Commercial Microwave Links (CMLs)

• Commercial Microwave Links are point-to-point radio connections used for both communication and opportunistic weather monitoring.
• They utilize signal attenuation models to estimate precipitation, fog, and humidity, with metrics like RMSE and correlation validating performance.
• Hybrid retrieval frameworks, including physics-based, deep learning, and data assimilation methods, enhance accuracy in real-time meteorological nowcasting.

Commercial Microwave Links (CMLs) are point-to-point microwave radio connections operating between fixed sites such as cellular base stations and form a core component of modern wireless communication infrastructure. These links, typically in the 21–39 GHz frequency range and with path lengths ranging from hundreds of meters to several kilometers, are highly sensitive to atmospheric phenomena that cause microwave attenuation, including rainfall, fog, and variations in water vapor. In the last two decades, CMLs have become a widely used opportunistic environmental sensor network, enabling path-averaged retrieval of precipitation, humidity, and other near-surface atmospheric parameters via the analysis of received signal level (RSL) fluctuations archived by network operators. Their deployment density and areal coverage, combined with minimal incremental cost due to reuse of operational data, have positioned CMLs as a major source for high-resolution, near-ground meteorological information supplementing traditional gauge and satellite observations.

1. Microwave Propagation Physics and Attenuation Mechanisms

Microwave propagation in the lower troposphere is affected by the absorption and scattering of electromagnetic waves by hydrometeors (rain, fog, clouds) and atmospheric gases (mainly water vapor and oxygen). The total attenuation $A_{\text{tot}}$ over a link of length $d$ can be expressed by the path integral:

$$A_{\text{tot}} = \int_0^d \left[\gamma_{\text{hydrometeor}}(x) + \gamma_{\text{gas}}(x)\right]\ dx$$

For fog, the Rayleigh approximation (valid up to $\sim$200 GHz) yields:

$$\gamma_{\text{fog}}(f,T,\text{LWC}) = \kappa(f,T)\cdot\text{LWC}$$

where $\kappa(f,T)$ is the fog-specific attenuation coefficient determined by frequency and temperature, and $\text{LWC}$ is liquid water content. For rain, the classical power-law model relates specific rain-induced attenuation $k$ to rain rate $R$ as:

$A = k\,L = a\,R^b L$

where $A$ is attenuation in dB, $a$ and $b$ are empirically determined constants, and $L$ is link length. Gaseous attenuation is modeled per ITU-R P.676-6:

$$\gamma_{\text{gas}}(f,p,T,e) = 0.1820\,f\,N''(f,p,T,e)$$

where $N''$ is the imaginary component of atmospheric refractivity, and $f$ is frequency in GHz. Wet antenna attenuation (WAA) introduces an additional, nonlinear uncertainty, especially during rainfall or dew formation. For water vapor, attenuation increases with frequency, peaking near absorption lines (notably at 22.235 GHz), enabling path-integrated humidity retrieval (David, 2018, Li et al., 2 Dec 2025, David et al., 2018).

2. Sensing Modalities: Precipitation, Fog, and Humidity Retrieval

2.1 Rainfall Estimation

CMLs provide path-averaged rainfall estimates by inverting rain-induced attenuation using the power-law relation:

$k = a\,R^b$

where the values of $a$ and $b$ are frequency- and polarization-dependent, as determined by drop-size distribution and local meteorological conditions. Attenuation is deduced by referencing real-time RSL observations to a rolling “dry” baseline RSL, correcting for system and environmental drifts. Principal error sources include wet antenna attenuation, local spatial inhomogeneities, baseline estimation artifacts, and non-uniform DSD (Li et al., 2 Dec 2025, Bianchi et al., 2018).

2.2 Fog Detection

Fog monitoring leverages the sensitivity of microwave attenuation to liquid water in droplets with Mie-size parameter $x \ll 1$. Heavy fog yields attenuation coefficients $\gamma_{\text{fog}} \sim 0.31$ dB/km at 38 GHz ($T{=}15^{\circ}$C, $\kappa{\sim}0.8$ (dB/km)/(g/m$^3$)). In regression-based approaches, linkwise attenuations $A_i$ are modeled as:

$A_i = A_w + \gamma_{\text{fog}} L_i$

where $A_w$ represents wet antenna losses and $\gamma_{\text{fog}}$ is retrieved by multi-link regression. Fog is declared when $\gamma_{\text{fog}}$ exceeds a practical threshold, e.g., $0.05$ dB/km, reliably distinguishing fog from stratus and precipitation when cross-referenced with local rain gauges and humidity data (David, 2018).

2.3 Humidity Retrieval

Microwave attenuation by water vapor enables 2D humidity field reconstruction. The per-link retrieval proceeds by comparing RSL against a calibrated reference for typical (median) humidity, with attenuation numerically inverted using the ITU-R P.676-6 formula. Spatial interpolation (e.g., Shepard’s method) merges multi-link estimates, yielding 2D vapor density fields with gauge-correlated validation (Pearson $0.60$–$0.92$, RMSD $1.9$–$4.15$ g/m$^3$) (David et al., 2018).

