Mesoscale Meteorology: Sea, Lake, and Land Breeze Circulations 7, 9 March 2017 Introduction Breeze-type circulations result from differential heating

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1 Mesoscale Meteorology: Sea, Lake, an Lan Breeze Circulations 7, 9 March 2017 Introuction Breeze-type circulations result from ifferential heating (aytime warming, nighttime cooling) of lan an water surfaces. They are perhaps the best-known of a larger class of ifferential heating bounaries. For a given heating, the requisite ifferential heating primarily results from lan both warming an cooling more rapily than water ue to their ifferent specific heat capacities; other contributions arise from more heating going to evaporation an to greater epth over water. The aytime circulation is a sea breeze when the water boy is an ocean or sea; lake breeze when the water boy is a lake; or river breeze when the water boy is a river. Unless state otherwise, these notes use sea breeze to refer to sea, lake, an river breezes. The nighttime circulation is a lan breeze inepenent of the water boy type. The name escribes from where the breeze blows; e.g., a sea breeze blows from water to lan. Each are primarily warm-season phenomena, with lan warmer than water uring the ay an cooler than water at night. The horizontal pressure graient magnitue across a sea breeze circulation is on the orer of 1 hpa per 50 km; for smaller-scale water boies, this magnitue is corresponingly smaller. Breeze circulations result from this horizontal pressure graient an accompanying flow acceleration, as is escribe physically in more etail later in these notes. Sea breezes exten to a epth of km with v 3 10 m s -1 maximize above the frictional layer (~ m above the surface). The return flow is eeper (~2 3 km eep) but weaker ( v ~ 2 5 m s -1 ). Sea breezes an their return flow evelop nearly simultaneously. Lan breezes are generally weaker than sea breezes. The typical wih of the sea or lan breeze s leaing ege is ~ m. A slope of ~1/10 20 is foun along the breeze s leaing ege; a short istance rearwar, the slope ecreases to ~1/100. Horizontal convergence along the breeze s leaing ege is O(10-3 to 10-4 s -1 ), supporting upwar vertical velocities in excess of 1 2 m s -1 along the breeze s leaing ege. Sea breeze fronts separate a comparatively warm over-lan air mass from an avancing air mass that originates over comparatively col waters. Sea breeze fronts are similar to ensity currents: enser, cooler air rushes uner an isplaces upwar warmer, less ense air. The same is true for lan breeze fronts, except propagation is from lan to water. Both sea an lan breeze fronts are akin to synoptic-scale col fronts, except on smaller spatiotemporal scales. However, it shoul be note that lan breeze fronts are not retreating sea breeze fronts; the two are istinct features. A sea breeze front may propagate a great istance inlan uring the ay, where it issipates shortly after sunset, with a subsequent but separate lan breeze front eveloping shortly thereafter along the immeiate shoreline as the lan s temperature cools below that over water. Sea breeze front passage is accompanie by reuce temperature, increase relative humiity (rv rises an rvs ecreases), a win irection from the upwin water boy, an sometimes increase win spee. Lan breeze front passage is similar, except with a win irection from the upwar lanmass. Sea an lan breezes are important contributors to the warm-season thunerstorm climatology at tropical to subtropical latitues, particularly near irregularly-shape coastlines an peninsulas. At such latitues, the over-lan air mass is typically conitionally unstable with large surface-base 1

