INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 28: 961–972 (2008) Published online 1 August 2007 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/joc.1586
Humidity parameters from temperature: test of a simple methodology for European conditions Yvonne Andersson-Sk¨old,a* David Simpsonb,c and Viel Ødegaardb a
Swedish Geotechnical Institute, Gothenburg, Sweden Norwegian Meteorological Institute, Oslo, Norway Radio & Space Science, Chalmers University of Technology, Gothenburg, Sweden b
c
ABSTRACT: Atmospheric water content is important for local and regional climate, and for chemical processes of soluble and solute species in the atmosphere. Further, vapour pressure deficit (D) is one of the key controls on the opening of stomata in plants and is thus an important force for evapotransporation, plant respiration and biomass production and for the uptake of harmful pollutants such as ozone through the stomata. Most meteorological stations typically measure both temperature and relative humidity (RH). However, even if recorded at finer time resolution, it is usually the daily or often monthly means of RH which are published in climate reports. Unfortunately, such data cannot be used to obtain the changes in RH or vapour pressure deficit over the day, as this depends strongly on the diurnal temperature variation during the day and not upon the mean temperature. Although RH typically changes significantly over the day, the ambient vapour pressure is often remarkably constant. Here a simple method to estimate diurnal vapour pressure is evaluated, based upon an assumed constant vapour pressure, and that recorded minimum temperatures approximate dew-point temperatures. With a knowledge of only temperature, we will show that day to day estimates of vapour pressure, humidity and especially D, can be made with reasonable accuracy. This methodology is tested using meteorological data from 32 sites covering a range of locations in Europe. Such a simple methodology may be used to extract approximate diurnal curves of vapour pressures from published meteorological data which contains only minimum temperatures for each day, or where humidity data are not available. Copyright 2007 Royal Meteorological Society KEY WORDS
humidity; RH; vapour pressure deficit
Received 18 April 2007; Accepted 3 June 2007
1.
Introduction
The ability of water to absorb, release and transfer heat over long distances as well its ability to transport other species and act as a medium for chemical transformation makes water of unique importance in the atmosphere. The local atmospheric water content is important for chemical processes of soluble and solute species in the atmosphere (e.g. adsorption and absorption of gases in the atmosphere and the products and kinetics of several chemical atmospheric transformation reactions), as well as the deposition of nutrients and pollutants to the biosphere (e.g. Jones, 1992; Stull, 1988; Campbell and Norman, 1998). Humidity indices are also used as measures of human discomfort (Schoen, 2005), and can even be used to estimate such things as lifting condensation level (cumulus cloud-base, Lawrence 2005). Water content is expressed in a number of common units. An important term is the ambient water vapour pressure, e (kPa), which expresses the partial pressure of water vapour. At a given temperature, T , water vapour * Correspondence to: Yvonne Andersson-Sk¨old, Swedish Geotechnical Institute, Chalmers Vasa, Hugo Grauers gata 5 B, SE 412 96 Gothenburg, Sweden. E-mail:
[email protected] Copyright 2007 Royal Meteorological Society
pressure in the atmosphere cannot exceed the saturation vapour pressure, es (T ) (kPa) by any significant amount. Dew point temperature (Td ) is defined as the temperature to which air has to be cooled (at constant pressure) to reach its saturation vapour pressure, thus e(T ) = es (Td ). Relative humidity (RH) is closely related to these variables. Two slightly-different definitions of RH are in common use, based upon either dry mass mixing ratio or vapour pressure (Bohren and Albrecht, 1998; Lawrence, 2005). We use the pressure-based definition: RH =
e es (Td ) = es (T ) es (T )
(1)
RH may be given as a fraction or in percentage. Of particular importance for this paper, the vapour pressure deficit, denoted D (kPa), is defined by the difference between saturation and ambient water content: D = es (T ) − e
(2)
D is one of the key controls on the opening of stomata in plants and is thus an important force for evapotranspiration, plant respiration and biomass production (e.g.
