THE UNIVERSIT Y O F MICHIGAN COLLEGE OF ENGINEERING Department of Meteorology and Oceanography Technical Report NOo 1 INVESTIGATIONS WITH A MATHEMATICAL MODEL OF THE LAKE BREEZE John Wo Wilson E Wendell Hewson Project Director ORA Project 08650 Sponsored by, DEPARTMENT 0F HEALTHs EDUCATION AND WELFARE U0 S PUBLIC HEALTH SERVICE NATIONAL CENTER FOR AIR POLLUTION CONTROL GRANT NOo 5 RO1 AP 00380-03 BETHESDA MARYLAND administered throughOFFICE OF RESEARCH ADMINISTRATIONo ANN ARBOR August 1967

TABLE OF CONTENTS LIST OF TABLES v LIST OF FIGURESvii ABSTRACT ix ACKNOWLEDGMENTS xi 1, INTRODUCTION 1 2. THE MOROZ LAKE BREEZE MODEL 1 30 THREE PERTURBATIONS ON THE MODEL 3 o Maximum temperature increase 3 3,2 Land breeze 13 303 Diffusivity profile modification 15 4o SUMMARY AND CONCLUSIONS 24 5 SUGGESTIONS FOR FUTURE WORK 24 APPENDIX SUMMARY OF UNPERTURBED RESULTS 25 BIBLIOGRAPHY 32 iii e e e 1BB,

Table 1 LIST OF TABLES Air temperature over the land at a location well inland from the lakeshoreo Air temperature over the land at a location well inland from the lakeshoreo Maximum temperature perturbation. Air temperature over the land at a location well inland from the lakeshoreo Land breeze Page 2 5 6 14 3 v

LIST OF FIGURES Figure Page 1 The across shore wind component (u, in 7 m secl-) in the model plane 4 hrs after time zero for the increased land temperature perturbation 2 The across shore wind component (u, in 8 m sec-1) in the model plane 6 hrs, after time zero for the increased land temperature perturbationo 3 The vertical wind component in cm sec in 9 the model plane 6 hrs, after time zero for the increased land temperature perturbationo 4 The across shore wind component (u, in 10 m sec 1) in the model plane 9 hrs. after time zero for the increased land temperature perturbation. 5 The vertical wind component in cm sec in 11 the model plane 9 hrso after time zero for the increased land temperature perturbationo 6 The across shore wind component (u, in 12 m sec-1) in the model plane 12 hrso after time zero for the increased land temperature perturbation. 7 Diffusivity profile used by Moroz (straight 17 line) and by Wilson in the perturbed Moroz model (curved line) 8 The across shore wind component (u, in 18 m sec-1) in the model plane 4 hrso after time zero for the diffusivity profile modification 9 The across shore wind component (u, in 19 m sec-1) in the model plane 6 hrs. after time zero for the diffusivity profile modification o vii

Figure Page -1 10 The vertical wind component in cm sec in 20 the model plane 6 hrs, after time zero for the diffusivity profile modificationo 11 The across shore wind component (u, in 21 m sec-1) in the model plane 9 hrs0 after time zero for the diffusivity profile modification o 12 The vertical wind component in cm sec in 22 the model plane 9 hrso after time zero for the diffusivity profile modificationo -1 13 The vertical wind component in cm sec in 23 the model plane 12 hrso after time zero for the diffusivity profile modificationo a The across shore wind component (u0 in 26 m sec-1) in the model plane 4 hrso after time zero (After Moroz) b The across shore wind component (u, in 27 m sec-1) in the model plane 6 hrso after time zero. (After Moroz) c The vertical velocity wind component in 28 cm sec-1 in the model plane 6 hrso after time zero0 (After Moroz) d The across shore wind. component (u, in 29 m sec 1) in the model plane 9 hrso after time zero0 (After Moroz) e 1The vertical velocity wind component in 30 cm sec-1 in the model plane 9 hrs. after time zero0 (After Moroz) f The across shore wind component (u, in 31 m sec-1) in the model plane 12 hrso after time zero0 (After Moroz) viii

