uncertainties in estimating the mixing depth-comparing three mixing-depth models with profiler...

Pergamon Atmospheric' Environment Vol. 31, No. 18, pp. 3023 3039, 1997 1997 Elsevier Science Ltd

All rights reserved, Printed in Great Britain PII: ~ I , , J ~ L " - Z ~ I I J ( ~ I I T J ~ I l~ - - [ J 1352--2310/97 $17.00 + 0.00

U N C E R T A I N T I E S I N E S T I M A T I N G T H E M I X I N G D E P T H - - C O M P A R I N G T H R E E M I X I N G - D E P T H M O D E L S

W I T H P R O F I L E R M E A S U R E M E N T S

STEPHEN BERMAN Earth Science Department, College at Oneonta, State University of New York, Oneonta, NY 13820, USA

JIA-YEONG KU Division of Air Resources, New York State Department of Environmental Conservation, Albany, NY

12233, USA

and

JIAN ZHANG and S. TRIVIKRAMA RAO* Department of Atmospheric Science, State University of New York at Albany, Albany, NY 12222, USA

(First received 29 October 1995 and in final form 30 December 1996. Published July 1997)

Abstract--Determining the temporal evolution of the mixing depth is a complex problem in air pollution modeling. In this paper, mixing depths derived from three algorithms, RAMMET-X, MIXEMUP, and CALMET, are compared with estimates derived from a 915-MHZ radar profiler and Radio Acoustic Sounding System (RASS) located at Schenectady, NY, for nine clear summer days, Besides wind and temperature soundings, the profiler system also provided estimates of the mixing depth based on refractive index structure parameter (C, 2) measurements. For the nine test days studied, mixing depths ranged from 1.6 km in midafternoon to 150-250 m at night, based on C. 2. Mixing depths obtained from CALMET and MIXEMUP were in good agreement with C. 2 estimates throughout the day, but especially in the afternoon when they agreed to within 100 m. In contrast, estimates from RAMMET-X displayed considerably less diurnal variation, with afternoon mixing depths 300~00 m lower than profiler estimates, and nighttime values similarly too high. A separate "analytical method" based on an analysis of the profiler system's wind and temperature profiles, is offered as an alternate way for estimating the mixing depth. Mixing depths derived from the analytical method agreed well with C. 2 estimates at the times of the maximum and minimum, but displayed a much faster growth rate during the morning and a slightly slower decay rate in the evening. It is well known that ozone concentrations predicted by photochemical models are very sensitive to the mixing depth, The impact of the uncertainties inherent in the estimation of the mixing-depth profile on the ozone concentrations is examined through Ozone Isopleth Research Model (OZIPR) simulations. The results reveal that the variability in the OZIPR-predicted ozone concentration due to the uncertainties in the specification of the evolution of the mixing height is comparable or greater than that of different chemical mechanisms in the OZIPR model. © 1997 Elsevier Science Ltd.

Key word index: Mixing depth, C. 2, radar profiler, air pollution.

l. INTRODUCTION

A critical parameter in determining air pollution concentrations near the ground is the depth through which the pollutants are mixed, the so-called "mixing depth". Recent analyses with the Urban Airshed Model (UAM-IV) indicate that ozone concentrations predicted by the model are extremely sensitive to errors and uncertainties in the mixing depth profile (Rao et aL, 1994). The selection of appropriate control

*Author to whom correspondence should be addressed.

strategies will also depend on the spatial and temporal variability of the mixing depth across the modeling domain (Sistla et al., 1995). Consequently, routine and reliable mixing depths are needed to improve model performance, to build confidence in assessing the efficacy of emission control strategies, and to assist in the forecasting of pollution episodes. Under sunny daytime conditions, the mixing depth typically extends 1-2 km above the heated ground until it is abruptly halted by a stable, capping layer. On clear nights, a stably stratified layer develops at the ground, extending upward several hundred meters to the top of the surface temperature inversion. In general, only the lowest part of the nocturnal stable layer is turbulenL

3023

3024 S. BERMAN et al.

although weak and sporadic turbulence may extend to higher levels.

The object of this study is to compare estimates of mixing depths obtained from three models: RAMMET-X (U.S. EPA, 1990; Kelly, 1981), MIXEMUP (Lolk and Douglas, 1993), and CAL- MET (Scire et al., 1995) with estimates derived from a 915-MHZ radar profiler and Radio Acoustic Sounding System (RASS) on nine clear summer days over Schenectady, NY, a medium-sized urban location. These particular models were selected because they are widely used in the air pollution community, use distinctly different algorithms for estimating the mixing depth, and because their codes were readily available to us. Complications due to significant cloud cover, rugged topography, and coastal effects were purposely avoided to allow a baseline comparison of the models. Furthermore, this study addresses the temporal evolution of the mixing depth only and not its spatial variation. All the aforementioned models are designed to be initialized with surface and upper- air data available from nearby National Weather Service (NWS) stations. Though NWS surface observations are available hourly, upper-air soundings are made only twice daily at specific rawinsonde sites spaced roughly 400 km apart. This coarse resolution may be a limiting factor in the models' performance. To date, there have been very few studies comparing mixing depth estimates obtained from these models with real-time measurements of the atmosphere's wind, temperature, and turbulence structure, as derived from on-site radar profilers (Marsik et al., 1995).

2. DATA

In the summer of 1994, the Electric Power Research Institute (EPRI) initiated an intensive program of boundary-layer measurements at several sites in the northeast. Known as the 1994 Northeast Air Quality Study (NEAQS'94), its purpose was to collect and disseminate high-quality field data to assist the air pollution community in finding effective options for managing high ozone concentrations and precursor VOC and NOx emissions. A primary focus of the study was to acquire comprehensive data on emissions, atmospheric constituents, and meteorology to support the rigorous evaluation of ozone air-quality models. Surface and upper air meteorological measurements were made at Schenectady, NY, Kralltown, PA, Stratford, CT, and New Brunswick, NJ. Each site was equipped with a 3-beam 915-MHZ radar profiler for measuring winds aloft. A triangulation of the three radar beams (one vertical, two tilted) determined the three components of the wind velocity. The radar's maximum vertical range was approximately 3000 m, with a resolution of 60-100 m. A separate RASS was used for measuring temperatures aloft. Its maximum vertical range was approximately 1500 m, with a

resolution of 60-100 m. Besides measuring winds and temperatures, the profiler also provided refractive index structure data from which C] was computed. Finally, a 10 m mast at each site supplied surface meteorological data (temperature, wind, humidity, and solar radiation).