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Campbell and Norman, 1998; Jarvis and McNaughton, 1986; Jones, 1992; Kimball et al., 1997, and references therein) and for the uptake of harmful pollutants such as ozone through the stomata (Emberson et al., 2000; Simpson et al., 2001 2007). Ambient vapour pressures have a diurnal variation which is driven mainly by diurnal temperature changes, and typically minimum vapour pressure is reached at the time when temperature is at the minimum. The ambient vapour pressure variation is often quite small, however, especially in temperate humid climates. In the absence of air mass changes the vapour pressure can be relatively stable during the day and from day to day. The slightly higher vapour pressure during the day than at night can often even be ignored in comparison with other sources of uncertainties in the measurements (Campbell and Norman, 1998). On the other hand, even if water vapour concentrations were constant throughout the day, RH can vary significantly because of the diurnal temperature changes, and the fact that es (T ) is a very strong function of temperature. The fact that the RH may, in general, vary without significant variation in the ambient water content means that RH alone often gives little information about the daily atmospheric water content. If measurements of humidity or dew-point and ambient temperature are available with good time resolution, then accurate estimates of D over the day present no problems. However, it is frequently the case that no information about RH or Td with adequate time-resolution is available. In particular, even if meteorological stations record RH or Td at fine time resolution, it is usually the daily or often monthly means of RH which are published in climate reports. Unfortunately, such data cannot be used to obtain the changes in RH or vapour pressure deficit over the day, as this depends strongly on the diurnal temperature variation during the day and not upon the mean temperature. Therefore it has been suggested that the minimum daily temperature can be taken as the dew point temperature and D estimated from this (Campbell and Norman, 1998; Dyer and Brown, 1977; Kimball et al., 1997). Such methodologies have been tested and found to work well for the United States (Kimball et al., 1997), but less well in the arid climate of India (Butler, 1992). Further, the literature deals mainly with monthly or daily average values of Td , and not the hourly variation which is often of importance for modelling plant behaviour. To our knowledge, such simple methodologies have not been evaluated in Europe. One motivation for this paper has been to evaluate whether such simple assumptions could perform satisfactorily in this region. The second motivation was to further focus on the humidity parameters around noontime, since this corresponds to the time of maximal stomatal uptake for vegetation (Jones, 1992; Emberson et al., 2000), and to investigate how well we could predict day to day variations in such parameters. Copyright 2007 Royal Meteorological Society
2.
Basis of estimation method
The basis of the simplified methodology presented here rests on two basic hypotheses: 1. The measured daily minimum temperature (usually recorded at 6 GMT in Europe), Tn , is a reasonable estimate of the dew-point temperature, Td , (and hence of water vapour pressure, e) of the air at that time of day. 2. The dew-point temperature (or water vapour pressure) can be regarded as approximately constant throughout the day, so that Tn can also be used as an estimate of Td throughout the day. The validity of these hypotheses is discussed below, but when true, Tn gives a good estimate of e. With the assumption that e remains constant over the day, RH can then be calculated at all other times of day from a knowledge of temperature alone. If we denote the approximate vapour pressure estimated by this methodology as ea , and the approximated RH and vapour pressure deficit as RHa , Da , we can express these assumptions as: Real-world Approximation Td = Td (t) Td = Tn e = es (Td ) ea = es (Tn ) RH = e/es (T ) RHa = ea /es (T ) = es (Td )/es (T ) = es (Tn )/es (T ) Vapour pressure deficit D = es (T ) − e Da = es (T ) − ea
Dew-point temperature Vapour pressure Relative humidity
where Td = Td (t) indicates that Td is a function of time. 2.1.
