Low probability of intercept-based resource allocation algorithm for distributed phased array radar network

Three-dimensional mosaic method of dual-polarization parameters for a high-density radar network

In recent years, maritime radar networks have become essential for ensuring the safety and security of maritime operations. However, with the increased interconnectivity of these systems, they have also become vulnerable to cyber-attacks, posing significant risks to critical infrastructure. Traditional intrusion detection systems (IDS) often struggle to detect sophisticated and evolving attacks in real-time due to their reliance on manual feature extraction and shallow machine learning techniques. This research addresses this gap by introducing MARINERNet, a deep learning-based intrusion detection system designed specifically for maritime radar networks. The proposed system uses a novel architecture that integrates 1D convolutional layers, squeeze-and-excitation blocks, and residual connections to automatically extract relevant features from raw radar network data, enhancing detection accuracy without manual intervention. MARINERNet is evaluated on both binary and multiclass classification tasks, demonstrating state-of-the-art performance. Specifically, the model achieves 98.52% accuracy for multiclass classification and perfect accuracy for anomaly detection (binary classification). The approach is scalable, capable of handling large datasets, and adaptable to real-time intrusion detection, making it suitable for deployment in dynamic radar environments. This research not only provides an effective solution for detecting intrusions in maritime radar networks but also contributes to the broader field of cybersecurity by offering a robust, deep learning-based approach that can be applied to other network systems.

Abstract Airborne multi-frequency radars provide valuable information regarding the size, density, and shape of ice hydrometeors. Higher values of the dual-frequency reflectivity ratio (DFR), for instance, are often associated with the presence of larger ice crystals with potential implications for snowfall at the surface. The three-year Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) field campaign aimed to address the linkage between airborne remote sensing and in situ microphysics by collecting data obtained through the close coordination of a “satellite-simulating” ER-2 and “storm-penetrating” P-3 aircraft. In regions of prominently higher Ku- and Ka-band DFR along the P-3 flight track, the solid-phase mass-weighted mean diameter (D m ) was 66% larger, the liquid-equivalent normalized intercept parameter (N w ) 123% lower, the effective density (ρ e ) 73% smaller, and the ice water content (IWC) 46% higher for the 21 events studied. Use of a pre-existing neural network radar retrieval allowed for the vertical structure of microphysical properties to be compared to the larger DFR signatures, with similar conclusions valid for D m and N w at all altitudes studied. Analysis of the in-situ microphysics data and the radar retrieval complement the relationship between bulk microphysical properties and multi-frequency radar signatures that allow for microphysical processes such as aggregation and deposition to be inferred for different environments (e.g., at particular temperature ranges, or depths below cloud top).

Abstract Vertically pointing Doppler cloud radars have been operated for over a decade by research networks around the globe, providing important insights into cloud microphysical processes and dynamics. In contrast, national weather radar networks mainly provide data at low elevation angles to cover large areas and generally operate at longer wavelengths (typically at C- or S-band). Nonetheless, most polarimetric weather radars are also capable of collecting vertical profiling measurements, and such ‘birdbath’ scans are already used routinely for radar calibration. DWD’s birdbath scan, for example, is repeated every 5 min within the operational scanning cycle and records the standard radar moments and full Doppler spectra. Analysis methods developed for cloud radars can be readily applied to C-band birdbath data, opening another avenue to study precipitation processes. Despite the lower sensitivity and coarser time resolution of C-band birdbath scans, our comparison of vertical C-band and Ka-band radar observations of winter and summer precipitation events shows remarkable agreement for light to moderate precipitation. One important advantage of a C-band system is the much weaker attenuation due to heavy precipitation so that the entire vertical structure of severe weather systems, such as hailstorms, can be resolved. As birdbath scans are already performed in many weather radar networks, these birdbath data should be leveraged to complement sparse cloud radar observations. Using this ‘new’ data source, novel vertical cloud and precipitation products can be developed for validating model outputs and satellite observations, but also for operational warning products.

