ML20247F948
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| Issue date: | 06/30/1991 |
| From: | Hanna S SIGMA RESEARCH, INC. |
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{{#Wiki_filter:0 , 0 Final Task Report 1 ESEERCO Project EP S9-14 fl LJ f' L,]J Review of Formulas and Observations of Thermal Internal Boundary ; I Layers in Shoreline Environments j p-, June, 1991 ra b Prepared by: [ Sigma Research Corporation L ' 234 Littleton Road, Suite 2E I Westford, MA 01886 O', Principal Investigator Steven R. Hanna O Prepared for: l Empire State Electric Energy Research Corporation , 1155 Avenue of the Americas New York, New York 10036 i NEW YORK POWER AUTHORITY DOCUMENT REVIEW STATUS ETAlpih9t-1 2 ACCEPTED 2 O ACCEPTED AS NOTED RESUBMITTAL NOT REQUIRED 3 O ACCEPTED AS NOTED RESUBMITTAL REQUIRED 4 O NOT ACCEPTED Pennissen to proceed does not consmute acceptance or approval of design detaas, cak:utatens, analysis, test methods or m.torials developed or seiected } ty the suppler and does not eve sup from tut compitance wtm coa"uSaT,'t*a*c. . REVIEWED Bd , TITLE:: 5.1 6 v" 6 W . 9905200099 990226
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" Copyright @ 1991 EMPIRE STATE ELECTRIC ENERGY RESEARCH CORPORATION. All rights reserved."
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" LEGAL NOTICE" I
"This report was prepared an an account of work j sponsored by the Empire State Electric Energy Research Corporation ( 'ESEERCO' ). Neither ESEERCO, members of t.bt.t.HCO nor any person acting on behalf of either:
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Prepared by Sigma Research Corporation, 234 Littleton Road, Suite 2E, Westford, Massachusetts. I I i I I i 1 111 1 o L >
O \ Abstract The theoretical basis for the growth of the Thermal Internal Boundary Layer (TIBL) at coastlines was examined, several existing TIBL formulations were compared with field data, and the best formulations were recommended. Seven analytical formulas for the TIBL height were discussed and compared with aircraft observations at the coastlines of Lake Erie, Lake Michigan, Japan and Long Island, NY. Two of the simpler empirica formulas were found to be more robust and agree as well with the observations as the more theoretical formulas. These two formulas, one of which is in the Offshore and Coastal Dispersion model, were recommended for routine use. IIM W i,ts ER 4 ll.it mal lui ist lds the w ed
, u
U Table of Contents Page
~.xecutive
- Summary
- 1. Introduction 1-1
- 2. TIBL Formulas 2-1 2.1 Overview of Theoretical Concepts 2-1
- 2. 2 List of Formulas 2-6
- 3. TIBL Observations 3-1
- 4. Comparisons of Formulas with Observations 4-1
- 5. Recommendations 5-1
- 6. References 6-1 N
E] M M id iu i v11 l 6-- - ~ _.
List of Illustrations Figure Page { 1-1 Potential temperature cross section was made following an 1-2 east-west traverse of Lake Michigan shoreline at Oak Creek, j Wisconsin, 5 August 1971, with NCAR instrument Queen Air. A weak conduction inversion is capped by a stable layer over the lake, with an elevated synoptic subsidence inversion about 4000 ft. The heavy line denotes the top of the layer heated by penetrative convection from the surface: the Mermal Internal Boundary Layer (TIBL) (Lyons, 1975). l l 1-2 Flight track turbulence reports. Plots of relative 1-2 I turbulence values noted by observer in aircraft taken during the same time period as Figure 1-1. 1-3 Typical wind vectors and smoke pattern observed in Chicago 1-4 during sea breeze situations. The sea breeze front is marked ! by a dashed line with arrowheads (Lyons, 1975). 1-4 Illustration of coexistence of sea breeze and TIBL. Wind 1-5 vectors are shown. Clouds can form in the convergence zone at the sea breeze front. 1-5 Lidar observation across the California coast near Ventura 1-6 for September 20, 1985, 1439-1452 PDT (Lidar) and 1535 PDT (NTD winds) (from McElroy and Smith, 1990). The ground is marked by the top of the white area, the near-surface layer is marked by the dark line, and the top of the boundary layer is marked by the top of the medium-shaded area. 2-1 Schematic diagram of an internal boundary layer (Venkatram, 2-2 1986). 2-2 The IBL concept applied to the sea-land transition. For 2-5 z > z above land, the wind profile is assumed to be in equilibrium with the local stress and stability over land (dashed line) (from Van Wijk et al., 1990). 2-3 The measured height of the TIBL (h) versus stability (1/L) 2-8 indicated by the symbols (x) as presented by Bergstrom et al. (1988). The solid line indicates that the height of the TIBL has been calculated with a numerical model. The dashed line illustrates a linear approximation through the measured points (from Van Wijk et al., 1990). 2-4 The IBL height (Zg ) as a function of distance from the coast 2-10 calculated with equation (2-9) (dashed lines) and calculated with a numerical model (solid lines) for three different situations (neutral, very stable (L = 36 m) and very unstable (L = -28 m), from Van Wijk et al. (1990). 3-1 Ten selected TIBL tops monitored by aircraft during the 1974 3-2 i field program on the west shore of Lake Michigan (Lyons. 1975). The thick line is the prediction of equation (2-16). ix
_ _ _ . _ ~ 3-2 Hip of Long Island, Nsw York showing principal flight tracks 3-3 i (numbered) (Reynor et al., 1979). 3-3 Turbulence cross-section during run S14 at Brookhaven with 3-4 strong winds and overcast skies (Raynor et al., 1979). 3-4 Nanticoke experimental design schematic surface and airborne 3-5 plume / air quality measurements upwind, within and downwind of fumigation zone (CS = COSPEC/ SIGN-X) (Portelli, 1982). 3-5 Profiles of depth of internal boundary layer at Nanticoke 3-6 with distance inland at different times f'.ST) on 1 June (Kerman et al., 1982). The thick line is the prediction of equation (2-16). 3-6 Relationship between h determined by turbulence (solid 3-11 line), h gdeterminedbNmperature(dashedline)todistance from the coast at Kashihara, Japan (from Gamo et al., 1982). ' The thick line is the prediction of equation (2-16). 4-1 Predicted and observed TIBL values for the onshore neutral 4-2 BNL BL #6 case (Stunder and Sethuraman, 1985). 4-2 Predicted and observed TIBL values for the onshore stable BNL 4-3 BL #13 case (June 13, 1978, 1530 EST) (Stunder and Sethuraman, 1985). 4-3 Vari.ation of TIBL height h with distance x (Hsu, 1988). 4-4 I<' 4-4 Modeled IBL heights versus observed ones (Bergstrom et al., 4-5 3 1988). g 4-5 Empirical formulas (2-16) for TIBL height (thick solid line) 4-6 plotted together with observations from a number of field 1 studies. BNL data are from Raynor et al. (1979), Nanticoke data are from Kerman et al. (1982), and Australian uata are from Rayner (1987). (Hanna, 1987.) E' B B B t B x B
List of Tables Table Page 3-1 Internal boundary layer characteristics at Nanticoke (1 3-7 June,) (h, internal boundary layer height; x, distance inland; N , effective Brunt-Vaisalla frequency of onshore flow; H, Iurface heat flux u, mean wind speed to height hl (Kerman et al., 1982). 3-2 Internal boundary layer characteristics at Naticoke (6 June) 3-8 p, (Kerman et al., 1982). , w ) 3-3 List of the thickness of the Internal Boundary Layer at 3-10 Kashihara. Japan given by h h at every 2 km R I downwinddistanceoverthela,ndh,h, andh,YcbessoftheIBL tfi determined by the variation of the lapse rate along the downwind distance above the land; h , thickness of the IBL determined by the horizontal temperature variation; h t thickness of the IBL determinedbythehorizontalturE6Ie,nce variation (from Gamot et al., 1987).
