The standard water vapor channel depicts relative humidity
Soden and Bretherton (1993, 1996) showed that water vapor channel brightness temperature varies as a function of the layer average relative humidity, the normalized base level pressure and the satellite zenith angle. They presented a linear expression showing that the brightness temperature in a given image changes as the weighted logarithm of relative humidity, where relative humidity is modified by viewing angle and normalized base level pressure. This can be expressed in a relatively simple analytical form as
where T6.7 is the remotely sensed brightness temperature, expressed in degrees K, q is the satellite zenith angle, and p0 is the ratio between the pressure of the 240K isotherm and 350 hPa, a reference pressure level.
This helps explain why standard images of brightness temperature from the water vapor channel typically exhibit the warmest brightness temperatures in the vicinity of subtropical high pressure systems while the brightness temperatures over the poles are often much cooler.
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These variations correspond well to layer average relative humidity. But the images confound our ability to contrast the absolute amount of water vapor in this responding layer across an image. Relative humidity is a function of both water vapor pressure and temperature (because saturation vapor pressure is a function of temperature; the Clasius-Clapeyron equation describes this relationship). In meteorology, we have an intuitive understanding of this, if we hold the amount of water vapor in the air constant, and vary the temperature, we will see the relative humidity increase (with falling temperatures) or decrease (with rising temperatures). For our satellite images, this means that two regions can have the same layer average relative humidity, as evidenced by identical brightness temperatures; however we don't know how much water vapor is present in the layer unless we know the corresponding layer average temperature.
For example, imagine an atmospheric layer with exactly the same amount of moisture everywhere in the absolute sense of uniform specific humidity, or uniform water vapor mixing ratio. In this atmosphere, the GOES water vapor channel would still observe variations in the relative humidity that correspond to temperature variations. Regions that have a higher temperature in this atmosphere (subtropical high pressure centers) will have a correspondingly lower brightness temperature. By contrast, the polar regions, which are cold, will be closer to saturation for the same amount of water vapor, thus, they have a higher relative humidity, and will show up as regions of colder brightness temperature.
Once it was understood that T6.7, the quantity typically displayed in water vapor images, scales primarily as the logarithm of the layer average relative humidity adjusted for viewing angle, we realized we could develop a more quantitative product that truly represented specific humidity. An algorithm was developed to derive the specific humidity from fields of the GOES imager brightness temperature, T6.7. This is described in the Algorithm section of this tutorial.