Abstract The fully digital Horus polarimetric phased array radar (PAR) represents a transformative leap for weather observation, offering unprecedented flexibility in scanning strategies, and enhanced data quality. Developed by members of the Advanced Radar Research Center (ARRC) at the University of Oklahoma, Horus leverages a fully digital S-band architecture to implement advanced scanning, including one- and two-dimensional beam spoiling and simultaneous transmission of multiple beams. These capabilities enable rapid-scan reconfiguration to capture evolving atmospheric conditions, optimizing trade-offs between spatial resolution, temporal resolution, and data quality. While spatial resolution is constrained by the physical antenna aperture, Horus achieves unprecedented improvements in temporal resolution and scanning agility compared to traditional radars. Operational since late 2022, Horus has demonstrated high-temporal-resolution observations of severe convective storms and efficient surveillance of stratiform precipitation, providing critical data for better understanding storm evolution. Its fully digital design supports flexible scanning strategies for high-fidelity measurements of impactful weather. In this article, we present Horus observations with these advanced scanning modes of a severe weather event in Oklahoma in 2024 where multiple tornadoes occurred. These observations showcase Horus’ ability to capture storm evolution with high temporal resolution across diverse beamforming configurations. The ability to seamlessly switch between scanning modes makes Horus well suited for tracking rapidly evolving storm features and studying fine-scale precipitation structures. The scanning techniques demonstrated with Horus highlight the potential of fully digital phased array radar technology to advance weather observations, improve storm monitoring, and enhance warning decision-making in future radar networks.

Message Passing-Based Distributed Track-Level Fusion Tracking for Space-Based Radar Networks With Time-Varying Topology

Abstract Reliable rainfall estimation is essential for hydrological modeling, particularly as climate change intensifies rainfall extremes and challenges water resource management. In many intertropical basins, sparse observation networks limit quantitative precipitation estimation, making satellite precipitation products (SPPs) a key alternative. However, SPP performance varies geographically and must be assessed against high-resolution reference data. This study first evaluates five state-of-the-art SPPs at their native resolution (0.1°, 30 min) against high-resolution weather radar observations in French Guiana. Second, it introduces a correction framework that combines image classification with tailored bias adjustment. Rain fields are first grouped into clusters using k -means applied to their spatial features, distinguishing different rainfall structures. Within each cluster, a quantile matching by parts (QMP) correction scheme trained on weather radar data is applied. The correction scheme is first adjusted on a training dataset consisting of 4000 coincident radar and satellite rain maps. Then, it can be applied to other satellite rain maps and outside the radar coverage. The main findings are as follows: 1) Among the evaluated products, Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) (IMERG) Final shows the best performance, but IMERG Late is selected for application due to its shorter latency. 2) The cluster-specific QMP correction reduces SPP bias from −20% to +4%, improves the rainfall intensity distribution, and improves the spatial variability of the rain fields and the diurnal cycle. 3) In hydrological simulations of the Mana River basin, the corrected product improves the Kling–Gupta efficiency from 0.36 to 0.83 compared to benchmark simulations using radar data. Overall, this relatively simple and computationally light method improves satellite-based rainfall estimation for various potential applications in data-scarce tropical regions, offering a scalable solution as radar networks expand globally.

Abstract. This paper addresses a major challenge in assimilating 3D radar reflectivity data with a localized ensemble transform Kalman filter (LETKF). In the case of observations with significant reflectivity and small or zero corresponding simulated reflectivities for all ensemble members, i.e., when the ensemble spread is vanishing, the filter ignores the observations based on its low-variance estimate for the background uncertainty. For such low-variance cases, the LETKF is insensitive to observations and their contribution to the analysis increment is effectively zero. Targeted covariance inflation (TCI) has been suggested to deal with the ensemble spread deficiency (Yokota et al., 2018; Dowell and Wicker, 2009; Vobig et al., 2021). To actually make TCI work in a fully cycled convective-scale data assimilation framework, here we will introduce a process-oriented approach to the TCI in combination with a conditional approach formulating criteria under which targeted covariance inflation is efficient. The process-oriented conditional TCI addresses the challenge of underrepresented reflectivity in the prior by constructing artificially simulated reflectivities for each ensemble member based on current observations and typical convective processes. Furthermore, certain conditions are used to restrict this spread inflation process to a carefully selected minimal set of eligible observations, reducing the noise introduced into the system. We will describe the theoretical basis of the new TCI approach. Furthermore, we will present numerical results of a case study in an operational framework, for which the TCI is applied to radar observations at each hourly assimilation step throughout a data assimilation cycle. We are able to demonstrate that the TCI is able to clearly improve the assimilation of radar reflectivities, making the system dynamically generate reflectivity that would otherwise be missing. Related to this, we are able to show that the fractional skill score of radar reflectivity forecasts over lead times of up to 6 h is significantly improved by up to 10 %. All of the results are based on the German radar network and the ICON-D2 model covering central Europe.

