Representation of low-tropospheric temperature inversions in ECMWF reanalyses over Europe

Despite the fact that tropospheric temperature inversions are thought to be an important feature of climate as well as a significant factor affecting air quality, low-level cloud formation, and the radiation budget of the Earth, a quantitative assessment of their representation in atmospheric reanalyses is yet missing. Here, we provide new evidence of the occurrence of low-tropospheric temperature inversions and associated uncertainties in their parameters existing among reanalyses produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) and upper-air soundings for Europe covering the period 2001–2010. The reanalyses utilized here include (1) surface-input reanalyses represented by ERA-20C and CERA-20C as well as (2) full-input reanalyses represented by ERA-Interim and ERA5. The upper-air soundings were derived from the Integrated Global Radiosonde Archive (IGRA), version 2. The data consists mainly of air temperature and geopotential height from the model levels (ModLev) and pressure levels (PresLev) of ECMWF reanalyses. The results show that the frequency of surface-based inversions (SBI) and elevated inversions (EI) is largely in agreement among the reanalyses. The quality of their representation depends, however, on the inversion type, season, and region. Over the vast majority of IGRA upper-air stations, SBI frequency is overestimated and EI frequency is underestimated by ECMWF reanalyses. Substantially larger uncertainties arise from the selection between the data of ModLev and PresLev of the reanalyses—the differences in the frequency of the temperature inversions are particularly large for summertime SBI suggesting that PresLev are not capable of resolving the main features of shallow and weak SBI.


Introduction
Atmospheric reanalyses, which are spatially and temporally coherent datasets providing a synthesized estimate of the past and current state of the Earth's atmosphere, have recently become widely used both in climate and environmental research as well as outside scientific applications (Gregow et al 2016, Hersbach et al 2018. They consist of diverse assimilation schemes, input observations, and numerical models, which may generate some uncertainties among various reanalysis types. According to Fujiwara et al (2017), the reanlayses may be grouped into two main categories: (1) surface-input reanalyses assimilating only surface observations and (2) full-input reanalyses assimilating also data from other sources, such as satellite and upper air soundings. The latter are thought to offer a more accurate representation of the atmospheric state. Rohrer et al (2018) claimed, for instance, that the full-input reanalyses show better agreement within the spectrum of the parameters of anticyclones, cyclones, and circulation types as compared to the surface-input reanalyses. Moreover, a pronounced tendency to underestimate air temperature and precipitation extremes was found in the surface-input reanalyses by Donat et al (2016). They highlighted that the time series of climate extreme indices calculated on the basis of those reanalyses are usually 'less extreme' as compared to those obtained from the instrumental observations. Referring to the extreme weather events, such as floods, hurricanes, and storm surges, also Brönnimann (2017) pointed out that their magnitude is significantly underestimated by the ensemble mean of the 20th Century Reanalysis. The modern, full-input reanalyses resolve the atmospheric state more accurately, however, biases may still exist. As an example, some convective parameters that favour the development of thunderstorms, such as the most unstable convective available potential energy (MUCAPE), are typically overestimated; while the others, such as the mixed layer convective available potential energy (MLCAPE), are underestimated by the full-input ERA-Interim reanalysis (Taszarek et al 2018).
Although previous research suggested that climate models and reanalyses may experience difficulties in resolving the state of the lower troposphere under extremely stable atmospheric stratification (e.g. Tjernström and Graversen 2009, Lüpkes et al 2010, Medeiros et al 2011, a quantitative assessment of their quality in terms of temperature inversions' occurrence is still missing from the scientific literature. Attempts to evaluate the ability of the atmospheric reanalyses to resolve fundamental parameters of the temperature inversions were made by Wetzel and Brümmer (2011) and Zhang et al (2011). For instance, Wetzel and Brümmer (2011) found that the frequency of wintertime surface-based inversions over the Arctic is underestimated in the ERA-40 reanalysis as compared to in-situ observations. The intra-annual variability of the inversions' depth and strength agrees, in turn, well among the datasets (Wetzel and Brümmer, 2011). Also, the study by Zhang et al (2011) confirmed that there is a relatively good agreement between the ERA-Interim reanalysis and upper air soundings in terms of the spatial distribution and seasonal variability of the surface-based temperature inversions over the Arctic and Antarctic. However, some biases in the magnitude of their parameters still occur, e.g. the ERA-Interim reanalysis usually overestimates slightly the frequency of the surface-based inversions. Typically, the uncertainties are smaller in winter and autumn than in summer and spring (Zhang et al 2011).