% 5-1 Estimated height of the Thermal Internal Boundary Layer for two recommended equations.
5-2 E M l i n a n l M d
I Exscutive Summary Interaction of plumes with the Thermal Internal Boundary Layer (TIBL) is of interest to sources located near shorelines. Because several formulations of the TIBL exist, the objectives of this task were to review the theoretical basis for the growth of the TIBL at coastlines, compare several formulations with field data, and recommend the best available formula. The TIBL is generated as a stable air mass flows over the land surface during the daytime when the sun is warming the surface, and has a slope of approximately 1/10. Several analytical formulas for the TIBL height, h, are discussed. Field experiments are reviewed in which TIBL's were observed by aircraf t over Long Island (NY), Nanticoke (Lake Erie). Lake Michigan, and Kashihara (Japan). The formulas are compared with the field data, with the result that the simpler empirical formulas (h a x or h a x ) yield as good agreement as the more theoretical formulas, with a typical uncertainty of about + 50%. E ~ The two recommended formulas for TIBL growth are (i) the formula used in the Offshore and Coastal Dispersion model (h = 0.1 x for x s 2000m, and h = 200
+ 0.03 (x-2000) for x > 2000m) and. (2) the formula proposed by Hisra and Onlock (1982) and Esu (1988) (h = A x1 # , where A is 4.9,2.7, 1.7 and 1.2 for overland Pasquill-Gifford classes A, B, C and D).
M e Ls 1 a xiii j i j
&j t 1 Fl kg 1. Introduction The earth's surface is marked by great spatial variations over most land areas. There can be rapid variations in roughness (e.g , grassy area to corn field), thermal characteristics (e.g., plowed asphalt parking lot to snow covered field) and moisture content (e.g., lake to desert). As the air flows from one surface to anothe: and it is modified at the bottom, the depth of the modified layer increases with distance. The boundary between the modified air near the surface and the unmodified air aloft is called the Internal Boundary Layer (IBL). Hunt and Simpson (1982) and Garratt (1990) review all types of IBL's, pointing out that researchers in the 1950's and 1960's were first concerned with IBL's resulting from changes in surface roughness, where the IBL slopes are found to have slopes of about 1/10. The surface roughness change problem was studied extensively in laboratory and small-scale field programs (e.g., Elliot, 1958).
N The subject of the current review is the class of IBL's generated as stable air over a cold lake flows over a land surface heated by the sun. The Q resulting IBL is called a Thermal Internal Boundary Layer (TIBL), a name that appears to have been first coined by Lyons (1975). In particular, this review is concerned with TIBL's on the southeast shore of Lake Ontario. Our review reveals that there have been no field experi5ents to collect TIBL data in this I L_d area, but that there have been several field experiments at similar sites. For example, Lyons (1975) presents the TIBL observations in Figures 1-1 and 1- 2. which are based on aircraf t observations on the Lake Michigan shoreline
'~ near Oak Creek,' Wisconsin. These figures illustrate several characteristics of TIBL's.
+ Overwater temperature gradients are stable.
- Overland temperature gradients are neutral to unstable.
- The TIBL slope is roughly 1/10.
l[ - Turbulence levels under the TIBL are much greater than above the TIBL. 1-1
POTENTIAL TEMPERATURE. *X 5 AUGUST 1971
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9 < These characteristics can cause shoreline fumigation of stack plumes, which
- an occur when a plume is released at the shoreline into the stable air above i the TIBL, but then intercepts the growing TIBL at some distance inland, where l
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is rapidly mixed or fumigated to the ground. Ground-level concentrations can t ze relatively high during these conditions. [ The TIBL concept can be complicated by the co-existence of sea breezes. I Both phenomena can occur at the same time, and the interactions are not addressed by current models. Figure 1-3 illustrates a mesoscale sea-breeze front observed by Lyons (1975) over the southwest shore of Lake Michigan. In this example, the direction of the general synoptic flow is from the land towards the lake, but a sea breeze develops that opposes this flow to an
, inland distance of about 5 to 10 km. A TIBL would form in this sea breeze,
- i. and the vertical structure could be as showr in the schematic diagram in 4 Figure 1-4. Inland, the TIBL and the sea breeze would merge in some way, and eventually be diffused by the convergence and vertical motions at that location. The models discussed in this report ignore interactions with the sea breeze front.
! Both the TIBL and the sea breeze are significantly affected by complex terrain near the shoreline. For example. Figure 1-5 shows lidar observations by McElroy and Smith (1990) of the vertical structure of the boundary layer across the California coast near Ventura. Coastal terrain rises steeply to elevations of several hundred meters. The boundary layer is stable over the ocean in the left part of the figure, as indicated by horizontal layering of the dark bands. In the inland valley, the t)p of the convective boundary layer is irregular, with a height of about 700 m above local terrain. Over j the coastal and inland mountains, the boundary layer is not well-defined and the TIBL is certainly difficult to see. Because there are not many ,
' observations of TIBL's along steep shorelines, no theories exist in the )
literature for this situation. l The remaining sections in this report are organized so that general TIBL l theories are first discussed, then TIBL observations are reviewed. Finally, comparisons of theories and observations are presented and specific TIBL a formulas are recommended, 1
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- 2. TIBL Formulas This section provides a summary'of many available TIBL formulas.
