The observational campaign was conducted at the Athalassa atmospheric observatory in Nicosia, Cyprus (35.15° N, 33.40° E, 160 m a.s.l. (meter above sea level)), situated in the central Mesaoria plain. The site is characterized by complex topography, bounded by the Troodos Mountain to the southwest and the Pentadaktylos Mountain to the north, as shown in Fig. 1a. This study presents the first comprehensive analysis of radiometric data acquired under the CYGMEN infrastructure project, established to monitor the thermodynamic state of the Eastern Mediterranean atmosphere. To ensure robust thermodynamic profiling and validation, three primary datasets were collated, as shown in Table 1.

The conversion of GNSS-derived ZWD to PWV is governed by a proportionality factor, Π, whose accuracy is largely dictated by the Tm. To assess the fidelity of thermodynamic inputs for GNSS meteorology, we evaluated three distinct Tm derivation strategies. For profile-resolving instruments (MWR and RS), Tm values were computed by integrating the vertical profiles of physical temperature, T(z) (K), and absolute humidity, ρv(z) (kgm-3). Consistent with Bevis et al. (1992), Tm is defined as the mean temperature of the atmosphere weighted by the water vapour partial pressure, which can be expressed in terms of vapour density as shown in Eq. (): 5Tm=∫zsurfztopρv(z)dz∫zsurfztopρv(z)T(z)dz In practice, the continuous integrals were discretized using the trapezoidal rule from the surface (zsurf) to the highest available profile level (ztop). This approach assumes linear variation of T and ρv between measurement levels. For standalone GNSS retrieval (where no dynamic profiles are available), Tm was derived from the HGPT2 (Hourly Global Pressure and Temperature 2) model (Mateus et al., 2021). HGPT2 is an advanced “blind” empirical model, meaning its outputs are independent of the specific observational year. While dynamic NWP models provide superior real-time meteorological data, “blind” models like HGPT2 remain heavily utilized in standard geodetic GNSS processing where real-time meteorological or NWP data streams are unavailable. It is constructed from a comprehensive 20 year historical baseline of atmospheric data from the ERA5 global reanalysis. Unlike standard static climatologies, HGPT2 leverages the full ERA5 spatial resolution (0.25°×0.25°) and provides temporal resolution at 1 h intervals for any given Day of Year (DOY). It achieves this by employing a time-segmentation concept, modeling thermodynamic variables via long-term mean values combined with annual, semi-annual, and quarterly periodic functions.

Applying the linear correction model (as formulated in Sect. 2.2.1) successfully re-centers the error distribution. To quantify the benefits of sensor synergy in integrated water vapour estimation, this study defines and contrasts two distinct GNSS PWV retrieval architectures. The first, “Standard Retrieval” which is a control method utilizes the ZTDGNSS combined with the Tm derived empirically from the HGPT2 climatological model (Böhm et al., 2015). Second “Synergistic Retrieval” which proposed method couples ZTDGNSS with a physical Tm derived directly from a collocated MWR. For the synergistic approach, the dimensionless conversion factor (Π) was calculated dynamically using the MWR-derived Tm following Eq. () and Eq. (). 6PWV=Π⋅ZWD7Π=106ρwRvk2′+(k3/Tm) where ρw represents the density of liquid water (1000 kgm-3) and Rv is the specific gas constant for water vapour (461.52 Jkg-1K-1). To assess the sensitivity of the Π to the choice of thermodynamic coefficients, three widely used formulations were employed in this study, following Davis et al. (1985)/Thayer (1974), Bevis et al. (1994), and Rüeger (2002), as shown in Table 2.

