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CHAPTER 4: ATMOSPHERIC TRANSPORT

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  1. CHAPTER 4: ATMOSPHERIC TRANSPORT • Forces in the atmosphere: • Gravity • Pressure-gradient • Coriolis • Friction to R of direction of motion (NH) or L (SH) Equilibrium of forces: In vertical: barometric law In horizontal: geostrophic flow parallel to isobars gp P v P + DP gc In horizontal, near surface: flow tilted to region of low pressure gp P v gf P + DP gc Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html

  2. Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz: P(x) P(x+dx) Pressure-gradient force Vertical area dydz Acceleration Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html 大氣壓力的分佈都是不均勻的,兩點間的壓力差除上距離就是壓力梯度(pressure gradient),如果氣壓梯度不等於零(也就是說兩點間氣壓不相等),就會產生氣壓梯度力(pressure gradient force),氣壓梯度力會把兩地間的空氣從氣壓高的一邊推向氣壓低的一邊,於是空氣流動起來,如果在一個靜止的平面上風向與壓力梯度互相垂直。

  3. Coriolis Force (Northern Hemisphere): • An air parcel (mass) begins to move from the Equator toward North Pole along the surface of the earth. • The parcel moves closer to the axis of rotation: r decreases • The parcel’s angular velocity is GREATER THAN the angular velocity of the earth’s surface at the higher latitude. It deflects to the right of it’s original trajectory relative to the earth’s surface. In the Southern Hemisphere, the parcel would appear to deflect to the left.

  4. We thus find in all cases that the Coriolis force is exerted perpendicular to the direction of motion, to the RIGHT in the Northern Hemisphere and to the LEFT in the Southern Hemisphere. Angular velocity of the Earth=2π/day Coriolis acceleration( c) = F/m = 2v sin(). Coriolis accelerationincreases as  (latitude) increases, is zero at the equator.

  5. 因為地球是一個旋轉的橢圓體,當壓力梯度存在時,氣流就開始由高壓區往低壓區運動,當風一旦起步向前,科氏力立刻產生,科氏力與運動的方向垂直,而且在北半球會將風拉向右邊(見下圖)。受到科氏力的影響,風向開始往右偏轉,風向偏轉的同時,科氏力也不斷地向右偏轉,也就是越來越轉到氣壓梯度力的反方向去。當風向被拉轉到與氣壓梯度力的方向垂直時,氣壓梯度力依舊存在,且其大小和方向都沒改變,但科氏力則變為與氣壓梯度力大小相等但方向相反,所以合力為零,沒有外力作用氣流就靠著慣性等速前進,由圖可以看出,在平衡狀態下,風向與等壓線保持平行,如只考慮壓力梯度力與地轉偏向力平衡,所得到的風稱為地轉風(geostrophic wind)。

  6. Vg geostrophic wind (m/s)  7.29 10-5 radian/s l latitude Dx distance (m) DP pressure diff. (N/m2) Vgeostrophic= • For air in motion, not on the equator, • Coriolis Force  Pressure gradient force • Air motion is parallel to isobars GEOSTROPHY The geostrophic approximation is a simplification of very complicated atmospheric motions. This approximation is applied to synoptic scale systems and circulations, roughly 1000 km. (It is easiest to think about measuring the pressure gradient at a constant altitude, although other definitions are more rigorous. ) DP/DX

  7. 地轉風和梯度風都忽略了地面摩擦力的影響,在高空中此一假設並不會產生太大的誤差,但在地面附近因為受到地面摩擦和熱力的影響,使得風速減慢,摩擦力的影響不可忽略。在地面上1-2km高度通常稱為行星邊界層 (planetary boundary layer, PBL)或大氣邊界層(見圖3-8),此層摩擦力是不能忽略的,行星邊界層以上的大氣稱為自由大氣(free atmosphere),在自由大氣中地面摩擦力則可忽略。

