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NASA NTRS2001

Bio-Optical Measurement and Modeling of the California Current and Polar Oceans

This Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) project contract supports in situ ocean optical observations in the California Current, Southern Ocean, Indian Ocean as well as merger of other in situ data sets we have collected on various global cruises supported by separate grants or contracts. The principal goals of our research are to validate standard or experimental products through detailed bio-optical and biogeochemical measurements, and to combine ocean optical observations with advanced radiative transfer modeling to contribute to satellite vicarious radiometric calibration and advanced algorithm development. In collaboration with major oceanographic ship-based observation programs funded by various agencies (CalCOFI, US JGOFS, NOAA AMLR, INDOEX and Japan/East Sea) our SIMBIOS effort has resulted in data from diverse bio-optical provinces. For these global deployments we generate a high-quality, methodologically consistent, data set encompassing a wide-range of oceanic conditions. Global data collected in recent years have been integrated with our on-going CalCOFI database and have been used to evaluate Sea-Viewing Wide Field-of-view Sensor (SeaWiFS) algorithms and to carry out validation studies. The combined database we have assembled now comprises more than 700 stations and includes observations for the clearest oligotrophic waters, highly eutrophic blooms, red-tides and coastal case two conditions. The data has been used to validate water-leaving radiance estimated with SeaWiFS as well as bio optical algorithms for chlorophyll pigments. The comprehensive data is utilized for development of experimental algorithms (e.g., high-low latitude pigment transition, phytoplankton absorption, and cDOM).

Mitchell, B. Greg↗
NASA NTRS2001

Satellite Ocean Color Validation Using Merchant Ships

A collaborative measurement program for evaluating satellite-derived ocean color has been developed based on ships of opportunity (merchant, oceanographic) and specific instrumentation, the SIMBAD radiometer. The purpose of the measurement program is to complement, in a cost-effective way, dedicated evaluation experiments at sea, which are expensive, cannot be carried out over the full range of expected oceanic and atmospheric conditions, and generally provide a few match-ups. Ships participate in the program on a volunteer basis or at a very small cost, and measurement procedures do not interfere with other ship activities. The SIMBAD radiometer is a portable, easy-to-operate instrument that measures the basic ocean color variables, namely aerosol optical thickness and water-leaving radiance, in typical spectral bands of ocean-color sensors, i.e., 443, 490, 560, 670, and 870 nm. Measuring these variables at the time of satellite overpass is usually sufficient to verify satellite-derived ocean color and to evaluate atmospheric correction algorithms. Any ordinary crew can learn quickly how to make measurements. Importantly, the ship is not required to stop, making it possible to collect data along regular routes traveled by merchant ships in the world's oceans.

Frouin, Robert↗
NASA NTRS2002

The Change in Oceanic O2 Inventory Associated with Recent Global Warming

Oceans general circulation models predict that global warming may cause a decrease in the oceanic O2 inventory and an associated O2 outgassing. An independent argument is presented here in support of this prediction based on observational evidence of the ocean's biogeochemical response to natural warming. On time scales from seasonal to centennial, natural O2 flux/heat flux ratios are shown to occur in a range of 2 to 10 nmol O2 per Joule of warming, with larger ratios typically occurring at higher latitudes and over longer time scales. The ratios are several times larger than would be expected solely from the effect of heating on the O2 solubility, indicating that most of the O2 exchange is biologically mediated through links between heating and stratification. The change in oceanic O2 inventory through the 1990's is estimated to be 0.3 - 0.4 x 10(exp 14) mol O2 per year based on scaling the observed anomalous long-term ocean warming by natural O2 flux/heating ratios and allowing for uncertainty due to decadal variability. Implications are discussed for carbon budgets based on observed changes in atmospheric O2/N2 ratio and based on observed changes in ocean dissolved inorganic carbon.