In the previous studies (Palarz et al 2018(Palarz et al , 2020 we provided a comprehensive climatology of the surface-based and elevated inversions occurring over Europe and the north-eastern Atlantic based on the ERA-Interim reanalysis. We found that the lowtropospheric temperature inversions experience some temporal variability, which is determined mainly by the inversion type. The surface-based inversions exhibit a clear diurnal cycle closely related to the Earth's radiation budget-thus, radiative cooling of the active surface is thought to be the major factor initiating the development of the temperature inversions over Europe (Kassomenos et al 2014, Stryhal et al 2017. In turn, the day-night variability of the elevated inversions is far less pronounced. They occur most frequently over areas influenced by extensive high-pressure systems-the permanent Azores High and semi-permanent Siberian High, which implies that their development is linked to the large-scale subsidence and adiabatic heating of air parcels (Palarz et al 2020). However, an evaluation of the quality of multiple reanalyses under extremely stable atmospheric stratification has not been performed for mid-latitudes yet.
For the first time, we provide here a quantitative assessment of the uncertainties in the parameters of the low-tropospheric temperature inversions among the reanalyses produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) and upper air soundings over Europe. The remainder of the paper is organized as follows: section 2 gives a description of the datasets as well as outlines the methods applied for both identification of the temperature inversions and inter-comparison of their parameters obtained by applying various datasets. In section 3 we provide the results, while discussion and summary are presented in section 4.

ECMWF reanalyses and upper air soundings
This study is based on the newest reanalyses produced by ECMWF, namely ERA-Interim, ERA5, ERA-20C, and CERA-20C, as well as upper air soundings derived from the Integrated Global Radiosonde Archive (IGRA).
The reanalyses utilized here constitute of two categories: (1) the century-long, surface-input reanalyses represented by ERA-20C and CERA-20C as well as (2) the modern, full-input reanalyses represented by ERA-Interim and ERA5 (Fujiwara et al 2017, Hersbach et al 2018-detailed information on them are shown in table 1. From all of ECMWF reanalyses, we extracted data of air temperature and geopotential height for the entire vertical cross-section of the troposphere, i.e. from 1000 to 100 hPa, both from the model levels (ModLev) and pressure levels (PresLev). The geopotential values, which are not accessible on ModLev, were computed on the basis of the scripts recommended by ECMWF (2019a) by applying the data on the log of surface pressure and specific humidity. As shown in table 1, both horizontal and vertical resolution of the reanalyses varies greatly among each other. Referring the horizontal resolution, we utilized the data on 0.25 • × 0.25 • , which is the native resolution of the ERA5 reanalysis. The output resolution was set to 0.25 • × 0.25 • in the ECMWF data server web interface, which means that the downloaded data were bilinearly interpolated by default. Referring the vertical resolution, in turn, additional computations were performed for the data from PresLev, which, in the lower troposphere, are available at a fixed resolution of 25 hPa.

Contingency table
where E is the proportion of forecasts that would have been correct if forecasts and observations were independent and assuming the same proportion of forecasts of occurrence to nonoccurrence, so that for a (2 × 2) contingency table a Perfect value of each score is indicated as bolded.
