Reconstruction of 3D DPR Observations Using GMI Radiances

Three‐dimensional global precipitation observation is crucial for understanding climate and weather dynamics. While spaceborne precipitation radars provide precise but limited observations, passive microwave imagers are available much more frequently. In this study, we propose a deep learning approach to reconstruct active radar observations using passive microwave radiances. We introduce the Hybrid Deep Neural Network (HDNN) model, which utilizes reflectivity profiles from the Dual‐frequency Precipitation Radar (DPR) onboard the Global Precipitation Measurement (GPM) Core Observatory Satellite as the “target” and combines radiances from the GPM Microwave Imager (GMI) with supplementary reanalysis data to serve as the “features.” Results underscore the HDNN's exemplary performance, with a root mean square error below 4 dBZ across all altitude levels, and a consistent accuracy across different precipitation types. Its efficacy is further illustrated when applied to typhoon cases of Haishen and Khanun, emerging as a superior tool for capturing 3D structures of expansive precipitation systems.


Introduction
Precipitation, a key component of the Earth's hydrological cycle, plays a critical role in maintaining the global climate system (Kidd & Huffman, 2011).An accurate and comprehensive observation of precipitation systems, particularly their three-dimensional (3D) structures, is vital.It aids in understanding the microphysical processes and dynamics within these systems.Such understanding is essential for enhancing numerical weather prediction (NWP) models and for assessing the impact of climate change on both regional and global precipitation patterns.
The Global Precipitation Measurement (GPM) mission, a joint initiative between NASA and the Japan Aerospace Exploration Agency, primarily aims to deliver accurate global precipitation measurements, thereby enhancing our comprehension of Earth's water cycle and weather patterns (Draper et al., 2015).Central to this mission is the GPM Core Observatory satellite equipped with two pivotal instruments: the GPM Microwave Imager (GMI) and the Dual-frequency Precipitation Radar (DPR).The GMI's 13 distinct frequency channels can capture both vertically and horizontally polarized radiances within the range of 10.6-183 GHz.Each of these channels is sensitive to different physical properties of hydrometeors, encompassing particle size, phase (either liquid or frozen), and concentration.For instance, the lower frequency channels are more sensitive to large raindrops and can penetrate deeper into the cloud, providing information about the lower levels of precipitation systems.Conversely, higher frequency channels are particularly sensitive to ice particles found in the upper cloud layers, subjected to scattering properties of larger ice aggregates and graupel.The synergistic use of these 13 channels significantly enhances the robustness and accuracy of retrieval algorithms.Methods like the Goddard profiling algorithm (GPROF) (Kummerow et al., 2001(Kummerow et al., , 2015) ) leverage such a diversity of channel sensitivities to produce more reliable hydrometeor vertical profiles.Collectively, GMI's channels constitute a robust toolkit for delineating the vertical structure of precipitation around the globe.In contrast, the DPR, a precipitation radar, operates on two frequencies (Ku-band and Ka-band), delivering high-resolution 3D depictions of precipitation structures, including the vertical distribution and particle size distribution of precipitation particles (Hou et al., 2014).Nevertheless, the limited scope of observation, namely a swath width of 245 km, constrains its capability to capture the entire intricate internal structure of large, intense precipitation systems like typhoons.Here, the GMI, with a broader observational scope (approximately 885 km in scanning swath width), is regarded with a distinct advantage in providing a comprehensive view of such expansive precipitation systems.Furthermore, while DPR stands out as the solitary scanning precipitation radar presently in space, numerous passive microwave imagers similar to GMI are orbiting Earth on various satellites and platforms, such as SSM/I on the DMSP satellite series and MWRI on the Fengyun satellite series.Consequently, at a given point of the globe, passive microwave observations are available much more frequently than spaceborne radar measurements (Guilloteau et al., 2018).
Essentially, GMI provides a comprehensive spectrum of data across the entire precipitation column, encompassing details from surface levels to elevated cloud altitudes.This information has the potential to reconstruct the vertical radar reflectivity observed by DPR.Therefore, given the distinct sensitivities and capabilities of GMI's 13 channels and the high-resolution three-dimensional observations of DPR, there appears to be a promising mapping function between the two.However, constructing such a mapping involves a deep understanding of the macrophysical and microphysical processes within cloud and precipitation systems.Fortunately, deep learning techniques have demonstrated unprecedented prowess in handling complex, high-dimensional data sets and capturing the underlying relationships between input and output variables in recent years, even when these relationships are nonlinear and multifaceted.Within the scope of three-dimensional cloud retrievals, deep learning has proven invaluable in reconstructing cloud structures observed by cloud radar using satellite imagery data.For instance, Haynes et al. (2022) utilized machine learning methods to detect low clouds in multilayer scenes using satellite imagery, showcasing the potential of these techniques in complex atmospheric conditions.Similarly, F. Wang, Liu, et al. (2023) made strides in retrieving vertical cloud radar reflectivity from MODIS cloud products using a conditional generative adversarial network, demonstrating the capabilities of deep learning in detailed cloud characterization.Moreover, Y. Wang, Gong, et al. (2023) moved toward physics-informed neural networks for 3D multi-layer cloud mask reconstruction, indicating a growing trend of integrating physical principles into deep learning models for enhanced accuracy and interpretability.Yet, it's noteworthy that the scattering from precipitation might not be completely represented by the 13 GMI channels (Turk et al., 2018).The DPR, on the other hand, can capture intricate patterns of scattering properties, presenting a superior depiction of diverse precipitation phases.By leveraging feature enhancement techniques within deep learning, models can better interpret and learn associated patterns, especially when supplemented with auxiliary features (Bengio et al., 2013).In bridging GMI and DPR observations, incorporating ancillary data, such as temperature profiles or other atmospheric parameters, can further refine the accuracy of reconstructions and provide a richer context for the deep learning model.
To the best of our knowledge, there is currently limited research on the reconstruction of precipitation radar observations using passive microwave radiances.Our study aims to contribute to this area by exploring the application of deep learning to reconstruct reflectivity measured by Ku-band of DPR using GMI radiances.This novel deep learning model holds potential practical value in situations where DPR observations are unavailable or compromised due to instrument limitations.Ultimately, our goal is to offer a richer, three-dimensional visualization of precipitation systems by employing GMI for DPR-like reflectivity reconstruction.