Keeling, Ralph↗
NASA NTRS2002

Oceans, Ice Shells, and Life on Europa

The four large satellites of Jupiter are famous for their planet-like diversity and complexity, but none more so than ice-covered Europa. Since the provocative Voyager images of Europa in 1979, evidence has been mounting that a vast liquid water ocean may lurk beneath the moon's icy surface. Europa has since been the target of increasing and sometimes reckless speculation regarding the possibility that giant squid and other creatures may be swimming its purported cold, dark ocean. No wonder Europa tops everyone's list for future exploration in the outer solar system (after the very first reconnaissance of Pluto and the Kuiper belt, of course). Europa may be the smallest of the Galilean moons (so-called because they were discovered by Galileo Galilei in the early 17th century) but more than makes up for its diminutive size with a crazed, alien landscape. The surface is covered with ridges hundreds of meters high, domes tens of kilometers across, and large areas of broken and disrupted crust called chaos. Some of the geologic features seen on Europa resemble ice rafts floating in polar seas here on Earth-reinforcing the idea that an ice shell is floating over an ocean on this Moon-size satellite. However, such features do not prove that an ocean exists or ever did. Warm ice is unusually soft and will flow under its own weight. If the ice shell is thick enough, the warm bottom of the shell will flow, as do terrestrial glaciers. This could produce all the observed surface features on Europa through a variety of processes, the most important of which is convection. (Convection is the vertical overturn of a layer due to heating or density differences-think of porridge or sauce boiling on the stove.) Rising blobs from the base of the crust would then create the oval domes dotting Europa's surface. The strongest evidence for a hidden ocean beneath Europa's surface comes from the Galileo spacecraft's onboard magnetometer, which detected fluctuations in Jupiter's magnetic field consistent with a conductor inside Europa. The most likely conductor: a somewhat salty ocean.

Schenk, Paul↗
NASA NTRS2001

Seasonal Variation in Precipitation Patterns to the Global Ocean: An Analysis of the GPCP Version 2 Data Set

An analysis of temporal and spatial variation of oceanic precipitation was conducted on the GPCP version two data set. While the precipitation patterns observed are generally similar to the previous climatologies, new features and greater detail of global precipitation were revealed from out analysis of the GPCP data set. High precipitation waw observed in the inter-tropical convergence zone, the South Pacific convergence zone, and the storm tracks in the North Pacific and Atlantic Oceans. Low precipitation was observe in the Polar regions and in the subtropics of the East Pacific, East Atlantic, and the Southeast and Northwest Indian Ocean. The spatial coverage of these high and low precipitation regions changed thruough the year. A strong seasonal cycle or precipitation was observed for the Northern and the Southern Hemispheres and for each ocean basin. Global precipitation also varied significantly with both latitude and longitude, with a latitudinal maximum at 56 degrees South, 39 degrees South, 4 degrees South, 6 degrees North, 39 degrees North, and 56 degress North, and a longitudinal maxiumum over each ocean. The seasonal varying precipitation patterns are a foundation for evaluating the effect of wet deposition on ocean circulation, flux of chemical species, and its effect on marine ecosystems.

Miller, Richard↗
NASA NTRS2003

Fresh Water Content Variability in the Arctic Ocean

Arctic Ocean model simulations have revealed that the Arctic Ocean has a basin wide oscillation with cyclonic and anticyclonic circulation anomalies (Arctic Ocean Oscillation; AOO) which has a prominent decadal variability. This study explores how the simulated AOO affects the Arctic Ocean stratification and its relationship to the sea ice cover variations. The simulation uses the Princeton Ocean Model coupled to sea ice. The surface forcing is based on NCEP-NCAR Reanalysis and its climatology, of which the latter is used to force the model spin-up phase. Our focus is to investigate the competition between ocean dynamics and ice formation/melt on the Arctic basin-wide fresh water balance. We find that changes in the Atlantic water inflow can explain almost all of the simulated fresh water anomalies in the main Arctic basin. The Atlantic water inflow anomalies are an essential part of AOO, which is the wind driven barotropic response to the Arctic Oscillation (AO). The baroclinic response to AO, such as Ekman pumping in the Beaufort Gyre, and ice meldfreeze anomalies in response to AO are less significant considering the whole Arctic fresh water balance.