The reanalyses provide, access to data at all PresLev, which means that for high-altitude regions, such as the Alps or the Carpathians, they are extrapolated below the surface. Following the recommendation of ECMWF (2019b), we masked out those regions by using the surface geopotential height. Analogous computations were not applied for ModLevhere, the vertical dimensions of ECMWF reanalyses are defined by an eta (η) coordinate, which transitions from purely pressure coordinate at the top and upper levels of the model to a hybrid pressuresigma coordinate at the mid-to low-levels, and finally to a terrain-following sigma (σ) near the surface (ECMWF, 2018). As a reference dataset, the upper air soundings derived from the enhanced, version 2 of IGRA were applied. They contain information on air pressure, temperature, geopotential height, relative humidity, dew point depression as well as wind direction and speed at the mandatory levels specified by the World Meteorological Organisation (WMO) and at levels at which a measured variable deviates from linearity. Detailed description of the IGRA dataset as well as information on the quality assurance procedure applied in its production are given by Durre et al (2006). Here, we utilized the data from 70 upper-air sounding stations listed in table 2. All of the stations met the criteria of less than 30% missing data in air temperature time series on a monthly basis, which was recommended previously by Guo et al (2008). Since the IGRA dataset reports geopotential height (z in meter) only at the mandatory pressure levels, we calculated the thickness of the layer (z L ) between level i of reported geopotential (z i ) and level of unknown geopotential (z i+1 ) based on the hydrostatic balance formula (Gilson et al 2018): where t i , t i+1 is the air temperature at levels of z i and z i+1 (t in Kelvin), p i , p i+1 is the air pressure at levels of z i and z i+1 (p in hectopascal), R is the ideal gas constant (287 J K −1 kg −1 ), and g is the gravitational acceleration (9.81 m s −2 ). Although the overlapping period for ECMWF reanalyses is 1979-2010, we restricted our study to the years 2001-2010 in order to avoid potential inhomogeneity in the time series of the upper-air soundings caused by major changes in sensor types, data correction methods, or station relocation (Gilson et al 2018). In addition, keeping in mind the temporal and spatial patterns of the low-tropospheric temperature inversions over Europe discussed by Palarz et al (2018) and Palarz et al (2020), we examined only the nocturnal temperature inversions occurring in winter (from December to February-DJF) and summer (from June to August-JJA). Usually, the temperature inversions occur most frequently then.

Methods for the identification of temperature inversions
The tropospheric temperature inversions were identified following the definition of Kahl (1990) and applied later by among others Wetzel andBrümmer (2011), Zhang et al (2011), and Gilson et al (2018). The same detection algorithm had been successfully used in our previous studies on the temperature inversions (Palarz et al 2018(Palarz et al , 2020. Specifically, each of the vertical profiles of air temperature obtained from the reanalyses or upper air soundings was scanned upward to locate the first layer in which air temperature increases with altitude. The inversion base (B) was defined as the bottom of the first layer in which the temperature increases with altitude; whereas the inversion top (T) was defined as the bottom of the first subsequent layer in which the temperature decreases with altitude. The air temperature (t) and geopotential height (z) were then determined at the levels of the inversion base (t B , z B ) and top (t T , z T ). By analogy with preceding studies (e.g. Stryhal et al 2017, Czarnecka et al 2019), we distinguished two types of the temperature inversions: (1) surfacebased inversions (SBI) beginning immediately at the lowest level of the reanalyses or upper air soundings and (2) elevated inversions (EI) having bases located at a higher altitude. A quantitative measure of both SBI and EI is given by three parameters, i.e. their frequency (FQ % ), depth (∆ z = z T −z B ), and strength (∆ t = t T −t B ).
