Sensitivity of mesoscale model urban boundary layer meteorology to urban morphology

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Introduction
The urban boundary layer (UBL) is a term frequently used to refer to the atmospheric boundary layer (ABL) over an urban area, a type of ABL distinguished by its underly-Figures

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Full Consequently, these artificial surfaces and additional anthropogenic sources can alter the local energy balance.This combination of disruption to the local dynamics and energy balance has broad local and regional implications on meteorology and air quality.
The depth of the roughness sublayer (RSL) over vegetation typically varies from 0.5 to 50 m above the ground (Garratt, 1992) or approximately 2 × z R to 5 × z R or more (Roth, 2000), where z R is the roughness element height.Where tall buildings are the roughness elements, the observed RSL depth may occupy the bulk of the surface layer (Rotach, 1999;Barlow and Coceal, 2009), substantially affecting the flow in and around the urban area.The urban RSL can be further subdivided into a shear layer, above the height of the local structure (canopy) rooftop, and a canyon layer below.
In the shear layer, the logarithmic wind profile likely holds (Cheng and Castro, 2002).Within the canyon layer, however, the observed wind profile is often described as exponential (Macdonald, 2000), requiring alternate formulation.In addition, the urban RSL is particularly sensitive to the structural height (Cheng and Castro, 2002), orientation, dimension and density, collectively referred to as the urban "morphology".The turbulent motions and circulations with and above the urban canopy affect the rate and direction of dispersion of pollutants within and above the urban canyon, contributing to the local air quality (Klein et al., 2007).
The urban surface energy budget is also sensitive to the morphology (Oke, 1981(Oke, , 1982)).Tall buildings can cast shadows, reducing the infiltration of direct short wave radiation into urban canyons, while potentially increasing diffuse radiation via reflection (Mills, 2004).Tall buildings can also reduce canyon wind speed, limiting the upward turbulent heat flux and canyon ventilation.These buildings can also act as heat storage mechanisms, increasing daytime up-take and nighttime emission to the urban environment.This effect may be considered part of an anthropogenic heat flux contribution to Introduction

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WRF-ARW model
This study uses the Weather Research and Forecasting Model (WRF) Advanced Research (ARW) version 2.2 (Skamarock et al., 2007) to simulate the mesoscale meteorology.The model time integration uses a third-order Runge-Kutta scheme; horizontal advection of momentum and scalars uses a fifth-order scheme, third-order in the vertical.This study makes use of the model's Rayleigh damping term to stabilize vertical momentum when the vertical velocity approaches the Courant number for stability as well as a sixth-order numerical diffusion term in the horizontal momentum equations to filter short-wave numerical noise.Horizontal eddy viscosity is determined from the Smagorinsky first-order closure method (Smagorinsky, 1963).Two-way interactive nested grids are invoked, with a 4-grid point relaxation zone boundary condition.This study selects the Mellor-Yamada-Janjic (MYJ) ABL scheme (Janjic, 2002) and accompanying Eta surface layer model to parameterize the ABL.Vegetation and other land surface processes are parameterized using the Noah land surface model (LSM) (Chen and Dudhia, 2001).Cloud microphysics is parameterized according to the WRF Single Moment 3-Class scheme (Hong et al., 2004).Cumulus cloud parameterization is applied only in the coarsest model grid (see Sect. 2.2) according to the Kain-Fritsch scheme (Kain, 2004;Kain and Fritsch, 1993).Longwave radiation is parameterized according to Rapid Radiative Transfer Model of Mlawer et al. (1997) and shortwave radiation according to Chou and Suarez (1994).Initial conditions are taken from NCEP Eta 212 grid (40 km) model analysis (a.k.a.,"AWIP") data available from the University Corporation for Atmospheric Research (UCAR) in three-hour increments at 26 vertical levels from 1000 hPa to 50 hPa.The AWIP data initializes the parent domain (see Sect. 2.2) and all nested grids at the start of model integration and provides boundary conditions for the parent domain.Introduction

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Full To model the urban environment, WRF-ARW v2.2 provides a single layer urban canopy model (UCM) of Kusaka et al. (2001).This UCM represents urban areas as two-dimensional street canyons of infinite length without specified street orientation, designed as an extension to the Noah LSM.The UCM balances all energy sources locally at the four-layer road, wall and roof surfaces of each model grid cell: The surface energy balance is achieved independently at each surface (roof, wall and road) by iteratively (Newton-Raphson) manipulating the local skin surface temperature to adjust the heat fluxes the sum is sufficiently close to zero and the skin surface temperature (T s ) and diagnostic mean canyon air temperature (T c ) are in steady-state.The contribution of heat flux from each surface is scaled according to the normalized length of the roof (R), wall (h) and road (R W ) where R +R W = 1.The LSM defines the (total) heat flux from the urban grid cell surface as the sum of flux from artificial/anthropogenic surfaces and the natural surface (grassland), partitioned according to the grid cell fractional coverage by the artificial surface (f URB ), e.g., for sensible heat flux: A diagnostic mean canyon wind speed is computed from an exponential function subject to the geometry of the canyon and speed of the flow above (Kusaka and Kimura, 2004).Further detail of the UCM and its coupling to WRF are presented by Kusaka et al. (2001) and Kusaka and Kimura (2004).Some minor adjustments were made to the parameter settings for application to the Detroit-Windsor domain.The internal roof and wall temperature were set to 298.15 K to reflect a typical summertime interior building temperature.The internal road (ground) temperature was set to 295.25 K to reflect the approximate seasonal (JJA) average surface (2 m a.g.l.) temperature at Detroit-Windsor.A four-class urban land surface type approach (Grimmond and Oke, 1999) is used in place of the default three-class approach.Table 1 lists the principal gridded urban parameters by type, a blend of values recommended by Grimmond and Oke (1999) and morphological estimates from remote sensing imagery.The non-gridded urban parameters (e.g., surface albedo, thermal conductivity and surface emissivity, etc.) were selected following a review of Introduction