Abstract Determining surface precipitation type is an operational forecasting challenge, particularly in complex cold-season precipitation events and in areas with a dearth of observations. This paper describes a new radar algorithm proposed for the NEXRAD network called the surface Hydrometeor Classification Algorithm (sfcHCA). The sfcHCA produces estimates of surface precipitation types within the radar surveillance area by merging output from the existing NEXRAD Hydrometeor Classification Algorithm (HCA) Level-III product with surface precipitation-type diagnosed from a 1D steady-state discrete particle model initialized from numerical weather prediction model data. The sfcHCA introduces three new HCA classes for freezing rain, ice pellets, and freezing rain/ice pellet mixtures, as well as several novel features such as the utilization of range-defined quasi-vertical profiles, polarimetric radar particle size distribution retrievals for model initialization, merging logic for combining model-diagnosed surface precipitation-type classifications with existing HCA output, and a radar melting layer-based adjustment algorithm to correct for erroneous background model data. The sfcHCA was validated against more than 15,000 manned ASOS station reports and over 30,000 mobile Precipitation Identification Near the Ground (mPING) reports across 225 cases spanning all CONUS NEXRAD sites. Probability of detection rates within 20 km of manned ASOS observations were 97.1%, 78.3%, 72.7%, 68.1%, and 56.0% for rain, snow, rain/snow mix, freezing rain, and ice pellets, respectively. This algorithm should provide useful information for nowcasting surface precipitation type evolution and offering impact-based decision support.

The precise reconstruction of target scattering centers (TSCs) using sensors plays a crucial role in feature extraction and identification of non-cooperative targets. Radar sensor networks (RSNs) are well suited for this task, as they are capable of illuminating targets from multiple aspect angles and rapidly capturing reflected signals. However, the complex geometry and diverse material composition of real-world targets result in significant variations in the radar cross-section (RCS) observed at different angles. Although these RCS responses are interrelated, they exhibit considerable angular diversity. Furthermore, achieving precise spatiotemporal registration and fully coherent processing is infeasible for RSNs composed of small mobile sensor platforms, such as drone swarms. Therefore, an intelligent algorithm is required to extract and accumulate correlated and meaningful information from the target echoes received by the RSN. In this work, a novel collaborative TSC reconstruction framework for RSNs is proposed. The framework performs similarity evaluation on wide-angle high-resolution range profiles (HRRPs) to achieve adaptive angular segmentation of TSC models. It combines the expectation–maximization (EM) algorithm with an enhanced Arctic puffin optimization (EAPO) algorithm to effectively integrate echo information from the RSN in a non-coherent manner, thereby enabling accurate TSC estimation. The proposed method outperforms existing mainstream approaches in terms of spatiotemporal registration requirements, estimation accuracy, and stability. Comparative experiments on measured datasets demonstrate the robustness of the framework and its adaptability to complex target scattering characteristics, confirming its practical value.

Abstract Accurate forecasts of the development and evolution of deep, moist convection in convection-allowing models (CAMs) remain a challenge in part owing to the difficulties inherent in modeling the microphysical and internal structures of convection, which can affect storm mode, intensity, and longevity. We hypothesize that underused Weather Surveillance Radar-1988 Doppler (WSR-88D) and GOES-16 observations can improve forecasts of deep convection in CAM ensembles. Since the upgrade to the national network of WSR-88D radars was completed in 2013, polarimetric radar data offer a wealth of information about the shape, size, and type of hydrometeors present in precipitation. Several distinct polarimetric signatures within deep convection have been identified, such as the differential reflectivity (ZDR) column, that can aid significantly in characterizing internal storm structures and improve CAM representation of convection. In addition, GOES-16 infrared all-sky brightness temperatures (BTs) provide complimentary information on cloud structures and cover that radars cannot directly measure. The CAM ensemble in this study uses the Advanced Research version of the Weather Research and Forecasting Model with the High-Resolution Rapid Refresh configuration at 3-km horizontal grid spacing and with 40 ensemble members. Observations are assimilated using an Ensemble Kalman Filter, where the radar and satellite observations are assimilated jointly and separately, and results are compared in four proof-of-concept experiments. Results indicate that the assimilation of BT observations improves forecasts of a severe convective event, which are further improved with the assimilation of ZDR observations. While BT assimilation alone improves the convective forecast, ZDR observations provide additional improvements to updraft helicity tracks, precipitation, and hail forecasts. Significance Statement There are several challenges associated with predictions of severe weather in numerical weather models, including the time and location of thunderstorm initiation as well as the hazards associated with severe thunderstorms, including hail, flash flooding, and tornadoes. This study explores using a combination of underused satellite and radar observations to better define the atmospheric state used to start the weather prediction models, with the hope that this will lead to better forecasts before and during the thunderstorms. Results show that underused observations from routinely available Doppler weather radars and a geostationary satellite, all of which are currently available, can work synergistically to improve forecasts of thunderstorms as well as their hazards.

