In recent years, extreme weather events have become more frequent and variable, and the vertical thermodynamic structure of the planetary boundary layer (PBL) plays a central role in their formation and evolution. The development of low-altitude aviation increases the demand for reliable boundary-layer observations, which motivates more efficient and accurate measurement techniques and targeted mechanistic studies. Microwave remote sensing operates in the presence of clouds and precipitation and supports long-term continuous unattended monitoring, which provides clear advantages for all-sky applications. In the microwave region, gaseous absorption is primarily controlled by temperature, pressure, and water-vapor density. Under cloudy or precipitating conditions, hydrometeors, including cloud water, rain, ice, snow, and graupel, additionally contribute to the total extinction through absorption and scattering, thereby modifying the microwave opacity and the observed brightness temperatures. Although satellite-based microwave radiometers provide extensive coverage of the atmosphere, they cannot reliably retrieve PBL temperature and humidity over land because land-surface microwave emissivity is highly variable and introduces significant uncertainty in the measured radiances (Martinet et al., 2020). This limitation causes an observation gap between the surface and the upper troposphere (National Research Council, 2009), which is precisely the critical region where energy and water-vapor exchanges occur between the land surface and the free atmosphere (Wu et al., 2024).

Ground-based microwave radiometers (GMRs), operating in an upward-looking configuration, provide continuous retrievals of temperature and humidity profiles under all-sky conditions, with high temporal resolution and moderate vertical resolution that decreases with height within the PBL (Cimini et al., 2006; Wei et al., 2024). GMRs can capture rapid boundary-layer variability, and contribute to understanding PBL dynamical processes while helping to bridge the observation gap between the surface and the upper troposphere (De Angelis et al., 2017). Compared with radiosondes, GMRs can offer high-frequency, continuous observations that are not affected by wind advection and therefore show stronger local representativeness, which enables long-duration all-weather monitoring within the PBL (Madhulatha et al., 2013). Under clear-sky conditions, the atmosphere is nearly transparent in the window channels; absorption in the K-band is dominated by water vapor, whereas the V-band is primarily controlled by oxygen absorption. With cloud and precipitation, optical thickness increases rapidly because cloud water, rain, ice, snow, and graupel contribute additional absorption and scattering. All-sky microwave observations are therefore both valuable and challenging, motivating the development of a fast, accurate all-sky radiative-transfer operator for GMRs.

Radiative transfer models (RTMs) provide the essential link between atmospheric state variables and observed radiances, and fast RTMs are indispensable for variational assimilation in modern numerical weather prediction (NWP) systems (Hu and Han, 2021; Weng and Liu, 2003; Yang et al., 2020). Early applications were limited to clear-sky oceanic conditions due to the difficulty of simulating cloud and precipitation microphysics, as well as surface emissivity. With subsequent advances, mainstream fast RTMs such as CRTM (Weng et al., 2005), RTTOV (Saunders et al., 1999), and ARMS (Weng et al., 2020; Yang et al., 2020) have been extended to all-sky capabilities, which has enabled the operational assimilation of cloud-affected satellite radiances (Bauer et al., 2010; Geer et al., 2017). Despite being less affected by surface emissivity and capable of providing continuous, high temporal resolution boundary-layer observations, the assimilation of GMR observations has lagged behind satellite applications, owing to the lack of suitable forward models and effective methods for handling water vapor and hydrometeors. High-accuracy monochromatic tools (e.g., MonoRTM; Clough et al., 2005), together with absorption models such as MPM (Rosenkranz, 1998), are widely used as references, but they are computationally too expensive for routine, instrument-level broadband simulations at the temporal resolution required by GMR retrieval and data-assimilation applications. When each broadband channel is approximated by a single monochromatic calculation at the channel centre frequency, systematic brightness-temperature biases of a few kelvin (∼2–3 K) have been reported (Yang and Min, 2015). To our knowledge, only two dedicated fast radiative transfer models for ground-based microwave radiometers are currently available, RTTOV-gb in Europe (Cimini et al., 2019) and ARMS-gb in China (Shi et al., 2025). RTTOV-gb was a significant development; however, recent studies report substantial biases in water-vapor channels (Cao et al., 2023) and the lack of an operational cloud-scattering option, leaving many cloud-affected GMR observations unused. ARMS-gb v1.0 is a fast radiative transfer model for GMRs that incorporates a line-by-line trained gaseous absorption scheme and an advanced water-vapor vertical interpolation with tangent-linear and adjoint modules for Jacobian evaluation. Validation against benchmark simulations and real observations demonstrated that the performance of ARMS-gb v1.0 is comparable to or better than RTTOV-gb in humid environments and is useful for observation-minus-background (O–B) monitoring. Despite these advances, ARMS-gb v1.0 remains a clear-sky model, and RTTOV-gb accounts only for absorption by cloud liquid water, precluding direct all-sky assimilation of GMR radiances. Additionally, variational systems rely on a forward-model operator with its associated Jacobians, while the observation-error covariance accounts for radiometric noise, representativeness, and forward-model uncertainties. Therefore, a fast and accurate all-sky RTM with tangent-linear and adjoint capabilities is essential. Here, we describe several new aspects of ARMS-gb v2.0, which incorporates hydrometeor scattering and absorption modules together with a numerically stable multiple-scattering solver, and provides forward, tangent-linear, and adjoint modules under all-sky conditions to support the direct assimilation of GMR observations.

