the inland boundary layer at low latitudes: ii sea-breeze influences

THE INLAND BOUNDARY LAYER AT LOW LATITUDES:

II SEA-BREEZE INFLUENCES

J. R. GARRATT and W. L. PHYSICK

CSIRO Division of Atmospheric Research, Private Bag No. 1. Mordialloc. Victoria, 3195, Australia

(Received 16 October, 1984)

Abstract. Two-dimensional mesoscale model results support the claim of evening sea-breeze activity at Daly Waters, 280 km inland from the coast in northern Australia, the site of the Koorin boundary-layer experiment, The sea breeze occurs in conditions of strong onshore and alongshore geostrophic winds, not normally associated with such activity. It manifests itself at Daly Waters and in the model as a cooling in a layer 500-1000 m deep, as an associated surface pressure jump, as strong backing of the wind and, when an offshore low-level wind is oresent. as a collapse in the inland nocturnal jet.

Both observational analysis and model results illustrate the rotational aspects of the deeply penetrating sea breeze; in our analysis this is represented in terms of a surge vector - the vector difference between the post- and pre-frontal low-level winds.

There is further evidence to support earlier work that the sea breeze during the afternoon and well into the night - at least for these low-latitude experiments - behaves in many ways as an atmospheric gravity current, and that inland penetrations up to 500 km occur.

1. Introduction

Most studies on sea breezes have concentrated on mid-latitude regions (generally above 40” N) where penetrations inland, even under favourable synoptic conditions, are limited to less than 100 km or so (e.g., Simpson et al., 1977; Atkinson, 1981, Chapter 5). At latitudes equatorwards of about 35 deg, much greater penetrations have been reported; for example, 200 km or more according to early Australian work referred to in Simpson et al. (1977), 250 km inland of the Pakistan coastline as described by Holmes (1972). More recently, Clarke (1983) described sea-breeze behaviour in tropical regions of Australia where observations, supported by two-dimensional (2D) numerical model results gave penetrations to 500 km. In such cases, the breeze travelled throughout the night before dissipation occurred shortly after sunrise on the second day.

For a given synoptic wind, inland penetration probably depends on two main factors. The first of these involves solar heating which, under clear skies, will depend on latitude and season; this will manifest itself through boundary-layer heating, itself dependent upon the surface turbulent heat flux and hence the surface Bowen ratio (e.g., Physick, 1980). The second factor involves latitude directly, with increasing penetration as latitude decreases. This seems to be related to the rotational aspects of the sea breeze and the influence of the Coriolis acceleration (Pearson, 1973; Neumann, 1977). To date, most sea-breeze studies have dealt with mid latitudes and low ambient wind situations (Atkinson, 1981); thus the present study of sea-breeze activity at 16’ S with geostrophic winds up to 13 m s- ’ should be of particular interest.

In part I of our study (Garratt, 1985) observations from the Koorin boundary-layer

Boundary Layer Meteorology 33 (1985) 209-231. 0006-8314/85.15. 0 1985 by D. Reidel Publishing Company.

210 J. R. G.~RRA~T AND w. L. PHYSICK

I I I 132"E 135"E 138OE

LONGITUUE

Fig. 1. Location of Daly Waters, the coastline, model coastline AB, rectangular axes (x, y) and geostrophic wind G, at an angle fi (positive as shown) to coastline normal.

experiment in northern Australia (Clarke and Brook, 1979) were analysed in a study of nocturnal jet development. The site lay some 280 km inland from the nearest coastline to the northeast in a predominantly northeasterly geostrophic flow (Figure 1). The analysis was supported by numerical model calculations, with special emphasis on the role of longwave radiative cooling on turbulent decay and its influence on jet evolution. However the observed jet, and features of the ageostrophic wind field below 500 m height, did not evolve according to one-dimensional (1D) predictions. The associated collapse of the nocturnal boundary layer (NBL), disruption of the low-level jet and cessation of near-surface turbulent activity have been discussed by Garratt (1982 and 1985). The observed behaviour was strongly suggestive of sea-breeze activity at the site on most evenings of the experiment. Here we investigate the sea-breeze influence on inland jet evolution, and the features of deeply penetrating sea breezes at low latitudes in general. We utilize both observations and 2D numerical model results.

2. Observations

2.1. INTRODUCTION

Figure 1 shows the location of the main site at Daly Waters, the coastline in the region and the dominant geostrophic wind direction. Some aspects of the Koorin experiment (Clarke and Brook, 1979) and details of the data base have been described in Garratt (1985). Relevant analyses ofnighttime observations can be found in Garratt (1982,1983,

THE INLAND BOUNDARY LAYER AT LOW LATITUDES 211

TABLE I

Details of data subsets, days within each subset being chosen according to the mean Go direction between 1500 and 2400 hr Central Standard Time. Number of days in each subset is denoted by W, whilst uX and

vp are defined relative to X, y axes in Figure 1.

