The purpose of this thread is to provide a basic introduction to the concept of isentropic surfaces as well as how to analyze isentropic surface data.
Updates:
2011-12-19 - Added case study/verification of example forecast
Isentropic means "same entropy". It can be shown that entropy is conserved when potential temperature doesn't change. Thus, isentropic surfaces are surfaces of constant potential temperature (theta). You can get a 3D picture of the atmosphere by analyzing different isentropic surfaces since potential temperature almost always increases with height, but for the purposes of analyzing synoptic weather patterns, it can be assumed to always increase with height (see sidebar at bottom).
I know of the following sites that provide isentropic analyses or forecasts:
Most of these sites display the isentropic surfaces similarly. They usually contain pressure, wind vectors, and either moisture content or theta-e. Pressure gives a sense of height. Why are these fields shown? They show large scale lift and moisture transport. Try picturing the following scenario, which is universally typical of isentropic surfaces: There is a general meridional (north-south) temperature gradient on the globe, with warmer temperatures towards the equator. Since potential temperature increases with height, isentropic surfaces slope upwards towards cold air (when looking along a constant height or constant pressure surface). In the absence of latent heat release due to phase changes of water, air parcels are restricted to isentropic surfaces. Thus, when restricted to a given isentropic surface, the vertical motion of an air parcel can be diagnosed from its horizontal motion along that surface. Thus, to follow the parcel, follow the surface. You can thus identify areas of synoptic scale vertical motion quite easily by looking for areas in which the horizontal winds are along the gradient of pressure on an isentropic surface. By looking at the amount of moisture present at a given location, you can also get a sense of the amount of moisture transport taking place as well.
Let's take a look at an example isentropic surface plot. Open up this image. It shows a GFS forecast of the 301 K isentropic surface valid 12Z 19 December 2011. Pressure is shown in blue. I've outlined illustrative areas.
Now let's add moisture back into the picture (this image). Mixing ratio is plotted in green. When there is a strong moisture gradient in the absence of a pressure gradient, moisture transport is indicated. Look in the light blue area from the previous image (most of Texas). Note the strong moisture gradient with winds perpendicular to the gradient. There may not be much isentropic lift occurring here, but there is strong moisture transport! You can see the nose of the moisture plume extend all the way northeastward towards Chicago. The shape of it stands out quite well, too. However, look towards the red area where strong descent was occurring. There is a moisture gradient here, but it is coincident with a pressure gradient. This is perhaps one of the pitfalls of isentropic surfaces - vertical sampling. The moisture gradient here is likely more a sign of the vertical gradient of moisture than of strong horizontal dry air advection. It still shows that parcels traveling along this surface will bring drier air along with them as they ride down the 301 K surface into western Texas, however, since moisture can be considered to be conserved for large scale descent like this.
-----------------------------------------------------------------------
Updated 2011-12-19 with verification of the previously mentioned forecast
-----------------------------------------------------------------------
The 12Z isentropic surface analyses are in, so we can verify the GFS's forecast from three days ago. Check the links below for images for the different surfaces. These were all taken from the COD site.
-280K
-285K
-290K
-296K (the COD site offers 294K and 296K, but not 295K)
-300K
-305K
-310K
It should make sense that the 280K surface shows the highest pressure values because it is the lowest of the available isentropic surfaces. Notice how parts of SW TX and into Mexico are blacked out. That's because the 280 K surface drops below the terrain there, meaning the surface potential temperature is above 280 K there. Let's analyze each of these. Note that I'll be focusing on the southern/southwestern US even though there are interesting features in other areas on these maps.
But Jeff, there will be clouds, precip, rain, and storms in some of these areas! Potential temperature won't be conserved in many of these circumstances! Isentropic surfaces are USELESS!
It's true that the preceding discussion was based on the assumption that an air parcel maintained its potential temperature. It's also true that water phase changes screw up the thermodynamics by adding or removing latent heat to/from a parcel. However, the effect that phase changes have on temperature are well known. To account for this, some of the above sites also show equivalent potential temperature (theta-e, see sidebar) on the isentropic surfaces. However, even if they don't, you can still account for changes in potential temperature on an isentropic surface. Most of the time, you will be concerned with areas where unsaturated parcels are expected to saturate. So this will occur in areas with lift or strong convective activity. But don't fret! When the potential temperature of a parcel of air changes, it simply jumps to another nearby isentropic surface! You may not be able to view this nearby isentropic surface, but adjacent isentropic surfaces will tend to have the same shape and slope, so it's easy to estimate what will happen on those nearby isentropic surfaces. Not to mention, since potential temperature increases with height, then increasing the potential temperature of an air parcel means it will be lifted along an even steeper slope. Unfortunately, you may not be able to determine exactly when/where a parcel will saturate using isentropic surface data unless you have RH or, what some maps include, condensation pressure deficit. Condensation pressure deficit is the distance (in pressure units) a parcel must rise to become saturated. Earl Barker's site contains this data, but it is the one of the four listed that does. Therefore I won't go into it much further. I will only add that lower condensation pressure deficits imply that a parcel is closer to becoming saturated. Thus it won't take much more lift to cause it to jump isentropic surfaces.