Data Collection and Processing
Figure 1a shows the GPM scan pattern.KuPR, which features a nadir-looking cross-track scanning capability, employs 49 scan beams.These beams, with incidence angles falling within the ±17°range, allow for a scan swath width spanning 245 km.Operating at the Ku-band frequency, KuPR is pivotal in delivering detailed precipitation observations.The footprint size of KuPR is maintained at approximately 5 km due to the Nyquist scan design.
Conversely, GMI functions as a conical-scanning passive microwave (PMW) imager.It operates with a fixed scan angle set at 48.5°.The GMI has an effective footprint size of 4.4 km × 7.2 km.Each GMI scan yields 221 footprints, spanning a swath width of 885 km.Notably, this swath is approximately four times wider than that of the KuPR scan.
A deep learning model was constructed to establish a mapping function between KuPR's vertical profile of reflectivity (VPR) and GMI's 13-channel brightness temperature, with the ultimate goal of reconstructing KuPR's VPR spanning the GMI's swath.The input data comprised calibrated and coregistered brightness temperatures (Tc) from both GMI's low-frequency channels (10.65∼89.0GHz) and high-frequency channels (166 and 183 GHz) from GMI Level-1CR (Version 07, Berg, 2022).Additionally, hourly temperature profiles (T) from the ERA5 reanalysis data (Hersbach et al., 2023) were incorporated as auxiliary input to provide critical insights into the atmosphere's vertical structure, such as the height of the melting layer.For output, VPR with attenuation correction is provided in the standard level 2 KuPR data files (version 07, Iguchi & Meneghini, 2021).The data sets from August to September 2022 were chosen for model training and testing due to this period marking the peak of intense convective systems in the Northern Hemisphere, 80% of the data is used as a training set and the remaining 20% is used as a test set.
Figure 1b illustrates the preprocessing steps applied to data sets for model training and testing.Initially, polarization differences (PD) were computed using five pairs of vertically and horizontally polarized channels from the GMI at frequencies of 10.65, 18.7, 36.5, 89, and 166.5 GHz.PD is derived from the difference between the brightness temperatures of vertically and horizontally polarized channels (PD = Tc V -Tc H ), provides insights into scattering properties of precipitation particles (Geer et al., 2021).While both vertically and horizontally polarized temperatures capture useful information, PD emphasizes asymmetries in the scattering mechanisms which are particularly pronounced in mixed-phase and ice regions of precipitation systems.It effectively enhances the model's sensitivity to varied precipitation structures and phases, providing a more nuanced input feature than using the polarized temperatures independently.It also improves the training efficiency of the model by leveraging handcrafted features that are directly relevant to precipitation characterization.
Subsequently, the reflectivity profiles from KuPR were filtered based on three variables provided by the standard level 2 KuPR data files: 1. Precipitation flag, signifying the presence or absence of precipitation (HDF5 data set named as/FS/PRE/ flagPrecip, 0 and 1 for no precipitation and precipitation, respectively).2. Surface type, identifying if the observed area is an oceanic region (HDF5 data set named as/FS/PRE/land-SurfaceType, values of 0-99 for ocean).3. Storm Top height, to ensure the storm extends to significant altitudes (HDF5 data set named as/FS/PRE/ heightStormTop, no less than 8 km).
This selection ensured that the final VPR data, originating from intense oceanic storms, extended from the Earth's surface to altitudes up to 8 km.
After the above processing, we matched the GMI data with the filtered KuPR observations, prioritizing spatial proximity and a scan time discrepancy of no more than 80 s between the paired footprints.Meanwhile, centered on the matched GMI footprint, patch extraction was performed to capture localized spatial features in the brightness temperature fields, allowing the model to effectively learn spatial patterns and correlations at different scales (Malmgren-Hansen et al., 2019).As an effort to understand how different extents of spatial information might impact the model's training, patches of varied sizes-1 × 1, 3 × 3, 9 × 9, and 15 × 15-were tested.A significant aspect to bear in mind is the disparity in view angles between the GMI and KuPR.The viewing volume from the conical-scanning microwave imager (GMI) differs from that of the cross-track scanner (KuPR) due to its intrinsic design (Figure 1a).Even when we match the closest points between GMI and KuPR, there are subtle spatial and angular discrepancies.These discrepancies mean that the matched observations from the two instruments might correspond to different atmospheric conditions.As the patch size increases, the GMI observation area potentially covers the KuPR viewing volume.This expanded coverage can reduce the mismatch errors due to discrepancies in GMI and KuPR viewing volumes.Consequently, a larger patch size might enhance the model's accuracy in learning and reconstructing KuPR's VPR by providing a more comprehensive spatial context and mitigating some of the challenges posed by the misalignment.Finally, the temperature profiles closest in time were interpolated to the spatial coordinates of the GMI-KuPR data pair using bilinear interpolation techniques.
Before training, the data underwent Min-Max Normalization to enhance the model's performance, ensure robust generalization, and prevent training instabilities (Ioffe & Szegedy, 2015).This method scales data to a specified range, commonly between 0 and 1, ensuring a uniform dynamic range across all data.
Following the preprocessing steps, we extracted Tc patches spanning 13 channels and PD patches covering five channel pairs, all available in three distinct sizes.These patches were paired with reflectivity profiles and temperature profiles.To reduce information redundancy and improve computational efficiency, the eight vertical polarization channels of Tc patches, the five PD patches, and the temperature profile are used as the input features for the model.