Terahertz (100 GHz–10 THz) photonics combines semiconductor technology and optical concepts to powerful, high-performance systems. It became an established technique and is now at a competitive level as compared to previously dominating electronic and purely optical approaches. This Perspective provides an overview of the state of the art and latest developments in sources, detectors, and systems for terahertz key applications. Photonic spectroscopic systems achieve Hz-level linewidth, tunability, and frequency coverage over more than 6 THz in a single system and a dynamic range beyond 90 dB/Hz at 1 THz. This article points out mixed photonic–electronic wireless communication systems with data rates beyond 1 TBit/s and first industrially deployed purely photonic systems in non-destructive testing and carves out integration perspectives using photonic integrated circuits as well as promising future directions, including domains that were covered solely by electronic systems in the past, such as radar, spectrum analysis, and vector network analysis.

Abstract In summer, many sea-breeze fronts (SBFs) are observed propagating from the sea to inland areas. However, there has been an absence of in-depth studies on whether and how these SBFs alone initiate convection initiation (CI) inland. We selected an inland CI event that occurred near Beijing on 17 May 2019 to analyze how the SBF triggers CI during its inland progression. The 3-km continuously cycled analyses with 12-min updates, produced by assimilating observations from radar and dense surface networks, revealed that as the northwestward-moving SBF reached Beijing, it interacted with the warm and dry southerly flow, mountains, and city landscape. These interactions created local conditions of strong convergence and high humidity, conducive to CI. The mountains and cities blocked and changed the direction of winds behind the SBF from southeasterly to easterly, enhancing local convergence and moisture along with the westerly downslope flow from the mountains. Meanwhile, the reduction in wind speed allowed the wet, cold air mass behind the SBF to catch up with the enhanced convergence zone, enabling the air parcel to rise from the surface to the level of free convection (LFC), thereby triggering convection. The new storm then merged with the eastward-propagating convective systems from the western mountains to form the record-breaking heavy rainfall. Sensitivity studies were conducted to quantify the effects induced by mountains, cities, and both. It was found that mountains played a vital role in enhancing convergence by changing the wind direction of the SBF, while cities primarily contributed to slowing down the SBF, thereby aligning wind convergence with water vapor and enabling the moist air to be lifted to the LFC. Significance Statement It is a common phenomenon worldwide that SBFs from the sea penetrate inland areas and interact with other mesoscale circulations to trigger CI and develop severe weather, leading to considerable loss of life and property. Most previous studies on SBF primarily focused on CI near the seashore, with inland SBFs farther from the coastline receiving less attention. Consequently, it remains a challenge to understand and predict whether and where SBFs trigger CI inland. Our study of a severe storm initiated by an SBF reveals that complex topography (mountains and city landscape) plays a key role in CI by altering the wind direction, wind speed, and moisture convergence of the SBF.

ABSTRACTAnthropogenic change is predicted to result in widespread declines in insect abundance, but assessing long‐term trends is challenging due to the scarcity of systematically collected time series measurements across large spatial scales. We develop a novel continental‐scale dataset using a nationwide network of radars in the United States to generate a 10‐year time series of daily aerial insect density and assess temporal trends. We do not find evidence of a continental‐scale net decline in insect density over the 10‐year period included in this study; instead we find a mosaic of increasing and declining trends at the landscape scale. This spatial variation in density trends is associated with climatic drivers, where areas with warmer winters experience greater declines in insect density and areas with cooling winter trends see increases in density. Winter warming has a stronger negative effect on density at higher latitudes. After assessing temporal trends, we also use the 10‐year dataset and atmospheric variables to model insect aerial abundance, finding that on a typical summer day approximately a hundred trillion (1014) flying insects are present in the airspace, representing millions of tons of aerial biomass. Our results provide the first continental‐scale quantification of insect density and its response to anthropogenic warming and demonstrate the utility of weather surveillance radar to provide large‐scale monitoring of insect abundance.

