Quantifying uncertainties in climate data: measurement limitations of naturally ventilated thermometer screens

Climate science depends on accurate air temperature measurement. To achieve this, well ventilated thermometers protected from direct sunlight and precipitation are needed, commonly through using louvred enclosures known as screens or shields. Maintaining good natural ventilation is critical for accurate measurements. Ventilation effects on air temperature uncertainties are quantified here using an aspirated thermometer as a reference, for air temperatures spanning −2.8 °C to 35.5 °C. Of 81462 5 min mean temperature values obtained, 50% were within ±0.07 °C of the reference and only 2% lay beyond −0.66 °C to 0.47 °C, where negative values represent the naturally ventilated screen thermometer underestimating air temperature. Larger absolute differences arose from a combination of radiation exchange and time response effects, which are separated here. Firstly, using 20s data, the exponential time response of the naturally ventilated thermometer is shown to vary with wind speed u as u −0.5, and exceeds the conventional 1 min averaging time for wind speeds up to 5 ms−1 (at 2 m height), increasing to at least 15 min when calm. Secondly, radiation exchange effects (both by day and by night) dominated at low wind speeds (<1 ms−1 at 2 m height). Insufficient time response damps recording of temperature extremes, potentially also influencing climatological means. A new method to reduce the uncertainties is presented. This reduces negative skew in the temperature bias from −1.05 to −0.26, and, for almost 90% of the data, also reduces the spread.


Introduction
Air temperature is a central parameter for climate studies.Nevertheless, it is troublesome to measure accurately, requiring standardised protective thermometer enclosures.These commonly operate by passing air naturally over the thermometers, whilst providing shelter from direct sunlight and rain.As measurements of 'air temperature' obtained with naturally ventilated thermometer screens form the backbone of the instrumental climate record, recognising the associated uncertainty in the temperature measurements obtained is important.Here, the limitations of natural ventilation on thermometers in a standard screen is investigated experimentally and quantified, with corrections proposed to improve the measurements.
In the UK and Ireland, successors of the thermometer enclosure (or 'screen') design originated by Thomas Stevenson and adopted by the British Meteorological Office from the 1870s are still widely used (Gaster 1882, Burt 2013).Operation of a Stevenson screen depends on natural airflow, but this is variable and occasionally insufficient for accurate air temperature measurement.This fundamental limitation was originally recognised by Aitken (1884), and has subsequently been confirmed by numerous national and international screen comparisons (see, for example, Harrison 2010, Lacombe et al 2011, Clark et al 2014and Buisan et al 2015), with empirical and theoretical corrections investigated and proposed (e.g.Erell et al 2005, Nakamura and Mahrt, 2005, Bernard et al 2019).Naturally ventilated thermometer screens nevertheless remain in widespread use globally, with many derivative versions (Sparks 1972, Parker 1994), including changes in construction materials from wood to plastic (Perry et al 2007).These arrangements usually provide the daily climatological mean, maximum and minimum temperatures, as well as at other times, whether read manually by an observer or, increasingly, logged by computer.
Here, an experimental comparison is made between temperatures found from a 'traditional' naturally ventilated thermometer screen, with those obtained from an aspirated thermometer typical of modern climate measurement networks (Richardson et al 1999, Diamond et al 2013).Improved time resolution now available (e.g. compared with Nakamura and Mahrt (2005)) allows further quantification of the absolute air temperature accuracy of the traditional screen, separating lag time and radiation effects.Explicit parameterisation of the lag time variation with wind speed is provided, and a new method for temperature bias correction evaluated.

Air temperature measurement considerations
Two principal factors influence the accuracy of air temperatures measured using a naturally ventilated thermometer screen (NVTS): response time and radiation error (Brock andRichardson 2001, Harrison 2014).Firstly, the time response (as characterised by the exponential lag time) determines how quickly the NVTS thermometer responds to changes in air temperature.If the response time exceeds that of environmental air temperature fluctuation timescales, the resulting damped response will underestimate extreme values.The second factor, radiation error, arises from direct heating and cooling effects on the NVTS, from radiation exchange with its surroundings.

Response time
Power law relationships with wind speed are typically used to describe heat transfer, such as for the time response of a cylindrical thermometer sensor (Burt and dePodesta 2020).In the case of a thermometer in a naturally ventilated screen, the exponential lag time τ follows a power law equation of the form where u is the wind speed at screen height (HMSO 1981).n is typically -½, and A varies with the screen size and type (Harrison2011).Assuming A=8.2 for a Stevenson screen with u in ms −1 (Bryant 1968), for u=1 ms −1 then τ=8.2min.The lag time can be determined experimentally from observing temperature changes (e.g.Harrison 2014).If the environmental temperature rises steadily from T a at a rate K, a thermometer of finite lag time τ will show a lagged temperature variation with time T(t) given by where T 0 is the initial reading of the finite lag thermometer (HMSO 1981).τ can be found by using measurements from a second thermometer of negligible lag time (see also Supplementary Information (available online at stacks.iop.org/ERC/3/061005/mmedia)).The instantaneous temperature difference ΔT between two such thermometers a time t after a steady temperature change begins is

Radiation exchange
The effect of solar heating on a thermometer-the 'radiation error'-can be represented as where ΔT R is the temperature difference between the thermometer and its environment, and S represents the short-wave radiation flux (Harrison 2014).