Deep Learning Models
To manage the diverse nature of our input data, comprising both brightness temperature patches and temperature profiles, we employed a Hybrid Deep Neural Network (HDNN, Yuan et al., 2020).This sophisticated model seamlessly integrates different neural network architectures, specifically tailored to our data set.As shown in Figure 1c, HDNN consists of a Convolutional Neural Network (CNN) module and a Multi-Layer Perceptron (MLP) module.The CNN module is employed for its proficiency in spatial analysis, utilizing convolutional layers (Conv) to extract spatial information from brightness temperatures, while the MLP module leverages its fully connected layers (FC) to efficiently process the sequential nature of temperature profiles, adept at extracting their structural features.
In this research, we orchestrated a series of experiments to contrast and assess the reconstructive performance of three distinct models -HDNN, CNN, and an MLP model based on the same test samples.We utilized an MLP model as a benchmark for a quantitative assessment of the HDNN network's prowess.Concurrently, the CNN model was employed to evaluate the enhancement brought about by temperature profiles in the model's reconstruction capability.To further investigate the impact of spatial information on model performance, we conducted a comprehensive analysis of different patch sizes.In addition to the 1 × 1 pixel-based MLP model, we tested larger patches with dimensions of 3 × 3, 9 × 9, and 15 × 15 for both CNN and HDNN models.
Here, the architecture of the CNN model is identical to that of the CNN module in HDNN.The full architectures of MLP and CNN modules used in the study can be found in Table S1