  8. 在行星邊界層內,風不僅受到氣壓梯度力和科氏力的制約,而且還受到地面摩擦力的作用。下圖說明行星邊界層內各個力量的平衡。如果沒有摩擦力,在氣壓梯度力Fp和科式力Fc平衡的條件下,風本來沿著等壓線方向等速前進(V),加入摩擦力的考量之後,因為摩擦力Ff作用的方向與風向相反,因此風速VR會減小,由於風速減小科式力也跟著減小為FCR,於是氣壓梯度力便超過被削弱了的科氏力,而把風拉向低氣壓一側。這時候科氏力為了與風向保持垂直,摩擦力為了與風向保持反向,它們都跟著風向一起向左偏轉。當磨擦力和科氏力的合力(FF+FCR)偏轉到和氣壓梯度力大小相等方向相反時,矛盾著的雙方力量對比又恢復到平衡狀態,這時候風便以穩定的速度和一定的交角斜穿等壓線,從高壓一側向低壓一側吹去。在行星邊界層內,風不僅受到氣壓梯度力和科氏力的制約,而且還受到地面摩擦力的作用。下圖說明行星邊界層內各個力量的平衡。如果沒有摩擦力,在氣壓梯度力Fp和科式力Fc平衡的條件下,風本來沿著等壓線方向等速前進(V),加入摩擦力的考量之後,因為摩擦力Ff作用的方向與風向相反,因此風速VR會減小,由於風速減小科式力也跟著減小為FCR,於是氣壓梯度力便超過被削弱了的科氏力,而把風拉向低氣壓一側。這時候科氏力為了與風向保持垂直,摩擦力為了與風向保持反向,它們都跟著風向一起向左偏轉。當磨擦力和科氏力的合力(FF+FCR)偏轉到和氣壓梯度力大小相等方向相反時,矛盾著的雙方力量對比又恢復到平衡狀態,這時候風便以穩定的速度和一定的交角斜穿等壓線,從高壓一側向低壓一側吹去。

  9. 這種有摩擦力參與,氣壓梯度力與科氏力、摩擦力保持平衡條件下所產生的風稱為摩擦風。摩擦力愈大,摩擦風的風速就愈小,向左偏轉和等壓線之間的交角也愈大。根據調查和統計,這種交角在海洋上為15~20度,在陸上一般達到30~45度,而在崎嶇不平的山地區域,甚至比這個角度更大。  在高低氣壓的區域,等壓線以高低氣壓中心為中心,呈環形閉合的。如果是在高空自由大氣裏,按照氣壓與風的關係,風幾乎平行等壓線的環旋轉,在北半球,高氣壓區以順時針方向流轉,在低氣壓區以逆時針方向流轉。如果是在地面,則按照氣壓與摩擦風的關係,在高氣壓區,風一面以順時針方向流轉,一面向周圍氣壓低的地方輻散開來,形成順時針外流的螺旋式氣流;而在低氣壓區,風一面以逆時針方向流轉,一面向低壓中心區域匯流輻合進去,形成逆時針內流的螺旋式氣流。這種有摩擦力參與,氣壓梯度力與科氏力、摩擦力保持平衡條件下所產生的風稱為摩擦風。摩擦力愈大,摩擦風的風速就愈小,向左偏轉和等壓線之間的交角也愈大。根據調查和統計,這種交角在海洋上為15~20度,在陸上一般達到30~45度,而在崎嶇不平的山地區域,甚至比這個角度更大。  在高低氣壓的區域,等壓線以高低氣壓中心為中心,呈環形閉合的。如果是在高空自由大氣裏,按照氣壓與風的關係,風幾乎平行等壓線的環旋轉,在北半球,高氣壓區以順時針方向流轉,在低氣壓區以逆時針方向流轉。如果是在地面,則按照氣壓與摩擦風的關係,在高氣壓區,風一面以順時針方向流轉,一面向周圍氣壓低的地方輻散開來,形成順時針外流的螺旋式氣流;而在低氣壓區,風一面以逆時針方向流轉,一面向低壓中心區域匯流輻合進去,形成逆時針內流的螺旋式氣流。

  10. Air converges near the surface in low pressure centers, due to the modification of geostrophic flow under the influence of friction. Air diverges from high pressure centers. At altitude, the flows are reversed: divergence and convergence are associated with lows and highs respectively Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html

  11. CLIMATOLOGICAL SURFACE WINDS AND PRESSURES(January) Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html

  12. CLIMATOLOGICAL SURFACE WINDS AND PRESSURES(July)

  13. 500 hPa (~6 km) CLIMATOLOGICAL WINDS IN JANUARY:strong mid-latitude westerlies

  14. 500 hPa (~5 km) CLIMATOLOGICAL WINDS IN JULYmid-latitude westerlies are weaker in summer than winter Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html

  15. TIME SCALES FOR HORIZONTAL TRANSPORT(TROPOSPHERE) 1-2 months 2 weeks 1-2 months 1 year Source: Jacob, http://acmg.seas.harvard.edu/people/faculty/djj/book/powerpoints/index.html