The marine atmospheric surface layer (MASL) is a complex environment due to the prominent role of turbulence further complicated by air-sea interactions. These complexities, and the harsh environment, make it logistically and financially difficult to obtain instantaneous measurements of the vertical distribution of temperature and humidity near the ocean surface, which is needed, among other applications, for predicting the performance of radar systems and for accurate modeling of the atmosphere and ocean. As such, refractivity inversion methodologies have been developed to inversely determine the vertical distribution of refractivity using radio frequency (RF) signals. This research builds upon these inverse methods by adding a retrieval of thermodynamic variables that uses a RF-based vertical refractivity profile along with measurement of thermodynamic variables at a (single) reference height to estimate the vertical distribution of temperature and humidity within the MASL (Hackett et al., “Remote Sensing of Humidity and Temperature from X-Band Radar Measurements in the Marine Atmospheric Surface Layer,” United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM), Boulder, CO, USA, pp. 111-111, Jan. 2025).

The use of radar to remotely sense atmospheric properties could provide accurate, high-resolution measurements that are essential for a variety of civil and military applications. Radar remote sensing within the marine atmospheric surface layer (MASL) has been performed for atmospheric refractivity (e.g., D. M. Pastore, S. E. Wessinger, M. J. Stanek, R. J. Burkholder, T. Haack, Q. Wang, and E. E. Hackett, “Refractivity Inversions from Point-to-Point X-band Radar Propagation Measurements”, Radio Science, vol. 57, issue 2, 1–16, Feb. 2022). This refractivity is related to humidity, temperature, and pressure. Humidity has the largest effect on atmospheric refractivity and therefore theoretically, has the greatest potential to be inferred from radar-based refractivity. This study examines a methodology that may allow for the remote sensing of humidity in the MASL using X-band inferred atmospheric refractivity as an intermediary. Previous studies have shown that humidity gradients can be estimated with ground-based wind profiling radars using:

Water quality has traditionally been measured via in situ sensors and satellites. The latter has limited applicability for smaller inland water bodies, while the former requires significant logistics, labor, and expense for routine sampling, and reactive/spurious sampling is often not feasible as a result (e.g., sampling pre-/post-storm). Consequently, small uncrewed aircraft system-based (sUAS-based) sampling has emerged as a potential solution to bridge these sampling gaps and challenges. But sampling from an sUAS is complicated by the need to pump water from depth, rather than suspending a sensor from the sUAS, due to concern over sampling sUAS-impacted waters. Here, we measure the water flow below a hovering sUAS in a laboratory by applying the particle image velocimetry flow measurement technique. Observations suggest the development of two counter-rotating vortices under the sUAS, where, in the center of the vortex pair, water is upwelled to the surface, which would, therefore, be a sampling location relatively free of contamination by the sUAS. This location coincides with the still spot on the water surface underneath the sUAS; thus, if one wanted to sample water by suspending a sensor underneath an sUAS, then the optimal sampling location would be within this still spot.

The propagation of electromagnetic (EM) waves at X-band frequencies within the marine atmospheric surface layer (MASL) are influenced by variations in the index of refraction of the air. Variations in the index of refraction cause changes in the direction of propagation of EM waves. In some cases, vertical variations in the index of refraction are significant enough to trap and carry the EM wave energy over longer distances relative to normal atmospheric conditions. The high degree of sensitivity of the EM wave propagation to the index of refraction makes it possible to perform inversions for vertical profiles of atmospheric refractivity based on radar measurements. In the MASL, which extends from the surface to tens of meters above the ocean surface, the index of refraction is sensitive to changes in atmospheric humidity and temperature, especially humidity. Vertical variations of humidity and temperature in the MASL can be significant and complex due to the water vapor and heat exchange with the ocean. Direct measurement of these variations is challenging because of the difficulty in making accurate profile measurements near the ocean surface (e.g., due to platform interference); yet, the vertical distributions of humidity and temperature within the MASL are important to climate science, weather forecasting, as well as a number of civil and military engineering applications. Thus, a remote method of obtaining highresolution vertical profiles of humidity and temperature in the MASL would enable advancement of related science and engineering applications.

