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Theor. Appl. Climatol. (2008) 94: 225–239 DOI 10.1007/s00704-007-0356-7 Printed in The Netherlands 1 2 Department of Statistics and Actuarial Financial Mathematics, University of the Aegean, Karlovasi, Samos, Greece School of Environmental Sciences, University of East Anglia, Norwich, U.K. A comparison of temperature inversion statistics at a coastal and a non-coastal location influenced by the same synoptic regime A. E. Milionis1 , T. D. Davies2 With 13 Figures Received 10 January 2007; Accepted 29 August 2007; Published online 11 January 2008 # Springer-Verlag 2008 Summary The primary aim of this work is to examine to what extent the climatology of atmospheric temperature inversions at one location is site specific, and to what extent it reflects a wider area for which the same synoptic conditions can be assumed. To this end radiosonde data from a coastal and a non-coastal location in eastern England separated by 210 km and influenced by the same synoptic conditions are used. Analysis of these data shows that there is a pronounced difference between the inversion climatologies at the two sites. The vertical distribution of base-heights of inversions has a very distinct maximum at a height of about 200 m at the location proximate to the coast. This maximum is not present at the inland location, and the difference is due to both sea-breezes and advection from the sea due to synopticscale wind field. Examining the vertical distributions of baseheights of inversions at the two locations under conditions that either maximize or minimize the effect of sea-breeze it is found that the differences in the two distributions are to a certain extent deterministic (therefore predictable) rather than random, as the dominant mechanisms which are responsible for these differences (diurnal and yearly cycles) have an obvious regularity. Using standard statistical methods it is further shown that, apart from this difference, nearly all other inversion statistics for the two locations are similar when the atmospheric layer from surface to 700 hPa is taken into consideration. However, when only the first inversion Correspondence: A. E. Milionis, Department of Statistics and Actuarial Science, University of the Aegean, Karlovasi 82300, Samos, Greece, e-mail: [email protected], on leave from the Bank of Greece, Department of Statistics in each temperature profile is considered, the inversions activity throughout the year, defined with the aid of an index, in the two locations is not correlated, indicating that for the lowest part of the surface-700 hPa region, local factors overwhelm the synoptic conditions. Thus, these results provide evidence that the inversion climatology at one location can be generalised over a wider area where the same synoptic regime can be assumed. Given that, at least to an extent, any differences in the characteristics of inversions due to local factors can be inferred once the underlying mechanisms are carefully studied, this work has also important implications for micrometeorological studies as for instance the local diffusion and transport of air pollutans. 1. Introduction The development of the climatology of (statically) stable layers in the lower atmosphere is of importance since, amongst other reasons, it is related to the ability of the atmosphere to inhibit vertical motion. With a few exceptions (Sivaramakrishnan et al. 1972; Nodzu et al. 2006) it is the isothermal lapse rate that is taken as the limiting one, and only layers with negative lapse rates, (the so-called temperature inversion layers), are considered. That happens not so much because there is any strong physical reason for such a separation, but due to the fact that the first stable layer encountered in a temperature profile 226 A. E. Milionis, T. D. Davies is most often an inversion layer (Milionis and Davies, 1992, 1994a). For this reason many studies on the effect of atmospheric conditions on air pollution relate air pollution episodes with temperature inversions (e.g. Kukkonen et al. 2005; Janhall et al. 2006; Malek et al. 2006; Kerminen et al. 2007). Additionally, several of the existing inversion climatologies are restricted to the surface inversions or the first elevated inversions only (e.g. Hosler 1961; Tyson et al. 1976; PrestonWhyte et al. 1977). In our previous research on inversion layers (Milionis and Davies 1992, 1994a, 1994b, 2002, 2007) we used radiosonde data from the U.K. upper air station at Hemsby (52 390 N, 1 410 E, at an elevation of 14 m) to: (a) establish the main characteristics of the climatology of inversion layers (Milionis and Davies 1992, 1994a, 2002, 2007) and (b) examine their effect on groundlevel air pollution (Milionis and Davies 1994b). In order to explain some of the results we made assumptions about the effect of the local topography, in particular the proximity of Hemsby to the North Sea (the upper air station is located 1.5 km from the coast). These assumptions, although reasonable, need further justification, and one way to test for that is to compare the inversion statistics for Hemsby with those from non-coastal stations. As the influence of local factors are expected to affect the statistics of inversions mainly in the first kilometre or so above the ground, this comparison is important particularly due to the significance that the inversion layers of this atmospheric region have in local-scale diffusion and transport of air pollutants. Although the largest part of the published research work on inversion climatology refers to data from a single location (e.g. Milionis and Davies 1992, 2007; Prezerakos 1998; Abdul-Wahab 2004; Kassomenos and Koletsis 2005), there are several studies on the comparison of inversion climatologies for different locations, in particular coastal and non-coastal locations (Hosler 1961; Preston-Whyte et al. 1977; Nodzu et al. 2006), which are worthy to be briefly reviewed. Hosler (1961), in his study of frequencies of surface and near surface inversions over the contiguous