ABSTRACT Although the lake breeze is considered an important mesometeorological phenomenon, there has not been much work done to mathematically describe it. Many studies of sea breezes have been carried out; some of the results are applicable to the lake breeze, but others are not. Moroz in 1965 modelled the lake breeze using modifications of some of the sea breeze ideas, and a computer program is now available to serve as the model0 This study perturbs this model in three ways, each different in concept0 The first perturbation is simply a data change. the maximum temperature of the land is increased by 3 o2~C The model correctly predicts the increase of the lake breeze circulation0 The next modification involves trying to model a land breeze, as yet not attempted with the modelo No circulation characteristic of a land breeze is produced, but reasons are presented to possibly explain why. In the last case the model itself is changed by substituting an eddy diffusivity profile which decreases from the top of the boundary layer to the top of the model as the square of the height, instead of linearly as previously used. The movement of the lake breeze is slowed, but its strength remains as in the unperturbed model. ix

ACKNOWLEDGMENTS The author is indebted to Dr. Alan L. Cole for his suggestions and advice during this study, and to Dr. William J, Moroz for his guidance in using the computer program which serves as the model under consideration in this paper. xi

1. INTRODUCTION The Great Lakes are without a doubt very influential in determining local meteorological situations within many miles of their shorelines. The influence of Lake Michigan has been shown both during the winter, in relation to the snow belt (Thomas, 1964), and in the summer affecting thunderstorms (Moroz and Hewson, 1966; Lyons, 1966 Lyons and Wilson, 1967)o Air pollution is becoming an increasingly important problem, and the effects of Lake Michigan upon pollutants have been pointed out by both Lyons (1966) and Lyons and Wilson (1967)o Many of the above effects can be linked to the lake breeze circulation along the shore of the lakeo If models of the lake breeze were available these effects could be studied in a more mathematical way, and perhaps give some insight into their mechanisms, Moroz (1965) has developed such a model, and an extension of his work will be discussed in detail in this paper Three types of perturbations are introduced, one at a time, into the model. The first involves increasing the maximum temperature of the land by 30o2~C This should produce a more intense lake breeze For the second case, the land temperatures are changed so as to represent a nighttime situation, which should produce a land breezeo This has not before been tried using the Moroz model0 As a last modification, the model itself is modified by changing the eddy diffusivity profile from the top of the boundary layer to the upper boundary of the model0 2o THE MOROZ LAKE BREEZE MODEL The mathematical model of Moroz is summarized here, but for a more complete description the reader is referred to the origional worko The model uses the differential equations of motion and heating, the equation of continuity, and the hydrostatic equation, and computes fields of wind (both onshore and alongshore), temperature, diffusivity, pressure, and poten

tial temperature. Finite differencing of the equations is done on an IBM 7090 computer. Some of the relations are taken from Estoque's work on the unbounded sea breeze model. The lake breeze model is of the semi-bounded typei.e. the grid extends normal to the shoreline a finite difference into the lake but an infinite distance over lando The tangential component extends to infinity both up and down the coastline. An expanding grid is used in the horizontal, with close spacing near the shore and increasing distance between grid lines as the distance from the shoreline increases in both directionso Vertical spacing of the grid is linear above the top of the constant flux layer, with a spacing of 100 m This extends to 3050 m, where all influences from the lake are assumed to vanisho The depth of the constant flux (or surface boundary) layer is taken as 50 m. The result of the gridding technique is a 16 x 32 grid, set up in the x-z plane. Distances along the y (North= South) axis are not considered, since the lake breeze is viewed as being homogeneous in this directiono The inputs to the computer model are the initial surface pressure and temperature at the shoreline, prevailing lapse rate, grid spacing (by changing this the model is applicable to other lakes), and hourly temperatures for a station far enough inland to be considered not under lake effects. This is taken to be Grand Rapids, 53 km from Lake Michigan Initial conditions dictate that land and water surface temperatures are equal at the beginning of the calculations (called time zeroo in reality about 0600 LST)o There can be no geostrophic wind blowing through any of the model bo)undaries. This is the only other initial restrictionO Calculations are performed at time intervals of five minutes, with hourly results being printedo After twelve hours, computational instabilities become large due to the manner in which the equations are handled, and the results become masked by the instability waves. They become even worse after sixteen hours, Twenty-five minutes of computer time are required to model sixteen hours of real time. The Appendix contains the results of an unperturbed