Hakkinen, Sirpa↗
NASA NTRS2004

Measurements of Ocean Surface Scattering Using an Airborne 94-GHz Cloud Radar: Implication for Calibration of Airborne and Spaceborne W-band Radars

Scattering properties of the Ocean surface have been widely used as a calibration reference for airborne and spaceborne microwave sensors. However, at millimeter-wave frequencies, the ocean surface backscattering mechanism is still not well understood, in part, due to the lack of experimental measurements. During the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE), measurements of ocean surface backscattering were made using a 94-GHz (W-band) cloud radar onboard a NASA ER-2 high-altitude aircraft. The measurement set includes the normalized Ocean surface cross section over a range of the incidence angles under a variety of wind conditions. Analysis of the radar measurements shows good agreement with a quasi-specular scattering model. This unprecedented dataset enhances our knowledge about the Ocean surface scattering mechanism at 94 GHz. The results of this work support the proposition of using the Ocean surface as a calibration reference for airborne millimeter-wave cloud radars and for the ongoing NASA CloudSat mission, which will use a 94-GHz spaceborne cloud radar for global cloud measurements.

Li, Li-Hua↗
NASA NTRS2004

Airborne Spectral Measurements of Ocean Directional Reflectance

During summer of 2001 NASA's Cloud Absorption Radiometer (CAR) obtained measurement of ocean angular distribution of reflected radiation or BRDF (bidirectional reflectance distribution function) aboard the University of Washington Convair CV-580 research aircraft under cloud-free conditions. The measurements took place aver the Atlantic Ocean off the eastern seaboard of the U.S. in the vicinity of the Chesapeake Light Tower and at nearby National Oceanic and Atmospheric Administration (NOAA) Buoy Stations. The measurements were in support of CLAMS, Chesapeake Lighthouse and Aircraft Measurements for Satellites, field campaign that was primarily designed to validate and improve NASA's Earth Observing System (EOS) satellite data products being derived from three sensors: MODIS (MODerate Resolution Imaging Spectro-Radiometer), MISR (Multi-angle Imaging Spectro-Radiometer) and CERES (Clouds and Earth s Radiant Energy System). Because of the high resolution of the CAR measurements and its high sensitivity to detect weak ocean signals against a noisy background, results of radiance field above the ocean are seen in unprecedented detail. The study also attempts to validate the widely used Cox-Munk model for predicting reflectance from a rough ocean surface.

Gatebe, Charles K.↗
NASA NTRS2007

Interannual and Decadal Variability of Ocean Surface Latent Heat Flux as Seen from Passive Microwave Satellite Algorithms

Ocean surface turbulent fluxes are critical links in the climate system since they mediate energy exchange between the two fluid systems (ocean and atmosphere) whose combined heat transport determines the basic character of Earth's climate. Deriving physically-based latent and sensible heat fluxes from satellite is dependent on inferences of near surface moisture and temperature from coarser layer retrievals or satellite radiances. Uncertainties in these "retrievals" propagate through bulk aerodynamic algorithms, interacting as well with error properties of surface wind speed, also provided by satellite. By systematically evaluating an array of passive microwave satellite algorithms, the SEAFLUX project is providing improved understanding of these errors and finding pathways for reducing or eliminating them. In this study we focus on evaluating the interannual variability of several passive microwave-based estimates of latent heat flux starting from monthly mean gridded data. The algorithms considered range from those based essentially on SSM/I (e.g. HOAPS) to newer approaches that consider additional moisture information from SSM/T-2 or AMSU-B and lower tropospheric temperature data from AMSU-A. On interannual scales, variability arising from ENSO events and time-lagged responses of ocean turbulent and radiative fluxes in other ocean basins (as well as the extratropical Pacific) is widely recognized, but still not well quantified. Locally, these flux anomalies are of order 10-20 W/sq m and present a relevant "target" with which to verify algorithm performance in a climate context. On decadal time scales there is some evidence from reanalyses and remotely-sensed fluxes alike that tropical ocean-averaged latent heat fluxes have increased 5-10 W/sq m since the early 1990s. However, significant uncertainty surrounds this estimate. Our work addresses the origin of these uncertainties and provides statistics on time series of tropical ocean averages, regional space / time correlation analysis, and separation of contributions by variations in wind and near surface humidity deficit. Comparison to variations in reanalysis data sets is also provided for reference.

