Relative Humidity: To Average, or Not to Average?

Lowe (1976)¹ described the following model for calculating saturation vapor pressure:

where T is temperature in Celsius and the values for the fitted coefficients (α) are as follows:

While there are other methods to obtain saturation vapor pressure that we could consider, the Lowe model is used in Campbell Scientific data loggers, so I’ll limit my discussion to that method for the purposes of this article.

There are two reasons why a simple average of RH over a given data interval is generally not the best practice. First, RH is a calculated value. Mathematicians and statisticians advise us that it is better to use the original data in operations such as averages, then calculate the desired value. In addition, RH is, by definition, limited to values between zero and 100. Therefore, values near those upper and lower bounds cannot vary as much as those toward the middle, which violates statistical assumptions.

The second and more important reason not to use simple averaging for RH is that the value can change rapidly with temperature, especially at higher temperatures. Figure 1 shows the relationship between temperature and saturation vapor pressure based on the Lowe model.

Of particular note is that saturation vapor pressure changes more rapidly at higher temperatures. Therefore, simple arithmetic averages of RH at higher temperatures are likely to have greater error. Averaging over longer intervals is also likely to result in greater error.

How to Correctly Average RH

The preferred method to obtain an average RH over a given interval is to average the vapor pressure and saturation vapor pressures, then calculate RH from those averages. Here's a link to download a CRBasic program that does just that. During each scan, this program calculates vapor pressure and saturation vapor pressure, then stores the vapor pressure averages in a temporary, hidden table. Those values are then used to calculate RH, and all the values are stored in the main hourly table.

To illustrate the difference between the two methods of calculating an average for RH (simple arithmetic versus from averaged vapor pressures), I collected data from a weather station near the Campbell Scientific facilities in Logan, Utah, for approximately 17 months. A program similar to the one described above was used, and data were stored at four intervals:

• 30 minutes
• 1 hour
• 3 hours
• 24 hours

Figure 2 shows the results:

If the two methods were the same, we would expect all the datapoints to line up on the red 1:1 lines. For the half-hour and hourly intervals, there is good agreement. However, for longer intervals, error increases substantially. Interestingly, at least in these data, error due to simple averaging nearly always results in a positive bias. In other words, a simple arithmetic average almost always overestimates the mean relative humidity.

The World Meteorological Organization (WMO)² and the American Association of State Climatologists (AASC) both recommend that uncertainty (error) in the RH measurement be less than 3%. In the worst case, error due to averaging RH would be additive to the sensor error. As an example, if a sensor specification states that it is within 2.3% over most of the range, any additional error would need to be limited to less than 1% to conservatively meet the WMO and AASC recommendations.

Table 1 shows some statistics for the difference in averaging methods (simple average minus vapor pressure average) including mean, maximum, and minimum, as well as some percentiles. Fifty percent of the data are between the 25 and 75 percentiles, and 95% of the data are between the 2.5 and 97.5 percentiles.

Table 1. Comparison of Difference Between Simple Average and Averaging Vapor Pressures

For both the half-hour and hourly intervals, most of the data are within 1% of each other. Therefore, simple averages may be acceptable for these intervals, depending on the sensor you’re using and the purpose of the data, among other considerations. However, greater intervals show substantial bias and demonstrate that a simple average of RH would not represent the data well. In addition, it’s worth noting that it might be more informative for many data needs to store other metrics such as dewpoint or, simply, vapor pressure. 

I hope this helps clarify why it is generally not a good idea to average relative humidity for mathematical and statistical, as well as pragmatic, reasons. If you truly need an average RH, especially over longer time intervals, the better practice is to use the average observed and saturation vapor pressures to calculate RH over each time interval. You’re welcome to modify the downloadable example program as needed. Alternatively, simply store the observed vapor pressure and temperature (easily done in a Campbell Scientific data logger). From these, both the relative humidity and dewpoint can be calculated in post-processing if needed.

If you have any questions about averaging relative humidity (RH), please post them below.