2 CAPE an minimal CIN, such that locally-enhance ascent along the sea or lan breeze front is sufficient to lift parcels to their LFCs. Thunerstorm formation is less common on higher latitue sea an lan breeze fronts ue to less supportive ambient thermoynamic air mass properties. In the absence of appreciable synoptic-scale flow, sea breeze intensity is irectly proportional to the cross-breeze temperature ifference. This implies stronger sea breeze fronts in spring an early summer when the climatological lan-water temperature contrast is largest. Despite this, thunerstorm formation along the sea breeze is most frequent when the ambient environment is most supportive of thunerstorms (e.g., a warm, moist ambient air mass with large surface-base CAPE), which generally occurs uring meteorological summer in the Unite States. Unerlying soil characteristics also control circulation intensity; e.g., breeze circulations are climatologically weaker over Louisiana than ajacent states since the southern part of the state is ominate by marshes with a similar heat capacity to water. Breeze circulations are also weaker in proximity to smaller, shallower water boies that warm an cool more rapily than their larger counterparts. The intensity of a sea, lake, or river breeze is greatest near the immeiate shoreline an weakens with inlan extent for two reasons. First, the cross-breeze temperature ifference is greatest near the shoreline an iminishes with inlan extent as insolation an sensible heat fluxes act to warm the initially-cooler air mass after it eparts from its source region. Secon, the Coriolis force acts to eflect the win into a shore-parallel irection with time an, by extension, inlan extent. The epenence on the Coriolis force means that, all else being equal, sea, lake, an river breezes at lower latitues will progress further inlan than at higher latitues. Further, these factors result in sea an lan breezes having greatest intensity in the afternoon an preawn hours, with intensity remaining approximately constant thereafter until near sunset or sunrise, respectively. Sea an lan breeze intensity an propagation are controlle by the synoptic-scale flow (assume in graient win balance) an stability. Onshore flow weakens convergence an ascent along the sea breeze front s leaing ege an reuces the lan-water temperature ifference across the sea breeze front ue to the avection of water-coole air over lan. These factors result in a weaker sea breeze front, but one that propagates inlan more rapily. Lan breeze fronts are similarly weaker for offshore flow. Sea breeze fronts are stronger, but propagate inlan less rapily, with offshore flow; the same is true with onshore flow for lan breeze fronts. Both are stronger when the environmental lapse rate is steeper (i.e., static stability, proportional to the change in potential temperature with height, is low); both are weaker when the environmental lapse rate is smaller. This helps to explain why sea breeze fronts are stronger (an eeper) than lan breeze fronts: stability is lower over lan uring the ay, near peak heating, than over water at night. Conceptual Overview: Thickness Perspective A straightforwar interpretation of the sea, lake, lan, an other breeze circulations is obtaine from consieration of the hypsometric equation, obtaine by substitution of the ieal gas law into the hyrostatic equation an subsequent integration between two pressure surfaces pbot an ptop (noting that we also substitute a layer-mean virtual temperature to take it out of the integration): 2

3 R Tv = p ztop zbot g p This equation escribes the thickness (i.e., change in height) between two isobaric surfaces pbot an ptop as being irectly proportional to the layer-mean virtual temperature. Higher layer-mean virtual temperature results in greater thickness, implying lower zbot at pbot an higher ztop at ptop. Consier the case of a sea, lake, or river breeze. For a layer of limite (e.g., 100 hpa) epth near the surface, layer-mean virtual temperature an thickness are higher over lan than over water. This results in horizontal height graients on isobaric surfaces at the top an bottom of the layer, with lower heights over lan at the bottom an over water at the top of the layer. The resulting horizontal pressure graient force causes an acceleration towar lan at the bottom an towar water at the top of the layer. The overturning circulation is complete by ascent along the leaing ege of the sea breeze over lan an by escent along the back ege of the sea breeze over water. Conceptual Overview: Circulation Perspective We start with the three-imensional momentum equation, neglecting friction, applie on constant height surfaces: bot top v 1 = 2Ω v p + g ρ Here, v is the three-imensional win vector, Ω is the three-imensional angular velocity vector, an g is the gravitational vector. All other terms have their conventional meaning. Consier some close area, such as a box or circle, with area A. We wish to take the line integral of the momentum equation over this close area: v l = 2 1 ( Ω v) l p l + ρ g l Here, l is a line segment locally tangent to the perimeter of the close area A. Consier the left-han sie of this equation. From the chain rule, we can show that: ( v l) ( l) v = l + v The secon right-han term represents a change in the change of position along the perimeter of the close area following the motion or a change in velocity. It can be written as: v ( l) 1 2 = v v = ( v ) Consier the line integral of this aroun a close region, where the start an en points along the close area are ientical: the value of v 2 is equal at the start an en of the line integral. Thus, the 2 3