U.S.A., concludes that inversion frequencies at stations in coastal areas reflect marine influences. Low level stability, depending on whether the nearby water surface is colder or warmer that the adja- cent land may be either inhibited or enhanced due to advection. As Hosler found, for coastal areas along the south-eastern States and Gulf of Mexico, the formation of inversions is inhibited particularly overnight, while the cold waters of the North Atlantic Ocean cause higher frequencies of inversions at coastal stations, particularly during the day, due to the cool sea-breezes. Preston-Whyte et al. (1977), studying the climatology of the lowest (i.e. first) elevated inversions over Southern Africa, found that the height of the first elevated inversion is greater over the plateau than over coastal areas. They argued that the height at which elevated inversions occur depends not only on the prevailing synoptic situation, but also on the degree of surface heating and upward convective and turbulent mixing. Nodzu et al. (2006) using radiosonde data for a period of 29 years from 14 upper air costal and non-coastal stations in the Indochina Peninsula investigate the interaction between temperature inversions (more precisely layers with =z>10 K km1 , where represents the potential temperature and z the height) and seasonal changes in convective activity during the dry season to rainy season transition. They conclude that the 14 upper air stations can be classified according to three types of vertical thermal stability, by examining the temporal variations of the distribution of the base-height of inversions. As a general rule, however, in all the above mentioned studies differences in the characteristics of inversions for different locations are attributed to the combined effect of topography and the synoptic conditions. Therefore, in that way it is in general not possible to isolate the true effect exclusively due to topography. The only work in which the focus was exactly on the effect of topography is the one of Riordan et al. (1986), who using data from two meteorological towers, compared the strength and frequency of inversions at two dissimilar sites, one of which was on the shore of Lake Robinson in South Carolina, U.S.A., and the other at a top of a hill about 175 km away. Despite the differences in the local conditions, they found many similarities between the inversion climatologies at both sites; for example, high correlation in the dayto-day values of the strength of the inversions in the predawn hours, which indicated an overall synoptic control. A comparison of temperature inversion statistics In this work a comprehensive study on the comparison of inversion statistics derived using data from two different locations will be undertaken including all inversions up to 700 hPa at two U.K. upper air stations (Hemsby and Crawley), aiming to examine the effect of local factors ceteris paribus. To this end the two locations have been chosen so as to assume that they are influenced by the same synoptic regime. In that way it will be made possible to test previous assump- 227 tions about the topographic effects on the inversion Climatology derived from the Hemsby record. Further, having identified possible influences caused by local topography, it is important to examine to what extent differences in the inversion characteristics caused by such influences could be potentially predictable. This is of much importance in order to assess the extent to which the conclusions from climatological analysis of inversions at a site can be applied more widely. Fig. 1. Location of Hemsby and Crawley 228 A. E. Milionis, T. D. Davies 2. The data Temperature, humidity, and wind data were used from the upper air stations of Hemsby and Crawley. Hemsby, as shown in Fig. 1, is situated 1.5 km from the coast in eastern England (52 390 N, 1 410 E) at an elevation of 14 m, in an extensive area of low relative relief. The upper air station of Crawley is located about 210 km SW of Hemsby, and its distance from the sea is about 32 km. The raw radiosonde data were provided by the U.K. Meteorological Office and cover a period of five years (1976–80). The data used for this study are based on the so-called significant levels and have been derived from the raw radiosonde data for the midday and midnight soundings (for further details on the data, see Milionis and Davies 1992, 1994a, 2002). Adjacent inversions with different lapse rates were merged to give a deeper inversion. The isobar level of 700 hPa was chosen as the reasonable upper limit for the study of the tropospheric inversion climatology in the two sites, as above that pressure surface both the frequency of occurrence and the mean potential temperature difference of inversions decrease very rapidly (a detailed analysis and evidence is presented in Milionis and Davies 1992). 3. Methodology In our recent analysis of the Hemsby record we conclude that the prevailing weather exerts a strong influence on the statistics on inversion layers (Milionis and Davies 2007). Therefore, it is important to control for this influence in order to identify the effect of local topography. This can be made possible by considering data from two (or more) sites where there is justification for assuming that they are influenced by the same synoptic regime. Given that this assumption is justified, then the two (or more) sites should be chosen so that they have different local geography. The upper air station of Crawley fulfils these requirements, as it can be assumed that it is largely influenced by the same synoptic regime, and the influence of the sea is of less importance. The first step for the study of a possible seabreeze effect on the statistics of inversions is to examine the vertical distribution of the base height of inversion layers for the two locations. If there are differences in these two distributions, it is important to examine possible variations in these differences in the vertical distributions of the base-heights of inversions that may be caused by