditions at times between application of the analysisupdates. Even if the IAU improved the flow field at agiven time, the flow fields are so strongly influenced byboundary conditions from the coarser-resolution do-main that the flow soon returns to the nonassimilatedvalues.

We also investigated the sensitivity of temperatureerrors to land surface initialization, specifically soiltemperature. The effects of soil moisture initializationwere not considered here (see Chow et al. 2006). Thesurface soil temperature for all grids was initialized witha positive constant offset from the near-surface air tem-perature of 0.24 K, which is based on the observedtemperature difference at site BB. The choice of thedeep soil temperature was more difficult because nodetailed dataset exists for deep soil temperature in Ja-pan. We therefore explored the effect of the deep soiltemperature on the flow field by using three differentvalues as a positive constant offset from the near-surface temperature of 0, 10, and 15 K. (The deep soiltemperature is generally higher than surface soil tem-perature in winter.) Figure 2 shows the evolution of thenear-surface temperature and surface soil temperatureat site BB. The near-surface temperature was measuredat 5.5 m above ground level in the field campaigns. TheARPS data at the surface are from the lowest modellevel, which for the horizontal winds and temperature isat zmin/2 (10 m for the 190-m grid). During the night,the soil surface cools and heat is transferred from thedeep soil to the surface. In the zero offset case (T � 0K), the surface soil temperature dramatically decreaseswith time because the deep soil temperature cannotadequately compensate for the heat loss at the surface.The decrease causes the surface temperature to de-crease at night, resulting in a delay of the temperaturerise in the morning. The near-surface temperature dif-ferences in the cases with T � 10 or 15 K are small,but the soil temperature in T � 15 K is too high duringthe night. Based on these comparisons, a temperature

offset of T � 10 K was chosen as an appropriate valuefor case III. For the other cases, a constant offset fromthe near-surface temperature ranging from 5 to 10 Kwas selected according to a similar comparison proce-dure. The soil temperature setting did not strongly af-fect wind velocity and direction as compared with thedifferences seen in near-surface temperature.

4. Evaluation of the simulated concentration fields

Figure 3 shows contours of ground concentrationsfrom the observations and from ARPS for cases I andIII. Concentrations are normalized by the sourcestrength Q. In case III, the ground concentration dis-tribution in the ARPS is in good agreement with that inthe observations, but in case I the simulated concentra-tion plume fails to overlap with the observed plume.This is caused by wind direction errors at site A ofRMSE 42.24° and a bias of 6.06°, as shown in Table 3.As noted above, these RMSE and bias errors are notlarge relative to other typical simulation results, but theeffect on the simulated concentration fields is verylarge. Direct comparisons of concentration values atthe concentration sensor sites with ARPS results wouldin some cases lead to 100% error. Instead of a direct

FIG. 2. Surface data time series comparisons at site BB for(a) near-surface temperature and (b) surface soil temperature:observations (filled circles), T � 0 K (open circles), T � 10 K(open squares), and T � 15 K (open triangles).


point-by-point comparison of concentration values, thearc maximum concentration is used to evaluate theARPS model performance in this section. The arcmaximum concentration is the maximum concentrationobserved along an arc of sensors selected at variousdistances from the source (Olesen 2000). The use of arcmaximum concentration for model evaluation is fairly

standard for evaluation of dispersion models and fieldexperiments.

Figures 4 and 5 show the arc maximum ground con-centrations and the scalar plume orientation defined asthe position of the maximum ground concentration av-eraged for 30 min from release points AA for cases I–Vor BB for cases VI and VII. During the field campaign,

FIG. 3. Contour of ground concentration for (a) case I and (b) case III, with (left) field observations and (right) ARPS results.Sensor and source locations are shown with black dots and black triangles, respectively.


