**CONCEPTUAL IMPLICATIONS OF THE SIMPLIFIED EQUATION OF CONTINUITY
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**A. THE PRINCIPLE OF DINE'S COMPENSATION
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Now, observations show that the vertical velocity at the Tropopause and at

the ground is nearly zero. Take a look at the above picture. Let's use the Equation of Continuity to say something about the midtropospheric vertical velocity field.

You need to rewrite the equation to solve for the vertical velocity at 500 mb. To do this you need to expand the term for the vertical divergence (right hand side of the expression) "in your mind". How would you do it?

Just like you would determine a temperature gradient between two points: the temperature at Point 2 minus the temperature at Point 1 divided by the distance between the two points. So, the term is expanded in the following manner

Now, solve ALGEBRAICALLY for the vertical velocity at 500 mb.

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**DISCUSSION QUESTION
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*What is the vertical velocity at 500 mb for the above example?
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But the equation works for the lower half of the diagram too!!

**DISCUSSION QUESTION
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*What is the horizontal divergence at the ground for the above example?
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You have conceptually developed one of the great principles applied in weather analysis and forecasting: **DINE'S COMPENSATION.
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**DINE'S COMPENSATION
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Upper tropospheric divergence tends to be "balanced" by mid-tropospheric upward vertical motion and lower tropospheric convergence.

Upper tropospheric convergence tends to be "balanced" by mid-tropospheric downward vertical motion (subsidence) and lower tropospheric divergence.*
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**DISCUSSION QUESTION
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*What sort of weather pheonmena (clouds, fair, precipitation etc.) does each "half" of the principle of Dine's Compensation imply?
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**B. THE PRESSURE TENDENCY EQUATION
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In reality, the balance implied by Dine's Compensation is never exact. Let's examine this notion in a simple-minded way, retaining our model of the troposphere which has a "divergent" upper half and a "convergent" lower half.

**DISCUSSION QUESTION
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*Can you think of two reasons why the upper tropospheric divergence (or convergence) almost always exceeds that in the lower troposphere?
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Because of this imbalance, upper tropospheric divergence is not quite balanced by lower level convergence and more mass leaves the top of the air column than enters the bottom. Substitution of the Equation of State into Equation of Continuity, and making synoptic-scaling assumptions yields another very important equation. This equation essentially provides the answer to the question: How do pressure changes (in this context) at sea-level occur (of course, the general expression relates to the bottom of an air column no matter where the base of the air column is found).