Since the subject of this paper is limited to the temporal evolution of the mixed layer, only the Schenectady site was studied. Schenectady forms part of the Albany-Schenectady-Troy metropolitan area with a total population of nearly one million. Its urban setting is in keeping with the typical application of these models. The radar profiler, RASS, and surface meteorological mast were installed at the Schenectady County Airport, a site located well in- land and without significant topographic relief. Re- sponsibility for collecting the profiler data, quality- assuring it, and archiving it was given to Sonoma Technology, Incorporated (STI). In addition to providing hourly-averaged wind and temperature profiles, STI also computed C, 2 values, applying the algorithm proposed by Dye et al. (1995). Surface observations and rawinsonde soundings needed to in- itialize the model runs were obtained from the Al- bany NWS forecast office, located 12miles to the southeast.

3. ESTIMATING MIXING DEPTH FROM PROFILER

MEASUREMENTS

3.1. C~ m e t h o d

One way to estimate the mixing depth uses C~ measurements obtained from radar reflectivities. Turbulence produces fluctuations in the atmosphere's temperature, humidity, and pressure fields. These, in turn, lead to variations in the atmosphere's refractiv- ity index, which is measured by C~. C~ can be computed from signal-to-noise ratios (for example, see White et al., 1991). Wyngaard and LeMone (1980) found that C~ reached a maximum at the capping inversion, located at the top of the convective boundary layer. Other studies have shown that C~ is useful for estimating daytime mixing depths in cloud-free convective boundary layers (White, 1993; Angevine, 1994). More recently, an algorithm for estimating mixing depths from median C~ profiles was developed by Dye et al. (1995) which was field-tested with aircraft profiles of temperature, turbulence, and pollution concentrations. C~ showed best agreement with aircraft profiles under clear, daytime conditions. Agreement deteriorated at night owing to spurious signal returns from migrating birds and at times when deep convective clouds remained persistently over the profiler. Also, C~ measurements appeared unable to resolve the mixing depth when multiple stratified layers were present. In summary, C, 2 appears to be a fairly reliable indicator of daytime mixing depths, but its ability to estimate the depth of the nocturnal boundary layer is not well-established.

Uncertainties in estimating the mixing depth 3025

3.2. Analytical method

A second way to obtain the mixing depth is to estimate it from an analysis of wind and temperature profiles. Although rawinsonde temperature soundings are often used for this purpose, the only rawinsonde measurements available in this study were the routine 00 and 12 UTC releases made by the NWS. To gain increased temporal resolution, we, instead, used the hourly virtual temperature and wind profiles provided by the radar's RASS and profiler systems. A profile-based "analytical" method was then developed to serve as an independent check of the C 2 technique, and to supplement it at times when C, 2 values were either not available, or judged to be unreliable. The method was designed for use on relatively clear days when radiative influences of extensive cloud cover would be minimal. The analytical method is actually a composite of three different estimation techniques, each designed for use in a different part of the diurnal heating cycle.

3.2.1. Early morning - - transition to convective conditions. In the hours following sunrise surface heating breaks through the temperature inversion, and the mixing depth grows rapidly. On clear days the virtual potential temperature profile becomes superadiabatic close to the ground, followed by a well-mixed adiabatic layer above, and capped by an upper stable layer. The radar profiler's RASS provided hourly virtual temperature soundings with a vertical resolution of 100 m. Height was converted to pressure using the hypsometric formula, and Poisson's equation provided the virtual potential temperature. During the morning hours, the depth of the mixed layer was taken to coincide with the level of the strongest positive virtual potential temperature gradient.

3.2.2. Midday convective conditions. Rapid attenu- ation of acoustic signals under convective conditions limits the vertical range of RASS-based virtual temperature profiles to 1 km, or less. By late morning the mixed layer often exceeds this height. In contrast, radar profilers can measure winds to heights of 3 kin, or more. For estimating the depth of the mixed layer in midday, a method employing these higher- altitude wind profiles was developed for use in this study.

Under fully convective conditions boundary layer winds tend to be subgeostrophic in speed and fairly uniform in direction. A narrow entrainment zone sep- arates the mixed layer from the stable layer above. Wind speed increases sharply in the entrainment zone, approaching its geostrophic value in the free atmosphere above. The analytical method uses the average wind speed between 300 and 500 m as representative of the boundary-layer flow and the average wind speed between 2500 and 3000 m as representative of the free atmosphere. The two wind speeds were averaged together to produce a speed characteristic of the interface between the layers, i.e. the entrainment zone. This "'entrainment zone wind speed" was then located

on the wind speed profile, and its corresponding height found by linear interpolation. This height was used as the depth of the mixed layer during convective daytime conditions.

This procedure is designed to be applied to a wind profile with a fairly standard shape, i.e. having slower wind speeds in the boundary layer, followed by distinctly stronger speeds aloft, separated by a narrow transition zone. If the speed difference between the upper and lower layers is small (less than 2 m s- ~) or if the wind profile is erratic, a distinct transition zone may not exist. Also, in cases of strong temperature advection, or baroclinicity, the wind speed profile may depart from the idealized shape. When this occurred we analyzed the vertical gradients of wind speed, searching for a simple pattern in the gradient profile. If a distinct peak was found, the corresponding height was assigned to the depth of the mixed layer. About 20% of the time a distinct maximum in the speed gradient could not be found. In such cases the wind direction profile was also examined and the height of the maximum wind direction gradient was used for the mixing depth. By examining both the wind speed and wind direction profiles, we were able to resolve all cases.

3.2.3. Nighttime, stable condit ions-- between sunset and sunrise. Owing to surface radiational cooling, a ground-based temperature inversion usually develops after sunset under clear skies and extends upward to a depth of several hundred meters in the course of the night. However, only the lower portion of the inversion layer remains turbulent. The height of this layer (h) is best estimated from measurements of pollutant concentrations in the vertical of which, unfortu- nately, there are few. Alternatively, it can be estimated from turbulence intensities using instrumented masts, low-flying aircraft, or upward-pointing sodars and lidars. In the absence of direct measurements, a number of indirect techniques have been proposed based on the analysis of wind and temperature profiles. Agreement of these profile-based techniques with direct measurements of h remains tentative, however.

Below is a list of some profile-derived heights that have been proposed for estimating the depth of the nocturnal boundary layer:

h~, height of the low-level wind maximum hi, height of the surface temperature inversion ho, height of the adiabatic layer hai, height at which the Richardson number reaches

a critical value.

Using wind and temperature profiles from the Wangara field experiment, Mahrt et al. (1982) showed that hu, hi, and ho had similar values (271, 213, and 224 m, respectively) when averaged over 60 nighttime hours. In contrast, using a cutoff value of 0.5 for the Richardson number, the authors showed that hai had an average value of only 69 m for the same hours. Moreover, h,, hi, and h0 correlated poorly (r < 05)


with u,/ f , a diagnostic relation obtained from sim- ilarity theory. However, hRi showed a fairly high cor- relation (r = 0.8) with u . / f The authors concluded that the weak relationship found with h,, hi, and ho was partly due to their inability to represent the actual depth of the turbulent layer. Similar results were found in a study by Yu (1978). Using acoustic sounder measurements of h, Arya (1981) also found low correlations between h,, ho and h.