This paper is organized as follows. Section 2 describes the two main developments in ARMS-gb v2.0: the computation of hydrometeor optical properties and a multiple-scattering solver. Section 3 explores sensitivity to hydrometeor water content and particle size across the water-vapor and oxygen microwave absorption bands. Section 4 evaluates all-sky simulations with the updated RTM against six months of field measurements from ground-based observations collected in China for a 14-channel and a 22-channel GMR, and examines error characteristics and sources for retrieval and data assimilation. Section 5 concludes with a summary and perspectives.

The primary advancement in ARMS-gb v2.0 is the extension from clear-sky to all-sky applications while retaining the gaseous absorption parameterization, clear-sky solver, and vertical interpolation scheme of v1.0 for continuity. In the microwave regime, we solve a scalar radiative transfer equation for brightness temperatures, and atmospheric attenuation is determined by temperature, pressure, water-vapor density, and hydrometeor microphysical properties, so hydrometeors can significantly perturb the radiance field even when gas absorption is well captured. Figure 1 compares the time series of observed and simulated clear-sky brightness temperatures measured by YKW-1, a 22-channel GMR, at Yan'an Station (36.34° N, 109.27° E). For context, the corresponding liquid and solid hydrometeor profiles from the fifth-generation ECMWF atmospheric reanalysis (ERA5, Hersbach et al., 2020) are also shown. The forward simulations simply consider gaseous absorption and do not include any cloud or precipitation scattering information. The simulations accurately track observations during cloud-free periods, whereas departures grow in water-vapor and weak-oxygen channels when hydrometeors are present, which motivates a consistent representation of their combined effects. To address this, ARMS-gb was updated with two new modules. The first is a cloud optics module that calculates the bulk scattering properties of cloud particles. These properties are derived by integrating the single-particle attributes of various hydrometeors (cloud water, rain, ice, snow, and graupel) over the particle size distribution, utilizing a precomputed look-up table (LUT). The second is an all-sky radiative transfer solver that accounts for multiple scattering and emission, applies appropriate lower boundary conditions, and enables physically consistent simulations under all-sky conditions.

In this section, ARMS-gb v2.0 is evaluated against collocated GMR brightness-temperature observations. Clear-sky simulations provide channel-dependent O–B baselines, while the primary evaluation of the all-sky capability focuses on cloudy non-precipitating scenes. Precipitation cases are examined separately to characterize rain-contaminated O–B departures and are not treated as strict validation of the radiative transfer model.

