Atms 4320 / 7320 – Lab 5 Using the Kinematic Method in Estimating Vertical Motions

Kinematic  the study of atmospheric flows without regard to the forces that bring them about. Vertical motions in the atmosphere are important. These are the result of unbalanced flows, and the resulting divergence/convergence patterns that are induced.

Using the Kinematic Method in Estimating Vertical Motions We can’t measure vertical motions directly, so we must calculate them. Recall from Thermo. that vertical motions are the result of small differences between the pressure gradient force term and gravity (when examining hydrostatic balance). Vertical motions are also indicators of meridional circulations, or “secondary circulations” that result from unbalanced flow.

Using the Kinematic Method in Estimating Vertical Motions Example: straight jet max:

Using the Kinematic Method in Estimating Vertical Motions In thermo. we talked about the relationship between  (vertical motion in the x,y,p,t coordinate system) and w (x,y,z,t). There are various ways to calculate vertical motion. We can examine our fundamental equations, and simply solve for w:

Using the Kinematic Method in Estimating Vertical Motions Examples: Continuity equation 1st Law of Thermodynamics

Using the Kinematic Method in Estimating Vertical Motions These have the advantage of being computationally straightforward (‘the quick and dirty” calculation), and easy to interpret, i.e., using the first law, vertical motion is the result of temperature advections, or diabatic heating, and modulated by the Stability field.

Using the Kinematic Method in Estimating Vertical Motions Or we can combine all the basic (primitive) equations to get an Omega equation:

Using the Kinematic Method in Estimating Vertical Motions Using the Continuity equation in x,y,p,t coordinates, we get simply: Then separate into horizontal and vertical components, Integrate w/r/t pressure, and:

Using the Kinematic Method in Estimating Vertical Motions Thus we get an equation that states that the vertical motion at any level is the result of the integrated divergence/convergence fields occurring below that level. This “Kinematic Method” is used quite often to calculate vertical motion.

Using the Kinematic Method in Estimating Vertical Motions Let’s examine, then typical vertical motion and divergence/conv ergence profiles (Walthorn and Smith, 1995):

Using the Kinematic Method in Estimating Vertical Motions Fig a. is vorticity, Fig b, is vortadv, temp adv, Fig. c is omega and S, and Fig. d is S times omega and Latent heating

Using the Kinematic Method in Estimating Vertical Motions Various simplifications of the Kinematic Method.

Using the Kinematic Method in Estimating Vertical Motions Vertical integral implies that error in our calculation builds up as we integrate upward due to 1) numerical error in estimating divergence (derivatives), and 2) error inherent in measuring the winds.

Using the Kinematic Method in Estimating Vertical Motions The O’Brien Correction: J.J. O’Brien (1970 Jour. Appl. Met. pp ) Solves this problem by assuming that all vertical motion and divergence at the upper boundary is in “error” since vertical motion should go to zero at tropopause height.

Using the Kinematic Method in Estimating Vertical Motions This “error” in the divergence and vertical motion fields is then distributed linearly or quadratically along the whole profile in an amount proportional to the distance from the bottom boundary. The O’Brien Correction is used by most investigators who use the kinematic method to calculate vertical motion.

Using the Kinematic Method in Estimating Vertical Motions The End!