In view of these findings, it is apparent that h,, hi, and ho all tend to overestimate the depth of the nocturnal boundary layer at night. While hRi may be a better estimator, it was not computed here because the 100 m vertical spacing used in our wind and temperature profiles was judged to be too coarse for obtaining meaningful Richardson numbers. Although mixing at night is confined to a shallow layer near the ground, weak and intermittent turbulence may extend to much higher levels, allowing for the slow dispersion of contaminants through the depth of the stable layer. This is more likely to be true in an urban setting where anthropogenic heat sources and increased surface roughness due to the density and placement of build- ings can help sustain turbulence levels even in a stable atmosphere. Using RASS temperature soundings, we computed hi for the hours between sunset and sunrise to serve as a rough upper boundary on the air's dispersive ability in an urban environment. A three- point parabolic fit of the virtual temperature profile in the vicinity of the temperature maximum was used to determine this height more precisely.

4. ESTIMATING MIXING DEPTH FROM MODEL

COMPUTATIONS

Three standard mixing-depth models, RAMMET- X, MIXEMUP, and CALMET, were selected for evaluation with the observational methods described above. The models are initialized with 12 UTC and 00 UTC rawinsonde soundings obtained from the NWS station at Albany, NY.

4.1. R A M M E T - X

RAMMET-X is a one-dimensional model that uses two standard NWS temperature soundings and hourly surface temperatures to estimate the mixing depth, The maximum mixing depth was determined by extending the maximum surface temperature upward to the intersection of the 00 UTC (afternoon) sounding, assuming a dry adiabatic lapse rate. Sim- ilarly, the minimum mixing depth was determined by extending the minimum surface temperature upward to the intersection of the 12 UTC (morning) sounding. Hourly mixing depths were then linearly interpolated between the maximum and minimum mixing heights, following the hourly variation of surface temperature. The model provides two mixing depths: one for a ru- ral environment, the other for an urban one. A heat island effect is incorporated in the urban estimate. The

urban mixing depth was the one selected for this study. RAMMET-X code has been recommended for use with the Environmental Protection Agency's Urban Airshed Model (U.S. EPA, 1990).

4.2. M I X E M U P

MIXEMUP is a one-dimensional, diagnostic model based on the Benkley and Schulman (1979) technique. MIXEMUP calculates a mechanical mixing depth for the nighttime hours and both a mechanical and convective mixing depth for the daytime hours. The larger of the two mixing depths, convective or mechanical, is then selected as the mixing depth for the daytime.

The daytime convective mixing depth is estimated by using the "parcel method", which compares the hourly surface potential temperature with the potential temperature at each level of the morning (12 U TC) sounding. If the surface potential temperature is less than that at the first sounding level, the atmosphere is considered to be stable and no convective mixing takes place. The temperature difference at 70kPA between the 12 UTC (morning) and 00 UTC (evening) is calculated to account for any cold or warm advection taking place over the 12 h period. The effect of advection is incorporated by subtracting from the hourly surface temperature the difference in temperature between the two soundings at 70 kPA, weighted according to the time elapsed since the 12 UTC sounding. For example, if the temperature at 70 kPA has increased from the time of the morning sounding to the time of the evening sounding, the result is a decrease in surface temperature and a corresponding decrease in convective mixing depth.

The mechanical mixing depth is calculated with the formula H = cu./J; derived by Zilitinkevich (1972). Here c is an empirical constant, u, is the friction velocity, and f is the Coriolis parameter. The formula is further simplified by making the mechanical mixing depth proportional to the surface wind speed, i.e., H = CoUlo, where Co is an empirical constant and Ulo is the wind speed at 10 m, averaged over 3 con- secutive hours to smooth out hourly variations. MIXEMUP provides three options for calculating the mechanical mixing depth: H = 125 Ulo, as suggested by Benkley and Schulman (1979), H = 28 U3/o2 from Nieuwstadt (1984), and H = 60 Uto, from Koracin and Berkowich (1988). The parameterization suggested by Benkley and Schulman was the one adopted here because we anticipated that it would better simu- late the larger surface roughness characteristic of urban areas.

4.3. C A L M E T

CALMET consists of both a diagnostic wind field model and a meteorological boundary layer model. Mixing height is calculated by the boundary layer model, which has a two-dimensional advective component that was not used in this application. The


mixing-height algorithm, developed by EARTH TECH, uses an energy balance approach to estimate the surface heat flux in driving the growth of the mixed layer (Scire et al., 1995). The parameterizations used in the energy budget are based primarily on Holtslag and van Ulden's (1983) paper.

During the daytime, CALMET calculates the mixing height as the maximum of the convective and mechanical mixing heights. The convective mixing height at time (t + 1) is estimated from time (t) in a stepwise manner as a function of sensible heat flux (Maul, 1980). The mechanical mixing height (neutral stability) is estimated from Venkatram's (1980a) relationship h = (Bu,) / ( fNB) I/2, where u, is the friction velocity, f is the Coriolis parameter, and NH is the Brunt Vaisala frequency in the stable air above.

During the nighttime, CALMET uses the minimum of the two mixing heights. The first mixing height is estimated by Venkatram's (1980b) relationship tl = B2 ,,3/2 where B 2 = 2400 (constant). The second formula from Zilintinkevich (1972) is given as h = 0 . 4 (u,L~[') 1/2, where L is the Monin-Obukhov length.

For this study we applied the CALMET model to one location only. The parameters selected were for the default urban setting: surface roughness (1 m), surface albedo (0.18), Bowen ratio (1.5), soil heat parameter (0.25), anthropogenic heat flux (0.0 Win-z) , and leaf area index (0.2). Anthropogenic heat flux varies widely between sites and times of year. The zero default value is acceptable in this study because the anthropogenic heat flux is expected to be a relatively small component of the total heat flux on warm summer days. (A zero value would probably not be satis- factory on cold, winter days, however.) The model also requires the input of two temperature soundings 12 h apart plus hourly surface observations of temperature, wind speed, humidity, and opaque sky cover. Hourly surface measurements and twice-daily rawinsonde soundings were supplied from the Albany NWS station.

5. E S T I M A T I N G T H E M I X I N G D E P T H O N N I N E T E S T D A Y S

5.1. Overall comparison

Nine test days in July and August 1994 were selected for analyzing mixing depths over Schenectady, NY. The nine days were chosen because they were generally clear, warm periods without precipitation events, making them conducive for the formation of ground-level ozone. On one of the days (13 July), there was an ozone "episode" reported in New York City, 150 miles to the south, with hourly ozone concentration levels exceeding the federal standard of 120 ppb. Table 1 lists the test dates together with a summary of the percentage of maximum possible sunshine received at ground level, maximum surface temperature, and sunrise/sunset times.

