Estimating the Measurement Uncertainty for RH and other Variables at the Monthly Scale

The Plan

With any climate data it is important to be aware of, and quantify if possible, any errors in the values for each data point. This is done by estimating a spread of uncertainty.

After Brohan et al. 2006, and our HadISDH.landq product (Willett et al. 2013), for any monthly mean value from a station we have previously estimated uncertainty from three components:
 
1) The Climatology:
In many cases the climatology is imperfectly calculated due to incomplete temporal sampling.

2) The Inhomogeneity:
Any adjustments applied have an uncertainty estimate and there is additional uncertainty for the estimate of missed adjustments.

3) The Measurement:  
Any instrument has an inherent error (level of accuracy) specific to instrument and environmental conditions.

In the landq version of HadISDH we described what we believed to be satisfactory methods of estimating these uncertainties. For Climatology and Inhomogeneity, the methods can be identical for all other variables that we wish to produce a HadISDH version of (e.g., RH, e, Td, Tw, T). Measurement uncertainty is a little different.

For q, we defined measurement uncertainty based on the standard uncertainty in wetbulb temperature measurement of 0.15 degrees Celsius applied to q for a range of temperature and saturation (RH) levels. However, it is a little bit more complex than that in the full definition.

How we estimated the measurement uncertainty for monthly mean specific humidity anomalies:

The BIPM Guide to the Expression of Uncertainty in Measurement (BIPM, 2008) describes uncertainties as belonging to one of two categories. Type A uncertainties are those which can be estimated from analysis of repeated observations. Type B uncertainties are those which cannot be estimated by repeated observations, and so must be estimated from a priori knowledge of the measurement apparatus and the measuring conditions. 
   
Type A:
In a meteorological context it is not possible to derive Type A estimates of uncertainty because the measurand – the weather – is intrinsically variable, and so the variability due to the instruments themselves cannot be isolated. Since Type A uncertainties are likely to be random and uncorrelated, they should reduce with temporal and spatial averaging to a large extent. For this reason we do not include a Type A component in our estimation.

Type B = UOBr +UOBs:
Type B uncertainties may have randomly varying components, UOBr , and components which cause “systematic” errors, UOBs. Since the station metadata do not reliably record the instrumentation used, we can derive estimates of the Type B uncertainty of an individual measurement based on knowledge of hygrometers in use in the field. Until the 1980s, psychrometers were probably the most common type of hygrometer, but since then there has been a move towards electronic devices (typically capacitance sensors) and dewcels which can be more readily automated. Typically, electronic devices have a lower uncertainty than psychrometers, and so we can conservatively estimate Type B uncertainty assuming that all humidity measurements were taken using aspirated psychrometers.

Assume all measurements taken with a psychrometer:
Psychrometer errors, in general, are not random or symmetrically distributed, and they may be correlated with other meteorological variables, such as wind speed. However, we expect that within any one month, the Type B uncertainty of measurement for psychrometers will contain some random component, UOBr, whose effect can be reduced by averaging, and a systematic component, UOBs, whose effect will be unaffected by averaging.

Estimating UOBr for q:
Using 0.15 C as the standard uncertainty of wetbulb temperature measurement above 0 C, the resulting standard uncertainty in RH varies from 1 %rh to 3 %rh, decreasing with increasing T and increasing with decreasing RH (NPL/IMC, 1996 - see Table 1 with extrapolation for subzero temperature). Considering everything at the monthly temporal resolution, the concomitant uncertainty in q (UOBq) is estimated from the uncertainty in RH. This is done by calculating the change in vapour pressure, e, caused by changes of ±1 standard uncertainty in %rh. Combining this with an estimate of the saturation vapour pressure calculated from simultaneous monthly mean T, under the necessary (and in many cases incorrect) assumption that the T data are homogeneous, the resulting change in q can be estimated. The reading uncertainties of the wet bulb and dry bulb temperatures are unlikely to be biased, and so we assume that the resulting uncertainty is randomly distributed. We thus estimate the random component of the uncertainty in the monthly mean as:   