Subset n GO B atgaz abgiaz __ (s - ‘) -

Direction Magnitude (m s-‘)

Range Mean

A 4 342-016" 008" 6.8 -22" 0.0019 0.0019 3 5 030-046" 040" 8.2 10" 0.0024 0.0024 c 6 050-064" 059" 8.2 29" 0.0021 0 D 8 065-081" 075" 12.9 45" 0.0024 - 0.0010

1985) and as in Garratt (1985) we have grouped the observations according to surface geostrophic wind direction (Table I) to provide four subsets A to D.

Because of the complexity of the coastline, a 3D mesoscale model would be necessary to describe re~ist~c~y all aspects of the sea breeze. However, we start with the assumption that the presumed sea-breeze activity at Daly Waters is most likely the result of the major sea breeze originating from the coastline along AB, and not from sea breezes related to the more distant coastline to the north and northwest, The influence of the coastline ‘bend’ at A upon the sea-breeze structure and penetration inland towards Daly Waters is unknown; we discuss in the summary the validity of the above assumption, based on comp~sons of model results with observations.

Sea-breeze effects at any point inland from AB, including Daly Waters, will depend, inter aliu, upon distance of the location from the coastline and upon the magnitude and direction of the geostrophic wind. Thus for present purposes we support the observations with 2D model simulations, and investigate sea-breeze penetration in conditions of moderate geostrophic winds and the dependence of sea-breeze structure upon geostrophic wind direction relative to the coastline. We then define, for future purposes, rectangular Cartesian coordinate axes (x, y) as shown with Go, the surface geostrophic wind, making an angle /? to the coastline normal; p > 0 implies clockwise rotation from the inland normal. Individual runs have /3 varying between - 40’ to 60’ approximately, with a strong correlation between geostrophic wind magnitude and wind direction (hence a).

2.2. SEA-BREEZE ARRIVAL

On most evenings, the passage of the sea breeze was marked by the sudden backing of the wind, usually with a decrease in wind speed and no discernible temperature change near the surface. The arrival time varied during the course of the experiment between sunset and 0100 hr approximately and depended significantly upon geostrophic wind direction (Figure 2). The observed cross-isobar flow angles a (q, referring to the surface value) and wind differences 1 V j - j G 1, averaged between 50 and 250 m heights,

212

0200

2400

Y F 2200 2

5

2000

I 18001 I 1 I I 1 I I / I I

-30 -10 10 30 50 70 G, DIRECTION

L-l I I I -40 -20 0 20 40 60

0

Fig. 2. Time of arrival of the sea breeze, defined by significant backing of 100 m wind, as a function of geostrophic wind direction. Data for each night are shown as open circles, with the pecked curve drawn

by eye to represent the trend in the data.

are shown in Figure 3 for each data subset and for three hours each side of sea-breeze passage. In the four subsets A to D, time t = 0 corresponds to local times of 1930,2200, 2300, and 2400 hr, respectively. The sequence illustrates the sudden decrease in 1 X/ at passage, with values reaching a maximum of 60’ for subset C, where post-change winds blow more or less parallel to the low-level geostrophic wind. In contrast, sudden changes in wind magnitude are small at passage for subsets A and B (/I E 0), but are r 2 to 3 m s- ’ (a decrease in 1 VI) for subset D (see also Figure 5). In the absence of any sea-breeze influence, 1 V 1 - 1G i would tend towards positive values in all cases, consistent with the formation of a low-level jet at heights of about 250 m (Garratt, 1985).

On many days, changes in a coincide with observed pressure jumps produced by the advection of cooler air over the site. Sample pressure traces for five individual evenings are reproduced in Figure 4, where the sequence from top to bottom corresponds to fl varying between about - 10” and 55’ ; maximum pressure jump amplitudes occur for subset D (largest p) and are on the order of 0.5 to 1 mbar.

2.3. LOW-LEVEL CHANGES

Vertical profiles of mean wind speed and cross-isobar flow angle (negative for balanced boundary-layer flow in the Southern Hemisphere) for the four data subsets are shown in Figure 5, before and after sea-breeze passage with profiles separated in time by 1 or 2 hr. For wind speed, small increases throughout the first kilometre for subsets A and B compare with significant decreases below about 600 m on passage for subset D - referred to as the ‘jet collapse’. Changes in z are substantial and are generally confined


-6Or

o- -3 -2 -1 0 1 2 3

(a) t Ihl

01 ' I / I I I 1 -3 -2 -1 0 1 2 3

bf t lhl

Fig. 3(a). Mean G(, for layer 50 to 250 m, for 4 subsets A to I) as a function of time, in hours, relative to sea-breeze passage at t = 0. (b) As in (a), except IV1 - ;G 1.