Figure 1 shows a plot of mixing depth vs hour of day obtained from running the three models (RAMMET-X, MIXEMUP, CALMET) together with estimates derived from profiler measurements (C, 2 and Analytical), averaged over the nine test days. The curves all exhibit a distinct diurnal cycle, averaging between 150 and 250m in the hours before sunrise, increasing to a maximum of 1200-1600 m in midafternoon. We next compare model-derived mixing depths with each other and with profiler observations, paying particular attention to maximum and minimum mixing depths, morning growth rates, and evening collapse rates.

Mixing height estimates from RAMMET-X show considerably less diurnal variation than those obtained from the other methods. In particular. RAMMET-X under-predicts the midday maximum by 350-450 m and over-predicts nighttime values by similar amounts. In contrast, CALMET and MIXEMUP's mixing depths agree to within 100 m of the profiler-based estimates (C, z and analytical) at the afternoon peak and the early morning minimum. It is during the transition times of day the, morning growth period and late afternoon collapse period - - that larger discrepancies are seen. The mixed layer grows rapidly between the hours of 06 EST and 12 EST as the convective regime is re-established. Rates of growth vary considerably, however, ranging from about 100mh -1 (RAMMET-X) to about 300 m h l (analytical), with the other methods having rates that fall in between these extremes. The atmosphere's rapid transition to convective conditions may be preventing the profiles from reaching equilibrium during the morning hours. The analytical method is particularly sensitive to the effects of non- stationarity, since it relies on three different profile estimation techniques at different times of the morning: the height of the surface inversion (hi) until sunrise, the height of the adiabatic layer (ho) through midmorning, and finally, the height of the entrainment zone from midmorning into the afternoon. It is difficult to get all three techniques to match up when the boundary layer is changing rapidly. I n particular, the wind profile may not be in full equilibrium during the morning as it adjusts from its nighttime accelerated flow to its slower, more uniform, daytime shape. These higher average wind speeds may account for the higher mixing depths and larger growth rates observed for the analytical method in the morning, as compared to the other estimation techniques.

When the temperature inversion reforms around sunset, convection is again cut off from the surface, and the mixed layer begins to collapse. Rates of decay vary from about 6 0 m h -1 (RAMMET-X) to 4 0 0 m h (CALMET), with the other methods having rates in the 200-300 m h -1 range. CALMET appears particularly sensitive to the time of sunset; its mixing depth falls 1.2 km in the hour between 19 EST and 20 EST. This rapid rate of decay is a positive feature of the


Table 1. Summary of the nine test dates (data from Albany County Airport)

Test Date % Max. Max. Sfc Temp Sunrise/sunset times (1994) Possible sunshine (°C) (EST)

11 July 95 27.2 12 July 90 29.4 04:28/19:33 13 July 82 31.1 19 July 72 31.7 04:34/19:28 29 July 83 28.9 31 July 86 28.3 04:46/19:17 6 August 100 22.2 7 August 100 25.6 04:43/19:08 8 August 94 27.2

2000

NEAQS'94 Study (Schenectady, NY) Average Mixing Depth over 9 Clear Days

15oo ,~- ~ . ' ~ l~ '~ ; ,

1000 .~'

:8

500 , , \ ~ ",,

0 = l = = ] n = = I = l l h t = = ~ l l = ~ t * l t q ¢ 5 9 13 17 21

Hour (EST)

Fig. 1. Averaged mixing depth over nine clear sky days from various methods.

Rammet - - v - -

Mixemup - - o

Calmet

Cn2

Analytical

model, reflecting the mixing height's quick response to the sudden removal of surface heating. In contrast, the Analytical Method's decay rate of 175 m h-1 is fairly slow. This may be reflecting the wind profile's relatively slow adjustment to changing surface conditions. Slower still is RAMMET-X's rate of decay, its mixing height remaining above 600 m as late as midnight.

5.2. Two case studies

To get a better idea of the mixing depth's day-to- day variability, we computed the standard deviation of mixing depth for each hour of the day. The results for C, z, CALMET, and MIXEMUP are shown in Fig. 2a-c. The standard deviations are about the same for the three methods, varying in 250-300m in midday to about half that amount at night. Although the test days were mostly sunny periods, differences in cloud cover, vertical stability, and temperature advection can apparently vary the depth of the mixed layer by several hundred meters. In general, mixing depths from all methods (except RAMMET-X) show best agreement with C 2 at the times of maximum and minimum, and worst agreement during transition periods.

Photochemical modeling applications reveal that ozone concentrations and the efficacy of an emissions control strategy predicted by the models are extremely sensitive to the growth of the mixed layer in the morning when emissions are injected into the atmosphere (Rao et al., 1995). A summary of average mixing depths and growth rates for the 9 d is given in Table 2. Mixing depths are also listed for 0700 EST and 1700 EST, times of heaviest commuter traffic; nitrogen oxides (NOx) and volatile organic compound emissions (VOC) from motor vehicles are known to be the primary ozone precursors during these periods. The depth of the mixed layer at these hours of the day is a critical factor in determining peak ozone concentrations later in the day. The last row of Table 2 lists the average standard deviation of mixing depth for all hours of the 9 d. Two of the nine test days, 7 August and 19 July, were examined in greater detail.

5.2.1. Clear d a y - - 7 August, 1994. Seventh August was a clear day (100% possible sunshine recorded) with a stationary anticyclone situated over eastern New York State. The surface temperature reached a maximum of 25°C in the afternoon. Winds remained light and variable throughout the day from


2000

-•'•1500 r -

o~ 1000 cr~

500

NEAQS'94 - 9 Clear Days Cn2: Means and St. Deviations

4 7 10 13 16 19 22

I _ 1 1 _ _

Cn2

Cn2 + sd

Cn2 - sd

(a) Hour (EST)

Fig. 2a. Means and standard deviations of the mixing height over nine clear sky days from C, 2 data.

NEAQS'94 Study Calmet: Houdy Means and Std. Devs.

1800

E 1400 ¢ -

~ - 1 0 0 0 a

c 600

200

-200

(b)

/ i

j L

J ~L

, I, [

, r , , r , , , I ' ' r ' ' I ' ' I

4 7 10 13 16 19 22 Hour (EST)

Fig. 25. Same as Fig. 2a, except data from CALMET model output.

Calmet-NCAR

Calmet + sd

Calmet - sd

2000

NEAQS'94 - 9 Clear Days Mixemup: Means and St. Deviations

,-- 1500 E

v

O .

o~ 1000 Q

._c

._x 500

(c) 4 7 10 13 16 19 22

Hour (EST)

Mixemup

Mixemup + sd

Mixemup - sd

Fig. 2c. Same as Fig. 2a, except data from MIXEMUP model output.