Experimental investigations
The inverse power law relationships of eq1 and eq4 show that the greatest influences on NVTS air temperature measurements occur in light winds.These have been investigated experimentally in a range of temperature, radiation and wind speed conditions, using instruments installed at the Reading University Atmospheric Observatory 1 (RUAO).

Instrumentation
The experiments compared measurements from two accurate platinum resistance thermometers (PRTs), see e.g.Foken and Bange (2021), between 7 November 2019 and 16 August 2020.One PRT was exposed in a naturally ventilated screen, and the other, as a reference, in a force-ventilated screen alongside, drawing air at the same height.The NVTS was a MetSpec 'large' Stevenson screen, and the ventilated screen a Young model 43502.This screen was chosen for low power and therefore negligible heating, longevity and air intake from below to minimise wind direction effects.Both PRTs were the same make and model (Campbell Scientific PT100/3), for which the specified accuracy is better than ±0.1 °C at 0 °C, and within ±0.2 °C at ±100 °C (class AA in IEC (2008)); the Young screen specifies a maximum radiation error of 0.2 °C in 1000 Wm −2 radiation flux.
Thermometer resistances were sampled every second by a Campbell Scientific CR9000X data logger.Many other meteorological instruments operate at the same site, including for measuring radiative fluxes and wind speed.In particular, the net radiation R n is found using independent measurements of the downward and upwards 'long wave' and 'short wave' radiation fluxes, denoted by L dn , L up , S g and S up respectively, which are related by The four component Kipp and Zonen CNR4 radiometer used responds between 300nm to 2800nm for short wave radiation, and 4.5 to 42 μm for long wave radiation 2 .Wind speeds are also measured at a range of heights, using Vector Instruments A100 cup anemometers.Differences in temperature between the naturally and mechanically ventilated thermometers are analysed for ventilation, lag time and radiation exchange effects.For this, the temperature difference, T diff , is regarded as representing the NVTS temperature bias in determining the true air temperature, i.e. by assuming that the aspirated PRT provides air temperature with negligible uncertainty and time response.

Results
Examples of the combined meteorological measurements are provided in figure 1, for a clear day (25 December 2019) and a day of broken cloud (15 May 2020) respectively.The NVTS thermometer, conventionally referred to as the 'dry bulb' thermometer (T dry ) and the aspirated thermometer (T asp ) are shown in the upper panels, followed by the short wave and long wave radiative fluxes, wind speeds near the surface (at 1.12 m, 2 m and 5 m, denoted u 1.12 , u 2 and u 5 ).The difference T diff between T dry and T asp , defined as T diff =T dry − T asp, is given in the lower panel, where positive T diff indicates that the NVTS environment is warmer than air temperature as determined by the aspirated screen.
Figure 1 shows that T diff is usually small (=0.5 °C) whenever the low-level wind exceeds about 1 ms −1 , but that larger values of T diff occur at lesser wind speeds.For the December day (figure 1(a) to (d)), T diff > 1.0 °C occurs in the late afternoon (figure 1(d)), when the wind speed drops, and T diff becomes more variable: the effect is so pronounced that it can even be seen directly in figure 1(a), around the daily temperature maximum which is evidently over-estimated by the NVTS T dry .For the May day (figure 1(e) to (h)), early and late parts of the day have relatively calm conditions, during which the largest T diff occur.At about 06UTC, the post-sunrise rapid temperature increase highlights the slower response of the NVTS compared with the aspirated thermometer.Around noon, variable solar radiation (figure 1(f)) arises from broken cloud cover, yielding air temperature fluctuations.These fluctuations also illustrate the different time responses of the NVTS and aspirated sensors, as cloud-induced fluctuations initially appear in T diff , but diminish after 12UTC, when the wind increases.
Figure 2(a) shows the range of the full temperature dataset, with figure 2(b) and table 1 summarising the distribution of T diff.The preliminary conclusions from figure 1 are borne out, as very many values have |T diff |=0.5 °C, and 50% of T diff values are within −0.07 °C to 0.06 °C.This also demonstrates that the two thermometers are closely matched.A skew towards negative T diff indicates a tendency of the NVTS for air temperature underestimation.

