Evaluation of Mixing Height Over Complex Coastal Terrain G. Latini

Evaluation of mixing height over complex

coastal terrain

G. Latini/" R. Cocci Grifoni,^ G. Passerini, ™ T. Tirabassi,® ^ Dipartmento di Energetica, Universita di Ancona via Brecce bianche, 60100 Ancona, Italy

™ Fisbat CNR, Bologna

Abstract

The mixing height is one of the fundamental parameters to characterise its structure and is required in dispersion models. This paper is concerned with the evaluation of the hmix in a coastal area (Esino Valley) by a semi-empirical estimates of boundary layer parameters like the Monin-Obukhov length L and the roughness length ZQ. A preliminary evaluation of the methodology is presented.

1 Introduction

Substances emitted into the atmospheric boundary layer are dispersed horizontally and vertically due to the action of turbulence and eventually become well-mixed over this layer. Therefore, it has become customary to use the term "mixed layer" (ML). The mixing height hmLt, in the field of air pollution meteorology, is the thickness of the boundary layer; the boundary layer is the

vertical extent that is directly influenced by the surface roughness. Dispersion models need the knowledge of Mixed Layer to determinate the turbulent domain in which dispersion takes place. In principle, the depth of ML can be inferred from vertical profiles of quantities such as wind speed and direction, temperature and humidity, directly influenced by turbulent mixing.

However, the profiles of the above atmospheric parameters are difficult to achieve, thus it is often evaluated from ground level measurements. In this study the temporal evolution of the PEL vertical structure for a central region of Italy (Marche) comprising valleys, hills, urban and industrial zones

1074 Air Pollution

(Fig.l), has been investigated during the period 10/21 January and 10/20 July 1998 by semi-empirical point of view. In particular, the result of a sunny day (July 16) and a cold day (Jan. 15) are presented. It is well known that hmix and 1\L are inversely proportional and that L, characteristic stability parameter of the surface layer, can also be considered as a function of the Turner class and ZQ. Thus, the above parameters are empirically estimated by a simple method for a central Italian zone (Esino Valley). The purpose of this paper is also to test the ability of this simple" semi-empirical model to simulate the growth of the daytime mixing height. The computed mixing height values have been compared with data derived mostly from American measurements (Kansas) and Italian evaluations (Florence). In order to deal with a complex orography, a grid with appropriate refinement in space discretisation is considered for the ground roughness ZQ estimate. The semi- empirical estimate is developed for a resolution of nxn Km grid squares corresponding to a survey map. The results are average values for the coefficient zO and the parameter L in single cells.

2 The Esino Valley

Marche is an italian region made up of valleys nearly parallel, all looking out onto the Adriatic Sea One of these is the Esino valley (in the province of Ancona) characterised, as all the others, by a river bed that is roughly perpendicular to the coast and in a NE direction. The valley is surrounded by hillsides in increasing height as they distance from the coast. The first hills rise close to the coast and at this distance the height does not exceed 100 m. A further 20 km inland, the height does not exceed 200 m. At about 30 km the valley undergoes a sharp narrowing near the gorge "della Rossa" where the height exceeds 1000m The area taken into consideration will be the lower valley of Esino. The considered area covers 20 km inland from the coast and 20 km wide.

The climate in this area is classified under subcoastal. There is an all year round sea breeze although of different intensity and influenced by a heavy component fromNW. The sea breeze is caused by the different temperatures in the air bodies above the sea on one side and the coast on the other. This gives way to a meandering current along the coast with a parallel component to the coast caused by the synoptic winds in altitude; the component perpendicular to the coast, according to the direction is called coastal or sea breeze based on the origin of the winds. In the presence of discontinuity as in the hillsides situated at the entrance of the valley, the force of the sea breeze enforces the breeze coming from the valley.