Figure 6 compares the mean O–B departures for each channel at Yan'an and Karamay during April–June 2025. The cloudy-scene comparison includes ARMS-gb v1.0, ARMS-gb v2.0 with Mie- and DDA-based scattering treatments, and RTTOV-gb. To assess whether the persistent clear-sky baseline departures arose primarily from the ARMS-gb clear-sky radiative-transfer calculation, MonoRTM was used as a high-accuracy clear-sky radiative-transfer reference. The MonoRTM simulations used the same ERA5 profiles and GMR channel settings as ARMS-gb. Each channel was represented by 256 monochromatic calculations across its nominal bandwidth, and the resulting radiances were averaged to obtain channel-equivalent brightness temperatures. Following the selection of cloudy non-precipitating scenes and the removal of invalid records, 1012 hourly profiles per channel and model were retained for Yan'an and 1014 for Karamay. The clear-sky statistics used 402 valid profiles at Yan'an and 420 at Karamay. The ARMS-gb and MonoRTM baselines exhibit similar channel-dependent structures, with maximum differences of approximately 0.38 K at Yan'an and 0.30 K at Karamay. This agreement indicates that the ARMS-gb clear-sky radiative-transfer calculation is unlikely to be the dominant source of the persistent baseline departures. The residual departures may also reflect uncertainties in instrument calibration, channel characterization, collocation, and ERA5 background profiles.

The difference between the cloudy-sky mean O–B and the corresponding clear-sky baseline provides an additional diagnostic of hydrometeor treatment. In the water-vapor and weak oxygen absorption bands, both ARMS-gb v2.0 configurations produce cloudy-sky departures closer to the clear-sky baseline than ARMS-gb v1.0. For YKW-1, the clear-sky baseline has local maxima of approximately 5 K near channels 5 and 10. Relative to this baseline, ARMS-gb v1.0 produces an additional departure of approximately 3.6 K at channel 5 and 1.8–2.8 K across channels 6–12. Both ARMS-gb v2.0 configurations substantially reduce these differences, generally keeping them within approximately ±1 K, although the residual at channel 5 reaches 1.3–1.5 K. For YKW-2, the clear-sky baseline ranges from approximately 0.3 to 0.8 K in channels 1–6, increases to approximately 3 K at channel 7, and decreases at higher frequencies. ARMS-gb v1.0 produces additional departures of approximately 1.5–1.8 K in channels 1–6 and more than 2 K at channels 8 and 9, whereas ARMS-gb v2.0 reduces them to within approximately ±0.7 K. RTTOV-gb also improves upon ARMS-gb v1.0 in many hydrometeor-sensitive channels but generally remains farther from the clear-sky baseline than ARMS-gb v2.0. The Mie- and DDA-based results are broadly similar, with maximum differences of approximately 0.33 K at Yan'an and 0.17 K at Karamay. In the weak oxygen absorption channels, however, the DDA-based treatment generally produces O–B departures slightly closer to the corresponding clear-sky baselines than the Mie-based treatment. Differences between the two treatments diminish in the strongly absorbing oxygen channels, consistent with their weaker sensitivity to hydrometeors.

Given the high temporal resolution of GMR observations, the temporal variation of O–B provides a direct assessment of model performance under changing atmospheric conditions. Figure 7 shows the time series of O–B for ARMS-gb v2.0 at four representative YKW-1 channels at Yan'an from 10 March to 30 June 2025. Clear sky, cloudy, and precipitation periods are indicated by the scene classification bar above the panels. During most clear sky and cloudy periods, O–B remains close to zero. Compared with Fig. 1, where neglecting hydrometeor absorption and scattering leads to pronounced departures in the water vapor and weak oxygen absorption channels during cloudy periods, Fig. 7 shows that including the absorption and scattering effects of cloud particles in ARMS-gb v2.0 improves the simulation of brightness temperatures under cloudy conditions. Larger positive departures occur mainly during precipitation, particularly at 22.234 and 26.234 GHz, indicating underestimation of the largest brightness temperature enhancements. These departures may reflect both uncertainties in atmospheric hydrometeors and measurement effects near the instrument and should not be attributed solely to errors in the radiative transfer model. Departures are generally smaller at 52.804 GHz and especially at 53.848 GHz, consistent with the weaker sensitivity of the more strongly absorbing oxygen channels to water vapor and hydrometeors.

