Lab 6 – Atms 4320 / 7320
On the use of isentropic maps in weather analysis and forecasting I.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Concept of Isentropic Analysis and interpretation I. “SLU” method. We’ll examine this week, and next week we’ll look at SUNYA method.
Supplementary reading: Market et al. (2000) NWD Dec. pp. 31 – 37.
It has become commonplace to examine the atmosphere in x,y, coordinates.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
If atmosphere is hydrostatic and adiabatic, then as we said in Atms 4310 / 7310 potential temperature is a conserved quantity.
If so, then parcels will follow lines of constant , or we must consider those parcels to be “tied” to that surface!
0dt
d
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Thus, we can:
1) examine the motions of that surface with time to infer vertical motions, and
2) examine the wind fields and infer “upglide” and “downglide” of air parcels.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
This is the “elevator – escalator” concept of looking at atmospheric motions. Recall, we stated that vertical motions are important to examine in synoptics. They are part of the secondary atmospheric circulations.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Let’s start with , which is vertical motion in x,y,p coords.
Ok, in x,y, coords we express as (we’ll see this later when we talk of coord transformations).
z
pwpV
t
p
dt
dphh
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
The equation
(1) (2) (3)
p
dt
dppV
t
p
dt
dphh
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Thus, vertical motions are the result of:
Term 1: The change in the location of a pressure surface.
Term 2: The isentropic “upglide” or advection of P on .
+ pressure advection +
0t
p
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Term 3: Diabatic Heating (product of Stability and diabatic heating, static stab modulates):
stabilityor
pdt
dor
p
1
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
It had been assumed that terms 1 and 3 cancelled, however, we can show very easily that this is not so:
Start with Continuity in x,y, .
1
0
pS
where
SVSSt
inv
invinvinv
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Integrate from level 1 to level 2.
0
0
2
1
2
1
2
1
2
1
2
1
dt
dSdVSdS
t
and
dSdVSdSt
invinvinv
invinvinv
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Aha, now rearrange and look at new LHS:
012
2
1
t
p
t
pdVS
dt
dS invinv
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Then insert into our initial equation and:
Viola!
12
2
1
t
p
t
pdVSpV
t
p
dt
dpinvhh
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
If we choose level 1 to be our level of interest and level 2 to be above level 1, then the pressure tendency of the above surface will reflect diab. Heating.
12
2
11
1
t
p
t
pdVSpV
t
p
dt
dpinvhh
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Thus, term 1 cannot completely cancel term 3. Can show the same thing by choosing level 1 to be below you and level 2 to be your level of interest. Then bottom surface will reflect diab. Heating. Typically, though we want to see integrated diabatic heating throughout troposphere.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
The equation:
So there is also that “pesky” integrated stability flux term.
12
2
12
2
t
p
t
pdVSpV
t
p
dt
dpinvhh
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
How to get term 1: Qualitatively?
Simply examine two maps of pressure on a theta surface and infer the change.
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
How to get term 2: Qualitatively?
How do you get temperature advection Qualitatively?
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
Term 3: can calculate as well, or infer.
Recall for heating:
Cooling:!
0
0
thendt
d
ifthen
S
Since
!
0
0
thendt
d
ifthen
S
Since
Lab 6 - On the use of isentropic maps in weather analysis and forecasting I.
The end!
Assignment time!
Recommended