to a layer adjacent to the surface some 500 to 1000 m deep. These observations are consistent with observed temperature profiles and we show in Figure 6 a sequence of individual potential temperature (8) profiles observed each side of the pressure jumps referred to in Figure 4. Pecked curves represent estimates of expected profiles in the presence of radiative cooling only (e.g., Garratt and Brost, 1981), so that hatched areas represent cooling by cool air advection due to the sea breeze. This cooling, averaging 1.5 to 4 K throughout the layer, is consistent hydrostatic~ly with the pressure-j~p amplitudes but does not penetrate right to the surface because of the strong surface inversion evolving at the time of sea-breeze passage (see model results in Section 4).

3. Details of Mesoscale Mode1

We have used the dry, hydrostatic, 2D version of the mesoscale model described recently by McNider and Pielke (1981). The version used here has 16 levels in the vertical, with top at 6000 m, staggered to give 10 levels below 1200 m, and 44 horizontal grid points, nominally at 10 km spacing except that staggering is introduced close to each

214 1. R. GARRATT AND W. L. PHYSICK

polmbl 1

990~~ t 0 11 989,

993

992

I J+---r- 01

9911

991 r

I

992

991

992 1

991 ~~,

027

20 21 22 23 24 01 LOCAL TIME

Fig. 4. Surface pressure (mbar) vs time on 5 individual evenings; vertical arrow indicates time of sea-breeze passage.

lateral boundary. The coastline is set at grid point 36 (the sea lies between this and the righthand lateral boundary at grid point 44), with grid point 8 corresponding to the position of Daly Waters inland from AB in Figure 1. We take z,, = 0.5 m* over sloping terrain of slope 0.0008, close to that observed; include barochnity as observed with &J,J& varying between 0.001 and 0.003 s- ‘, and c?L~~/?z between - 0.0025 and 0.0025 s -- ‘, and take sea temperature as 301 K. We note that, because of the complex topography in the region of Daly Waters, the local fall-line vector (FLV) points towards 315” (see Figure 1 in Garratt, 1985) and is therefore approximately parallel to the coastline, whilst the upwind FLV is directed towards the coastline. In the 2D model the latter situation only can be simulated, but the sea-breeze properties probably depend little on the 3D nature of the inland topography. The model is initialised with a smoothed, near adiabatic temperature profile observed near sunset, with subsidence inversion at 2 km and surface temperature r, set at 301 K. The initial wind profile is

* Aerial photographs of vegetation distribntion suggest that this value, to within a factor of two, is applicable for at least 50-100 km upwind (i.e., towards the coast). In any case, sea-breeze penetration, for example, is not very sensitive to z0 variations of an order of magnitude or so (e.g., Clarke, 1984).

THE INLAND BOUNDARY LAYER AT LOW LATITUDES

800

600

z (ml

400

200

O- 0 -20 -40 -60 0 -20 -40 -60

(a)

IOOO-

800-

600-

Zlmi

400 -

b

zoo-

/ I /

1 t

/

a O-200

0wI-l 0 4 J3 120 4 8 120 4 8 120 4 8 12 16

a b

Fig. 5(a). r profiles for 4 subsets A to D $5 to 1 hour before - b - and l/z to 1 hr after - a - the sea-breeze passage. (b) As in (a) for /VI.

216 J. R. GARRAl-i AND W. L. PHYSICK

12OOr

EOO-

Z(m) 600

&Oil b

295 297 299 301

1200

1000 j 07

800 Zlml

293 295 291 299 301

0 (K)

295 297 299 301 297 299 301 303 f+(K)

Fig. 6. 0 profiles before (b) and after (a) sea-breeze passage on 5 individual occasions corresponding to examples in Figure 4. Pecked profiles indicate expected profile in the absence of the sea breeze, and based

on radiative cooling only.

obtained by integrating the momentum equation through several inertia1 periods until steady state, balanced conditions are achieved. Time t = 0 is taken as 1739 hr local time on day 1, and the model integrated in time for 36 hr, so that a sea breeze evolves on day 2 and penetrates inland right through the second night.

Five main simulations were completed for analysis, these being a compromise between direct comparison with observations and a general investigation of low latitude sea breezes in conditions of moderate to strong onshore and along-shore geostrophic flow over rough, sloping terrain. Simulations S3, Sl, S2, and S4 had G, = 12.5 m s- ’ with /I varying as - 45 ‘, 0’) 45 ‘, and 90’ respectively, whilst simulation S5 had G, set at 6.25 m s I” ’ for /I = 0.