Robertson, Franklin R.↗
NASA NTRS2006

Offshore Radiation Observations for Climate Research at the CERES Ocean Validation Experiment

When radiometers on a satellite are pointed towards the planet with the goal of understanding a phenomenon quantitatively, rather than just creating a pleasing image, the task at hand is often problematic. The signal at the detector can be affected by scattering, absorption, and emission; and these can be due to atmospheric constituents (gases, clouds, and aerosols), the earth's surface, and subsurface features. When targeting surface phenomena, the remote sensing algorithm needs to account for the radiation associated with the atmospheric constituents. Likewise, one needs to correct for the radiation leaving the surface, when atmospheric phenomena are of interest. Rigorous validation of such remote sensing products is a real challenge. In visible and near infrared wavelengths, the jumble of effects on atmospheric radiation are best accomplished over dark surfaces with fairly uniform reflective properties (spatial homogeneity) in the satellite instrument's field of view (FOV). The ocean's surface meets this criteria; land surfaces - which are brighter, more spatially inhomogeneous, and more changeable with time - generally do not. NASA's Clouds and the Earth's Radiant Energy System (CERES) project has used this backdrop to establish a radiation monitoring site in Virginia's coastal Atlantic Ocean. The project, called the CERES Ocean Validation Experiment (COVE), is located on a rigid ocean platform allowing the accurate measurement of radiation parameters that require precise leveling and pointing unavailable from ships or buoys. The COVE site is an optimal location for verifying radiative transfer models and remote sensing algorithms used in climate research; because of the platform's small size, there are no island wake effects; and suites of sensors can be simultaneously trained both on the sky and directly on ocean itself. This paper describes the site, the types of measurements made, multiple years of atmospheric and ocean surface radiation observations, and satellite validation results.

Rutledge, Charles K.↗
NASA NTRS2010

Mechanical Extraction of Power From Ocean Currents and Tides

A proposed scheme for generating electric power from rivers and from ocean currents, tides, and waves is intended to offer economic and environmental advantages over prior such schemes, some of which are at various stages of implementation, others of which have not yet advanced beyond the concept stage. This scheme would be less environmentally objectionable than are prior schemes that involve the use of dams to block rivers and tidal flows. This scheme would also not entail the high maintenance costs of other proposed schemes that call for submerged electric generators and cables, which would be subject to degradation by marine growth and corrosion. A basic power-generation system according to the scheme now proposed would not include any submerged electrical equipment. The submerged portion of the system would include an all-mechanical turbine/pump unit that would superficially resemble a large land-based wind turbine (see figure). The turbine axis would turn slowly as it captured energy from the local river flow, ocean current, tidal flow, or flow from an ocean-wave device. The turbine axis would drive a pump through a gearbox to generate an enclosed flow of water, hydraulic fluid, or other suitable fluid at a relatively high pressure [typically approx.500 psi (approx.3.4 MPa)]. The pressurized fluid could be piped to an onshore or offshore facility, above the ocean surface, where it would be used to drive a turbine that, in turn, would drive an electric generator. The fluid could be recirculated between the submerged unit and the power-generation facility in a closed flow system; alternatively, if the fluid were seawater, it could be taken in from the ocean at the submerged turbine/pump unit and discharged back into the ocean from the power-generation facility. Another alternative would be to use the pressurized flow to charge an elevated reservoir or other pumped-storage facility, from whence fluid could later be released to drive a turbine/generator unit at a time of high power demand. Multiple submerged turbine/pump units could be positioned across a channel to extract more power than could be extracted by a single unit. In that case, the pressurized flows in their output pipes would be combined, via check valves, into a wider pipe that would deliver the combined flow to a power-generating or pumped-storage facility.

Jones, Jack↗
NASA NTRS2010

The Impact of Ocean Observations in Seasonal Climate Prediction

The ocean provides the most significant memory for the climate system. Hence, a critical element in climate forecasting with coupled models is the initialization of the ocean with states from an ocean data assimilation system. Remotely-sensed ocean surface fields (e.g., sea surface topography, SST, winds) are now available for extensive periods and have been used to constrain ocean models to provide a record of climate variations. Since the ocean is virtually opaque to electromagnetic radiation, the assimilation of these satellite data is essential to extracting the maximum information content. More recently, the Argo drifters have provided unprecedented sampling of the subsurface temperature and salinity. Although the duration of this observation set has been too short to provide solid statistical evidence of its impact, there are indications that Argo improves the forecast skill of coupled systems. This presentation will address the impact these different observations have had on seasonal climate predictions with the GMAO's coupled model.

