Mixing
How can temperature be calculated given relative humidity and dew point?
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
While looking into the better indicator of how miserable it feels outside, either dew point or relative humidity, I came across this statement:
The optimum combination for human comfort is a dewpoint of about 60 F
and a RH of between 50 and 70% (this would put the temperature at
about 75 F).
Source: http://www.theweatherprediction.com/habyhints/190/
This led me to this calculator that will calculate the temperature given relative humidity and dew point - for example a dew point of 70 degrees F and a relative humidity of 90% results in a temperature of 73.11 degrees F. The web site for this calculator says the values are based on the August-Roche-Magnus approximation and gives the following equation to calculate temperature:
$T =243.04 Large fracfrac17.625 TD243.04+TD-lnleft(fracRH100right)17.625+lnleft(fracRH100right)-
frac17.625 TD243.04+TD$
Given the equation I'm still having a hard time figuring out how the temperature is being calculated. Can somebody please explain how temperature is being calculated in simple terms?
meteorology
edited Aug 18 at 16:38
Camilo Rada
6,70911956
asked Aug 18 at 15:25
wanderweeer
1,7761426
add a comment |Â
up vote
1
down vote
favorite
While looking into the better indicator of how miserable it feels outside, either dew point or relative humidity, I came across this statement:
The optimum combination for human comfort is a dewpoint of about 60 F
and a RH of between 50 and 70% (this would put the temperature at
about 75 F).
Source: http://www.theweatherprediction.com/habyhints/190/
This led me to this calculator that will calculate the temperature given relative humidity and dew point - for example a dew point of 70 degrees F and a relative humidity of 90% results in a temperature of 73.11 degrees F. The web site for this calculator says the values are based on the August-Roche-Magnus approximation and gives the following equation to calculate temperature:
$T =243.04 Large fracfrac17.625 TD243.04+TD-lnleft(fracRH100right)17.625+lnleft(fracRH100right)-
frac17.625 TD243.04+TD$
Given the equation I'm still having a hard time figuring out how the temperature is being calculated. Can somebody please explain how temperature is being calculated in simple terms?
meteorology
edited Aug 18 at 16:38
Camilo Rada
6,70911956
asked Aug 18 at 15:25
wanderweeer
1,7761426
1
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
While looking into the better indicator of how miserable it feels outside, either dew point or relative humidity, I came across this statement:
The optimum combination for human comfort is a dewpoint of about 60 F
and a RH of between 50 and 70% (this would put the temperature at
about 75 F).
Source: http://www.theweatherprediction.com/habyhints/190/
This led me to this calculator that will calculate the temperature given relative humidity and dew point - for example a dew point of 70 degrees F and a relative humidity of 90% results in a temperature of 73.11 degrees F. The web site for this calculator says the values are based on the August-Roche-Magnus approximation and gives the following equation to calculate temperature:
$T =243.04 Large fracfrac17.625 TD243.04+TD-lnleft(fracRH100right)17.625+lnleft(fracRH100right)-
frac17.625 TD243.04+TD$
Given the equation I'm still having a hard time figuring out how the temperature is being calculated. Can somebody please explain how temperature is being calculated in simple terms?
meteorology
edited Aug 18 at 16:38
Camilo Rada
6,70911956
asked Aug 18 at 15:25
wanderweeer
1,7761426
While looking into the better indicator of how miserable it feels outside, either dew point or relative humidity, I came across this statement:
The optimum combination for human comfort is a dewpoint of about 60 F
and a RH of between 50 and 70% (this would put the temperature at
about 75 F).
Source: http://www.theweatherprediction.com/habyhints/190/
This led me to this calculator that will calculate the temperature given relative humidity and dew point - for example a dew point of 70 degrees F and a relative humidity of 90% results in a temperature of 73.11 degrees F. The web site for this calculator says the values are based on the August-Roche-Magnus approximation and gives the following equation to calculate temperature:
$T =243.04 Large fracfrac17.625 TD243.04+TD-lnleft(fracRH100right)17.625+lnleft(fracRH100right)-
frac17.625 TD243.04+TD$
Given the equation I'm still having a hard time figuring out how the temperature is being calculated. Can somebody please explain how temperature is being calculated in simple terms?
meteorology
edited Aug 18 at 16:38
Camilo Rada
6,70911956
asked Aug 18 at 15:25
wanderweeer
1,7761426
edited Aug 18 at 16:38
Camilo Rada
6,70911956
edited Aug 18 at 16:38
Camilo Rada
6,70911956
edited Aug 18 at 16:38
Camilo Rada
6,70911956
6,70911956
asked Aug 18 at 15:25
wanderweeer
1,7761426
asked Aug 18 at 15:25
wanderweeer
1,7761426
asked Aug 18 at 15:25
wanderweeer
1,7761426
1,7761426
1
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36
add a comment |Â
1
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36
1
1
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
To understand that formula it is better to start from the more intuitive dependence of dew point with temperature and relative humidity, as illustrated by the following graph
From Wikipedia.