Abstract This paper offers an in‐depth analysis of the 10–11 May 2024 solar storm's time evolution. It integrates the European Heliospheric Forecasting Information Asset (EUHFORIA) and Gorgon‐Space models to explore the effects on Earth's magnetosphere, including its state and reactions, ionospheric currents, and cross‐polar cap potential (CPCP) responses to the solar wind. Observations from Super Dual Auroral Radar Network (SuperDARN) are used to validate the numerical findings. Two specific time frames on May 10 are examined: one representing quiet conditions and another with active polar cap convection cells. This allows for an assessment of how well the simulations align with the actual observations. The investigation includes a thorough look at the temporal evolution, the number of convection cells, and their spatial distribution within the polar cap and CPCP area. Additionally, the research explores the scattered patterns of convection cells, including instances of multiple cell formations. The study compares the simulated and CPCP values with observed data from ground magnetometers and SuperDARN to gauge consistency. The encouraging overall agreement suggests the numerical results could offer improvements for addressing the underestimation of CPCP in SuperDARN observations. Furthermore, the model's ability to estimate the magnetopause radius is evaluated against previous models, while temporal structures in the plasma convection maps predicted by the EUHFORIA/Gorgon‐Space models are also scrutinized.

BackgroundEvidence remains insufficient to clarify whether hyperglycemia or hyperlipidemia exerts a greater influence on the development of liver steatosis and fibrosis. Furthermore, it remains uncertain whether distinct glucose-lipid metabolic profiles are associated with an increased risk of these hepatic conditions.MethodsWe used NHANES data to assess liver steatosis and fibrosis via Controlled Attenuation Parameter (CAP) and Liver Stiffness Measurement (LSM), then propensity-score weighted regression was used to access associations between seven glycolipid metabolic biomarkers and the two liver indices. Radar plots and network analysis were utilized to illustrate metabolic distribution patterns and delineate key metabolic signatures distinguishing four liver health phenotypes: Healthy Control, Steatotic Liver, Fibrotic Liver, and Combined Steatotic-Fibrotic Liver. Linear regression analyses were further conducted to compare the levels of steatosis and fibrosis across eight metabolic subgroups, categorized according to distinct combinations of dyslipidemia, dysglycemia, and insulin resistance. Lastly, a tree-based algorithm was employed to identify distinct glycolipid metabolic profiles associated with increased severity of hepatic steatosis and fibrosis.ResultsA total of 9698 individuals were included (mean age: 44.26:pm:20.80 years). Propensity score-weighted regression showed that TG, GLU, HbA1c, and HDL were significantly associated with both CAP and LSM, while TC and LDL were associated with CAP only. Radar plots and network analysis revealed that the steatosis-fibrosis group had the most adverse metabolic profile, with the lowest HDL, highest insulin, HbA1c, and GLU levels. TG and GLU consistently ranked as the top two central metabolic hubs across all liver groups, while HbA1c ranked third except in the steatotic-fibrotic group, where insulin resistance prevailed. Among subgroups with a single metabolic abnormality, CAP was highest in the insulin resistance (IR)-only group (B = 14.433, P < 0.001), followed by the dysglycemia-only group (B = 10.142, P < 0.001), and lowest in the dyslipidemia-only group. In IR-associated subgroups, CAP was significantly higher when IR co-occurred with dysglycemia (B = 57.393, P < 0.001) than with dyslipidemia (B = 53.635, P < 0.001). The triple abnormalities group exhibited the highest overall CAP (B = 79.811, P < 0.001) as well as the highest liver stiffness measurement (LSM) (B = 1.543, P < 0.001). Tree-based analysis further identified that CAP was highest in individuals with insulin ≥ 14.705 µU/mL and GLU ≥ 5.861 mmol/L, while LSM was highest in those with insulin between 17.1 and 28.205 µU/mL, HbA1c ≥ 6.15%, and GLU ≥ 7.861 mmol/L.ConclusionsMetabolic abnormalities related to hyperglycemia may be more closely associated with hepatic steatosis and fibrosis than those related to hyperlipidemia.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13098-025-01945-9.