Rienecker, Michele↗
NASA NTRS2010

Analysis of Atmosphere-Ocean Surface Flux Feedbacks in Recent Satellite and Model Reanalysis Products

Recent investigations have examined observations in an attempt to determine when and how the ocean forces the atmosphere, and vice versa. These studies focus primarily on relationships between sea surface temperature anomalies and the turbulent and radiative surface heat fluxes. It has been found that both positive and negative feedbacks, which enhance or reduce sea surface temperature anomaly amplitudes, can be generated through changes in the surface boundary layer. Consequent changes in sea surface temperature act to change boundary layer characteristics through changes in static stability or turbulent fluxes. Previous studies over the global oceans have used coarse-resolution observational and model products such as ICOADS and the NCEP Reanalysis. This study focuses on documenting the atmosphere ocean feedbacks that exist in recently produced higher resolution products, namely the SeaFlux v1.0 product and the NASA Modern Era Retrospective-Analysis for Research and Applications (MERRA). It has been noted in recent studies that evidence of oceanic forcing of the atmosphere exists on smaller scales than the usually more dominant atmospheric forcing of the ocean, particularly in higher latitudes. It is expected that use of these higher resolution products will allow for a more comprehensive description of these small-scale ocean-atmosphere feedbacks. The SeaFlux intercomparisons have revealed large scatter between various surface flux climatologies. This study also investigates the uncertainty in surface flux feedbacks based on several of these recent satellite based climatologies

Roberts, J. Brent↗
NASA NTRS2010

Improving NOAA's NWLON Through Enhanced Data Inputs from NASA's Ocean Surface Topography

This report assesses the benefit of incorporating NASA's OSTM (Ocean Surface Topography Mission) altimeter data (C- and Ku-band) into NOAA's (National Oceanic and Atmospheric Administration) NWLON (National Water Level Observation Network) DSS (Decision Support System). This data will enhance the NWLON DSS by providing additional inforrnation because not all stations collect all meteorological parameters (sea-surface height, ocean tides, wave height, and wind speed over waves). OSTM will also provide data where NWLON stations are not present. OSTM will provide data on seasurface heights for determining sea-level rise and ocean circulation. Researchers and operational users currently use satellite altimeter data products with the GSFCOO NASA data model to obtain sea-surface height and ocean circulation inforrnation. Accurate and tirnely inforrnation concerning sea-level height, tide, and ocean currents is needed to irnprove coastal tidal predictions, tsunarni and storm surge warnings, and wetland restoration.

Guest, DeNeice C.↗
NASA NTRS2010

Detection of Natural Oil Seeps in the Atlantic Ocean Using MODIS

Natural oil seepage is the release of crude oil into the ocean from fissures in the seabed. Oil seepage is a major contributor to the total amount of oil entering the world s oceans. According to a 2003 study by the National Academy of Sciences (NAS), 47 percent of oil entering the world s oceans is from natural seeps, and 53 percent is from human sources (extraction, transportation, and consumption). Oil seeps cause smooth oil slicks to form on the water s surface. Oil seeps can indicate the location of stores of fossil fuel beneath the ocean floor. Knowledge of the effect of oil seepage on marine life and marine ecosystems remains limited. In the past, remote sensing has been used to detect oil seeps in the Gulf of Mexico and off of the coast of southern California. This project utilized sun glint MODIS imagery to locate oil slicks off of the Atlantic coast, an area that had not previously been surveyed for natural oil seeps using remote sensing. Since 1982, the Atlantic Ocean has been closed to any oil and gas drilling. Recently, however, the U.S. Minerals Management Services (MMS) has proposed a lease for oil and gas drilling off the coasts of Virginia and North Carolina. Determining the location of seepage sites in the Atlantic Ocean will help MMS locate potential deposits of oil and natural gas, thereby reducing the risk of leasing areas for petroleum extraction that do not contain these natural resources.