Model performance at Yan'an was evaluated against YKW-1 observations collected during January–June 2025. The analysis included 2135 quality-controlled hourly cases classified as cloudy and non-precipitating. Figure 8 presents scatterplots of observed versus simulated brightness temperatures with fitted regression lines and reports the coefficient of determination (R2), root mean square error (RMSE), and median O–B. Probability density functions (PDFs) above each panel show the corresponding distributions of observed and simulated brightness temperatures. To assess the robustness of the improvement in correlation, we excluded the few data points with very high brightness temperatures from the analysis. ARMS-gb v2.0 produced the highest R2 values at the selected channels in the water vapor and weak oxygen absorption bands. At 22.234 GHz, the R2 values were 0.95, 0.96, and 0.95 for ARMS-gb v1.0, ARMS-gb v2.0, and RTTOV-gb, respectively. RTTOV-gb showed intermediate agreement. At 30.000 GHz, where brightness temperatures were more strongly affected by hydrometeors, R2 increased from 0.55 for ARMS-gb v1.0 to 0.77 for ARMS-gb v2.0. A similarly pronounced improvement occurred at 51.248 GHz, where ARMS-gb v2.0 reduced the RMSE from 5.23 to 3.22 K and increased R2 from 0.52 to 0.81 relative to ARMS-gb v1.0. RTTOV-gb improved upon ARMS-gb v1.0 but remained less accurate than ARMS-gb v2.0. At the higher-frequency oxygen-band channels near 53–55 GHz, the simulations from all three models clustered closely around the 1:1 line, although ARMS-gb v2.0 generally produced the lowest RMSE and tightest scatter. Overall, ARMS-gb v2.0 achieved better agreement with the observed brightness temperatures than ARMS-gb v1.0 and RTTOV-gb, with the clearest improvements at 30.000 and 51.248 GHz.

The diurnal variation in the ARMS-gb v2.0 O–B departures was examined using cloudy non-precipitating cases from January–June 2025. Figure 9 presents the corresponding mean departures for each YKW-1 channel and local hour. Distinct diurnal patterns were evident in both the water-vapor and oxygen absorption bands. In the lower-frequency water-vapor channels (channels 1–7), the departures were weakly positive overnight and increased to approximately 1–3 K in the early morning. They then decreased to near-zero or slightly negative values around midday before increasing again in the late afternoon and evening. Diurnal amplitudes were larger in the oxygen absorption band, particularly for channels 9–12. These channels reached midday minima ranging from approximately -6 to -3 K and evening maxima of approximately 3–6 K, with a secondary positive peak in the early morning. By contrast, the higher-frequency oxygen-band channels (channels 15–22) remained close to zero and showed comparatively weak diurnal variability throughout the day. These patterns may reflect combined contributions from mismatches in the ERA5 representation of boundary-layer and cloud evolution, residual radiative-transfer errors, and temperature-dependent instrumental or calibration effects. Because O–B statistics alone cannot distinguish these contributions, the patterns should not be attributed to a single error source. Their systematic time dependence should nevertheless be considered when developing bias-correction schemes and specifying observation errors for all-sky retrieval and data assimilation.