From the observational analysis, it was found that B close to 45 ’ represents a critical region in terms of sea-breeze ‘intensity’ since then, in the Southern Hemisphere, low-level offshore flow results if I c1 j > 45 * giving relatively strong low-level convergence and a sharp sea-breeze front. In the observations, values of 1 XI are generally high because of the very rough surface with z,, = 0.5 m. For example, x at 1800 hr, and


averaged from the surface to 1 km height, has a value r - 50’ (all data) and - 45 ’ (subset D, p = 45”). In comparison, model values are significantly smaller being typically in the range - 20” to - 30” on both nights 1 and 2. Overall model values of / a 1 are 20” smaller at 1800 hr, thus requiring a value of B = 65 ’ to achieve along-shore low-level flow as observed in subset D, The smaller values of / cx found in the model, compared to those observed, are due, in small part, to the surface-layer relations used to calculate U, , the surface friction velocity (e.g., increasing the Von Karman constant from 0.35 to 0.41 would increase / ai by about 4” in neutral conditions). In addition, inability to match model thermal winds to those observed could contribute to the difference, since ~1 seems to be quite sensitive to thermal wind (e.g., Arya and Wyngaard, 1975).

4. Model Results at the Daly Waters Grid Point

Reference to Table II suggests that simulations S 1 and S5 (or at least the implied results intermediate between these two) should represent approximately subsets A- and B-type conditions, and simulation S2 and S4 the conditions appropriate to subset D, taking into consideration values of p, G,, and ’ r! at 1800 hr local time.

TABLE II

Relevant quantities appropriate to all simulations and data subsets - for 1800 hr local time

Simulation Go B la/ I4 + B Data Go B /a/ Id+8 ms-’ subset ms-’

3 12.5 -45” 32” - 13” 1 12.5 0” 28” 28” A 6.8 -22” 49” 21” 5 6.25 0” 30” 30” B 8.2 10” 53” 63” 2 12.5 45” 22” 61” c 8.2 30” 51” 81” 4 12.5 90” 30” 120” I) 12.9 45” 43” 88”

In Figure 7, calculated time changes in low-level cc (up to 175 m in height) and surface pressure p,, at grid point 8 are shown for several relevant simulations. There are several noteworthy features which should be emphasised.

(i) The sea-breeze passage, as indicated by the rapid change in 01 and the pressure jump, tends to be concentrated between 1900 and 2300 fir, and therefore compares favourably with observed passage times (Figure 2).

(ii) The magnitude of the change at passage 1 Aa 1 below 500 m or so is r 15 ’ -35 ’ for S 1 and S5, and r 35”-75 ’ for S2 and S4, which compares favourably with 20” and 40” for subsets A and D (Figure 3a) respectively.

(iii) Significant pressure jumps occur on passage of the breeze, with amplitudes 2 0.5 to 1 mbar for S2 and S4 comparable with observations (Figure 4).

In Figure 8, temperature profiles before and after sea-breeze passage for several simulations are shown. These illustrate advective cooling in a layer varying in depth

218 J. R. GARRAlIT AND W. L. PHYSICK

PO 909

Imbarl 983

986 t

15 17 19 21 23 01 03 05 07 09

LOCAL TIME

Fig. 7. 2D model calculations of Z (mean from 19 m to I13 m) and pO as function of time at grid point 8 for several simulations. For S4. values are extrapolated to grid point 8 from grid point 18, using value of

c = 4.6 m s^ ’ (see legend of Table VI).

1200 r 55 1oooj

I

800 Zlmi cl

600

400 F / 1

Fig; 8

296 298 300 302 304 301 303 305 300 302 304 298 300 302 304 306

9 IK!

2D model B profiles 1 hr before (b) and after (a) sea-breeze passage at grid point 8 (grid point 18 for S4).


1200r

IOOO-

800- Zlm)

600-

400 -

zoo-

b a

&?ilLl! 0 4 8 12 4 8 12 16 4 8 12 16 0 4 8 12

1000 -

800- Zlmi

605 -

U30-

200 -

O....

Fig. 9. 2D model (VI and cx profiles as in Figure 8.

between 600 and 1200 m, of m~itude several degrees K ~ornp~ab~e with the observed cooling (Figure 6). Note that a distinctive low-level capping inversion does not occur until b = 90”, ‘when offshore flow in the model has been achieved, though there is no such systematic behaviour in the observations.

Wind speed and z profiles are shown in Figure 9. These show strong similarities with observed profiles (Figure 5), the most si~~c~t result being the jet coliapse for p = 90” (S4). This corresponds with strong offshore flow prior to the sea-breeze arrival and probably also occurs at smaller values of p in the range 45 ’ < /3< 90”. For data subset D, with p = 45 ‘, 1 CI 1 at 1800 hr is E 45 ‘, increasing to z 60’ by 2300 hr and therefore comprising a signikant offshore component in the presence of strong low-level winds near 250 m.

