Abstract This study reviews the current state of spaceborne atmospheric tomography and assesses its scientific potential to address key science questions related to the carbon cycle, planetary boundary layer (PBL), and clouds and aerosols. We explore a range of hypothetical mission architectures to characterize the multidimensional trade space of tomographic performance, which depends on observation geometry, instrument characteristics, and the target field. We identified the effective vertical and horizontal reconstruction resolutions as a key parameter linking tomographic capabilities to scientific return. Our evaluation uses the newly developed JPL Tomography Simulator, which efficiently simulates tomographic reconstruction of realistic cloud and water vapor fields under various observational configurations. Simulations show that a system with 9 viewing angles within ±70° of nadir could achieve effective resolutions on the order of tens of meters for clouds and hundreds of meters for water vapor in both the horizontal and vertical. These fine-resolution volumetric observations would support detailed studies of PBL thermodynamics, entrainment processes, and three-dimensional radiative effects in clouds. The findings may extend to other atmospheric constituents, such as trace gases and aerosols, which share similar spatial structures. We further identify tomographic technology maturation targets that would improve mission formulation rigor with research program support. In particular, we highlight the promise of machine learning approaches to overcome the significant computational demands of current tomographic reconstruction techniques. These advancements have the potential to improve future observing system design and scientific return across a broad range of atmospheric disciplines. Significance Statement This study assesses the potential of atmospheric tomography for addressing key questions related to the carbon cycle, the planetary boundary layer (PBL), and clouds and aerosols. No current single technology provides the required combination of fine horizontal and vertical resolution for many science questions identified in the NASA PBL Incubation Study Team Report. Compared to proposed observing systems consisting of joint orbital and suborbital components, tomographic remote sensing could provide the necessary observations at finer resolution or at reduced cost. The main area for advancement is reducing the computational demands of current tomography algorithms, thereby maturing the method toward operational use. If successful, tomography could unlock atmospheric measurements with unprecedented resolution and spatial coverage.

Cloud droplet size plays a key role in precipitation formation, the cloud radiative effect, and the coupling of clouds to atmospheric turbulence. Due to this confluence of processes, measurements of droplet size are critical to our understanding of the climate system. Satellite remote sensing is the primary means of collecting these measurements over the globe and it is generally considered that multi-spectral or polarized measurements are required to isolate droplet size from droplet concentration. Here, we challenge this paradigm. We hypothesize that key information about the droplet size is encoded in the multi-scale structure of multi-angle imagery enabling the retrieval of droplet size from monochrome non-polarized measurements in the visible spectrum. We prove this hypothesis using forward and inverse (i.e., tomographic) 3D radiative transfer modeling based on realistic cloud models. We demonstrate that a vertical profile of droplet effective radius and the 3D volume extinction coefficient of the cloud can be retrieved using high-resolution (↭ 50 m) imagery at nine viewing angles using only the red channel. We attribute this success to the turbulent nature of cumuliform clouds that produces tenuous, optically thin regions at cloud edge that are only detectable at high spatial resolution. Observations of these regions are sensitive to scattering phase function, hence to droplet size, due to the dominance of low-order scattering. Finally, we verify that the addition of multi-spectral measurements in the shortwave infrared improves the tomographic retrieval of both the 1D droplet effective radius profile and the 3D extinction coefficient field through their improved sensitivity to regions where higher-order scattering dominates.