factors which either inhibit or enhance the sea-breezes. If such variations do exist, stronger evidence for the sea-breeze effect will be documented as further insight on the underling physical mechanisms will be provided. Moreover, it is of great importance to examine further these variations and find out, whether or not, they are of deterministic (hence, predictable) or random character. Indeed, if the variations in the differences in the vertical distributions of the baseheights of inversions in the two locations are (at least to an extent) deterministic, then knowledge of the pattern of these variations will make it possible (again to a certain extent) to infer the character of the one distribution from the other. To follow the proposed approach it is necessary to examine the vertical distributions of the base heights of inversions at the two locations separately for midday and midnight, summer and winter. This is because, on average, there is a positive day-time temperature differential between the land and the sea in summer, so the seabreeze circulation is expected to be more common than during winter. On the other hand, at midnight, the temperature differential between the land and the sea often decreases or even reverses its direction. Hence, the difference in the vertical distribution of base heights of low level inversions at the two locations should be maximised in summer at midday and be minimised in winter at midnight. In fact if the sea-breeze is indeed the dominant factor which is responsible for any differences in the vertical distribution of base-heights in the two locations, the two distributions should look very similar in winter at midnight. Further, as it is assumed that Hemsby and Crawley are under the same synoptic regime, it must be examined if different weather patterns affect the statistics of inversions at Crawley in much the same way as at Hemsby. To this end, it makes sense to examine the statistics of inversions: (a) in each location separately under different weather patterns; (b) at both locations for each of the "major" weather patterns. As far as the definition of the major weather patterns is concerned, the well-known Lamb’s weather classification (LWC) which refers to the daily weather A comparison of temperature inversion statistics 229 Table 1. The weather types for each weather class Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic Anticyclonic (A) West (AW) East (AE) South (AS) North (AN) North West (ANW) North East (ANE) South West (ASW) South East (ASE) Cyclonic Westerly Cyclonic (C) Cyclonic West (CW) Cyclonic East (CE) Anticyclonic South (CS) Cyclonic North (CN) Cyclonic North West (CNW) Cyclonic North East (CNE) Cyclonic South West (CSW) Cyclonic South East (CSE) Westerly (W) South Westerly (SW) over the British Isles (Lamb 1972) can be used. This classification scheme, although subjective, it is consistent with the so-called objective classifications schemes (e.g. the so-called Jenkinson objective version of LWC (Jenkinson and Collison 1977), and on some occasions reflects better the true synoptic conditions (see for example Jones et al. (1993) for a comparison of the two weather classification schemes). According to the LWC, a particular weather type is one of the possible combinations between eight directional types, each corresponding to a 45 directional sector and two non directional types, namely; cyclonic and anticyclonic. Purely directional or purely anticyclonic or cyclonic types are included in the classification, so altogether there are 26 weather types. Days where no particular weather type could be recognized are termed unclassifiable. The classification refers to the average weather over a period of 24 h. The most frequent weather types are westerly, anticyclonic, and cyclonic and will be the basis for the three weather classes that we shall use to examine inversion statistics. Hybrid directional anticyclonic and directional cyclonic types will be grouped together with the pure anticyclonic or cyclonic, respectively, to form the anticyclonic and cyclonic classes used in this study. The South-West (SW) type will be grouped together with the westerly type as they are associated with very similar air masses (P. M. Kelly, Climatic Research Unit, University of East Anglia, personal communication) to form the Westerly class. Table 1 shows the weather types which comprise each class. If the assumption that, apart from the geographic influences, which mainly affect the base-heights of inversions, the inversion climatology developed at one site can be applied to the whole geographic region which is under the same synoptic regime, then the following two hypotheses should be valid: Hypothesis (a): for the same weather class the statistics of inversions at the two locations must not differ; Hypothesis (b): the three weather classes must cause the same differentiation in the inversion statistics at the two locations. The inversion characteristics which will be considered in this study are: the strength T (difference in the dry-bulb temperatures between the top and the base of the inversion), the depth H (difference between the height of the top and the height of the base of the inversion), the difference in dew point temperature between top and base of elevated inversions (Td), the lapse rate, and the difference in the potential temperature between the top and the base of the inversion (), which will be called ‘‘intensity’’ of inversion hereafter. It can be shown that the intensity of inversions is directly proportional to their ability to inhibit the vertical movement of pollutants (see Milionis and Davies 1992). At this point it should be noted that the stability of an air parcel depends on the difference in the density of this air parcel as compared to the density of the surrounding air. As virtual temperature is defined as the temperature that dry air must have to equal the density of moist air for the same pressure, it is evident that variations in virtual temperature can be used equivalently to variations in density. For