Saturation Mixing Ratio Calculator

Introduction : this calculator is used to demonstrate how one might use a mathematical model to "forecast" a meteorological variable, in this case a temperature dewpoint. In this calculator, it is assumed that one can measure (using simple meteorological measuring devices such as might be found at any home improvement store) two values:

  1. Surface temperature (in degrees Celsius)
  2. Relative Humidity (as a percentage)

Given these two values, how might one "forecast" a temperature dewpoint? A series of algorithms, or calculations, can be performed to determine the vapor pressure of water (in millibars, or mb) if the atmosphere is saturated (i.e, if the relative humidity is 100%) or the actual vapor pressure if the atmosphere is not completely saturated. The main equation is:

Saturated vapor pressure (SVP) = 6.11 x 10((7.5T)/(T+237.3))

Once we have calculated the SVP, we can adjust it for an atmosphere that is less than completely saturated:

Actual vapor pressure (VP) = SVP x RH / 100

For example, in the calculator below, the input values are 10.0o Celsius with a relative humidity of 65%. The vapor pressure of a saturated atmosphere at the given temperature calculates (click on the "Evaluate" button) to 12.283 mb of pressure. What is the actual vapor pressure, given that the atmosphere is only at 65% of its capacity? The calculator provides a value of 7.984 mb of pressure.

Once we have this value, we can forecast the current temperature dewpoint in degrees Celsius. Using the lookup table below the calculator, we need to determine the temperature which corresponds the closest to the actual vapor pressure, in this case a vapor pressure of 7.984 mb. Looking at the table, 7.984 mb is somewhere between 7.580 (a temperature of 3o Celsius) and 8.135 (a temperature of 4o Celsius).

3.0o Celsius 7.580 mb
3.5o Celsius 7.858 mb
4.0o Celsius 8.135 mb
We would predict that the value of 7.984 mb corresponds to a temperature of approximately 3.7o Celsius, and that is the expected forecasted value for the temperature dewpoint

Calculator

Input Values:

Surface Temperature (C)
Relative Humidity

Results:

Saturation Vapor Pressure
Actual Vapor Pressure

Table of Saturated Vapor Pressures as a function of Temperature

T (degrees C) SVP (mb) T (degrees C) SVP (mb) T (degrees C) SVP (mb)
-20 1.247 11 82.009 42 82.009
-19 1.359 12 14.030 43 86.416
-18 1.481 13 14.982 44 91.026
-17 1.612 14 15.991 45 95.847
-16 1.753 15 17.058 46 100.886
-15 1.905 16 18.188 47 106.152
-14 2.069 17 19.383 48 111.653
-13 2.246 18 20.646 49 117.398
-12 2.435 19 21.980 50 123.395
-11 2.639 20 23.389 51 129.653
-10 2.858 21 24.877 52 136.183
-9 3.093 22 26.447 53 142.993
-8 3.345 23 28.102 54 150.093
-7 3.615 24 29.847 55 157.493
-6 3.904 25 31.686 56 165.205
-5 4.213 26 33.623 57 173.237
-4 4.544 27 35.663 58 181.602
-3 4.898 28 37.809 59 190.309
-2 5.276 29 40.067 60 199.372
-1 5.679 30 42.442 61 208.801
0 6.110 31 44.937 62 218.608
1 6.569 32 47.560 63 228.806
2 7.059 33 50.314 64 239.408
3 7.580 34 53.206 65 250.425
4 8.135 35 56.241 66 261.872
5 8.726 36 59.425 67 273.761
6 9.354 37 62.764 68 286.108
7 10.022 38 66.264 69 298.924
8 10.731 39 69.932 70 312.226
9 11.484 40 73.774 71 326.028
10 12.283 41 77.797 72 340.345