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Modelling study of sea breezes in a complex coastal environment
Atmospheric Environment 34 (2000) 2873}2885
Modelling study of sea breezes in a complex coastal environment X.-M. Cai *, D.G. Steyn School of Geography and Environmental Sciences, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Atmospheric Science Program, Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2 Received 4 January 1999; received in revised form 8 November 1999; accepted 17 December 1999
Abstract This study investigates a mesoscale modelling of sea breezes blowing from a narrow strait into the lower Fraser valley (LFV), British Columbia, Canada, during the period of 17}20 July, 1985. Without a nudging scheme in the inner grid, the CSU-RAMS model produces satisfactory wind and temperature "elds during the daytime. In comparison with observation, the agreement indices for surface wind and temperature during daytime reach about 0.6 and 0.95, respectively, while the agreement indices drop to 0.4 at night. In the vertical, pro"les of modelled wind and temperature generally agree with tethersonde data collected on 17 and 19 July. The study demonstrates that in late afternoon, the model does not capture the advection of an elevated warm layer which originated from land surfaces outside of the inner grid. Mixed layer depth (MLD) is calculated from model output of turbulent kinetic energy "eld. Comparison of MLD results with observation shows that the method generates a reliable MLD during the daytime, and that accurate estimates of MLD near the coast require the correct simulation of wind conditions over the sea. The study has shown that for a complex coast environment like the LFV, a reliable modelling study depends not only on local surface #uxes but also on elevated layers transported from remote land surfaces. This dependence is especially important when local forcings are weak, for example, during late afternoon and at night. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Mesoscale modelling; Sea breezes; The lower Fraser valley; Mixed layer depth; CSU-RAMS
1. Introduction The lower Fraser valley (LFV) of British Columbia, Canada, is located on the eastern side of the Strait of Georgia and extends to the Fraser canyon in the east. The LFV basin is bounded by the Coast Mountains in the north and the Cascade Range in the east. On the western side of the Strait of Georgia, sits Vancouver Island, which bounds the LFV in the west (see Fig. 1). The topography of the region results in severely constrained low-level ventilation, causing frequent buildup of air pollution. In recent years, population in the LFV has increased rapidly, and as a result so have emissions of various types of air contaminants, such as nitrogen oxides (NO ), volatile organic compounds (VOC), carbon V * Corresponding author. Fax: #44-121-4145528. E-mail address: [email protected] (X.-M. Cai).
monoxide, sulphur dioxide, and particulate matter (Joe et al., 1996). Under stagnant synoptic high-pressure systems during the summer time, shallow but intense subsidence inversions above the boundary layer act as a lid over the region, suppressing the vertical transport of pollutants. Because of high temperatures, this meteorological condition also favours the production of ozone from NO and V VOC (McKendry, 1994). Consequently, the LFV su!ers from severe ozone episodes under these particular meteorological conditions (Pryor et al., 1995; Steyn et al., 1997). In this coastal area, the meteorology is also accompanied by local, thermally forced daytime sea breezes which advect emissions inland, bringing cold air from the sea surface, forming an even shallower mixed layer (Steyn and Faulkner, 1986; Chen and Oke, 1994). Mountains around the LFV cause regional, topographically driven daytime upslope winds, nighttime downslope drainage winds (Hay and Oke, 1976), and mesoscale mountain/valley circulation #ows. Recently, McKendry et al.
1352-2310/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 0 ) 0 0 0 7 9 - 0
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Fig. 1. Map of LFV and locations of observational stations which provide the data used to evaluate the model. The UTM coordinates are used in this "gure.
(1997) demonstrated that the `chimney e!ecta and `convective debrisa were responsible for the formation of elevated ozone layers observed above the basin area. It is recognized that modelling of meteorology is essential to understanding of pollutant transport, and therefore is the "rst important step towards photochemical modelling of ozone episodes. There have been many studies of sea breezes in other areas with complex coastlines (Physick and Abbs, 1991; Tjernstrom and Grisogono, 1996; Helmis et al., 1997; Melas et al., 1998). For the LFV, there have been several studies on sea- or land breezes and up- or down-slope #ows. Steyn and McKendry (1988) used a three-dimensional hydrostatic numerical model to simulate a well-developed sea breeze on 23 August 1985. Their simulation was performed with a horizontally homogeneous initialization on a 35;29;26 grid with a horizontal spacing of 5 km. Their simulations overestimated wind speed, especially during the night. Miao and Steyn (1994) applied an early non-hydrostatic version of the Colorado State University
Regional Atmospheric Modelling System (CSU-RAMS) to the same day and the same domain as those in Steyn and McKendry (1988), but using a "ner horizontal grid spacing of 2.5 km. Though their overall model performance was better than that of Steyn and McKendry (1988), they still found a progressively increasing wind speed over night in the Strait of Georgia. This excluded the possibility of multi-day simulations, which are necessary for modelling of photochemical processes during a multi-day air pollution episode. The overestimates of wind speed in both studies might be attributed to the single-grid con"guration combined with homogeneous initialisation. Hedley and Singleton (1997) used a system (a combination of the MC2 and CALMET models) to simulate meteorological conditions during the photochemical episode of 17}21 July 1985. Their model employed a 10 km horizontal grid spacing within a larger domain simulated by MC2, and a 5 km horizontal grid spacing within a smaller domain simulated by CALMET. Although some comparisons with observation
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show a reasonable model performance for the multi-day simulation, the model system signi"cantly underestimates the diurnal temperature cycle amplitude and overestimates wind speeds near the coastline. From the above discussions, it is evident that previous modelling studies of sea-breezes in the LFV failed to produce satisfactory meteorological (especially wind) "elds. It is a concern that the inadequacies of the wind "elds will render them inappropriate for application in a comprehensive air quality model (e.g., Urban Airshed Model). In addition, it is unlikely to obtain the correct temperature and MLD if wind "elds are not correctly modelled. For this reason, the present study aims to examine the application of CSU-RAMS with nested grid con"guration to the LFV during the period studied by Hedley and Singleton (1997). Evaluation of the model performance will be conducted through comparison with surface observational data. Wind "elds produced by the model will be analysed to provide some insight into sea/land breezes and slope/valley winds. The vertical structure of wind and temperature from observation and modelling will be examined and discussed. In addition, MLD will be diagnosed from the model output and compared with observed MLDs at three stations.
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used for both grids. Considering the timescale of dominating motions in Grid 1 is larger than that in Grid 2, the e!ects of the given nudging coe$cient are stronger in Grid 1 and weaker in Grid 2. As the timescale of a seabreeze episode is smaller than 6 h, it is unlikely that the mesoscale features of sea breezes are signi"cantly suppressed by the simulation (see Cai et al., 1998); in fact, this is shown by the results of Grid 2 in the current study (not presented here). Table 1 also gives the UTM coordinates for Grids 2 and 3. The domain for Grid 3 is presented in Fig. 1, which shows that the LFV basin is an almost #at, triangular region, its northern mountain range is approximately along the east}west direction, and its eastern mountain range is approximately in the southwest} northeast direction. It is noted that Vancouver city area, approximately around the symbol of solid triangle (Queen Elizabeth Park, or QEP) in Fig. 1, is close to the Coast Mountains, and may therefore be signi"cantly a!ected by up- and downslope winds. In the vertical direction, the second vertical mesh point (for w at 50 m, and the remaining vertical mesh spacings
2. Model con5guration In the current simulation, CSU-RAMS (Pielke et al., 1992) is used, and a two-way interactive nested grid con"guration with three grids is employed, each grid covering a di!erent domain size (see Fig. 2). Speci"cation of domain size and grid spacing for three grids is given in Table 1. Analysed "elds are produced by the Isentropic Analysis package (part of CSU-RAMS) for every 12 h based on gridded dataset from US National Centers for Environmental Prediction (NCEP) global model. At every time step during model runs, nudging "elds of wind, temperature, and humidity are obtained by linear interpolation of the two closest analysis "elds. Meanwhile, Grids 1 and 2 are nudged towards their respective nudging "elds. A nudging time scale of 21 600 s (6 h) is
Fig. 2. Con"guration of nested grids. The "gure box is the boundary of Grid 1; dot-dashed line is the boundary of Grid 2; and dashed line is the boundary of Grid 3.
