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How to Calculate Precipitable Water

In meteorology, the study of weather, scientists consistently need to know how much water vapor is present in the atmosphere to make appropriate weather forecasts. One way to determine atmospheric water vapor quantity is by using precipitable water. Precipitable water is the measure of the depth of water that would result at the surface if all water vapor in a thin vertical column from the atmosphere instantly precipitated, falling to the surface as rain. All water vapor from the surface to the 300 millibar level in the atmosphere is considered precipitable water.

Instructions

- 1
  Gather values for constants needed in the precipitable water equation. Constants for this equation are mass of a water molecule, scale height of water vapor, mass density of liquid water and the Boltzmann constant. These values are approximately 18 amu, or atomic mass unit, 1.5 kilometers, 1000 kg/m^3 and 1.38066E-23 J/K, respectively.
- 2
  Determine surface temperature in terms of Kelvin. This information can be determined using a simple outdoor thermometer or data from a weather center. To get temperature in Kelvin, use this formula: Tk = Tc + 273. In this equation, "Tk" is the surface temperature in Kelvin and "Tc" is surface temperature in Celsius. If your surface temperature is in Fahrenheit, first convert Fahrenheit to Celsius and then use this equation. To convert from Fahrenheit to Celsius, use this equation: Tc = (5/9) * (Tf -- 32). "Tf" represents surface temperature in Fahrenheit and "Tc" is once again surface temperature in Celsius. Generally, "Tk" ranges between 250 and 310 Kelvin on Earth.
- 3
  Calculate the value for water vapor partial pressure at the surface. This is done using this equation: Po = 2.409E12 * RH * theta^4 * e^(-22.64 * theta). In this equation, "Po" represents water vapor partial pressure at the surface in microbars, "RH" represents relative humidity in a percentage and "theta" is equivalent to inverse temperature in Kelvin. "Theta" is calculated using this formula: Theta = 300 / Tk. In this particular equation, "Tk" again represents surface temperature in Kelvin.
- 4
  Calculate precipitable water using this equation using determined values: h = (mw * Po * H) / (rho * k * Tk). In the precipitable water equation, "mw" represents the constant mass of a water molecule, "Po" is once again the water vapor partial pressure at the surface, "H" is the constant scale height of water vapor, "rho" is the mass density of liquid water, "k" is the Boltzmann constant and "Tk" is the surface temperature in Kelvin. "h" represents the amount of precipitable water. This determined value is in millimeters.

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