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Domain
The area of interest is the Detroit-Windsor metropolitan area, estimated population: 4 726 779 (Statistics Canada, 2006, United States Census Bureau, 2010) straddling the USA-Canada border (Fig. 1).This urban area is located in the Great Lakes region of North America, an area of generally flat topography adjacent to multiple, large fresh water bodies.The Detroit River separates the cities of Detroit and Windsor and extends from Lake St. Clair in the east to Lake Erie in the south.The model domain consists of one parent grid, stretching across the contiguous US and southern Canada, and three telescopically nested grids (∆x = 37.5,7.5,1.5 and 0.3 km, respectively).Grid 1 extends across 140 (86) gridpoints from west to east (north to south); both grids 2 and 3 are of squares of 36 gridpoints per side and grid 4 is a square of 66 gridpoints per side.The model was run with 59 vertical levels and set to have approximately 21 levels in the lowest kilometer.
The resolution of the innermost grid (d04) approaches the limit of viability for application of the MYJ scheme to represent ABL turbulence; the scale of some eddies in the afternoon well-mixed layer in cases examined here likely briefly exceed the d04 grid scale.However, model TKE damping at the highest resolutions (energy cascade compensation) leads to an effective model resolution of approximately 7∆x (Skamarock, 2004), or approximately 2.1 km in d04 here.This scale exceeds h ABL throughout the d04 grid in the test cases examined here.In addition, Miao et al. (2009) demonstrate successful implementation of the MYJ ABL scheme in WRF at similarly high resolution (0.5 km) under fair-weather, warm-season conditions using the single layer UCM with comparable vertical resolution.Similarly, Guti érrez et al. ( 2010) and Salamanca et al. (2010) indicate success with a 0.333 km grid scale using the Bougeault-Lacarr ère (BouLac) ABL scheme (Bougeault and Lacarr ère, 1989) with WRF, a TKE-prediction scheme like MYJ.Introduction

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Full To create a high-resolution four-class urban land surface type dataset, the international border bisecting the domain necessitated a splice of three sources of land surface type data.These sets included the USGS National Land Cover Dataset (NLCD, 2001), the NOAA Coastal Resources Center (CRC) Land Use Dataset and the Ontario Ministry of Natural Resources (MNR) Land Cover dataset.The USGS NLCD (2001) set consists of a raster image of Albers Equal Area Conical projection with 22 land surface type categories equally spaced at a resolution of one arc-second.Among the 22 land use categories are four designed to characterize the urban surface: (1) developed, open space, (2) developed, low intensity, (3) developed, medium intensity and (4) developed high intensity, in order of increasing density of structures and of anthropogenic influence on the surface.These categorical surface classifications are selected for the four-class scheme used here; the morphological differences can be found in Table 1.The NOAA CRC data is of identical projection and resolution to USGS NLCD ( 2001), but distinguishes only two categories of urban surface (low and high intensity).The NOAA CRC data covers the Lake St. Clair watershed, covering approximately 20-25 m inland of the lake shore, including the city of Windsor.The MNR data is a raster image of Lambert Conformal Conic projection with 28 land surface types and pixels evenly spaced in intervals of 25 m available with geo-reference coordinates.Of the 28 land surface types, one is reserved for classification of urbanized surfaces.To create a common set of land surface types, the MNR categories were mapped to the corresponding USGS categories with the MNR urban type assigned to the developed, medium intensity category.The MNR data covers all land surfaces within Ontario.
A series of spliced land surface type datasets were using GIS algorithms and software.To enable tests of systematically varying land surface type resolution, the sets were gridded into intervals of 10, 20, 30, 60 and 120 arc-seconds in separate procedures.In regions of resource data overlap (USGS NLCD, NOAA CRC, MNR), all three resources contributed equally to the categorical assignment of each grid cell.An exception is made for those cells classified as urban surface, in which case classification was left to the mode classification of the USGS NLCD (2001) dataset over Detroit and Introduction

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Full the NOAA CRC dataset over Windsor.The resulting five blended, gridded land surface datasets are raster images of uniformly spaced pixels with categorical assignments to one of the 33 land surface types defined by the USGS NLCD (2001).Remote sensing imagery provided verification of the land surface raster images.

Case studies
The heterogeneity of the geometry, density and materials of the urban surface preclude explicit resolution of flow in a mesoscale model.The five gridded raster images of the Detroit-Windsor metropolitan area described above provide a source to understand how change in the representation of the urban surface under a common model resolution manifests through the model-estimated meteorology.This study runs five test cases, distinguished only by the scale of surface representation in arc-seconds (s): 10, 20, 30, 60 and 120.The finest resolution case (10 s) was chosen to reflect the "neighborhood" scale O (10 2 m), capable of capturing the mean geometric and thermodynamic properties of a particular urban neighborhood without the need to explicitly resolve individual buildings or street canyons, as would likely be necessary at finer resolutions.Model estimates from case 10 s runs represent the model's best-guess for simulation of the meteorology.Departure from these model estimates in coarser case runs (20 s, 30 s...120 s) represents sensitivity to the morphology of the urban environment, which varies with the scale of representation.dry and generally cloud-free over the analysis area, dominated by synoptic-scale high pressure (1016-1019 hPa).In Period 1, nearly calm winds on 23 June yield to increasing south-southeast flow late on 24 June.Low-level winds gradually veer to southwest after 00:00 UTC 25 June as high and mid-level cloud cover increase gradually ahead of a weak extratropical cyclone.In Period 2, morning low-level wind speeds are nearly calm, increasing to 2-5 m s −1 from the southwest by afternoon.