Table 1 Speci"cation of three grids. ¸ , ¸ and ¸ are domain sizes in the x, y and z directions, respectively; N , N and N are the number of V W X V W X mesh points in the x, y and z directions, respectively; *x and *y are the mesh spacings in the x and y direction, respectively; *t is time increment; and UTM-x and UTM-y represent the range of the UTM coordinates in the x- and y-directions, respectively. The UTM coordinates for Grid 1 are not available since they are out of the current UTM zone Grid
¸ V
¸ W
¸ X
N V
N W
N X
*x, *y (km)
*t (s)
UTM-x (km)
UTM-y (km)
1 2 3
1360 410 162.5
1200 370 122.5
18.8 18.8 18.8
35 42 66
31 38 50
26 26 26
40 10 2.5
30 15 15
* [320, 730] [453.75, 616.25]
* [5280, 5650] [5383.75, 5506.25]
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are increasing with a ratio of 1.2, with the maximum grid spacing being 2000 m. Consequently, the "rst vertical mesh point for u, v, and ¹ is at about 23.86 m and the vertical dimension of the domain is about 18.8 km. At the top of the domain, a rigid lid condition is applied to all variables. To prevent the re#ection of upward gravity waves by this lid condition, a nudging layer is imposed from 4 km above with a time scale of 600 s. Five soil levels are applied at 0.0, 0.1, 0.3, 0.6, and 1.0 m. Smagorinsky's deformation turbulence closure scheme is used in the horizontal direction and Mellor}Yamada's second-order closure scheme is used in the vertical direction. Simulation starts at 1600 Paci"c Standard Time (PST) 16 July 1985, with 12 extra hours to allow nonphysical components to be di!used or dissipated. Simulation ends at 0400 PST on July 21 so that a total of four-day's results are available for analysis. 3. Statistical evaluation In this study, we employ a statistical evaluation method proposed by Willmott (1981) to validate model results from near-surface measurements. Data used in the evaluation are collected at the observational stations shown in Fig. 1. Surface wind speed and direction were monitored at 28 sites at 10 m height, (denoted by symbol solid and open circles in Fig. 1). Temperature was monitored at 10 sites at 1.5-m height (denoted by solid dot in Fig. 1). One site at QEP in Vancouver (denoted by solid triangle in Fig. 1) provides vertical pro"les of wind, temperature and humidity at about every hour during the daytime for 17 and 19 July 1985. This latter dataset is used to compare modelled vertical pro"les of these quantities, as well as the model-derived mixed layer depth (MLD). Two sites (denoted by open triangle in Fig. 1), one at Delta and the other at Surrey, provide MLD data measured by acoustic sounder. 3.1. Evaluation method Willmott (1981) proposed a quantitative evaluation of model performance, which was applied by Steyn and McKendry (1988), and Miao and Steyn (1994). In this evaluation method, n measurement surface stations provide a time series of observational data, denoted by O(t), or (O (t),2, O (t),2, O (t)). Predicted result output by G L model at the same locations are denoted by P(t), or (P (t),2, P (t),2, P (t)). O(t) and P(t) can be considered G L vectors in an n-dimensional real-value space, RL, changing with time t. A weighted norm in RL can be de"ned by
L u "m " G G G , (3.1) L u G G where n is a vector in RL, and u is a weighting vector in RL. The `distancea between any two vectors, n and g, in #n#"
RL is thus ""n!g"". A quantity, PH(t), is de"ned as the least-squares linear regression of P(t) on O(t), i.e., PH"a#bO , where a and b are regression coe$cients. G G Therefore, the three quantities: systematic and unsystematic components of the root-mean-squared di!erences and the total root mean-mean-squared di!erence, are actually the distances between P(t), O(t), and PH(t) RMSD """P!O"", Q RMSD """PH!P"", S RMSD"""P!O"".
(3.2) (3.3) (3.4)
If prediction and observation are identical, i.e. P"O"PH, all three distances above are zero. According to Willmott (1981), RMSD is a measure of linear Q variation in the model bias. The statistic RMSD , howS ever, is a measure of the non-linear discrepancy between prediction and observation. Another important measure is the index of agreement d, de"ned as (""P!O"") , (3.5) d"1! L u ("P !OM "#"O !OM ")/ L u G G G J G G where OM is the averaged (over n stations) observational value. This index ranges from 0.0 (no agreement) to 1.0 (perfect agreement, when prediction is the same as observation). De"nitions (3.1)}(3.5) can be extended to the case in which the data O are wind vectors by replacing the G absolute value operator, " ) ", in Eqs. (3.1) and (3.5) by ordinary wind vector norm. 3.2. Surface temperature Fig. 3 presents evaluation results for surface temperature. It is demonstrated in Fig. 3(a) that for mean temperature, modelled results are in good agreement with observation. In the "rst day, the model underestimates temperature during the daytime and slightly overestimates it during the night. A discontinuity in observed temperature in the early morning of July 18 is caused by di!erent number of stations available for evaluation: three stations before 0100 PST of 18 July and 10 thereafter. The increasing rate of temperature during the daytime (from 0600 PST to 1800 PST) for each day is well captured by the model. Modelled spatial standard deviation (SD) of temperature is also in good agreement with the daytime observation (see Fig. 3(b)), but it is smaller than the observed values at night. Fig. 3(c) indicates that, except for 17 July RMSD dominates RMSD for the Q S daytime, while RMSD dominates RMSD at night. We S Q notice from Figs. 3(c) and 4(d) that during the day, RMSD is low (about 1}23C) and the index of agreement almost reaches unity, but during the night, RMSD is high (about 2}33C) and the index of agreement drops to about 0.4. The above results suggest that the model performs very well for the daytime, but has some di$culty in
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Fig. 3. Time variation of temperature statistics from 17}21 of July 1985. (a) Mean temperature, (b) standard deviation of temperature, (c) root-mean-square di!erence (RMSD for total, RMSDs for systematic, and RMSDu for unsystematic), and (d) the index of agreement.
Fig. 4. Time variation of wind statistics from 17}21 of July 1985. (a) Mean wind speed, (b) mean wind direction, (c) standard deviation of wind, (d) root-mean-square di!erence (RMSD for total, RMSDs for systematic, and RMSDu for unsystematic), and (e) the index of agreement. Mean speeds and directions are derived from vector averages.
reproducing correct surface temperature at night. This is probably due to subgrid scale variations in the observed temperatures caused by unresolved e!ects in surface radiation inversion. However, in comparison with modelled temperatures in Hedley and Singleton (1997), the current study represents a signi"cant improvement.
Modelled wind directions during the daytime also agree fairly well with the observations, but on 17 and 20 July the model anticipated the land-breeze to sea-breeze transition by roughly 1 h and presented sudden rather than gradual changes in wind direction. At night, the model generally overestimates wind speed by 0.5}1.0 m s\ and fails to reproduce a weak land breeze (the modelled southerly wind in contrast to the observed easterly wind). However, this deviation in wind direction may not be very important to transport of air pollutants since the wind speeds are usually below 1 m s\. In Fig. 4(c), we present the standard deviations of wind with respect to all wind stations. It is noted that magnitudes of the modelled SD are often larger than the observed ones at night. The value range of SD is close to that of the mean wind speed, indicating that the locally weak winds dominate and there is a high spatial variability at night. During daytime, magnitudes of the modelled
3.3. Surface wind Figs. 4(a) and (b) demonstrate the model performance for mean wind speed and direction averaged over 28 stations. The results show a clear sea-breeze cycle, characterized by diurnal variation of wind speed and direction. Both observational data and model output show higher wind speed during daytime than at night. During the daytime, modelled wind speeds are about the same as these observed except for the day of July 20 during which the model overestimates wind speed by about 1 m s\.
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SD are slightly smaller than observational values, presumably due to strong horizontal smoothing inherent in the model formulation. As Willmott (1981) explained, RMSD represents Q trend-like di!erences between observed and modelled "elds, and RMSD represents the irreducible deviation S between observed and modelled "elds. In Fig. 4(d), RMSD are fairly large in the "rst and the last days, Q implying that the modelled results systematically depart from the observed data at these times. During daytime, in general, all RMSD values are slightly smaller and those at night. Unlike temperature, RMSD for wind dominQ ates RMSD at almost all times. The index of agreement S in Fig. 4(e) shows that model performance is good in daytime (generally greater than 0.5), and poor at night (generally less than 0.5).
4. Analyses of results 4.1. Surface wind xelds Fig. 5(a) presents modelled and observed wind "elds at 1000 PST on 17 July 1985. The gridded and thick arrows are modelled and observed wind vectors, respectively. We plot modelled wind vectors at only every other mesh point in both x- and y-directions. The solid curves indicate coastal lines and dashed lines represent a terrain contour of 100 m. At 1000 PST on 17 July as shown in Fig. 5(a), a sea breeze was just building up along the coastline, whereas the wind along the Strait of Georgia was fairly strong. Up-slope winds were observed to build up over the mountainsides, and were stronger than the sea breeze at this time of the day. In most of the LFV
Fig. 5. Surface wind "eld (10 m) at (a) 1000 PST, (b) 1600 PST, (c) 2200 PST July 17 1985, and (d) 0400 PST July 18 1985. The gridded arrows are modelled wind vectors and thick ones are observed wind vectors. Coordinates are in UTM unit. Solid curves represent the coastline and dotted curves indicate the terrain contour at 100 m.