Reahard, Ross↗
NASA NTRS2009

Skill Assessment of a Spectral Ocean-Atmosphere Radiative Model

Ocean phytoplankton, detrital material, and water absorb and scatter light spectrally. The Ocean- Atmosphere Spectral Irradiance Model (OASIM) is intended to provide surface irradiance over the oceans with sufficient spectral resolution to support ocean ecology, biogeochemistry, and heat exchange investigations, and of sufficient duration to support inter-annual and decadal investigations. OASIM total surface irradiance (integrated 200 nm to 4 microns) was compared to in situ data and three publicly available global data products at monthly 1-degree resolution. OASIM spectrally-integrated surface irradiance had root mean square (RMS) difference= 20.1 W/sq m (about 11%), bias=1.6 W/sq m (about 0.8%), regression slope= 1.01 and correlation coefficient= 0.89, when compared to 2322 in situ observations. OASIM had the lowest bias of any of the global data products evaluated (ISCCP-FD, NCEP, and ISLSCP 11), and the best slope (nearest to unity). It had the second best RMS, and the third best correlation coefficient. OASIM total surface irradiance compared well with ISCCP-FD (RMS= 20.7 W/sq m; bias=-11.4 W/sq m, r=0.98) and ISLSCP II (RMS =25.2 W/sq m; bias= -13.8 W/sq m; r=0.97), but less well with NCEP (RMS =43.0 W/sq m ;bias=-22.6 W/sq m; x=0.91). Comparisons of OASIM photosynthetically available radiation (PAR) with PAR derived from SeaWiFS showed low bias (-1.8 mol photons /sq m/d, or about 5%), RMS (4.25 mol photons /sq m/d ' or about 12%), near unity slope (1.03) and high correlation coefficient (0.97). Coupled with previous estimates of clear sky spectral irradiance in OASIM (6.6% RMS at 1 nm resolution), these results suggest that OASIM provides reasonable estimates of surface broadband and spectral irradiance in the oceans, and can support studies on ocean ecosystems, carbon cycling, and heat exchange.

Gregg, Watson, W.↗
NASA NTRS2012

NASA In Situ Data Needs to Support the Operational Calibration and Validation of Ocean Color Satellite Data Products

Calibrating ocean color satellite instruments and validating their data products requires temporal and spatial abundances of high quality in situ oceanographic data. The Consortium for Ocean Leadership Ocean Observing Initiative (OOl) is currently implementing a distributed array of in-water sensors that could provide a significant contribution to future ocean color activities. This workshop will scope the optimal way to use and possibly supplement the planned OOl infrastructure to maximize its utility and relevance for calibration and validation activities that support existing and planned NASA ocean color missions. Here, I present the current state of the art of NASA validation of ocean color data products, with attention to autonomous time-series (e.g., the AERONET -OC network of above-water radiometers), and outline NASA needs for data quality assurance metrics and adherence to community-vetted data collection protocols

Werdel, P. Jeremy↗
NASA NTRS2012

Sensitivity of Ocean Reflectance Inversion Models for Identifying and Discriminating Between Phytoplankton Functional Groups

The daily, synoptic images provided by satellite ocean color instruments provide viable data streams for observing changes in the biogeochemistrY of marine ecosystems. Ocean reflectance inversion models (ORMs) provide a common mechanism for inverting the "color" of the water observed a satellite into marine inherent optical properties (lOPs) through a combination of empiricism and radiative transfer theory. lOPs, namely the spectral absorption and scattering characteristics of ocean water and its dissolved and particulate constituents, describe the contents of the upper ocean, information critical for furthering scientific understanding of biogeochemical oceanic processes. Many recent studies inferred marine particle sizes and discriminated between phytoplankton functional groups using remotely-sensed lOPs. While all demonstrated the viability of their approaches, few described the vertical distributions of the water column constituents under consideration and, thus, failed to report the biophysical conditions under which their model performed (e.g., the depth and thickness of the phytoplankton bloom(s)). We developed an ORM to remotely identifY Noctiluca miliaris and other phytoplankton functional types using satellite ocean color data records collected in the northern Arabian Sea. Here, we present results from analyses designed to evaluate the applicability and sensitivity of the ORM to varied biophysical conditions. Specifically, we: (1) synthesized a series of vertical profiles of spectral inherent optical properties that represent a wide variety of bio-optical conditions for the northern Arabian Sea under aN Miliaris bloom; (2) generated spectral remote-sensing reflectances from these profiles using Hydrolight; and, (3) applied the ORM to the synthesized reflectances to estimate the relative concentrations of diatoms and N Miliaris for each example. By comparing the estimates from the inversion model to those from synthesized vertical profiles, we were able to identifY those bio-optical conditions under which the inversion model performs both well and poorly.

Werdell, P. Jeremy↗