This decrease in near-surface winds in simulation 54 on passage of the sea breeze leads to a related decrease in u * , somewhat analogous to subset D observations (e.g., Garratt, 1982), although absolute magnitudes of u* and the magnitude of the change are different to those observed. The horizontal variation of u * through the sea breeze at 0000 hr for

220

5 9 13 17 21 25 29 33 37 ClRlO POINT

ibl

18 20 22 24 02 04 LOCAL TIME

LOCAL TIME

Fig. I O(a). ?D model calculations of u * variations across the array at 0000 hr for S4. (b) Time variation of u.+ at grid point 18 for S4. (c) Observed time variation - mean values for days 7 and 27; span of the two

values at any given time is indicated by the vertical bar.

S4, time variations of U, at grid point 20 (160 km inland, when sea-breeze passage occurs at 2300 hr) and observed values for Days 7 and 27 (average) from subset D are shown in Figure 10. Differences relate, in part, to the fact that large gradient Richardson numbers observed near the surface are never approached in model simulations (partly because of inadequate cooling and partly because su~cient~y low wind speeds, and hence wind shears, are not achieved).

5. Surge Vector and Rotation

We represent the prefrontal, undisturbed (though diurnally varying) wind field by the wind vector V, which will be taken as a suitable layer average, e.g., the bounda~-layer depth h. The postfrontal wind field will be modified by the mesoscale pressure gradient across the front, Zp,/Sx (with the gradient t3pm/Zy taken as zero), p, being the mesoscale pressure perturbation.


FRONT la) COASTLINE

2400 2100 1800 1500 1200

i i i

I I I I I I I

300 200 100 xlkm)

(b)

Fig. 11(a). Schematic of wind vectors relevant to sea-breeze propagation, showing position of the sea-breeze front, with the x and y axes per~n~cu~~ and parallel to the coastline respectively. (b) Model (continuous arrow) and observed (pecked arrow) mean surge vectors; M = model, 0 = observed, with times

of passage indicated.

The post-frontal wind field is designated by a wind vector V,, suitably averaged vertically, and we define a surge* wind vector v,~ as

v, = v, - v, (11 whose dynamical and rotational properties are of particular interest here. The schematic representation in Figure 11 shows that an angle y describes rotation of v, on the coastline normal.

From Figure 11 we note that

/v,/ cosy = - (u, - Ub)

which, for y small, suggests

Iv,/ EU,-U~E -AU.

(24

(2b)

* The sea breeze acts as a surge of cooler air though not necessarily with a sudden increase in near-surface winds on passage at any one location (e.g., Clarke, 1983). If a headwind (offshore component) exists, prefrontal winds may actually decrease.

222 I. R. GARRATT AND W. L. PHYSICK

TABLE III

Observed characteristics of the surge vector Y$ (V,, V, are taken 1 hr ahead of, and I hr behind, the change, averaged between surface and 500 m). The equivalent value of x is

280 km

Subset Time of sea breeze passage

B V.7 ‘1

Magnitude direction ms-’

A 2000 -22" 3.7 008" -22 B 2200 + lo0 6.4 018” - 12 c 2300 30" 6.0 000" -30 D 2400 45" 6.9 346" -44

TABLE IV

Surge vector characteristics for 2D simulations. Local time is shown as 15, 18, 21 and 24 hr respectively,

Sim Iv,/ (nl s- ‘) Au(ms-i) P -. 15 18 21 24 15 18 21 24 15 I8 21 24

3 2.2 3.2 2.3 - -2.0 - 3.2 -2.0 - -23 -20 -29 - I 1.5 3.2 - - - 1.4 -3.4 - - -7 -11 - - 5 4.1 4.9 - - -4.2 -4.8 - - -3 -10 - - 2 2.4 3.8 5.0 - - 2.0 - 3.9 -4.1 - 28 -2 -32 - 4 7.0 10.6 11.0 11.8 - 6.6 -- 10.6 - 10.4 - 10.0 18 4 -19 -33

In Table III we show observed properties of the surge vector at Daly Waters for the four data subsets. By comparing subsets A and B with simulations S 1 and S5 (or at least the implied results ~te~ediate between these two), and subset D with simulations S2 and S4 (refer to Table II), we see that the obse~ations summarised in Table III are broadly consistent with 2D model results given in Table IV in the form of / v, /, ~7 and Au, for all simulations and at various times separated by three-hourly intervals. Note that /v, j z -Au mainly because 1 y/ 5 30”. Rotation of the v, vector as the sea breeze travels inland is shown in Figure 11, together with the observed mean vector at Daly Waters; again there is good consistency in the overall behaviour.