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basin, winds were very weak. Compared with the observational winds (thick arrows), the model results provide a good representation of the real-wind "eld at this time. In the afternoon at 1600 PST, as the sea-breeze front intruded into the LFV area, the magnitude of the breeze was about the same as that of the up-slope winds (see Fig. 5(b)). The whole LFV basin was dominated by westerly winds, which arised from combined e!ects of up-slope winds and sea breezes. In contrast, winds near the middle strait were very weak. Southerly winds were found along Howe Sound, Indian Arm, Pitt Lake, Stave Lake, and Harrison Lake (referring to Fig. 1 for these locations). The spatial structure of up-slope winds in Fig. 5(b) was not resolved by Hedley and Singleton (1997). Comparing with observation, the model in the present study performs very well for this particular time. At 2200 PST, as shown in Fig. 5(c), wind conditions were generally calm over land, including mountain areas, but were still fairly strong over in the Strait of Georgia. The southerly and southwesterly winds in the strait are reproduced by the model but not at correct magnitudes (too large in the north and too small in the south). The observed wind pattern at 0400 PST of the next day was about the same as that at 2200 PST on 17 July and there was no clear sign of land breeze in the basin area (see Fig. 5(d)). The model reproduces the pattern, but introduces opposite wind directions in the northern part of the Strait of Georgia. Comparing with the previous modelling studies (Steyn and McKendry, 1988; Miao and Steyn, 1994; Hedley and Singleton, 1997), the current simulation provides the more detailed wind structure of sea breezes and up-slope winds. This may be attributed to use of a nonhydrostatic model, a higher-order turbulent closure scheme, nested grid con"guration, and "ner grid spacing. Modelled wind "elds on other days are similar to those at the corresponding hours of 17 July and so are not shown here. Although the observed wind patterns over the land almost duplicate themselves from day to day during the episode period, those over the Strait of Georgia are di!erent from day to day. The model reproduces the sea breezes over the land, and this implies that the major mechanisms in thermally driven #ow are well parameterized in CSU-RAMS (Pielke et al., 1992). As long as other forcings do not dominate, the model will produce a satisfactory wind "eld. It is shown in Fig. 5 (a) and (c) that the model sometimes fails to provide an accurate description of wind pattern over the strait for 1000 PST and 2200 PST 17 July. This failure also occurs at 0400 PST 18 July, 2200 PST 19 July, 1000 PST, and 2200 PST 20 July, which are not shown here. In order to correctly predict sea breezes and the MLD near the coast, it is important to correctly simulate the winds over the Strait of Georgia. Fig. 5 shows that the modelled sea breeze penetrated slightly too early over the land. Its e!ect on the predicted MLD will be discussed in Section 4.4.
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4.2. Temperature proxle at the Queen Elizabeth Park Fig. 6 presents the comparison of vertical temperature pro"les between model and observation at the QEP in Vancouver (indicated by a solid triangle in Fig. 1) on 17 July 1985. The tethersonde data were not smoothed, and the model outputs are hourly averaged results, which are labeled at the half hour. Therefore, the tethersonde data obtained from the closest times are chosen for comparison with the hourly averaged model results. The vertical coordinate is referenced to sea level, and the elevation of the station at the QEP is 134 m. From 0930 PST to 1530 PST, not only mean temperature but also the height of the inversion base is reproduced by the model. During the period of 1730 PST}1930 PST, a warming above 400 m asl is not captured by the model. This signi"cant warming of several degrees within 2}3 h was unlikely caused by subsidence, since a lapse rate of about 0.008 K m\ (the observed value estimated from Fig. 6) would only result in about 0.3 K warming for two hours if a divergence of 10\ s\ near the ground is assumed (Steyn and McKendry, 1988). Nor was it likely that this warming caused by the sea-breeze return #ow because the wind directions below 1 km asl during the period were westerly (see Fig. 8(e) and (f)). One reasonable explanation is that it might result from the advection of a warm layer from northwest (the synoptic wind direction) of the site. The warm layer could be originated from a land surface outside of the inner grid, either on the east or the west side of the Strait of Georgia (see the map in Fig. 2). It may be a thermal layer shed from the fully developed convective boundary layer in the area was advected over the strait and dynamically decoupled from the stable marine boundary layer underneath. Advection over the strait of a distance about 80 km under the speed of about 8 m s\ (Grid 2 modelling results in the area at z"1 km) took about 3 h. Following this assumption, the thermal layer shed from a source area at 1400 PST could arrive at the sounding station at 1700 PST. Unfortunately, lack of data prohibits a further detailed investigation into the exact location of the source of the warm layer, although a backtrajectory test based on modelled wind "elds of Grid 2 shows that the air parcels arriving several levels (500, 600, and 700 m asl) above the QEP at 1730 PST came from the east side of the Strait of Georgia (not shown). This analysis demonstrates that for a complex coastal environment like the LFV, modelling of the vertical structure of the lower atmosphere needs a reliable prediction of wind conditions in an extended area over the sea surface (the Strait of Georgia in our case) as well as over the neighbouring land surfaces. At 1930 PST, the mixed layer became shallower as the air aloft was further warmed. Unfortunately, there were no vertical sounding available either at night, or for the day of 18 July to examine the further development.
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Fig. 6. Comparison between modelled and observed temperature pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f) 1930 PST on 17 of July 1985.
Comparison of temperature pro"les for July 19 has also been made (not shown here). Temperatures below 1 km in the early morning estimated by the model are about 4}5 K lower than those obtained from tethersonde observation. As sea breezes are built up in the morning, the di!erence between observed and modelled temperature pro"les is gradually reduced. The modelled temper-
ature pro"les in the late afternoon are almost identical to those observed. Noting that the model analysis is based on an Eulerian frame, the improved modelling results (compared with observation) in the afternoon do not necessarily mean too much thermal production by the model so as to compensate a colder temperature at night. The above-mentioned error of 4}5 K has been
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advected further inland, and the pro"les in the late afternoon are actually "ngerprints of the atmosphere west of the station. Again, at 1730 PST, the temperature above the mixed layer was warmed by the advected air which is not well predicted by the model, but the underestimate of temperature is smaller than that of 17 July.
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4.3. Wind proxle at Queen Elizabeth Park A comparison of wind speed pro"le between modelled results and the tethersonde data observed on 17 July is presented in Fig. 7. At 0930 PST, the observed wind speed is light at about 1}2 ms\, with the modelled wind pro"le in good agreement above 400 m asl and slightly
Fig. 7. Comparison between modelled and observed wind speed pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f ) 1930 PST on 17 of July 1985.
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overestimated below this height. At 1130 PST, the observed mean wind speed near the surface increases to about 4 ms\ as a sign of the onset of a sea-breeze, and the model produces a slightly larger value from the surface to 500 m asl. At 1330 PST, as the sea-breeze is fully established, the modelled wind speed is very close to the
observed one, reaching about 5 m s\ near the top of the boundary layer. In the afternoon at 1530 PST and 1730 PST, the modelled wind pro"les still follow the observed pattern near the surface, but fail to reproduce an upper level jet above 500 m asl. This jet could be attributed to the warm air advection discussed in Section 4.2. At 1930
Fig. 8. Comparison between modelled and observed wind direction pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f ) 1930 PST on 17 of July 1985.