Performance Evaluation of HDNN Models
In Moreover, an analysis was conducted to evaluate the influence of different brightness temperature patch sizes on the reconstruction.For the CNN model, an exploration of different brightness temperature patch sizes showed some notable outcomes.While patch sizes of 9 × 9 and 15 × 15 yielded very similar results, reducing the patch size to 3 × 3 led to an increase in model errors, particularly near the freezing height.However, this increase was relatively modest, especially when compared with the MBE, suggesting that the 3 × 3 patches still maintain a competitive performance in certain aspects.Within the HDNN framework, variations in patch size had relatively minor impacts on the results.The 15 × 15 patch size was found to slightly enhance model accuracy and stability, with both RMSE and STD falling below 4 dBZ across all altitudes.An intriguing observation from the error profiles is the altitude-dependent variability in errors.The near-surface and melting layers exhibit larger discrepancies, whereas higher altitudes tend to present reduced errors.One of the challenges when using the microwave channels' brightness temperatures to reconstruct VPR lies in the melting layer.At this specific altitude, large errors are inherent due to the complex phase changes and scattering properties of melting particles.However, HDNN models show a measurable advantage over CNN models, particularly near the melting layer's altitude.These improvements in the accuracy of HDNN can be attributed to its adept utilization of the vertical temperature gradient information, underscoring the significance of integrating nuanced atmospheric data into the reconstruction process.
Based on the comparative results, we opted for the HDNN architecture with a patch size of 15 × 15 for a more comprehensive error analysis.However, it's important to acknowledge the practical limitations associated with this choice.The larger patch size necessitates increased computational resources for training and great data space for storing, presenting challenges in terms of efficiency and scalability.Figure 3 illustrates the reconstruction errors of VPR for various precipitation types using the selected HDNN compared with the MLP model.The results indicate a pronounced discrepancy in the MLP model's reconstruction capabilities across different precipitation regimes, with convective precipitation echoes exhibiting notably higher errors compared to stratiform precipitation.In contrast, the HDNN model displayed a more consistent performance across precipitation types, with a substantial reduction in reconstruction errors relative to the MLP model.The hybrid structure of HDNN, which combines the strengths of both deep neural networks and convolutional layers, enables it to capture both local spatial features and global dependencies in the data.This holistic approach to feature extraction might offer the HDNN model an advantage in understanding and reconstructing diverse precipitation patterns.On the other hand, the MLP, being a feed-forward network, might not be as adept at capturing spatial hierarchies and dependencies present in precipitation structures, leading to its varied performance across different precipitation regimes.