2.1 Overview of Theoretical Concepts Theories and formulas for the.TIBL height are reviewed and discussed in
-the model comparison paper by Stunder and Sethuraman (1985) and the coastal meteorology book by Hsu (1988). Perhaps the best discussion of the theoretical aspects of TIBL development is provided by Venkatram (1986), who bases his analysis on the variables and parameters shown in Figure 2-1, and defined below:
eg (*C): Water Surface Temperature o g (*C): Land Surface Temperature e , (*C): Mixed Layer Potential Temperature over Land 40 ( *C): Temperature Jump at Top of TIBL y = de/dz (*C): Potential Temperature Gradient over Water (Assumed Constant) h(0) (m): TIBL Height at Shoreline h(x) (m): TIBL Height at Inland Distance x H,(x) (w/m ): Upward Heat Flux from Land Surface u(z) (m/s): Wind Speed, as a Function of Height Note that it is assumed that the TIBL may be initiated a short distance offshore, since water temperatures near the shoreline may be warmer than they are farther offshore. Consequently the initial TIBL height at the shoreline is h(0). Furthermore, it is assumed that the shoreline extends to infinity in the cross-wind direction'and that all variables are spatially homogeneous in that direction. The energy fluxes across the vertical lines AB and CD and the horizontal j line AD on Figure 2-1 can be used to derive a formula for the TIBL height,- ') h(x). 2-1
1 {' i, l 1 Stable Layer a 1 t=N*r Stable C B -- l~ onshore , as :/ g( 1 Flow I Qn Convective h(0)- TiBL h(x) A ( O t s, pf, a a a 4 o Water Land Hfx) U warc Hest Flux x ,- i 1 l Figure 2-1. Schematic diagram of an internal boundary layer (Venkatram. 1986). 2-2
Energy outflow through CD - Energy inflow through AB = Heat flux through AD 1 h(x) h(0) x p,Cp u(x,z)e(x,z)dz - u(0,z)e(0,z)dz = (2-1) H,(x)dx 0 0 O { where p, is the air density (assumed constant in x and z), and C p is the specific heat at constant pressure.
.j l In order to obtair. an analytical solution to equation (2-1), Venkatram (1986) makes the following assumptions:
I Q,=H/p,C isp assumed constant. I Ae = F(de/dz)h (entrainment assumption). Qg /Q, = - F/(1-$) = -0.2 (i. e. , F = in) where Q gis the upward component of the energy flux doe to entrainment at h. Researchers haveobservedthatQ/Q,=-0.2. t u ,= constant mean wind in TIBL layer. With these assumptions, the following formula is suggested: (2-2) h (x) = h (0) + We/ z)u, Oox Venkatram then assumes that the heat flux, Q,, is equal to eu,(e - s y), where u, is the friction velocity and a is a site-specific proportionality constant. Sincetheratiou,/u,isrelativelyinvariant,hesuggeststhe formula (e -e) h (x) = h (0) + a' * ~3' ( e/dz t i i 2-3 l t i i
This formula has also bxn sugg2sted by othsr rsccerchsro, and lendo to a hax relation that is recognized as a fundam2ntal relation in the analysis of TIBL's. Venkatram (1986) points out that the TIBL height cannot increase indefinitely, and suggests an interpolation formula: (2-4) h (x) = h (0) + (h, - h (0))(1 - e ) l where h, is the equilibrium height that is approached at large x, and rL is a length scale that'must be determined from the data. There are several difficulties with equations (2-2) and (2-3), due to the restrictive assumptions that have been applied. Some of these problems are listed below: The vertical position of the TIBL is difficult to verify, since it j can be defined by a temperature jump, a wind speed discontinuity, or a turbulence discontinuity. Furthermore, Garratt (1990) points out that there are really two TIBL's-the top of the layer modified by the surface (i.e., the definition used above), and the top of the i I inner layer in which the boundary layer has reached its new equilibrium with the underlying surface. There is a factor of 3 or ! 4 difference between the two definitions. I
- The wind speed profile (u(z) in equation (2-1)) can be significantly different over the water, at the coastline, and over the land. For example, Van Wijk et al. (1990) present Figure 2-2, in which the ,
idealized wind profiles for overwater and overland locations are given. However, most of the TIBL theories ignore this variation. The sensible heat flux. Q,, is not constant with distance from the ! shoreline. It is expected that, as the TIBL grows, the sensible \ . heat flux itself will grow due to feedback from the boundary layer. Theoverwatertemperaturegradient,de/dz, is not likely to be constant with height. Most boundary layer theories and observations wouldindicatethatde/dzwouldbegreatestnearthesurface. 2-4
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C n 4 Figure 2-2. The IBL concept applied to the sea-land transition. For z > z above land, the wind profile is assumed to be in equilibrium with the local stress and stability over land (dashed line) (from Van Wijk et al., 1990). 2-5 I'
B
- The water and land surftes tcuperatures, go and e in equntion (2-3) are not easily observed or defined. Since temperature, 0, shows its largest variation near the surface, it could vary by several degrees from the surface skin temperature as measured by a radiometer, to the air temperatures 0.1 m above the surface, to the l air temperature at a standard measurement level of 10 m on a meteorological tower.
Another approach to the theoretical analyJis of TIBL growth involves the analogy between the growth of the TIBL as the air flows inland, and the growth of the convective mixed layer with time at a fixed inland position. The latter phenomenon has received much study, and is the source of the Q/Q,=0.2assumptionusedbyVenkatram(1986). The convective mixed layer ! t grows due to the sensible heat flux, Q,, which enters the layer from the bottom and the sensible heat flux Q , which enters the layer from the top. The s}. ace derivative, u(d(along-wind heat flux)/dx), used to analyze TIBL's is equivalent to the time derivative, d(along-windheatflux)/dt,usedto analyze mixed layer growth at a fixed position. Deardorff and Willis (1982) conducted a detailed laboratory experiment of the latter phenomenon and suggested an analytical formula that fit their observations. This formula was used by Hanna et al. (1985) to express TIBL growth in the first l version of their Offshore and Coastal Dispersion (OCD) model, but was abandoned in the second version bect.use it was found to yield unrealistically j large TIBL growths. It was discovered that the problem was that the empirical i parameterization in the Deardorff and Willis model were derived from i observations where the inversion growth, dh/dt, was small compared with the typical TIBL growth rate, udh/dx. Consequently the empirical formulas for entrainment, etc., gave unreasonable results for conditions outside of the range of their derivation.
- 2. 2 List of Formulas:
Several TIBL formulas were tested by Stunder and Sethuraman (1985), and many others have been suggested by individual researchers. Many equations have an h a x 1/2 form, as shown below. 2-6 i L
[ t h = 8.8(x/uae)1/2 Van der Hoven (1967) (2-5) l l where as is the total vertical potential temperature difference across the l overwater inversion. l
'u ' 'x(Tg - T,)' 1/2 I
h= - Raynor et al. (1979) (2-6)
, s ,
de/dz , where T and T yare measured at about 10 m above the surface and de/dz is valid for the layer from about 50 m to 100 m above the sea surface.
