Answer_4-WXF - Page 1 of 8 MPO551 Homework #4...

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Unformatted text preview: Page 1 of 8 MPO551 Homework #4 Xiaofeng Wang (1) Weather analysis1 Left column: North America, 500mb isotachs (blue solid lines) and vorticity contours (red dotted line and shading for high vorticity) Right column: North America, Surface isobars (blue lines) and 1000 ­500mb thickness contours (isothermals; red dotted lines) Nov.09, 00UTC Nov.09, 12UTC 1 The 500mb and surface charts are from “NOAA Satellite and Information Service, Online Climate Data Directory” (website: Page 2 of 8 Nov.10, 00UTC Nov.10, 12UTC Nov.11, 00UTC Page 3 of 8 Nov.11, 12UTC Surface analysis in US, including isobars, fronts, winds, and other data in each observation station Nov.09, 00UTC Nov.10, 00UTC Nov.09, 12UTC Nov.10, 12UTC Page 4 of 8 Nov.11, 00UTC Nov.11, 12UTC The weather charts, at 12UTC, Nov.09, are used to qualitatively analyze QG vorticity, QG tendency and Omega. [A] QG Vorticity: (Analysis based on 500mb chart, at 12UTC, Nov.09) !!! !" = −! ∙ ∇!! − ! !! + !! ! !" !" The trough is located near Great Lakes. To the east of the trough, relative vorticity decreases and planetary vorticity increases along ! , so large relative vorticity and small planetary vorticity will be advected ! northeastward. So the advection term −! ∙ ∇!! > 0and−! !! = −! ∙ ∇!! < 0. These two vorticity advection ! ! terms affect the locate time derivative of !! oppositely. The advection of relative vorticity tends to increase local !! , forcing troughs to move eastward, while the planetary vorticity advection tends to decrease local !! , moving troughs westward. Similarly, to the east of the ridge, which is located near the west coast of United States, −! ∙ ∇!! < 0, so local ! !! will decrease with ridges moving eastward. And planetary term −! !! = −! ∙ ∇!! > 0, increasing !! and ! pushing ridges westward. For weather systems of synoptic scale, the term of relative vorticity advection dominates. Therefore, the total pattern of the troughs and ridges is moving eastward, evidenced by a sequence of 500mb weather charts shown on previous pages. [B] QG Tendency Equation: (Analysis based on 500mb chart and 1000 ­500mb thickness charts at 12UTC, Nov.09) Page 5 of 8 ∇2 + !!! ! !" ! !" ! ! = −!! ! ∙ ∇ ! 12 ! !!! !Φ ∇ Φ+! − − ! ∙∇ − ! !! !" ! !" !!! ! ∇+ !" ! !" ! 2 , != !Φ !" ! ∝  −! The first term on the right ­hand side is the advection of absolute vorticity. The second one is related to the rate of change with pressure of the horizontal thickness advection. !! In the second term on the right ­hand side, − !" (the thickness of the layer beneath 500mb) is proportional to layer ­averaged temperature, so − ! !" − !!! !Φ ! ∙∇ − ! ! !" ∝  − ! !" −! ∙ ∇! ! To the west of the ridges, which is in the regions of warm advection, wind blows northeastward from high !! thickness to low thickness, so −! ∙ ∇ − !" > 0. The wind blows more parallel to the isotherms at 500mb ! level than at surface level (shown on Page 6), so the magnitude of thickness/temperature advection is weaker !! on 500mb level. −! ∙ ∇ − !" decreases with height. ! For warm advection to the west of the ridges, such as the regions offshore near the west coast of United State, !! ! −! ∙ ∇ − !" > 0, − !" − ! ! !! ! !! ! ∙ ∇ − !" ! < 0, ∴  −! < 0, ! = !Φ !" > 0. So the warm advection beneath will build the ridges in the upper troposphere. !! ! For cold advection to the east of the troughs, −! ∙ ∇ − !" < 0, − !" − ! != !Φ !" ! !! ! !! ! ∙ ∇ − !" ! > 0, ∴  −! > 0, < 0. So the cold advection beneath will deepen the troughs in the upper troposphere. After comparing the troughs and ridges in 500mb charts at 00UTC and 12UTC, Nov.09, the phenomena of deepening and building are very evident for troughs and ridges, respectively. [C] Omega Equation: −! ∝  !! ! ∙ ∇ !! + ! , !" != !" ≈ −!"# !" Thermal wind relationship: ! ! = !!! − !!! ∝  !