A Markov chain approach is developed to model polarized mid-to long-wave infrared radiative transfer in an optically anisotropic medium. Such a medium contains oriented non-spherical particles with azimuthal randomness. Our model considers variations of temperature, pressure, gas concentration, and particle size distribution in the vertical dimension of the medium and resolves the total and polarized radiation in twodimensional angular space. It also accounts for emission, scattering, and absorption of the medium, as well as directional and polarized surface emission and reflection. Illustrative simulations are performed using MODIS infrared bands centered at 9.73, 11.03, and 12.02 mu m and several standard model atmospheres containing oriented dust or ice spheroids. The results are compared to those obtained for spherical droplets. Our preliminary numerical results demonstrate that while infrared brightness temperature contains information about particle amount, size, and layer height, adding multi-angle and spectro-polarimetry provides further remote sensing sensitivity to type, orientation, and morphology of the non-spherical particles. When reliable a priori information on the atmospheric physical temperature and absorbing gas profiles is available, infrared multi-angle polarimetry is a promising tool to fill the gap of shortwave and microwave remote sensing by resolving micro-meter scale particle properties to which shortwave and microwave frequencies have less sensitivity. Our simulation also reveals that solar radiation exerts a pronounced influence on the top-of-atmosphere brightness temperature when the wavelength approaches the short-wavelength end of the mid-wave infrared (approximate to 3-4 mu m).

Computed cloud tomography (CCT) converts multi-angle imagery of vertically-developed cumulus into 3D gridded distributions of extinction coefficients. Existing CCT algorithms have 3D radiative transfer (RT) code at their core to predict the multi-angle images that are compared with observations in an optimization scheme. However, both 3D RT (iterative solution of a 5-dimensional integral equation) and optimization over 10s to 100s of thousands of unknowns (the 3D gridded extinction coefficients) are slow to converge. The larger the cloud, the slower the convergence, thus limiting current CCT methods to relatively small clouds in weak convection regimes. Moreover, large opaque clouds have a special optical characteristic called a “veiled core’ (VC). It is the region deep inside the cloud where detailed spatial structure has only noise-level impact on observations. Robust CCT will therefore retrieve a simplified VC structure defined by a small number of parameters, but still yield accurate estimates of cloud-scale properties such as total water content. We therefore develop a “VC-aware’ CCT algorithm with just two parameters to fit inside the VC. The new CCT has two stages. The first uses machine learning to infer from the multi-angle imagery the integrals of extinction along every view from every pixel; it is described in a companion paper. Here, we present an new algebraic reconstruction technique (ART) to retrieve the extinction values from their line-integrals that accounts adaptively for the VC. It performs well in both efficiency and accuracy on two test cases, even in the presence of random noise in its input.

Cumuliform clouds in Earth's lower atmosphere play important roles in the radiative balance and hydrological cycle of the climate system. Yet key processes unfolding in these clouds, such as aerosol interactions and precipitation initiation, are still poorly understood. Current space-based cloud observation methods are inadequate for inferring the internal structure of clouds outside of a narrow transect that is probed actively by radar and lidar. Cloud tomography is an emerging technique that uses passive imaging of a cloud target from multiple locations with a large angular range to infer internal cloud structure. Many low convective clouds only have a lifetime of 15-25 min, necessitating autonomous scheduling of observation targets as they appear. Onboard autonomous scheduling is formulated as a mixed-integer optimization problem (MILP) with a finite time horizon and a reward scheme designed to maximize the angular range of the observations. A finite time horizon MILP scheduler is well suited to this mission because the short lifetime of low convective clouds creates a natural time horizon. This MILP can solve for an optimal observation schedule in a maximum time of 15 ms on a desktop CPU. The MILP scheduler is able to observe nearly 60% more targets than a conventional push-broom camera configuration. This initial result is promising and demonstrates the need for continued research in this area.

Optical communications (OC) through water bodies is an attractive technology for a variety of applications. Thanks to current single-photon detection capabilities, OC receiver systems can reliably decode very weak transmitted signals. This is the regime where pulse position modulation is an ideal scheme. However, there has to be at least one photon that goes through the pupil of the fore optics and lands in the assigned time bin. We estimate the detectable photon budget as a function of range for propagation through ocean water, both open and coastal. We make realistic assumptions about the water’s inherent optical properties, specifically, absorption and scattering coefficients, as well as the strong directionality of the scattering phase function for typical hydrosol populations. We adopt an analytical (hence very fast) path-integral small-angle solution of the radiative transfer equation for multiple forward-peaked scattering across intermediate to large optical distances. Integrals are performed both along the directly transmitted beam (whether or not it is still populated) and radially away from it. We use this modeling framework to estimate transmission of a 1 J pulse of 532 nm light through open ocean and coastal waters. Thresholds for single-photon detection per time bin are a few km and a few 100 m. These are indicative estimates that will be reduced in practice due to sensor noise, background light, turbulence, bubbles, and so on, to be included in future work.

