Arden Buck Equations: Precision Modeling of Saturation Vapor Pressure
In the field of meteorology and thermodynamics, calculating the saturation vapor pressure—the maximum amount of water vapor that can exist in the air at a given temperature—is critical for understanding atmospheric processes. While several methods exist, the Arden Buck equations provide a highly accurate set of empirical correlations specifically designed for moist air.
Developed to improve upon previous models, these equations offer optimized curve fits that provide greater accuracy than the Goff–Gratch equation within a specific temperature range of -80 to 50 °C (-112 to 122 °F). Because atmospheric conditions vary significantly depending on whether water is in a liquid or solid state, Buck developed different equations to suit these specific environments.
ไม่มีภาพประกอบKey Facts
- Optimized Range: Highly accurate between -80 °C and 50 °C (-112 °F to 122 °F).
- Versatility: Includes distinct formulas for both liquid water and ice.
- Superiority: Offers improved accuracy over the Goff–Gratch equation in its target range.
- Application: Used to calculate saturation vapor pressure (Ps) in hPa.
Mathematical Formulas
The equations suggested by Buck (1996), which serve as modifications to his earlier 1981 work, are divided based on the phase of water present in the air.
Saturation Over Liquid Water (T > 0 °C)
When the temperature is above freezing, the following formula is used to determine the saturation vapor pressure:
Ps(T) = 6.1121 exp((18.678 - T/234.5) * (T / (257.14 + T)))
Saturation Over Ice (T < 0 °C)
For temperatures below the freezing point, the relationship changes to account for ice:
Ps(T) = 6.1121 exp((23.036 - T/234.5) * (T / (265.52 + T)))
In these formulas, Ps(T) represents the saturation vapor pressure in hectopascals (hPa), T is the air temperature in degrees Celsius, and exp(x) denotes the exponential function.
Enhancement Factors and Pressure Variations
Beyond basic vapor pressure, Buck (1981) identified enhancement factors. These coefficients are necessary to account for the non-ideal behavior of moist air at different atmospheric pressures. The following table outlines these factors across various temperatures and pressure levels (1,000 mb, 500 mb, and 250 mb).
| Temperature (°C) | 1,000 mb | 500 mb | 250 mb |
|---|---|---|---|
| -80 | 1.00410 | 1.00200 | - |
| -70 | 1.00360 | 1.00180 | - |
| -60 | 1.00640 | 1.00320 | 1.00160 |
| -50 | 1.00580 | 1.00290 | 1.00140 |
| -40 | 1.00520 | 1.00260 | 1.00130 |
| -30 | 1.00470 | 1.00240 | 1.00120 |
| -20 | 1.00440 | 1.00220 | 1.00120 |
| -10 | 1.00410 | 1.00220 | 1.00120 |
| 0 | 1.00395 | 1.00219 | 1.00132 |
| 10 | 1.00388 | - | - |
| 20 | 1.00400 | 1.00251 | - |
| 30 | 1.00426 | 1.00284 | - |
| 40 | 1.00467 | 1.00323 | - |
| 50 | 1.00519 | - | - |
Frequently Asked Questions
What is the primary advantage of the Arden Buck equations?
The primary advantage is their increased accuracy in calculating saturation vapor pressure for moist air within the temperature range of -80 to 50 °C, specifically when compared to the Goff–Gratch equation.
When should I use the liquid water formula versus the ice formula?
You should use the liquid water formula when the temperature (T) is greater than 0 °C, and the ice formula when the temperature is less than 0 °C.
What unit of measurement is used for vapor pressure in these equations?
The saturation vapor pressure (Ps) is measured in hectopascals (hPa).
What are enhancement factors?
Enhancement factors are coefficients used to adjust vapor pressure calculations to account for the effects of different atmospheric pressures (such as 1,000 mb, 500 mb, or 250 mb) on moist air.
Does the Arden Buck equation work at all temperatures?
While the equations are highly optimized for the range of -80 to 50 °C, they are specifically designed to provide high accuracy within this specific window.