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PST, the observed wind speed increases with height, but the model only captures the wind speed below 400 m asl, and underestimates it above this height. For wind direction, Fig. 8 indicates signi"cant vertical variability of very low wind speeds in the early morning. At 1130 PST, the major characteristics of wind direction, i.e. a dominant westerly wind between 300 and 800 m asl, are reproduced by the model. At 1330 PST, a westerly sea breeze, is predominant in the boundary layer, and the model simulates it reasonably well. At 1530 PST, the model produces good results in the layer between 300 and 700 m asl. From 1730 PST to 1930 PST, the model results are in good agreement with the observation. In general, the observed wind direction is well reproduced by the model. The comparison of wind speed and direction pro"les between model and observations for the day of 19 July has also been made, but not shown here. In general, the agreement of modelled wind pro"les with observation is much better than that for 17 July especially in the morning. In the late afternoon, the model slightly overestimates wind speed above the boundary layer. The overall performance of the modelling system is better than that of Hedley and Singleton (1997), which generally overpredicted the wind speed in the boundary layer. 4.4. The mixed layer depth Since the MLD directly a!ects modelled concentration of chemical species, it is important to estimate it accurately. There have been a few studies on the MLD in this area (Steyn and Oke, 1982; Batchvarova et al., 1999). CSU-RAMS produces three-dimensional TKE "elds, which contain information from which MLD may be estimated. Arritt and Physick (1989) proposed to diagnose MLD by "nding the level of the "rst local or absolute minimum of TKE above the surface. In the present case, however, the modelled vertical pro"le of TKE at 䉱 in Fig. 1 has a simple vertical distribution which smoothly increases with height from a small value to a maximum and decreases monotonically near the top of the boundary layer (not shown here). These model results are consistent with some observations (Stull, 1988). Therefore, application of Arritt and Physick's definition is di$cult because of the absence of TKE minima. Instead, we propose to de"ne the MLD top as a level where TKE "rst decreases across a critical value, E . 2 The typical range of maximum TKE (denoted by E ) 2 in the LFV basin is about 0.5 m s\ (in kinematic units). The value of 0.03 m s\ (6% of E ) is used as 2 E and sensitivity of E to the results of MLD has 2 2 been tested by altering E . In Fig. 9, the MLDs with 2 E "0.05 m s\ (10% of E ) at the three sites are 2 2 presented by dashed line and the MLDs with E "0.03 m s\ by solid lines. The diagrams show 2 that the modelled MLD during the daytime is insensitive
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to the choice of E in the value range of 6}10% of 2 E . In other words, the value of E "0.03 m s\ is 2 2 suitable for this purpose. In Fig. 9, the comparisons between the observed and modelled MLDs at three stations are presented, in which dots denote the observational data and lines represent the modelled results. These three stations are: (a) QEP; (b) Delta; (c) Surrey. The data at (a) are originally tether sonde temperature pro"les as mentioned above, while (b) and (c) are obtained from acoustic sounder. Modelled MLDs are given as hourly averaged values and are interpolated using inverse square distance weighting from the four mesh points nearest to the point of observation. As shown in the "gure, the model generally underestimates MLD at QEP on 17 July but gives good results for July 19. This is closely associated with simulation of wind over the Strait of Georgia. As discussed in Section 4.1, due to too large a westerly wind produced by model in the strait throughout the whole day on 17 July the momentum of modelled cold marine air could signi"cantly reduce the MLD at QEP (about 10 km from the coast). On 19 July however, the observed winds at 0400 PST and 1000 PST in the Strait of Georgia reached 6 m s\ (not shown here), which has about the same value as the modelled wind speed on July 17. This wind speed causes small MLDs to which the modelled MLDs on 19 July are very close. At Delta, the model presents a good estimate for 19 July, but overestimates MLD for 20 July. This overestimate was also caused by the misrepresentation of the observed southerly wind from Boundary Bay (not shown). Since the Delta site is about 5 km north to the Boundary Bay (the open triangle in Fig. 1), the MLD structure at the site is subject to the southerly wind. At the Surry site which is geographically far away from any coast, model performance is generally good. This shows that the model is able to reproduce MLD in a nearly #at inland area. A more important implication from this comparison is that a correct simulation of MLD near coast relies on a correct simulation of wind pattern over the sea. Hedley and Singleton (1997) have also compared their model-derived MLDs with the same observational data. Their results of MLD show smaller di!erences between the near-coast and central-basin sites and therefore tend to overestimate the MLD at the QEP and Delta sites.
5. Conclusions The study presents a successful multi-day simulation of sea-breeze conditions in the LFV without the use of nudging in the inner grid (Grid 3). In general, modelled results agree well with observation during the daytime, because under a stagnant synoptic system, local thermal forcing controls boundary layer meteorology. An index of agreement with an average of about 0.6 is achieved by
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Fig. 9. The MLD at three sites: (a) QEP; (b) Delta; (c) Surrey. Circles are observed data; lines are modelled results from two di!erent critical values of TKE. Time period is from 17}July 20.
the model for the daytime surface wind. During the night, the model produces too large a downslope wind, with an index of agreement of about 0.4. Similar results hold for temperature: modelled results agree very well with observation during the day (the index of agreement of about 0.95) but poorly during the night (the index of agreement near 0.4). The vertical pro"les of modelled wind and temperature have been compared with tethersonde data for 17 and 19 July. The overall comparison of wind speed and direction is generally satisfactory. In late afternoon, however, the model does not capture an elevated warm layer advected from a land surface outside of the inner grid. Apart from
this, the modelled temperature pro"les agree very well with the tethersonde data pro"les, especially in the afternoon. The study has shown that for a complex coast environment like the LFV, a reliable modelling study depends not only on correct simulation of local surface #uxes but also on elevated layers transported from remote areas. This dependence is remarkably important when local surface #uxes are not dominant during late afternoon and at night. The MLD over the whole domain is estimated through the model output of 3D TKE "eld. Comparisons of the model results with the observed data at three stations in the LFV basin show that the TKE method produces
X.-M. Cai, D.G. Steyn / Atmospheric Environment 34 (2000) 2873}2885
reliable results of the MLD during the daytime. A good estimate of the MLD at a place near coast relies on the correct simulation of wind conditions over the sea. Acknowledgements The study was supported by NSERC grants to Steyn. CSU-RAMS is developed by the Atmospheric Science Department at Colorado State University under support of the National Science Foundation and the Army Research O$ces. The observational data were provided by the Atmospheric Environment Service, the British Columbia Ministry of Environment, Lands and Parks, the Greater Vancouver Regional District, and Dr. I. McKendry at the University of British Columbia. References Arritt, R.W., Physick, W.L., 1989. Formulation of the thermal internal boundary layer in a mesoscale model. II. Simulations with a level-2.5 turbulence closure. Boundary-Layer Meteorology 49, 411}416. Batchvarova, E., Cai, X.-M., Gryning, S.-E., Steyn, D.G., 1999. Modelling internal boundary layer development in a region with complex coastline. Boundary-Layer Meteorology 90, 1}20. Cai, X.-M., Steyn, D.G., Uno, I., 1998. Analytical investigation of a mesoscale model with Newtonian nudging. Meteorology and Atmospheric Physics 64, 231}241. Chen, J.M., Oke, T.R., 1994. Mixed-layer heat advection and entrainment during the sea-breeze. Boundary-Layer Meteorology 68, 139}158. Hay, J.E., Oke, T.R., 1976. The Climate of Vancouver. Tantalus Research, Vancouver. Hedley, M., Singleton, D.L., 1997. Evaluation of an air quality simulation of the Lower Fraser Valley.1. Meteorology. Atmospheric Environment 31, 1605}1615. Helmis, C.G., Tombrou, M., Asimakopoulos, D.N., Soilemes, A., Gusten, H., Moussiopoulos, N., Hatzaridou, A., 1997. Thessaloniki '91 "eld measurement campaign.1. Wind "eld and atmospheric boundary layer structure over greater Thessaloniki area, under light background #ow. Atmospheric Environment 31, 1101}1114. Joe, H., Steyn, D.G., Susko, E., 1996. Analysis of trends in tropospheric ozone in the Lower Fraser Valley, British Columbia. Atmospheric Environment 30, 3413}3421.
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Mckendry, I.G., 1994. Synoptic circulation and summertime ground-level ozone concentrations at Vancouver BritishColumbia. Journal of Applied Meteorology 33, 627}641. Mckendry, I.G., Steyn, D.G., Lundgren, J., Ho!, R.M., Strapp, W., Anlauf, K., Froude, F., Martin, J.B., Banta, R.M., Olivier, L.D., 1997. Elevated ozone layers and vertical down-mixing over the Lower Fraser Valley BC. Atmospheric Environment 31, 2135}2146. Melas, D., Ziomas, I., Klemm, O., Zerefos, C.S., 1998. Flow dynamics in Athens area under moderate large-scale winds. Atmospheric Environment 32, 2209}2222. Miao, Y., Steyn, D.G., 1994. Mesometeorological modelling and trajectory analysis during an air pollution episode in the Lower Fraser Valley, BC. Transactions of Regional Photochemical Measurement and Modelling Studies Conference, pp. 249}281. Physick, W.L., Abbs, D.J., 1991. Modeling of summertime #ow and dispersion in the coastal terrain of southeastern Australia. Monthly Weather Review 119, 1014}1030. Pielke, R.A., Cotton, W.R., Walko, R.L., Tremback, C.J., Lyons, W.A., Grasso, L.D., Nicholls, M.E., Moran, M.D., Wesley, D.A., Lee, T.J., Copeland, J.H., 1992. A comprehensive meteorological modeling system } RAMS. Meteorology and Atmospheric Physics 49, 69}91. Pryor, S.C., Mckendry, I.G., Steyn, D.G., 1995. Synoptic-scale meteorological variability and surface ozone concentrations in Vancouver British-Columbia. Journal of Applied Meteorology 34, 1824}1833. Steyn, D.G., Bottenheim, J.W., Thomson, R.B., 1997. Overview of tropospheric ozone in the Lower Fraser Valley, and the Paci"c '93 "eld study. Atmospheric Environment 31, 2025}2035. Steyn, D.G., Faulkner, D.A., 1986. The climatology of seabreezes in the Lower Fraser Valley B.C. Climatological Bulletin 20, 21}39. Steyn, D.G., McKendry, I.G., 1988. Quantitative and qualitative evaluation of a three-dimensional mesoscale numerical model simulation of a sea breeze in complex terrain. Monthly Weather Review 116, 1914}1926. Steyn, D.G., Oke, T.R., 1982. The depth of the daytime mixed layer at two coastal sites: a model and its validation. Boundary-Layer Meteorology 24, 161}180. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Acad. Publishers, Dordrecht. Tjernstrom, M., Grisogono, B., 1996. Thermal mesoscale circulations on the Baltic coast.1. Numerical case study. Journal of Geophysical Research-Atmospheric 101, 18979}18997. Willmott, C.J., 1981. On the validation of models. Physical Geography 2, 168}194.