×∇(!), so thermal wind is parallel to the isothermals. ! To the east of troughs, ∇ !! + ! ~∇!! < 0, ! ! > 0, !" < 0, ∴  ! !!! !" ∙ ∇ !! + ! > 0, ! < 0, ! > 0, so upward motion will be further strengthened with troughs and lows moving eastward. Page 6 of 8 To the east of ridges, ∇ !! + ! ~∇!! > 0, ! ! > 0, !" < 0, ∴  ! !!! !" ∙ ∇ !! + ! < 0, ! > 0, ! < 0, so downward motion will be further strengthened with ridges and highs moving eastward. [D] Discussion of the development of the low pressure over the U.S. From 500mb charts, at 00UTC, Nov.09, the axis of the trough is located near 100°W, while at 00UTC, Nov.11, the axis is located 82.5°W. So the speed of the low pressure system is about 17.5/2=8.75 (degree/day). Given that latitude ! is 40 degrees and Earth radius is 6370 km, the speed of 8.75 degrees per day is equivalent to 8.6 m/s. Based on the equation analysis above and the 500mb charts, we know that the trough is deepening, low pressure system is strengthening, and on the chart at 12UTC, Nov.10, a cutoff low pressure appeared (shown in the following 500mb chart at 12UTC, Nov.10). With the gradually southward deepening of troughs, cold air in the trough is encircled by relatively warm air, and is cut off from the cold air in the north. Then a closed circulation forms, generating cutoff low. On 500mb and surface isobar charts at 00UTC, Nov.09, trough is to the west of the low pressure center at the surface. But with time elapsing, trough at 500mb level gradually catches up with low pressure center at the surface. So the vertical tilting is weakening, replaced by vertical alignment. From 500mb vorticity charts, we find that in the trough region, there are some finer stuctures with strong vorticity, especially near the regions of trough axis. And deeper troughs correspond to higher and more extensive vorticity, perhaps due to the stronger interaction of cold and warm air advection beneath the trough. From the surface analysis in US, we find that a significantly long cold front formed at 12UTC, Nov.09, and then swept the entire eastern US. At 12UTC, Nov.10, the catching up of cold front with warm front generated an occluded front near the low pressure center in Canada. On Nov.11, cold front left mainland US. 12UTC, Nov.10, 500mb, T and Φ contours In the regions of low pressure center and nearby, strong upward motion of air parcels will lead to more condensation of water vapor into water droplets. So, precipitation there will be stronger, evidenced by the following radar chart at 12UTC, Nov.09. In the southern part of US, a clear rain belt existed, corresponding well to the position of cold front in the surface chart. The front induced rain belt is more obvious in the radar chart at 00UTC, Nov.10. Page 7 of 8 (2) General characteristics of total cloud cover in the tropics Fig. 1 Visual Channel F C A E B D H G Fig. 2 Vapor IR Page 8 of 8 In tropics, large amount of solar radiation is absorbed by the surface (land and ocean). High surface temperature is responsible for more vigorous water evaporation and more instability of the air at the surface. These instable air parcels abundant with water vapor will generate more clouds in the process of upward motion. So, clouds cover most of the regions in tropics. From Frame A and C in Fig. 1, we find deep convections with corresponding more water vapor in Fig.2. In Frame F, there is a tropical cyclone. From Frame B in Fig.1, this frame encircles a region of cloud belt with relatively more deep convections in it. When it comes to the same region in Fig.2, more water vapor is concentrated here. So it is obvious that this region is part of inter ­tropical convergence zone (ITCZ). In ITCZ, convergence at the bottom and strong upward motion result in more water vapor concentration and more deep convections. Frame D and E show shallow convections (shallow cumulus clouds), which contribute little to water vapor concentration shown in Fig.2. After a comparison of Fig.1 and Fig.2, shallow convections spread everywhere in tropics, while deep convections is limited in certain regions. In Frame G, off the west coast of continent, stratocumuli, associated with large ­scale subsidence and low sea surface temperature (SST), cover most of the region. This region is under the descending branch of Walker Circulation with relatively dry air. The equator ­ward surface wind stress off the west coast of South America generates westward Ekman drift and attendant upwelling in this region. So the SST is low. The relatively high air temperature at high levels induced by large ­scale subsidence and low SST produce an inversion and thus a stable boundary layer. So in this background environment, deck of stratocumulus clouds with stable structure and weak convection forms. To the west of the stratocumulus region, stratocumulus clouds gradually deform into shallow cumulus clouds (Frame H), perhaps due to the combination of weaker upwelling of the ocean, higher SST and weaker inversion. ...
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This note was uploaded on 01/08/2012 for the course MPO 551 taught by Professor Zhang,c during the Summer '08 term at University of Miami.

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