3030 S. B E R M A N et al.

Table 2. Mixing depth summary for the nine test days

C, 2 Analytical CALMET MIXEMUP RAMMET

Max. ht (m) 1596 1590 1576 1567 1157 Time of Max 16 EST 14 EST 17 EST 16 EST 15 EST Growth rate (m h- 1) 120 267 182 160 113 (6 11 EST) ht at 0700 EST (m) 412 276 503 193 592 Collapse rate - 384 - 259 - 412 - 212 - 93 (17-20 EST)(mh 1) h at 1700 EST (m) 1412 1305 1576 1532 1112 Avg Stand. Dev: (m) 228.7 186.6 207.6 232.2 310.4

2000

NEAQS'94 Study Aug. 7, 1994 - Schenectady, NY

RAMMET

MIXEMUP

CALMET

- - e .

~E~. 1 5 0 0 ~ , "

.x 500 ~; Cn2

0 . . . . . . . . . . . . . . . . . . . . . . ANALYTIC 1 5 9 13 17 21

Hour (EST)

Fig. 3. Temporal evolution of the mixing height for 7 August, 1994 from various methods.

the surface to the 85 kPA level. Plots of mixing height vs time are shown in Fig. 3. Mixing heights estimated from CALMET, MIXEMUP, and C 2 roughly paral- lel each other throughout the day and night, and are within 50 m of each other when the mixed layer reached both its maximum and minimum depths. In contrast, RAMMET-X under predicts the afternoon peak by 400 m as does the Analytical Method, which is too low by 300 m. There is also some disagreement as to when the mixing depth begins to collapse. C, 2 and MIXEMUP estimates show the collapse starting at 18 EST, while CALMET's decline begins at 19 EST. RAMMET-X's estimates fall off very slowly after sunset, remaining above 600 m at midnight. Morning and evening rawinsonde temperature soundings from Albany on 7 August are provided in Fig. 4. The difference between the 12 UTC and 00 UTC soundings suggests a small amount of warm advection took place at levels below 700 mb. Table 3 summarizes the mixing depths obtained from the five methods.

5.2.2. Cloudy day 19 July, 1994. The second day selected for study, 19 July, had significant amount of cloud cover for much of the 24 h, but no precipitation. The sky was reported as having broken or overcast conditions consisting mainly of stratocumulus and altocumulus clouds from midnight until 11 EST. Fog and haze were observed from 01 to 07 EST, the haze continuing until noon. From noon until 19 EST the

sky was mostly sunny with scattered cumulus clouds. Scattered cirrus was observed between 20 and 21 EST. In spite of the morning cloud cover, the surface temperature reached a maximum value of 30.6°C by midafternoon. The upper-air soundings plotted in Fig. 5 show negligible temperature advection throughout the lower atmosphere. Thus, the rise in surface temperature can be attributed almost entirely to the effects of solar heating.

Unlike the other models, CALMET incorporates the effect of cloud cover into its calculations of the surface heat budget using Holstlag and van Ulden's (1983) energy budget parameterizations. Clouds emit long-wave radiation to the surface which helps offset nighttime radiational cooling. Low clouds are more effective at this than high clouds. Clouds also reduce the atmosphere's transmissivity of incoming solar short-wave radiation, helping to lower surface temperatures during the day. Holstlag and van Ulden's (1983) energy budget equations contain an "opaque sky cover" parameter (N). Opaque sky cover is defined by the NWS as "the amount (to the nearest tenth) of cloud layers or obscuring phenomena (aloft or surface-based) that completely hides all or a portion of the sky and/or higher clouds that may be present." The opaque sky cover is always less than, or equal to, the total sky cover. Holtslag and van Ulden parameterize the downward long-wave radiation


4000

3000

2000

1000

I

I

I

l

% %

% %

Albany, NY

.... 12Z 08/07/94

00Z 08/08/94

% %

% %

% %

% %

' I ' I ' I ' I '

5 10 15 20 Temperature (C)

Fig. 4. Morning and evening rawinsode temperature soundings from Albany airport, New York on 7 August, 1994.

r

25

Table 3. Mixing depth summary for 7 August, 1994

C~ Analytic CALMET MIXEMUP RAMMET

Max. ht (m) 1596 1280 1630 1586 1141 Time of Max 17 EST 15 EST 17 EST 14,15 EST 14,15 EST Growth rate (m h- 1) 105 198 187 89 104 (6-11 EST) ht at 0700 EST (m) 127 363 318 100 490 Collapse rate (m h - 1) - 490 - 124 - 510 - 457 - 105 ( 17-20 EST) ht at 1700 EST (m) 1596 1176 1630 1566 1141

from clouds with the term c2N, where Cz = 60 W m -z, an appropriate value for mid-latitude locations. At its maximum value CEN is about 20% the size of other long-wave radiation fluxes.

The equation used for incoming short-wave radiation Qsw is given by Holtslag and van Ulden (1983) as~

Qsw=(alsinc~+a2)(1 +biN b~) (1)

where ~b is the solar elevation angle (degrees), N i s the opaque sky cover, and the radiation coefficients (al, a2, bl , bz) are assigned the values 9 9 0 W i n -2, - 3 0 W m 2, - 0 . 7 5 , and 3.4, respectively. The first

factor on the right-hand side of equation (1) represents the extraterrestrial solar radiation received on a h0ri-. zontal surface attenuated by average water vapor and turbidity. The second factor further depletes the,


3 0 0 0 - -

2 0 0 0

tO00

0

5

% %

% %

%

' I ' I ' I

10 15 20 Temperature (C)

Albany, NY

12Z 07/I 9/94

00Z 07/20/94

% %

% %

%

' I

25

%

I

30

Fig. 5. Same as Fig. 4, except for 19 July, 1994.

incoming solar radiation according to the amount of sky cover. For clear skies (N = 0) the factor has a value of 1.0, indicating no depletion. For overcast skies (N = 1) the factor equals 0.25, resulting in depletion of incoming short-wave radiation to 25% of the clear skies value. The parameterization used by Holtslag and van Ulden does not distinguish between higher and lower clouds or between cloud types.

Sky cover can be obtained in various ways. The NWS reports opaque sky cover to the nearest tenth from an hourly surveillance of the sky by its trained observers. These observations are later sent to the National Climate Data Center (NCDC) in Asheville, NC, for reformatting and storage. The NWS also transmits hourly surface airways (SA) observations to the National Meteorological Center (NMC). The SA messages contain cloud amounts and ceiling data, but not sky cover. Instead, sky cover is derived from the cloud information by applying an algorithm developed by NMC's Techniques Development

Laboratory (TDL). The algorithm yields total sky cover in oktas (0-7), with "8" reserved for obscured conditions. Opaque sky cover is also calculated, but only in four categories, namely, 0, 4, 8, or 10 corresponding, respectively, to clear, scattered, broken, or overcast conditions. NMC's data set is subsequently transmitted to the National Center for Atmo- spheric Research (NCAR) for numerical modeling and archiving.