Modelling study of sea breezes in a complex coastal environment X.-M. Cai *, D.G. Steyn School of Geography and Environmental Sciences, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Atmospheric Science Program, Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2 Received 4 January 1999; received in revised form 8 November 1999; accepted 17 December 1999
Abstract This study investigates a mesoscale modelling of sea breezes blowing from a narrow strait into the lower Fraser valley (LFV), British Columbia, Canada, during the period of 17}20 July, 1985. Without a nudging scheme in the inner grid, the CSU-RAMS model produces satisfactory wind and temperature "elds during the daytime. In comparison with observation, the agreement indices for surface wind and temperature during daytime reach about 0.6 and 0.95, respectively, while the agreement indices drop to 0.4 at night. In the vertical, pro"les of modelled wind and temperature generally agree with tethersonde data collected on 17 and 19 July. The study demonstrates that in late afternoon, the model does not capture the advection of an elevated warm layer which originated from land surfaces outside of the inner grid. Mixed layer depth (MLD) is calculated from model output of turbulent kinetic energy "eld. Comparison of MLD results with observation shows that the method generates a reliable MLD during the daytime, and that accurate estimates of MLD near the coast require the correct simulation of wind conditions over the sea. The study has shown that for a complex coast environment like the LFV, a reliable modelling study depends not only on local surface #uxes but also on elevated layers transported from remote land surfaces. This dependence is especially important when local forcings are weak, for example, during late afternoon and at night. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Mesoscale modelling; Sea breezes; The lower Fraser valley; Mixed layer depth; CSU-RAMS
1. Introduction The lower Fraser valley (LFV) of British Columbia, Canada, is located on the eastern side of the Strait of Georgia and extends to the Fraser canyon in the east. The LFV basin is bounded by the Coast Mountains in the north and the Cascade Range in the east. On the western side of the Strait of Georgia, sits Vancouver Island, which bounds the LFV in the west (see Fig. 1). The topography of the region results in severely constrained low-level ventilation, causing frequent buildup of air pollution. In recent years, population in the LFV has increased rapidly, and as a result so have emissions of various types of air contaminants, such as nitrogen oxides (NO ), volatile organic compounds (VOC), carbon V * Corresponding author. Fax: #44-121-4145528. E-mail address: [email protected] (X.-M. Cai).
monoxide, sulphur dioxide, and particulate matter (Joe et al., 1996). Under stagnant synoptic high-pressure systems during the summer time, shallow but intense subsidence inversions above the boundary layer act as a lid over the region, suppressing the vertical transport of pollutants. Because of high temperatures, this meteorological condition also favours the production of ozone from NO and V VOC (McKendry, 1994). Consequently, the LFV su!ers from severe ozone episodes under these particular meteorological conditions (Pryor et al., 1995; Steyn et al., 1997). In this coastal area, the meteorology is also accompanied by local, thermally forced daytime sea breezes which advect emissions inland, bringing cold air from the sea surface, forming an even shallower mixed layer (Steyn and Faulkner, 1986; Chen and Oke, 1994). Mountains around the LFV cause regional, topographically driven daytime upslope winds, nighttime downslope drainage winds (Hay and Oke, 1976), and mesoscale mountain/valley circulation #ows. Recently, McKendry et al.
1352-2310/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 0 ) 0 0 0 7 9 - 0
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Fig. 1. Map of LFV and locations of observational stations which provide the data used to evaluate the model. The UTM coordinates are used in this "gure.
(1997) demonstrated that the `chimney e!ecta and `convective debrisa were responsible for the formation of elevated ozone layers observed above the basin area. It is recognized that modelling of meteorology is essential to understanding of pollutant transport, and therefore is the "rst important step towards photochemical modelling of ozone episodes. There have been many studies of sea breezes in other areas with complex coastlines (Physick and Abbs, 1991; Tjernstrom and Grisogono, 1996; Helmis et al., 1997; Melas et al., 1998). For the LFV, there have been several studies on sea- or land breezes and up- or down-slope #ows. Steyn and McKendry (1988) used a three-dimensional hydrostatic numerical model to simulate a well-developed sea breeze on 23 August 1985. Their simulation was performed with a horizontally homogeneous initialization on a 35;29;26 grid with a horizontal spacing of 5 km. Their simulations overestimated wind speed, especially during the night. Miao and Steyn (1994) applied an early non-hydrostatic version of the Colorado State University
Regional Atmospheric Modelling System (CSU-RAMS) to the same day and the same domain as those in Steyn and McKendry (1988), but using a "ner horizontal grid spacing of 2.5 km. Though their overall model performance was better than that of Steyn and McKendry (1988), they still found a progressively increasing wind speed over night in the Strait of Georgia. This excluded the possibility of multi-day simulations, which are necessary for modelling of photochemical processes during a multi-day air pollution episode. The overestimates of wind speed in both studies might be attributed to the single-grid con"guration combined with homogeneous initialisation. Hedley and Singleton (1997) used a system (a combination of the MC2 and CALMET models) to simulate meteorological conditions during the photochemical episode of 17}21 July 1985. Their model employed a 10 km horizontal grid spacing within a larger domain simulated by MC2, and a 5 km horizontal grid spacing within a smaller domain simulated by CALMET. Although some comparisons with observation
X.-M. Cai, D.G. Steyn / Atmospheric Environment 34 (2000) 2873}2885
show a reasonable model performance for the multi-day simulation, the model system signi"cantly underestimates the diurnal temperature cycle amplitude and overestimates wind speeds near the coastline. From the above discussions, it is evident that previous modelling studies of sea-breezes in the LFV failed to produce satisfactory meteorological (especially wind) "elds. It is a concern that the inadequacies of the wind "elds will render them inappropriate for application in a comprehensive air quality model (e.g., Urban Airshed Model). In addition, it is unlikely to obtain the correct temperature and MLD if wind "elds are not correctly modelled. For this reason, the present study aims to examine the application of CSU-RAMS with nested grid con"guration to the LFV during the period studied by Hedley and Singleton (1997). Evaluation of the model performance will be conducted through comparison with surface observational data. Wind "elds produced by the model will be analysed to provide some insight into sea/land breezes and slope/valley winds. The vertical structure of wind and temperature from observation and modelling will be examined and discussed. In addition, MLD will be diagnosed from the model output and compared with observed MLDs at three stations.
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used for both grids. Considering the timescale of dominating motions in Grid 1 is larger than that in Grid 2, the e!ects of the given nudging coe$cient are stronger in Grid 1 and weaker in Grid 2. As the timescale of a seabreeze episode is smaller than 6 h, it is unlikely that the mesoscale features of sea breezes are signi"cantly suppressed by the simulation (see Cai et al., 1998); in fact, this is shown by the results of Grid 2 in the current study (not presented here). Table 1 also gives the UTM coordinates for Grids 2 and 3. The domain for Grid 3 is presented in Fig. 1, which shows that the LFV basin is an almost #at, triangular region, its northern mountain range is approximately along the east}west direction, and its eastern mountain range is approximately in the southwest} northeast direction. It is noted that Vancouver city area, approximately around the symbol of solid triangle (Queen Elizabeth Park, or QEP) in Fig. 1, is close to the Coast Mountains, and may therefore be signi"cantly a!ected by up- and downslope winds. In the vertical direction, the second vertical mesh point (for w at 50 m, and the remaining vertical mesh spacings
2. Model con5guration In the current simulation, CSU-RAMS (Pielke et al., 1992) is used, and a two-way interactive nested grid con"guration with three grids is employed, each grid covering a di!erent domain size (see Fig. 2). Speci"cation of domain size and grid spacing for three grids is given in Table 1. Analysed "elds are produced by the Isentropic Analysis package (part of CSU-RAMS) for every 12 h based on gridded dataset from US National Centers for Environmental Prediction (NCEP) global model. At every time step during model runs, nudging "elds of wind, temperature, and humidity are obtained by linear interpolation of the two closest analysis "elds. Meanwhile, Grids 1 and 2 are nudged towards their respective nudging "elds. A nudging time scale of 21 600 s (6 h) is
Fig. 2. Con"guration of nested grids. The "gure box is the boundary of Grid 1; dot-dashed line is the boundary of Grid 2; and dashed line is the boundary of Grid 3.