case, as taken from the Moroz paper, for comparison with results obtained in this study. 3. THREE PERTURBATIONS ON THE MODEL 3 1 Maximum temperature increase The purpose of this change was to see if a stronger lake breeze circulation would be generated by the model as intuitively predicted for reality. Table 1 gives the hourly Grand Rapids temperatures as used by Moroz, and Table 2 gives the increased values used in this study. Since the model requires that land and water be at equal temperature at time zero, this was preserved but the maximum for the day was increased by 3.20C. Because of the increased heating one would expect to see a stronger lake breeze, but not until several hours had passed. Figure 1 shows the onshore component of the wind, u, for the perturbed case four hours after time zero, By comparing it with Figure a in the Appendix, one can see that the two patterns are almost identical. The lake breeze has a velocity of 1 m sec-l about 150 m above the shoreline, and it extends 7-8 km inland. The return flow is centered at 500 m in the unperturbed case, but almost 700 m in the new oneO The lake breeze two hours later is shown in Figures 2 and b. No major change is yet evident the maximum velocity has increased to 2 m sec-, but has shifted 2-3 km inland and stayed at a height of 150 m. The offshore flow aloft is now 0.6 m sec 1 in the case with augmented heating, and has increased its height to 1000 m (800 m in the original case). The warmed case does show that the boundary of the lake breeze (the zero isotach) has moved 100 m higher than in the unwarmed case, A small return flow at 200 m is beginning to appear in both figures, but it is somewhat larger in Figure 2. Vertical velocity structures for the same time are represented by Figures 3 and c. In Figure 3 it is more apparent that a change is occurring in the flowo Both upward motion over the land and downward motion over the water have intensified by 2 cm sec- The time of maximum heating is eight hours after time

zero. One hour after maximum heating or nine hours after time zero the flow patterns are as they appear in Figures 4 and do Computationally introduced instability waves are beginning to form over the shorelineo The perturbed case definitely has a more well-developed lake breeze. Over the shoreline it extends to a height of almost 1000 m, whereas in Figure d it is only 550 m higho Increased heating of the air seems to have increased the onshore maximum from 3 to 4 m sec1, and the offshore maximum from 1 to 3 m sec 1 Notice that in Figure 4 the return flow core is situated almost directly above the onshore maximum, whereas in Figure d there is a definite tilt to the west with heighto A secondary onshore cell at 3 km over the lake is present in both cases, but stronger in the heated oneo At 18 km over the land a strong offshore flow with a return at 1400 m is much more evident than in Figure do The same pattern, only smaller, is evident 19 km over the lake in Figure 4, but entirely lacking in Figure d. Vertical velocities, presented in Figures 5 and e, show just how strong the lake breeze has become by additional heating The upward motion over the land is now 27 m sec1, compared with 9 cm sec-1 without the temperature increase0 Over the water the vertical velocities differ by a factor of more than four These new values are closer to Estoque's (1960) results for his sea breeze modelo Also present in his work and in the perturbed case studied here is the secondary maximum of sinking motion far inland from the rising air maximum By twelve hours after time zero the instability waves have become rather large and are distorting the pattern considerab ly The lake breeze developed with a warmer air perturbation has penetrated 25 km inland, and the maxirmum on shore flow has moved to 18 km inland and strengthened to 6 m sec 0o The return flow has not progressed as rapidly; it is centered at 9 km and is weakening Smaller cells are developing over the lake, but the flow in these cells is fairly weako Figures 6 and e illustrate these flow sittationso

TABLE 1 AIR TEMPERATURE OVER THE LAND AT A LOCATION WELL INLAND FROM THE LAKESHORE* Time Hrs o O** 1 2 3 4 5 6 7 8 9 Temperature oK 294.0 295.8 297.3 29809 299,9 300.8 301.4 301.9 302.1 301.9 Time Hrs. 10 11 12 13 14 15 16 17 18 19 Temperature OK 301o3 299.9 298.1 296.7 295.5 294.3 293.3 292.4 291.8 291,2 * After Moroz (1965) ** Time zero corresponds to the time when over land air temperature equals water temperature. -5 -

