Estimating the Measurement Uncertainty for all Humidity Variables Based on T, Tw and RH

Overview

Historically, all humidity observations were made using a wet bulb thermometer. Increasingly, RH sensors (or dewpoint sensors) are being used. In some cases, the reported humidity value has already undergone some conversion also using the dry bulb temperature value.

So, any single measurement uncertainty could well be a combination of both the dry bulb temperature uncertainty and either the wet bulb uncertainty or RH sensor uncertainty. Precise dates and station IDs for the change over from wet bulb thermometer to RH sensor are unknown but we know that all UK observations are now made using and RH sensor and that these instruments have become more common since weather stations became automated.

To deal with this optimally, given the unknowns, we assume that all measurements contain dry bulb temperature uncertainty and all measurements pre-1980 contain wet bulb uncertainty. From 1980 onwards some will begin to use RH sensors so RH sensor uncertainty can be swapped for wet bulb uncertainty for an increasing number of stations over time since the 1980s, especially for the UK.

Quantity of uncertainty derived from wet and dry bulb thermometers

Brohan et al. (2006) report that the 1sigma Type B random component of measurement error in the dry bulb thermometer is ~0.2 degrees C. See previous post for a description of Type A and B measurement uncertainties.

Willett et al. (2013) (thanks to NPL co-authors) report that the 1sigma Type B random component of measurement error in the wet bulb thermometer is ~0.15 degrees C. 

Considering the wet bulb uncertainty only this results in approximately 15 %rh uncertainty at -50 degrees C dry bulb temperature and 0.8 %rh uncertainty at 50 degrees C dry bulb temperature. This results in a maximum error in q (specific humidity) assuming the worst case scenario of saturation of 0.003 g/kg at -50 degrees C dry bulb temperature and 0.639 g/kg at 50 degrees C dry bulb temperature. GIVE STATS FOR e AND Td TOO. This is summarised for various dry bulb thresholds in Table 1.

Table 1 Humidity uncertainty estimates derived from wet bulb uncertainty for 10 degree dry bulb temperature bins.
   Dry bulb   | Uncertainty (%rh) | Uncertainty in |  Uncertainty in | Uncertainty in |    
temperature | given by 0.15 ◦ C | hourly specific | hourly vapour | hourly dewpoint |
      (◦ C)      |     uncertainty in  |     humidity     |    pressure     |   temperature    |                  

                  | wet bulb depression|      g/kg       |         hPa        |   degrees C    |

---------------------------------------------------------------------------------------------------------------------
<= −50                        15                  0.003          
−40                             15                  0.012              
−30                             15                  0.035            
−20                             10                  0.064             
−10                               5                  0.080             
0                                   2.75             0.104              
10                                1.8                0.137               
20                                1.35              0.196              
30                                1.1                0.293             
40                                0.95              0.445              
>= 50                          0.8                 0.639             

Quantities of uncertainty derived from RH sensors

STILL TO DO

Methods for quantifying uncertainty in all HadISDH variables

To derive monthly uncertainties from the actual measurement uncertainties we must divide by the SQRT of the number of  observations in the month. At minimum this should be 4 measurements per day for 15 days of the month N=60.

ADD IN UNCERTAINTY IN T BY JUST SUMMING WITH WET BULB/RH SENSOR ERROR FOR A WORST CASE SCENARIO??? 

FOR T: easy - +/- 0.2deg

WET BULB ERROR pre 1980 (mostly) of 0.15 degrees resulting in 15%rh at -50 deg C T and 0.8 %rh at 50 deg C T (or more if summed with dry bulb uncertainty)

Scale all uncertainties based on %rh uncertainty at the homogenised simultaneous dry bulb temperature using 10 degree bins (Table 1).

FOR Tw - easy - +/- 0.15 degrees C (or +/- 0.35 if summing with dry bulb uncertainty)

FOR RH - easy - apply dry bulb temperature dependent %rh uncertainty. 
If no temperature data exist for candidate station then assume moderate uncertainty of 3%rh (see Table 1).

FOR q - use homogenised RH and scale %rh with dry bulb temperature bin
          qsat = (q/RH)*100 
          q+UNC = ((RH+UNC)/100)*qsat
          qUNC = (q+UNC)-q
If no RH data exist for the candidate station then assume 80 %rh in all cases and derive q uncertainty from there. If no temperature data exist for candidate station then assume moderate uncertainty of 3%rh (see Table 1).

FOR e - use homogenised RH and scale %rh with dry bulb temperature bin     
          esat = (e/RH)*100 
          e+UNC = ((RH+UNC)/100)*esat 
          eUNC = (e+UNC)-e
If no RH data exist for the candidate station then assume 80 %rh in all cases and derive q uncertainty from there. If no temperature data exist for candidate station then assume moderate uncertainty of 3%rh (see Table 1).

FOR Td - use homogenised RH and scale %rh with dry bulb temperature bin    
         e = e calculated from Td
         esat = (e/RH)*100
         e+UNC = ((RH+UNC)/100)*esat
         Td+UNC = Td+UNC calculated from e+UNC
         TdUNC = (Td+UNC)-Td
If no RH data exist for the candidate station then assume 80 %rh in all cases and derive q uncertainty from there. If no temperature data exist for candidate station then assume moderate uncertainty of 3%rh (see Table 1).

RH SENSOR ERROR (post 1980 - progressively)
STILL TO DO