Table 1 Speci"cation of three grids. ¸ , ¸ and ¸ are domain sizes in the x, y and z directions, respectively; N , N and N are the number of V W X V W X mesh points in the x, y and z directions, respectively; *x and *y are the mesh spacings in the x and y direction, respectively; *t is time increment; and UTM-x and UTM-y represent the range of the UTM coordinates in the x- and y-directions, respectively. The UTM coordinates for Grid 1 are not available since they are out of the current UTM zone Grid
¸ V
¸ W
¸ X
N V
N W
N X
*x, *y (km)
*t (s)
UTM-x (km)
UTM-y (km)
1 2 3
1360 410 162.5
1200 370 122.5
18.8 18.8 18.8
35 42 66
31 38 50
26 26 26
40 10 2.5
30 15 15
* [320, 730] [453.75, 616.25]
* [5280, 5650] [5383.75, 5506.25]
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are increasing with a ratio of 1.2, with the maximum grid spacing being 2000 m. Consequently, the "rst vertical mesh point for u, v, and ¹ is at about 23.86 m and the vertical dimension of the domain is about 18.8 km. At the top of the domain, a rigid lid condition is applied to all variables. To prevent the re#ection of upward gravity waves by this lid condition, a nudging layer is imposed from 4 km above with a time scale of 600 s. Five soil levels are applied at 0.0, 0.1, 0.3, 0.6, and 1.0 m. Smagorinsky's deformation turbulence closure scheme is used in the horizontal direction and Mellor}Yamada's second-order closure scheme is used in the vertical direction. Simulation starts at 1600 Paci"c Standard Time (PST) 16 July 1985, with 12 extra hours to allow nonphysical components to be di!used or dissipated. Simulation ends at 0400 PST on July 21 so that a total of four-day's results are available for analysis. 3. Statistical evaluation In this study, we employ a statistical evaluation method proposed by Willmott (1981) to validate model results from near-surface measurements. Data used in the evaluation are collected at the observational stations shown in Fig. 1. Surface wind speed and direction were monitored at 28 sites at 10 m height, (denoted by symbol solid and open circles in Fig. 1). Temperature was monitored at 10 sites at 1.5-m height (denoted by solid dot in Fig. 1). One site at QEP in Vancouver (denoted by solid triangle in Fig. 1) provides vertical pro"les of wind, temperature and humidity at about every hour during the daytime for 17 and 19 July 1985. This latter dataset is used to compare modelled vertical pro"les of these quantities, as well as the model-derived mixed layer depth (MLD). Two sites (denoted by open triangle in Fig. 1), one at Delta and the other at Surrey, provide MLD data measured by acoustic sounder. 3.1. Evaluation method Willmott (1981) proposed a quantitative evaluation of model performance, which was applied by Steyn and McKendry (1988), and Miao and Steyn (1994). In this evaluation method, n measurement surface stations provide a time series of observational data, denoted by O(t), or (O (t),2, O (t),2, O (t)). Predicted result output by G L model at the same locations are denoted by P(t), or (P (t),2, P (t),2, P (t)). O(t) and P(t) can be considered G L vectors in an n-dimensional real-value space, RL, changing with time t. A weighted norm in RL can be de"ned by
L u "m " G G G , (3.1) L u G G where n is a vector in RL, and u is a weighting vector in RL. The `distancea between any two vectors, n and g, in #n#"
RL is thus ""n!g"". A quantity, PH(t), is de"ned as the least-squares linear regression of P(t) on O(t), i.e., PH"a#bO , where a and b are regression coe$cients. G G Therefore, the three quantities: systematic and unsystematic components of the root-mean-squared di!erences and the total root mean-mean-squared di!erence, are actually the distances between P(t), O(t), and PH(t) RMSD """P!O"", Q RMSD """PH!P"", S RMSD"""P!O"".
(3.2) (3.3) (3.4)
If prediction and observation are identical, i.e. P"O"PH, all three distances above are zero. According to Willmott (1981), RMSD is a measure of linear Q variation in the model bias. The statistic RMSD , howS ever, is a measure of the non-linear discrepancy between prediction and observation. Another important measure is the index of agreement d, de"ned as (""P!O"") , (3.5) d"1! L u ("P !OM "#"O !OM ")/ L u G G G J G G where OM is the averaged (over n stations) observational value. This index ranges from 0.0 (no agreement) to 1.0 (perfect agreement, when prediction is the same as observation). De"nitions (3.1)}(3.5) can be extended to the case in which the data O are wind vectors by replacing the G absolute value operator, " ) ", in Eqs. (3.1) and (3.5) by ordinary wind vector norm. 3.2. Surface temperature Fig. 3 presents evaluation results for surface temperature. It is demonstrated in Fig. 3(a) that for mean temperature, modelled results are in good agreement with observation. In the "rst day, the model underestimates temperature during the daytime and slightly overestimates it during the night. A discontinuity in observed temperature in the early morning of July 18 is caused by di!erent number of stations available for evaluation: three stations before 0100 PST of 18 July and 10 thereafter. The increasing rate of temperature during the daytime (from 0600 PST to 1800 PST) for each day is well captured by the model. Modelled spatial standard deviation (SD) of temperature is also in good agreement with the daytime observation (see Fig. 3(b)), but it is smaller than the observed values at night. Fig. 3(c) indicates that, except for 17 July RMSD dominates RMSD for the Q S daytime, while RMSD dominates RMSD at night. We S Q notice from Figs. 3(c) and 4(d) that during the day, RMSD is low (about 1}23C) and the index of agreement almost reaches unity, but during the night, RMSD is high (about 2}33C) and the index of agreement drops to about 0.4. The above results suggest that the model performs very well for the daytime, but has some di$culty in
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Fig. 3. Time variation of temperature statistics from 17}21 of July 1985. (a) Mean temperature, (b) standard deviation of temperature, (c) root-mean-square di!erence (RMSD for total, RMSDs for systematic, and RMSDu for unsystematic), and (d) the index of agreement.
Fig. 4. Time variation of wind statistics from 17}21 of July 1985. (a) Mean wind speed, (b) mean wind direction, (c) standard deviation of wind, (d) root-mean-square di!erence (RMSD for total, RMSDs for systematic, and RMSDu for unsystematic), and (e) the index of agreement. Mean speeds and directions are derived from vector averages.
reproducing correct surface temperature at night. This is probably due to subgrid scale variations in the observed temperatures caused by unresolved e!ects in surface radiation inversion. However, in comparison with modelled temperatures in Hedley and Singleton (1997), the current study represents a signi"cant improvement.
Modelled wind directions during the daytime also agree fairly well with the observations, but on 17 and 20 July the model anticipated the land-breeze to sea-breeze transition by roughly 1 h and presented sudden rather than gradual changes in wind direction. At night, the model generally overestimates wind speed by 0.5}1.0 m s\ and fails to reproduce a weak land breeze (the modelled southerly wind in contrast to the observed easterly wind). However, this deviation in wind direction may not be very important to transport of air pollutants since the wind speeds are usually below 1 m s\. In Fig. 4(c), we present the standard deviations of wind with respect to all wind stations. It is noted that magnitudes of the modelled SD are often larger than the observed ones at night. The value range of SD is close to that of the mean wind speed, indicating that the locally weak winds dominate and there is a high spatial variability at night. During daytime, magnitudes of the modelled
3.3. Surface wind Figs. 4(a) and (b) demonstrate the model performance for mean wind speed and direction averaged over 28 stations. The results show a clear sea-breeze cycle, characterized by diurnal variation of wind speed and direction. Both observational data and model output show higher wind speed during daytime than at night. During the daytime, modelled wind speeds are about the same as these observed except for the day of July 20 during which the model overestimates wind speed by about 1 m s\.
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SD are slightly smaller than observational values, presumably due to strong horizontal smoothing inherent in the model formulation. As Willmott (1981) explained, RMSD represents Q trend-like di!erences between observed and modelled "elds, and RMSD represents the irreducible deviation S between observed and modelled "elds. In Fig. 4(d), RMSD are fairly large in the "rst and the last days, Q implying that the modelled results systematically depart from the observed data at these times. During daytime, in general, all RMSD values are slightly smaller and those at night. Unlike temperature, RMSD for wind dominQ ates RMSD at almost all times. The index of agreement S in Fig. 4(e) shows that model performance is good in daytime (generally greater than 0.5), and poor at night (generally less than 0.5).
4. Analyses of results 4.1. Surface wind xelds Fig. 5(a) presents modelled and observed wind "elds at 1000 PST on 17 July 1985. The gridded and thick arrows are modelled and observed wind vectors, respectively. We plot modelled wind vectors at only every other mesh point in both x- and y-directions. The solid curves indicate coastal lines and dashed lines represent a terrain contour of 100 m. At 1000 PST on 17 July as shown in Fig. 5(a), a sea breeze was just building up along the coastline, whereas the wind along the Strait of Georgia was fairly strong. Up-slope winds were observed to build up over the mountainsides, and were stronger than the sea breeze at this time of the day. In most of the LFV
Fig. 5. Surface wind "eld (10 m) at (a) 1000 PST, (b) 1600 PST, (c) 2200 PST July 17 1985, and (d) 0400 PST July 18 1985. The gridded arrows are modelled wind vectors and thick ones are observed wind vectors. Coordinates are in UTM unit. Solid curves represent the coastline and dotted curves indicate the terrain contour at 100 m.
