To characterise the IWV over Europe and to assess the reanalyses, 1-hourly GPS IWV retrievals obtained from 108 stations are used (Fig. 1). Most GPS stations are from the EPN network (Bruyninx et al., 2001). The GPS observations are from January 1994 to December 2018 with an average time length of 21 years and an average integration rate of 92 % (Table S1 in the Supplement). The integration rate is the ratio between the number of available daily IWV data points and the theoretical number of all possible observations in the time range. The IWV retrievals were estimated with GPS zenith total delay (ZTD) provided by the Nevada Geodetic Laboratory (NGL; Blewitt et al., 2018). The GPS ZTD products from NGL were used because it covers a long time period of 25 years so that it allows for better evaluations of the diurnal and annual climatological averages and long-term trends. In comparison, another ZTD dataset from EPN-Repro2 (Pacione et al., 2017) only has about 19 years of data, ending in 2014.

The NGL processes the GPS data using the newly improved GipsyX v1.0 software in precise point positioning (PPP) mode (Bertiger et al., 2020). Reprocessed orbits and clocks from the Jet Propulsion Laboratory (JPL) Repro 3 were used together with the 2014 International GNSS Service (IGS) reference frame (IGS14; Rebischung and Schmid, 2016). The observations were weighted based on an elevation (e)-dependent function of sin⁡e. The cutoff elevation angle was set to 7∘. The first-order effect of the ionosphere was removed by employing ionosphere-free combinations of the GPS observations. The second-order effect was corrected with the International Geomagnetic Reference Field 12 (IGRF-12; Thébault et al., 2015) and JPL's ionosphere maps. As for the modelling of tropospheric delay, the Vienna Mapping Function 1 (VMF1; Boehm et al., 2006) and its associated a priori zenith hydrostatic delay (ZHD) were adopted.

The IWV derived from six commonly used global atmospheric reanalyses, namely the newly released fifth generation global reanalysis (ERA5) and its predecessor ERA-Interim (ERAI) from ECMWF; the Japanese 55-year Reanalysis (JRA-55) from the Japan Meteorological Agency (JMA); the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), from NASA's Global Modeling and Assimilation Office (GMAO); and the Climate Forecast System Reanalysis (CFSR) and NCEP-DOE AMIP-II Reanalysis (NCEP-2) from the National Centers for Environmental Prediction (NCEP), is analysed. The features of the reanalyses are summarised in Table 1. It is worth noting that JRA-55 only provides humidity information at 27 pressure levels from 1000 to 100 hPa, though it has 37 levels in total. These six reanalyses are selected as their IWV products have covered the period of the ground-based GPS data available since 1994. Despite ERAI having been decommissioned and superseded by ERA5 in August 2019, we still include it for the purpose of evaluating the progress of its successor ERA5. We therefore restricted the time range of all data records to a common period from 1994 to 2018.

The zenith total delay (ZTD) estimates derived from GPS data processing can be converted into IWV, the total amount of water vapour present in a vertical atmospheric column from the Earth's surface to the top of the atmosphere in units of kilogram per square metre, using the following equation (Bevis et al., 1992): 1IWV=106RV⋅k2′+k3/Tm⋅ZTD-ZHD, where RV denotes the gas constant for water vapour, k2′ and k3 are atmospheric refractivity constants (Bevis et al., 1994), and Tm denotes the weighted mean temperature: 2Tm=∫HsHtopeTdp∫HstopeT2dp, where e and T are water vapour pressure and temperature profiles of the geopotential heights of the GPS station (Hs) to the top level of reanalysis (Htop), respectively.

The ZHD was modelled as follows (Saastamoinen, 1972; Davis et al., 1985): 3ZHD=2.2768ps1-2.66×10-3⋅cos⁡2φs-2.8×10-7Hs, where ps denotes the pressure at the GPS station with a latitude of φs and a height of Hs. The ps and Tm are computed by using the ERA5 pressure-level product (see Yuan et al., 2021, and references therein). ERA5 is selected as it can provide a 1-hourly product without temporal interpolation.

IWV values at the GPS stations are also calculated from the six reanalyses. In this calculation, the pressure-level products of the reanalyses are used rather than their surface-level IWV products, though it requires a heavier workload. This is because the GPS station and its nearby reanalysis surface grids are usually related to different heights. Vertical IWV adjustment is therefore usually required for the intercomparison between the IWV estimates from GPS and reanalyses. Compared to the reanalyses' surface-level products, their pressure-level products allow for a better characterisation of the vertical distribution of water vapour and tends to minimise the errors of the vertical adjustment (Parracho et al., 2018).

