Gaussian Process Regression for Estimating EM Ducting Within the Marine Atmospheric Boundary Layer

We show that Gaussian process regression (GPR) can be used to infer the electromagnetic (EM) duct height within the marine atmospheric boundary layer (MABL) from sparsely sampled propagation factors within the context of bistatic radars. We use GPR to calculate the posterior predictive distribution on the labels (i.e. duct height) from both noise-free and noise-contaminated array of propagation factors. For duct height inference from noise-contaminated propagation factors, we compare a naive approach, utilizing one random sample from the input distribution (i.e. disregarding the input noise), with an inverse-variance weighted approach, utilizing a few random samples to estimate the true predictive distribution. The resulting posterior predictive distributions from these two approaches are compared to a "ground truth" distribution, which is approximated using a large number of Monte-Carlo samples. The ability of GPR to yield accurate and fast duct height predictions using a few training examples indicates the suitability of the proposed method for real-time applications.Comment: 15 pages, 6 figure

Impact of Data Selection on the Accuracy of Atmospheric Refractivity Inversions Performed over Marine Surfaces

Within the Earth’s atmosphere there is a planetary boundary layer that extends from the surface to roughly 1 km above the surface. Within this planetary boundary layer exists the marine atmospheric boundary layer, which is a complex turbulent surface layer that extends from the sea surface to roughly 100 m in altitude. The turbulent nature of this layer combined with the interactions across the air-sea interface cause ever changing environmental conditions within it, including atmospheric properties that affect the index of refraction, or atmospheric refractivity. Variations in atmospheric refractivity lead to many types of anomalous propagation phenomena of electromagnetic (EM) signals; thus, improving performance of these EM systems requires in-situ knowledge of the refractivity. Efforts to inversely obtain refractivity from radar power returns have done so using both reflected sea clutter and bi-static radar approaches. These types of inversion methods are driven by radar measurements. This study applies a bi-static radar data inversion process to estimate atmospheric refractivity parameters in evaporative ducting conditions and examines the impacts of radar propagation loss data quantity and source location on the accuracy of refractivity inversions. Genetic algorithms and the Variable Terrain Radio Parabolic Equation radar propagation model are used to perform the inversions for three refractivity parameters. Numerical experiments are performed to test various randomly distributed amounts of synthetic data from a 100 m altitude by 60 km range domain. To compare the impact of location of data on the inverse solutions, three domains were examined from which data was sourced, including the whole domain (0 m to 100 m altitude and 0 km to 60 km range), a lower domain (0 m to 60 m altitude and 0 km to 60 km range), and a long-range domain (0 m to 100 m altitude and 30 km to 60 km range). Comparisons of inversion performance across experiments involved evaluation of several metrics: fitness scores, fitness-distance-correlations, the root-mean-square-errors of refractivity profiles, and percent errors of each individual refractivity parameter. The results of the data quantity experiments show that propagation loss measurement coverage of approximately 1% of the prediction domain yields the most accurate refractivity estimates. It is concluded that this amount of data is needed to sufficiently eliminate non-unique solutions that were observed using smaller data quantities. The results of the regional study indicate that the long-range domain produced slightly more accurate results with less data compared to the other regions. From the results of these experiments and prior studies, four specific sampling patterns were developed that were hypothesized to generate accurate inversion results. It was shown that the pattern containing the most data cells with the widest spread over the domain generated inversion results with the highest parameter and refractivity accuracy; although, a second pattern that sourced data concentrated in a short range low altitude region performed similarly with significantly less data. The results from this study enable advancement of refractivity inversion techniques by providing insight into where and how many EM measurements are needed for successful refractivity inversions. Improvements in refractivity inversion techniques enable performance improvements of EM sensing and communication technologies