Evaporation ducts (EDs) are an atmospheric phenomenon that can cause anomalies in X-band radar systems (8-12 GHz) by extending their range beyond the geometric horizon, potentially leading to positioning uncertainties. Additionally, the lateral spatial variations of the ED over similar to 60 km may cause further effects. However, the extent to which these lateral variations need to be incorporated for accurate propagation predictions, and whether such effects need to be accounted for in related applications such as refractivity inversion techniques, remains unclear. In addition, few studies have discussed the impacts of heterogeneous EDs on X-band propagation loss relative to a homogeneous ED. To address these questions, this article explores the impact of linear variations of ED height and duct shape over range on X-band propagation loss relative to a laterally homogeneous ED. It is found that significant differences in X-band propagation are likely to occur when horizontal variations of ED height or shape transition the environment's trapping conditions downrange of the radar transmitter. Furthermore, it is shown that during such transitional trapping environments, heterogeneous refractivity inversions perform more accurately, on average, than homogeneous refractivity inversions. However, utilizing heterogeneous inversion methods when the true environment is homogeneous can lead to less accurate inversely determined refractivity.

Particle image velocimetry (PIV) flow measurements are common practice in laboratory settings in a wide variety of fields involving fluid dynamics, including biology, physics, engineering, and medicine. Dynamic fluid pressure is a notoriously difficult property to measure non-intrusively, yet its variation is a driving flow force and critical to model correctly. Techniques have been developed to estimate the pressure from velocity and velocity gradient measurements. Here, we highlight a novel application of boundary conditions when applying such pressure estimation techniques based on two-dimensional PIV data; the novel method is especially relevant to problems with complex boundary conditions. As such, it is demonstrated with PIV measurements of in vivo fish suction-feeding, which represents a challenging flow environment. Suction-feeding is a common method for capturing prey by aquatic organisms. Suction-feeding is a complex fish–fluid interaction governed by various hydrodynamic forces and the dynamic behavior of the fish (motion and forces). This study focuses on estimating the pressure within the flow field surrounding the mouth of a Bluegill sunfish (Lepomis macrochirus) during suction-feeding utilizing two-dimensional PIV measurements. High-speed imaging was used for measurements of the fish kinematics (duration and amplitude). Through the Poisson equation, the pressure field is estimated from the PIV velocity measurements. The boundary conditions for the pressure field are determined from the integral momentum equation, separately for three phases of the suction-feeding cycle. We demonstrate the utility of the technique with this case study on fish suction-feeding by quantifying the pressure field that drives the flow towards the buccal cavity, a feeding mechanism known to be dominated by pressure spatial variations over the feeding cycle.

Air properties influence the propagation of electromagnetic waves in the marine atmospheric surface layer (MASL) through several mechanisms such as absorption, scattering, and refraction. At X-band, atmospheric refractivity is the main factor influencing the propagation, but at higher frequencies, air properties such as temperature and humidity can also directly influence propagation. Many existing technologies including numerical weather prediction, similarity theory, or in-situ atmospheric measurements are used to make estimates of temperature and humidity, but each of these technologies have their own limitations. Remote sensing technologies that estimate air properties are generally applied over broad vertical spatial scales at coarse resolution; however, refractivity inversions based on radar data have been used to estimate vertical profiles of refractivity in the MASL at fine vertical resolution. These methodologies commonly use propagation loss measured from bi-static X-band radar or ocean surface clutter paired with machine learning algorithms or look-up tables to inversely determine these vertical profiles of refractivity. However, these inversion technologies are currently limited to estimating refractivity; extension to other air properties would enable their remote sensing at fine resolution within the MASL. Thus, this work explores the development of an inverse technique for retrieving temperature and humidity from modified refractivity measurements. Such measurements can be inferred from refractivity inversion techniques based-on radar measurements. With this extension, inverse methods offer an additional tool for remotely estimating vertical distributions of temperature and/or humidity in the MASL.