This phenomenon is caused by a difference in temperature between the land and air around slopes. The highest intensity of the sea breeze/valley breeze occurs during the warmest hours (about 3 P.M.) and its decreasing starts after the sunset. During the night, you may have some hours of calm before the mountain breeze/land breeze starts again. Usually stability is associated with the mountain breeze, while unstable

Air Pollution 1075

conditions to the sea; in this scenario, the increase of the mixed layer starts from the coast. That layer marks both the condition of stability high above the MBL

(Marine Boundary Layer) and the instability of the CBL (Convective Boundary Layer) on the coast. The meteorological output data here in analysed, is related to the measuring performed by the Italian Air Force Weather Station in Falconara Marittima (1STAT), located in Chiaravalle airport, 2 km from the coast and more or less in the middle of the Esino valley (43.37 Lgt. -13.22 Long. - 12m height).The output data comes from the measuring performed hourly and gives information in both frequencies and monthly/ seasonal distribution of speed, direction and directional persistence of wind, atmospheric stability and air temperature.

ona

**%/v ,^ / V**,aJ&s#Agu^jT%& \\ -v ^^1^7 ^ AtotrtrfN .^^m^^v*^,'^

Fig.l

3 The Estimation Method

Meteorological measurements of boundary layer parameter are not often available and therefore, in most cases, the PBL parameters are not measured directly but inferred from standard meteorological information (van Ulden and Holstag').

3.1 Estimation of ZQ

It is adequate to estimate the surface roughness length ZQ using tables that give typical zO values based on land use (Zannettf).

A grid with appropriate refinement in space discretisation is considered for the ground roughness ZQ estimate. The semiempirical estimate is developed for a resolution of nxn Knf (n=l,2,40) grid squares, depending on the single evaluation, or measurements, and corresponding to a survey map Typically, ZQ is about O.lm in rural areas and ZQ is about 1.0m in urban and forested areas.

1076 Air Pollution

3.2 Estimation of L

The Monin-Obukhov length I is a rough measure of the height at which turbulence is generated by buoyancy equal that by wind shear. It is a parameter that characterises the stability of the surface layer and it is calculated from ground-level measurements. It is evaluated from (Panofsky and Dutton*)

-H.'

where w* is the friction velocity, k is von Karman constant, x>' and 7" are the surface values of the fluctuating components of the vertical wind and temperature, respectively. Often the only available characterisation of stability is a P-G stability class (Turner*). Colder's normograms relating P-G class to estimates of L, given ZQ, have been fitted by Liu at al/ and were adapted for use here as:

P-G CLASS A B

A -0.0875 -0.1029 B -0.03849 -0.1714

C -0.00807 -0.3049 D 0.0 0.0 E 0.00807 -0.3049

F 0.03849 -0.1714

where ZQ and L are in meters.

3.3 Estimation of hmix in Unstable Condition

With positive heat flux at the ground (sunny conditions) and some wind, we have both mechanical turbulence and heat convection. However it is well known from the energy budget of turbulence, the generation of mechanical turbolence decreases rapidly with increasing height, being it is proportional to the vertical heat flux at the surface. In contrast, the generation of heat convection varies very slowly with the height. A simple equation for hmix under convective conditions can be derived from the budget of heat energy (Panofsky and Dutton^):

h m = ZjWz& «*u r-A

Air Pollution 1077

where F is the adiabatic lapse rate and A is the lapse rate at sunrise. In Esino valley the lapse rate at sunrise is not available and so the value of F- A can be computed as:

with LO the Monin- Obukhov length at sunrise and

JQ = KI + K2 / sin cp

where KI. K/2 are constants and q> is maximum solar elevation. The central focus of this paper is mainly on estimating the mixing height of the Esino Valley (in order to use it in a air pollution model) attempting the development of a suitable method that considers only two parameters :T(t) and ZQ

where a is a constant

4 Validation of the Method

To test the performance of the above method, sets of data observed on 1984 at Dodge city station, Municipal Art (Kansas) Lat37.767 and at Ximeniano station,

Florence (Italy) Lat. 43.77 were used to compare with the predicted and the observed values.