Hopefully you enjoyed this introductory tutorial to analyzing isentropic surfaces. Please post questions in response to this thread. Other experts, make sure to correct me if I was wrong about something or mislead people.
-------------------Sidebars--------------------
-When might potential temperature not increase with height?
It would help to use a skew-T to understand vertical gradients of potential temperature. The lapse rate of actual temperature would have to exceed the dry-adiabatic lapse rate, which is about 9.8 K/km in the troposphere, in order for potential temperature to decrease with height. Similarly, if the temperature lapse-rate were exactly 9.8 K/km, then potential temperature would be constant with height. This tends to occur in the PBL during the hottest part of days during the warm season. In these situations, it's not uncommon for a very shallow super-adiabatic layer to form within the lowest 100 m or so of the surface. In this layer, the potential temperature would decrease with height. However, super-adiabatic is an absolutely unstable stratification. When such a layer forms, it will quickly stabilize by rising due to buoyant forces. However, additional external forcing will cause the layer to form again. Such external forcing usually comes in the form of very strong heating from the sun coupled with strong sensible heat flux at the surface. This sounding shows a well-mixed PBL in which theta is approximately constant with height and a super-adiabatic layer very near the surface.
-What is equivalent potential temperature?
Equivalent potential temperature, or theta-e, accounts for the latent heat that would be added to a parcel of air through phase changes due to condensation of water vapor. The equivalent temperature of an air parcel is the temperature it would attain if all of the water vapor in it condensed and all of the latent heat went directly into heating that parcel. The equivalent potential temperature is just the equivalent temperature of a parcel of air brought down (or up) to 1000 mb. While potential temperature is conserved only for unsaturated vertical motion, and wet-bulb potential temperature is conserved for only saturated vertical motion, equivalent potential temperature is conserved for both saturated and unsaturated vertical motion. Thus the equivalent potential temperature of a parcel is the same throughout all vertical motions! It only changes when diabatic heating from radiation, horizontal advection, or phase changes occurs.
Although the stability of a parcel can be written in terms of theta-e, what's different is that unstable stratifications occur when theta-e decreases with height, which is much more common than potential temperature decreasing with height.
Updates:
2011-12-19 - Added case study/verification of example forecast
Isentropic means "same entropy". It can be shown that entropy is conserved when potential temperature doesn't change. Thus, isentropic surfaces are surfaces of constant potential temperature (theta). You can get a 3D picture of the atmosphere by analyzing different isentropic surfaces since potential temperature almost always increases with height, but for the purposes of analyzing synoptic weather patterns, it can be assumed to always increase with height (see sidebar at bottom).
I know of the following sites that provide isentropic analyses or forecasts:
- The COD site (weather.cod.edu -> Weather Analysis Tools -> Analysis Data -> Isentropic Maps under Upper-air products)
- The University of Oklahoma - Oklahoma Weather Lab - HOOT site
- Iowa State's cumulus site (Numerical models -> Fcst Theta Sfcs (NAM))
- Earl Barker's site (http://www.wxcaster.com/isentropic.htm)
Most of these sites display the isentropic surfaces similarly. They usually contain pressure, wind vectors, and either moisture content or theta-e. Pressure gives a sense of height. Why are these fields shown? They show large scale lift and moisture transport. Try picturing the following scenario, which is universally typical of isentropic surfaces: There is a general meridional (north-south) temperature gradient on the globe, with warmer temperatures towards the equator. Since potential temperature increases with height, isentropic surfaces slope upwards towards cold air (when looking along a constant height or constant pressure surface). In the absence of latent heat release due to phase changes of water, air parcels are restricted to isentropic surfaces. Thus, when restricted to a given isentropic surface, the vertical motion of an air parcel can be diagnosed from its horizontal motion along that surface. Thus, to follow the parcel, follow the surface. You can thus identify areas of synoptic scale vertical motion quite easily by looking for areas in which the horizontal winds are along the gradient of pressure on an isentropic surface. By looking at the amount of moisture present at a given location, you can also get a sense of the amount of moisture transport taking place as well.
Let's take a look at an example isentropic surface plot. Open up this image. It shows a GFS forecast of the 301 K isentropic surface valid 12Z 19 December 2011. Pressure is shown in blue. I've outlined illustrative areas.