Reliable use of ground-based microwave radiometer observations in numerical weather prediction and nowcasting requires quantitative characterization of their error properties under different weather conditions, particularly during precipitation. Figure 10 summarizes the mean O–B and RMSE for YKW-1 at Yan'an under clear-sky, cloudy non-precipitating, and precipitating conditions from January to June 2025. In the six-month statistics, clear-sky departures were comparatively small, with mean O–B generally close to zero and RMSE around 2 K. Cloudy non-precipitating conditions produced modestly larger departures, although RMSE remained below 3 K for most channels. During precipitation, however, RMSE exceeded 35 K across much of the water-vapor band and peaked above 40 K at channel 7, while mean O–B reached nearly 30 K. The precipitation-related departures were largest in the water-vapor and weak oxygen absorption channels and decreased toward the strongly absorbing oxygen channels. These large departures should not be interpreted solely as atmospheric radiative-transfer errors. The simulations represent atmospheric rainwater absorption and scattering, whereas wet-radome and other near-instrument effects remain in the observations and are neither corrected nor represented in ARMS-gb v2.0. The observed and simulated conditions are therefore not fully equivalent during precipitation. Additional uncertainty arises from the representation of rainwater profiles and raindrop size distributions. Water deposited on the radome can also alter its effective microwave transmission and emission, while raindrop impacts and evaporation near the instrument may introduce further perturbations. Because these atmospheric and instrument-related contributions cannot be separated using O–B statistics alone, the precipitation cases are used here to characterize the practical magnitude of rain-contaminated departures rather than to provide strict model validation. Precipitation-affected GMR observations should therefore be used in retrieval and data assimilation only after applying rain-specific quality control, wet-radome corrections, and appropriate observation-error characterization.

This study presents ARMS-gb v2.0, a fast all-sky radiative transfer model for ground-based microwave radiometers. The model extends the previous version by adding a hydrometeor absorption and scattering module and implementing the accelerated discrete ordinate method for multiple scattering. It also provides tangent-linear and adjoint capabilities for all-sky variational applications. It supports simulations of cloud water, rain, ice, snow, and graupel using optical-property LUTs computed with Mie theory for liquid hydrometeors and DDA for frozen hydrometeors. The sensitivity experiments showed that brightness-temperature responses depend strongly on channel frequency, hydrometeor water path, and particle effective radius. Liquid hydrometeors generally enhanced downwelling brightness temperatures through absorption and thermal emission, whereas frozen hydrometeors generally produced cooling through scattering in weak oxygen absorption channels.

To evaluate the performance of ARMS-gb v2.0 under cloudy non-precipitating conditions, we conducted six-month experiments using observations from the 22-channel YKW-1 at Yan'an and the 14-channel YKW-2 at Karamay. ARMS-gb and MonoRTM produced similar channel-dependent clear-sky O–B departures at both sites, providing reference baselines for the cloudy-sky evaluation. Compared with ARMS-gb v1.0, ARMS-gb v2.0 brought the cloudy-sky mean O–B closer to the corresponding clear-sky baseline, with the differences generally remaining within ±1 K. At Yan'an, R2 increased from 0.55 to 0.77 at 30 GHz and from 0.52 to 0.81 at 51 GHz, where RMSE decreased from 5.23 to 3.22 K. The Mie- and DDA-based configurations yielded broadly comparable results, with the DDA-based treatment showing a slight advantage in the weak oxygen absorption channels. During precipitation, GMR observations are affected by atmospheric rainwater, wet-radome effects, and other near-instrument processes, resulting in large and difficult-to-separate errors. Rain-affected observations should therefore not be used routinely in retrieval or data assimilation unless these errors are quantitatively characterized and explicitly accounted for.

Overall, the results show that ARMS-gb v2.0 provides an improved forward-model framework for simulating GMR brightness temperatures under cloudy non-precipitating conditions. Future work will extend instrument coverage, including higher-frequency systems, and improve the quantitative characterization of atmospheric and instrument-related uncertainties during precipitation. The model will also be integrated into one-dimensional variational retrieval and data-assimilation frameworks to support more reliable use of GMR observations for boundary-layer monitoring under cloudy and, ultimately, precipitation-affected conditions.