TABLE 2 AIR TEMPERATURE OVER THE LAND AT A LOCATION WELL INLAND FROM THE LAKESHORE MAXIMUM TEMPERATURE PERTURBATION Time Hr s. 0 1 2 3 4 5 Temperature OK 294.0 296,2 297.7 299.0 302.0 303.5 304.5 304.9 305.2 305.0 Time Hrs. Temper atur e oK 10 11 12 13 14 15 16 17 18 19 304.5 302.0 300.8 298.8 296,9 295.4 294, 5 293.6 292.4 292.0 6 7 8 9 -6 -

25 M 4 o lO 4 O-I -0. I 5 H / % 10 -'-~4^ 1 ' / I U 0 \ -0 Le -18 -9 - 3 918 Distance Inland in km Fig. 1. The across shore wind component (u, in m sec ) in the model plane 4 hrs. after time zero, for the increased land temperature perturbation.

25 e 20 4-) t // \ IM / -0.2 o,, U) 15 0), a) 15 _ / % I I x O Di 10 -0.6 -P~I 1 v tI \ _l I 5 I I " " -0.,2 --- —--,- '. 0t - -0. 2. x__ ^ — '-30 -18 -9 -3 6 3 9 18 Lake Distance Inland in km Fig. 2. The across shore wind component (u, in m sec ) in the model plane 6 hrs. after time zero, for the increased land temperature perturbation.

25 I I 20 L) -P O ^r 15 -rd +1.0 * H10 +3.0 0' -1.0 5 0 -30 Lake -18 -9 -3 0 3 9 18 Lake - Distance Inland in km Fig. 3. The vertical wind component in cm sec in the model plane 6 hrs. after time zero, for the increased land temperature perturbation.

25 9n / / / I -0.2 N / / N. N.b I I I I I I I I -nA I 0.2 /./ J / S4 -0.2 /. / a) \ -= ' '~~~~cr~ ~~~~~B ' 0 15 / ' oU. \ I \, I ^ ^a~ ~~~~~" \ / \ *!. o -5.: \,..o 10 2ji-2 +, l::::,\ 0 —,4a~ — -0 2 / 0.2 '"0 ~6 Q) 0.2 - - -1 -9 - 00,, 3 9 18,3 Distance Inland in km 2.0 - 2.0~ 4O Lakee Fig. 4. The across shore wind component (u, in m seci1) in the model plane 9 hrs. after time zero, for the increased land temperature perturbation. 0

30 25 zoo 20 -1.- ) 0 3l0 0 / \ /-3.0 \ -3.1 U 15 9- 1 3. 0 3CI *r 15.0 \ \, /-5. +I o, 15.0 0 Lake 8 0 --- —------- Distance Inland in km Fig. 5. The vertical wind component in cm sec) in the model plane 9 hrs. after time Zero, for the increased land temperature perturbation. I

30 25.. - / -, \ \ —.- 1, 1.0 /II 1 1 U), '' ' \ ' 0.2 r 20,\\ - \ \ |o.,\.\,^,, /\ _ -/ ) 0.6 o ', ', \ \\\\ / / / --- '// 4-I o 4 \ v I \-0.6., /.2 o 15 /- o \' x \" \ - -' '( /i!/ I I-, IX \ II.% I 10 /-1.0 I tin //I / \-. / // /. / s / Io,,p/' 2.0 -. 2:Distance Inland in km Fig. 6. The across shore wind component (u, in m sec ) inNthe model plane 0.2 hrs. -0.2 the increased land temperature perturbation. ' L- I Distance Inland in km Fig. 6. The across shore wind component (u, in m sec ) in'the model plane 12 hrs. after time zero, for the increased land temperature perturbation.

3.2 Land breeze The Moroz model is primarily a lake breeze model, and until the present there have been no published attempts to produce a land breeze with it, or for that matter with other lake or sea breeze models, For a first approximation to the land breeze, the input data for the Moroz model were modified to force the over land air temperature to decrease from a value of 210C at time zero, 2200 LST, to a minimum of 12~C nine hours later at 0700 LST. This is fairly strong cooling, with a temperature change of 90C, but it was chosen to accent any land breeze which might develop. The hourly temperatures are given in Table 3. There should be some nocturnal inversion present over the land; unfortunately its strength is not known, and local effects (sand, sand dunes, and trees) make estimating it with any accuracy very riskyo It was decided to run the model without the inversion, partly for this reason and partly because the model would have to be extensively modified unless the inversion were to go to 3050 m, which does not seem very realistic The last problem when considering the use of the Moroz model for a land breeze, is the eddy diffusivity profileo With the inversion mentioned, the Richardson number Ri = ---- /az) (1) R T (v/az)2 will be positive, and in the forced convection regimeo Estoque (1959) has said that the eddy diffusivity for momentum in this regime can be expressed as K = k z (1+2Ri)2 -v (2) m az where k is von Karman s constant 004, and K =-3 Eecause the Richardson number is different at night than during the day the value for the diffusivity at any height in the model will be different. Again, because the land breeze has not been investigated in the light of the model, values for the Km profile are not known. As a first approximation, the daytime profile was used to see what type of flow patterns the model would produceo With the approximations discussed above, no land breeze -13 -