UOBr = UOBq / √No. of OBS in month
  
There are a number of weaknesses in this approach. Firstly, these non-linear conversions are imperfect for monthly mean data. Secondly, when the monthly RH value is already close to 100 %rh, the addition of uncertainty in RH can then result in estimates > 100 %rh. Thirdly, errors will also be introduced because the simultaneous monthly mean T data have not been homogenised. This is due to the issue of maintaining physical continuity when homogenising across simultaneously observed variables which will be addressed in future work. False wet bulb depressions may occur at 100 %rh, but the low-resolution conversion between humidity variables makes accurate detection of such cases impossible. However, limiting the new RH (%rh + derived uncertainty in %rh - necessary for estimating equivalent uncertainty in vapour pressure and then specific humidity) to 100 %rh can imply an unrealistically small uncertainty. To counter this, we have set a minimum threshold for UOBr of two standard deviations below the mean by examining the UOBr estimates for each month for the station. All values below this threshold are assumed to be unrealistically low and are substituted with the mean value of UOBr for that station.

What about UOBs:
In addition to randomly varying components, the Type B uncertainty of measurement of each station, will also have contributions which do not reduce on averaging, UOBs. We have not included an explicit assessment of usys because we consider that their effect on our estimate of qanom is likely to be small - assuming that the data have been homogenised to remove any systematic non-climate influence. For example, where instruments or observing practices change or stations move, UOBs will change, and so we expect that some fraction of UOBs should be found during homogenisation, and removed - as older data are adjusted to the more recent 'reference period'. The remaining uncertainty in either applied adjustments or missed adjustments is accounted for explicitly in the Inhomogeneity uncertainty component. Where instruments or observing practices do not change, then we can assume that UOBs will be substantially unchanged. So we expect that a substantial
fraction of UOBs will be common to qanom and qclim . Thus, when calculating qanom we can expect this fraction of the uncertainty to cancel.


Table 1 Estimates of standard uncertainty in humidity measurements calculated in terms of equivalent psychrometer uncertainty to represent a “worst case scenario”. At lower temperatures the measurement uncertainty becomes large, but the low absolute specific humidity values make only a small contribution to global estimates of specific humidity.

   Dry bulb     |   Uncertainty in %rh | Specific humidity | Uncertainty in   |   UOBr (g kg−1 )
temperature  |  given by a 0.15 ◦ C |      (g kg−1 ) at      | hourly specific  |
      (◦ C)         |     uncertainty in        |       saturation       |     humidity         |             
                       | wet bulb depression|                                |    (g kg−1 )         |
---------------------------------------------------------------------------------------------------------------------
<= −50                        15                               0.02                     0.003                 0.001 
−40                             15                               0.08                     0.012                 0.002
−30                             15                               0.23                     0.035                 0.005
−20                             10                               0.64                     0.064                 0.008
−10                               5                               1.60                     0.080                 0.010
0                                   2.75                          3.78                     0.104                 0.013
10                                1.8                             7.60                     0.137                 0.018
20                                1.35                         14.54                    0.196                  0.025
30                                1.1                           26.60                    0.293                  0.038
40                                0.95                         46.82                    0.445                  0.057
>= 50                          0.8                            79.85                    0.639                  0.082

A Measurement Uncertainty Model for other humidity variables:

We should be able to use a similar process for all other humidity variables. In many ways it is preferable at this stage to keep the uncertainty model the same as in the first version of HadISDH.1.0.0 for q. However, I am aware that there has been some recent work on estimating the uncertainty in RH measurements which may be sensible to incorporate. Also, if there is anything we have done previously that now we think was not ideal - we can improve it.

For RH, the simplest method would be use the RH uncertainty at a given temperature from Table 1.

A Measurement Uncertainty Model for Temperature:

References:

BIPM (Bureau International des Poids et Mesures): Guide to the Expression of Uncertainty in Measurements. Joint Committee for Guides in Metrology JCGM 100, available at: http://www.bipm.org/en/publications/guides/gum.html (last access: August 2012), 120 pp., 2008.

Brohan, P., Kennedy, J. J., Harris, I., Tett, S. F. B., and Jones, P. D., 2006: Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850, J. Geophys. Res., 111, D12106, doi:10.1029/2005JD006548.

NPL/IMC (National Physics Laboratory and The Institute of Measurement and Control): A Guide to the Measurement of Humidity, The Institute of Measurement and Control, London, 68 pp., 1996.

Willett, K. M., C. N. Williams Jr., R. J. H. Dunn, P. W. Thorne, S. Bell, M. de Podesta, P. D. Jones and D. E. Parker, 2013: HadISDH: an updateable land surface specific humidity product for climate monitoring. Climate of the Past, 9, 657-677, doi:10.5194/cp-9-657-2013.