'u ,' # '2(T - T,)x,1/2 h= -
Venkatram (1977) (2-7)
. s ,
e @ -0 , whereF=1/7andde/dzisassumedconstantoverwater.
,1/2 20 x h= Weisman (1976) (2-8)
(de/dz)u. In equations (2-6) and (2-7), the ratio u,/u is typically assumed to be about 0.05. 'Ihe reader will note that all of these formulas imply h a FI ' and
~
h a(de/dz) 1' , which are the same functional dependencies as shown in the theoretical equation (2-3). Thedependenceofhonu,/uisdifferentin equations (2-6) and (2-7), since equation (2-6) is an empirical hypothesis and equation (2-7) is based on a theoretical derivation. Monin-Obukhov similarity theory is used as the basis for the following alternative TIBL formula:
. 63M h = 0.2 x Van Wijk et al. (1990) (2-9) l In equa't ion (2-9), L is the Menin-Obukhov length, which is positive for stable conditions, negative for unstable conditions, and = for neutral conditions.
This formula is the result of a theoretical analysis begun by Smedman and 1 Hogstrom (1983) and Bergstrom et al. (1989). The behavior of h with L at a i distance of about 500 m from the shoreline is illustrated in Figure 2-3, from l 2-7
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10.03 -0.02 -0.01 0.00 0.01 0.02 0.03 1/L (1/m) l l l l I 4 l Figure 2-3. The measured height of the TIBL (h) versus stability (1/L) indicated by the symbols (x) as presented by Bergstrom et al. (1988). The solid line indicates that the height of the TIBL has been calculated with a numerical model. The dashed line illustrates a linear. approximation through the measured points (from Van Wijk et al., 1990). l l 2-9
- _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ = _ _ _ _ _ _ - _ -
Van Wijk et al. (1990). It should be mentioned that L is calculated for the overland boundary layer. The predicted growth of the TIBL for three stability classes is shown in Figure 2-4. I f An extremely simple empirical formula has been suggested by Misra and Onlock (1982) and Hsu (1986, 1988, 1989): h = Ax (2-10) where both h and x are expressed in meters. The following values are ' suggested for the " constant," A: A = 2.7 to 5.6 (Misra and Onlock (1982), from Nanticoke field experiment) l A = 1.91 i .38 (Hsu (1986), from four field experiments) i The value of A can be estimated theoretically from equation (2-8), using the ! following definitions: I Q, = u.e. Sensible heat flux (2-11)
-u,/*.
L= T M nin-Obukhov length (2-12) 1/2 N= h s Brunt-Vaisalla frequency (2-13) { When these definitions are substituted into equation (2-8) the following i equation results: ' l 1/2
'1/2 u.
1 h= 7 - (2-14) u u. s s s i l r ,1/2 r ,1/2 5 "" 1 Consequently, A = 7 g . Isothermal conditions 6 , , - s 2-9
e4 500-
/ " unstable
/
400- - ;
/
/
300- , v /
/
/
e / N 200 - '
/
/ neutral
/
/ , **'.=~~
~~~
100 - ,' ' , , , 0 _ __sa 6000 t ble O 1000 2000 3000 4000 X (m) l Figure 2-4. The IBL height (z ) as a function of distance from the coast calculated with ehation (2-9) (dashed lines) and calculated with a numerical model (solid lines) for three different situations (neutral, very stable (L = 36 m) and very unstable (L = -2E m), from Van Wijk et al. (1990). 2-10
over the water (i.e., N = 0.017s' ), can be assumed and Briggs' wind profile formula can be adapted: I.
= 2. 5 t.n(z/(z,(1 - 4z/L)0. 6)) (2-15)
If it is assumed that 2 9- 0.01 to 0.1 m and z ~ 10 to 100 m, we obtain tha l estimates of A in the table below: Pasquill '5 ,1/2 u, _u u u. A= ~ 3 Class L(m) u, (m/s) (m/s) u/u N (-L)1/2
. A -3 m 10 2 .20 4. 9 B 10 m 13 3 .23 2. 7 C -30 m 17 5 .29 1. 7 D -100 m 20 8 .40 1. 2 The Pasquill stability class in the table is obtained from the graphs given by Golder (1972). The table shows that the value of A given by Misra and Onlock l (1982) is in the range from Pasquill class A and B (moderately to very uastable),
and the value of A given by Hsu (1986) is in the range for Pasquill j class C (slightly unstable). The final TIBL height equation to be tested is the empirical formula discussed by Hanna et al. (1985) and Hanna (1987): h = 0.1x (x s 200G m) (2-16a) h = 200m + 0.03(x-2000) (x > 2000 m) (2-16b) This formula represents a best-fit to a number of data bases, and conforms to the "1/10 slope" rule frequently mentioned in the literature (e.g., Stunder and Sethuraman 1985 Hunt and Simpson 1982, and C.rratt 1990). I i 2-11 i i
l 3. TIBL Observations A few limited field observations of TIBL's have been made using aircraf t or remote sounders. These data will be compared with model predictions in Section 4. In this section, overviews of some of the field observations are given. Lake Michigan - Lyons (1975) review article provides some examples of TIBL height cross-sections, as seen in Figures 1-1 and 1-2. He used an aircraft to locate the TIBL, based on temperature observations and qualitative measures of turbulence. Ten TIBL's from this same study are plotted in Figure 3-1, for inland distances of up to 20 km. Note that at a distance of 10 km, the TIBL heights range from about 200 to 700 m, with a median of about 500 m. Long Island - Brookhaven National Laboratory conducted a series of aircraft observations of the TIBL growth over Long Island. Figure 3-2 gives a map of the area showing some principal flight tracks (Stunder and Sethuraman, 1985). Because the aircraf t operations could not be conducted below a level of 150 m, the TIBL observations could not begin until about 2 or 3 km inland, where the TIBL grew above that height. An example of a turbulence cross-section during one run is given in Figure 3-3. where the boundary separating heavy and light turbulence is assumed to correspond to the TIBL (Raynor et al., 1982). I Nanticoke - A comprehensive field study of meteorological conditions and diffusion around the Nanticoke power plant on the north shore of Lake Erie was summarized by Portel11 et al. (1982). Figure 3-4 contains a schematic diagram of the experimental design. Aircraft were used to measure the TIBL, and the results of the TIBL study were reported by Kerman et al. (1982). Several observed TIBL's on June 1, 1978, at Nanticoke are plotted in Figure 3-5, showing a median TIBL height of about 400 m at a downwind distance of about 10 km. l The Nanticoke data for two days (June 1 and 6, 1978) are given in Tables l ( 3-1 and 3-2, respectively. For each hour, the table includes the TIBL height at 3 to 5 inland distances, the Brunt-Vaisalla frequency ((g/T)(de/dz))1/2 , l 3-1
~ -
TEN THERMAL INTERNAL BOUNDARY LAYERS [TIBL5] W "om - _ ex - .