TABLE 3 AIR TEMPERATURE OVER THE LAND AT A LOCATION WELL INLAND FROM THE LAKESHORE LAND BREEZE Time Hr s 0 1 2 3 4 5 6 7 8 9 Temperature OK 294.0 293 3 292.4 291.8 291.2 290.0 287.3 286.4 285o5 285 0 Time Hrs Temper atur e oK 10 11 12 13 14 15 16 17 18 19 285 2 287.2 289 o0 291.0 292.5 294.0 295.3 296.0 297.0 298 5 -14 -

was produced by the model. The onshore wind was positive and of the order of 10-4 m sec1 all nighto When heating started again in the morning some semblance of order returned to the patterns, but computational instability had masked any quantitative values by that time. It thus appears that more realistic modifications will be required before the Moroz model can represent the land breeze. 303 Diffusivity profile modification Moroz mentions that the least acceptable feature of his lake breeze model is the method used to evaluate the turbulent transfer of heat and momentum. He arbitrarily specifies a value of 500 cm2 sec-1 for the eddy diffusivity Km at the top of the constant flux layer, and then decreases it linearly to zero at the top of the model. Figure 7 shows the profile. If this profile could be changed so as to weight the lower heights with a steeper curve, the entire model would be affected because of the increased transport of heat and momentum in the lower levels. This was chosen as the third perturbation for consideration; the new profile (and hence what will be called the new model) is shown in Figure 7. The function used was a simple square of the height. Figure 8 shows the across shore wind component isotachs for four hours after time zero. By comparing this with the unperturbed results, Figure a, one can see only two changes The return flow above the lake breeze is not as strong as before, and onshore flow weakens sooner as it moves out over the lake. Six hours after the inception of the lake breeze the differences between the new and old models are becoming more pronounced, as a comparison between Figure 9 and Figure b illustrates. Maximum onshore velocity seems to be moving inland slower than in the original model, and it is slightly weaker. The return flow is spread over a larger area, and has almost reached the ground ahead of the zero isotach marking the leading edge of the lake breeze. Figure 10 shows the vertical velocity pattern; comparison with Figure c in the Appendix shows almost no difference. The two zero isotachs are probalby a consequence of the weak flow surrounding the regions in the lake breeze flowO -15 -

Nine hours after time zero the area of maximum onshore flow is still lagging the unperturbed results. Figure 11 shows the remainder of the pattern to be fairly compatible with Figure d, except for one feature. A small wave has been introduced at a mean height of 2500 m. The vertical velocities under the new model appear in Figure 12. They are generally smaller than those of Figure e, and have several smaller cells developing, mostly over the water. Three hours later, the wave on the 9 hour across shore wind pattern has become large enough to slightly distort the return flow over the shoreline at 2200 m An offshore flow of 1 m sec'1 is evident 9 km into the lake; this is not present in the unmodified model. At 18 km inland and 1500 m a 3 m sec-1 onshore core appears; this is on the other model, but much weaker. -16 -

30 25 U) a) 20 - \ \<20 10 0 100 200 300 400 50( 2 -1 Eddy Diffusivity in cm sec Fig. 7. Diffusivity profile used by Moroz (straight line) and by Wilson in the perturbed Moroz model (curved line). ~rl ~ ~ ~ Ed ifuiiyinc2sK Fi.7 ifsvtypoieue y oo srih -17 -

25 U) 20 0n a0 2 I 0a -0'2 ci i 15 i rd I H 1 0 S t -0'./ Distance Inland in km 00 - % \.......x~ O - — '' 0........................____ ~ - — ' '/ -30 Lake -18 -9 -3 0 3 9 18 ^.r. 5~~~~~~~~Distance Inland in km Fig. 8. The across shore wind component (u, in m sec ) in the model plane 4 hrs. after time zero, for the diffusivity profile modification.