Model verification
To test the validity of model estimates in the urban boundary layer, a thorough verification of the model configuration is necessary.The BAQSMet 2007 field campaign included a series of flights by a Twin Otter aircraft measuring meteorological and chemical quantities at various heights across southwestern Ontario and adjacent areas around Detroit.The Twin Otter datasets serve as the crux of model verification data in the Detroit-Windsor domain, supported with additional data from radiosondes, METAR and a VHF wind profiler.
To complement this verification with a more precise diagnosis of model performance within and above the urban canopy, additional model comparison studies were conducted over Oklahoma City, OK, USA (omitted here).These comparison studies utilized measurements from the Joint Urban 2003 field campaign (Allwine et al., 2004) to verify model estimates.

Instrumentation
BAQS-Met 2007 field data includes a series of measurements taken on-board the National Research Council (NRC) Twin Otter Atmospheric Research Aircraft (hereinafter: Twin Otter).Instrumentation aboard included an array of air sampling equipment and meteorological instruments (Srinivasan and Bastian, 2008).Two flights crossed the urban core grid of the domain and are used here for model verification: Flight #12 Introduction

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Full at White Lake, Michigan, (KDTX: 42.70 • N, 83.47 • W) provide a useful comparison for temperature, water vapor mixing ratio (q), wind speed (u) and wind direction (u θ ).This station is located within the second grid of the model  (Hocking and Hocking, 2007), provides hourly horizontal wind speed and direction measurements in 500 m range gates throughout much of the troposphere.Data is available for comparison during both study periods when and where sufficient signal return is present, but no data is available during Flight #12.The wind profiler is situated in the second model grid, approximately 50 km south-southeast of the urban core of Detroit-Windsor (Fig. 2).

Data quality control
Measurement of the true air velocity on-board the Twin Otter is subject to uncertainty caused by the blending of instrumentation to produce the final dataset (Srinivasan and Bastian, 2008).A correction was made to compensate for a systematic horizontal wind error for the two flights examined here (Ms. Katherine Hayden, Environment Canada, personal communication, 2009).To reduce bias in vertical velocity measurements, the 1 Hz instantaneous moments of vertical velocity were detrended by removing the mean vertical velocity.Introduction

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Full To mitigate white noise in these datasets of 1 Hz sampling frequency, a one-minute average was taken for all variables.This averaging period was selected to facilitate model-measurement comparison; model estimates were archived in one-minute sampling intervals (instantaneous) for the duration of each flight.The 1 Hz data was retained for the calculation of turbulence kinetic energy (TKE) per unit mass.
To verify model estimates, this study uses a 16-point linear interpolation algorithm to map model estimates to observation space (Eq.2).Given an observed variable y at y(i 0 , j 0 , k 0 , l 0 ) where i 0 and j 0 reflect the horizontal position, k 0 the vertical position and l 0 the temporal position, the algorithm seeks the nearest model estimates of the model variable x, which may be a variable identical to y or in need of conversion (e.g., dew point temperature to mixing ratio).The algorithm extracts x at the four model grid points surrounding y(i 0 ,j 0 ,k 0 ,l 0 ) in horizontal, two-dimensional space at the two model vertical levels that enclose the height of the observation (k 0 ).The algorithm then extracts these eight points at the two model output times that enclose the observation time (l 0 ).The algorithm then interpolates the model variable to the point of observation, x(i 0 ,j 0 ,k 0 ,l 0 ), by applying weights to x at the 16 grid points determined earlier.The weights are inversely proportional to the three-dimensional distance (d ) or time (t) between the model grid point and the observation according to Eq. ( 2) flight level varies between roughly 300 to 500 m a.g.l., except in the final minutes when the aircraft descends to approximately 170 m a.g.l.
A majority of measurements are clustered near 510 m a.g.l.(Fig. 3).Comparison indicates a cold model bias in air temperature (Table 2), though this bias is noticeably smaller where Twin Otter data is most abundant.Mamrosh et al. (2002) report a mean bias of around + 1 K for commercial aircraft (ACARS) measurements vs. adjacent radiosonde measurements (within 10 km), below 400 hPa.Ballish and Kumar (2008) find a bias of + 0.6 to 1.5 K at 925 hPa using AMDAR data, which is roughly 20 to 40 hPa above most flight measurements here.Although instrumentation differs among these comparisons, this may partly explain the cold model bias.Comparing against 00Z 4 July 2007 radiosonde data (Fig. 4), model estimates overestimate temperature by 1-2 K in the lowest 2 km, and by ∼2 K above that.
There is also a significant dry model bias (around −2.5 g kg −1 ) relative to Twin Otter measurements (Table 2) that appears to be insensitive to height.This dry bias is not present in model comparison to the radiosonde data.Mamrosh et al. (2002) indicate a mean dew point temperature bias of approximately + 1.8 K in ACARS data, offering one possible explanation.Model performance with wind estimation is less clear; the model consistently overestimates scalar-average horizontal wind speed vs. Twin Otter measurements.Comparison with radiosonde data suggests model overestimation below the model-estimated boundary layer depth (h ABL ∼ 939 m), with varying performance above.Wind direction also shows discrepancy vs. Twin Otter measurements.Some of this can be explained by the relatively light wind speeds.This discrepancy, together with an unexplained backing of the winds, leaves some uncertainty in the Twin Otter wind measurements.Model estimated wind direction shows strong coherence with the 00Z 4 July 2007 radiosonde data (Fig. 4), with a model RMSE of 7.79 • for the full profile (Table 2).Model estimated TKE shows fairly strong coherence with observations, including a local peak near 400 m a.g.l.(not shown).Introduction