Validity of assumptions
Of course, the assumptions presented above are intended to be approximations, and neither assumption holds true everywhere. Kimball et al. (1997) has discussed the validity and limitations of Tn -based methods for the United States and Alaska, but we will review here some of the important points. The assumption that Td ≈ Tn , which is equivalent to saying that RH approaches 100%, is a rule of thumb used in weather forecasting (Dyer and Brown, 1977). This approximation is widely used for a number of applications (Dyer and Brown, 1977; Campbell and Norman, 1998; Kimball et al., 1997, Running et al., 1987), and follows from the physical meaning of Td , which is related to the temperature at which dew forms (see Bohren and Albrecht 1998 for a critical discussion of this point). Cooling of the surface at night (due to outgoing longwave radiation) takes place everywhere, at least in the absence of strong advective effects. As the air cools, air temperatures approaches Td . If the temperature falls close to Td water starts to condense, and further heat loss results in greater condensation rather than falling temperatures. In extreme circumstances temperatures may fall below Td , but under normal conditions air temperature remains above or equal to Td (Bohren and Albrecht, 1998). Int. J. Climatol. 28: 961–972 (2008) DOI: 10.1002/joc
HUMIDITY PARAMETERS FROM TEMPERATURE
Indeed, nocturnal cooling frequently causes RH to approach 100% during the night in a wide range of climates (Kimball et al., 1997). Of course, many exceptions occur, and such exceptions are seen for the sites used in this study. For example, Figure 1 illustrates the range of RH values found for each of the synoptic hours at the site Prague in central Europe. Although these data are available only at 3-h intervals, and thus may miss the exact time of minimum temperature, it seems clear that many of the nighttime RH values lie below 100%. Indeed, the median RH values at 3 GMT and 6 GMT lie around 90%, with 100% lying outside the range of these data. Of course, one reason for this is that air temperatures, measured at screen heights of typically 2 m, are usually greater than temperatures at the surface, where dew normally forms. In the model of Dyer and Brown (1977), for example, dew formation was assumed to start when RH exceeded 90%, but air temperatures decreased after this time, and they indeed assumed that Tn was equivalent to Td . A number of situations can give rise to low RH at night. Windy conditions for example can mix warm, dryer, air from aloft down towards the surface, and temperatures might not fall sufficiently for RH to reach 100%. As another example, at mountain-sites meteorological stations are often affected by topographic flows, or simply by air-masses advected into the site which have little contact with the ground surface, so values of RH 0.8 for noontime D. The reasons behind the strong seasonal differences in performance for Narvik are discussed in section 5.
5.
Discussion
As noted in section 1, we make two main assumptions in our methodology, which are, briefly, that (1) Tn approaches Td , or equivalently that RH approaches 100% at night; (2) that Td estimated from the nighttime Tn is a good surrogate for Td throughout the day. Indeed, this second assumption does seem to hold quite well for many of our sites. The differences between Tn and Td (12) are usually within a few degrees, with mean std. deviations of 3.2 ° C in winter and 2.8 ° C in summer. Many of the factors discussed in section 2.1 will lead to situations where RH is less than 100% at nighttime. Thus, with our methodology (which assumes RH ≈ 100%) we would expect that we over-predict the vapour pressure during the morning, and consequently for the rest of the day under many circumstances, and especially in ‘dry’ conditions. This expectation is supported by the statistics shown in Table II, which show a positive intercept (i.e. the model predicts consistently high RH), and slope of less than one. Examination of these statistics on a stationby-station basis (not shown) shows that this relation holds in almost every case. Further, nearly all sites show correlations between Td (12) − Tn and noontime RH, with days of low RH being associated with cases where Tn > Td (12), and days of high RH being associated with cases Copyright 2007 Royal Meteorological Society
where Tn < Td (12). Thus, those days producing lower noontime RH are also those where we find Td (12) is much lower than Tn , and hence RHa > RH. Conversely, days with high RH are associated with Td (12) > Tn (presumably due to daytime inputs of water vapour or air mass changes), giving RHa < RH. (Put more simply, on dry days we tend to overpredict RH, and on humid days to underpredict.) The availability of water is a key factor also, as the amount of evaporation can modify the diurnal cycle of temperature and moisture. At high latitudes, the seasonal cycle of temperature is large, and soil and even sea freezing plays a major climatic role. In spring, water is not available for evaporation until the snow melts and the ground (or sea) thaws (e.g. Betts, 2004). In general the