6 hr 25 k I I I I I I I I I I % I \ r% S U, a) a) 0 (U) rd a) C t1 I a) ro r.f (5 z tn *Hq a) 20 H 15 i I I I I I I I -0.2 I I I I 1 I I I 10 h / \ -0.6 I I - I AI I- + 5 k - - _ WN_ "I,,- - 0.2'_ - -0.6 0. 2 -, _ - - 0 I Lake -18 -9 L ak e~~~~~ 3 9 18 Distance Inland in km Fig. 9. The across shore wind component (u, in m sec ) in the model plane 6 hrs. after time zero, for the diffusivity profile modification.

6 hr 25 (U a) 0 CO a)::l o rn 4J 0d a, -.-I I (1 20 15 I 0 1o 10 - 0 I 5, O L -3 I I I I 0 Lake -18 -9 -3 0 3 9 Distance Inland in km 18 Fig. 10. The vertical wind component in cm sec in the model plane 6 hrs. after time zero, for the diffusivity profile modification.

9 hr - - "O'. 00 1% 25 - Mn 20 \ a) -P I ~0 ~~~0~~~~~~~~~~ '/ 15 - ), d - / ro^~~~~~~~~~~ ^"" /-0.6 I s 10 ' ( -^, I+ N) —,-" "'-o-2^,- 1 IF~~-I~~ 0.6 1/1 0.2 10 ' ' 4-),,, I \I - - - 0.6 -3~~~~0 -— 1 - 5 )-20.2 Lake -9 ~~ /002 0..., Distance Inland in km -30 -18 -9 13 9 18 Fig. 11. The across shore wind component (u, in m sec ) in the model plane 9 hrs. after time zero, for the diffusivity profile modification. '0 30

9 hr 30 0 25 20 - Lk 0 1 15, =N)~~~a *H 2-1 -75432 1 0 - -- 5 -0 -30 -18 -9 -3 0 3 9 18 30 Lake Distance Inland in km Fig. 12. The vertical wind component in cm sec in the model plane 9 hrs. after time zero, for the diffusivity profile modification. I lb

12 hr 30 /\ /.,.' —. \ i rd 1 \ a.j.2 s \ ~~\ / ^ ~~ -\ I I / \ \ x\.100' \ ^ -0 / 0 \'* \\ 20J I 10 0 \0\\ (E3 I \ % \ \ \',/ t 4 J0.6 " --, -- -- -- - -—., - \ \, 0 ~rI.c0.2............... ) *0 1-,,0. -30 _ _ -18 -9 -3rd 3 9 18 30 Distance Inland in km -4 Fig. 13. The across shore wind component (u, in m sec ) in the model plane 12 hrs. after time zero, for the diffusivity profile modification.

4. SUMMARY AND CONCLUSIONS Of the three types of perturbations imposed on the Moroz model, each produced its own characteristic results. Increasing the maximum temperature intensifies the lake breeze and moves it further inlando An hour after maximum heating, vertical velocities are triple the values with no excess heating, and the maximum onshore velocity is greater, but not by as much. Trying to introduce a land breeze into the model was not successful, but some additional work with nocturnal temperature and diffusivity profiles might correct this. Substituting a new diffusivity profile that allowed Km to decrease as the square of the height decreased the movement of the lake breeze, but not its strength. After the time of maximum heating, however, computationally introduced instability waves developed on the isotach pattern and distorted it. 5o SUGGESTIONS FOR FURTHER WORK Perturbations of all three kinds presented here (new data, new situation, or change in the model) are possible, but in the last one lies the widest range of possibilities The two biggest problems are the edddy diffusivity profile and the computational instability introduced after the model has run through several hours of meteorological timeo If solutions to these problems were available the model would be more versatile, and could possibly remain accurate through lake breeze decay and land breeze development. Another interesting modification would be to incorporate a prevailing geostrophic wind into the model, and test its effect on the lake breeze. Haurwitz (1947) has modelled a sea breeze with a geostrophic wind involved, his results provide an interesting staring point from which to work. -24 -