Following many previous papers (e.g. Gilson et al 2018, Czarnecka et al 2019), we restricted our investigation to the temperature inversions whose bases are located up to 3000 m above ground level (AGL), which for low altitudes regions is comparable with the pressure level of 700 hPa. EI depth and strength were calculated solely for the lower-most inversion layer, which is consistent with the studies carried out by Stryhal et al (2017), Czarnecka et al (2019), and Palarz et al (2020). Note also that upper air soundings with fewer than five measurement levels below 700 hPa were discarded from this analysis since we assumed that they may not resolve the vertical structure of the lower troposphere accurately (Kahl et al 1992).

Methods for the inter-comparison of temperature inversions' parameters derived from ECMWF reanalyses and upper air soundings
While a general view on the frequency of SBI and EI is provided on maps created separately for ECMWF reanalyses and upper-air soundings, a more comprehensive comparison of SBI and EI parameters was performed for the ten IGRA upper-air stations indicated in table 2-shaded rows. They have been selected to be representative of various regions over Europe. Following previous study on the relationship between the tropospheric humidity inversions and temperature inversions by Naakka et al (2018), in-situ observations were compared to the data gained from the grid point closest to each upper-air sounding station.
In order to assess the ability of ECMWF reanalyses to resolve the temperature inversions' parameters, we implemented a variety of deterministic verification measures. Firstly, SBI and EI were regarded as so-called binary events and evaluated utilizing verification measures calculated on the basis of the contingency table-its example and list of the selected measures used in the study are shown in table 3. Secondly, the temperature inversions' depth and strength were evaluated in terms of continuous measures, such as mean systematic error (ME), mean absolute error (MAE), root mean square error (RMSE), and the Pearson's correlation coefficient (ρ). In this paper, we provide Taylor diagrams, in which the degree of correspondence among the various datasets is quantified by three measures, i.e. the Pearson's correlation coefficient, centred root-mean-square error, and standard deviation (Taylor 2001).

Frequency of low-tropospheric temperature inversions
As stated previously, the data from both ModLev and PresLev of ECMWF reanalyses was used for the investigation of the temperature inversions' occurrence. In all reanalyses, some uncertainties among these two data types were found. Surprisingly, their spatial patterns are very similar among the reanalyses although the number of ModLev varies greatly from 60 for the ERA-Interim reanalysis to 137 for the ERA5 reanalysis. As an example, figure 1 illustrates the spatial distribution of the difference in the frequency (FQ DIFF ) of the temperature inversions calculated on the basis of the data from ModLev and PresLev for the ERA5 reanalysis. The findings introduced below are, however, relevant for all ECMWF reanalyses. In general, the magnitude of FQ DIFF depends on the inversion type, season, and region. Across mainland Europe, the frequency of summertime SBI identified by applying the data from ModLev is about 30% higher as that obtained by applying data from PresLev. This suggests that a substantial part of summertime SBI is too shallow to be realistically resolved by the data gained from PresLev. Considering wintertime SBI, in turn, FQ DIFF is more spatially heterogeneous. Its magnitude does not exceed 10% over Eastern Europe, where SBI development is usually supported by the large-scale subsidence occurring in the Siberian High. As confirmed by Palarz et al (2018), wintertime SBI occurring there are rather deep and strong, thus they can be precisely resolved by the data from both ModLev and PresLev. The difference among the two data types is far more pronounced over the other parts of mainland Europe, in particular over high-altitude regions. Usually, SBI result there from the radiative cooling of the Earth's surface and thus they are rather shallow and weak. On the other hand, the uncertainties identified in EI frequency are slightly smaller and more spatially coherent. The frequency of EI calculated by applying the data from ModLev is, however, still positively biased in comparison to data derived from PresLev. Interestingly, over the Mediterranean Sea, the frequency of the summertime temperature inversions calculated based on the data from ModLev is positively biased for EI, while negatively biased for SBI compared to this from PresLev. We hypothesize that this might be a result of incorrect distinction between SBI and EI, however, further research is needed for a detailled analysis of this feature.