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basin, winds were very weak. Compared with the observational winds (thick arrows), the model results provide a good representation of the real-wind "eld at this time. In the afternoon at 1600 PST, as the sea-breeze front intruded into the LFV area, the magnitude of the breeze was about the same as that of the up-slope winds (see Fig. 5(b)). The whole LFV basin was dominated by westerly winds, which arised from combined e!ects of up-slope winds and sea breezes. In contrast, winds near the middle strait were very weak. Southerly winds were found along Howe Sound, Indian Arm, Pitt Lake, Stave Lake, and Harrison Lake (referring to Fig. 1 for these locations). The spatial structure of up-slope winds in Fig. 5(b) was not resolved by Hedley and Singleton (1997). Comparing with observation, the model in the present study performs very well for this particular time. At 2200 PST, as shown in Fig. 5(c), wind conditions were generally calm over land, including mountain areas, but were still fairly strong over in the Strait of Georgia. The southerly and southwesterly winds in the strait are reproduced by the model but not at correct magnitudes (too large in the north and too small in the south). The observed wind pattern at 0400 PST of the next day was about the same as that at 2200 PST on 17 July and there was no clear sign of land breeze in the basin area (see Fig. 5(d)). The model reproduces the pattern, but introduces opposite wind directions in the northern part of the Strait of Georgia. Comparing with the previous modelling studies (Steyn and McKendry, 1988; Miao and Steyn, 1994; Hedley and Singleton, 1997), the current simulation provides the more detailed wind structure of sea breezes and up-slope winds. This may be attributed to use of a nonhydrostatic model, a higher-order turbulent closure scheme, nested grid con"guration, and "ner grid spacing. Modelled wind "elds on other days are similar to those at the corresponding hours of 17 July and so are not shown here. Although the observed wind patterns over the land almost duplicate themselves from day to day during the episode period, those over the Strait of Georgia are di!erent from day to day. The model reproduces the sea breezes over the land, and this implies that the major mechanisms in thermally driven #ow are well parameterized in CSU-RAMS (Pielke et al., 1992). As long as other forcings do not dominate, the model will produce a satisfactory wind "eld. It is shown in Fig. 5 (a) and (c) that the model sometimes fails to provide an accurate description of wind pattern over the strait for 1000 PST and 2200 PST 17 July. This failure also occurs at 0400 PST 18 July, 2200 PST 19 July, 1000 PST, and 2200 PST 20 July, which are not shown here. In order to correctly predict sea breezes and the MLD near the coast, it is important to correctly simulate the winds over the Strait of Georgia. Fig. 5 shows that the modelled sea breeze penetrated slightly too early over the land. Its e!ect on the predicted MLD will be discussed in Section 4.4.
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4.2. Temperature proxle at the Queen Elizabeth Park Fig. 6 presents the comparison of vertical temperature pro"les between model and observation at the QEP in Vancouver (indicated by a solid triangle in Fig. 1) on 17 July 1985. The tethersonde data were not smoothed, and the model outputs are hourly averaged results, which are labeled at the half hour. Therefore, the tethersonde data obtained from the closest times are chosen for comparison with the hourly averaged model results. The vertical coordinate is referenced to sea level, and the elevation of the station at the QEP is 134 m. From 0930 PST to 1530 PST, not only mean temperature but also the height of the inversion base is reproduced by the model. During the period of 1730 PST}1930 PST, a warming above 400 m asl is not captured by the model. This signi"cant warming of several degrees within 2}3 h was unlikely caused by subsidence, since a lapse rate of about 0.008 K m\ (the observed value estimated from Fig. 6) would only result in about 0.3 K warming for two hours if a divergence of 10\ s\ near the ground is assumed (Steyn and McKendry, 1988). Nor was it likely that this warming caused by the sea-breeze return #ow because the wind directions below 1 km asl during the period were westerly (see Fig. 8(e) and (f)). One reasonable explanation is that it might result from the advection of a warm layer from northwest (the synoptic wind direction) of the site. The warm layer could be originated from a land surface outside of the inner grid, either on the east or the west side of the Strait of Georgia (see the map in Fig. 2). It may be a thermal layer shed from the fully developed convective boundary layer in the area was advected over the strait and dynamically decoupled from the stable marine boundary layer underneath. Advection over the strait of a distance about 80 km under the speed of about 8 m s\ (Grid 2 modelling results in the area at z"1 km) took about 3 h. Following this assumption, the thermal layer shed from a source area at 1400 PST could arrive at the sounding station at 1700 PST. Unfortunately, lack of data prohibits a further detailed investigation into the exact location of the source of the warm layer, although a backtrajectory test based on modelled wind "elds of Grid 2 shows that the air parcels arriving several levels (500, 600, and 700 m asl) above the QEP at 1730 PST came from the east side of the Strait of Georgia (not shown). This analysis demonstrates that for a complex coastal environment like the LFV, modelling of the vertical structure of the lower atmosphere needs a reliable prediction of wind conditions in an extended area over the sea surface (the Strait of Georgia in our case) as well as over the neighbouring land surfaces. At 1930 PST, the mixed layer became shallower as the air aloft was further warmed. Unfortunately, there were no vertical sounding available either at night, or for the day of 18 July to examine the further development.
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Fig. 6. Comparison between modelled and observed temperature pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f) 1930 PST on 17 of July 1985.
Comparison of temperature pro"les for July 19 has also been made (not shown here). Temperatures below 1 km in the early morning estimated by the model are about 4}5 K lower than those obtained from tethersonde observation. As sea breezes are built up in the morning, the di!erence between observed and modelled temperature pro"les is gradually reduced. The modelled temper-
ature pro"les in the late afternoon are almost identical to those observed. Noting that the model analysis is based on an Eulerian frame, the improved modelling results (compared with observation) in the afternoon do not necessarily mean too much thermal production by the model so as to compensate a colder temperature at night. The above-mentioned error of 4}5 K has been
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advected further inland, and the pro"les in the late afternoon are actually "ngerprints of the atmosphere west of the station. Again, at 1730 PST, the temperature above the mixed layer was warmed by the advected air which is not well predicted by the model, but the underestimate of temperature is smaller than that of 17 July.
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4.3. Wind proxle at Queen Elizabeth Park A comparison of wind speed pro"le between modelled results and the tethersonde data observed on 17 July is presented in Fig. 7. At 0930 PST, the observed wind speed is light at about 1}2 ms\, with the modelled wind pro"le in good agreement above 400 m asl and slightly
Fig. 7. Comparison between modelled and observed wind speed pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f ) 1930 PST on 17 of July 1985.
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overestimated below this height. At 1130 PST, the observed mean wind speed near the surface increases to about 4 ms\ as a sign of the onset of a sea-breeze, and the model produces a slightly larger value from the surface to 500 m asl. At 1330 PST, as the sea-breeze is fully established, the modelled wind speed is very close to the
observed one, reaching about 5 m s\ near the top of the boundary layer. In the afternoon at 1530 PST and 1730 PST, the modelled wind pro"les still follow the observed pattern near the surface, but fail to reproduce an upper level jet above 500 m asl. This jet could be attributed to the warm air advection discussed in Section 4.2. At 1930
Fig. 8. Comparison between modelled and observed wind direction pro"le at (a) 0930 PST, (b) 1130 PST, (c) 1330 PST, (d) 1530 PST, (e) 1730 PST, and (f ) 1930 PST on 17 of July 1985.