Fig 3 live 4/C

the sensors were not actually located along arc lines, sosensors were selected along prescribed arcs (centeredon the release point). Sensors were selected at 400-mintervals, with a margin of error of 200 m. The scalarstatistics in Figs. 4, 5 were averaged for 30 min. In caseI, ARPS simulates the arc maximum concentrationrelatively well even though the simulated plumespreads south of Mount Tsukuba while the observedplume spreads north of the mountain (see Fig. 3a). Incases II and III, the ARPS concentrations agree wellwith the observations because the scalar plume orien-

tation is accurate. The main reason for good agreementin cases I–III is that the horizontal velocity and turbu-lent fluctuations are in good agreement with observa-tions. Figure 6 shows the vertical distributions of hori-zontal velocity, wind direction, and the horizontal andvertical turbulent fluctuations at site AA for cases I–Vand site BB for cases VI and VII. The turbulent fluc-tuations are defined as the root-mean-square values ofthe velocity fluctuations, which are the deviations fromthe time-averaged velocity. The velocity and turbulentstatistics in Fig. 6 were averaged for 10 min as shown in

FIG. 4. Arc maximum concentration for cases I–VII: observa-tions (filled circles) and ARPS results (solid line).


Table 1. In cases IV, VI, and VII, ARPS overpredictsthe concentration in the vicinity of the release points.This is because the computational mixing adds artificialdiffusion, resulting in a wider spread of the scalar, es-pecially with the low wind speeds present in these cases.With low wind speeds, advection effects are negligibleand the plume diffuses quickly in the vertical direction,leading to high concentrations (relative to observa-tions) at the ground near the elevated release point. Incase V, the ARPS concentrations agree well with theobservations, though the simulated plume spreads in adifferent direction (see Fig. 5e). The reason for this

disagreement can unfortunately not be evaluated be-cause of the lack of observation data. The RMSE andbias of the mean scalar plume orientation (calculatedusing all seven cases) are 63.22° and �37.5°, which isalmost the same deviation observed in the simulatedand observed wind directions, as shown in Table 3.Thus, if the difference in simulated and observed winddirections is large, the scalar cannot be transported inthe proper direction.

To evaluate the output of a model with observationsquantitatively, Hanna et al. (1991, 1993) recommendthe use of the following statistical performance mea-

FIG. 5. Scalar dispersion direction for case I–VII: observations(filled circles) and ARPS results (solid line).


FIG. 6. Vertical distributions of horizontal veloc-ity, wind direction, and the horizontal and verticalturbulent fluctuations at the tracer release point(site AA or site BB): observations (filled circles)and ARPS (solid line). No observation data areavailable for Case V.


sures: the fractional bias (FB), the geometric mean bias(MG), the normalized mean-square error (NMSE), thegeometric variance (VG), and the fraction of predic-tions within a factor of 2 of observations (FAC2). Theyare defined as

FB �1L �

j�1

L 1Nj

�i�1

Nj �Ci,jo � Ci,j

p �

0.5�Ci,jo � Ci,j

p �, �4�

MG �1L �

j�1

L 1Nj

�i�1

Nj

exp�lnCi,jo � lnCi,j

p �, �5�

NMSE �1L �

j�1

L 1Nj

�i�1

Nj �Ci,jo � Ci,j

p �2

Ci,jo Ci,j

p , �6�

VG �1L �

j�1

L 1Nj

�i�1

Nj

exp�lnCi,jo � lnCi,j

p �2, and

�7�

FAC2 � fraction of data that satisfy

0.5 �1L �

j�1

L 1Nj

�i�1

Nj Ci,jp

Ci,jo � 2.0 , �8�

where L is the total number of cases, Nj is the numberof selected sensors for each case, Co is the observedconcentration, and Cp is the model-predicted concen-tration. The selected sensor locations are those fromthe arc maximum concentration from each case. A per-fect model would have MG, VG, and FAC2 equal to 1.0and FB and NMSE equal to 0.0. The FB and NMSEmay be overly influenced by infrequently occurringhigh observed or model-predicted concentrations,whereas MG and VG may provide a more balancedtreatment of extreme high and low values.

Chang and Hanna (2004) suggest that a good modelwould be expected to have about 50% of the predic-tions within a factor of 2 of the observations (i.e.,FAC2 0.5), a relative mean bias within �30% of themean (i.e., �0.3 � FB � 0.3 or 0.7 � MG � 1.3), anda relative scatter of about a factor of 2 or 3 of the mean(i.e., NMSE � 4 or VG � 1.6). Note that these guide-lines are based on ensemble concentrations that arecollected from several realizations in a dataset, thussmoothing out the observed and simulated concentra-tion values. In contrast, we compare time-averagedconcentrations at selected sensor locations for each ofthe seven cases, making our statistics more sensitive tomodel errors. In our simulations, we find FAC2 � 0.51,FB � �0.2, MG � 0.98, NMSE � 1.184, and VG �13.51. The main factors in the errors are wind velocityand direction bias, gaps in sensor spacing, and the dif-

ference in receptor position and height between themodel and observations. The VG has a large value be-cause of the overestimate of the concentrations nearthe release point for cases IV and VI. However, thevalues for all quantitative measures except the VG arewithin acceptable error bounds. Thus, based on com-paring the results of the ARPS with observations of arcmaximum concentration, the simulations presentedhere reproduce the observed ground concentrationwithin acceptable error bounds.