< .m - _
Low stacx ---* d u- .. a. -
- =
/ -
s2 Ei-/ 2 u,. sf.cx- -- _y l a y ,, . u. e i . . M 4 G 48 m ol5TANCE INLAND (KILoadETE3tS) e l l l l Figure 3-1. Ten selected TIBL tops monitored by aircraft during the 1974 field program on the west shore of Lake Michigan (Lyons, 1975). The thick line is the prediction of equation (2-16). l 3-2
LONG ISLAND SOUNO
< t* 00' N
72 W d ruine, 72*so* reenoort Piece
'a a - ,,,,,,e, Po,e / Island d*N** t Lilite Motteluck' conic Jp c,eos g (1) BNL "I
,,, :r. ,l- ;;-
x - , f C3 ($ North See g10 Bridge-homotan (6) (8) (9) (3) (4) O 10 g
\(2) !-N- %
g, ha *Esesport
' ? Wcos ) Log.
\
! 8P S*#"P'"**I poetic Southompton GreIt BeoEn " 40' 50' B Ch I necock Wes empton g[I"g mit h Moriches Cupeogue f Point Inlet Beech Watch Hill o 7;3 l ATLANTIC OCE AN l
,m )
J l I I !l l Figure 3-2. Map of Long Island. New York showing principal flight tracks (numbered) (Raynor et al., 1979). I 3-3 l l
I i I i l i ll l l l 700 ll
' ' * *
- i i . i i i li 6 6 i 600 - l LIGHT I b 400
( ll s- i 5 C 300 - x l
'200 gp HEAVY -
40 0 -
/ / .
/ / ,
/ l 0
OCEAN ' / c.,a ems . _
, 0# '
-l 0 1 2 3 4 5 6 7 8 9 10 il 12 13 14 DISTANCE FROW OCEAN (km) l I
I! I' I; t Figure 3-3. Turbulence cross-section during run S14 at Brookhaven with strong winds and overcast skies (Raynor et al., 1979). 3-4 l 5' 1 a -- - - - - --
ll!;ll1! \\ ; [,
's R
@u =C A
E8 HA g L eo n rd on bi rw f E l $ in aw) T P
/, o2 O dd8 C ~ n 9 I ad1 L n E
H ea c i anl fil m'g 5 rh e ut t sir c woP i ,( f a i I
- p.
- td an) mix ew-h pN cuG
> s I sS nt /
gnC f i eE smP eeS drO uC - s l s -
- aa=
t e - he nmS g _ e my( C _ it
's'f rie el n pao xuz eq O !
n - J A eeo kl i V A
/ oat c/a H i eg --
t mi R num
- gly/
E - ' al u N pf
~
/ .
\1 - t 8 v
4 i ^ 3
\ g5 _
/
m ; 5 e f, s _,5 r
- u 9: %
l g
. 1
. i g
- F
_ f ' Y, p_ ?
}
r9
/ \
^ -
/ I i _
^.
s55 W 5 _ 5._m1- _ y
~
, ll ll ll' I
Il. I'
, I o a NANTICOKE BOUNDARY L AYER PROFILES _
.a _
.nt g7 _
JUNE 1,1978 _ I6 0
- 10 II 1
.o 12 _
O3
$- /
13 j e - p s # .- .." to 0 '$ I3 "
,7 O /
5 2 w _ ll 1, a
- - d * -
I t t t t I I t i I t t t t t
- a. 13 15 0 1 2 3 4 $ o 1 8 9 to il 12 la DISTANCE INLAND (km) - along mean wind direction l lj i
l I I' l Figure 3-5. Profiles of depth of internai boundary layer at Nanticoke with distance inland at different times (L.ST) on 1 June (Kerman g, et al., 1982). The thick line is the prediction of equation I (2-16). 3-6 l
' Table 3-1. Internal boundary layer characteristics at Nanticoke (1 June), [h, internal boundary layer height; x, distance inland; N . effective Brunt-Vaisalla frequency of onshore flow: H. surface Seat flux; u.
mean wind speed to height hl (Kerman et al. , 1982). h x N H u L. S. T. (m) (km) (sec~I) (va-2) g, ,,c-1) 1100 200 2. 5 0.0130 184 3. 8 375 5. 3 0.0175 400 6. 0 0.0170 420 6. 7 0.0175 500 8. 9 0.0164 1200 175 2.1 0.0152 234 4. 8 275 4.1 0.0148 I 325 5. 5 0.0144 350 6. 5 0 0139 450 9. 0 0.0145 1300 150 1. 5 0.0212 265 5. 0 250 3. 6 0.0180 350 5. 6 0.0176
; 325 8. 0 0.0177 375 8. 8 0.0170 1400 125 1. 4 0.0233 265 5.1 200 3. 5 0.0233 275 5. 3 0.0192 325 7.1 0.0188 425 10.5 0.0187 1500 125 1. 5 0.0233 224 5. 0 200 3. 4 0.0260 250 5. 5 0.0249 275 9. 0 0.0238 300 12.5 0.0223 1600 75 1. 5 0.0380 177 5. 0 150 3. 4 0.0355 230 5. 5 0.0287 280 6. 7 0.0255 300 8. 9 0.0247 1700 100 1. 5 0.0427 117 5. 0 175 3. 3 0.0335 225 5. 4 0.0285 250 6. 9 0.0270 275 12.8 0.0253 L
l : 3-7 l
I Table 3-2. Internal boundary layer characteristics at Nanticoke (6 Juna) (Kerman et al., 1982.) l h x N H u 1.. S. T. (m) (km) (sec ) (wn-2) (m sec"I) 0900 '175 1. 8 0.0174 106 5. 5 300 6. 0 0.0164 320 9. 0 0.0178 350 12.5 0.0170 li 425 18.0 0.0154 1000 300 6. 0 0.0190 172 6. 3 360 9. 0 0.0174 ! 350 12.5 0.0175 425 18.0 0.0154 650 25.0 0.0124 g ? 1100 200 1. 8 0.0209 246 6. 5 l 325 6. 0 0.0199 500 18.0 0.0160 625 25.0 0.0151 l 12.00 200 1. 8 0.0219 284 6. 0 325 6. 0 0.0188 375 12.5 0.0170 l 550 18.0 0.0147 B 1300 150 1. 8 0.0222 330 6. 0 200 6. 0 0.0221 320 9. 0 0.0178 l 1400 125 1. 8 0.0344 298 6. 5 200 6. 0 0.0246 240 9. 0 0.0198 250 9. 5 O.0201 300 13.0 0.0164 400 18.0 0.0136 g 1500 125 1. 8 0.0243 275 6. 5 l 400 6. 0 0.013') 800 13.0 0.0100 1600 800 75 18.0
- 1. 8 0.0100 0.0258 255 7. 0 l'l(
500 6. 0 0.0092 1150 18.0 0.0064 l'j 1700 100 1. 8 0.0184 160 5. 8 s 400 6. 0 0.0100 550 9. 5 0.0093 ll 650 18.0 0.0085 l l I: I 3-8