We use a customized radiative transfer model to show that sharp (∼10 m resolution) images of the Venus surface can be achieved at night in spectral windows free of CO2 absorption found between 1.0 and 1.2μm using a camera at 47 km altitude, just below the planet’s optically thick clouds. This is in spite of the Rayleigh scattering by the dense but still semi-transparent lower atmosphere, and the potential for underlying hazes beneath the clouds. The thermal radiation transmitted directly to the camera forms images of spatially varying surface emissivity and/or temperature at the native sensor resolution, platform stability permitting and under reasonable seeing conditions. Near-isotropic Rayleigh scattering dominates in the 1.0μm window. Combined with near-Lambertian reflections off the base of the cloud layer, the diffuse light field builds up a background radiance from surface emission averaged spatially out to several 10s of km, i.e., beyond the camera’s field-of-view. At the longer wavelengths (1.1 and 1.18μm windows), the sub-cloud atmosphere itself partially absorbs (hence less direct light), and therefore weakly emits (hence more background light), but the rapidly decreasing Rayleigh scattering compensates and contrast is maintained. In all cases, we demonstrate that the directly-transmitted surface-leaving radiance from the native sensor resolution element (∼10 m) is a significant fraction of the total radiance, and thus can be detected above the background light. Extending down to the 0.85 and 0.90μm spectral windows, there is less direct and more background due to the enhanced Rayleigh scattering, but the resulting reduction in contrast can be mitigated by co-adding the ∼10 m pixels. This technological advance will open a new era in Venusian geology by enabling discrimination between different surface materials at fine scales. Moreover, potentially active volcanism on our sister planet may be revealed by surface spots that are much hotter than their surroundings.

Marine food chains are highly stressed by aggressive fishing practices and environmental damage. Aquaculture has increasingly become a source of seafood which spares the deleterious impact on wild fisheries. However, continually monitoring water quality to successfully grow and harvest fish is labor intensive. The Hybrid Aerial Underwater Robotic System (HAUCS) is an Internet of Things (IoT) framework for aquaculture farms to relieve the farm operators of one of the most labor-intensive and time-consuming farm operations: water quality monitoring. To this end, HAUCS employs a swarm of unmanned aerial vehicles (UAVs) or drones integrated with underwater measurement devices to collect the in situ water quality data from aquaculture ponds. A critical aspect in HAUCS is to develop an effective path planning algorithm to be able to sample all the ponds on the farm with minimal resources (i.e., the number of UAVs and the power consumption of each UAV). Three methods of path planning for the UAVs are tested, a Graph Attention Model (GAM), the Google Linear Optimization Package (GLOP) and our proposed solution, the HAUCS Path Planning Algorithm (HPP). The designs of these path planning algorithms are discussed, and a simulator is developed to evaluate these methods’ performance. The algorithms are also experimentally validated at Southern Illinois University’s Aquaculture Research Center to demonstrate the feasibility of HAUCS. Based on the simulations and experimental studies, HPP is particularly suited for large farms, while GLOP or GAM is more suited to small or medium-sized farms.