A visual inspection of figures 2 and 3 implies that the frequency of both SBI and EI is generally in agreement among ECMWF reanalyses. Typically, SBI are rarely found over marine areas, which is thought to be a consequence of large heat capacity of water providing the possibility of absorbing large amounts of solar energy without significant changes in near-surface air temperature (Palarz et al 2018). Across mainland Europe, in turn, SBI reach substantially higher frequency, especially in summer. The frequency of summertime SBI frequency tends to be slightly higher for the ERA-Interim reanalysis as compared to the other reanalyses. Moreover, all ECMWF reanalyses seem to overestimate the frequency of summertime SBI at most of IGRA upperair stations. In winter, a higher SBI frequency is attained over mountain areas, such as the Alps, the Carpathians, and the Scandinavian Mountains as well as over high altitudes regions of the Iberian Meseta and the Anatolian Plateau. These findings agree well among the reanalyses although, on a more regional scale, some uncertainties are prevalent. The CERA-20C reanalysis, for example, indicates a higher frequency of wintertime SBI over the Scandinavian Mountains as compared to the other ECMWF reanalyses. Similarly to summer, also the frequency of wintertime SBI is overestimated by ECMWF reanalyses at most of IGRA upper-air stations. Slightly larger uncertainties among ECMWF reanalyses are found for EI frequency. They are most pronounced in winter over a marine area west of the Iberian Peninsula and Eastern Europe, which are considered as the two main regions of the most frequent EI occurrence over the domain studied (Palarz et al 2020). For both of those areas, the frequency of wintertime EI reach the highest values for the ERA5 reanalysis. Besides, the vast majority of IGRA upper-air stations reports slightly higher EI frequency compared to the reanalyses. The frequency of summertime EI indicates, in turn, a clear distinction between land and marine areas. In all ECMWF reanalyses, EI frequency reaches higher values over the Atlantic Ocean and the Mediterranean Sea, whereas lower values over mainland Europe. Particularly low values of summertime EI frequency are found for the ERA-Interim reanalysis. A visual comparison among the datasets suggests that also summertime EI are underestimated in ECMWF reanalyses, especially over Central and Western Europe.
Further evaluation of the ability of ECMWF reanalyses to resolve the temperature inversions' parameters is performed on the basis of the data   collected from the ten IGRA stations mentioned before. Figure 4 illustrates the variability in the values of the deterministic verification measures separately for each inversion type and season. Overall, the ability of ECMWF reanalyses to resolve the temperature inversions' occurrence is related to their type, season, and region. Considering large variability in the verification measures, the latter factor is thought to be of high importance here. This variability is particularly large for SBI. Note, however, that over some of the IGRA upper-air stations, the temperature inversions occur very rarely. For such cases, by definition, the application of some verification measures, in particular POD and POFD, may be limited and could give misleading interpretation. As deduced from the FAR values the reanalyses tend to detect SBI, when they actually do not occur, more frequently in winter than in summer. In turn, the values of PC, PSS, and HSS calculated for SBI are characterised by comparable values for both seasons, but some differentiation between the full-input and surface-input reanalyses seems to be visible here-ERA-Interim and ERA5 usually reach slightly higher values as compared to ERA-20C and CERA-20C. In general, the verification measures calculated for EI are much more coherent spatially. Most of them, i.e. PC, POD, FAR, PSS, and HSS, reach values closer to the perfect value for wintertime EI. The values of most verification measures, apart from POFD and FAR, imply that the ERA5 reanalysis tends to detect EI slightly better than the ERA-Interim reanalysis.