This study utilizes in situ measurements and numerical weather prediction forecasts curated during the Coupled Air–Sea Processes Electromagnetic Ducting Research (CASPER) east field campaign to assess how thermodynamic properties in the marine atmospheric surface layer influence evaporation duct shape independent of duct height. More specifically, we investigate evaporation duct shape through a duct shape parameter, a parameter known to affect the propagation of X-band radar signals and is directly related to the curvature of the duct. Relationships between this duct shape parameter and air sea temperature difference (ASTD) reveal that during unstable periods (ASTD < 0), the duct shape parameter is generally larger than in near-neutral or stable atmospheric conditions, indicating tighter curvature of the M-profile. Furthermore, for any specific duct height, a strong linear relationship between the near-surface-specific humidity gradient and the duct shape parameter is found, suggesting that it is primarily driven by near-surface humidity gradients. The results demonstrate that an a priori estimate of duct shape, for a given duct height, is possible if the near-surface humidity gradient is known.

Evaporation ducts (ED) are an atmospheric phenomenon that can cause inaccuracies in X-band radar systems by enhancing EM energy at ranges beyond the radar horizon. To predict these propagation anomalies, ED characteristics are estimated based-on prevailing meteorological conditions, where these characteristics are commonly assumed to be laterally homogeneous over range, i.e., evaporation duct characteristics don't vary down range from the radar transmitter. While this assumption is reasonable over the open ocean, it commonly breaks down in coastal regions, where it has been shown that the shape of the duct, the strength of the duct ( $M-\text{deficit}$ ), and/or height of the duct (duct height) is likely to vary over range. Some works have investigated the effects of incorrectly assuming homogeneity and found nonnegligible differences in radar propagation loss predictions (J. Goldhirsh, and D. Dockery, “Propagation Factor Errors Due to the Assumption of Lateral Homogeneity,” Radio Science, vol. 33, issue 2, Mar. 1998). Because of these findings, this work aims to explore under which conditions and to what extent range-dependent variations of the evaporation duct may play a significant factor in accurately predicting radar performance, in-turn exploring the validity and scope of the commonplace lateral homogeneity assumption.

Current methodologies for predicting atmospheric refractivity in the marine atmospheric surface layer (MASL) include numerical weather prediction models, Monin-Obhukov similarity theory, and inversion modeling techniques. It is known numerical weather prediction models have limited vertical resolution and similarity theory has nonunique solutions in stable atmospheric conditions. As such, inverse modeling of refractivity using X-band radar systems offers promise to fill-in these modeling gaps without extensive meteorological measurements. Inverse modeling estimates a vertical distribution of refractivity using point-to-point X-band radar propagation loss (PL) measurements. These inverse methods can be implemented using a global optimization technique to iteratively estimate parameters of a parametric refractivity model until a set of parameters produces PL that matches the radar measurements well.

Evaporation ducts (EDs), created by rapid decreases of humidity with altitude and typically observed in marine environments, are well known to greatly influence X-band propagation. Specifically, EDs can trap X-band signals leading to anomalous radar propagation such as extended signal ranges and/or target positioning errors. Over the past decades, research has focused on evaporation duct height (EDH), a key feature of EDs, which occur where the modified refractivity $(M)$ vertical gradient is zero, delineating the top of the trapping layer. EDH's effect on X-band propagation has been studied extensively including the impact of its variation over range, whereas evaporation duct shape and its associated propagation effects are largely absent from literature. This gap can be partly attributed to the difficulty in separating “shape effects” of the duct height from other contributors to the shape because of the M-profile's (approximately) log-linear shape during evaporation ducting conditions. When ED shape varies for a given duct height, these changes in shape can be quantified by changes in the M-deficit of the refractivity profiles, which influences X-band propagation as reported in prior studies. We also know, from Monin-Obukhov boundary layer similarity theory, that different M-profile shapes can be associated with different stability functions indicating duct shape is related to atmospheric stability.