4 positive an negative contributions in the line integral must cancel, such that is has a net value of zero. Thus, v l = ( v l) Here C = v l, with C being circulation, quantifying flow rotation aroun the close area. C equals the average vorticity in the close area an is positive for counterclockwise rotation. The first right-han sie term of the line-integrate form of the momentum equation escribes the circulation contribution from the Earth s rotation. It can be shown that: = C A 2 ( Ω v) l = 2Ω Note that Ω on the left-han sie is a vector an Ω on the right-han sie is a scalar (= x 10-5 ra s -1 ). Ae is the projection of the close region s area on a horizontal plane intersecting the Equator; it is equal to A at the poles an equal to zero at the equator. The secon right-han sie term of the line-integrate form of the momentum equation is known as the solenoial term. It escribes circulation changes in a baroclinic atmosphere, where ensity (an temperature) varies on an isobaric surface. We can expan this term as follows: 1 ρ 1 ρ x y z e ( xi + yj zk) p l = i + j + k + Completing the ot prouct an simplifying the result, we obtain: 1 ρ x y z x + y + z = Finally, the thir right-han sie term of the line-integrate form of the momentum equation is a gravitational term. Expaning this term an using the efinition of the geopotential, we obtain: g l = p ρ ( gk) ( xi + yj + zk) = gz = For a close path, where flow aroun that path starts an ens at a common location, there is no net change in geopotential; all positive an negative contributions cancel. Thus, this term is zero. Consequently, the circulation equation is given by: C p A = 2Ω ρ This equation is Bjerknes circulation theorem an escribes the change in (relative) circulation following the motion: solenoial term (the absolute circulation) minus the circulation associate with the Earth s rotation. We now wish to consier the contributions from each in isolation. e Φ 4

5 Consier first the solenoial term; i.e., C p ρ Substituting with the ieal gas law, where p = ρrtv, we obtain: C p RTv p R Tv = ( p) Let us consier a vertical circulation with top an bottom surfaces foun along isobaric surfaces at the top an bottom of the sea breeze circulation. The line integral along these segments is zero by efinition; ( p) is zero for constant p. The vertical segments of this circulation are foun on opposite sies of the sea breeze circulation equiistant from the sea breeze front s leaing ege; we will assume ascening (escening) motion along the warm (col) sie of the front. On the warm sie of the front, the line integral is equivalent to a traitional integral from pbot to ptop, i.e., C up = ptop pbot R T v ( p) Letting Tv be approximate by a layer-mean virtual temperature, this equation becomes: C up = R T v warm p p bot top Similarly, on the col sie of the front, the line integral is equivalent to a traitional integral from ptop to pbot (since we start at the top of the layer an integrate ownwar along the line segment), i.e., C own = pbot ptop R T v p ( ) bot p = R Tv col ptop The total circulation change is the sum of these two components, i.e., C p = R p bot top ( T T ) v warm Because T v > T warm v, the net circulation change is positive, resulting in stronger ascent in the col warm air an stronger escent in the col air. For fixe pbot an ptop, given observations of the layer-mean virtual temperature on either sie of the sea breeze front one can compute the change in circulation ue to the solenoial term. Because circulation is the line integral of velocity about the perimeter of the close region, the resulting change in velocity aroun the close region can be compute by iviing the circulation change by the close region s perimeter. Note, however, that both circulation an velocity changes compute in this manner neglect Coriolis an friction. v col 5

6 Consier next the term relate to the Earth s rotation, i.e., C A 2 Ω The only contribution to this term results from the change following the motion in the projection of the close region s area onto a horizontal plane intersecting the Equator. Initially, Ae is ~0; a vertical plane of limite epth has negligible projection onto such a horizontal plane. However, as time progresses, the Coriolis force results in the win being eflecte to the right at both the top an bottom of the sea breeze circulation (particularly at higher latitues). Consier the case the Lake Michigan lake breeze. Start at the Milwaukee shoreline. The initial vertical circulation is entirely in the x-z plane. As the easterly near-surface flow procees inlan, it is eflecte to the right; conversely, as the westerly near-surface return flow aloft evolves, it is also eflecte to the right. This results in a circulation with a component in the horizontal (x-y) plane; i.e., Milwaukee to Menomonee Falls near the surface, Menomonee Falls back to Milwaukee in the return branch. Over time, this increases the projection of the close region s area onto the horizontal plane that intersects the Equator. Because of the leaing negative, this counteracts the solenoial term an results in a smaller increase in circulation following the flow. Consequently, sea an lan breeze front intensity is largest in the afternoon an preawn hours; later, the expecte circulation increase from continue warmer layer-mean virtual temperature over lan for the sea breeze is partially offset by the Coriolis force. Because of the Earth s curvature, this reuction is smaller at low latitues; the istortion of the close region into the x-y plane is smaller, an the projection of this area to the horizontal plane intersecting the Equator is also smaller. e 6