Influences on the rotation of the sea-breeze winds have been discussed by Neumann (1977). However he considered the local wind V, (in our notation) as indicating the ‘direction of the sea-land breeze’, and he derived a simplified relation for the rate of turning of this wind, viz. &, where tan a, = t;,/u,. He did not make allowance therefore for diurnal funds-layer effects acting on this wind. By using v,, such effects shoufd be minimised since both V, and V, will be affected similarly.


We derive j, (y is positive if rotated anticlockwise from the inland coastline normal) as follows (refer to Figure 11). We have

Au E u, - I.+, and Au = v,-v,, with tarry= -Av/Au. (3)

Equation (3) is differentiated with respect to time, and after suitable algebraic manipulation (see Appendix), ay/at is given by the sum of the three terms,

$=f+ 0.5 sin2y. aP, + F pAu ax '

where F is the frictional term given by

F= ~lvs/-~Va/ - lV,l)(V, x V,). (5)

In Neumann’s (1977) analysis, 4 was given by the sum off, a term associated with ap,Jdx (not the same as in Equation (4)) and a term involving un and vn. In our case, $ involves f, an analogous mesoscale term and a frictional term; the large-scale pressure gradient is eliminated since this influences V, and V, in a similar way. We have estimated terms in Equation (4) from the model simulations, with the exception of the mesoscale pressure term since ap,Jax is difficult to assess on individual occasions. Rather it is inferred as a residual, to indicate its relative contribution to *j. Results are shown in Table V.

TABLE V

Model values of sea-breeze rotation using surge vector characteristics. Terms Tl, T2, and T3 refer to the three terms on the right-hand side of Equation (4). Tl = f; T2 = (0.5 sinZy/pAu) ilp,/ax;

T3 = F(friction).

Simulation Period Duration Sy ON (model)

ay/dr Tl T3

x IO5 (s ‘)

T2 (Residual)

1 12-1800 6 - 13” - 1.1 -4 - 1.6 4.5 2 12-2100 9 -91” -4.9 -4 - 1.6 0.7 3 12-2100 9 -9” -0.5 -4 - 0.7 4.2 4 15-0300 12 - 57” -2.3 -4 -0.1 1.8

Generally, model changes in y (67) over periods of 6 to 12 hr are significant. According to Table V all terms on the right-hand side of Equation (4) are comparable, as found by Neumann for comparable terms in the j, equation, with friction acting with the Coriolis acceleration to rotate the sea breeze anticlockwise. This compares with the implied clockwise rotation due to the mesoscale pressure gradient, which consistently makes a positive contribution to 4.

According to model calculations, rotation of v, to give “J = 90”) i.e., with the sea breeze travelling parallel to the coastline, must occur somewhat farther inland than x = 280 km, at least under conditions of onshore or along-shore geostrophic flow.

224 J. R. GARRATT AND W. L. PHYSICK

6. General Features of Sea Breeze

Both the observations at Daly Waters and model simulations (see also Clarke, 1983) emphasise the deep inland penetration of the sea breeze, where it is well defined as a cool surge under conditions of moderate G, (5 12.5 m s ‘), both onshore and along- shore. Reasons for this behaviour must relate primarily to the low latitude of the investigation, where v, has a rotational period comparable with the inertial period of 46 hr, and the strong heating of the land surface in the dry season. In the model simulation, maximum land surface temperatures occurred near to 1300 hr, typically being 18 K higher than the sea temperature. Pressure jumps of the mature inland sea breeze are up to 0.5 to 1 mbar in magnitude, significantly greater than values normally associated with sea breezes in Europe. This is also reflected in the temperature difference across the sea-breeze front and depth (h) of the sea breeze. For example, at 1800 to 2100 hr local time simulation S5, with fl= 0 and G,, = 6.25 m s- ‘, had

2 ,s2 si .-

I /

16

1 14 L

J!, 11

2400 0 , , , , ,

1

:

52 84 / ' &a ‘ 1

1200 L/

(3 d

01 I I I I I I I I 100

DW 2oo 300 100 F 500

xlkml

Fig. 12. Vertical velocity fields at 5 times as functions of z and x for simulations S2 and S4 - units of w inms~‘(x100).


Ad = 2.5 K and h E 1200 m (hAB = 3000 Km), similar to values observed at Daly Waters and comparable with A8 = 1.5 K and h E 600 m (hAL\B = 900 K m) for sea breezes in the UK during summer described in Figure 18 of Simpson et al. (1977).

For much of the day and night, the position of the sea-breeze front is readily identifiable through the vertical velocity (w) maximum. We show in Figure 12 the inland movement of the w maxima for two simulations over a 12 hr period - 1200 to 2400 hr local time. Several noteworthy features include,

(i) The well documented acceleration of the front near sunset (e.g., Physick, 1980). (ii) The w maxima are < 0.2 m s- ’ well into the night at distances greater than

200 km, and occur at heights of about 1 km. (iii) The sea breeze is identified initially in conditions of onshore or along-shore geostrophic flow at 20 to 50 km inland near 1100 to 1200 hr local time.