5. Concentration sensitivity tests

The preceding error analysis confirms the sensitivityof simulated concentration fields to errors in simulatedmean wind direction. These errors are largely due toerrors in lateral boundary forcing. Attempts to improvethe representation of the velocity field included dataassimilation and land surface initialization options, asdescribed in section 3. The mean velocity field errorstatistics are well within standard acceptable ranges formesoscale simulations, but the consequences of thesewind errors on the simulated scalar concentration fieldscan be very large, as discussed in section 4. This sectionevaluates the effects of chosen numerical schemes onthe concentration predictions by investigating param-eters that affect turbulence and hence scalar mixing.We specifically examine the effects of computationalmixing, the update intervals used for lateral boundaryforcing, and grid resolution, using case III as our testcase.

a. Computational mixing

Computational mixing is used to damp high-frequency motions that can build up because of non-linear interactions at small scales. This artificial mixingsupplements the turbulence model at the highest fre-quencies to limit unphysical oscillations in the numeri-cal solution. Because large values of computationalmixing tend to relax the instantaneous velocity towardthe base-state field, the computational mixing coeffi-cients should be chosen to be as small as possible. Ingeneral, second- or fourth-order computational mixingis used, with fourth-order mixing preferred because itdamps out short-wavelength noise more selectivelythan does second-order mixing. In mesoscale simula-tions, large computational mixing coefficients may notdramatically change the simulated flow fields becausethe computational mixing removes only the very smallscale noise. In high-resolution simulations, however,the small-scale motions, which the computational mix-ing might remove, may be very important because they


are part of the resolved turbulent flow field. The choiceof computational mixing may therefore strongly affectthe velocity and scalar fields.

In ARPS, the computational mixing term is added tothe right-hand side of the governing equations as

�Cmix��x�y�2��4��

�x4 ��4��

�y4 �� Cmix�z4��4��

�z4 �,

�9�

where � � � is the perturbation of from its base-state value , and the coordinates here are in compu-tational space. Here, Cmix is the computational mixingcoefficient and is chosen to be the same for the hori-zontal and vertical mixing terms. The base-state value isassumed to be horizontally homogeneous, time invari-ant, and hydrostatically balanced. Computational mix-ing is applied to all computed variables.

To investigate the sensitivity of the results to thecomputational coefficient, three different computa-tional mixing coefficients of 1.0 � 10�4, 5.0 � 10�4, and1.0 � 10�3 are used on the 190-m grid for case III. Notethat coefficient values of less than 1.0 � 10�4 result inoscillations in the flow field.

Figures 7 and 8 show the vertical distributions ofhorizontal wind direction and horizontal and verticalturbulent fluctuations at sites AA and BB. Sites AAand BB are located on the windward and leeward sidesof the mountain ridge, respectively. Observation valuesand ARPS results are averaged for 10 min (1550–160015 November). The computational mixing does not af-fect the time-averaged velocity and wind directionstrongly, but it affects the horizontal and vertical tur-bulent fluctuations. With smaller values of the compu-tational mixing coefficient, the turbulent fluctuationsbecome closer to the observations.

Figure 9 shows the arc maximum ground concentra-tion averaged for 30 min (1530–1600 15 November). Asthe computational mixing coefficient decreases, thepeak of the concentration profile shifts upwind, givingbetter agreement of the results with the observations.This change of the ground concentration is attributed tothe change in turbulent fluctuations. As the computa-tional mixing increases, the vertical turbulent fluctua-tions became smaller (as shown in Fig. 8) and the tracergas does not reach the ground early enough from itselevated release point. Note that the computationalmixing causes the opposite effect under low windspeeds as discussed in section 4. The computationalmixing acts to decrease vertical turbulent fluctuationsbut also acts to spread scalars by artificial diffusion.Under low wind speeds, the artificial scalar diffusiondominates because of the smaller advection, leading to

high ground concentrations near the source. In anycase, we conclude that, although it does not greatlyaffect mean velocity field quantities, the computationalmixing coefficient is a very important factor for predict-ing scalar dispersion.