The scheme of the calculation is illustrated in Fig. 2. We assume a GPS station with a geopotential height of Hs is located between two adjacent reanalysis pressure levels (pj and pj+1). We first determine its eight surrounding reanalysis grid nodes at these pressure levels (Ni(j) and Ni(j+1), i=1,2,3, and 4) and four auxiliary points (Ai). The auxiliary points are located at the GPS station height, whereas their horizontal locations are identical to the associated reanalysis nodes. We then calculate the related meteorological variables at each auxiliary point. Exponential and linear interpolations are employed for the vertical corrections of pressure and temperature, respectively. If the auxiliary point is lower than the lowest pressure level (e.g. 1000 hPa), an extrapolation of these variables is conducted. For details of the vertical adjustment, readers are referred to Schüler (2001) and Wang et al. (2005). Next, we calculate the IWV at each auxiliary point by using a vertical integration: 4IWVi=∫HsHtopqgdp, where q and g are specific humidity and gravitational acceleration profiles from Hs to the reanalysis top level, respectively.

It is noteworthy that a geopotential height system is employed in the reanalyses. Accordingly, the geopotential heights (Hgp) of the GPS stations rather than their ellipsoidal (Hel) or orthometric heights (Hor) are used in the above calculations. The conversion of height systems is carried out as follows (Dirksen et al., 2014; Wang et al., 2016; World Meteorological Organization, 2018): Hor=Hel-N, 5Hgp=γs(φs)9.80665⋅Rφs⋅HorRφs+Hor,6γs(φs)=9.7803251+1.93185×10-3⋅sin⁡2(φs)(1-6.69435×10-3⋅sin⁡2(φs))0.5,7R(φs)=6.378137×1061.006803-6.706×10-3⋅sin⁡(φs)2, where N is the geoid heights in metre from the Earth Gravitational Model 2008 (EGM2008; Pavlis et al., 2012).

In the end, we estimate the IWV at the GPS station using a horizontal interpolation with an inverse distance weighting algorithm (Jade and Vijayan, 2008).

Representativeness differences arise in the comparison of the IWV derived by the ground-based GPS and reanalyses (Bock and Parracho, 2019). This is because local variations of IWV measured by the GPS might fail to be resolved by the reanalyses due to their coarse horizontal resolution. The representativeness differences can be evaluated statistically as proposed by Bock and Parracho (2019): 8δmax⁡=max⁡IWVi-IWVk,ik=1,2,3,4,i≠k, where IWVi and IWVk are the IWV values of the horizontal auxiliary points Ai and Ak, respectively (Fig. 2). Bock and Parracho (2019) found that the measure δmax⁡ was correlated with the standard deviation of the IWV differences between GPS and ERAI (σΔ) and thus concluded that the representativeness differences between the IWV from GPS and ERAI contributed to their discrepancies. Here, we extend their work by estimating and comparing the representativeness statistics of the six reanalyses with various spatial resolutions (Table 1).

The 1-, 3-, and 6-hourly IWV time series are screened by using a robust outlier detection method as follows (Yuan et al., 2021). For each data point, the data within a 30 d window centred at this point are extracted. The 25th percentile (Q1), 75th percentile (Q3), and interquartile range (IQR) of the subsequent time series are then calculated. Finally, the data point is identified as an outlier if it is outside the range of (Q1-1.5×IQR,Q3+1.5×IQR). The IQR threshold and the 30 d sliding window are adopted, as they allow for a good robustness and a proper accommodation for the natural variability of IWV. On average, about 1 % of data were filtered out by the data screening.

In this study, the performances of reanalysis IWV products in daily time series, diurnal cycle and variations, monthly annual cycles, and long-term linear trends are evaluated. As the temporal resolutions of the datasets are different, temporal interpolation and aggregation are conducted. To obtain daily mean IWV values, the 1-, 3-, and 6-hourly IWV time series are aggregated if they have at least 12, 4, and 2 data points in a day, respectively. The daily mean IWV time series at each station is further aggregated into monthly mean IWV series if there are at least 15 data points available in a month.

The GPS IWV time series can be inhomogeneous due to changes in GPS data processing strategies and station-related changes like hardware changes or changes in the electromagnetic environment (Van Malderen et al., 2020; Nguyen et al., 2021, and references therein). We employed a homogenisation approach as described in Appendix A with step-by-step details and examples at two stations (HERS and ERLA).