IOOO- Zlmi

800 -

600-

400-

I

400 300 200 100 0

Fig. 13. Height--x cross sections of @for S2 (2100 hr) and S4 (0100 hr), open arrow indicates w maximum and the closed triangle the position of the pressure jump.


Table VI gives details of model calculated sea-breeze speeds (c), inland arrival time

at grid point 8 and penetrations. The inland penetration and magnitude of vertical velocity maxima are generally consistent with results of Clarke (1983) under similar conditions. There is some dependence of c and w maxima upon Pwhich must be a direct result of the presence of tail or head winds at low levels. The time of arrival of the front at grid point 8 is comparable with those observed and shown in Figure 2.

Simpson (1969) has emphasised the gravity-current nature of the sea breeze, as have Clarke (1984) and Physick and Smith (1985) in a detailed analysis of the low-latitude sea breeze. We show in Figures 13 and 14 fields of (1 and relative normal velocity 21-c during late evening for two simulations (S2 and S4). The tf fields reveal an air mass cooler (at mid levels) by several degrees K than the environment, perturbing an intense

x (km1

1200/-

IOOO-

800 - Z(ml -10

Fig. 14. As in

x ikm)

Figure 13 for relative normal velocity u - c; c = 11.1 and 5.6 m s ’ for respectively.

s2 and S4


TABLE VI

Model calculated sea-breeze speeds, arrival time and inland penetrations for all five simulations. For grid point 8 in 54, arrival time is estimated by extrapolation using mean speed between 2400 and 0300 hr (runs were terminated

at 0300 hr). A.T. = arrival time at grid point 8; +, = inland position at 2100 hr; w,,,,, is value at 2100 hr.

Simulation G, P A.T. XII-4 Wmax % c(m s-‘) m ss’ (km) (m s-‘) (ms-‘)

1500 1800 2100 2400

s3 12.5 -45” 2015 310 0.09 - 8.8 6.3 7.6 - - Sl 12.5 0” 1900 400 0.12 _ 12.5 8.3 9.0 - - S5 6.25 0” 2300 200 0.11 - 6.25 4.2 5.6 10 - s2 12.5 45” 2200 240 0.11 - 8.8 5.6 6.9 11.1 - S4 12.5 90” 0600 120 0.21 0 1 5.6 5.6 5.6

low-level nocturnal inversion. The u component relative to the sea-breeze front, U-C, with positive values indicating motion from right to left in Figure 14, shows a finite core of fluid moving towards the leading edge of the gravity current, and reminiscent of gravity currents in the laboratory (Simpson and Britter, 1980). In the case of simulation S4 the small volume of positive U-C implies that the front is just about to outrun the supply of cool air, and enter the vortex or dissipating stage (Simpson et al. 1977). The open arrows indicate the position of maximum upward vertical velocity (Figure 12) implying a relative fl&v around the head typical of atmospheric and laboratory gravity currents.

Two-Dimensions gravity currents in a still, shear-free environment should propagate with the densimetric velocity c, given by

C* =i ,(g’,)‘P (6)

where k is a constant, analogous to a Froude number of the flow, g’ = gA0/0, where A&s the temperature excess of the environment over the gravity current (unambiguously defined if we are dealing with two well-mixed fluids, but requiring suitable horizontal and vertical averages if this is not the case) and h is the depth of the sea-breeze. In the presence of a head- or tailwind, u,, Simpson and Britter (1980) have shown that the velocity c is modified as

c = c, + 0.7 u,. (7)

This is confirmed by Thorpe et al. (1980). Strictly Equations (6) and (7) should apply to steady-state flow only, but they appear to apply to accelerating gravity flows, e.g., squall-line outflows (Garratt et al., 1985) and the vortex stage of the sea breeze. In order to examine the value of k in our simulations, we have chosen calculated values of quantities in Equation (7) at 3-hrly intervals, giving 13 occasions in all. The prefrontal velocity and temperature were calculated at a point 30 km upstream of the front, and vertically averaged up to a height equal to k. The temperature of the sea breeze was taken as the vertically averaged temperature 30 km behind the front. The difference A B varied between 0.3 K (Sl and S3 at 1500) to 5.1 K (54 at 2400), with h typically between 550 m (54 at 0300) and 1650 m (Sl, S2, S3 at 1200, and 1500 hr).

228 J. R. GARRATT AND W. L. PHYSlCK

From Equations (6) and (7) we find

k = 0.65 + 0.2

consistent with the sea-breeze results of Simpson (1969).

7. Summary

In part I (Garratt, 1985), observations were described of the evolving nocturnal jet, and of numerical model results on the influence of radiative cooling on turbulent decay. Amongst other things, reference was made to a mid-evening disturbance causing, in the extreme case, jet collapse and strong backing of the wind.