Table 4 shows the hourly total and opaque sky cover recorded for 19 July from both the NCAR and NCDC data sets. (Oktas have been converted to tenths for the NCAR total sky cover data). Although the differences between NCAR and NCDC sky cover values are not large, we decided to run CALMET with each set of data to see how the mixing depth would be affected. The results are shown in Fig. 6 together with a hypothetical clear day (N = 0) case. In all cases, the boundary layer reaches its maximum depth at 17 EST, but with different values depending


Table 4. Sky cover values for 19 July, 1994

Hour NCAR NCDC NCAR NCDC (EST) Total sky cover Total sky cover Opaque sky cover Opaque sky cover

Ol 0.4 0.6 0.4 0.3 02 0.9 0.6 0.8 0.6 03 1.0 1.0 1.0 1.0 04 1.0 1.0 1.0 1.0 05 1.0 1.0 1.0 1.0 06 1.0 1.0 1.0 1.0 07 1.0 l.O 0.8 1.0 08 0.9 0.8 0.4 0.5 09 0.6 1.0 0.8 0.5 10 0.9 0.9 0.8 0.6 11 0.9 0.9 0.8 0.6 12 0.9 0.8 0.8 0.6 13 0.9 0.6 0.8 0.4 14 0.7 0.4 0.4 0.4 15 0.7 0.4 0.4 0.4 16 0.7 0.4 0.4 0.4 17 0.7 0.2 0.4 0.2 18 0.7 0.2 0.4 0.2 19 0.7 0.4 0.4 0.1 20 0.3 0.3 0.0 0.1 21 0.3 0.2 0.0 0.0 22 0.0 0.0 0.0 0.0 23 0.0 0.0 0.0 0.0 24 0.4 0.0 0.0 0.1

2000

~" 1500

0~ 1000 Q O3 .c_. X $ 500

N E A Q S ' 9 4 S t u d y

July 19, 1994 - CALMET mixing depths

/,ff , '

5"

• , . , , , , , , , , , , , ,

4 7 10 13 16 Hour ( E S T )

o

Calmet - C lear

Calmet - N W S - x -

Calmet - N C A R

19 22

Fig. 6. CALMET mixing heights estimated based on the clear sky as well as the opaque sky cover obtained from NWS and NCAR schemes.

on the sky cover: Clear 1767m, N W S 1653m, N C A R 1543 m. The relatively small differences between the curves suggest tha t the cloud cover, t hough extensive at times, was not thick enough to appreci- ably reduce the s t ream of incoming solar radiat ion. This becomes more appa ren t when we compare incoming solar rad ia t ion (measured at the profiler site) received on August 7 (100% possible sunshine) with tha t received on 19 July (72%). C o m p a r i n g the area under the two curves in Fig. 7, we find tha t the total solar rad ia t ion received on 19 July was approximate ly 89% of the total received on 7 August. Thus, the cloud cover present on 19 July was es t imated to be

able to reduce total incoming shor t -wave rad ia t ion only by 11%0.

Since measurements of incoming solar rad ia t ion were available, we decided to use them to check the accuracy of equa t ion (1). Figure 8 compares hourly incoming shor t -wave rad ia t ion observed at the profiler site on 19 July with calculat ions made using equa t ion (1). Two different calculat ions were made: one with N C A R sky cover values, the o ther with N W S sky covers. Figure 9 shows overall agreement between observed and calculated values. The N W S curve slightly over predicts the a m o u n t of solar radi- a t ion reaching the g round at nearly every hour, while


1000

N E A Q S ' 9 4 - Observed Solar Radiat ion Schenectady, NY: Aug. 7 & July 19

E

t - o .m_ "O t~ n-

800

600

400

200

0

,\

/ / / ' ' / '

4 7 10 13 16 19 22 Hour (EST)

Fig. 7. Observed solar radiation at Schenectady, NY on 19 July and 7 August, 1994.

the NCAR curve slightly under predicts the observed values in the hours around noon. Nevertheless, the differences appear relatively small. These results,

though preliminary in nature, lend some confidence to the heat-budget and sky cover parameterizations used in the CALMET model.

Figure 8 shows the hourly plot of the mixing depth estimates from all methods for 19 July. CALMET was run using NCAR sky cover values. On this day, both MIXEMUP and CALMET estimated the maximum mixing depth to be about 1.6 km, which falls 500 m short of C2's peak mixing depth of 2.1 km; the reason for this sizeable discrepancy is not clear, RAMMET- X's peak mixing depth is again too low (1141 m), and its rate of collapse in the evening hours is much too slow. CALMET's estimates show close agreement with C 2 every hour after 10 EST, except for its lower maximum. The rapid collapse of CALMET's mixing depth beginning at 18 EST matches C,2's equally pre- cipitous decline of an hour earlier. CALMET's early morning values, ranging from 500 to 900 m, are several hundred meters too high, however. The high values may be due to the dependence of both models on the surface wind speed for parameterizing the depth of the nocturnal boundary layer. As stated

1000

800

~ 600

O -= 400 .~_ "O t~ n- 200

NEAQS'94 - Solar Radiation July 19, 1994 - Calculated vs Observed

j , -

/f \ ,

/j

// _2 4 7 10 13 16 19 22

Hour (EST)

Observed

Calculated - NCAR

Calculated - NWS

Fig. 8. Comparison of the solar radiation estimated based on NCAR and NWS schemes with observed data.

2500

2ooo

~ 1500

n:: .~. i000

50O

N E A Q S ' 9 4 S t u d y July 19, 1994 at Schenectady, NY

/\,

i ' ':~' '~ ' 'fo' '1'3' ~1'6' '1)' '~2' Hour (E, ST)

RAMMET

MIXEMUP

CALMET-NCAR

Cn2

ANALYTIC

Fig. 9. Same as Fig. 3, except for 19 July, 1994.

Uncertainties in estimating the mixing depth

Table 5. Mixing depth summary for 19 July, 1994

3035

C, 2 Analytical CALMET CALMET MIXEMUP RAMMET-X

Max. ht (m) 2120 2268 Time of Max (EST) 16 14 Growth rate (m h - 1) 231 259 (6 11 EST) ht at 0700 EST (m) 233 139 Collapse rate (m h- l) - 594 207 (17 20 EST) ht at 1700 EST 1910 1180

1653 1543 1607 1009 17 17 17. 18 16. 17 49 21 138 112

593 593 471 324 - 5 1 8 - 481 162 - 104

1653 1543 1607 1009

earlier (see Section 4), CALMET calculates the height of the nocturnal boundary layer as the minimum of two heights. The first is given by Venkatram's formula

3,.2 where B2 2400), and the second is (h = B 2 U. , = given by Zilintinkevich's formula (h = 0 . 4 ( u , L / f ) 1/2, where L is the Monin Obukhov length). Both for- mulas depend on accurate estimates of u, which is parameterized as a function of surface wind speed. The resulting high values of h suggest that the parameterization scheme for u, may be too simple for nighttime use over urban locations. MIXEMUP's nighttime values are similarly high (500 m) in the early morning hours. MIXEMUP uses the formula h = 125 Ulo, suggested by Benkley and Schulman (19791, where Ulo is the surface wind speed, measured 10 m above the ground. Late night and early morning wind speeds on 19 July averaged 3 4 ms-1. Using these speeds, Benkley and Schulman's formula yields mixing depths of 375-500 m. After it reaches its maximum mixing depth at 17 EST, MIXEMUP takes 4 h longer than C, 2, to fall to its nighttime minimum of 100 m. Table 5 summarizes the mixing depth estimates for all five methods.