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Full Examining model performance vs. time (Fig. 5), Twin Otter temperature measurements during an ascent near 00:12 UTC 4 July suggest a highly unstable local lapse rate of 13 K km  measurements indicate significant fluctuation, varying by as much as 6 g kg −1 in the lowest 500 m a.g.l.(Fig. 3).This observed variation cannot be wholly explained by the flight path over Lake St. Clair, sudden wind shifts or any recent rainfall.There is a much stronger coherence of model estimates to radiosonde water vapor mixing ratio measurements, with RMSE under 1 g kg −1 and smaller mean bias.During the course of radiosonde ascent, model estimated h ABL increases from 250 to 350 m a.g.l., suggesting that the model overestimation of mixing ratio may be sensitive to the h ABL estimate (Fig. 4).Turner et al. (2003) report a dry bias of approximately 5% in their studies using the Vaisala RS80-H radiosonde (commonly used by NWS) with a general 5-10% difference in relative humidity measurements from a dual-launch of radiosondes.Miller et al. (1999) report a systematic dry bias in radiosonde measurements of relative humidity in comparison to both surface stations and aircraft measurements in the mixed layer.Thus, the model moist bias may be partly explained by a potential radiosonde measurement error.The model overestimates scalar-average horizontal wind speed comparing against both Twin Otter and radiosonde measurements (Figs. 3 and 4), with an RMSE of 2-3 m s −1 .Comparison vs. the Harrow VHF wind profiler for 7 July, with a relative abundance of model-measurement comparison points, yields a similar RMSE but with an improved mean bias that suggests a slight model underestimation (Fig. 6).Thus, bias in the model estimation of horizontal wind speed remains uncertain, but at least some local overestimation is likely present.Limited surface measurements from the Twin Otter missed landings also support model overestimation (Table 3).Model RMSE of wind direction vs. radiosonde and wind profiler measurements shows much less variability than that of Twin Otter measurements.Model estimates reasonably capture the profile of wind direction vs. Harrow measurements (Fig. 6) for both 7 July (Period 2) and Period 1.At both missed landings shown in Table 3, model estimated wind direction and METAR wind match very well, while Twin Otter measurements show noticeable departure.Introduction

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Full Evaluating the model performance vs. time (Fig. 5), both missed landings at KDET show a pronounced spike in Twin Otter measured temperature not captured in the model.This may be due to interpolation of near surface temperature from local skin surface temperature and lowest vertical layer air temperature, potentially missing microscale variation.Though limited in number, model estimates are closer to METAR temperature than are the Twin Otter measurements (Table 3).The Twin Otter measures a sharp spike in mixing ratio at the CYQG missed landing (10:10 UTC), but not at either KDET missed landing, (10:21, 10:50 UTC) and shows a substantial increase in water vapor mixing ratio to the northwest, all absent from the model estimates.Model performance of mixing ratio is strong vs.METAR measurements at both the 10:10 and 10:50 missed landings (Table 3).
Model-estimated horizontal wind speed shows overestimation in time vs. Twin Otter measurements except over the urban core of Detroit (roughly 10:14-10:17 UTC) near 520 m a.g.l.Twin Otter observations capture the wind speed decrease (increase) on the approach (take-off) of the missed landings more clearly than do model estimates.
During the Flight #13 period, model-estimated and wind profiler-measured horizontal wind speed show strong coherence over the column (Fig. 6).Model performance of wind direction vs. Twin Otter observations is erratic in time (Fig. 5), with smallest bias at the time of missed landings.

Summary of model verification
Comparison of model temperature estimates with Twin Otter flight measurements yields a distinct model cold bias of 2-3 K over approximately the lowest 500 m a.g.l.This bias may be influenced by a 1 K warm bias common to commercial aircraft temperature measurements.Conversely, model comparison to radiosonde measurements at KDTX reveals a warm bias of about 1 K in the corresponding vertical region and aloft with an RMSE of 2-4 K.
Twin Otter measurements of mixing ratio are consistently and significantly higher than both model estimates and METAR observations where overlap exists.The latter 25924 Introduction

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Full  • .This result is particularly important for validating the penetration of lake-breeze fronts in this environment.

Sensitivity of the morphology to changing land cover resolution
This study hypothesizes sensitivity of mesoscale modeled urban meteorology to the scale of urban representation.This hypothesis presumes that the morphology of the urban environment changes with the scale of representation.Frequency distributions of urban land surface type reveal that nearly 20% more of the fourth grid of the model domain is classified as "medium intensity urban" in case 120 s than case 10 s (Fig. 7), resulting in change to the local and overall urban morphology accordingly (Table 1).Statistical assessment (coefficient of variation) of the principal morphology parameters (z R , f URB , and R/R W ) demonstrates a consistent loss of variability with decreasing resolution of the urban surface.This loss of variability is statistically significant (via Introduction

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Full 2 sample F-test) between all cases for the f URB parameter, but only compared with case 60 s and 120 s for z R and R/R W .These results establish a need to diagnose the response of the local meteorology to this statistically significant change in the urban morphology.