In predicting electromagnetic wave propagation within the marine atmospheric surface layer, it is common to assume steady homogenous conditions. However, discrepancies between predicted and measured propagation remain, which could be due in-part to turbulent fluctuations of the refractive index, spatially heterogenous evaporative ducting environments, and mischaracterization of the rough ocean bottom boundary. To better understand the relative importance of these contributors, this study explores the sensitivity of X-band propagation to parameters describing sea-state conditions and refractive environments, including turbulent fluctuations and spatially heterogenous conditions. This study employs the extended Fourier Amplitude Sensitivity Test to compute sensitivity indices that evaluate the leading-order effects and effects due to non-linear interactions between these refractive and sea state parameters on a parabolic wave equation electromagnetic wave propagation simulation. The parameters are delineated and evaluated in three atmospheric stability regime experiments: stable, neutral, and unstable, and consider both trapping and non-trapping propagation conditions. Parameter sensitivity indices are ranked for each experiment to examine the relative effects of the parameters on X-band propagation prediction. The results show that in neutral and stable regimes, mean evaporation duct characteristics have the greatest impact on propagation beyond the geometric horizon, while in unstable conditions, turbulence also plays a significant role. Additionally, in the lowest 10 m of the atmosphere, forward scattering from the rough sea-surface has the greatest effect on propagation predictions regardless of atmospheric stability.

Evaporation ducts are an observed electromagnetic phenomenon caused by rapid decreases of humidity with altitude. Sensing technologies that operate at X-band frequencies (8-12 GHz) exhibit extension of radar signals beyond the radar horizon and holes in coverage at high altitudes during evaporative ducting conditions. In addition, the evolution of the evaporation duct over range has been reported to cause further adverse effects on these technologies in some circumstances. However, in terms of the predictability of these effects, more research is still needed. This research explores evaporation duct variations over range and characterizes them based-on two numerical datasets from different latitudes, different hemispheres, and during different seasons as well as correlating their range distributions to distributions of other atmospheric variables. It is found, for both datasets, that most often a linear function accurately represents variations of evaporation duct characteristics over ~60 km in range, but higher-order functional distributions of evaporation duct characteristics with range do occur albeit less frequently. Furthermore, range distributions of mean wind speed and mean specific humidity within the evaporation layer are strongly correlated to the range distributions of duct height; while range distributions of duct shape are mainly related to the specific humidity gradient in the evaporation layer. The mid-latitude dataset exhibits more complex range distributions during frontal events; while the equatorial dataset shows the most complex range distributions near sunrise.

Measurements of vertical profiles of humidity within the marine atmospheric surface layer (MASL) are needed for a range of applications. Satellite-based and in-situ measurements play crucial roles in monitoring atmospheric variables, such as humidity, yet both methods face limitations. Satellites provide a broad overview of the Earth's atmosphere, capturing large-scale patterns and changes. However, their lack of vertical and temporal resolution makes them unable to discern fine-scale atmospheric phenomena within the MASL. In-situ measurements offer finer vertical and temporal resolution but are limited in horizontal and temporal coverage.