As for any solvent with a solute, the higher the temperature of the solvent the more solute it can hold. That's why hot water can dissolve more sugar than cold water. Or for a given quantity of sugar, hot water dissolves it faster than cold water.
The figure above says basically the same: Hotter air dissolves more water. Condensation happen when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.
As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.
I'll assign letters to each constant for simplicity, so that
$b=17.625$
and
$c=243.04$
With that, the dew point can be calculated as
$TD= large c LARGE fraclnleft(fracRH100right)+fracb Tc+Tb-lnfracRH100-fracb Tc+T$
(see Calculating the dew point)
I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$ you will go back to the formula you presented.
answered Aug 18 at 16:34
Camilo Rada
6,70911956
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
To understand that formula it is better to start from the more intuitive dependence of dew point with temperature and relative humidity, as illustrated by the following graph
From Wikipedia.
As for any solvent with a solute, the higher the temperature of the solvent the more solute it can hold. That's why hot water can dissolve more sugar than cold water. Or for a given quantity of sugar, hot water dissolves it faster than cold water.
The figure above says basically the same: Hotter air dissolves more water. Condensation happen when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.
As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.
I'll assign letters to each constant for simplicity, so that
$b=17.625$
and
$c=243.04$
With that, the dew point can be calculated as
$TD= large c LARGE fraclnleft(fracRH100right)+fracb Tc+Tb-lnfracRH100-fracb Tc+T$
(see Calculating the dew point)
I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$ you will go back to the formula you presented.
answered Aug 18 at 16:34
Camilo Rada
6,70911956
add a comment |Â
up vote
3
down vote
accepted
To understand that formula it is better to start from the more intuitive dependence of dew point with temperature and relative humidity, as illustrated by the following graph
From Wikipedia.
As for any solvent with a solute, the higher the temperature of the solvent the more solute it can hold. That's why hot water can dissolve more sugar than cold water. Or for a given quantity of sugar, hot water dissolves it faster than cold water.
The figure above says basically the same: Hotter air dissolves more water. Condensation happen when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.
As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.
I'll assign letters to each constant for simplicity, so that
$b=17.625$
and
$c=243.04$
With that, the dew point can be calculated as
$TD= large c LARGE fraclnleft(fracRH100right)+fracb Tc+Tb-lnfracRH100-fracb Tc+T$
(see Calculating the dew point)
I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$ you will go back to the formula you presented.
answered Aug 18 at 16:34
Camilo Rada
6,70911956
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
To understand that formula it is better to start from the more intuitive dependence of dew point with temperature and relative humidity, as illustrated by the following graph
From Wikipedia.
As for any solvent with a solute, the higher the temperature of the solvent the more solute it can hold. That's why hot water can dissolve more sugar than cold water. Or for a given quantity of sugar, hot water dissolves it faster than cold water.
The figure above says basically the same: Hotter air dissolves more water. Condensation happen when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.
As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.
I'll assign letters to each constant for simplicity, so that
$b=17.625$
and
$c=243.04$
With that, the dew point can be calculated as
$TD= large c LARGE fraclnleft(fracRH100right)+fracb Tc+Tb-lnfracRH100-fracb Tc+T$
(see Calculating the dew point)
I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$ you will go back to the formula you presented.
answered Aug 18 at 16:34
Camilo Rada
6,70911956
To understand that formula it is better to start from the more intuitive dependence of dew point with temperature and relative humidity, as illustrated by the following graph
From Wikipedia.
As for any solvent with a solute, the higher the temperature of the solvent the more solute it can hold. That's why hot water can dissolve more sugar than cold water. Or for a given quantity of sugar, hot water dissolves it faster than cold water.
The figure above says basically the same: Hotter air dissolves more water. Condensation happen when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.
As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.
I'll assign letters to each constant for simplicity, so that
$b=17.625$
and
$c=243.04$
With that, the dew point can be calculated as
$TD= large c LARGE fraclnleft(fracRH100right)+fracb Tc+Tb-lnfracRH100-fracb Tc+T$
(see Calculating the dew point)
I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$ you will go back to the formula you presented.
answered Aug 18 at 16:34
Camilo Rada
6,70911956
answered Aug 18 at 16:34
Camilo Rada
6,70911956
answered Aug 18 at 16:34
Camilo Rada
6,70911956
answered Aug 18 at 16:34
Camilo Rada
6,70911956
6,70911956
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fearthscience.stackexchange.com%2fquestions%2f14899%2fhow-can-temperature-be-calculated-given-relative-humidity-and-dew-point%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
@wanderweer I've added a more readable version of the equation using the LaTex syntax, please check it is OK. If so, you might want to delete the other version for compactness
– Camilo Rada
Aug 18 at 15:39
@Camilo Rada: Yes, the version you provided looks much better. I've deleted the old version. Thank you for the edit.
– wanderweeer
Aug 18 at 16:36