the overland sensible heat flux, the wind speed, and the change in near-surface buoyancy. These data can be used to check the TIBL formulas in Section 2. Kashihara - Gamo et al. (1982) reported a series of TIBL observations in Kashihara, Japan. They estimated the TIBL height, h, using three measures: 1) ~ 1 apse rate variations, 2) horizontal temperature variations, and 31 horizontal turbulence variations. The observations are given in Table 3-3 for inland distance increments of 2 km, to a maximum inland distance of 14 km. The TIBL height determined by turbulence is seen to be greater than that determined by temperature, as illustrated by the TIBL curves in Figure 3-6. At an inland distance of 5 km, the median heights of the two TIBL measures are about 400 m and 300 m, respectively. Gamo et al. (1982) test no formulas with their data, but Chara and Ogawa (1985) attempted to fit these data with a numerical model based on the kinetic energy and the enthalpy balances. There are TIBL observations at a few other sites, as reviewed by Stunder and Sethuraman (1985) and Hanna (1987). However, the four datasets briefly discussed above are the most extensive of the group. In most cases it is seen that aircraft are used to observe the TIBL, thus implying that useful data are not available at heights less than about 100 m. Most of the TIBL data are from inland distances ranging from 2 to 20 km. l 3-9
j!iI ll! I lI!l,l! 6 e 000 3
= e 3 33
% S a33 g 3
. s 0 6 3 4 a 4 1 1
, ) g 3 r 0 0 3 0a 0 00 a e y E
7 3 2 4 4 8 na r e h b 6 3 6 4
- 3) l 3 33 1
a c t h n d 3 i a e e . A 0 0 000 0 e0 h t v l n ) i
= 3 4
3 1 07 2 733 3 3 e3 S1 s s e o a i 7 h ( a i h b t m 8 m ) ) K d t a n r 9 k s 0 0 0 00 0 0 9 9 0 92 t d y e z o et 1 2 1 A 6 3' ( 3 1 24 7 4 8 2 a n b c i e , 00000
) ) ) n 00o000000 00 i n r d . r 4987 8 43 l 42 85 63 8 a 0
8 r w d a o l e 63336 33 a233233 43 3 e n y w n s e t h a ( ( 1 t L ) ) ) a o i i e D t 0 L d m d h I e a. 6 0 3 00000000 3 0867 623 3 0 00 33 r t b
. 2 3
( 67 336333 3 31 y m e d n y h m e o m ) 1 (
) )
r k t k s 0 0 0000000 a 00 a e i b t a o A 6 6 0 7 93 90 457 4 423423 i 3 7 d 2 d w G t ( 1 1 d 23 n u y n d f ) ) ) ) o r L o n w e o mo A r 00000 8 7 339 000000000 23 93 04 04 6 00 03 0 5 63333 333233232 44 3 B e B dI i s r ( 1 6 ( v m s f l e e r e ( g ) a e h e n . 0 5 D 3 00000000 4 4 3 3 8 3 ) 6 0 7 0 0 000 033 n t h t t k n 2 3 46333342 4 4 338 r a t e c o b ( e g d i i m 00 0 00000000 en t n h t s 0 I n e h s gf o ol s a B L I t
, r i
a a k a a r 20 63 00000
)
4 6 97 5060) 7 33243232 000000 o0 3 3 e0 9a 1 S A 833 03 29903 3 ( 4 r3 h e et v 3333 3 ( 323233 32 43 t d n e n k a h e f a ci r t h c br 0 0 00 00a00000 G000000 o n e 3 4 0 7 7 s3 4 3 4 4 ) 4 62033
, h e f ; e h 3 65 1 1 33233332 4433441 s t s o n l s h e
p
, a s i b o u k m s 00000 902 98 1
00m00O00 n1 03S80 0 9 00 a 4 3 n , yl s t r 6 34423 1 33234I 22 2 1 4 k h e a ut ) c b e n i r 00003 7 307 3 000 03 3 00 00 0 3 00 03 i h k r n 34323 323 34 2 44 h y : t c a l 1 _ t b d i v a ._ n f h t g e n al o t e n ,. 00000 3 4 4 35 000n00000000000040 320 a62 6292027 5 3642 h e r o E 44326 444t 43221 334232223 _ t v n , u z _ i e o gt i m . 00000 000n000O0000 03 f g h i h a r k 3 00 6 0 3 61 a37 0S 6 023 97 A o t t r o 4 33323 322t 228 I 1 212 2 n a r i d p a ; e h _ t _ s p e r n m e t 0o000 M w. M09 e800 _ a 7 n2 3 2 92 3 i a v a a e h 33413 32 22 2' 233 L J o v l t t tr 000000 00a0 00000000O000
. =
r 3 2 05 33 3697 65 03 1 4 7 0S 335 3 b 3345 43 31 2 1 3 1 3 231 2I I 1 2 3 m e e004e00no0o a 0e k A S322J3133a272i7s i S%3es00na0 3) e 2 2l l I 2 I l e b r s000 n00c n00 a A 0 6 8 322 o7 7 S312 t 005 223 T
,% . eb< bee 4 .b4&4.4 s AAAA3DtSSeE5333&3SCDDEEE 1 0l 2*
- 8 2 32 3 4913- - 2 7 1- l. 1 - 3 143 3 3 e
r 2 1 22622224 4 4 347777 4 7 77 711 1T 77 T 7 717 7 7 1 11 11 7 7 433377 a RCCGgRkGGGCGCGGCCCRGCCCC 4 L L t' AAg l t
- tt
- L' t L' L' Lt I AUt t t L M A A A u M w 'A A A A A A A A A A A M A A A A A - y.O .
l i l l l I
- Zta) ,~. .
I _ 1 I 550 -
- s
. k .,'~ -
l ~ l
- ~~
- 9 . % ;; '
l land Itkoi h'yj y i
,i5 i. cast 5
I 1 l Figure 3-6. Relationship between h determined by turbulence (solid line), turb hg determined by temperature (dashed line) to distance from the coast at Kashihara, Japan (from Gamo et al., 1982). The thick line l 1s the prediction of equation (2-16). l 3-11 i
- 4. Comparisons of Formulas with Observations The formulas in Section 2 are of the following types: ha x ,ha x.