4.1 Dodge city

An inland city only surrounded by uniform fields has been considered. The data offered in the SCRAM surface meteorological data files (http://www.epa.gov/scram001/t25.htm) comprise those parameters required by meteorological preprocessor programs. The SCRAM surface meteorological data files comprise data acquired from National Climatic Data Center (NCDC). The

SCRAM mixing height data files comprise data provided by NCDC in their "Twice Daily Mixing Height Data". The method was applied on two data sets. January 1, 1984 was day with stable condition over land during clear night with weak winds, unstable conditions in the daytime with positive heat flux at ground (i.e., sunny conditions), and no neutral conditions during daytime-nightime transition. January 4, 1984 was a day with neutral condition during night, weak unstable conditions in the daytime, and neutral conditions during daytime-nightime transition. The computed parameters are reported in Tab. 1.

1078 Air Pollution

1st January 1984 4th January 1984 -4.1°C 3.3°C To 1/L 0.017218 0.017218 sincp 0.535 0.535 0.6 1 a kt 1.953 1.953

Tab.l

The results are:

Hmix 1 January Hmix 4 January Afti\ 300 - ^r—*~*^, m m 250 300 x 200 ^^%^ "H 9 Mi . "5 140 . S^ = 100 * 100 f ^ SO 0 • — -^ o J f///*f/

For the 1* of January the mean hmix (in the morning) and the mean hmix (in the afternoon) computed values are 184.5m and 350.47 respectively; the AM mixing height and PM mixing height from SCRAM data files are 172 m and 353 m respectively.

For the 4* January the mean hmix (in the morning) and the mean hmix (in the afternoon) computed values are respectively 91m and 239m; the AM mixing height and PM mixing height from SCRAM data files are 104 m and 254 m respectively.

4.2 Florence city

Florence has been considered as a typical urban city. The measurement location is nearby Ximeniano (Florence). The studied episode is a sunny winter day (16^ of January 1985) with low winds. We have considered, for the comparison, mixing height values computed by PCRAMMET preprocessor program (EPA distribution). The results are shown in Fig.2.

Air Pollution 1079

TIME Evaluated Hmix

hmix (PCRAMMET)

9.00 183.02m 350.256 m

10.00 // 440.901 m 11.00 431.6m 514.204m 12.00 510.41m 518.354m

13.00 532.75 m 416.516m 14.00 491.75m 285.712 m

17.00 177.73 m 220.01 m

Hmix PCRAMMET Evaluated Hmix 600 600 __

f 40*"0 "• ^r^ ^ 400 *""^* "* — ""*"—--• V 300 • •^ \ ?w 30 *"0" / J 200 • """•***** J 200 • / 100 - 100 • 0 • 0 •

,*V*#«!*V*«V ^^^^^^^ Fig.2

The agreement between the computed and the observed internal boundary layer height is very good not only during the morning with a developing mixed layer, but also during the afternoon when the mixing layer is decaying. This proved

that the semi-empirical method was apparently suitable to be applied.

5 Mixing height evaluated in the Esino Valley

The region is characterised by a wide range of land use, varying from agricultural and horticulture fields, scattering housing in suburban areas, urban

areas, a river valley, hills, and industrial zones. The evolution of the mixed layer over this area was simulated on hourly basis. The values of the considered parameters are shown in Tab. 2. The simulation was performed over a domain of 20 x 20 Knf, using a 2x2 Km^ grid squares corresponding to a survey map, to compute the ground roughness ZQ.

The results are average values for the coefficient ZQ and the parameter L in single cells. Measurement of atmospheric data (wind and temperature) were supplied by IRPEM department of Ancona National Centre of Research (C.N.R). Two different thermodynamic situations have been studied: 1) January 29*, a cold day characterised by unstable conditions.

2) July 16*, a sunny day characterised by unstable conditions.