6 . O Z I P R S I M U L A T I O N S

In order to evaluate the impact of the uncertainties in the estimation of the mixing height on ozone concentrations, the Ozone Isopleth Research model (OZIPR) is employed. OZIPR is a one-dimensional box model for simulating ozone photochemical pro- duction in the boundary layer (Gery and Crouse, 1991). Very complex chemical mechanisms may be input into OZIPR to describe the chemical processes that occur within the modeled air mass. The three chemical mechanisms used in the OZIPR simulation are CB-IV (Gery et al., 1987), RADM (Stockwell, 1986) and CAL (Carter et al., 1986).

The OZIPR simulations were started with the in- itial and boundary conditions describing chemical species concentrations for a typical urban area at 08 local time. The typical temporal evolution of the mixing depth to the OZIPR simulation was provided by the averaged values estimated from the five different mixing-depth algorithms used on the nine test days at Schenectady, NY, during the NEAQS'94 study (see Fig. 11. OZIPR-predicted ozone concentrations for

each mixing depth profile and chemical mechanism are shown in Fig. 10a-c, respectively. The peak ozone concentrations predicted by OZIPR vary considerably when different mixing height profiles and chemical mechanisms are used.

In general, the results can be separated into three groups:

(1) RAMMET-X mixing depth yields the highest afternoon ozone concentrations (161 ppb);

(2) C, 2 and MIXEMUP mixing depths produce the lowest afternoon ozone concentrations ( ~ 115 ppb);

(3) CALMET and analytical mixing depths predict similar afternoon ozone concentrations which fall between those in groups (1) and (2) ( ~ 137 ppb).

Examination of the mixing-depth profiles obtained from the different algorithms between 08 to 20 EST (Fig. 1) indicates that the temporal variation of RAMMET-X estimates differs significantly from those of the other four algorithms, showing little morning growth after sunrise and little decay after sunset. Thus, RAMMET-X mixing depths underesti- mate the afternoon peak when compared with those from the other four algorithms and, consequently, overestimate the ozone concentration that develops over the urban area.

Table 6 shows the temporal evolution of the mixing depth from 08 to 20 EST for all five estimation techniques used: C 2, the analytical method, CALMET, MIXEMUP, and RAMMET-X. Hourly values of the coefficient of variation (the ratio of standard deviation to mean) are smallest in the afternoon hours and largest in the morning and evening hours. Wide variations in the morning mixing depth's growth rate also contribute to different amounts of dilution on ozone precursor emissions during the morning. This, in turn, leads to variations in the amount of ozone formed, as indicated by OZIPR simulations.

Table 7 lists the temporal evolution of ozone concentrations predicted by OZIPR (with CB-IV chemical mechanism) for C,2,, the analytical method, CALMET, MIXEMUP, and RAMMET-X, respectively. In this study, we selected ozone concentrations predicted from OZIPR (CB-IV) for C 2 mixing heights as the base-case profile for comparing ozone concentrations predicted with each mixing height and with


OZIPR (CB-IV) Predicted Ozone Profiles for Different Mixing Height Algorithms

180

160

~ 140

120

"~100

80

o ¢~ 60

40

20

. > < . - - - ~ < . . . . . > 4 . . . . x - - -

[ ]

C n 2

pmalytical

C,M.MET

- - Q -

M I X B M U P

K A M M E T

8 10 12 14 16 18 20 (a) Local Time (Hour)

Fig. 10a. OZIPR predicted ozone concentrations for each mixing height profiles by using CB-IV chemical mechanism.

180

160

~. 140

=o 120

"~100

o r~ 80

~ 6o

40

20

(b)

OZIPR (CAL) Predicted Ozone Profiles for Different Mixing Height Algorithms

/

8 10 12 14 16 18 20 Local Time (Hour)

Fig. 10b. Same as Fig. 10a, except for CAL chemical mechanism.

E 3

Cn2

CALMET

MIXEMUP - > ~ -

RAMMET

Analytical

OZIPR (RADM) Predicted Ozone Profiles for Different Mixing Height Algorithms

160

140

120

"~ 100

~ 8o

o ~ 60 ©

40

20

(c)

- x . . . . x

x " . : "-~"

,/e. / ,~ / m /

10 ' 12 14 16 18 Local Time (Hour)

Fig. 10c. Same as Fig. 10a, except for RADM chemical mechanism.

D

Cn2 - [ ] -

CALMET - o -

MIXEMUP x - -

RA/VlMET

Analytical

Uncertainties in estimating the mixing depth

Table 6. Variation in the mixing height from 08:00 to 20:00 (EST) (m)

3037

TIME STD/MEAN (EST) C, 2 Analytical CALMET MIXEMUP RAMMET-X MEAN STD (%)

08:00 353 513 630 258 714 493.6 169.0 34.2 09:00 472 1000 798 394 821 697.0 227.9 32.7 10:00 637 1276 907 565 915 860.0 251.0 29.2 11:00 982 1550 1097 960 1005 1118.8 220.6 19.7 12:00 1121 1551 1302 1270 1040 1256.8 175.6 14.0 13:00 1320 1499 1397 1357 1089 1332.4 135.6 10.2 14:00 1451 1590 1475 1480 1150 1429.2 147.6 10.3 15:00 1491 1518 1533 1547 1157 1449.2 147.3 10.2 16:00 1596 1478 1563 1567 1147 1470.2 166.3 11.3 17:00 1412 1305 1576 1532 1112 1387.4 167.1 12.0 18:00 861 1037 1566 1477 1025 1193.2 276.6 23.2 19:00 463 636 1404 1207 887 919.4 348.5 37.9 20:00 258 527 279 898 832 490.5 297.9 60.7

Table 7. OZIPR(CB-IV)-predicted ozone concentration

Dev of Dev of Dev of Dev of TIME Analytical CALMET MIXEMUP RAMMET-X AN CAL MIX RAM (EST) C~ (Ana) (CAL) (MIX) (RAM) (%) (%) (%) (%)