ABSTRACT Atmospheric duct interference (ADI) significantly impacts wireless long‐distance communications, radar systems, and naval activities via anomalous signal propagation in tropospheric ducting layers. The previously used predictive methods, anchored on physical models and meteorological data, proved not to be effective in capturing the complex spatiotemporal features of ADI. This paper introduces an Improved Whale Optimization Algorithm‐enhanced CNN‐GRU model (IWOA‐CNN‐GRU) that addresses these limitations through three key innovations: (1) a hybrid convolutional and recurrent network for joint spatiotemporal feature extraction, (2) an enhanced WOA with Lévy flight (where heavy‐tailed jumps mitigate local optima with 10% probability) and adaptive parameter optimization (dynamically balancing exploration/exploitation) to effectively optimize hyperparameters, and (3) robust generalization over a variety of atmospheric conditions over tropical coastal regions. Experimental results demonstrate the improved performance of the model with 98.50% validation accuracy and significant improvements in precision (0.95 ± 0.02), recall (0.96 ± 0.01), and F1‐score (0.95 ± 0.01), a 12%–15% improvement over baselines. The IWOA optimizer performed improved convergence ( p &lt; 0.01 in Wilcoxon rank‐sum tests) and reduced premature convergence cases by 37%, with the efficiency of computation being boosted by 14.2% during training time without compromising stability (σ 2 &lt; 0.005 for accuracy variance). These gains confirm the algorithm's suitability for real‐time prediction of ADI in operational networks, including radar and communication networks. This work establishes a new benchmark in machine learning–based ADI prediction, with significant implications for enhancing the reliability of wireless systems under changing atmospheric conditions.

Abstract. The observational consistency between ground-based weather radars significantly impacts the quality of mosaic products and severe convection identification products. The real-time monitoring of observational biases between radars can provide a basis for calibration and validation. This study designed a consistency verification method for weather radar networks based on the FY-3G precipitation radar (SGRCM) and a ground-based weather radar network consistency verification method (AWRCM). From January to October 2024, observational experiments were conducted in the South China region involving 19 S-band weather radars and 13 X-band phased-array weather radars. The aim was to analyze the influencing factors of the consistency verification methods and the observational biases of reflectivity factors for radars with different bands and systems. For the S-band weather radars, the difference in the bias between the two methods ranged from −1.5 to 1.4 dB, and the difference in the standard deviation ranged from −1.2 to 1.2 dB. For the X-band phased-array weather radars, the difference in the bias between the two methods ranged from −6.67 to 0.84 dB, and the difference in the standard deviation ranged from −0.38 to 1.51 dB. The evaluation results of the two methods show good consistency for weather radars with different bands. We selected one radar with a larger bias for recalibration and rectification, and the changes in bias before and after rectification thus provide a good indication of the improvement in network consistency among the radars.

Abstract. Continuous and reliable measurements of the mesosphere and lower thermosphere (MLT) are key to further the understanding of global atmospheric dynamics. Observations at horizontal scales of a few hundred kilometers (i.e., mesoscales) are particularly important since gravity waves have been recognized as the main drivers of various global phenomena, e.g., the pole-to-pole residual meridional circulation. Multistatic specular meteor radars are well suited to routinely probe the MLT at these scales. One way to accomplish this, is by investigating the momentum flux, horizontal divergence (∇H⋅u) and relative vorticity ((∇×u)z) estimated from the Doppler shifts measured by a radar network. Furthermore, the comparison between the horizontal divergence and the relative vorticity can be used to determine the relative importance of gravity waves (i.e., divergent motions) and strongly stratified turbulence (i.e., vortical motions). This work presents the first climatology of all these estimates together, as well as results on the probability distribution of the total momentum flux (TMF), and the comparison between ∇H⋅u and (∇×u)z, obtained from almost 10 years of continuous measurements provided by two multistatic specular meteor radar networks: MMARIA/SIMONe Germany, covering an area of more than 200 km radius around (53° N, 11° E), and MMARIA/SIMONe Norway, which covers an area of similar size, but around (69° N, 16° E). Among others, our results indicate that at middle latitudes the horizontal divergence and the relative vorticity are balanced around summer mesopause altitudes, while the former dominates over the latter above ∼ 90 km of altitude during parts of the fall transition. At high latitudes, the vortical motions dominate during late spring and early summer. Besides, the strongest 5 % of GWs contribute much more over northern Germany than over northern Norway, where the larger values of the excess-kurtosis indicate that the contribution from the small-amplitude GWs is also more significant at middle latitudes, especially during the summer. In other words, the TMF in the mesosphere and lower thermosphere over central Europe is considerably more intermittent at middle latitudes than at high latitudes.