High temporal resolution refractivity retrieval from radar phase measurements

Knowledge of the spatial and temporal variability of near-surface water vapor is of great importance to successfully model reliable radio communications systems and forecast atmospheric phenomena such as convective initiation and boundary layer processes. However, most current methods to measure atmospheric moisture variations hardly provide the temporal and spatial resolutions required for detection of such atmospheric processes. Recently, considering the high correlation between refractivity variations and water vapor pressure variations at warm temperatures, and the good temporal and spatial resolution that weather radars provide, the measurement of the refractivity with radar became of interest. Firstly, it was proposed to estimate refractivity variations from radar phase measurements of ground-based stationary targets returns. For that, it was considered that the backscattering from ground targets is stationary and the vertical gradient of the refractivity could be neglected. Initial experiments showed good results over flat terrain when the radar and target heights are similar. However, the need to consider the non-zero vertical gradient of the refractivity over hilly terrain is clear. Up to date, the methods proposed consider previous estimation of the refractivity gradient in order to correct the measured phases before the refractivity estimation. In this paper, joint estimation of the refractivity variations at the radar height and the refractivity vertical gradient variations using scan-to-scan phase measurement variations is proposed. To reduce the noisiness of the estimates, a least squares method is used. Importantly, to apply this algorithm, it is not necessary to modify the radar scanning mode. For the purpose of this study, radar data obtained during the Refractivity Experiment for H2O Research and Collaborative Operational Technology Transfer (REFRACTT_2006), held in northeastern Colorado (USA), are used. The refractivity estimates obtained show a good performance of the algorithm proposed compared to the refractivity derived from two automatic weather stations located close to the radar, demonstrating the possibility of radar based refractivity estimation in hilly terrain and non-homogeneous atmosphere with high spatial resolution.Ministerio de Economía y Competitividad | Ref. TEC2014-55735-C3-3-RXunta de Galicia | Ref. GRC2015/01

A Numerical Study Investigating Sensitivity of Radar Wave Propagation to the Marine Atmospheric Boundary Layer Environment

Radar is a remote sensor that is useful in scientific and military applications. The environment affects the accuracy of radar measurements as well as the predictability of a radar system’s performance. Because of the complexity of the dynamic processes occurring in the marine atmospheric boundary layer (MABL), which includes the lowermost troposphere and ocean surface, the impact of the environment on radar is intricate and difficult to assess. To better understand the relative importance of various aspects of the MABL environment on radar wave propagation, this study evaluates the sensitivity of radar wave propagation to the MABL environment using a global sensitivity analysis (SA) method, the extended Fourier amplitude sensitivity test (EFAST), and the Variable Terrain Radio Parabolic Equation (VTRPE) simulation, which calculates propagation power of radar waves in a wide variety of marine atmospheric conditions. A total of 16 environmental parameters are examined, 8 parameterizing the rough ocean surface, and 8 parameterizing the atmospheric vertical refractivity profiles. Radar frequencies of 3, 9, and 15 GHz are each simulated with horizontal (HH) and vertical (VV) polarization, resulting in sensitivity calculations for 6 different cases. The study is conducted for a domain of 1 km in altitude and 60 km in range using a low grazing angle generic air/sea surveillance radar. The relative importance of the different parameters varied much more with frequency than polarization. The EFAST method takes into account parameter interactions, which are found to be significant and can be essential to correctly interpret the significance of a parameter. Results show that the atmospheric mixed layer parameters are most important, particularly the height of the mixed layer. Overall, swell period is the most significant ocean surface parameter. However, sea directionality is also important at 3 GHz, and sea surface roughness and salinity are important at 9 and 15 GHz, respectively. Sensitivities to ocean surface parameters, except those related to directionality, become more prominent as radar frequency increases, and some sensitivity differences with respect to polarization occur regarding sea surface characteristics. Due to spatial variability of sensitivity throughout the domain, regional analysis is performed, using short (0-10 km), mid (10-30 km), and long (30-60 km) range, and low (0-200 m), mid (200-600 m), and high (600-1000 m) altitude divisions (9 regions). The most sensitive parameter in each low altitude region, from short to long range, is evaporation duct height and mixed layer height (mid and long range). The mixed layer height is the most sensitive parameter in all mid-altitude regions. At high altitude, the most sensitive parameter varies with frequency, except at short range where it is the mixed layer refractivity gradient (i.e., M-gradient). At mid-range, the most sensitive parameters are the inversion layer strength, mixed layer M-gradient, and mixed layer height for 3, 9, and 15 GHz respectively. At long range, the inversion strength is the most sensitive parameter at 3 GHz, while at 9 and 15 GHz it is the wind speed. These regional sensitivity results, along with those for the whole domain, can be used to determine which environmental parameters need to be specified with high accuracy when accounting for their effects on propagation for various radar systems and applications. This sensitivity information can also be used to help guide field measurements for simulation validation studies as it indicates what aspects of the environment need to be focused on for such experimental campaigns. Furthermore, these results provide guidance on prioritization of environmental characterization in numerical weather prediction (NWP) and inversion studies (e.g., refractivity from clutter (RFC) studies), which are the two most common numerical methods currently used to address environmental effects on propagation. Additionally, the methodology presented in this study can be used and applied to similar problems that seek to understand the sensitivity to environmental effects on other remote sensors, such as infrared (IR), optical, and acoustic sensors