Application of HDNN in Typhoon VPR Reconstruction
In this section, we deployed the refined HDNN model to reconstruct the VPR for two distinct typhoon cases, Typhoon Haishen and Typhoon Khanun, to evaluate their performance in complex meteorological scenarios.In Figure 4, we present the results using two formats: within the DPR swath, where HDNN reconstructions are matched with KuPR observations for a side-by-side comparison, and within the GMI swath, showcasing reconstructions derived from the comprehensive GMI observations.
The GPM Core Observatory satellite flew over Haishen at 09:21 UTC on 5 September 2020.At this time, KuPR data displayed Typhoon Haishen approaching its peak intensity, with a clear, symmetrical eye visible (Figure 4a).In Figure 4d, the 3D reflectivity profile demonstrates a decrease in reflectivity values with altitude.The observed low reflectivity at higher altitudes is generally indicative of frozen precipitation forms, such as snow, graupel, and Impressively, the model replicated the reflectivity of the typhoons with remarkable accuracy.For instance, the distinct features associated with Typhoon Haishen's eyewall, as observed through the KuPR, were well reproduced in the model's output (Figure 4b).Similarly, the descending gradient of reflectivity against altitude and the subsequent dominance of frozen precipitation forms were also accurately captured (Figure 4e).The MBE and RMSE for these reconstructed profiles stand at 0.35 dBZ and 3.90 dBZ, respectively.When considering Typhoon Khanun, the model's prowess continued to impress.The intense reflectivity values observed toward the south and east of the typhoon's center were effectively reconstructed (Figure 4h).The model also skillfully delineated the rainbands that spiraled around Khanun (Figure 4h).Notably, the vertical structures were also well captured (Figure 4k), reflecting an MBE and RMSE of approximately 0.33 dBZ and 3.58 dBZ respectively.
When reconstructing the reflectivity factor across the entire GMI swath, we gain a more comprehensive view of the typhoon's structure.For instance, the well-formed rainbands accompanied by intense reflectivity in the east of Typhoon Haishen's eyewall have been well reconstructed (Figure 4c), a feature not evident in the KuPR observations.Similarly, the outer rainband on the eastern side of Typhoon Khanun has been fully captured in the reconstruction (Figure 4i).This demonstrates the model's ability to leverage GMI data to depict detailed structures, even those that might be missing or less pronounced in KuPR measurements.
However, it's essential to highlight that the model was primarily trained using VPR of precipitation clouds that extend up to and beyond 8 km.Consequently, the reconstruction of such precipitation profiles is logical and justified.Yet, within the entirety of the typhoon's cloud system, there exist various scenarios of precipitation intensities and diverse cloud types, not all of which reach 8 km.In such scenarios, the model's reconstructed profiles might not be entirely accurate, leading to potential discrepancies.As illustrated in the figures, there are instances where artificial or spurious reflectivity is observed at certain heights, which can be attributed to the model's limitations in handling cloud types and precipitation intensities beyond its primary training data set.In addition, compared to direct observations, the model's reconstruction results appear relatively smoother.For instance, the high values in the eyewall are somewhat underestimated, and the adjacent moat region's low values are overestimated.This disparity might be attributed to the GMI's lower horizontal resolution compared to the KuPR.The inherent differences in instrument resolutions can lead to variations in capturing detailed structures and gradients, especially in complex regions such as the eyewall and rainbands of a typhoon.