this reason it would be better to use differences in the virtual potential temperature, instead of differences in potential temperature. However, as virtual temperature is defined as: v ¼ (1 þ 0.61r), where r is the mixing ratio, the 230 A. E. Milionis, T. D. Davies calculation of virtual temperatures requires humidity measurements and, as is well known, errors in the humidity measurements are common and much more serious than errors in temperature measurements in radiosonde data (see WMO 1975, 1983 for further details). Further, in almost all similar studies where use is made of radiosonde data, it is the potential temperature instead of the virtual potential temperature which is considered. For these reasons potential temperatures will be also be used in this work. Formal testing for the existence of possible differences in the statistics of inversions described above can be conducted by using standard statistical methods. To test hypothesis (a) a t-test can be used for the differences in the mean values of the statistics which correspond to the characteristics of inversions described above. To test hypothesis (b) the one way analysis of variance for the differences in the mean values of the same inversion characteristics for the three weather classes will be used. It is noted that the mean values of all the above mentioned inversion characteristics refer to averages over the entire sample period and over the entire surface-700 hPa region. 4. Results and discussion Figure 2 shows the distribution of inversion layers as a function of base-height, considering atmospheric layers of 200 m width, for both loca- Fig. 2. Fraction of inversions per mille as a function of base-height. All elevated inversions tions for the general case (i.e. both midday and midnight inversions and for the whole 1976–80 time period). It is very clear from Fig. 2 that the maximum of the distribution around 200 m at Hemsby, does not exist at Crawley. Apart from this, the two curves have a generally similar character. The most obvious reason for this difference in the two distributions is the sea-breeze effect which is present only at Hemsby (although there may be a small number of occasions where seabreeze penetrates as far inland as Crawley). According to the methodology outlined above, further evidence can be provided by examining the two distributions separately for summer and winter, midday and midnight. Hence, the distributions of inversions as a function of baseheights for Hemsby and Crawley were examined for the following cases: (i) (ii) (iii) (iv) summer (May–August), midday summer, midnight winter (November–February) midday winter, midnight The results are shown in Figs. 3–6. Examination of these figures shows that the number of inversions at Hemsby for case (i) is at a maximum around 200 m (Fig. 3) and this maximum is much more pronounced than in the general case (see Fig. 2), a fact which provides further evidence that the sea-breeze effect is the causal mechanism. Figure 4, which corresponds to case (ii), shows that this local maximum, although relatively weaker, still exists at midnight. Fig. 3. Fraction of inversions per mille as a function of base-height for the period May–August. Midday inversions A comparison of temperature inversion statistics Fig. 4. Fraction of inversions per mille as a function of baseheight for the period May–August. Midnight inversions Fig. 5. Fraction of inversions per mille as a function of base-height for the period November–February. Midday inversions Although a search of the literature indicates that at midnight, land-breezes have been observed rarely in the U.K., it is rather unlikely that seabreezes occur at midnight. Hence, the local maximum around 200 m in Fig. 4 needs further investigation. Another physical process that may be responsible for the local maximum around 200 m is advection from the sea, due to easterly winds driven by synoptic scale processes. Such processes must also be responsible for the local maximum at 200 m at Hemsby for case (iii) (Fig. 5), as the sea-breeze circulation is much less common during the winter than during the summer. Finally, for case (iv) (Fig. 6) the two 231 Fig. 6. Fraction of inversions per mille as a function of base-height for the period November–February. Midnight inversions distributions look very similar and the maximum at 200 m at Hemsby has diminished. This is a very important finding, as the sea is, on average, warmer than the land for the conditions of case (iv) and the sea-breeze effect is, by and large, eliminated. The remarkable similarity of the two distributions, once the sea-breeze effect disappears, is a very clear indication of the overall synoptic control. It is important to examine further the possible influence of the second physical mechanism (i.e. advection of cold air from the North Sea due to synoptic scale processes) which may also contribute for the maximum of the distribution around 200 m at Hemsby. This can be made possible by examining the distribution of inversion layers at Hemsby as a function of both baseheights and wind direction. Both sea-breeze and advection must be combined with on-shore winds, so the vertical distribution of the baseheights of inversions at Hemsby were examined separately for easterly winds (direction (45– 135 ), which are clearly on-shore winds, and westerly winds (direction 225–315 ), which are clearly off-shore winds. Again, midday and midnight inversions were considered separately for both the May–August and the November– February periods. The results are shown in Figs. 7–10. As can be seen, for the period May–August there is a very pronounced maximum in the distribution 232 A. E. Milionis, T. D. Davies Fig. 7. Fraction of inversions per mille for Westerly and Easterly winds as a function of base-height for the period May–August. Midday inversions, Hemsby Fig. 8. Fraction of inversions per mille for Westerly and Easterly winds as a function of base-height for the period May–August. Midnight inversions, Hemsby Fig. 9. Fraction of inversions per mille for