Performing calculations of thermodynamic processes in the atmosphere is often cumbersome Furthermore graphical representation of the vertical profiles for temperature and humidity as measured by radiosonde require consistency. For both applications thermodynamic diagrams are a very powerful solution in this clip I will explain how these diagrams are constructed and present a few elementary applications.
From the equation of state we know that pressure volume and temperature are the quantities that define the state of the atmosphere of these three pressure and temperature are of particular interest and they form the basis of a thermodynamic diagram.
Let's start with the temperature which is plotted along the horizontal axis Next comes pressure which is plotted along the vertical axis
if we have temperature then we can draw ice of therms that is lines of equal temperature. These will appear as vertical lines if we have pressure we can draw isobars that is lines of equal pressure these will appear as horizontal lines.
Drawing many more I saw will give us the base of the diagram
in meteorology the vertical axis usually represents height above the surface.
It implies that pressure decreases as you move upwards in the diagram.
Also note that pressure is plotted logarithmically where the distances between successive isobars are increasing as we go up through the atmosphere the name of the diagram is taken from the two axes and this is called the T. log P. diagram.
For practical purposes we need to make a small change in this diagram the isobars will remain the same but the iso firms need to be somewhat tilted to the right so that they appear skewed. So vertical eyes of therms now appear at a certain angle in the diagram the resulting diagram still has the same temperature axis but the eyes of therms all run from the bottom left to the top right this diagram is called the skew T. log peak diagram using this diagram we will proceed to draw additional Iceland.
Using temperature and pressure the following equation can be used to calculate the potential temperature think. It is now possible to calculate feta at each point in the diagram if we connect all the points with the same value of feta in the diagram we get a line along this line feta has a constant value of twenty degrees Celsius.
Such lines are called dry idea bats which are characterized by a constant value of feta.
The diagram now looks like this when many more dry Adya bats have been added to it the green lines sloping from top left to bottom right are the dry at the abouts.
The value of the potential temperature feta in degrees Celsius is given in green along the six hundred hectare Pascoe isobar You can also find the value of feta by following the dry addy about down to the one thousand hectare Pascal level as shown for the ten degrees Celsius dry addy of at.
We can also add information about humidity to this diagram.
For each temperature there is a unique value for the saturation water vapor pressure S. Using the definition of the mixing ratio W. and the value for pressure which is also known for each point on the diagram it is now possible to calculate the saturation mixing ratio W. S..
In the diagram this is indicated by the blue dashed lines also running from the bottom left to the top right the value of the mixing ratio in grams per kilogram is given in blue along the nine hundred hectare Pascale ice of our
it is also possible to draw the saturated addy about in the diagram using a similar process.
So the fifth and last set of lines in the diagram are the light green lines running from the bottom right to the top left.
Noticed the highlighted line at fifteen degrees Celsius the values can be read between seven hundred and six hundred hectare Pascale isobars this is also the temperature if you follow the line of the saturated Addie about all the way down to the one thousand had Tabasco level
Please note that the dry and the saturated Addie about have a distinctly different slope near the surface but run almost parallel high up into the atmosphere. The reason for this is the lack of water vapor at very high altitudes here there is not much water vapor left to get dense so dry and saturated Addie about are almost the same.
Now that our diagram is ready it is possible to incorporate the observations of temperature and dew point from many pressure levels into the diagram as we do this to read curves appear.
The red curve on the right is the temperature curve and the dashed line on the left represents the dew point temperature note that the dew point curve is always to the left of the temperature curve since the dew point cannot be higher than the temperature. When the two curves are far apart the dew point is much lower than the temperature and the air is dry when the two curves are close together or coincide the dew point is almost as high as the temperature and the air is human.
It is possible to derive a number of quantities from the two curves let's consider using an example where all values are at pressure level seven hundred hectare Pascale this same could be done for any other pressure level. The pressure in Hector Pascal can be read along the left vertical axis. On this level we can intersect the iso bar with the two red curves.
The right intersection point gives the temperature by following a line parallel to the ice of therms down to the horizontal axis we can find the value in this case minus five degrees Celsius
the left intersection point gives the dew point to temperature here it gives a value of minus thirteen degrees Celsius.
The saturated mixing ratio can be found by following the blue dashed saturated mixing ratio line from the right intersection point to the nine hundred hectare Pascale level in this case we find the value of three point nine grams of water vapor per kilogram of dry air.
This is not the actual amount of water vapor present in the air but the maximum amount that could be present if the water vapor was saturated at this level the actual amount of water vapor can be found from the dew point curve following the blue saturated mixing ratio lines from the left intersection point you can find the actual mixing ratio in this case two point zero grams per kilogram
finally the potential temperature feta can be obtained from the temperature curve using the right intersection point draw a line parallel to the dry at the abouts. At the six hundred hectare best gal level you can read the value of feta in this case it is twenty three degrees Celsius it is also possible to follow the dry addy of at to the one thousand hectare Pascoe level and estimate the temperature at this point.
We can use the diagram for easy calculations the relative humidity is equal to the ratio of the mixing ratio and the saturation mixing ratio.
Both quantities can be read from the diagram as we saw before. Now the calculation of the relative humidity is easy which we can see here is fifty one percent.
Inversions can also be found with the aid of the diagram at an inversion the temperature increases if we move upwards. I say therms slope to the right in this diagram in the case of an inversion the slope to the right in a part of the red line should be even greater than the slope of the gray line.
So the red line for example at six hundred hectare best gal should be tilted more to the right than the grey line. This means that it should be somewhat in the pink triangle obviously this is not the case since the slope indicated by the blue line is tilted in the other direction. In this diagram several inversions can be found.
Near eight hundred Hector Pascal a clear inversion is present as the red temperature curve slopes stronger to the right than the grey ice of therms However they do point decreases if we move upwards since it gets drier.
This is what is called a subsidy and inversion another subsequent inversion can be found near three hundred hectare Pascal.
Near nine hundred hectare best gal both temperature and dew point increase as you move upwards. This is called a frontal inversion since this inversion usually indicates the presence of a warm or cold front at this level which has warmer air above it.
Another frontal inversion can be seen near seven hundred hectare Pascal
a final inversion is where the troposphere ends and the stratosphere begins the troppo pause. The gradual decrease in temperature in the troposphere gives way to the increase in temperature that is a characteristic feature of the stratosphere.