Discussion
This research represents a preliminary attempt to reconstruct active microwave precipitation radar signals from passive microwave radiation.The results above demonstrate its feasibility, but there's still much space for improvements and refinements.In this section, we will outline the areas that can be enhanced and further perfected in our study.
A primary enhancement for future work involves not just integrating more diverse ancillary data but also exploring advanced deep learning algorithms to better capture the unique characteristics in VPR.Employing convolutional and recurrent neural networks or attention mechanisms, alongside integrating interpolated prognostic variables from NWP models, can impose additional constraints and improve the model's reconstruction power.Additionally, observations under a wider range of precipitation conditions should be incorporated into the training data set.By diversifying the precipitation scenarios covered, the model can be better equipped to handle varying precipitation structures and intensities.However, this comes with the trade-off of necessitating more intricate network parameters, incurring a significantly higher computational cost.It is crucial to highlight potential challenges associated with terrestrial applications.The inherent high emissivity of land surfaces poses a challenge in discerning precipitation information from low-frequency channel radiance.Furthermore, the differences in observational geometry and resolution between GMI and DPR introduce hard-toestimate errors to the model.Implementing correction and remapping methods may help minimize these discrepancies, subsequently reducing errors.However, such interventions might introduce other types of errors.

Conclusions
In this research, we utilized eight vertically polarized channels TB patches from GMI and the PD patches calculated from five channel pairs as inputs to the CNN module of HDNN.Besides, auxiliary data in the form of the ERA5 temperature profile was fed into the MLP module.Our target output was the VPR of KuPR.This design culminated in an HDNN deep learning model capable of reconstructing KuPR reflectivity profiles based on GMI radiances.The diverse CNN module frameworks were constructed based on varying patch sizes and executed a series of experiments to compare and evaluate the performance of HDNN, CNN, and an MLP model.For model training and testing, we selected 149,995 samples from August to September 2022, allocating 80% for training and 20% for testing.
In terms of performance assessment, both HDNN and CNN models outperformed the MLP model.Hybrid Deep Neural Network models, when contrasted with the CNN models, showcased superior capabilities owing to the added insights from the temperature profile-especially evident in its reconstruction of reflectivity near the melting layer.Our evaluations revealed an optimal performance from the model with a patch size of 15 × 15, as opposed to the 3 × 3 and 9 × 9 sizes, with both RMSE and STD below 4 dBZ across all altitudes.Impressively, the HDNN consistently showed robust performance across diverse precipitation scenarios.
In practical applications of the typhoons Haishen and Khanun, the model yielded encouraging outcomes.The unique characteristics of the typhoons, as identified through KuPR observations, were adeptly mirrored in the model's outputs.Beyond this, the model enabled a comprehensive three-dimensional representation of the typhoon within the GMI swath.

Figure 2 .
Figure 2. Mean Bias Error (top), Standard Deviation (middle), and Root Mean Square Error (bottom) error profiles for reflectivity reconstruction by Hybrid Deep Neural Network (left), Convolutional Neural Network (middle) and their differences (CNN-HDNN, right) at different input spatial patch sizes compared with Multi-Layer Perceptron model.The blue dashed line indicates the average height of the melting layer.

Figure 3 .
Figure 3. Mean Bias Error, Standard Deviation, and Root Mean Square Error error profiles for reflectivity reconstruction of different precipitation types by Hybrid Deep Neural Network (solid line) and Multi-Layer Perceptron model (dashed line).The blue dashed line indicates the average height of the melting layer.

Figure 4 .
Figure 4. Horizontal two-dimensional reflectivity structures at the eighth vertical layer (approximately 0.86 km above ground level) of Typhoon Haishen (09:21 UTC on 5 September 2020) and Typhoon Khanun (21:41 UTC 31 July 2023) (a-c; g-i) and their three-dimensional reflectivity structures (d-f; j-l).Observations from KuPR (Obs) are presented in the left column, Hybrid Deep Neural Network (HDNN) reconstructions within the Dual-frequency Precipitation Radar swath are displayed in the middle column, and HDNN reconstructions within the GPM Microwave Imager swath are shown in the right column.
Kingma & Ba, 2017)rmation S1.For the MLP model, only Tc and PD are prepared as inputs.During model training, the same optimizer (Adam,Kingma & Ba, 2017)and loss function (Mean Squared Error, MSE) are adopted to perform deep-learning optimization.All detailed descriptions and explanations of the models' construction in this study are provided in the supporting information.