Quantifying the meteorological response
Analysis of the change in model meteorology over the urban core of Detroit-Windsor concentrates on two areas: the surface energy balance and the meteorology within and above the urban canopy, including static and dynamic stability, temperature, moisture, turbulence kinetic energy, horizontal and vertical winds and estimated boundary layer depth.The evaluation examines (1) change to the grid-average value of pertinent quantities, (2) sources of local change within the grid and (3) variation in time of the root-mean-squared-deviation (RMSD) of pertinent quantities between case studies.The latter assessment provides a sound estimate of the magnitude of change that can be anticipated as a result of using coarser mesoscale urban representation, effectively contributing a rough "error bar" to quantities of interest to mesoscale atmospheric modelers.The RMSD assessment includes comparisons of all case studies (10 s, 20 s, 30 s, 60 s, 120 s).The remaining assessments focus exclusively on the change from case 10 s to case 20 s to understand the significance of the neighborhood scale on urban meteorology and the magnitude of change resulting from a very small reduction in the scale of urban representation.
The change in land cover resolution from case 10 s to case 20 s creates an abundance of model grid cells with changed urban land cover type (Fig. 7).With the presence of the Detroit River, this also includes the transition of cells from urban to nonurban (including water) classification and vice versa.For grid-average values, a principal consequence of this change in land cover resolution is a slight shift in the overall distribution of urban land cover type toward higher urban intensities, masking some of the heterogeneity of the true urban surface.Introduction

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Surface energy budget response
The surface energy budget for case 10 s (Fig. 8) illustrates the contribution of both the urban and natural surfaces to the local energy balance.A shift in grid-average urban intensity from case 10 s to case 20 s perturbs this surface energy balance.The daytime skin surface temperature of the urban solid surfaces (roof, wall, road) peaks around 10 K higher than the natural surface in this study, preceding peak air temperature above the canopy (∼22:00 UTC) by about 4 h (not shown).Consequently, this shift increases the grid-average skin surface temperature by up to 0.2 K (for a grid-average f URB increase of 0.014).This result confirms expectations of increased surface (skin) temperature associated with increased urban intensity.The natural skin surface temperature incurs little change except where grid cells are reassigned from land to water cover or vice-versa as a result of resolution of the Detroit River.
For the urban canopy, the immediate effect of a shift toward higher grid-average urban intensity is geometric: a taller canopy with increased building density, restricting canyon space.This reduces u c , enhancing the bulk transfer (drag) coefficient for heat (C H ) at the wall and road surfaces (C H also increases at the roof).The net result favors enhanced sensible and latent flux from the urban canopy (l v E urban , H urban ).To restore equilibrium in the surface energy budget, the model iteratively reduces the skin surface temperature at the wall, road and roof surfaces, reducing G urban , H urban , l v E urban and the outgoing (longwave) radiation.These urban fluxes are additionally sensitive to local temperature and moisture gradients.
Among all surface energy budget components, the latent heat flux (l v E total ) demonstrates the most significant response between case 10s and case 20 s (Fig. 9).The contribution from the urban component (l v E urban f URB ) is minimal due to limited moisture availability (β), remaining below 10 Wm −2 at peak.Thus, the change in l v E total derives principally from the natural surface component of the grid cells, (1−f URB )l v E natural , during the daytime when l v E natural is strongest.The change in f URB contributes toward the bulk of the daytime decrease in l v E total with l v E natural responsible for the remainder.The latent heat flux from a vegetation-covered surface here derives mostly from canopy Introduction

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The grid-average contributions to available energy changes little between cases; the change in l v E natural derives largely from the water vapor demand at the lowest model layer (∼28 m a.g.l.), which varies locally.The RMSD of l v E total (Fig. 10) over the urban core peaks at 45 Wm −2 at 18:00 UTC (14:00 LT), coincident with the time of the strongest flux (Fig. 8) and nearly 25% of its value.RMSD increases monotonically, in phase, for case 10s vs. progressively coarser cases, approaching 35% of the total flux value for case 10 s vs. case 120 s.This demonstrates significant daytime sensitivity of model estimated l v E total to the scale of urban representation and the potential gain from use of the neighborhood scale (case 10 s) in urban surface representation.It also suggests that much coarser representations yield only a marginal increase in RMSD from the neighborhood scale.
The response of the surface sensible heat flux (H total ) to the land cover resolution change entails contributions from both the urban (H urban ) and natural (H natural ) surface components.Daytime grid-average H total increases from case 10 s to case 20 s, the sum of an increase from H urban f URB and a decrease from H natural (1−f URB ) (Fig. 9).The net increase in f URB reduces the proportion of total flux from natural surfaces contributing partly toward the early afternoon reduction of H natural (1 − f URB ).H natural itself also decreases due to the reduced daytime natural surface skin temperature, shrinking the local natural skin surface-to-2 m temperature gradient and, hence, the flux.
While the grid-average contribution of H urban f URB to H total is positive, grid-average change to H urban itself is negative.The skin surface temperature reduction along the canopy roof, walls and road grows to 0.5 K by mid-afternoon, with diagnostic canyon air temperature (T c ) decreasing by approximately half that.Additionally, the shift toward higher urban intensity favors greater building density, at the expense of canyon width.In the afternoons, the peak temperature difference between the roof surface and the air above the canopy (∼+ 6 K) is considerably smaller than that between the canyon wall or road surfaces and the canyon air temperature (∼+ 9 K, + 12 K, respectively), not shown here.Combined, these changes reduce grid-average H urban by approximately Introduction