To address critical gaps identified by the National Academies of Sciences, Engineering, and Medicine in the current Earth system observation strategy, the 2017-27 Decadal Survey for Earth Science and Applications from Space recommended incubating concepts for future targeted observables including the atmospheric planetary boundary layer (PBL). A subsequent NASA PBL Incubation Study Team Report identified measurement requirements and activities for advancing the maturity of the technologies applicable to the PBL targeted observables and their associated science and applications priorities. While the PBL is the critical layer where humans live and surface energy, moisture, and mass exchanges drive the Earth system, it is also the farthest and most inaccessible layer for spaceborne instruments. Here we document a PBL retrieval observing system simulation experiment (OSSE) framework suitable for assessing existing and new measurement techniques and determining their accuracy and improvements needed for addressing the elevated Decadal Survey requirements. In particular, the benefits of large-eddy simulation (LES) are emphasized as a key source of high-resolution synthetic observations for key PBL regimes: from the tropics, through subtropics and midlatitudes, to subpolar and polar regions. The potential of LES-based PBL retrieval OSSEs is explored using six instrument simulators: Global Navigation Satellite System-Radio Occultation, differential absorption radar, visible to shortwave infrared spectrometer, infrared sounder, Multi-angle Imaging SpectroRadiometer, and microwave sounder. The crucial role of LES in PBL retrieval OSSEs and some perspectives for instrument developments are discussed.

Our global understanding of clouds and aerosols relies on the remote sensing of their optical, microphysical, and macrophysical properties using, in part, scattered solar radiation. These retrievals assume that clouds and aerosols form plane-parallel, homogeneous layers and utilize 1D radiative transfer (RT) models, limiting the detail that can be retrieved about the 3D variability in cloud and aerosol fields and inducing biases in the retrieved properties for highly heterogeneous structures such as cumulus clouds and smoke plumes. To overcome these limitations, we introduce and validate an algorithm for retrieving the 3D optical or microphysical properties of atmospheric particles using multi-angle, multi-pixel radiances and a 3D RT model. The retrieval software, which we have made publicly available, is called Atmospheric Tomography with 3D Radiative Transfer (AT3D). It uses an iterative, local optimization technique to solve a generalized least squares problem and thereby find a best-fitting atmospheric state. The iterative retrieval uses a fast, approximate Jacobian calculation, which we have extended from Levis et al. (2020) to accommodate open and periodic horizontal boundary conditions (BCs) and an improved treatment of non-black surfaces. We validated the accuracy of the approximate Jacobian calculation for derivatives with respect to both the 3D volume extinction coefficient and the parameters controlling the open horizontal boundary conditions across media with a range of optical depths and single-scattering properties and find that it is highly accurate for a majority of cloud and aerosol fields over oceanic surfaces. Relative root mean square errors in the approximate Jacobian for a 3D volume extinction coefficient in media with cloud-like single-scattering properties increase from 2 % to 12 % as the maximum optical depths (MODs) of the medium increase from 0.2 to 100.0 over surfaces with Lambertian albedos <0.2. Over surfaces with albedos of 0.7, these errors increase to 20 %. Errors in the approximate Jacobian for the optimization of open horizontal boundary conditions exceed 50 %, unless the plane-parallel media providing the boundary conditions are optically very thin (∼0.1). We use the theory of linear inverse RT to provide insight into the physical processes that control the cloud tomography problem and identify its limitations, supported by numerical experiments. We show that the Jacobian matrix becomes increasing ill-posed as the optical size of the medium increases and the forward-scattering peak of the phase function decreases. This suggests that tomographic retrievals of clouds will become increasingly difficult as clouds become optically thicker. Retrievals of asymptotically thick clouds will likely require other sources of information to be successful. In Loveridge et al. (2023a; hereafter Part 2), we examine how the accuracy of the retrieved 3D volume extinction coefficient varies as the optical size of the target medium increases using synthetic data. We do this to explore how the increasing error in the approximate Jacobian and the increasingly ill-posed nature of the inversion in the optically thick limit affect the retrieval. We also assess the accuracy of retrieved optical depths and compare them to retrievals using 1D radiative transfer.

Does radiometry (e.g., signal-to-noise ratio) limit the performance of near-IR subcloud imaging of our sister planet's surface at night? It does not. We compute subcloud radiometry using above-cloud observations, an assumed ground temperature, sub-cloud absorption and emission modeling, and Rayleigh scattering simulations. We thus confirm both archival and recent studies that deployment of a modest subcloud camera does enable high-resolution surface imaging.

