Metr 430

 NAME ________________________________________

Fall 2012

 

Lab 1: Estimating the Temperature Change Due to Advection

For this exercise, you will need to estimate the contribution to the local change in temperature that advection would make. In this exercise you will learn how to do that, but also will make a 1 hour "forecast" of the temperature at San Francisco in which advection was the only factor. To do this, the simplified Temperature Tendency Equation is written in a form that the infinitesmal derivatives can be estimated by their point values. Their point values can be estimated using an method called "Finite Differences" that we will explore another time..

I. Rewriting the temperature tendency equation into a useful form.

 Term A

 =

 Term B

 +

 Term C

Fixed Location

 

 

Temperature Change at Weather Station

 

 

 =

 

Temperature Changes Experienced by Air Parcels Themselves

 +

 Advection

 

 

Temperature Changes Due to Import of Air Parcels of Different Temperature Replacing Initial Air Parcels

(Equation 1)

First we can simplify the equation above if we can assume that the air parcels do NOT experience temperature changes as they move from place to place. In that case the temperature change observed at the weather station will be entirely due to temperature advection

Rewriting the equation (1) with the simplifying assumption that Term B=0 yields

 

(Equation 2)

All that was done to obtain (2) was to multiply (1) through by the time interval.

II. A Simple Forecast Equation

Now, let's assume that you need to answer the question "what will the temperature advection contribution to the local temperature change experienced over 1 hour be?" For the purposes of this exercise, you will make the reasonably good assumption that the temperature advection will be unchanging across the 1 hour period. This is an example of "finite differencing" or making the assumption that the gradient of a quantity measured by a derivative is estimated well by taking the difference of the two observations on either side of the interval.

∆T = Tf - Ti

(Equation 3)

Well, first you would need a simple forecast equation. Solving for the final Temperature in Equation (3) and substituting Equation (2) we get.

 (Equation 4)

where Ti is the initial temperature at San Francisco and Tf is the "forecast" temperature.

III. Concept Map

How do you go about estimating the temperature advection during the 1 hour period we are considering?

 

 Question 2: Write up a simple concept map of what you need to know in order to answer the question "how much will the temperature change at San Francisco over the 1 hour period?" (Hint, you will need to list the things in equations 2a and 3 that you need to find)

Do that on the back of this sheet.

 

Of course, you need to obtain the surface streamlines and isotherms for the present time. Once you do that, you need to sketch a streamline that intersects your forecast station. This is the line or curve along which the distance s will be marked off. Incidentally, on synoptic charts a reasonable distance overwhich to evaluate the temperature gradient to estimate the advection is 100 miles (or 100 km). Remember to keep all the units consistent.

But, this is done for you in Figure 1.

Fig. 1. Chart showing the portion of a streamline segment that is used to calculate the contribution of the temperature advection to the temperature change at the observer's location. Assume the observer is at San Francisco. The wind is shown as a vector, with the air parcel at A shown moving towardst he observer. The distance is 100 km between location A and San Francisco and the wind speed is 100 km/h.

Next, highlight the portion of the streamline that intersects the station back 100 miles (100 km) (a simple way to mark of this distance will be discussed in class). In figure 1, the streamline extends from the observer at San Francisco to point A.

The temperature gradient is evaluated (finite differenced) this way:

where T2 is the temperature furthest downwind on the segment (in this case, at the forecast station) and T1 is the temperature furthest upwind on the segment. The temperatures are estimated by simply reading directly off of the isotherms. For the example shown in Fig. 1, T2 would be the temperature at San Francisco (observer) (15) and T1 would be the temperature at A (30).

Next, the result of the last step is multiplied by the average wind speed on the segment (you can get this by reading the wind barbs plotted on the chart and getting an average value for the region of the segment of streamline that you are considering). For the example in Fig. 1, note that the average wind would be 100 km/ hr. Make sure the units are consistent. If the distance is in miles, then the wind speed needs to be in miles per hour. If the distance is in km or m, then the wind speed should be in km/h or m/s.

 

Question 3: Rewrite the equation in Section 1 above using the correct calculus format.

 

Question 4. Using Fig 1, compute the temperature change due to advection and the resulting forecast temperature at the end of the hour period considered, assuming a (ridiculous) wind speed of 100 km/h.

Question 5. Using Fig 1, write a simple "rule" for visualizing the nature of the temperature advection on, say, a surface weather map. (Example: if air moves across the isotherms from lowered value isotherms to higher value therms, I expect there to be (cold/warm) (choose one based upon the example here) temperature advection.)

Question 6.

(a) On the map distributed in class, determine the nature (sign) of the (thickness) temperature advection at A and B.

(b) On the same map, plot a blue arrow for every intersection of streamline and (thickness) temperature contour in cold advection areas and a red arrow for every intersection in warm advection areas. (See Example)