Here, we only provide a brief introduction to the approach. We first avoided inhomogeneities due to changes in GPS data processing strategy by using the homogeneously reprocessed GPS ZTD product. We then homogenised the GPS IWV time series by using the RHtestsV4 software (Wang and Feng, 2013). This software is especially developed for the detection and adjustment of changepoints in climatic time series, and it has been used in the homogenisation of IWV time series in previous studies (Ning et al., 2016; Schröder et al., 2016; Van Malderen et al., 2020).

We took the IWV time series from all six reanalyses as references for the GPS IWV homogenisation and used a strategy to avoid the impacts of possible changepoints in individual reanalyses. However, we did not homogenise the reanalyses IWV time series because they represent the native quality of the reanalyses that we would like to assess. In addition to matching the detected changepoints with inspecting GPS metadata information (GPS station log files and IGS mail archives (IGSMAIL)), we also allowed for possible undocumented changepoints in the GPS IWV time series.

To evaluate the performances of the reanalyses in reproducing IWV, the Kling–Gupta efficiency (KGE) is employed as a metric. The KGE is a composite index introduced by Gupta et al. (2009) and modified by Kling et al. (2012). It takes bias, variability, and correlation into account in the equation below: 9KGE=1-(β-1)2+(γ-1)2+(r-1)2, with 10β=μRμG,11γ=CVRCVG=σR/μRσG/μG, where μR, σR, and CVR are the mean value, standard deviation, and coefficient of variation of the reanalysis IWV time series, respectively. μG, σG, and CVG are the corresponding parameters for GPS. β and γ indicate the consistencies in the mean and variability, respectively. In the case of μR and μG being equal to zero, such as for the diurnal anomalies in Sect. 4.3, γ=σRσG. r indicates the Pearson correlation coefficient between the GPS and reanalyses time series. With perfect consistencies in mean, variability, and correlation, the values of β, γ, and r are identical to 1, respectively. From Eq. (9), it follows that a larger KGE score indicates a better consistency. Ideally, the KGE metric reaches its maximum of 1.

In addition, to be comparable to some previous studies, we also used the root mean square estimation of the IWV differences between the reanalyses and GPS: 12rmsΔ=∑i=1nIWVR-IWVG2n, where IWVR and IWVG are the IWV time series at a specific station from reanalysis and GPS, respectively, and n is number of data points in the IWV time series.

Figure 3 compares the standard deviations of daily IWV difference (σΔ) and the representativeness statistic (δmax⁡) for the six reanalyses. The first point to note is that σΔ and δmax⁡ are strongly correlated for all the reanalyses, with r values from 0.76 for NCEP-2 to 0.90 for ERA5. The result is in line with Bock and Parracho (2019), who compared ERAI to a global GPS network. Figure 3 indicates that the representativeness differences contribute to the discrepancies between the reanalyses and GPS. The larger σΔ and δmax⁡ values are found at stations close to mountains or seas, such as BZRG (Bolzano, Italy; 46.50∘ N, 11.34∘ E) and TORI (Turin, Italy; 45.06∘ N, 7.66∘ E) at the foothills of the Alps and ALME (Almería, Spain; 36.85∘ N, 2.46∘ W) near the west coast of the Mediterranean Sea. On the whole, ERA5 is characterised by the lowest σΔ and δmax⁡, with values of 0.5–1.6 and 0.2–2.1 kg m-2, respectively. In contrast, NCEP-2 has the largest σΔ and δmax⁡, with values of 1.1–3.0 and 1.8–5.2 kg m-2, respectively. The difference could be due to the fact that the spatiotemporal resolution of ERA5 is much higher than of NCEP-2 as indicated in Table 1. This result indicates that ERA5, with improved spatiotemporal resolution and data assimilation, is capable of reducing the discrepancy and representativeness difference with respect to GPS.

Figure 4 shows the geographical distributions of the ratio of mean β, the ratio of coefficient of variation γ, the correlation r, and the synthetic KGE metric for the six reanalyses by using the daily GPS IWV time series as references. Moreover, the statistics of these scores are displayed in Fig. 5 with box-and-whisker plots. From the first column of Figs. 4 and 5a we can see that β scores are slightly larger than 1 for all the reanalyses except JRA-55, indicating a general wet bias with respect to the GPS IWV. For example, MERRA-2 has the largest median β with a value of 1.04, indicating a general wet bias of 4 %. Only JRA-55 scores a median β smaller than 1 (0.99, Fig. 5a), indicating a slight dry bias of 1 %. The wet and dry biases in the reanalyses have partly been reported by several previous studies. For instance, Schröder et al. (2018) concluded that CFSR, ERAI, and MERRA-2 are too moist over Europe compared to the ensemble mean of various satellite and reanalysis IWV records, whereas JRA-55 has negligible bias there. The wet bias in ERAI over Europe was also noted by Parracho et al. (2018). Analysing the reasons of the biases is of potential interest; however, it would go beyond the scope of this paper.