Westerly and Easterly winds as a function of base-height for the period November–February. Midday inversions, Hemsby Fig. 10. Fraction of inversions per mille for Westerly and Easterly winds as a function of base-height for the period November–February. Midnight inversions, Hemsby of the base-heights at 200 m for both midday and midnight with easterly winds at Hemsby. This is in sharp contrast with the corresponding distributions for westerly winds, where there are very low frequencies at that height (Figs. 7 and 8). However, the maximum for easterly winds at midnight is clearly of lesser magnitude than the one at midday. For the period November– February the very distinct maximum at about 200 m for easterly winds, which was present during the period May–August, has now become a local maximum of much smaller relative magnitude at midday (Fig. 9), and has almost completely disappeared at midnight (Fig. 10). On the other hand, for westerly winds, as during the period May–August, the number of inversions with base-height around 200 m is relatively low. Consequently, the character of the Figs. 7– 10 confirmed the conclusions drawn from the study of Figs. 2–6. All the previous Figures have shown that, apart from the sharp difference in the distributions of base-heights of inversions around 200 m in Hemsby and Crawley, which was attributed to the sea-breeze effect and advection owing to synoptic scale processes, the two distributions are very similar. Moreover, the way that this difference varies as a function of time is, to a certain extent, deterministic, hence, predictable. This is an encouraging first indication that the inversion climatology which is developed at one location can be assumed for a wider geographic region, once the influence of local geography has been isolated. Further, as the prevailing weather is an A comparison of temperature inversion statistics 233 Table 2. Analysis of variance for the characteristics of elevated inversions (Hemsby) Weather class A C W–SW F-stat. Inversion characteristics Intensity (K) Depth (m) Mean s.d. Mean 5.00 3.60 4.41 49.76 2.8 2.1 2.4 260.5 166 209.5 138 243.8 137 18.36 s.d. Strength ( C) Td ( C) Lapse rate ( C=m) Mean s.d. Mean s.d. Mean s.d. 2.21 1.36 1.81 36.41 2.0 1.3 1.9 3.51 1.83 2.8 20.75 5.1 3.8 4.5 1.28 1.12 1.13 2.48 1.6 1.8 1.6 Table 3. Analysis of variance for the characteristics of elevated inversions (Crawly) Weather class Inversion characteristics Intensity (K) A C W–SW F-stat. Depth (m) Strength ( C) Td ( C) Lapse rate ( C=m) Mean s.d. Mean s.d. Mean s.d. Mean s.d. Mean s.d. 4.81 3.69 4.38 34.20 2.70 2.04 2.40 252.1 217.9 234.2 10.02 151 139 136 2.11 1.34 1.87 29.03 1.9 1.4 1.9 4.01 2.61 3.93 12.84 5.4 4.4 5.6 1.28 1.07 1.28 1.80 2.1 2.2 2.0 important factor that affects the statistics of inversions (Milionis and Davies 2007), it is important to examine whether or not the major weather classes defined previously affect the statistics of inversions in the two locations in the same way. To this end, a one way analysis of variance will be performed to examine the differences in the mean values of the various statistics of inversions for the three weather classes. Remarks about the assumptions for the application of the method, as well as further details are given in Milionis and Davies (2007). In this work, together with the mean values and the corresponding standard deviations for the inversion statistics for the three weather classes, the values of the F-statistic will be presented. An F-value with one asterisk (‘ ’) will indicate that the result from the F-test is significant at 10% level, two asterisks (‘ ’) will indicate that the result is significant at 5% level, and no asterisk will indicate that the quoted F-value is not significant at 10% level. Table 2 shows the results of the one way analysis of variance for the statistics of elevated inversions for Hemsby, while Table 3 shows the corresponding results for Crawley. From Tables 2 and 3 it is apparent that the differences in the mean values of the intensity of elevated inversions for the three weather classes for both Hemsby and Crawley are statistically significant, with the anticyclonic class having the highest value of mean intensity and the cyclonic class the lowest. The same conclusion is drawn for the depth as well as the strength of elevated inversions for both locations. For the lapse rate the differences are not significant at the 5% level for both locations. This is reasonable as, for both locations, both the strength and the depth are progressively lower for the anticyclonic, westerly, and cyclonic classes, so their ratio does not change significantly in the three weather classes. For the differences in the mean values of Td, although for the three weather classes the differences are significant, a more careful examination reveals that this result for Crawley is only due to the fact that for the cyclonic class the value of Td is much lower than for the other two weather classes. Indeed, a significant value of the Fstatistic only confirms the existence of significant differences among the means and it does not follow necessarily that every subset of two means shows a significant difference. The latter may be investigated separately by means of the socalled multiple comparison tests. From the several existing tests of such kind (see for example Hsu 1996; Montgomery 2000) the so-called Fisher’s Least Significant Distance (LSD) test (Fisher 1966) will be used in the present case. 234 A. E. Milionis, T. D. Davies For the application of this test all differences of pairs of class-means are compared with LSD. The latter is defined as: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 1 þ LSD ¼ ta=2 Sw N1 N2 where, ta=2 is the critical value of the t-distribution at significance level a, Sw is the within samples estimate of the population variance, N1 , N2 are the samples sizes of the two classes. When the difference between the two means is found greater than LSD then the null hypothesis (i.e. that the two means do not differ significantly is rejected