- Let's look at the red outlined area in Texas, southeast New Mexico, and northern Mexico. Note the large angle between the wind vectors and the isobars. With lower pressure indicating higher heights to the west and higher pressure indicating lower heights to the east, this shows that the 301 K surface is sloping downward as one heads east across W TX. The wind directions thus imply strong isentropic descent is occurring.
- Now look just to the east of the previous area, into the rest of Texas (shaded light blue). There is a strong low-level jet stream coming off the Gulf. However, note the general absence of a pressure gradient, indicating little slope to the isentropic surface. The wind vectors are pretty much perpendicular to the gradient, so with a motion from lower to higher pressure, this indicates isentropic lift. However, it isn't very strong.
- Look now to the north in the green boxed area. There is a moderate gradient of pressure suggesting the 301 K surface is sloping downward from northwest to southeast. The winds are at about a 30 - 45 degree angle to the gradient in this region, but the winds aren't that strong. Thus, there is weak isentropic descent occurring here.
- Finally, look at the light brown circled region along the Atlantic coast. There is a noticeable pressure gradient, as well as strong winds in this area. However, the winds are pretty much parallel to the pressure gradient, indicating that there is no lift occurring here.
Now let's add moisture back into the picture (this image). Mixing ratio is plotted in green. When there is a strong moisture gradient in the absence of a pressure gradient, moisture transport is indicated. Look in the light blue area from the previous image (most of Texas). Note the strong moisture gradient with winds perpendicular to the gradient. There may not be much isentropic lift occurring here, but there is strong moisture transport! You can see the nose of the moisture plume extend all the way northeastward towards Chicago. The shape of it stands out quite well, too. However, look towards the red area where strong descent was occurring. There is a moisture gradient here, but it is coincident with a pressure gradient. This is perhaps one of the pitfalls of isentropic surfaces - vertical sampling. The moisture gradient here is likely more a sign of the vertical gradient of moisture than of strong horizontal dry air advection. It still shows that parcels traveling along this surface will bring drier air along with them as they ride down the 301 K surface into western Texas, however, since moisture can be considered to be conserved for large scale descent like this.
-----------------------------------------------------------------------
Updated 2011-12-19 with verification of the previously mentioned forecast
-----------------------------------------------------------------------
The 12Z isentropic surface analyses are in, so we can verify the GFS's forecast from three days ago. Check the links below for images for the different surfaces. These were all taken from the COD site.
-280K
-285K
-290K
-296K (the COD site offers 294K and 296K, but not 295K)
-300K
-305K
-310K
It should make sense that the 280K surface shows the highest pressure values because it is the lowest of the available isentropic surfaces. Notice how parts of SW TX and into Mexico are blacked out. That's because the 280 K surface drops below the terrain there, meaning the surface potential temperature is above 280 K there. Let's analyze each of these. Note that I'll be focusing on the southern/southwestern US even though there are interesting features in other areas on these maps.
- 280 K: there is an interesting large-scale convergence pattern over the southwest United States. Note how southeasterly, southwesterly, and northerly flow seem to meet up along two boundaries, one running NW-SE across the Colorado Plateau area, the other running SW-NE across TX/OK/KS (where it becomes diffuse). The boundaries seem to intersect near the TX-NM border. There is a notable pressure gradient there, so you should infer that interesting weather is going on there. Knowing that isentropic surfaces slope towards cold air, you should be able to infer some degree of isentropic lift near or along that pressure gradient. It's hard to tell since there are few, if any, wind barbs within the pressure gradient, though. It should be pretty obvious that there is a front there, given the inferred temperature contrast.
- 285 K: The pressure gradients seem stronger in the same area at 285 K than at 280 K. The V-shaped notch of cold air in CO/NM is still present. Notice, however, how the pressure gradient that was oriented SW-NE on the 280 K surface seems to have twisted slightly and moved west on the 285 K surface. This is a sign of a temperature inversion across W TX/E NM/OK PH. Notice how the 925 mb contour barely moves between the 280 K and 285 K surfaces. That means that the potential temperature changes from 280 K to 285 K in a very thin layer around 925 mb. Note across the rest of Texas also there is a slight moisture gradient in the absence of much of a pressure gradient. Thus, although there is little, if any, isentropic lift there, there is certainly moisture transport occurring.
- 290 K: The pressure gradient remains near the NM-TX border, with the values indicating still the presence of very weak lapse rates (maybe not a full-out inversion at this height). A moisture tongue is quite visible given the strong moisture gradient over the western Gulf of Mexico, eastern Texas, and northward. You also see a strong pressure and moisture gradient in NW Mexico. This is a sign of the cold, dry upper-level low. Evidence for the dry punch associated with this low is corroborated by a look at water vapor satellite. Given the sparsity of observations in Mexico, it is not surprising that the analysis is a little off, especially in terms of the gradient.