boundary layer is dry during winter and spring due to the low availability of water evaporation (ibid ). This explains the large differences seen between Td and Tn at the Narvik site, which occur during the winter months when the ground is snow-covered and/or frozen. Correlation coefficients are much better for e and D than for RH. This partly reflects the strong seasonal cycles in the former parameters, with much higher values in summer than winter. Another factor is that the errors in predicting RH have been found to be higher in the winter months, when temperatures and thus vapour pressures are low. Finally, as discussed for Rome, much of the better performance for D compared to RH can be explained by the importance of temperature for D. Noontime temperature is often significantly greater than nightime and dew-point temperatures, and the exponential Int. J. Climatol. 28: 961–972 (2008) DOI: 10.1002/joc
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970 (a) 3.0 Roma 2.5 2.0 1.5 1.0 0.5 0.0 40 30 20 10 0 −10 −20 r b n Ja Fe Ma (b) 3.0 2.5 Roma 2.0 1.5 1.0 0.5 0.0 40 30 20 10 0 −10 −20 r b n Ma Ja Fe (c) 3.0 2.5 Roma 2.0 1.5 1.0 0.5 0.0 30 20 10 0 −10 −20 −30 r b n Ja Fe Ma
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Figure 8. Comparison of observed and estimated (subscript a) parameters for (a) Rome, Italy, (b) Prague, Czech. Rep., and (c) Narvik, Norway, 1997. Upper plot for each site shows noontime values of vapour pressure deficit, D. and lower plots show temperature parameters (cf Figure 7). This figure is available in colour online at www.interscience.wiley.com/ijoc
dependence of es upon T makes D (= es (T ) − es (Td )) more dependent upon accurate values of T than of Td . Indeed, moderate errors in Td and thus es (Td ) have relatively low impact on D. Thus, the simple methodology may even show quite poor performance for RH, but with good performance statistics for e and D. This is seen clearly in the extreme case of Narvik (Figures 8–9), where good correlation is achieved for D despite having the worst performance in terms of bias in RH. For many environmental problems this good correlation for e and D is more important than good performance for RH and so the proposed methodology seems very satisfactory. Considering the spatial variation in model performance, then it is evident from Figures 3–4 that many of the sites where performance is poorest are located Copyright 2007 Royal Meteorological Society
near the coast. This may well be due to the effects of sub-100% RH in marine air masses, or sea-breeze effects. The poorer performance for Geneva (site 21) and Budapest (site 20) is more puzzling, since sites just a little further north show very good performance (sites 16, 17, 18, i.e. Wroclaw, Prague and Saarbrucken). A possible explanation is that Geneva and Budapest are both subject to more extreme winters, and less affected by maritime air masses, than the other sites.
6.
Summary and conclusions
In this study, we set out to test the validity of the idea that early-morning temperature values can be used to assess changes in RH, vapour pressure (e) and vapour pressure deficit (D) over the course of a day and season. Int. J. Climatol. 28: 961–972 (2008) DOI: 10.1002/joc
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Figure 9. Scatter-plots of observed and estimated (subscript a) noontime vapour pressure deficits for (a) Rome, Italy, (b) Prague, Czech. Rep., and (c) Narvik, Norway, 1997.
The idea rests upon the observation that vapour pressure values are often very stable over the day, and that if we assume RH levels are close to 100% during nighttime, then temperature alone is sufficient to predict humidity parameters. We are particularly interested in the performance of such a methodology for predicting noontime values of D, because of its strong link to stomatal uptake and hence pollutant uptake (Emberson et al., 2000; Simpson et al., 2007). This methodology has been tested using meteorological data from 32 sites covering a range of locations in Europe, with a focus on predicting day to day changes in noontime values. The results show good agreement between the observed and estimated values of RH, e and D, with relative biases of less than 2%. Correlations are moderate for RH, but rather good for e and especially D. The better performance for D compared to RH can be explained by their very different seasonal variations, the greater importance of temperature for absolute values of D than RH, and the fact that noontime temperature is often significantly greater than nightime and dew-point temperatures. The exponential dependence of es upon T Copyright 2007 Royal Meteorological Society