APPENDIX SUMMARY OF UNPERTURBED RESULTS -25 -

4 hr 20 CI 15 4 -0 Uo a) r / -0.2 10 / tsJ ~ ~ ~ 4' I+ mH mop 0,6 \0 5 - L020-11 -18 -9 -3 3 9 Lake -^^~~~~~_ ~Distance Inland in km Fig. a. The across shore wind component (u, in m sec ) in the model plane 4 hrs. after time zero. (After Moroz)

6 hr 25 (U) a) -) 0 rOl 1a) rd r. -H WI 20 15 / / / / / / I I I I1 I 10 - -0.2 I I 5 1 - 0.2 - -2 ~.~0-2~~~~~~~~~A ol I _ _0.6 0_ " 0 -_ 0 I * ^ cl~~ 11jl #~~~~~II — 00"1 C ftwo 0.22. -( 0 -30 -18 -9 -3 Lake ~i_ -./ 3 9 Distance Inland in km -1 Fig. b. The across shore wind component (u, in m sec ) in the model plane 6 hrs. after time zero. (After Moroz)

6 hr 25 rn a) 0 U) nl a) -4 -H wd 20 15 10 I 5 0 3 9 18 Distance Inland in km -I Fig. c. The vertical velocity wind component in cm sec in the model plane 6 hrs. after time zero. (After Moroz)

9 hr 25 _ -" en u4 a) 0 (i) rc a) I:.,l I 43 -I:ii 20 r A~ ~ O -0.2 — ' / /.0 I I I I I 15 1 /r 0.2 I \+ \ l\, N.. 10 l0 -- / %. j / / - _ — 0.2 _y~LI 5 _ -. 0 _,_ - - _ _ ~ - 0. 2 -O ~ _- / 1-00~. d-.. W. 6 -- 1 I -1.0 _J 0 _ v..... I -- -30 -18 -9 -3 3 9 18 Lake -- c. __ Distance Inland in km Fig. d. The across shore wind component (u, in m sec ) in the 9 hrs. after time zero. (After Moroz) model plane

9 hr 25 co Q) Dsac 3 W) 15 k ~~~~4~~~~-1 'U 10 0 ~~~~~J~~ ~~-)r ~-3 5 -30 -18 -9 -3 3 9 18 3 Lake Distance Inland in km Fig. e. The vertical velocity wind component in cm sec in the model plane 9 hrs. after time zero. (After Moroz) )

12 hr 25 / 1-8 / N 20 rd - - 1.0 m-r2 -0.2 J m* o -0.6.6 -wo M I / -30 -18 -9 -3 3 9 18 3 Lake Distance Inland in km _ p-0 Fig. f. The across shore wind component (u, in m sec ) in the model plane 12 hrs. after time zero. (After Moroz) 30

BIBLIOGRAPHY Estoque, MoAo,, 1959: A preliminary report on a boundary layer numerical experiment. G.oRoD Res. Notes No. 20, Bedford, Mass, __ 1960: A theoretical investigation of the sea breezeo Quar. J. of Royo Met. Soc., 86, 523-534. Haurwitz, B o 1947: Comments on the sea breeze circulationo Jo of Met o, 4, 1-8o Lyons, WoA., 1966: Some effects of Lake Michigan upon squall lines and summertime convectiono Proco of 10th Confo on Great Lakes Research, Univ. of Mich., Great Lakes Res. Divo Pub. 15, 259-273 ____ and JoW. Wilson, 1967 (in print): Some effects of a lake upon summertime cumulus and thunderstorm distributions. Reso Paper of Satellite and Mesometeorology Res. Proj., Depto of Geophysical Sci= ences, Univ. of Chicago, Chicago, Illo Moroz, W J,, 19650 The lake breeze circulation along the shoreline of a large lakeo Tech. Report, Dept. of Meteorology and Oceanography, Univo of Mich., Ann Arbor, Micho, and EoW. Hewson, 1966 The mesoscale interaction of a lake breeze and low level outflow from a thunderstorm. Jo of Applo Meto, 5, 148-155o Thomas, MoKo, 1964: A survey of Great Lakes snowfallo Proc. of 7th Conf. on Great Lakes, Univo of Mich., Great Lakes Res Div. Pub 12, Ann Arbor, Micho

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