Regarding the consistency in variability, most of the γ scores are less than 1, with the associated median values ranging between 0.96 and 0.98 (Fig. 5b). The results indicate a good reproduction of daily IWV variability by the reanalyses, albeit with a slight underestimation. The correlations are also pretty good with median values larger than 0.97 (Fig. 5c). However, the scores in variability and correlation are lower for the coastal stations, as shown in the second and third columns of Fig. 4, respectively. In particular, γ and r of NCEP-2 are less than 0.96 for some coastal stations located in western and southern Europe. This could be explained by the representativeness differences that impact the consistency of the IWV from reanalyses and GPS in their variabilities. For a coastal GPS station with an on-site measurement of IWV, part of its associated four reanalysis grid nodes may be located over the sea whereas others over land. As a consequence, the representativeness difference for such a coastal site is more severe than inland stations surrounded with flat terrain due to land–sea thermal contrast (Drobinski et al., 2018).

Figure 5d compares the overall consistency in daily IWV evaluated using KGE. It can be seen that ERA5 is characterised by the largest median KGE (0.97). The result reveals the superiority of ERA5 over the other reanalyses. Moreover, comparing β, γ, and r (Fig. 5a–c) shows that r tends to contribute the least to the overall inconsistency, indicating that improving the consistencies in both mean values and variabilities is more important for the daily IWV time series.

Starting with the all-time-averaged amplitudes of the diurnal GPS IWV harmonic shown in Fig. 6e, two remarkable values can first be noted at stations NICO (Nicosia, Cyprus; 33.14∘ N, 33.40∘ E; 161.9 m) and ZECK (Zelenchukskaya, Russia; 43.79∘ N, 41.57∘ E; 1143.4 m), with values of 1.2 and 1.0 kg m-2, respectively. Moreover, the diurnal harmonics at the Mediterranean Coast are generally stronger than at the other regions in Europe (0.5–0.8 kg m-2 versus 0–0.5 kg m-2). Obvious seasonal differences can also be seen in their diurnal harmonics, with significantly larger amplitudes in summer (June, July, and August; JJA) than in the other seasons due to the stronger solar heating effect with minimal cloud coverage in Mediterranean summers (Enriquez-Alonso et al., 2016). However, the semidiurnal harmonics are much weaker, and their seasonal variations are less significant (Fig. 6f–j). The all-time-averaged semidiurnal amplitudes are lower than 0.22 kg m-2, except for the two stations NICO and ZECK with values of 0.4 and 0.3 kg m-2, respectively. The ratios between the all-time-averaged semidiurnal and diurnal amplitudes are lower than 30 % at 88 % of the stations (95 out of 108). As for the phases, the diurnal and semidiurnal terms are generally consistent over seasons (Fig. 6k–t), and their all-time-averaged peaks are within 15:00–21:00 and 01:00–06:00 LST at 90 % of the stations (97 out of 108), respectively.

In order to compare the characteristics of diurnal IWV amplitudes at different stations, we calculated each station's relative amplitude as the ratio between their respective (semi) diurnal amplitudes and mean IWV as displayed in Fig. 7a and d. We classified the GPS stations into three types according to their geographical characteristics (Fig. 7a) and analysed their relationships with each station's altitude and distance to sea (SeaDist). Firstly, we divided the stations with a limit of 20 km on their SeaDist. We further separated the stations located at the Mediterranean Coast (MedCoast; SeaDist <20 km; 32∘ N < lat <46∘ N, 5∘ W < long < 45∘ E) from the other coastal (OtherCoast) stations because their characteristics are quite different as can be seen from Fig. 7a. Consequently, the 108 stations are classified into 62 Inland stations, 12 MedCoast stations, and 34 OtherCoast stations.