Causes of the air temperature bias
Although table 1 shows that large |T diff | are rare, estimating or reducing air temperature biases becomes important when comparing temperatures predicted by weather forecast models with near-surface observations, and for assessing reliability of extreme values obtained at different sites.

Wind speed effects on temperature bias
Following the wind speed influence expected from section 2, T diff is plotted against u 2, (figure 2(c)).This clearly demonstrates that the widest spread of T diff occurs during low wind speeds, when u 2 <1ms −1 .The spread of T diff with u 2 can be represented by binning the T diff values by wind speed and calculating the associated bin standard deviation.Figure 2(d) shows the form of the response.By fitting a power law, the variation in |T diff | can be found from (1.96 σ Tdiff )=p u 2 q , where p=0.311and q = −0.36.The exponent q is broadly consistent with the physical processes represented by equations (1) and (4).

Wind speed effects on screen time response
Because the lag time τ is a central parameter in the NVTS response, it is now determined explicitly.Assuming T asp responds much more rapidly than the NVTS, successive samples of T asp and T dry during steady changes can provide relative rates of change to derive τ. (This methodology based on equation (2) is described in the Supplementary Information).Figure 3(a) shows the derived lag times, binned by wind speed.The τ variation with wind speed follows equation (1) with A=(2.89±0.14)minutes and n=−0.49±0.04,where the uncertainties are 1.96 standard errors.τ becomes approximately steady for u 2 >2 ms −1 (as for Harrison, 2011), but as u 2 →0, τ →∞, although free convection will maintain a finite value in practice.Figure 3(b) provides additional context, using equation (3) to calculate the temperature error for different thermometer lag times, during a steady temperature increase.The temperature bias variation presented in figure 2(d) can therefore be largely explained by the increase of NVTS lag time with decreasing wind speed.

Representing the air temperature bias
Whilst the range of T diff estimated in section 4.1 solely used wind speed information, further understanding of the physical processes may allow T diff variations to be estimated from other quantities and therefore, potentially, corrected.The effect of time response on tracking rapid changes in air temperature is considered first, by assuming that the air temperature responds to the radiative heating or cooling of the surface beneath it.This assumption is justified by figure 4(a), which plots the rate of change of the more rapid aspirated thermometer, dT asp /dt, against R n .For most R n values (−50 Wm −2 to 600 Wm −2 ), there is proportionality between R n and dT asp /dt.The NVTS damping effect on rapid temperature changes will therefore also vary with R n .This is made apparent in figure 4(b), by plotting T diff against R n .In this well-ventilated case (u 2 >1ms −1 ), T diff varies inversely with R n .This is consistent with the NVTS lag causing a negative temperature bias during rapid temperature increases, as suggested by figure 3(b).
Under light winds, only very slow NVTS changes occur in response to air temperature changes (figure 3(b)).The T diff data have therefore been selected for light wind conditions.During poor ventilation (u 2 <0.5ms−1 ), figure 4(c) shows that the response of T diff to R n is reversed from figure 4(b), i.e.T diff becomes directly proportional to R n , consistent with the radiation error response of equation (4).For intermediate ventilation (0.5ms −1 <u 2 <1ms −1 ), figure 4(d), T diff remains proportional to R n , but less strongly so.
To summarise, the two physical processes influencing the accuracy of air temperatures, as outlined in section 2, have been distinguished.At low wind speeds (u 2 <0.5 ms −1 ), direct radiation exchange dominates and T diff is directly proportional to R n .At greater wind speeds (u 2 >1 ms −1 ), T diff becomes inversely proportional to R n , indicating that the time response effects become dominant.In either case, a linear approximation satisfactorily represents the variation; table 2 lists the coefficients determined.

Correcting the air temperature bias
These findings are now applied to the entire dataset.In figure 5(a), dT asp /dt is shown, plotted against simultaneous measurements of R n and u 2 .Regions of rapid temperature changes appear on figure 5(a) for the greatest and least R n values, as expected from figure 4(a).These are absent for u 2 <1ms −1 , and the proportionality with R n emphasises the radiation effects in this region.(This also justifies the different fitted lines of figures 4(b), (c) and (d)).
In figure 5(b), all T diff values obtained are plotted against R n and u 2 and characteristic regimes are again apparent.Firstly, when the wind speed u 2 exceeds about 1ms −1 , with large R n (e.g.strong sunshine), the NVTS temperature falls below air temperature (blue on the right of figure 5(b)), whereas, for negative R n (e.g. a clear night), the NVTS temperature exceeds air temperature (red on the left of figure 5(b)).This arises because the NVTS response time is insufficient to cool or warm rapidly enough to track the air temperature change.Secondly, when u 2 is small (<1ms −1 ), the NVTS temperature excess appears approximately proportional to R n (increasingly red from left to right along the bottom of figure 5(b)).When calm and sunny, the NVTS radiation exchange is therefore dominated by solar heating.Together, these results confirm that, firstly, that the NVTS is  Table 2. Coefficients of fitted lines to T diff =m R n +c.