Chapter 15 Satellite and Airborne Remote Sensing of Clouds and Aerosols Alexander Marshak, Alexander Marshak NASA Goddard Space Flight Center, Greenbelt, MD, USASearch for more papers by this authorAnthony B. Davis, Anthony B. Davis NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USASearch for more papers by this author Alexander Marshak, Alexander Marshak NASA Goddard Space Flight Center, Greenbelt, MD, USASearch for more papers by this authorAnthony B. Davis, Anthony B. Davis NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USASearch for more papers by this author Book Editor(s):Yangang Liu, Yangang LiuSearch for more papers by this authorPavlos Kollias, Pavlos KolliasSearch for more papers by this author First published: 30 November 2023 https://doi.org/10.1002/9781119529019.ch15Book Series:Geophysical Monograph Series AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat Summary We survey overhead remote sensing of cloud and aerosol properties, from either aircraft or satellites. Standoff distances range from NASA's P-3B aircraft at only ≈3.5 km above cloud top to DSCOVR at Lagrange-1, ≈1,500,000 km toward the Sun. Although not a remote-sensing technique per se, deployment of in situ radiometric sensors that collect photons rather than cloud particles is also briefly discussed. We run the spectral gamut from ultraviolet to microwaves, for both active and passive modalities. Emphasis is on the physics of sensors and retrieval algorithms. Moreover, since neither are perfect, we devote a section to uncertainty quantification. Pros and cons of high and low spatial resolutions are presented in connection with the need for fine or course spectral sampling and/or global coverage versus targeted operation. Angular sampling is also considered, particularly, in connection with polarization. We touch on the need for “research” algorithms applied to selected observations, often overflying a field campaign. These specialty algorithms require some level of human supervision and thus complement their operational counterparts, which must be globally applicable and automated with as few mishaps as possible. Finally, we do not shy away from describing a few “out-of-the-box” methods that open the path for future missions. References Abdalati , W. , Zwally , H. 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Our global understanding of clouds and aerosols relies on the remote sensing of their optical, microphysical, and macrophysical properties using, in part, scattered solar radiation. Current retrievals assume clouds and aerosols form plane-parallel, homogeneous layers and utilize 1D radiative transfer (RT) models. These assumptions limit the detail that can be retrieved about the 3D variability in the cloud and aerosol fields and induce biases in the retrieved properties for highly heterogeneous structures such as cumulus clouds and smoke plumes. In Part 1 of this two-part study, we validated a tomographic method that utilizes multi-angle passive imagery to retrieve 3D distributions of species using 3D RT to overcome these issues. That validation characterized the uncertainty in the approximate Jacobian used in the tomographic retrieval over a wide range of atmospheric and surface conditions for several horizontal boundary conditions. Here, in Part 2, we test the algorithm's effectiveness on synthetic data to test whether the retrieval accuracy is limited by the use of the approximate Jacobian. We retrieve 3D distributions of a volume extinction coefficient (sigma(3D)) at 40 m resolution from synthetic multi-angle, mono-spectral imagery at 35 m resolution derived from stochastically generated cumuliform-type clouds in (1 km)(3) domains. The retrievals are idealized in that we neglect forward-modelling and instrumental errors, with the exception of radiometric noise; thus, reported retrieval errors are the lower bounds. sigma(3D) is retrieved with, on average, a relative root mean square error (RRMSE) < 20 % and bias < 0.1 % for clouds with maximum optical depth (MOD) < 17, and the RRMSE of the radiances is < 0.5 %, indicating very high accuracy in shallow cumulus conditions. As the MOD of the clouds increases to 80, the RRMSE and biases in sigma(3D) worsen to 60 % and -35 %, respectively, and the RRMSE of the radiances reaches 16 %, indicating incomplete convergence. This is expected from the increasing ill-conditioning of the inverse problem with the decreasing mean free path predicted by RT theory and discussed in detail in Part 1. We tested retrievals that use a forward model that is not only less ill-conditioned (in terms of condition number) but also less accurate, due to more aggressive delta-M scaling. This reduces the radiance RRMSE to 9 % and the bias in sigma(3D) to -8 % in clouds with MOD similar to 80, with no improvement in the RRMSE of sigma(3D). This illustrates a significant sensitivity of the retrieval to the numerical configuration of the RT model which, at least in our circumstances, improves the retrieval accuracy. All of these ensemble-averaged results are robust in response to the inclusion of radiometric noise during the retrieval. However, individual realizations can have large deviations of up to 18 % in the mean extinction in clouds with MOD similar to 80, which indicates large uncertainties in the retrievals in the optically thick limit. Using less ill-conditioned forward model tomography can also accurately infer optical depths (ODs) in conditions spanning the majority of oceanic cumulus fields (MOD < 80), as the retrieval provides ODs with bias and RRMSE values better than -8 % and 36 %, respectively. This is a significant improvement over retrievals using 1D RT, which have OD biases between -30 % and -23 % and RRMSE between 29 % and 80 % for the clouds used here. Prior information or other sources of information will be required to improve the RRMSE of sigma(3D) in the optically thick limit, where the RRMSE is shown to have a strong spatial structure that varies with the solar and viewing geometry.

Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rainwater mixing ratios ( q c and q r , respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large-eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulated q c closely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulated q r properties, though, with bulk simulated q r consistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produce q r that is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

There are a handful of spectral windows in the near-IR through which we can see down to Venus' surface on the night side of the planet. The surface of our sister planet has thus been imaged by sensors on Venus-orbiting platforms (Venus Express, Akatsuki) and during fly-by with missions to other planets (Galileo, Cassini). The most tantalizing finding, so far, is the hint of possible active volcanism. However, the thermal radiation emitted by the searing (c. 475 degrees C) surface of Venus has to get through the opaque clouds between 50 and 70 km altitude, as well as the sub-cloud atmosphere. In the clouds, the light is not absorbed but scattered, many times. This results in blurring the surface imagery to the point where the smallest discernible feature is roughly 100 km in size, full-width half-max (FWHM), and this has been explained using numerical models. We describe a new analytical modeling framework for predicting the width of the atmospheric point-spread function (APSF), which is what determines the effective resolution of surface imaging from space. Our best estimates of the APSF width for the 1-to-1.2 micron spectral range are clustered around 130 km FWHM. Interestingly, this is somewhat larger than the accepted value of about 100 km, which is based on visual image inspection and numerical simulations.

The climate crisis we are facing calls for significant improvements in our understanding of natural phenomena, with clouds being identified as a dominant source of uncertainty. To this end, the emerging field of 3D computed cloud tomography (CCT) aims to more precisely characterize clouds by utilizing multi-dimensional imaging to reconstruct their outer and inner structure. In this paper, we propose a future Earth observation mission concept, driven by the needs of CCT, that operates constellation of NanoSats to provide multi-angular, spectrally-resolved, spatial and temporal scientific measurements of natural atmospheric phenomena. Our proposed mission, GEOSCAN, will on-board active steering capability to rapidly reconfigure networked swarm of autonomous Nanosats to track evolving phenomena of interest, on-demand, in real-time. We present the structure of the GEOSCAN constellation and discuss details of the mission concept from both science and engineering perspectives. On the science side, we out-line the types of remote Earth observation measurements that GEOSCAN enables beyond the state-of-the-art, and how such measurements translate to improvements in CCT that can lead to reduction in uncertainty of the global climate models (GCMs). From the engineering side, we investigate feasibility of the concept starting from hardware components of the NanoSat that form the basis of the constellation. In particular, we focus on the active steering capability of the GEOSCAN with algorithmic approaches that enable coordination from new software. We identify technology gaps that need to be bridged and discuss other aspects of the mission that require in-depth analysis to further mature the concept.