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Full 8 Wm −2 by mid-afternoon from case 10 s to case 20 s.Despite the grid-average reduction of H urban the grid-average increase of f URB forces a net increase in grid-average H urban f URB .Accounting for those grid cells that change from urban to non-urban classification and vice versa (such as by consequence of resolution of the Detroit River), this further increases H urban f URB , resulting in a net increase of approximately 10 Wm −2 in mid-afternoon, a 4% enhancement of its original contribution in case 10 s (Fig. 8).
The RMSD of H total (Fig. 10) over the urban core peaks at 62 Wm −2 around 17:30 UTC (13:30 LT), coincident with the time of the strongest H urban f URB (Fig. 8) and 18% of H total .As with l v E total , RMSD increases monotonically, in phase, for case 10s vs. progressively coarser cases, approaching 27% of the total flux value for case 10 s vs. case 120 s, further demonstrating significant local sensitivity.
Grid-average change to ground heat flux (G total ) from case 10 s to 20 s is virtually negligible (Fig. 9), but is the result of opposing change in the urban (G urban f URB ) and natural surface contributions G natural (1 − f URB ) that can result in more substantial changes locally.The G natural (1−f URB ) contribution registers a grid-average decrease in magnitude up to 2 Wm −2 (both day and night).As with sensible heat flux, this decrease is a result of reduction to both (1 − f URB ) and G natural .The decreased daytime natural surface skin temperature is nearly balanced by increased nocturnal temperature, reducing the local temperature gradient across the natural skin surface and, thus, G natural .Increased gridaverage f URB at case 20 s favors weighting rooftop "ground" heat flux more heavily than road "ground" heat flux.This change favors decreased daytime ground heat flux (∼2-3 Wm −2 ) and slightly increased nighttime flux.The contribution to total ground heat flux, G urban f URB , shows a net increase in magnitude (2-3 Wm −2 during the afternoon, 1 Wm −2 at night), due to increased grid-average f URB .
The RMSD of G total (Fig. 10) over the urban core peaks at 32 Wm −2 around 17:00 UTC (13:00 LT), coincident with the time of its strongest magnitude (Fig. 8) and 24% of G total .RMSD increases for case 10 s vs. progressively coarser cases, but with proportionally smaller increments than H total or l v E total , approaching 30% of the total flux value for case 10 s vs. case 120 s.Introduction

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Meteorological response
Within the urban canyon, the model estimated air temperature (T c ) scalar wind speed (u c ) and water vapor mixing ratio (q c ) are subject to variation in canyon geometry and heat flux.Comparing case 10 s and case 20 s, the increased ratio of R/R W and slight daytime (nightime) decrease (increase) of surface skin temperature along the canyon walls and road in case 20 s decrease grid-average T c up to 0.2 K in the afternoon and increase up to 0.1 K overnight.The u c quantity demonstrates a slight grid-average reduction (less than 0.1 m s −1 ).This is anticipated due to reduced mean canyon space at higher urban intensity.The grid-average q c shows little change.Local response in canyon meteorology is more substantial, vulnerable to change in the above-canopy wind speed and local canopy height.Versus case 20 s, the peak of T c , u c and q c RMSD (Fig. 11) is approximately 0.3 K, 0.2 m s −1 and 0.2 g kg −1 , respectively.Normalized by the mean, u c RMSD is greatest, though more precise diagnosis of street canyon flow requires more explicit resolution as in a computational fluid dynamics model.RMSD increases consistently for comparison of case 10 s vs. progressively coarser resolution test cases, though evening change in q c shows some variability.Above the canopy, there is also evidence of a response in the meteorology.Examining the sign of the Obukhov length scale (L: Obukhov, 1946;Monin and Obukhov, 1954), the static stability of the urban environment in these case studies shows a consistently unstable daytime surface layer after sunrise.A largely stable nighttime surface layer develops abruptly after sunset.Being a function of surface heat flux, the transition of L from daytime static instability to nighttime static stability is non-uniform and progresses inversely to the urban intensity.For Periods  Richardson, 1920) clearly distinguishes the dynamically unstable daytime well-mixed ABL from the laminar flow above and also reveals some difference in the evening residual turbulence strength between days during Period 1.
Changes in the surface representation from case 10 s to case 20 s provoke a patchwork of positive and negative change, mostly above 100 m a.g.l., but not enough to alter the flow classification.
Air temperature above the canopy responds to the change in T s due to changing scale of surface representation.Predictably, re-classification of urban grid cells to water grid cells from case 10 s to 20 s dominates the latter, given a typical 15-20 K T s difference in the afternoons.Wind direction subsequently influences the breadth of this effect.On the afternoon of 23 June, low-level easterly wind favors more substantial cold air advection resulting from increased water coverage in case 20 s, not found on 24 June (south-southeast winds) or 7 July (west-southwest winds).Later that day, after 21:00 UTC, a Lake Erie lake breeze front (LBF) penetrates the domain from the southsouthwest.The exchange of medium intensity urban land grid cells for water grid cells along the eastern part of the Detroit River delays the advance of the LBF (Fig. 12).Some local LBF acceleration and deceleration are also evident across the grid when comparing case 10 s and 20 s.Coastline resolution to the east of Windsor also affects the placement of a thermal internal boundary layer on 24 June.As the synoptic-scale wind rotates from south to southeast during the day, the fetch incorporates a progressively longer period over the cooler Lake St. Clair surface prior to reaching eastern Detroit.Its expansion into the urban core region is accelerated in case 20 s vs. case Introduction