Conditions
Gradient m (°C Well ventilated u 2 >1 ms −1 −4.00×10 -4 0.023 0.98 Moderately ventilated 0.5 ms −1 <u 2 1 ms −1 2.27×10 -4 −0.0015 0.58 Calm u 2 0.5ms −1 7.17×10 -4 −0.101 0.57 unable to fully capture positive-or negative-going temperature fluctuations even when conditions are apparently well ventilated, and, secondly, during poorly ventilated conditions, that the NVTS temperature is strongly influenced by radiation exchange.Use of the table 2 parameterisations as potential bias corrections to the data of figure 5(b) for different wind speed ranges is evaluated in figure 5(c).This demonstrates that the corrections act to diminish the screen temperature over-reading (red) and under-reading (blue) regions on the left and right-hand sides of figure 5(b), mitigating the time response effect.Further, the low wind speed radiation effects, apparent along the bottom of figure 5(b), are also reduced in figure 5(c).Table 3 summarises the T diff properties with and without the adjustments applied.Overall, these adjustments lead to less spread in 87% of the T diff data, and the negative skewness associated with the naturally ventilated screen's underestimation of air temperatures is reduced from −1.05 to −0.26.

Conclusions
Naturally ventilated thermometer screens permit accurate air temperature measurements, to ±0.1 °C in most circumstances.However, air temperature and the NVTS temperature can occasionally differ substantially by more than 0.5 °C in light winds because of a slow response.Absolute rates of temperature changes >0.5 °C min −1 occur in about 2% of cases in the mid-latitude UK (Burt and dePodesta 2020), but the variable response time of the NVTS limits its ability to track rapid temperature changes.The 1 min averaging period conventionally used in meteorology may therefore be insufficient with a NVTS.The coefficients explicitly determined here for the lag time parameterisation (equation 1), A=2.89min and n = −0.49,are useful for modelling screen time response, and establishing when the 1 min averaging criterion can be fulfilled.
The measured NVTS temperature is therefore only ever an approximation to air temperature.Likely temperature uncertainties can be estimated from the local wind speed, using measured or modelled values.Retrospective re-evaluation is possible: qualitative wind speed estimates using the Beaufort scale (e.g.Burt 2012) suggest, from figure 2(d), that when a wind strength of Beaufort force 3 (i.e.>4 ms −1 ) can be established, the maximum air temperature uncertainty will be about 0.2 °C.Whilst the detailed corrections will depend on the situation, instruments and the sampling interval used, the methodology presented here uses physical principles which should generalise to similar NVTS operating in a standard manner.
Widespread and enduring use of naturally ventilated thermometer screens has yielded a long series of reliable measurements on which the instrumental climate record depends.However, even during appreciable wind speeds (3 to 5 ms −1 at 2m height), these results show that the time response of a large screen is never sufficient for rapid atmospheric changes to be fully captured.Consequently, until this effect of natural variability is removed by the more extensive use of aspirated thermometers throughout climate observation networks, an influence on some recorded extremes in the climate record cannot be ruled out.The findings here suggest that this will also apply to underestimation of maximum temperatures and overestimation of minimum temperatures during low wind conditions, which may also influence climatological mean values at such times.

Figure 2 .
Figure 2. Distribution of (a) aspirated thermometer air temperatures (T asp ) made between 7 November 2019 and 16 August 2020 (5 min averages) at Reading, and (b) differences between naturally ventilated and aspirated thermometers (T diff =T dry − T asp ).(c) T diff plotted against simultaneous u 2 .(d) Spread of T diff binned by wind speeds (in steps of 0.2 ms −1 ) with a power law fit added and the number of observations (N obs ) in each bin shown.(5 min mean values are used and 1.96 standard deviations provide the 95% confidence range on T diff ).

Figure 3 .
Figure 3. (a) Lag time τ calculated for the naturally ventilated screen by assuming a first order response, with a power law fit added (dashed line marks τ =1 min).Values are medians, using 20s data binned into wind speed steps of 0.5 ms −1 .(b) Calculated difference between air temperature and thermometer temperature after 5 min for different lag times, assuming a steady rate of temperature change.

Figure 5 .
Figure 5. (a) Rate of change of temperature (aspirated thermometer), plotted against net radiation (R n ) and 2m windspeed u 2. (b) and (c) Temperature differences T diff plotted against R n and u 2 , (b) uncorrected for naturally ventilated screen time response and radiation error and (c) corrected using the relationships in figure 4. (Values used are 5 min means.Black pixels mark values lying outside the range of the colour bar).

Table 1 .
Summary statistics of temperature differences.

Table 3 .
Summary statistics for correction of air temperature uncertainties.