As can be seen from Fig. 7a–c, all OtherCoast stations are lower than 300 m, and their relative diurnal IWV amplitudes are the weakest, with a range from 0.3 % to 1.9 % and a median of 1.1 %. Within the altitude limit of 300 m, the Inland stations are characterised by moderately larger diurnal amplitudes (1.5 %–2.5 %). The results indicate the effect of land–sea breeze circulation on mitigating the intensity of the diurnal IWV cycle at the Atlantic coasts of Europe with respect to inland Europe. However, the land–sea breeze effect can be less significant for the MedCoast stations because their diurnal amplitudes are significantly larger (1.1 %–4.2 %) than the OtherCoast stations'. The stronger diurnal IWV cycles at the MedCoast stations can be explained by the stronger solar heating effect at the Mediterranean Coast than at the other European coasts, especially during summer daytime under stable and clear-sky weather conditions. In addition, it can be seen from Fig. 7b and e that the relative diurnal and semidiurnal IWV amplitudes are well correlated with altitudes, with correlation coefficients of 0.66 and 0.67, respectively. This relationship indicates the effect of orographic circulation, which can enhance the diurnal range of temperature at higher altitudes (Diedrich et al., 2016).

In addition, we selected six stations with various altitudes, SeaDist, and climates to illustrate the diversity of diurnal IWV cycles in Europe as shown in Fig. 8. The climate zones of the GPS stations are classified according to the Köppen climate classification system (Beck et al., 2018), and the properties of the stations are listed in Table S2.

Station NICO is located in Cyprus with hot semi-arid climate (BSh). Despite being only 21.5 km away from the coastline, NICO has the largest diurnal IWV amplitude with a value of 1.2 kg m-2, equivalent to a relative amplitude of 6.7 %. This is mainly due to the large diurnal temperature range in Cyprus, especially in summer (Price et al., 1999).

Both the MedCoast station VALE (Valencia, Spain; 39.48∘ N, 0.34∘ W; 27.0 m) and the OtherCoast station NEWL (Newlyn, UK; 50.10∘ N, 5.54∘ W; 11.0 m) are very close to the coastline, with SeaDist values of 1.2 and 0.5 km, respectively. However, their diurnal amplitudes are quite different (absolutely 0.8 kg m-2 versus 0.1 kg m-2, relatively 3.9 % versus 0.7 %). As explained earlier for the difference between the two station types, their weather conditions are different. VALE is located at the Mediterranean Coast with cold semi-arid (BSk) climate. Its strong diurnal cycle, especially in summer with an amplitude of 1.4 kg m-2 (4.6 %), is attributed to intense solar heating under minimal-cloud-coverage weather conditions. In contrast, NEWL is located at the coast of the English Channel with temperate oceanic (Cfb) climate, and its smaller diurnal amplitude can be due to the weaker solar heating effect under unstable and cloudy weather conditions, in addition to the land–sea breeze effect on mitigating diurnal temperature range.

Station ZECK is in the Greater Caucasus with humid continental (Dfb) climate. Its diurnal amplitude is much stronger than PENC's (Penc, Hungary; 47.79∘ N, 19.28∘ E; 248.3 m) with the same climate (1.0 kg m-2 and 7.9 % versus 0.2 kg m-2 and 1.5 %). As ZECK is much higher than PENC, their difference in amplitude is consistent with the pattern for most Inland stations, which can be explained by the effect of orographic circulation (Diedrich et al., 2016). In addition, KIR0 (Kiruna, Sweden; 67.88∘ N, 21.06∘ E; 469.3 m) is typical for many stations in northern Europe. Although its diurnal cycle is quite weak with an amplitude of only 0.1 kg m-2 (1.7 %), it is well fitted by the sinusoidal harmonic curve fitting.

Only the diurnal IWV cycle from the 1-hourly ERA5 time series was evaluated with respect to GPS, as the temporal resolutions of the other reanalyses are too coarse to characterise the diurnal cycle. However, we found significant shifts in the diurnal IWV anomalies between 09:00 and 10:00 (10:00–09:00) UTC as well as between 21:00 and 22:00 (22:00–21:00) UTC at part of the stations, such as NEWL and PENC displayed in Fig. 8. The ERA5 developers have noticed such mismatches in the diurnal cycles of individual meteorological variables, such as its near-surface wind, temperature, and humidity products (see Known Issues 8 and 9 in https://confluence.ecmwf.int/display/CKB/ERA5:+data+documentation#ERA5:datadocumentation-Knownissues, last access: 8 January 2023), and the problem is attributed to the edge effect in each ERA5 assimilation cycle (from 10:00 to 21:00 UTC and from 22:00 to 09:00 UTC+1 d). However, according to our knowledge, the magnitude of the mismatch in the diurnal cycle of ERA5 IWV and its spatiotemporal characterisations have not been investigated yet. Therefore, we will quantify and analyse the mismatch in the ERA5 IWV over Europe in this section.