1080 Air Pollution

Day Temp. KT Zo (l/L)o Hmix 29/1/98 8.00 3.5 0.18 0.013612596 2.332318011 187.6718 29/1/98 9.00 4.0 0.18 0.013612596 2.332318011 228.6425

29/1/98 10.00 4.6 0.18 0.013612596 2.332318011 280.1861 29/1/98 11.00 5.3 0.18 0.013612596 2.332318011 334.3731

29/1/98 12.00 5.6 0.18 0.013612596 2.332318011 359.4841 29/1/98 13.00 5.9 0.18 0.013612596 2.332318011 384.5951 29/1/98 14.00 7.0 0.18 0.013612596 2.332318011 467.858

29/1/98 15.00 7.1 0.18 0.013612596 2.332318011 475.7878 29/1/98 16.00 6.3 0.18 0.013612596 2.332318011 409.7061

29/1/98 17.00 5.0 0.18 0.013612596 2.332318011 311.9053 16/7/98 7.00 21.5 0.18 0.013612596 1.290225018 348.3058

16/7/98 8.00 22,5 0.18 0.013612596 1.290225018 484,3782 16/7/98 9.00 23.0 0.18 0.013612596 1.290225018 561.5651

16/7/98 10.00 23.2 0.18 0.013612596 1.290225018 591.1087 16/7/98 11.00 23.6 0.18 0.013612596 1.290225018 645.6808 16/7/98 12.00 24.0 0.18 0.013612596 1.290225018 707.1322

16/7/98 13.00 24.7 0.18 0.013612596 1.290225018 809.6579 16/7/98 14.00 24.6 0.18 0.013612596 1.290225018 782.3057

16/7/98 15.00 24.5 0.18 0.013612596 1.290225018 780.0263 16/7/98 16.00 24.3 0.18 0.013612596 1.290225018 741.292 16/7/98 17.00 24.4 0.18 0.013612596 1.290225018 759.5134

Tab.2

Mixing heights lw computed hourly with the semi-empirical method have been plotted in the same figure (Fig.3).

900 800

200 - 100

7.00 8-00 9M 10.00 11.00 12.00 13,00 14.00 15.00 16.00 17.0 time of the day

Fig.3

Air Pollution 1081

Generally the simple semi-empirical method describes a satisfactory time evolution of the whole mixed layer. Figure 3 shows a daily course mixed layer depth. In the summer day the depth grows from 200-250m after sunrise up to

800m; in the winter day the highest value of the mixed layer depth is 475.5m at 3.00PM.

6 Conclusion

The mixing depth is an important parameter for pollution studies but is difficult to compute because of complex interactions between the many physical processes that contribute to its evolution. A semi-empirical method has been applied to compute hmix in the inhomogeneous terrain. Given the complexity of orography and land use in the Esino Valley, a very fine spatial resolution has been considered. In the test examples Dodge city and Florence, shown in this paper, the method was based on measurements of only two parameters (T(t) and ZQ). This is a crude assumption for a complex coastal terrain but was found here to work reasonably well.

The simple method evaluates result in good agreement with experimental evidence, especially given its simplicity.

References

1. Holtslag, A. AM & Van Ulden, A.P., A Simple Scheme for Daytime Estimates of Surface Fluxes from Routine Weather Data, Journal of Climate and Applied Meteorology,22, pp. 517- 529, 1983. 2. Zannetti, P., Air Pollution Modeling, Computational Mechanics Publications, New York, pp.42, 1990.

3. Panofsky, H.A. & Dutton, J.A., Atmospheric Turbulence, Chapter 5, General Characteristics of Atmospheric Turbulence, John Wiley & Sons, New York, pp. 107-118, 1983. 4. Turner, D.B., Workbook of Atmospheric Dispersion Estimates, Office of Air

Programs Publication, A-P 26, Environmental Protection Agency, Research Triangle Park, pp.84, 1970. 5. Liu, M, Durran, P., Mundkur, P., Yocke, M. & Ames, J., The Chemistry,

Dispersion, and Transport of Air Pollutants Emitted from Fossil Fuel Plants in California: Data Analysis and Emission Impact Model, Final Report to Air Resources Board, contract no. ARE 4-258, Sacramento, California, pp. 387, 1976.