To rigorously quantify the uncertainty in the final PWV retrieval and avoid fragmented error attributions, standard error propagation must be applied to the fundamental conversion Eq. (6). Assuming the uncertainties in the wet delay and the conversion factor are uncorrelated, the variance of the final PWV (σPWV2) is expressed using partial derivatives as in Eq. (): 8σPWV2=∂PWV∂ZWD2σZWD2+∂PWV∂Π2σΠ2 Evaluating these primary partial derivatives yields the proportional contributions of the geodetic and thermodynamic components as shown in Eq. (): 9σPWV2=Π2σZWD2+ZWD2σΠ2 The uncertainty in the conversion factor (σΠ2) is itself a compound term driven by the Tm and the static atmospheric refractivity constants (k2′ and k3). Its variance is defined via partial derivatives as shown in Eq. (): 10σΠ2=∂Π∂Tm2σTm2+∂Π∂k2′2σk2′2+∂Π∂k32σk32 The sensitivity of the conversion factor strictly to Tm (the dynamic thermodynamic variable evaluated in this study) is quantified by its partial derivative and it represented as Eq. (): 11∂Π∂Tm=Πk3Tm2k2′+k3Tm This consolidated formulation establishes the exact mathematical limits of thermodynamic error propagation. As demonstrated in the sensitivity analysis (Sect. 3.4), this framework accurately isolates the dynamic uncertainties driven by Tm from the baseline static biases introduced by the chosen refractivity constants.

The vertical structure of the atmosphere was analyzed by segregating the dataset into two regimes: the PBL (0–2 km), where water vapour is concentrated, and the Free Troposphere (>2km). Additionally, the water vapour scale height (Hv) was calculated to parameterize the vertical distribution of moisture. Hv was derived for both RS and MWR by fitting an exponential decay function (Eq. 12) to the absolute humidity profile (ρv). 12ρv(z)=ρv,0⋅exp⁡-zHv where ρv(z) is the absolute humidity at height z, and ρv,0 is the surface humidity. This curve fitting was deliberately restricted to the lowest 4 km of the atmosphere. Because this layer contains the vast majority (>90%) of the tropospheric water vapour mass, bounding the fit prevents the algorithm from heavily weighting near-zero, noisy upper-tropospheric values that mathematically degrade the fit for the boundary layer. Furthermore, the scale height metric fundamentally assumes the atmosphere conforms to a well-behaved exponential decay. Profiles yielding Hv values outside the physically realistic range of 0.1–4.0 km were excluded from the statistical analysis to prevent artificial statistical skewing during complex meteorological states (e.g., deep convective mixing) where the underlying exponential model is invalid. Forcing a mathematical fit onto these non-exponential profiles yields physically meaningless artifacts. Therefore, a Quality Assurance filter was applied, bounding the analysis to the physically realistic range of 0.1km<Hv<4.0km. Profiles yielding values outside this range were discarded because they indicate the underlying exponential model itself is invalid for that specific atmospheric profile, preventing artificial statistical skewing in the instrument intercomparison. Profiles yielding Hv values outside the physically realistic range of 0.1–4.0 km were excluded from the statistical analysis. To evaluate the performance limitations of standard climatological models under varying hygrometric conditions, the systematic error (ΔPWV) was defined as the residual between the synergistic and standard approaches (Eq. 13): 13ΔPWV=PWVSynergistic-PWVStandard The dataset was stratified into discrete bins of 5 mm PWV to isolate regimes of moisture abundance. Within each bin, the mean bias and ±1σ uncertainty were computed. These statistics were utilized to determine the “Systematic Bias Threshold,” defined herein as the specific hygrometric threshold where the systematic model error exceeds 1 mm. Finally, the propagation of thermodynamic uncertainty into the moisture retrieval was quantified via linear regression analysis. This compared the relative error in Tm (HGPT2 vs. MWR) against the resulting relative error in PWV, serving as an empirical verification of the theoretical sensitivity approximation given in Eq. (): 14ΔPWVPWV≈ΔTmTm