FIG. 7. Vertical distributions of the horizontal velocity and winddirection at (a) site AA and (b) site BB for case III: observations(filled circles), Cmix � 1.0 � 10�4 (solid line), Cmix � 5.0 � 10�4

(dashed line), and Cmix � 1.0 � 10�3 (dotted line).


b. Update intervals for the lateral boundary forcing

In one-way grid nesting procedures such as the oneused by ARPS, the update interval for the lateralboundary conditions must be specified. In two-way

nesting, the nested finer domain and the outer coarserdomain interact at every time step of the outer coarse-grid integration. Existing two-way nesting schemes(such as those in the Weather Research and Forecast-ing Model and MM5), however, do not allow the ver-tical resolution to change between grid nesting levels.This means that high-resolution grids cannot be used inthe vertical direction when two-way nesting is applied,because the vertical levels must be suitable for all thenesting levels. The one-way nesting technique in ARPSallows adjustments in vertical resolution between grids,a very important feature for large-eddy simulationswhere the grid aspect ratio should be kept close tounity. In ARPS, the lateral boundary conditions for thenested finer domain are given by the stored coarser-domain output. Because larger data storage capacity isrequired when the update interval is smaller, a largerupdate interval is usually preferred to conserve compu-tational resources (storage and input/output overheadcosts). The optimal update interval has not been thor-oughly investigated, because in the past the intervalchoice was highly constrained by practical computingchoices. The standard or usually acceptable updateinterval for lateral boundaries in mesoscale simula-tions is a few hours (e.g., Nutter et al. 2004), but wechoose to pass finer-scale perturbations from the coarser-resolution simulation into the finer-resolution simula-tion through the lateral boundaries. Thus, we usehourly update intervals for the 45-km grid; 10-min in-tervals for the 15-, 5-, and 1.7-km grids; and 5-min in-tervals for the 570- and 190-m grids. Note that applyingupdates at hourly intervals for all grids did not changeany time-averaged quantities except scalar diffusionand led to worse results for turbulent fluctuations andground concentration as discussed later. Output datafrom the coarser grids were interpolated to generateinitial and boundary condition files for subsequentnested-grid simulations. The lateral boundary forcing islinearly interpolated at intermediate times between up-date intervals.

FIG. 8. Vertical distributions of the horizontal and verticalturbulent fluctuations at (a) site AA and (b) site BB forcase III: observations (filled circles), Cmix � 1.0 � 10�4 (solidline), Cmix � 5.0 � 10�4 (dashed line), and Cmix � 1.0 � 10�3

(dotted line).

FIG. 9. Arc maximum ground concentration for case III:Cmix � 1.0 � 10�4 (solid line), Cmix � 5.0 � 10�4 (dashed line),and Cmix � 1.0 � 10�3 (dotted line).


To investigate the effect of the lateral boundary forc-ing update interval Tb, four different update intervalsof 10 s, 60 s, 5 min, and 30 min are implemented on thesixth grid level for case III. The update intervals werechanged only during the last 3 h (1300–1600 15 Novem-ber) of the simulation; other time periods (2100 14November–1300 15 November) remain at 5-min inter-vals to conserve data storage space in the computer.The minimum update interval was set to be 10 s be-cause it corresponds to a spatial wave scale of about100 m (with a wind velocity of about 10 m s�1), whichcannot be generated on the coarser domain (fifth re-gion). The velocity and length scales that are fed intothe finer domain at the boundaries will be affected bynonlinear interactions to produce finer scales as al-lowed by the finer resolution and triggered by the finertopography. Thus, we expect a change in the repre-sented length scales at various distances from the lat-eral boundary.

Figures 10 and 11 show the vertical distributions ofhorizontal wind direction and horizontal and verticalturbulent fluctuations at sites AA and BB. The time-averaged horizontal wind speeds show some smalldifferences below 200 m, but the wind directions areunchanged. The horizontal and vertical turbulent fluc-tuations, however, generally became larger with smallerupdate interval. The effect on the arc maximum groundconcentrations is shown in Fig. 12, where it is clearthat the results agree best with the observations whenTb � 10 s.