means that moderate errors in Td and thus es (Td ) have relatively low impact on D. If we regard noontime vapour pressure deficit (D) as the most important parameter for this study, we obtain an average R 2 value of around 0.8, just using temperature data alone. More advanced methods have been proposed in the literature to evaluate Td , and these methods could certainly be used to refine our analysis (e.g. Kimball et al., 1997; Hubbard et al., 2003). However, such methods would require additional data or assumptions, and require modification for different parts of Europe, and an extensive evaluation which is beyond the scope of our study. We have shown that even the simplest methodology shows a rather good ability to predict noontime values of humidity parameters, especially D, in the summer months. It is difficult to know if such methodologies provide sufficient accuracy for different applications. This obviously depends on the application and the validity of the assumptions used for each particular site. For example, calculations of stomatal-uptake of ozone are moderately sensitive to uncertainties in D (Simpson et al., 2003), and in many cases our simplified methodology should provide Int. J. Climatol. 28: 961–972 (2008) DOI: 10.1002/joc
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adequate data for such calculations. The validity of the assumptions used can in many cases be assessed from expert knowledge for specific locations, or from periods for which relevant temperature and humidity were available. Lawrence (2005) gives a range of examples where even moderately accurate RH or Td estimates can be used in practical applications. However, we can note that even where observations of humidity parameters are available, these are typically uncertain measurements, subject to drift (Kimball et al., 1997), and of course suffer from data-gaps. The temperature-only based methodology, as tested here or from more advanced treatments, would enable a very useful and easy quality-control which could be used to at least flag for further inspection periods where the RH measurements look questionable, or are absent. Acknowledgements The work of YAS was supported by the Swedish Geotechnical Institute and Swedish Environmental Protection Agency (while working at the Earth Science Centre, Gothenburg). The work of DS was supported by the Cooperative Programme for Monitoring and Evaluation of the Long-range Transmission of Air pollutants in Europe (EMEP) under UNECE, and partially by EU NitroEurope IP (contract 017841). References Alduchov OA, Eskridge RE. 1996. Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology 35: 601–609. Betts A. 2004. The diurnal cycle over land. In Forests at the Land-Atmosphere Interface, Mencuccini M, Grace J, Moncreiff J, Mc Naughton KG. (eds). CABI Publishing: Wallingford, UK; 73–94. Bohren CF, Albrecht BA. 1998. Atmospheric Thermodynamics. Oxford University Press: New York. Butler D. 1992. Daily patterns of dew-point temperature in a semi-arid climate. Agricultural and Forest Meteorology 60: 267–278.
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Campbell G, Norman J. 1998. An Introduction to Environmental Biophysics. Springer-Verlag New York, Inc. Dyer J, Brown D. 1977. A climatic simulator for field-drying hay. Agricultural Meteorology 18: 37–48. Emberson L, Ashmore M, Cambridge H, Simpson D, Tuovinen J. 2000. Modelling stomatal ozone flux across Europe. Environmental Pollution 109(3): 403–414. Garratt J. 1992. The Atmospheric Boundary Layer. Cambridge University Press: Cambridge. Hornsteiner M. 2005. Local foehn effects in the upper Isar valley, part 1: Observations. Meteorology and Atmospheric Physics 88: 175–192. Hubbard K, Mahmood R, Carlson C. 2003. Estimating daily dew point temperature for the Northern Great Plains using maximum and minimum temperature. Agronomy Journal 95: 323–328. Jarvis P, McNaughton K. 1986. Stomatal control of transpiration: scaling up from leaf to region. Advances in Ecological Research 15: 1–49. Jones H. 1992. Plants and Microclimate. A Quantitative Approach to Environmental Plant Physiology, 2nd edn. Cambridge University Press: New York, USA. Kimball J, Running S, Nemani R. 1997. An improved method for estimating surface humidity from daily minimum temperature. Agricultural and Forest Meteorology 85: 87–98. Lawrence MG. 2005. The relationship between relative humidity and the dewpoint temperature in moist air. Bulletin of the American Meteorological Society 86: 225–233. New M, Hulme M, Jones P. 2000. Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate. Journal of Climate 13: 2217–2238. Running SW, Nemani RR, Hungerford RD. 1987. Extrapolation of synoptic meteorological data in mountainous terrain and its use for simulating forest evapotranspiration and photosynthesis. Canadian Journal of Forest Research 17: 472–483. Schoen C. 2005. A new empirical model of the temperature-humidity index. Journal of Applied Meteorology 44: 1413–1420. Simpson D, Tuovinen J-P, Emberson L, Ashmore M. 2001. Characteristics of an ozone deposition module. Water Air and Soil Pollution: Focus 1: 253–262. Simpson D, Tuovinen J-P, Emberson L, Ashmore M. 2003. Characteristics of an ozone deposition module II: sensitivity analysis. Water Air and Soil Pollution 143: 123–137. Simpson D, Emberson L, Ashmore M, Tuovinen J. 2007. A comparison of two different approaches for mapping potential ozone damage to vegetation. A Model Study. Environmental Pollution 146: 715–725. Stull R. 1988. An Introduction to Atmospheric Boundary Layer Meteorology. Kluwer Academic Publishers: Dordrecht.
Int. J. Climatol. 28: 961–972 (2008) DOI: 10.1002/joc