at 100(1 a)% confidence level. The application of this test to the differences in the mead values of Td for Crawley and the 5% level of significance gives: (a) for the pair C, A: difference in means ¼ 1.95, LSD ¼ 0.52; (b) for the pair C, W–SW: difference in means ¼ 1.32, LSD ¼ 0.59; and (c) for the difference A, W–SW: difference in means ¼ 0.09, LSD ¼ 0.55 Hence, the difference in the mean values of Td for the anticylonic and W–SW classes are not statistically significant while the difference in the mean values of each of these classes with the cyclonic class are both significant, as both are greater than the corresponding LSD value, conforming our previous assertion about the source of the significant result for Td in Crawley. This is the only difference in the two locations in terms of the influence of the prevailing weather. We note, however, that it is possible that these differences in the Td values for the two locations do not reflect physical reality (as, for example, the possible influence of the North Sea at the Hemsby data), but are simply a result of errors in the measurement of humidity. As mentioned in the previous section, the most serious errors in radiosonde data occur in the measurement of humidity. It is also important to examine whether or not, for each weather class, the differences in the mean values of the statistics of elevated inversions are statistically significant. The results for this comparison are shown in Table 4. This table quotes the values of the t-statistic for the means of each inversion statistic and for each Table 4. Results of the t-test for the differences in the mean values of the inversion characteristics in Hemsby and Crawley for the three main weather classes (mean values and standard deviations are shown in Tables 2 and 3) Weather Inversion characteristics class Intensity Depth Strength Td A C W–SW 1.46 0.79 0.23 1.07 1.09 1.10 0.27 1.27 0.57 2.02 3.44 4.04 Lapse rate 1.60 0.45 1.80 weather class. Differences significant at the 10% level are denoted with one asterisk (‘ ’). Differences significant at the 5% level are denoted by two asterisks (‘ ’). The results show that for the anticyclonic class the differences in the mean values of the inversion statistics are not significant for all characteristics except the difference in the dew point temperature, where the mean value is lower at Crawley and the difference is statistically significant at the 5% level. Exactly the same results are observed for the other two weather classes. As noted previously, the lower Td values in Crawley may be due to measurement error in humidity. The above analysis shows that the statistics which correspond to the main characteristics of elevated inversions (up to the 700 hPa pressure surface) in Hemsby and Crawley are not only differentiated in much the same way by the prevailing weather conditions, but also under the same prevailing weather the mean values of all the statistics of elevated inversions (except for Td) at the two locations do not differ. We should note at this point that all the mean values used in the previous statistical analysis of the characteristics of inversions have been calculated averaging over the entire period that the data cover. Therefore, any differences that might occur at a particular period of the year are smoothed out. The level of analysis based on the mean values, calculated as described above, suffices as a first step for a climatological study. However, it is also necessary to examine what happens for shorter periods (e.g. months). Of particular interest is to examine the degree of co-movement from period to period, i.e. to examine the extent to which the annual variations of the activity of inversions in the two locations follow each other. To proceed further, instead of examining each A comparison of temperature inversion statistics inversion statistic separately, the intensity of inversions can be combined with their frequency to create the so-called ‘‘activity’’ of inversions. An index which expresses the activity of inversions can be defined in the following way (Milionis and Davies 1994a, 2007): If N is the total number of available vertical temperature profiles (with or without inversions), n the corresponding number of profiles with one inversion at least, and K the corresponding total number of inversions, then the activity index AI is defined as the product of (mean intensity of inversions) times (average number of inversions per profile with one occurrence at least) times (proportion of temperature profiles with occurrence of one inversion at least), i.e.: PK PK #i i¼1 #i K n ¼ i¼1 AI ¼ n N K N 235 Fig. 12. Comparison of the annual cycle of the activity of surface inversions AI has two advantages: (1) it is computationally simple; (2) it is independent of the time period to which it is referring, a desirable property for a quantity which is a function of ‘‘intensity’’. Using this index the annual cycle of the activity of inversions – an important element in an inversion climatology – will be compared for the two locations. Figures 11–13 show the annual cycle of the AI-index for elevated, surface and all (elevated þ surface) inversions respectively, for both Hemsby and Crawley. For the surface inversions Fig. 13. Comparison of the annual cycle of the activity of all (surface þ elevated) inversions Fig. 11. Comparison of the annual cycle of the activity of elevated inversions only midnight soundings were taken into consideration. From these figures it is clear that, although there are some differences in the activity of inversions in individual months, overall there is quite a good agreement in the annual variations of the AI-index. This is confirmed by the values of the correlation coefficients between the annual cycles of Hemsby and Crawley, which are shown in Table 5. These coefficients express the linear co-movement of the activity of inversion for the two locations. All three correlations 236 A. E. Milionis, T. D. Davies Table 5. Values of the correlation coefficients between the annual cycles of