MWR-retrieved temperature T and ρv profiles were validated against collocated RS observations at 00:00 UTC and 12:00 UTC during March–October 2025. Profiles were stratified into the planetary boundary layer (PBL; 0–2 km) and free troposphere (>2km), as shown in Figs. 2 and 3. Mean vertical temperature profiles show agreement between MWR and RS (Fig. 2a and b). In the boundary layer (0–2 km), MWR retrieves temperature with high precision (r>0.98, RMSE<1.5K). Above 2 km, a cold bias is observed in the MWR retrieval, reaching -5.16K at 12 UTC (Fig. 2f). Despite this bias, the linearity remains strong (r≈0.97), indicating the sensor captures relative thermal variations aloft despite the absolute offset. This confirms the trend observed in the mean profiles, where the MWR underestimates temperatures in the mid-to-upper troposphere. Furthermore, horizontal balloon drift driven by prevailing winds inevitably causes the radiosonde to sample a different atmospheric volume than the MWR's strict zenith view. While this spatiotemporal mismatch introduces random scatter into the upper-level comparisons, it does not artificially skew the systematic biases identified in this study. Consequently, the RMSE increases substantially to approximately 6.4–6.7 °C. The stark contrast in accuracy between the lower and upper troposphere is a known characteristic of ground-based microwave radiometry (Parde et al., 2025; Pakkattil et al., 2025). The high accuracy below 2 km is attributed to the high information content of the opaque V-band channels (51–58 GHz), whose weighting functions peak near the surface. Above 2 km, these weighting functions broaden significantly, reducing vertical resolution and causing a “smearing” effect where the instrument provides a volume-averaged temperature rather than a precise point measurement. The observed cold bias is likely a result of the retrieval algorithm (e.g., neural network) relying heavily on a climatological a priori dataset that does not perfectly represent the thermal conditions of the transition season observed, or systematic offsets in the radiative transfer model (absorption coefficients) used for training.

The mean ρv profiles (Fig. 3a and b) show the expected exponential decrease of moisture with height. At 00 UTC, the profiles align reasonably well. However, at 12 UTC, the MWR profile exhibits a structural deviation between 1–2 km, failing to capture the smooth moisture gradient recorded by the RS. This discrepancy may be attributed to the MWR's limited vertical resolution during periods of active daytime mixing or complex humidity layering. The retrieval of humidity in the lower atmosphere shows moderate agreement but is less accurate than the temperature retrievals. Performance is notably better at night (00 UTC) with r of 0.878 and RMSE of 1.98 gm-3. At 12 UTC, the correlation drops to 0.744, and the scatter increases (RMSE=2.31gm-3). Because the integrated mass of the water vapour column is physically and numerically equivalent to its depth (assuming the standard density of liquid water), this physical quantity is exclusively referred to as PWV expressed in millimeters (mm) throughout this study to align with operational meteorological conventions. A negative bias persists at both times (-0.51gm-3 at 00 UTC and -0.91gm-3 at 12 UTC), indicating a tendency for the MWR to underestimate moisture content in the boundary layer, particularly during the day. Surprisingly, the statistical linearity for ρv improves slightly or remains stable above 2 km, likely due to the lower overall magnitude of humidity at these heights. The correlation coefficients remain stable (∼0.87). In contrast to the lower levels, the bias shifts to slightly positive values (0.23 gm-3 at 00 UTC and 0.46 gm-3 at 12 UTC), suggesting a slight moist bias in the MWR retrievals aloft. The linear fits (Fig. 3e and f) align closely with the 1:1 line, with slopes near unity (0.90 and 1.00), indicating that the MWR effectively captures the free tropospheric humidity trends despite the lower absolute values. The difficulty in retrieving accurate ρv profiles, particularly at 12 UTC, stems from the limited vertical resolution of the K-band channels (22–31 GHz). Unlike temperature profiling, humidity profiling offers very few independent degrees of freedom (typically<3), making it difficult for the MWR to resolve sharp vertical gradients often present at the top of the convective boundary layer during the daytime. The structural deviation and underestimation are common issues linked to the “smoothing” error inherent in passive radiometry, where sharp moisture inversions are averaged out. Furthermore, the persistent bias suggests potential uncertainties in the water vapour absorption models (spectroscopic parameters) or non-representative training data used in the retrieval algorithm.