09:00 24 30 23 26 22 25.0 - 4.2 8.3 -8 .3 10:00 45 48 45 46 44 6.7 0.0 2.2 - 2.2 11:00 62 65 65 60 67 4.8 4.8 - 3 . 2 8.1 12:00 79 87 83 73 91 10.1 5.1 - 7 . 6 15.2 13:00 92 107 102 89 113 16.3 10.9 - 3.3 22.8 14:00 104 116 119 100 133 11.5 14.4 - 3.8 27.9 15:00 114 127 129 108 148 11.4 13.2 -5 .3 29.8 16:00 115 133 135 112 157 15.7 17.4 - 2 . 6 36.5 17:00 119 135 138 115 161 13.4 16.0 - 3 . 4 35.3 18:00 119 135 138 115 161 13.4 16.0 - 3 . 4 35.3 19:00 117 134 137 114 159 14.5 17.1 - 2 . 6 35.9 20:00 117 133 136 114 158 13.7 16.2 - 2 . 6 3f0

each chemical mechanism. The variability in ozone concentrations, defined as the standard deviation of the base case normalized by the base case is about 13% in the afternoon, which can be attributed primarily to the differences among the mixing-height algorithms during the morning evolution period. Table 8 lists the temporal evolution of ozone concentrations predicted from the three chemical mechanisms for the C,2-derived mixing height. The CAL chemical mechanism predicts the highest ozone concentration while the R A D M chemical mechanism gives the lowest values among the three. The variability in ozone concentrations, as measured by the standard deviation, during the afternoon is about 8 %. These results reveal that the variability in the predicted ozone concentration due to uncertainties in the specification of the evolution of the mixing height during the morning is comparable to, or greater than, that attributable to uncertainties in the chemical mechanisms.

7. SUMMARY AND CONCLUSIONS

In this study we compared mixing depths estimated from the R A M M E T - X , M I X E M U P , and C A L M E T

models with C 2 estimates derived from a 915 M H Z profiler radar located at Schenectady, NY, over nine mostly clear days during July and August 1994. Although the C 2 method for estimating mixing depth is relatively new, it has been shown to be in good agreement with aircraft profiles of pollutant concentrations, turbulence, and temperature, particularly during daytime convective conditions. Its ability to delineate the height of the stable boundary layer at night is not as well-established, however. For pur- poses of this study, C,2-derived mixing depths were considered fairly reliable and served as a reference, for comparing model estimates.

An analytical method, using a combinat ion of wind and temperature profiles, was proposed as an alternate way of estimating the mixing depth. In the morning hours the analytical method locates the mi~ing depth from an analysis of potential temperature gradients; in the afternoon it associates the mixing depth with the entrainment zone separating boundary layer winds from upper level flow; at night it associates the top of the mixed layer with the height of the surface temperature inversion (h3. Though turbulent conditions at night tend to be found at heights lower than hi, the additional heat sources and greater


Table 8. OZIPR-predicted ozone concentrations with CZ-estimated mixing height algorithm (ppb)

TIME Dev of RADM Dev of CAL (EST) CB-IV RADM CAL (%) (%)

09:00 24 26 29 8.3 20.8 10:00 45 47 55 4.4 22.2 11:00 62 61 73 -- 1.6 17.7 12:00 79 76 94 -3.8 19.0 13:00 92 86 105 -6.5 14.1 14:00 104 96 113 - 7.7 8.7 15:00 114 104 121 - 8.8 6.1 16:00 115 105 122 - 8.7 6.1 17:00 ll9 106 125 - 10.9 5.0 18:00 119 106 124 - 10.9 4.2 19:00 117 104 123 - ll.1 5.1 20:00 ll7 104 122 - 11.1 4.3

surface roughness characteristic of an urban land- scape may allow contaminants to diffuse slowly through the depth of the stable layer. Thus, hi is regarded here as a rough upper bound on nighttime dispersion in an urban setting.

Results indicate that the mixing depths estimated from CALMET and MIXEMUP are in good overall agreement with those derived from profiler (C 2) measurements. When averaged over the nine test days, estimates from CALMET and MIXEMUP matched those from C, z to within 100 m for the afternoon peak. CALMET and MIXEMUP also re- produced the C, z, curve's growth and collapse rates reasonably well. The analytical method shows good agreement with C ] at the times of the midday maximum and early morning minimum, but shows a much faster morning growth rate and a slightly slower afternoon collapse rate.

Morning growth rates for C 2, CALMET, and MIXEMUP were similar, averaging 200 m h-1, but were only 100mh-1 for RAMMET-X, and 300 m h-1 for the Analytical Method. In late afternoon, C 2 estimates showed a rapid collapse of the mixing height, falling from 1.6 km to about 250 m between 16 and 20 EST. CALMET shows a similarly rapid decline, but most of it occurs in the hour following sunset, from 19 to 20 EST. Estimates from MIXEMUP and the analytical method decrease more gradually, falling at about half the rate of C 2. Slower still is RAMMET-X's rate of decay, its mixing height remaining above 600 m as late as midnight. In general, RAMMET-X comes in a dis- tant third behind CALMET and MIXEMUP, dis- playing slower morning growth rates, slower evening decay rates, afternoon maxima which average 350-400 m lower, and nighttime minima that are similarly too high when compared with the other methods.

OZIPR simulations indicate that predicted ozone concentrations in an urban area are not only affected by the maximum afternoon mixing depth, but also are very sensitive to the growth of the mixed layer in the morning. Differences in morning growth rates can

greatly affect the dilution of ozone precursor emissions which, in turn, determine the formation of ozone during the afternoon hours. Our results show that the variability in predicted peak ozone concentrations due to uncertainties in the evolution of the mixing depth appears comparable to, or greater than, that attributable to uncertainties in the chemical mechanisms.

Results from this study should be regarded tenta- tively, as the data used were limited to nine mostly clear summer days at a single, medium-sized urban location. The additional complications of significant cloud cover, strongly baroclinic conditions, rugged topography, or proximity to a coastline, were purposely avoided to allow us to make a baseline comparison of the models. With these limitations in mind, the good performance of MIXEMUP and CALMET when compared with estimates from C 2 is encourag- ing. As a supplementary technique, the analytical method performed almost as well. However, the analytical method requires access to detailed boundary- layer wind and temperature soundings, such as those supplied by a wind profiler and RASS system. Also, the analytical method assumes relatively simple wind and temperature profile shapes which may not apply under less ideal conditions.

Acknowledgements- One of the authors (S. T. Rao) grate- fully acknowledges the support for this study by the Empire State Electric Energy Research Corporation (ESEERCO) under contract No. EP9417. The authors would like to thank Dr Peter E. Coffey for his review and helpful comments on this manuscript.

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uncertainties in estimating the mixing depth-comparing three mixing-depth models with profiler...

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