the activity of inversions at Hemsby and Crawley All inversions Surface inversions Elevated inversions Correlation coefficient t-statistic 0.655 0.804 0.802 4.64 5.70 5.68 t-Values have beenﬃ calculated using the formula (Spiegel pﬃﬃﬃﬃﬃﬃﬃﬃﬃ r ðN2Þ p ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1988): t ¼ where r the correlation coefficient, and ð1r2 Þ the N the sample size The critical t-value for N 2 ¼ 10 degrees of freedom and 5% significance level is 2.23 are statistically significant at 5% level. For both surface and elevated inversions the annual cycle of one station can explain about two thirds of the annual cycle of the other station. However, combining surface and elevated inversions together, the coefficient of determination is reduced to 40%. It is also of interest to note that the values of the average monthly activity of inversions for Hemsby and Crawley are very close (4.86 and 4.95 K, respectively). We must also remark that, given the strong influence of the prevailing weather on the activity of inversions and the fact that for the study period the proportions of the various weather types are not representative of the average climatic conditions (Jones and Kelly 1982), the annual cycle discussed above should not be taken as representative of a longer period. Our study of the annual cycles was undertaken only for the examination of the co-movement of the activity of inversions in the two locations. The above analysis shows that the annual variation of the activity of temperature inversions throughout the surface-700 hPa layer is, by and large, independent of location, for those sites that are influenced by the same synoptic regime. At the same time, however, there is a substantial part in the annual variation of the activity of inversions in one location that cannot be explained by the corresponding variation in the other location, particularly when both elevated and surface inversions are considered together. We reckon that this unexplained part should be attributed primarily to the activity of inversions within the atmospheric boundary layer (ABL) which roughly corresponds to the atmospheric region surface-850 hPa. This region accommodates approximately 62% of the total number of in- versions and 68% of the inversion activity as compared to the whole surface-700 hPa region for Hemsby. The corresponding figures for Crawley are nearly identical (63% and 67% respectively). That means that for the region surface-850 hPa on the one hand the difference in the two distributions of base-heights of inversions will be accentuated further (as now the total number of inversions has been reduced), but on the other hand the conclusions from the statistical analysis based on the mean values of the inversion characteristics, by and large, will be the same as for the whole surface-700 hPa region. Further, the analysis regarding the annual cycle of the activity of inversions will be repeated this time using only the first inversion found in a temperature profile, which is the most important for the local-scale diffusion of air pollutants (see for instance Zannetti 1990) and, as a rule, is found up to the 850 hPa pressure surface. When only the first inversion of the temperature profile is taken into account for the calculation of the A-index the correlation coefficient for the monthly activity of inversions in the two locations is reduced to 0.40 and for 10 degrees of freedom corresponds to a t-statistic of 1.38 (see legend of Table 5 for the details of the calculation of the t-statistic), which is clearly not significant at the 10% level. Therefore, although on average the activity based on the first inversion of the temperature profile at Hemsby and Crawley does not differ, the way this activity is distributed during the year is not the same, indicating that the effect of local factors overwhelms that of synoptic conditions. This is reasonable as the main mechanism (sea-breeze) responsible for the differences in the annual variation of the activity of inversions associated with the ABL in the two locations is directly related to the annual cycle. However, as the mechanism to which these differences in the annual variation of the activity of inversions within the ABL are attributed has an apparent regularity, further investigation (not undertaken in this work) may reveal that these differences, to an extent, may be potentially predictable, as was the case with the differences in the base-heights of inversions. Before closing this section some clarifications on the use of the term ‘‘inversion climatology’’ are noteworthy. It is well known that the mean value of a sample, as a sample estimator of the A comparison of temperature inversion statistics true population value, is not only an unbiased estimator (i.e. its expected value coincides with the true value in the population) but also it is the best unbiased estimator (i.e. it has the minimum variance in the class of unbiased estimators). Further, the standard error of the sampling distribution of the mean value is given by the ratio of the standard deviation over the square root of the sample size. For the sample sizes, mean values and standard deviations presented in the results of this section it can be easily verified that the improvement in the standard error of the mean values would be, for most of the cases, approximately a tenth of a degree Celsius=Kelvin, or about six meters for inversion depths, if we use 20–25, instead of five years of data, assuming that the data series are covariance stationary. Hence, statistically, it is perfectly safe to derive statistics of inversion characteristics from the available data. It has been established in the international literature to refer to such statistics using the term ‘‘inversion climatology’’. Hence, the word ‘‘climatology’’ should not be taken at its face value on this occasion. Additionally, the particular data period we used, coincides with the one we used in our previous studies for Hemsby (e.g. Milionis and Davies 1992, 2002, 2007). In that way it was possible to examine the validity of previous results and assumptions, which were based on the Hemsby record, and to advance our understanding about the characteristics of temperature inversions. 