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Full 10 s, providing up to a 1.5 K difference locally in air temperature above the canopy (T a ∼ 28 m a.g.l.) between cases.
The RMSD of T a peaks at 0.2 K in the early afternoon (Fig. 11) for case 10 s vs. 20 s, slightly less than RMSD of T c .Comparing case 10 s to coarser resolutions, RMSD of air temperature shows only modest increases.Air temperature above the urban canopy (T a ) and higher in the ABL appears relatively insensitive to systematic change in the urban morphology except in local circumstances as described above.
The effect of changed surface representation has a dichotomous effect on TKE.Increased urbanization at case 20 s leads to a net increase in mean canopy height, promoting mechanical production of turbulence and resulting in a net gain in grid-average TKE near the surface.When the wind direction and strength favors advection of the daytime grid-average cooling influence of the increased water coverage in case 20 s, the grid-average cooler surface slightly weakens the strength of thermal plume updrafts and downdrafts, concurrently reducing TKE aloft within the boundary layer and thus slightly reducing grid-average model estimated h ABL , parameterized according to TKE strength (Janjic, 2002).
Locally, as the buoyant production of TKE in the ABL varies according to change in surface thermal properties, and shifting wind direction varies TKE strength, so does the model-estimated h ABL also vary.The RMSD of h ABL reveals considerable variability during the daytime, peaking above 300 m in the early afternoon (Fig. 11).Comparing case 10 s vs. progressively coarser urban surface representations yields RMSD exceeding 400 m.
The variation of q with surface representation follows the change in h ABL .Reduction of grid-average h ABL at case 20 s reduces dry air entrainment from aloft and leads to a grid-average net increase of q (up to 0.1 g kg −1 ) in the well-mixed layer during the afternoon.RMSD of q a peaks at 0.2 g kg −1 in the afternoon vs. case 20 s, expanding up to 0.3 g kg −1 vs. case 120 s (Fig. 11).With considerable variation in wind direction among Periods 1 and 2, the low-level (above-canopy) horizontal wind speed RMSD peaks between 0.5-0.7 m s −1 during the Introduction

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Full afternoon for comparison of the neighborhood scale to coarser scales (Fig. 11).Corresponding wind direction RMSD peaks in the early afternoon during ABL growth, reaching 25 • for comparison vs. case 20 s and up to 35 • for case 120 s.This sensitivity is of particular interest to the Detroit-Windsor metropolitan area, where such deviation can affect the timing and extent of influence of on-shore flow or LBF penetration.

Conclusions
The sensitivity of model mesoscale meteorology to the scale of representation of the urban surface is explored over several summer periods in the Detroit-Windsor metropolitan area.The response includes both periodic change (as a function of daily heating) and stochastic change (as from change in the direction and magnitude of low-level flow in response to varying surface morphology).The "effective model" resolution of approximately 2.1 km in the finest grid inhibits explicit inter-case comparison of the fine scale structure that would be expected to develop in response to a changing surface morphology; the model dampens this part of the KE spectrum and with it the variance of sensitivity to the surface morphology.However, the surface energy budget and other near-surface meteorological quantities forced largely by the surface parameterizations can be expected to show demonstrable sensitivity to change in the surface representation.
In the surface energy budget, the natural surface component of the total latent heat flux l v E natural (1 − f URB ) and the urban surface component of the total sensible heat In the absence of explicit resolution of flow in the urban boundary layer, there is potential benefit to the neighborhood scale of resolution of the urban environment with respect to boundary layer depth estimation and in the timing of lake-breeze frontal passages or thermal internal boundary layers.High urban intensity, as found in the urban core of major cities, is found to delay the onset of nocturnal static stability at the surface up to 2-3 h vs. non-urban surfaces.Increased urban intensity enhances mechanical production of turbulence kinetic energy just above the canopy, but has little influence of model estimated boundary layer depth.Scale of representation is also critical to cities with riparian or coastal interests, where temperature, turbulence kinetic energy and boundary layer depth are highly sensitive.Afternoon estimated boundary layer depth RMSD vs. the neighborhood scale exceeds 300 m, demonstrating significant sensitivity.
Modelers should be cognizant of the inherent error in state variable estimates evolving from a mesoscale urban surface parameterization.This study offers one attempt to quantify the nature and magnitude of sensitivity to scale and the potential error that arises with progressively coarser representations.Although the most acute response predictably corresponds to surface and low-level quantities, change in boundary layer depth and the timing of mesoscale circulations like lake-breeze fronts can yield broader impacts on real atmosphere simulations.Full  Full  Full

Symbols, acronyms and abbreviations
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Analysis is mostly limited to the fourth model grid (Fig.1), concentrating on two periods within the Border Air Quality and Meteorology Study (BAQS-Met) 2007 field campaign: 12:00 UTC 23 June-12:00 UTC 25 June 2007 (Period 1) and 00:00 UTC 7 July-00:00 UTC 8 July 2007 (Period 2), with the first six-hour period withheld from analysis to allow for model spin-up time.For both periods, local time in Detroit-Windsor is [UTC -4] hours.The surface water temperature is held constant according to initial conditions throughout the duration of the model integrations.The two periods provide a useful archive for response under varying wind speed and direction.Both periods are 25917 Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (3-4 July 2007) and Flight #13 (6-7 July 2007).Measurements of three-dimensional wind, temperature (T ), dew point temperature (T d ) and air pressure (p) were extracted for model verification.Several additional stationary sources supplement Twin Otter data toward model verification.Radiosonde launches (with GPS) by the US National Weather Service (NWS) Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

3. 3
Flight #12 BAQS-Met 2007 Twin Otter Flight #12 crossed through the third grid of the model domain between 00:05 and 00:48 UTC 4 July 007, exiting the northwest corner of the domain for 15 minutes within that period for a course change at Oakland International Airport (KTPK) in Pontiac, Michigan, USA (Fig. 2a).Within the third model grid, the 25920 Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