Here we have generally confirmed the disturbance as being a sea breeze passing the site. This is strongly suggested in the obse~ations, in terms of cooling and a related surface pressure jump at the time of wind backing, and in 2D mesoscale model results. These show that under conditions of strong daytime heating of the land surface in low latitudes, deeply penetrating sea breezes occur, even under conditions of strong onshore or along-shore geostrophic flow. Rotational aspects of the sea breeze are also apparent in the model (and observations, by implication). Our analysis is based on a modified version of the rotation equation used by Neumann (1977) who considered the turning of the local wind only, without taking into account the influence of diurnal boundary- layer effects. This is done here by taking the vector difference, identified as a wind surge vector characterising the sea breeze, of the post- and pre-frontal winds. The rotation of this then depends on the Coriolis parameter, the mesoscale pressure gradient and a frictional term. The sea breeze itself, as modelled, behaves in many ways as a two- dimensional gravity current.

The correspondence of the model results with the observations is striking and suggests that the complicated nature of the coastline in the Daly Waters region does not piay a significant role in determining the broad sea-breeze features observed at Daly Waters. This suggests, in turn, that the observed sea breeze can be identified with that originating from the main coastline between A and B in Figure 1. Such a result needs to be confirmed by a 3D numerical study.

The observed jet collapse, and mesoscale model results, provide evidence of deep sea-breeze penetration in Northern Australia in the dry season. These support the studies of Clarke (1983,1984) and Physick and Smith (1985) on the life cycle of the sea breeze and its penetration to distances up to 500 km before dissipating the following morning. It is of interest to note that the interaction of the sea breeze and inland nocturnal jet occurs within a deep, stably stratified layer (the result of radiative cooling). There is then the potential for internal wave generation and propagation; perhaps relevant to the problems of the Morning Glory (Clarke et al., 198 1; Clarke 1984) and the ubiquity of waves to be found in the lower atmosphere at night (e.g., Christie et al., 198 1).

Finally we make some briefcomments on the performance of the numerical mesoscale model used here. Its ability to simulate deeply penetrating sea breezes was impressive


and consistent with the results of Clarke (1984). Further it demonstrates the existence of significant sea-breeze influences with geostrophic winds as high as 12.5 m s - l.

Two problem areas were identified; firstly, cross-isobar flow angles, during the daytime in particular, were consistently smaller than those observed. To a small extent, this is related to the surface-layer formulation used in the model, and possibly to the absence of a vegetation canopy model and zero-plane-displacement. Otherwise it may be due to the problem of matching model thermal winds to those occurring in practice (which are difficult to assess). Secondly the radiation scheme used by us (see Mahrer and Pielke, 1977) gave cooling that was too small; however a modified scheme used in the model by McNider and Pielke (198 l), but not incorporated here, has achieved the desired increased cooling for them.

Acknowledgements

To Dr R. A. Pielke for making available the mesoscale model.

Appendix

We derive here an equation for the time rate of change of y representing rotation of the surge vector v,.

We take the 2D scalar momentum equations, viz.,

au at = fv - fvg - Fx - u ;

au au - = -fu + fug - F, - u - at ax

where friction terms are parameterised in terms of a drag coefficient, such that

F = G4Vl Y ~ = pvlV .

h

In the prefrontal region,

ic, = fv, - fug - Fxb

bb = - fub + fug - Fyb ,

and in the postfrontal region,

ic, = fv, - fv, - f 2 - F,, - u, 2

(Al)

(-42)

C-43)

644)

645)

(‘46)

647)


The geometry in Figure 11 shows that,

tan “/ = -Au/Au where

Au=uu,-uuh

Au 3 v, - v,

and we note that,

/v,~/~ = Au2 + Au2

Difl’erentiating (A9) with respect to time, gives

d;, 1 -= --______ dt Au sec2 ;I i

Now we combine Equations (A5) to (A8) to give

649)

(AlO)

(All)

6412)

(A131

Substituting these two equations into (Al l), using pa = pL6 for simplicity then, after some algebraic manipulation,

%f + O.;y- +; f i';- (IV,1 - /V,l)(U,% - 4zY!J + A dt v, 2

where the advection term A is given by,

(A141

tan y u,, au %l c’t? A=----- --.A+.pR,

sec2 7 Au ax set’ yAu 3x (AW

By making the reasonable assumption that

au, - Au and av, _ & 2X =Ax dx Ax

and using Equation (A9), it is readily shown that A = 0. Hence,

0.5 sin2y Csp, + p =f+T-- i?x

~ (IV,, - V,i)V, x v,. / v,r I 2

(A161


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the inland boundary layer at low latitudes: ii sea-breeze influences

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