To investigate the effect of the turbulence on thesimulated ground concentration, the energy spectra atsite AA, at site BB, and on the boundary of the sixthregion (190-m grid) are shown in Fig. 13. The spectraare calculated using data at 10-s intervals at the chosenobservation sites AA and BB or at a single point on theeastern boundary. All data were extracted at 100 mabove ground, which matches the tracer-gas releaseheight. The larger update intervals do not allow high-frequency motions except high-frequency noise ( f about 1.5 � 10�2 Hz) to be passed at the domainboundary (see Fig. 13a). The high-frequency noise ap-pears as a result of aliasing generated by linear inter-polation between update intervals. The larger updateintervals also damp the low-frequency motions at theboundary because the larger scales are smoothed asthey pass through the boundary. The reduction of thelow frequencies at the boundary of the nested coarserdomain generally results in a decrease of the turbulentfluctuations in the interior of the domain, as shown nearthe release point of the tracer gas (site AA; see Fig.13b). The effect of the larger update interval does notalways reduce larger turbulent motions, because the

energy spectrum at Tb � 30 min is larger than those atTb � 5 min at site AA; this is due to the change in themean flow below 200-m elevation as shown in Fig. 10a.Thus, high-frequency motions can be generated locally,but they are also generally affected by the boundaryupdate interval. Far from the upwind (eastern) lateral

FIG. 10. Vertical distributions of the horizontal velocity andwind direction at (a) site AA and (b) site BB for case III: obser-vations (filled circles), Tb � 10 s (solid line), Tb � 60 s (dashedline), Tb � 5 min (dotted line), and Tb � 30 min (dash–dottedline).


boundary at site BB, however, the difference betweenthe energy spectra is very small (see Fig. 13c) becausethe turbulent motions on the lee side of the mountainridge at site BB are strongly affected by the mountainridge and thus are not as sensitive to upwind conditions.As seen in Fig. 12, the increase of the turbulent fluc-tuations shifts the peak of the concentration curves up-

wind, and the effect is almost the same as the compu-tational mixing effect discussed in section 4a. Thus, theupdate interval does not strongly affect the time-averaged velocity quantities but is very important forestimating the scalar dispersion emitted from pointsources.

c. Grid resolution

Fine grid resolution can be particularly important forsimulating the scalar dispersion emitted from pointsources. To demonstrate the effect of the grid resolu-tion on the scalar dispersion, eight one-way nested gridswere used as listed in Table 2 to simulate case III. Theseinclude two additional grid refinement levels from thesix described previously. The sixth grid level in thisnesting sequence covers a much larger domain. Thesixth (6-H), seventh (7-H), and eighth regions (8-H) usehorizontal resolutions of 190, 65, and 25 m, respectively.

Figure 14 shows comparisons of the horizontal andvertical turbulent fluctuations from the 190-, 65-, and25-m grid resolutions. The higher-resolution simula-tions slightly increase the vertical turbulent fluctua-tions as expected, but the differences are not large. Thevariation in horizontal turbulent fluctuations is small.This is most likely due to the fact that turbulent fluc-tuations are dominated by motions that are alreadywell resolved in the 190-m grid resolution simulation.The arc maximum ground concentration, however, be-comes slightly larger with finer grid resolution as shownin Fig. 15 because there is better resolution and henceless smoothing of the concentration field—in particular,near the source. The present comparison of the con-centration becomes somewhat worse, but the differenceis very small and the error is within acceptable errorbounds as discussed in section 4. Higher grid resolutionhas the advantage of capturing smaller eddies and con-centration fluctuations, but the effect of grids finer than190-m spacing is found to be small as compared withthe improvements found by changing the computa-tional mixing and the update interval for the bound-

FIG. 12. Arc maximum ground concentration for case III: ob-servations (filled circles), Tb � 10 s (solid line), Tb � 60 s(dashed line), Tb � 5 min (dotted line), Tb � 30 min (dash–dotted line).

FIG. 11. Vertical distributions of the horizontal and verticalturbulent fluctuations at (a) site AA and (b) site BB for Case III:observations (filled circles), Tb � 10 s (solid line), Tb � 60 s(dashed line), Tb � 5 min (dotted line), and Tb � 30 min(dash–dotted line).


aries. It is possible that the use of two-way nesting,increased vertical resolution, improved lateral and sur-face boundary conditions (e.g., land use), or data as-similation is needed to appreciate fully the effects ofvery high horizontal spacing.