3. Algorithmic Frameworks and Data Assimilation

3.1 Physics-Based Retrieval

Baseline physics-based CML rainfall retrieval uses the power-law inversion, assuming homogeneity along the link. For fog and humidity detection, attenuation decomposition (least-squares regression across spatially distributed links) separates hydrometeor and gas-induced components, accounting for wet antenna effects and screening for precipitation using auxiliary measurements. Calibration over extended “dry” periods is essential for robust referencing.

3.2 Data-Driven and Hybrid Models

Emerging hybrid architectures, such as TabGRU (Transformer + BiGRU), incorporate deep learning on RSL sequences to learn latent nonlinear relationships (including WAA hysteresis, nonstationary noise, and diurnal cycles) jointly with spatial-temporal rainfall patterns. The TabGRU method, trained with concurrent gauge data, outperforms both the physics-based and standard deep learning baselines (e.g., $R^2$ up to $0.96$, RMSE reduction of 27–31%) and mitigates peak rainfall overestimation prevalent in power-law models (Li et al., 2 Dec 2025).

3.3 Statistical Data Assimilation

Variational Kalman filter (VKF) and 3D-Var frameworks assimilate CML, radar, and rain gauge data for optimal rainfall map estimation and nowcasting. The forward operator maps rain fields to linkwise attenuation, accounting for nonlinearities via link-specific parameters. Covariance propagation ensures temporally consistent error estimation, and Lagrangian persistence advects rainfall fields using radar-derived velocity vectors. Link observation errors are set based on network-specific instrument noise (e.g., 0.8–1.2 dB) (Bianchi et al., 2018).

4. Network Architecture, Operational Coverage, and Resolution

CMLs are typically deployed as bidirectional, line-of-sight microwave connections between cellular towers at heights of tens of meters above ground. Frequencies range from 21–39 GHz, with link lengths of 0.5–5 km for operational meteorological studies. Network density in urban regions can yield effective spatial sampling down to ~1 km². The temporal resolution depends on operator logging frequency, from daily snapshots to sub-minute intervals in advanced setups (David, 2018, David et al., 2018).

Tables summarize key technical parameters:

Parameter	Typical Range / Value	Context
Frequency	21–39 GHz	Rain, fog, humidity CML sensing
Link length ($L$)	0.5–5 km	Fog/rain networks; up to 10 km for humidity
RSL quantization	0.1 dB	Operator logging precision
Spatial coverage	$\sim$1 km² per link	Dense urban deployments

5. Performance Validation and Case Studies

Empirical validation across rain, fog, and humidity retrieval tasks demonstrates robust capabilities:

• For heavy fog, regression yielded $\gamma_{\text{fog}}\approx0.31$ dB/km during dense events and $<0.05$ dB/km for non-fog reference nights; detection accuracy and zero false-alarm in the tested cases (David, 2018).
• Rainfall retrieval with TabGRU achieved RMSE as low as $0.25$ mm/h, $R^2$ up to $0.96$, with substantial error reduction over pure power-law inversion, especially during peak events (Li et al., 2 Dec 2025).
• Two-dimensional humidity fields reconstructed using hundreds of links achieved gauge correlations $0.60$–$0.92$ and RMSD $1.9$–$4.15$ g/m$^3$ (David et al., 2018).
• In 3D-Var nowcasting, the assimilation of link data with radars and gauges improved short-term rainfall mapping, providing useful forecasts up to 20 minutes for stratiform and 15 minutes for convective scenarios (Bianchi et al., 2018).

6. Practical Applications, Integration, and Limitations

CML-based environmental monitoring is operationally attractive due to negligible incremental infrastructure cost and broad areal coverage, with natural sensitivity to near-surface atmospheric variability where traditional sensors perform poorly. It provides valuable early warnings for fog in transportation safety contexts, enhances high-resolution rainfall monitoring for smart cities, and critically supplements data assimilation systems for numerical weather prediction.

However, performance and sensitivity are constrained by link geometry (longer links improve signal-to-noise but increase gas uncertainty), network coverage (restricted to regions with CML infrastructure, often urban-biased), RSL logging practices, and calibration stability. Wet antenna effects, atmospheric refractive anomalies, and source separation (e.g., rain vs. fog) require rigorous statistical treatment or hybrid modeling for reliable operation (David, 2018, David et al., 2018, Li et al., 2 Dec 2025).

7. Prospects and Ongoing Challenges

Areal and temporal resolution of CML-based meteorological products can be further improved with greater provider collaboration (high-frequency logging, open access), advanced signal processing, and integrative use with traditional and satellite-based observations. Open research directions include generalization of hybrid retrieval models across diverse climates, better discrimination of microphysical regimes (drizzle vs. heavy rain), and dedicated WAA/dew classifiers.

Commercial microwave links have proven effective as opportunistic, high-density atmospheric sensor networks, capable of augmenting and often surpassing dedicated instrumentation under operational and economic constraints (David, 2018, Li et al., 2 Dec 2025, David et al., 2018, Bianchi et al., 2018).