Aerial drones have great potential to monitor large areas quickly and efficiently. Aquaculture is an industry that requires continuous water quality data to successfully grow and harvest fish. The Hybrid Aerial Underwater Robotic System (HAUCS) is designed to collect water quality data of aquaculture ponds to reduce labor costs for farmers. The routing of drones to cover each fish pond on an aquaculture farm can be reduced to the Vehicle Routing Problem. A dataset is created to simulate the distribution of ponds on a farm and is used to assess the HAUCS Path Planning Algorithm (HPP). Its performance is compared with the Google Linear Optimization Package (GLOP) and a Graph Attention Model (GAM) for routing problems. GLOP is the most efficient solver for 50 to 200 ponds at the expense of long run times, while HPP outperforms the other methods in solution quality and run time for instances larger than 200 ponds.

The probability distribution function of photon path length in a scattering medium contains valuable information on that medium. While strongly scattering optically thick media have been extensively studied, in particular, with resort to the diffusion approximation, optically thin media have received much less attention. Here, we derive the probability distribution functions for the lengths of singly- and twice-scattered photon paths in an isotropically scattering slab of optical thickness τ, for both reflected and transmitted photons. We show that, in the case of an optically thin slab, these photons dominate the overall response of the medium. We confirm that the second moment of the distribution deviates from the ballistic limit in the case of collimated illumination. Interestingly, we show that under diffuse illumination, the second moment of the distribution is dominated by unscattered transmitted photons, hence is proportional to lnτ, and independent of the phase function. Higher moments of order n (≥3) scale as Hnτn-2. When only reflected or transmitted photons are considered, the second moment scales as H2τ-1, whatever the illumination and viewing conditions. This provides direct access to τ. These theoretical results are extensively supported by Monte Carlo ray-tracing simulations. Extension to anisotropic scattering using these same simulations shows that the results hold, given a scaling factor for collimated illumination, and without any dependence on the phase function for diffuse illumination. These results overall demonstrate that the optical thickness of an optically thin slab can be estimated from the second moment of the distribution. Along with the fact that under diffuse illumination the geometrical thickness can be derived from the first moment of the distribution, this proves that the extinction coefficient of the medium can be estimated from the combination of both moments. This study thus opens new perspectives for non-invasive characterization of optically thin media either in the laboratory or by remote sensing.

We argue that the Earth Polychromatic Imaging Camera (EPIC) on the Deep Space Climate ObserVatoRy (DSCOVR) platform has blazed new pathways in observational technology, starting with its ∼ 1.5 × 106 km stand-off distance, but also in remote sensing science. We focus here on EPIC’s two oxygen absorption channels that 1) are unique in their spectral sampling and 2) have stimulated deep innovation in cloud remote sensing using Differential Oxygen Absorption Spectroscopy (DO2AS). Although first formulated 6 decades ago, DO2AS-based cloud probing from overhead assets is still an emerging observational technique. It is indeed somewhat paradoxical that one should use absorption by a gas to assay scattering by particles. After surveying the history of space-based DO2AS, and looking into its future, we see that EPIC/DSCOVR marks an inflection point in this important development. EPIC’s unique DO2AS capability motivated a notable sequence of papers revisited here. This research indeed spawned a rare occurrence of information content analysis coming from radically different—yet complementary—perspectives. First, we adopted the increasingly popular machinery of optimal estimation (OE) that is grounded in Bayesian statistics and uses a somehow linearized radiative transfer (RT) model. Nonetheless, OE feels like a black-box algorithm that outputs a number of “degrees of freedom” (a.k.a. independent pieces of information about clouds under observation). However, the very same conclusions are reached using fully transparent physics-based modeling for the RT, with a few approximations that enable closed-form analytical formulation. Lastly, we preview a novel DO2AS technique for regaining shortwave sensitivity to cloud optical thickness past the threshold where cloud reflectivity flattens off.