Unlike vertical profiling, the MWR excels in measuring total column quantities. The comparison with RS yields an excellent correlation (r=0.971) and a low RMSE of 1.72 kgm-2 (Fig. 4). This performance disparity – superior PWV versus degraded profiles – confirms that while the sensor cannot resolve vertical structural details due to smoothing error, the radiometric brightness temperature in the K-band remains strictly proportional to the total precipitable water mass. The GNSS-derived PWV shows a slight negative bias relative to RS (-0.45kgm-2), whereas it relative to the MWR exhibits a positive bias (+0.45kgm-2). The cumulative offset observed in the MWR-GNSS intercomparison (+0.89kgm-2) highlights the systematic differences in calibration and retrieval assumptions between active (GNSS) and passive (MWR) techniques. The GNSS underestimation is likely driven by errors in the Tm derived from the static HGPT2 model, a hypothesis further explored in Sect. 3.4. To further diagnose the structural limitations of the retrievals, we evaluated the water vapour Hv. While Hv is admittedly a single-parameter representation of the complex atmospheric moisture profile, it is a crucial parameter that provides a representative value for the rate at which water vapour decreases with altitude – a key factor in understanding atmospheric stability, cloud formation, and radiative transfer processes. In this study, it is utilized specifically as a diagnostic metric to quantify the vertical structural limitations of passive microwave remote sensing. The comparison of Hv calculated from RS and MWR profiles is shown in Fig. 5. Unlike the high-fidelity PWV retrievals, the MWR-derived scale height shows negligible correlation with RS observations (r=0.25, R2=-2.87) and a massive systematic positive bias of 0.62 km. The histograms (Fig. 5b) further elucidate this discrepancy: while the RS scale heights follow a narrow, physically realistic distribution centered around a mean (μ) of 1.51 km, the MWR distribution is artificially broad and shifted to significantly higher values (μ=2.13km).

The large scatter and ambiguity in the MWR estimates – which completely dwarf the individual least-squares fit uncertainties of the exponential regression – are a direct consequence of the instrument's physical limitations. Hv is highly sensitive to the sharp vertical gradient of humidity at the top of the planetary boundary layer. However, the K-band channels (22–31 GHz) utilized for humidity profiling possess broad weighting functions, restricting the vertical degrees of freedom to typically fewer than three. Because the MWR lacks the vertical resolution to capture sharp moisture inversions, the retrieval algorithm mathematically smears the moisture mass upward. This inherent “smoothing error” artificially elongates the vertical moisture profile, effectively inflating the calculated e-folding depth. Therefore, the inclusion of this Hv analysis serves to transparently demonstrate a critical operational boundary: while the MWR is an excellent standard for PWV, it is significantly unreliable and mathematically unsuited for characterizing vertical moisture compactness. The significant deviations observed in these macroscopic retrieval products necessitate a deeper investigation into the intermediate thermodynamic variables driving the conversion process. Consequently, the isolated performance of the Tm is evaluated in Sect. 3.3, followed by the introduction of a post-retrieval MWR calibration scheme in Sect. 3.4 designed to mitigate these native biases.

The accurate estimation of the Tm is critical for converting GNSS-derived ZWD into PWV. The performance of Tm derived from the MWR and the empirical GPT2w model (HGPT2) was evaluated against RS measurements, which serve as the “ground truth.” The results are presented in Fig. 6. The time series (Fig. 6a) illustrates the seasonal evolution of Tm from April–October 2025. The Radiosonde observations (black dots) show significant variability, capturing synoptic-scale weather fluctuations. The MWR-derived Tm (orange dots) tracks these fluctuations with remarkable precision, overlaying the RS points almost perfectly. In stark contrast, the HGPT2 model (blue dots) provides a smooth, climatological curve. While it captures the general seasonal trend, it completely misses the day-to-day thermodynamic variability, often overestimating Tm during cooler transient events and underestimating it during warmer anomalies. The empirical model shows only moderate performance (r=0.800) with a substantial spread (RMSE=4.54K). A systematic positive bias of 1.67 K indicates that HGPT2 generally overestimates the atmospheric temperature profile in this region. The scatter plot reveals a diffuse, “cloud-like” distribution, confirming its inability to capture real-time atmospheric dynamics. The MWR demonstrates superior performance, achieving a near-perfect correlation (r=0.981). The RMSE is significantly reduced to 2.33 K, which is nearly half the error of the empirical model. Interestingly, the MWR exhibits a negative bias of -1.91K, suggesting a systematic underestimation of Tm. Crucially, this bias does not originate in the free troposphere, but rather in the planetary boundary layer (0–3 km). Since Tm is weighted by water vapour pressure, this “cold bias” indicates the MWR is underestimating the intense near-surface heating or the sharp lapse rates characteristic of the Nicosia environment. Despite this offset, the tight linearity indicates that MWR is an excellent source for capturing real-time Tm variations. Comparing the large dataset of MWR against HGPT2 (N=12493) confirms the discrepancy between dynamic and static modeling. The correlation is lower (r=0.770) and the scatter is large (RMSE=4.89K), further proving that static empirical models are insufficient for high-precision GNSS meteorology compared to dynamic radiometer measurements. While errors in ZTD estimation contribute significantly to the overall uncertainty budget, the specific error introduced during the conversion from delay to water vapour is linearly dependent on the accuracy of Tm. Assuming a given ZTD, a standard rule of thumb states that a 1 % relative error in Tm translates to roughly a 1 % relative error in the resulting PWV. By switching from a static model (HGPT2, ∼4.5K error) to a dynamic sensor (MWR, ∼2.3K error), the uncertainty in the GNSS water vapour product is effectively halved. This validates the “synergistic” approach of using collocated MWR thermal data to process GNSS signals.