CHARACTERISTICS OF REFRACTIVITY AND SEA STATE IN THE MARINE ATMOSPHERIC SURFACE LAYER AND THEIR INFLUENCE ON X-BAND PROPAGATION

Predictions of environmental conditions within the marine atmospheric surface layer (MASL) are important to X-band radar system performance. Anomalous propagation occurs in conditions of non-standard atmospheric refractivity, driven by the virtually permanent presence of evaporation ducts (ED) in marine environments. Evaporation ducts are commonly characterized by the evaporation duct height (EDH), evaporation duct strength, and the gradients below the EDH, known as the evaporation duct curvature. Refractivity, and subsequent features, are estimated in the MASL primarily using four methods: in-situ measurements, numerical weather and surface layer modeling, boundary layer theory, and inversion methods. The existing refractivity estimation techniques often assume steady homogeneous conditions, and discrepancies between measured and simulated propagation predictions exist. These discrepancies could be attributed to the exclusion of turbulent fluctuations of the refractive index, exclusion of spatially heterogeneous refractive environments, and inaccurate characterization of the sea surface in propagation simulations. Due to the associated complexity and modeling challenges, unsteady inhomogeneous refractivity and rough sea surfaces are often omitted from simulations. This dissertation first investigates techniques for steady homogeneous refractivity and characterizes refractivity predictions using EDH and profile curvature, examining their effects on X-band propagation. Observed differences between techniques are explored with respect to prevailing meteorological conditions. Significant characteristics are then utilized in refractivity inversions for mean refractivity based-on point-to-point EM measurements. The inversions are compared to the other previously examined techniques. Differences between refractivity estimation methods are generally observed in relation to EDH, resulting in the largest variations in propagation, where most significant EDH discrepancies occur in stable conditions. Further, discrepancies among the refractivity estimation methods (in-situ, numerical models, theory, and inversion) when conditions are unstable and the mean EDH are similar, could be attributed to the neglect of spatial heterogeneity of EDH and turbulent fluctuations in the refractive index. To address this, a spectral-based turbulent refractive index fluctuation model (TRIF) is applied to emulate refractive index fluctuations. TRIF is verified against in-situ meteorological measurements and integrated with a heterogenous EDH model to estimate a comprehensive propagation environment. Lastly, a global sensitivity analysis is applied to evaluate the leading-order effects and non-linear interactions between the parameters of the comprehensive refractivity model and the sea surface in a parabolic wave equation propagation simulation under different atmospheric stability regimes (stable, neutral, and unstable). In neutral and stable regimes, mean evaporation duct characteristics (EDH and refractive gradients below the EDH) have the greatest impact on propagation, particularly beyond the geometric horizon. In unstable conditions, turbulence also plays a significant role. Regardless of atmospheric stability, forward scattering from the rough sea surface has a substantial effect on propagation predictions, especially within the lowest 10 m of the atmosphere

A Marine Radar Wind Sensor

A new method for retrieving the wind vector from radar-image sequences is presented. This method, called WiRAR, uses a marine X-band radar to analyze the backscatter of the ocean surface in space and time with respect to surface winds. Wind direction is found using wind-induced streaks, which are very well aligned with the mean surface wind direction and have a typical spacing above 50 m. Wind speeds are derived using a neural network by parameterizing the relationship between the wind vector and the normalized radar cross section (NRCS). To improve performance, it is also considered how the NRCS depends on sea state and atmospheric parameters such as air–sea temperature and humidity. Since the signal-to-noise ratio in the radar sequences is directly related to the significant wave height, this ratio is used to obtain sea state parameters. All radar datasets were acquired in the German Bight of the North Sea from the research platform FINO-I, which provides environmental data such as wind measurements at different heights, sea state, air–sea temperatures, humidity, and other meteorological and oceanographic parameters. The radar-image sequences were recorded by a marine X-band radar installed aboard FINO-I, which operates at grazing incidence and horizontal polarization in transmit and receive. For validation WiRAR is applied to the radar data and compared to the in situ wind measurements from FINO-I. The comparison of wind directions resulted in a correlation coefficient of 0.99 with a standard deviation of 12.8°, and that of wind speeds resulted in a correlation coefficient of 0.99 with a standard deviation of 0.41 m s^−1. In contrast to traditional offshore wind sensors, the retrieval of the wind vector from the NRCS of the ocean surface makes the system independent of the sensors’ motion and installation height as well as the effects due to platform-induced turbulence