Direct measurements of profiles of atmospheric properties near the ocean surface and within the marine atmospheric surface layer often contain a large degree of variability. The variability observed can be explained by numerous technical and natural reasons such as the temporal variability over the time span a profile is measured (unsteadiness in the mean), spatial variations (inhomogeneity), turbulent fluctuations, and measurement uncertainty. In this study, we explored the observed variability in vertical distributions of refractive index measured with a tethered-balloon-based marine atmospheric profiling system (MAPS). MAPS profiled the atmosphere from approximately 0.5 to 50 m, with instantaneous (order 1 s) measurements performed at each profiled altitude. To explore whether the observed scatter could be largely explained by (inertial-scale) turbulent fluctuations, we simulated refractive index fluctuations with a spectral-based turbulent refractive index fluctuation (TRIF) model. TRIF was optimized based on the MAPS measurements to determine a vertical length scale of the turbulence. The scales computed in the optimization were reasonable based on other estimates in the literature under similar conditions. However, finer-scale trends of the length scale with atmospheric stability did not match expectations, and thus the estimated length scales may be considered more as an order-of-magnitude estimate rather than an exact measurement of this scale. The ability to match the observed variability in the MAPS data using a turbulence model with a reasonable choice of vertical length scale suggests that the MAPS variability is dominated by physical processes such as turbulence rather than being primarily driven by measurement uncertainty.

Large knowledge gaps concerning the effect of ocean surface waves on near-surface vertical distributions of temperature and humidity exist due to practical limitations and sensor fidelity challenges of direct measurements. Measurements of temperature and humidity are classically made using rocket- or radiosondes and fixed weather stations and can utilize a tethered profiling system. However, these measurement systems have limitations when obtaining wave-coherent measurements near the sea surface. Consequently, boundary layer similarity models are commonly employed to fill in near-surface measurement gaps despite the documented shortcomings of the models in this region. Thus, this manuscript presents a near-surface wave-coherent measurement platform that measures high-temporal-resolution vertical distributions of temperature and humidity down to ~0.3 m above the instantaneous sea surface. The design of the platform is described along with preliminary observations obtained during a pilot experiment. Ocean surface-wave phase-resolved vertical profiles are also demonstrated from the observations.

This study investigates the use of numerical weather prediction (NWP) ensembles to aid refractivity inversion problems during surface ducting conditions. Thirteen sets of measured thermodynamic atmospheric data from an instrumented helicopter during the Wallops Island field experiment are fit to a two-layer parametric surface duct model to characterize the duct. This modeled refractivity is considered "ground truth" for the environment and is used to generate the synthetic radar propagation loss field that then drives the inversion process. The inverse solution (refractivity derived from the synthetic radar data) is compared with this ground truth refractivity. For the inversion process, parameters of the two-layer model are iteratively estimated using genetic algorithms to determine which parameters likely produced the synthetic radar propagation field. Three numerical inversion experiments are conducted. The first experiment utilizes a randomized set of two-layer model parameters to initialize the inversion process, while the second experiment initializes the inversion using NWP ensembles, and the third experiment uses NWP ensembles to both initialize and restrict the parameter search intervals used in the inversion process. The results show that incorporation of NWP data benefits the accuracy and speed of the inversion result. However, in a few cases, an extended NWP ensemble forecast period was needed to encompass the ground truth parameters in the restricted search space. Furthermore, it is found that NWP ensemble populations with smaller spreads are more likely to hinder the inverse process than to aid it.

Dynamic refractive environments within the marine atmospheric boundary layer (MABL) pose difficulties in the prediction of X‐band radar wave propagation due to natural phenomena such as evaporation ducts (ED). This study utilizes a unique data set collected during the Coupled Air‐Sea Processes and Electromagnetic Ducting Research (CASPER)‐East field campaign, including multiple refractivity estimation methods and twelve point‐to‐point (PTP) electromagnetic datasets, to assess the efficacy of PTP inversion techniques for remote sensing of atmospheric refractivity within the MABL. Comparison of refractivity between the inverse and other refractivity methods show reasonable evaporation duct height estimates by the inversion, and inverse‐based propagation predictions are also shown to be more accurate than propagation based on other refractivity prediction methods: numerical weather prediction, theory, and in situ atmospheric measurements. These results propose the effectiveness of a PTP metaheuristic radar inversion to remotely sense refractive environments from radar propagation measurements in stable and unstable atmospheric conditions.