- 296 K: The moisture tongue and dry punch are both very obvious at 296 K. There is also evidence of some weak to moderate isentropic lift across southern and eastern Texas as well as parts of eastern Oklahoma and northern Arkansas.
- 300 K: The 300 K surface looks qualitatively very similar to the 296 K surface. What you should notice, however, is how, even though the moisture and pressure patterns are the same, the pressure and mixing ratio are decreasing since the 300 K surface is higher than the 296 K surface.
- 305 K: Other than the area of interest near the trough/cyclone in the southern US, we're starting to get above significant weather features now. However, the moisture tongue is still quite visible and there is some moderate isentropic lift occurring across much of Texas. Strong pressure gradients remain across Mexico, continuing to show that cold, dry punch working around that trough.
- 310 K: The 310 K surface continues the trend of nearby surfaces looking similar to each other. Isentropic lift is evident across all but the PH and far northern parts of Texas. There is a hint that the moisture tongue is somewhat bifurcated since there is a local minimum across northern Texas.
But Jeff, there will be clouds, precip, rain, and storms in some of these areas! Potential temperature won't be conserved in many of these circumstances! Isentropic surfaces are USELESS!
It's true that the preceding discussion was based on the assumption that an air parcel maintained its potential temperature. It's also true that water phase changes screw up the thermodynamics by adding or removing latent heat to/from a parcel. However, the effect that phase changes have on temperature are well known. To account for this, some of the above sites also show equivalent potential temperature (theta-e, see sidebar) on the isentropic surfaces. However, even if they don't, you can still account for changes in potential temperature on an isentropic surface. Most of the time, you will be concerned with areas where unsaturated parcels are expected to saturate. So this will occur in areas with lift or strong convective activity. But don't fret! When the potential temperature of a parcel of air changes, it simply jumps to another nearby isentropic surface! You may not be able to view this nearby isentropic surface, but adjacent isentropic surfaces will tend to have the same shape and slope, so it's easy to estimate what will happen on those nearby isentropic surfaces. Not to mention, since potential temperature increases with height, then increasing the potential temperature of an air parcel means it will be lifted along an even steeper slope. Unfortunately, you may not be able to determine exactly when/where a parcel will saturate using isentropic surface data unless you have RH or, what some maps include, condensation pressure deficit. Condensation pressure deficit is the distance (in pressure units) a parcel must rise to become saturated. Earl Barker's site contains this data, but it is the one of the four listed that does. Therefore I won't go into it much further. I will only add that lower condensation pressure deficits imply that a parcel is closer to becoming saturated. Thus it won't take much more lift to cause it to jump isentropic surfaces.
Hopefully you enjoyed this introductory tutorial to analyzing isentropic surfaces. Please post questions in response to this thread. Other experts, make sure to correct me if I was wrong about something or mislead people.
-------------------Sidebars--------------------
-When might potential temperature not increase with height?
It would help to use a skew-T to understand vertical gradients of potential temperature. The lapse rate of actual temperature would have to exceed the dry-adiabatic lapse rate, which is about 9.8 K/km in the troposphere, in order for potential temperature to decrease with height. Similarly, if the temperature lapse-rate were exactly 9.8 K/km, then potential temperature would be constant with height. This tends to occur in the PBL during the hottest part of days during the warm season. In these situations, it's not uncommon for a very shallow super-adiabatic layer to form within the lowest 100 m or so of the surface. In this layer, the potential temperature would decrease with height. However, super-adiabatic is an absolutely unstable stratification. When such a layer forms, it will quickly stabilize by rising due to buoyant forces. However, additional external forcing will cause the layer to form again. Such external forcing usually comes in the form of very strong heating from the sun coupled with strong sensible heat flux at the surface. This sounding shows a well-mixed PBL in which theta is approximately constant with height and a super-adiabatic layer very near the surface.
-What is equivalent potential temperature?
Equivalent potential temperature, or theta-e, accounts for the latent heat that would be added to a parcel of air through phase changes due to condensation of water vapor. The equivalent temperature of an air parcel is the temperature it would attain if all of the water vapor in it condensed and all of the latent heat went directly into heating that parcel. The equivalent potential temperature is just the equivalent temperature of a parcel of air brought down (or up) to 1000 mb. While potential temperature is conserved only for unsaturated vertical motion, and wet-bulb potential temperature is conserved for only saturated vertical motion, equivalent potential temperature is conserved for both saturated and unsaturated vertical motion. Thus the equivalent potential temperature of a parcel is the same throughout all vertical motions! It only changes when diabatic heating from radiation, horizontal advection, or phase changes occurs.
Although the stability of a parcel can be written in terms of theta-e, what's different is that unstable stratifications occur when theta-e decreases with height, which is much more common than potential temperature decreasing with height.
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