E and h a x , with p in the range from 0.5 to 1.0. Differences in predictions are mainly due to differences in assumed proportionality constants and in preparation of input data. Stunder and Sethuraman (1985) have published the most extensive comparisons of TIBL formulas with observations. Figures 4-1 and 4-2 illustrate a comparison of seven formulas with observations during two Brookhaven National Laboratory (BNL) field tests. Ve have added a line for the OCD model prediction (Eq. 2-15). The predictions of the various models at any distance are seen to have a range of 50%, and none of the model predictions is consistently close to the observations. Based on a statistical analysis of the performance of the models, Stunder and Sethuraman (1985) found that the Weisman (1976) equation (2-8) produced the best agreement with observations. Hsu (1988) used data from three sources to derive the h = (1.91 t 0.38)x1 /2 relation that he proposed. Figure 4-3 contains these TIBL height data. If the Nanticoke data (in Figure 3-5) were added to this figure, they would fall about a factor of two above the line. The uncertainty in TIBL predictions is further illustrated in Figure 4-4, ' where Bergstrom et al. (1988) plot the predictions of their model (Equation 2-9) with observations. It can be concluded from this figure that an uncertainty of 2 30% exists in their predictions. l Hanna et al. (1985) found that the uncertainties in the theoretical equations, combined with difficulties in defining and specifying input parameters (i.e., de/dzorO g -B y), resulted in these formulas being unsuitable for routine applications. Instead, they suggested the simple ) empirical equation (2-16). Later, Hanna (1987) compared this equation with I several different data sets, with the results shown in Figure 4-5. The formula is seen to pass through the middle of the data, which are taken from field experiments in Long Island (Raynor et al. ,1979), Nanticoke (Kerman et al. , 1982), and Australia (Rayner, 1987). The only outlier is the BNL S14 i i 4-1 1
PL 1000-
,.A
. . .. . u '
..-' og y (Eq. 2-7)
_ g ',
t#w,b (Eq. 2-8) 0/
q 600 - g'- p P
'N .X*/
.X,
..' OCD (Eq. 2-16) 4 . ../
O' R h j,Y .c (Eq. 2-6) m 400 - 8 'X, /m ' 'g.
- 6./' 'a. W l ,
,g.
,.-e (Eq. 2-5)
/*f./ - ,
-e~~ l i
200 -
)
O' 8 l t 0 2 4 6 Downwind Distance (km)
*--+ Observed (08) x. x Peters (P) o- a P1cte (PL) c - a Reynor (R) l l e-e Von Der Hoven (VH) +--+ Venkatrem (V)
! o--o Weismen (W) l l Figure 4-1. Predicted and observed TIBL values for the onshore neutral BNL BL
#6 case (Stunder and Sethuraman. 1985).
4-4
i-IC00 - 800 - f e V (Eq. 2-7)
... F ,-
y
~
600 - f',p '9 l 3_ .. y..s -
.e .
lE _,i
+' / . OCD (Eq. 2-16) 9 H
E0 -
/e'., Q ".c R (Eq. 2-6)
V 0B
.** _, o A e7#
y e VH
.*~~ (Eq. 2-5)
/ -
. p a...a ] 7.-g PL P 200 - 4 ,,
0 W (Eq. 2-8)
,O' 'E", -E"'- 6, ,.f**" o . o
.Fy.<:
,esyo oo .g l l
.X * ~~ ~ x., .n -
0 , , , , , , , , , , , , O 2 4 6 3 10 12 Downwind Distance (km) 6---e Observed (CB) x- x Peters (P) a a Plate (PL) c - c Raynor (R) e---e von Der Hoven (VH) +--+ Venkatrom (V) o--o Weisman (W) Figure 4-2. Predicted and observed TIBL values for the onshore stable BNL BL
#13 case (June 13, 1978, 1530 EST) (Stunder and Sethuraman, 1985).
4-3
h I 1 l DATA SOURCES:
- Oru#het et eL 1982 40a =
- Smedmen and Hogstrom,1983 200 . a Ogawa and Chere,1985 , '.-
100 -
/*,,.
l , so -
/ ,,,*' ,, f'/
e
~
e / ;>' s 2 ao -
/*,s, ' ,,*'.
E g 20 - r h g to - e - e h a (1.91 2 0.38) Xb 4 - l 95% confidence limits l l 2 - l j to 20 40 so too 200 400 s001000 200o 4000 sooo FETCH,X,in meters
'1 l
l l l l I Figure 4-3. Variation of TIBL height h with distance x (Hsu, 1988). 4-4
M' o D x o v cn XX
- x x g
K ' M n
$O3 x ,, x x*
- l W# a XX X N
- d. {
M y X ! i l o y . E n ll l ) 0 30 60 90 12 0 kBL l l l l l ll 1
~
- l. l l
l nn - Figure 4-4. Modeled IBL heights versus observed ones (Bergstrom et al. 1988). i 4-5 i l I
)
~
800 - 7 i
# 1 I
1 l 1 1 4 I l i j 600 - s i .. g i 5 - r l s l l-I i 400 - t
- 1 l
l/ L I, .-
./l e-
! + . , e ch * b.
+ ..
4
,s / / l ,
A 200 - r i,,,.-
/ /
- - - BNL BL 6 e Aust. 3 Feb.
'8
--- - - - BN L BL 13 -{- Aust. 22 Feb.