6. Summary and conclusions

The ARPS large-eddy simulation code has been ap-plied to simulate scalar transport and dispersion frompoint source releases during a field campaign con-

FIG. 13. Energy spectra at (a) boundary, (b) site AA,and (c) site BB for case III: Tb � 10 s (solid line), Tb �60 s (dashed line), Tb � 5 min (dotted line), and Tb � 30min (dash–dotted line).


ducted near Mount Tsukuba in Japan. We have dem-onstrated the ability to apply LES in a mesoscale set-ting using up to eight grid nesting levels from horizontalresolutions of 45 km down to as fine as 25 m. Severalchallenges associated with scalar transport predictionsover complex terrain were described, together with rec-ommendations for numerical formulations that can im-prove simulation comparisons with observations. Theeffects of computational mixing, the update interval for

lateral boundary forcing on the flow, and higher gridresolution on scalar field predictions were investigated.The four major findings can be summarized as follows:

1) It is difficult for the high-resolution LES (ARPS) topredict exactly the ground concentration from asmall source by direct point by point comparisonbecause the mesoscale wind typically contains awind direction bias of a few dozen degrees. Com-parisons of simulation results with observations ofarc maximum concentrations, however, indicate thatthe simulations can nevertheless predict the groundconcentration within acceptable error bounds.

2) Changing the update intervals for the lateral bound-aries does not affect time-averaged quantities (wind,wind direction, etc.) but strongly affects the scalartransport. As the update interval is set to be smaller,the model accuracy is improved.

3) The computational mixing coefficient must be set toas small a value as possible because it significantlyaffects scalar dispersion. Some computational mix-ing, however, is required to prevent the occurrenceof artificial high-frequency motions in the simula-tions.

4) The representation of the concentration field im-proves at high grid resolutions of as fine as 190-mspacing in the horizontal plane. With finer resolu-tions (up to 25 m) the results do not improve, but thedifferences are small and still within acceptableerror bounds. When compared with the effects ofcomputational mixing and lateral boundary updates,however, the increased computational costs of theseextrafine simulations do not seem warranted at thistime.

LES applied in a mesoscale setting has the ability topredict scalar transport at high resolution while consid-ering unsteady flow boundary conditions (such as me-andering winds) and heterogeneous surface conditions.The simulations do not require prespecified wind direc-tions, as used in small-scale CFD applications, but do

FIG. 14. Vertical distributions of the horizontal and verticalturbulent fluctuations at (a) site AA and (b) site BB for case III:observations (filled circles), 190-m grid resolution (solidline), 65-m grid resolution (dashed line), and 25-m grid resolution(dotted line).

FIG. 15. Arc maximum concentration for case III: observations(filled circles), 190-m grid resolution (solid line), 65-m grid reso-lution (dashed line), and 25-m grid resolution (dotted line).


take advantage of the improved representation of tur-bulent fluxes provided by LES at high grid resolutions.Our approach, therefore, brings together elements ofboth the standard CFD and mesoscale approaches tocreate a general modeling tool for predicting contami-nant dispersion. The results, however, are very sensitiveto errors in mean wind direction (provided by the lat-eral boundary conditions), which determines the maindirection of the scalar plume. The simulations pre-sented here perform very well in estimations of arcmaximum concentrations and are able to take advan-tage of high resolution to provide accurate estimates ofconcentration fluctuations. Errors in the exact locationof high-concentration regions may be acceptable in cer-tain pollution regulation applications. On the otherhand, if contamination areas from a toxic gas releaseneed to be identified for emergency-response purposes,these simulations would not provide satisfactory pre-dictions. Thus, although the simulations described hereare a first step toward combining the fidelity of high-resolution CFD approaches with a mesoscale setting,much further work is needed to improve predictions ofscalar dispersion over complex terrain under generalatmospheric conditions.

Acknowledgments. The authors thank MeganDaniels and Ryo Onishi for many useful discussions.The datasets used for this study are provided from thecooperative research project of the JRA-25 long-termreanalysis by the Japan Meteorological Agency (JMA)and Central Research Institute of Electric Power In-dustry (CRIEPI). The first author was supported by afellowship from CRIEPI while in residence at the Uni-versity of California, Berkeley. The second author ac-knowledges support from NSF Grant ATM-0645784(Physical Meteorology Program: S. Nelson, ProgramDirector).

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