In this section, the PWV was derived using bias-corrected mean temperature (Tm) and constant values based on the study by Rüeger (2002), as mentioned in the Sect. 3.4. The impact of Tm errors on the final PWV product was analyzed to quantify the benefits of the synergistic retrieval method. Figure 10 visualizes the direct relationship between the relative error in Tm and the resulting relative error in PWV. The plot reveals a strictly linear relationship (R2=0.984) with a slope of 0.981. This confirms the theoretical approximation that (ΔPWV/PWV)≈(ΔTm/Tm). The color gradient indicates that this linear error propagation holds true across all PWV magnitudes (from<10mm to >45mm). This implies that temperature errors propagate directly into moisture errors regardless of the humidity level, making accurate Tm crucial at all times. Figure 11 investigates the systematic difference (ΔPWV) between the synergistic retrieval (using MWR Tm) and a standard retrieval (using empirical Tm) as a function of moisture abundance (PWV magnitude). For drier conditions (PWV<25mm), the difference is minimal (near zero), and the uncertainty (shaded region) is low. This suggests that for low humidity, the choice of Tm source is less critical. As atmospheric moisture increases (>25mm), a significant negative bias emerges. The curve dips sharply, reaching nearly -1.0mm at extreme humidity (45+mm). The “Systematic Bias Threshold” marker indicates that beyond 45 mm, the discrepancy exceeds 1.0 mm. The fact that the bias magnitude scales directly with total PWV provides physical confirmation that the error source is located in the boundary layer, where the bulk of the water vapour resides. The growing negative bias demonstrates that standard GNSS processing (using static models like HGPT2) systematically overestimates water vapour during extreme events compared to the more accurate synergistic method. Rather than extrapolating these localized errors to regional hydrological impacts, we emphasize the primary empirical observation: the systemic deviation of the standard empirical model scales proportionally with the magnitude of the PWV regime. Crucially, this systematic overestimation of moisture during extreme events is deeply intertwined with the diurnal cycle of the local atmosphere. This analysis quantifies the specific operational penalty of utilizing static climatological models in this region, demonstrating that HGPT2 incurs an PWV error exceeding 1.0 mm during severe thermodynamic events. As previously established (Fig. 7), the static HGPT2 model displays an exaggerated diurnal wave with an amplitude exceeding 8.5 K. Because the static model fails to account for the thermodynamic decoupling between the heated boundary layer and the cooler free troposphere during the day, this Tm error artificially inflates the amplitude of the GNSS-derived PWV diurnal cycle during peak solar insolation. By utilizing the synergistic retrieval approach, this spurious daytime moisture amplification is effectively mitigated. While further multi-site, long-term studies are required to assess the broader impacts on regional operational forecasting, our localized dataset clearly indicates that integrating real-time MWR thermal data successfully removes diurnal artifacts and reduces systematic measurement biases at this site.