I e' - [ ,,
, BNL S 14 l
. .). Nanticoke 1 June i Nanticoke 5 June
.. .L 0 12 14 16 6 8 10 0 2 4 x(km) l l
Figure 4-5. Empirical formula (2-16) for TIBL height (thick solid line) plotted together with observations from a number of field studies. BNL data are from Raynor et al. (1979), Nanticoke data are from Kerman et al.-(1982), and Australian data are from Rayner (1987). (Hanna, 1987.) 4-6 I I
experiment, where the large TIBL heigh
- is probably due to strong overland convection on that day. Equation (2-16) is also plotted on Figure 3-1 (Lake Michigan data) Figure 3-5 (Nanticoke data), and Figure 3-6 (Kashihara l data). In all of these figures, the formula passes near the middle of the 1
data. I 4-7
l 5. Recommendations The theoretical TIBL height equations derived in Section 2 would be preferable to empirical equations if the conditions assumed for their derivation were valid. However, at real-world sites, thevaluesofde/dzand rg -r g are ill-defined and the heat flux. Q,, and wind speed, u, are not constant with inland distance. Iftheobservedde/dzapproache.zero, the TIBL height approaches infinity. Furthermore, the behavior of the TIBL near the shoreline is uncertain because of the fact that near-shore water temperatures are generally warmer than off-shore, and because field data are inadequate in that region due to the reluctance of aircraft to fly lower than 100 m. For these reasons, we recommend that one of the robust empirical equations be used to estimate TIBL height. By robust, we mean that the formula is not apt to produce excessively large or small TIBL heights due to variations in input data. We prefer the OCD empirical equation (2-16), but would also support the Hisra and Onlock (1982) or Hsu (1988) equation, with "A" as defined in the table in Section 2: OCD: h = 0.1x x s 2000 m h = 200m + 0.03(x-2000) x > 2000 m Hsu: h = Ax (h and x in meters) where A = 4.9. 2.7, 1.7, and 1.2 for overland Pasquill classes A, B, C, and D, respectively. TIBL heights predicted by these formulas for several distances are given in Table 5-1. No TIBL data have been collected in regions with complex coastal terrain. The OCD model makes the assumption that the TIBL is ter.:3n following in these situations. If a field experiment is conducted along a steep shoreline, the data should be used to modify this assumption. 5-1
Table 5-1. Estimated haight of the Thsrmal Internal Boundary Layer for two recommended equations. Distance TIBL Height (Mile) (km) (m) OCD 0.1 0.16 16
- 0. 5 0.80 80
- 1. 0 1.61 161
- 1. 5 2.41 212
- 2. 0 3.22 237
- 3. 0 4.83 283
- 4. 0 6.44 333
- 5. 0 8.05 382 TIBL Height (m)
Distance Stability (Mile) (km) A B C D Hsu 0.1 0.16 62 34 22 15
- 0. 5 0.80 139 77 48 34
- 1. 0 1,61 197 108 68 48
- 1. 5 2.41 241 133 84 59
- 2. 0 3.22 278 153 96 68
- 2. 5 4.02 311 171 108 76
- 3. 0 4.83 340 188 118 83 ;
- 3. 5 5.63 368 203 128 90
- 4. 0 6.44 393 217 136 96
]
- 4. 5 7.24 417 230 145 102
- 5. 0 8.05 440 242 152 108 l
1 5-2 u__-__________-
_ - ~ _ _
- 6. References I Bergstrom, H., P.E. Johansson and A.S. Smedman, 1988: A study of wind speed modification and internal boundary-layer heights in a coastal region.
Bound. Lay. Heteorol., 12, 313-335.
Deardorff,
J.W. and G.E. Villis, 1982: Ground-level concentr*ons due to i fumigation in to an entraining mixed le.yer. Atmos. Env..an., 16, 1159-1170. Elliot, W.P., 1958; The growth of the atmospheric internal boundary layer. Trans. Am. Geophys. Union, 39, 1048-1054. Gamo, M., S. Yamamoto and O. Yokoyama, 1982: Airborne measurements of the free convective internal boundary layer during the sea breeze. J. of Meteorol. Soc. of Japan, 60, 1284-1298. Garratt, J.R., 1990: The internal boundary layer--A review. Bound. Lay. Meteorol,, 50, 171-203. Golder D., 1972: Relations among stability parameters in the surface layer. Bound, Lay. Meteorol., 3, 47-58. Hanna, S.R., 1987: An empirical formula for the height of tne coastal internal boundary layer. Bound. Lay. Meteorol., 40, 205-207. Hanna, S.R., L.L. Schulman, R.J. Paine, J.E. Pleim and M. Baer, 1985: Development and evaluation of the Offshore and Coastal Diffusion Model. J. Air Poll. Control Assoc., 35, 1039-1047. Hsu, 1986: A note on estimating the height of the convective .aternal boundary layer near the shore. Bound. Lay. Meteorol., 35, 311-316. Hsu, S.A., 1988: Coastal Meteorology. Academic Press, San Diego, 260 pp. (discussions of internal boundary layer can be found on pages 3, 123-128, 194-199, and 234). Hunt, J.C.R. and J.E. Simpson, 1982: Atmospheric boundary layers over non-homogeneous terrain, In Engineering Meteorology, E.J. Plate (ed.), Ch. 7, 269-318.
.l Kerman, B.R., R.E. Michle, R.V. Portelli, N.B. Trivett and P.K. Hisra, 1982: ! The Nanticoke shoreline diffusion experiment, June 1978, II. Internal boundary layer structure. Atmos. Environ., 16, 423-437.
Lyons, W.A., 1975: Turbulent diffusion and pollutant transport in shoreline l environments. Lectures on Air Pollution and Environmental Impact Analyses, AMS, 136-208. McElroy, J.L. and T.B. Smith, 1990r Lidar descriptions of mixing layer thickness characteristics in a complex terrain / coastal environment. To appear in J. Applied Meteoral. l 6-1
i Misra, P. K. and S. Onlock, 1982: Modeling continuous fumigation of Nanticoke l Generating Station plume. Atmos. Environ., 16, 479-489. Chara, T. and Y. Ogawa, 1985: The turbulent structure of the internal boundary layer near the shore. Bound. Lay. Meteorol., 32, 39-56. Portelli, R.V., 1982: The Nanticoke shoreline dispersion experiment, June Experimental design and program overview. Atmos. Environ., 1978 - I. 16, 413-421. Rayner, K.N., 1987: Dispersion of atmospheric pollutants from point sources in a coastal environment. Ph.D. Thesis, Hurdoch University,, Hurdoch, Vestern Australia 6150. Raynor, G.S. , S. Sethuraman and R.M. Brown, 1979: Formation and characteristics of coastal internal boundary layers during onshore flous. Bound. Lay. Meteoro1., 16, 487-514. Smedman, A.S. and U. Hogstrom, 1983: Turbulent characteristics of a shallow convective internal boundar. layer. Bound. Lay. Meteorol., 25, 271-287. Stunder, M. and S. Sethuraman, 1985: A comparative evaluation of the coastal internal boundary-layer height equations. Bound. Lay. Meteorol., 32, 177-204. Van der Hoven, I., 1967: Atmospheric transport and diffusion at coastal sites. Nuc. Safety, 8, 490-499. Van Wijk A.J., A.C. Beljaars, A.A. Holtslag and W.C. Turkenburg, 1990: Diabatic wind speed profiles in coastal regions: Comparison of an internal boundary layer (IBL) model with observations. Bound. Lay. Meteorol., 51, 49-75. Venkatram, A. , 1977: A model for internal boundary layer development. Bound. Lay. Meteoro1., 11, 419-437. Venkatram, A., 1986: An examination of methods to estimate the height of the coastal internal boundary layer. Bound. Lay. Meteoro1., 36, 149-156. Weisman, B., 1976: On the criteria for the occurrence of fumigation inland from a large lake--a reply. Atmos. Environ., 12, 172-173. 6-2 j}}