3. 4
Flight #13BAQS-Met 2007 Twin Otter Flight #13 crossed the third grid of the model domain between 10:03 and 10:57 UTC 7 July 2007, exiting the northwest corner of the domain for 13 min near the middle for a course change at KPTK (Fig.2b).Within the third model grid, the flight level varies across the lowest 520 m a.g.l., including three missed landings at airports within the model grid (10:10, 10:21, 10:50 UTC).Being an early morning transect, measurement points fall above the model estimated h ABL (<200 m a.g.l.throughout the period) except for the missed landings.The vertical comparison (Fig.3) confirms the cold and dry model bias seen in Flight #12, though both indicate a strong low-level temperature inversion.A model warm bias aloft vs. radiosonde data is apparent.However, the radiosonde may drift horizontally up to 300 km during a typical two-hour ascent (NOAA National Weather Service, 2010).A model dry bias vs. Twin Otter measurements is present, as in Flight #12.Whereas model estimates suggest a generally uniform water vapor mixing ratio, Twin Otter 25922 Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 and 2, (sunset ∼01:12 UTC) most developed, open space type urban land cover surfaces become statically stable within 30 min of 23:00 UTC, low intensity urban ∼23:50 UTC, medium intensity urban ∼00:30 UTC and high intensity urban ∼01:30 UTC.Low-level wind speed remains generally ≤3 m s −1 across the grid.Model estimates reveal limited, sporadic areas of static instability overnight over the high intensity urban surfaces, otherwise vacillating Discussion Paper | Discussion Paper | Discussion Paper | between weak and strong static stability.Around the time of sunrise (∼10:00 UTC), high intensity urban surface transition to static instability precedes the rest of the domain by about 30 min.The remaining urban surface types change between 10:40 and 11:00 UTC.Thus, local change in urban surface classification at some coarser representation may drastically alter the overlying model estimated static stability.This result is keenly pertinent to model applications sensitive to surface layer vertical mixing in the evenings and overnight.Assessment of the local dynamic stability by way of the bulk Richardson number (Ri b : Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | flux (H urban f URB ) are most sensitive, showing a net grid-average daytime decrease and increase, respectively, of up to approximately 10 Wm −2 for change from a 10 to Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | CrpGrslnd mixed cropland and grassland land surface type CrpPast mixed cropland and pasture land surface type CrpWood mixed cropland and woodland land surface type CFD Computational Fluid Dynamics CRC (NOAA) Coastal Resources Center DecBfFor deciduous broadleaf forest land surface type DecNfFor deciduous needleleaf Forest land surface type DNS Direct Numerical Simulation DTW Detroit-Windsor E kinematic moisture flux (l v E = latent heat flux) f URB fractional urban coverage g gram G ground heat flux G natural ground heat from the natural component of an urbanized grid cell G total ground heat flux from the G urban and G natural components of a grid cell G urban ground heat flux from the urban canopy Grasslnd grassland H natural sensible heat from the natural component of an urbanized grid cell H total sensible heat flux from the H urban and H natural components of a grid cell H urban sensible heat flux from the urban canopy Hz Hertz IrgCrpPst irrigated cropland and pasture land surface type JJA Junel v E natural latent heat from the natural component of an urbanized grid cell l v E total latent heat flux from the l v E urban and l v E natural components of a grid cell 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Fig. 9 .
Fig. 9. Change of flux (case 10 s-case 20 s) for sensible heat flux (a), latent heat flux (b) and ground heat flux (c) including the total (green) urban (red) and natural surface (blue) contributions to each.Change shown is averaged over all grid cells in the fourth model grid of the domain, plotted vs. time (UTC) for the period 02Z 24 June-02Z 25 June 2007 in units of Wm −2 .
domain, west of Detroit-Windsor.Profiles are extracted from the launch times nearest to Flights #12 and #13.During Twin Otter Flight #13, three missed landings took place at airports with hourly Ava- iation Routine Weather Reports (METAR) available from in-situ instruments at field level (Plymouth State University, 2010), two of which coincide within several minutes of METAR data, providing points of surface verification.A VHF wind profiler installation at Harrow, ON (42 • 42 N 83 • 28 W), part of the Ontario-Quebec VHF Wind Profiler Network −1, not captured by the model.This observed feature is not replicated during the subsequent descent (00:37-00:48 UTC), whereas the model response is proportionally opposite.Similar behavior is shown for wind speed with Twin Otter measurements indicating steadily increasing wind speed during ascent.The horizontal wind speed shows the strongest coherence of model and measurement directly over downtown Detroit, at 510 m a.g.l.Comparison of wind speed to 00:00 UTC METAR at Windsor Airport (CYQG: 42.27 • N, 82.97 • W) reveals surface (10 m a.g.l.) winds of less than 2.5 m s −1 , justifying the Twin Otter measurements.For wind direction, Twin Otter measurements suggest erratic change over short distances and largely differ from METAR at CYQG (south at 00:00 UTC, south-southwest at 01:00 UTC) and • N, 83.02 • W, south-southeast at both 00:00 and 01:00 UTC).These METAR wind directions match very well with model estimated wind direction.
two sources show excellent correspondence during the Flight #13 missed landings.Comparison of model estimates to radiosonde measurements also yields small RMSE with no clear bias in the lowest 500 m a.g.l.A potential dry bias in radiosonde measurement may explain evidence of a moist model bias aloft during Period 2.

Table 1 .
Values assigned to gridded urban parameters in the WRF urban canopy model according to surface type.