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PST, the observed wind speed increases with height, but the model only captures the wind speed below 400 m asl, and underestimates it above this height. For wind direction, Fig. 8 indicates signi"cant vertical variability of very low wind speeds in the early morning. At 1130 PST, the major characteristics of wind direction, i.e. a dominant westerly wind between 300 and 800 m asl, are reproduced by the model. At 1330 PST, a westerly sea breeze, is predominant in the boundary layer, and the model simulates it reasonably well. At 1530 PST, the model produces good results in the layer between 300 and 700 m asl. From 1730 PST to 1930 PST, the model results are in good agreement with the observation. In general, the observed wind direction is well reproduced by the model. The comparison of wind speed and direction pro"les between model and observations for the day of 19 July has also been made, but not shown here. In general, the agreement of modelled wind pro"les with observation is much better than that for 17 July especially in the morning. In the late afternoon, the model slightly overestimates wind speed above the boundary layer. The overall performance of the modelling system is better than that of Hedley and Singleton (1997), which generally overpredicted the wind speed in the boundary layer. 4.4. The mixed layer depth Since the MLD directly a!ects modelled concentration of chemical species, it is important to estimate it accurately. There have been a few studies on the MLD in this area (Steyn and Oke, 1982; Batchvarova et al., 1999). CSU-RAMS produces three-dimensional TKE "elds, which contain information from which MLD may be estimated. Arritt and Physick (1989) proposed to diagnose MLD by "nding the level of the "rst local or absolute minimum of TKE above the surface. In the present case, however, the modelled vertical pro"le of TKE at 䉱 in Fig. 1 has a simple vertical distribution which smoothly increases with height from a small value to a maximum and decreases monotonically near the top of the boundary layer (not shown here). These model results are consistent with some observations (Stull, 1988). Therefore, application of Arritt and Physick's definition is di$cult because of the absence of TKE minima. Instead, we propose to de"ne the MLD top as a level where TKE "rst decreases across a critical value, E . 2 The typical range of maximum TKE (denoted by E ) 2 in the LFV basin is about 0.5 m s\ (in kinematic units). The value of 0.03 m s\ (6% of E ) is used as 2 E and sensitivity of E to the results of MLD has 2 2 been tested by altering E . In Fig. 9, the MLDs with 2 E "0.05 m s\ (10% of E ) at the three sites are 2 2 presented by dashed line and the MLDs with E "0.03 m s\ by solid lines. The diagrams show 2 that the modelled MLD during the daytime is insensitive
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to the choice of E in the value range of 6}10% of 2 E . In other words, the value of E "0.03 m s\ is 2 2 suitable for this purpose. In Fig. 9, the comparisons between the observed and modelled MLDs at three stations are presented, in which dots denote the observational data and lines represent the modelled results. These three stations are: (a) QEP; (b) Delta; (c) Surrey. The data at (a) are originally tether sonde temperature pro"les as mentioned above, while (b) and (c) are obtained from acoustic sounder. Modelled MLDs are given as hourly averaged values and are interpolated using inverse square distance weighting from the four mesh points nearest to the point of observation. As shown in the "gure, the model generally underestimates MLD at QEP on 17 July but gives good results for July 19. This is closely associated with simulation of wind over the Strait of Georgia. As discussed in Section 4.1, due to too large a westerly wind produced by model in the strait throughout the whole day on 17 July the momentum of modelled cold marine air could signi"cantly reduce the MLD at QEP (about 10 km from the coast). On 19 July however, the observed winds at 0400 PST and 1000 PST in the Strait of Georgia reached 6 m s\ (not shown here), which has about the same value as the modelled wind speed on July 17. This wind speed causes small MLDs to which the modelled MLDs on 19 July are very close. At Delta, the model presents a good estimate for 19 July, but overestimates MLD for 20 July. This overestimate was also caused by the misrepresentation of the observed southerly wind from Boundary Bay (not shown). Since the Delta site is about 5 km north to the Boundary Bay (the open triangle in Fig. 1), the MLD structure at the site is subject to the southerly wind. At the Surry site which is geographically far away from any coast, model performance is generally good. This shows that the model is able to reproduce MLD in a nearly #at inland area. A more important implication from this comparison is that a correct simulation of MLD near coast relies on a correct simulation of wind pattern over the sea. Hedley and Singleton (1997) have also compared their model-derived MLDs with the same observational data. Their results of MLD show smaller di!erences between the near-coast and central-basin sites and therefore tend to overestimate the MLD at the QEP and Delta sites.
5. Conclusions The study presents a successful multi-day simulation of sea-breeze conditions in the LFV without the use of nudging in the inner grid (Grid 3). In general, modelled results agree well with observation during the daytime, because under a stagnant synoptic system, local thermal forcing controls boundary layer meteorology. An index of agreement with an average of about 0.6 is achieved by
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Fig. 9. The MLD at three sites: (a) QEP; (b) Delta; (c) Surrey. Circles are observed data; lines are modelled results from two di!erent critical values of TKE. Time period is from 17}July 20.
the model for the daytime surface wind. During the night, the model produces too large a downslope wind, with an index of agreement of about 0.4. Similar results hold for temperature: modelled results agree very well with observation during the day (the index of agreement of about 0.95) but poorly during the night (the index of agreement near 0.4). The vertical pro"les of modelled wind and temperature have been compared with tethersonde data for 17 and 19 July. The overall comparison of wind speed and direction is generally satisfactory. In late afternoon, however, the model does not capture an elevated warm layer advected from a land surface outside of the inner grid. Apart from
this, the modelled temperature pro"les agree very well with the tethersonde data pro"les, especially in the afternoon. The study has shown that for a complex coast environment like the LFV, a reliable modelling study depends not only on correct simulation of local surface #uxes but also on elevated layers transported from remote areas. This dependence is remarkably important when local surface #uxes are not dominant during late afternoon and at night. The MLD over the whole domain is estimated through the model output of 3D TKE "eld. Comparisons of the model results with the observed data at three stations in the LFV basin show that the TKE method produces
X.-M. Cai, D.G. Steyn / Atmospheric Environment 34 (2000) 2873}2885
reliable results of the MLD during the daytime. A good estimate of the MLD at a place near coast relies on the correct simulation of wind conditions over the sea. Acknowledgements The study was supported by NSERC grants to Steyn. CSU-RAMS is developed by the Atmospheric Science Department at Colorado State University under support of the National Science Foundation and the Army Research O$ces. The observational data were provided by the Atmospheric Environment Service, the British Columbia Ministry of Environment, Lands and Parks, the Greater Vancouver Regional District, and Dr. I. McKendry at the University of British Columbia. References Arritt, R.W., Physick, W.L., 1989. Formulation of the thermal internal boundary layer in a mesoscale model. II. Simulations with a level-2.5 turbulence closure. Boundary-Layer Meteorology 49, 411}416. Batchvarova, E., Cai, X.-M., Gryning, S.-E., Steyn, D.G., 1999. Modelling internal boundary layer development in a region with complex coastline. Boundary-Layer Meteorology 90, 1}20. Cai, X.-M., Steyn, D.G., Uno, I., 1998. Analytical investigation of a mesoscale model with Newtonian nudging. Meteorology and Atmospheric Physics 64, 231}241. Chen, J.M., Oke, T.R., 1994. Mixed-layer heat advection and entrainment during the sea-breeze. Boundary-Layer Meteorology 68, 139}158. Hay, J.E., Oke, T.R., 1976. The Climate of Vancouver. Tantalus Research, Vancouver. Hedley, M., Singleton, D.L., 1997. Evaluation of an air quality simulation of the Lower Fraser Valley.1. Meteorology. Atmospheric Environment 31, 1605}1615. Helmis, C.G., Tombrou, M., Asimakopoulos, D.N., Soilemes, A., Gusten, H., Moussiopoulos, N., Hatzaridou, A., 1997. Thessaloniki '91 "eld measurement campaign.1. Wind "eld and atmospheric boundary layer structure over greater Thessaloniki area, under light background #ow. Atmospheric Environment 31, 1101}1114. Joe, H., Steyn, D.G., Susko, E., 1996. Analysis of trends in tropospheric ozone in the Lower Fraser Valley, British Columbia. Atmospheric Environment 30, 3413}3421.
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Mckendry, I.G., 1994. Synoptic circulation and summertime ground-level ozone concentrations at Vancouver BritishColumbia. Journal of Applied Meteorology 33, 627}641. Mckendry, I.G., Steyn, D.G., Lundgren, J., Ho!, R.M., Strapp, W., Anlauf, K., Froude, F., Martin, J.B., Banta, R.M., Olivier, L.D., 1997. Elevated ozone layers and vertical down-mixing over the Lower Fraser Valley BC. Atmospheric Environment 31, 2135}2146. Melas, D., Ziomas, I., Klemm, O., Zerefos, C.S., 1998. Flow dynamics in Athens area under moderate large-scale winds. Atmospheric Environment 32, 2209}2222. Miao, Y., Steyn, D.G., 1994. Mesometeorological modelling and trajectory analysis during an air pollution episode in the Lower Fraser Valley, BC. Transactions of Regional Photochemical Measurement and Modelling Studies Conference, pp. 249}281. Physick, W.L., Abbs, D.J., 1991. Modeling of summertime #ow and dispersion in the coastal terrain of southeastern Australia. Monthly Weather Review 119, 1014}1030. Pielke, R.A., Cotton, W.R., Walko, R.L., Tremback, C.J., Lyons, W.A., Grasso, L.D., Nicholls, M.E., Moran, M.D., Wesley, D.A., Lee, T.J., Copeland, J.H., 1992. A comprehensive meteorological modeling system } RAMS. Meteorology and Atmospheric Physics 49, 69}91. Pryor, S.C., Mckendry, I.G., Steyn, D.G., 1995. Synoptic-scale meteorological variability and surface ozone concentrations in Vancouver British-Columbia. Journal of Applied Meteorology 34, 1824}1833. Steyn, D.G., Bottenheim, J.W., Thomson, R.B., 1997. Overview of tropospheric ozone in the Lower Fraser Valley, and the Paci"c '93 "eld study. Atmospheric Environment 31, 2025}2035. Steyn, D.G., Faulkner, D.A., 1986. The climatology of seabreezes in the Lower Fraser Valley B.C. Climatological Bulletin 20, 21}39. Steyn, D.G., McKendry, I.G., 1988. Quantitative and qualitative evaluation of a three-dimensional mesoscale numerical model simulation of a sea breeze in complex terrain. Monthly Weather Review 116, 1914}1926. Steyn, D.G., Oke, T.R., 1982. The depth of the daytime mixed layer at two coastal sites: a model and its validation. Boundary-Layer Meteorology 24, 161}180. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Acad. Publishers, Dordrecht. Tjernstrom, M., Grisogono, B., 1996. Thermal mesoscale circulations on the Baltic coast.1. Numerical case study. Journal of Geophysical Research-Atmospheric 101, 18979}18997. Willmott, C.J., 1981. On the validation of models. Physical Geography 2, 168}194.