Parameters of low-tropospheric temperature inversions
The degree of correspondence between the depth and strength of the temperature inversions derived from ECMWF reanalyses and IGRA upper-air stations has been quantified using the continuous verification measures. For brevity, we provide here Taylor diagrams that encompass information on the Pearson's correlation coefficient, centred rootmean-square error, and standard deviation (figure 5). The ability of ECMWF reanalyses to resolve the strength of the low-tropospheric temperature inversions strongly depends again on the inversion type, season, and region. Similarly to the verification measures calculated on the basis of the contingency table, also the continuous measures show relatively large spatial variations among the ten IGRA upper-air stations. They are particularly pronounced in winter. Typically, the Pearson's correlation coefficient between ECMWF reanalyses and IGRA upperair stations is weaker for EI than SBI reaching the lowest values for summertime EI. However, even for SBI, the correlation does not exceed 0.65, which implies that the temperature inversions' strength is rather inaccurately resolved by ECMWF reanalyses. Interestingly, for wintertime SBI and EI, the ERA5 reanalysis presents slightly lower values of standard deviation as compared to the other ECMWF reanalyses suggesting that improvements implemented in physical parametrization schemes and inclusion of more vertical levels may help in better representation of the temperature inversions' strength. Similar conclusions can be drawn for the depth of the temperature inversions (not shown in this paper).

Discussion and conclusions
In this study, we have shown that ECMWF reanalyses resolve reasonably well the occurrence of the lowtropospheric temperature inversions over Europe for the period 2001-2010. The quality of their representation is, however, determined by the inversion type, season, and region considered. Over the vast majority of IGRA upper-air soundings stations, SBI frequency is overestimated and EI frequency is underestimated by the reanalyses. Moreover, we found that the ERA-Interim reanalysis, which had been applied in our preceding studies (Palarz et al 2018(Palarz et al , 2020, experiences the largest differences as compared to the in-situ measurements. Our results have demonstrated, however, that the newer reanalyses produced by ECMWF, i.e. ERA5, ERA-20C and CERA-20C, which include improvements in physical parametrization schemes, allow for better representation of the thermal stratification of the lower troposphere. Typically, even the surface-input reanalyses resolve relatively well the main features of the temperature inversions although they assimilate substantially less amount of the input data as compared to the fullinput reanalyses.
Larger uncertainties exist, between the frequency of the temperature inversions calculated based on the data from ModLev and that calculated based on PresLev. Coarser vertical resolution of the data from the PresLev precludes an accurate representation of thin and weak SBI, thus mainly summertime SBI. Conversely, the frequency of EI is reasonably well represented in the data from both ModLev and PresLev, albeit still higher in ModLev. These findings underline that the selection of the data type, namely between the data from ModLev or PresLev, plays an essential role in the outcome of the study and is usually far more important that the selection among multiple reanalyses.
Based on the values of the verification measures, we have shown that the ability of ECMWF reanalyses to detect the low-tropospheric temperature inversions depends on the inversion type, season and region. The latter factor seems to be of high importance here. Particularly regionally-dependent is the detection of SBI, whose development is often shaped by numerous local factors discussed in the preceding papers (e.g. Stryhal et al 2017, Gilson et al 2018, Palarz et al 2018, Czarnecka et al 2019. Conversely, EI detection is usually far less related to the microand mesoscale factors and thus may be better represented in the reanalyses. The evidence shown in this study indicates also that the ability of ECMWF reanalyses to resolve the temperature inversions' depth and strength is far more limited compared to their frequency. Although ECMWF reanalyses are capable of resolving the general patterns of the depth and strength of the temperature inversions on a seasonal basis, they experience significant uncertainties when considering individual cases of the temperature inversion's occurrence. Undoubtedly, the upper air-soundings are able to capture finer details of the thermodynamic state of the lower troposphere as compared to the reanalysis products (Bao and Zhang, 2013;Guo et al 2016;Nakka et al, 2018). Considering, however, the spatial and temporal availability, their application in climate research is often limited. Our study has shown evidence that ECMWF reanalyses provide a fairly accurate representation of the lower troposphere under extremely stable atmospheric stratification and can be utilized in follow-up research. Considering the importance of the atmospheric stratification for climate feedbacks, further investigation of the temperature inversions should focus on their representation in the climate models as well as their long-term variability under the changing climate.