Figure 9 compares the diurnal IWV cycle of ERA5 and GPS for each season at station PENC. From this figure, we can derive that there are no mismatches in the diurnal GPS IWV cycle, although the GPS IWV (slightly) relies on Tm (hence humidity and temperature) from ERA5 for the ZTD to IWV conversion, as shown in Eq. (2). GPS IWV estimates are therefore regarded as reference data to evaluate the mismatches in the diurnal cycle of ERA5 IWV. At station PENC, the mismatches in ERA5 are seasonal dependent, which are strongest in summer (JJA) but weakest in winter (DJF).

Figure 10 compares the shifts at 10:00–09:00 UTC and 22:00–21:00 UTC from ERA5 and GPS at all the stations, respectively. The shifts in the GPS IWV cycle are regarded as reference, representing the natural IWV changes at the two epochs. As can be seen from Fig. 10a–e and k–o, the ERA5 IWV series generally drop from 09:00 to 10:00 UTC and then jump from 21:00 to 22:00 UTC. The ERA5 artificial shifts at the two epochs are most significant in summer, with average values of -0.23 and 0.35 kg m-2. In contrast, the average natural shifts in summer estimated from GPS IWV are only 0.11 and -0.08 kg m-2. Moreover, the all-time-averaged natural shifts in GPS IWV are only 0.05 and -0.05 kg m-2. However, the artificial shifts in ERA5 IWV are -0.08 and 0.19. As can be seen from the geographic distributions of the shifts shown in Fig. 10e and o, the ERA5 shifts at 10:00–09:00 UTC are most significant at the Alps and in Eastern Europe, whereas the shifts at 22:00–21:00 UTC are more widespread in central Europe. The reasons for their geographical patterns are unknown and needs further investigation. Since the average diurnal amplitude of the reference GPS IWV is only 0.32 kg m-2, the artificial shifts in ERA5 IWV cannot be ignored when analysing the diurnal IWV cycle in these regions.

Diurnal anomaly represents high-frequency variations of IWV associated with weather phenomena like heavy rainfall. Therefore, evaluations of the consistencies between the IWV diurnal anomalies from reanalyses with respect to GPS are conducive to a better understanding of their performances in extreme weather, especially for ERA5 with a significantly enhanced temporal resolution of 1 h.

We first evaluated all the reanalyses with respect to GPS at 1 h temporal resolution. For the reanalyses with coarser resolutions (3 and 6 h), we interpolated their time series to 1 h by using cubic spline, which is slightly superior to linear interpolation. Statistics of the evaluation results are listed in Table 2. At the temporal resolution of 1 h, ERA5 scores the highest average γ, r, and KGE with values of 0.98, 0.89, and 0.88, respectively. The results indicate that the 1-hourly ERA5 diurnal anomalies have the best agreement with GPS in variability and correlation. However, NCEP-2 performs the worst, as it scores the lowest γ, r, and KGE with values of 0.75, 0.69, and 0.60, respectively. To be comparable to many other studies, we also evaluated the consistencies by using the more commonly used indicator – rms of IWV difference (rmsΔ) as shown in Eq. (12). Results show that ERA5 and NCEP-2 score the lowest and largest average rmsΔ values of 0.97 and 1.57 kg m-2, respectively. Therefore, we drew the same conclusion as from the KGE scores. The evaluations confirm the superiority of the 1-hourly ERA5 over the other reanalyses, most likely because of its enhanced spatiotemporal resolutions and other improvements in data assimilation.

For a fairer intercomparison, we also evaluated ERA5 and the other reanalyses at their respective native resolutions. Accordingly, we extracted the ERA5 IWV every 3 and 6 h. The comparison with MERRA-2 at its native resolution of 3 h shows that ERA5 achieves larger KGE (0.89 versus 0.86) and smaller rmsΔ (0.97 kg m-2 versus 1.15 kg m-2). Moreover, the average KGE value of the 6-hourly ERA5 IWV is 0.89, which is higher than those of CFSR, ERAI, JRA-55, and NCEP-2, with values of 0.86, 0.83, 0.79, and 0.60, respectively. The results indicate that ERA5 is still superior to the other reanalyses at the coarser temporal resolutions.