5. Summary and conclusions There is little doubt that an inversion climatology at one site is useful for several reasons. However, with data from one location only it is not possible to assess the extent to which the characteristics of inversion layers reflect the synoptic conditions and the extent to which they reflect local influences, as the two effects cannot be separated. In this work it is attempted to partial out the effect of local factors from that of synoptic conditions. The effect of local factors can be revealed controlling for the effect of the synoptic conditions, by considering two locations with different topography, but being influenced by the same synoptic conditions. On the other hand, the effect of the synoptic conditions can be revealed by the identification of the conditions 237 which eliminate the effect of local factors and examining the inversion characteristics at the two locations under such conditions. Following this approach the comparison of the basic inversion statistics at Hemsby and Crawley has shown that: (a) There is a pronounced difference in the vertical distribution of occurrence of inversions at the two locations: only the distribution at Hemsby has a local maximum around 200 m. This difference is attributed to the influence of the North-Sea. Advection of cooler maritime air, due to the sea-breeze effect, as well as due to synoptically driven easterly winds, are the possible processes that are responsible for this local maximum of occurrence of inversions. (b) Further confirmation of the conclusions in (a) is provided by considering the vertical distributions of the base-heights of inversions in the two location under conditions for which the sea-breeze is either maximized or minimized. It is shown that in winter at midnight, when the sea-breeze effect is eliminated, the two distributions are remarkably similar indicating the overall synoptic control. In contrast, in summer at midday, when the sea-breeze effect is at its maximum, the local maximum in the distribution of baseheights at 200 m in Hemsby is much more pronounced than in the general case. (c) The prevailing weather type, which was assumed to be the same in both locations, affects the statistics of the inversion characteristics in both locations in much the same way. This conclusion was drawn by showing that (i) the main weather classes (i.e. anticyclonic, cyclonic and westerly) differentiate the statistics of inversions in the same way for both locations, and (ii) under the same weather class the mean values of the inversion statistics do not differ in the statistical sense, with the exception of Td, where it is possible that the statistically significant difference in the mean value for all weather classes is a result of measurement error in humidity. (d) As the mean values of the inversion characteristics in (c) are calculated averaging over the entire time period, the month-to-month 238 A. E. Milionis, T. D. Davies variation (annual cycle) of the activity of inversions in the surface – 700 hPa atmospheric layer in the two locations was also examined. The annual cycle of the activity of inversions is qualitatively very similar in both locations and the variations in the monthly activity of inversions activity in the two locations are strongly correlated, with about two thirds of the variation in activity of both surface and elevated inversions within the year in one station being associated with the corresponding variations in the other station. (e) However, there is still an unexplained part in the within the year variation of the inversion activity in the two locations, which is attributed mainly to inversions in the lower part (approximately from the surface up to the 850 hPa level) of the surface-700 hPa atmospheric region. This is confirmed by taking into account only the first inversion of each profile for the calculation of the activity of inversions. In that case the inversion activity variations within the year in the two locations are not correlated. Given the difference in the local character of the two locations this work, on the one hand provides strong evidence that an inversion climatology at one location can be regarded as representative of a wider area for which the same synoptic regime can be assumed but, on the other hand, it indicates that it is necessary to impose constraints; these are associated with local factors which, near the ground, overwhelm the overall synoptic control. However, even if there are differences in inversion characteristics due to differences in local topography, such differences could, to a certain extent, be inferred if the underlying mechanisms follow a regular pattern. This was evidenced for the differences in the base-heights of inversions as the underlying mechanism was directly related to the yearly and daily cycles. Therefore, at least to a certain extent, the main features of an inversion climatology at one location can be reconstructed once we know the same features at a different location influenced by the same synoptic regime and the mechanisms which are responsible for any differences in the climatology of inversions in the two locations, if these mechanisms have a deterministic character. This important finding has useful implications, for micrometeorological applications, such as the study of local-scale atmospheric diffusion, where data for atmospheric stability should be collected from the same location as the sources of the pollution. Ideally, for such applications tower data are much more appropriate than radiosonde data. However, it is quite often that the atmospheric scientist has to face lack of availability of the most suitable data. Even in such cases this work provides encouraging evidence on how an inversion climatology for a different location can be usefully employed. 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