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SWIM: A Semi-Analytical Ocean Color Inversion Algorithm for Optically Shallow Waters

In clear shallow waters, light that is transmitted downward through the water column can reflect off the sea floor and thereby influence the water-leaving radiance signal. This effect can confound contemporary ocean color algorithms designed for deep waters where the seafloor has little or no effect on the water-leaving radiance. Thus, inappropriate use of deep water ocean color algorithms in optically shallow regions can lead to inaccurate retrievals of inherent optical properties (IOPs) and therefore have a detrimental impact on IOP-based estimates of marine parameters, including chlorophyll-a and the diffuse attenuation coefficient. In order to improve IOP retrievals in optically shallow regions, a semi-analytical inversion algorithm, the Shallow Water Inversion Model (SWIM), has been developed. Unlike established ocean color algorithms, SWIM considers both the water column depth and the benthic albedo. A radiative transfer study was conducted that demonstrated how SWIM and two contemporary ocean color algorithms, the Generalized Inherent Optical Properties algorithm (GIOP) and Quasi-Analytical Algorithm (QAA), performed in optically deep and shallow scenarios. The results showed that SWIM performed well, whilst both GIOP and QAA showed distinct positive bias in IOP retrievals in optically shallow waters. The SWIM algorithm was also applied to a test region: the Great Barrier Reef, Australia. Using a single test scene and time series data collected by NASA's MODIS-Aqua sensor (2002-2013), a comparison of IOPs retrieved by SWIM, GIOP and QAA was conducted.

shallow waters↗

Performance of JAXA’s SGLI standard ocean color products for oceanic to coastal waters: chlorophyll a concentration and light absorption coefficients of colored dissolved organic matter

We present the performance of JAXA’s SGLI standard algorithms for estimating chlorophyll a (chl a) concentration and the light absorption coefcients of colored dissolved organic matter (CDOM) using recently compiled high-quality data obtained from oceanic to coastal waters. Prior to the evaluation of the algorithms, we frst compare two forward models (Gordon et al. in J Geophys Res 93(D9):10909-10924, 1988: G88 and Park and Ruddick in Appl Opt 44(7):1236–1249, 2005: PR05) using a wide range of inherent optical properties (IOPs) to (1) examine if the water refectance is appropriately reproduced and (2) correct measured refectance in terms of its bidirectionality. Based on a good reproducibility of water refectance using the PR05, the optimized IOPs are further used for explaining errors in estimates of chl a concentration and CDOM absorption when using the SGLI, the GSM (Maritorena et al. in Appl Opt 41:2705–2714, 2002), and the QAA (Lee et al. in Appl Opt 41:5755, 2002) inversion algorithms. Results show that the mean error for estimating chl a concentration using the SGLI algorithm is 110% for our dataset. Although this error is lower than that of the GSM and the QAA algorithms, a signifcant underestimate at chl a higher than 2.0 mg m−3 is observed, which is further shown by independent match-up analyses. Another SGLI CDOM product includes the mean error of 50% and shows deviation at high CDOM range (>1.0 per m). A similar trend is observed for the GSM but not for the QAA when a global relationship of CDOM to colored detrital matter is applied. The sources of errors are discussed for potentially improving the retrievals

Second-generation GLobal Imager (SGLI)↗

Complexity of the Quantum Adiabatic Algorithm

The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.

Hen, Itay↗

Algorithm Development and Validation of CDOM Properties for Estuarine and Continental Shelf Waters Along the Northeastern U.S. Coast

An extensive set of field measurements have been collected throughout the continental margin of the northeastern U.S. from 2004 to 2011 to develop and validate ocean color satellite algorithms for the retrieval of the absorption coefficient of chromophoric dissolved organic matter (aCDOM) and CDOM spectral slopes for the 275:295 nm and 300:600 nm spectral range (S275:295 and S300:600). Remote sensing reflectance (Rrs) measurements computed from in-water radiometry profiles along with aCDOM() data are applied to develop several types of algorithms for the SeaWiFS and MODIS-Aqua ocean color satellite sensors, which involve least squares linear regression of aCDOM() with (1) Rrs band ratios, (2) quasi-analytical algorithm-based (QAA based) products of total absorption coefficients, (3) multiple Rrs bands within a multiple linear regression (MLR) analysis, and (4) diffuse attenuation coefficient (Kd). The relative error (mean absolute percent difference; MAPD) for the MLR retrievals of aCDOM(275), aCDOM(355), aCDOM(380), aCDOM(412) and aCDOM(443) for our study region range from 20.4-23.9 for MODIS-Aqua and 27.3-30 for SeaWiFS. Because of the narrower range of CDOM spectral slope values, the MAPD for the MLR S275:295 and QAA-based S300:600 algorithms are much lower ranging from 9.9 and 8.3 for SeaWiFS, respectively, and 8.7 and 6.3 for MODIS, respectively. Seasonal and spatial MODIS-Aqua and SeaWiFS distributions of aCDOM, S275:295 and S300:600 processed with these algorithms are consistent with field measurements and the processes that impact CDOM levels along the continental shelf of the northeastern U.S. Several satellite data processing factors correlate with higher uncertainty in satellite retrievals of aCDOM, S275:295 and S300:600 within the coastal ocean, including solar zenith angle, sensor viewing angle, and atmospheric products applied for atmospheric corrections. Algorithms that include ultraviolet Rrs bands provide a better fit to field measurements than algorithms without the ultraviolet Rrs bands. This suggests that satellite sensors with ultraviolet capability could provide better retrievals of CDOM. Because of the strong correlations between CDOM parameters and DOM constituents in the coastal ocean, satellite observations of CDOM parameters can be applied to study the distributions, sources and sinks of DOM, which are relevant for understanding the carbon cycle, modeling the Earth system, and to discern how the Earth is changing.

CDOM Properties↗

A Semianalytical Ocean Color Inversion Algorithm with Explicit Water Column Depth and Substrate Reflectance Parameterization

A semianalytical ocean color inversion algorithm was developed for improving retrievals of inherent optical properties (IOPs) in optically shallow waters. In clear, geometrically shallow waters, light reflected off the seafloor can contribute to the water-leaving radiance signal. This can have a confounding effect on ocean color algorithms developed for optically deep waters, leading to an overestimation of IOPs. The algorithm described here, the Shallow Water Inversion Model (SWIM), uses pre-existing knowledge of bathymetry and benthic substrate brightness to account for optically shallow effects. SWIM was incorporated into the NASA Ocean Biology Processing Group's L2GEN code and tested in waters of the Great Barrier Reef, Australia, using the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua time series (2002-2013). SWIM-derived values of the total non-water absorption coefficient at 443 nm, at(443), the particulate backscattering coefficient at 443 nm, bbp(443), and the diffuse attenuation coefficient at 488 nm, Kd(488), were compared with values derived using the Generalized Inherent Optical Properties algorithm (GIOP) and the Quasi-Analytical Algorithm (QAA). The results indicated that in clear, optically shallow waters SWIM-derived values of at(443), bbp(443), and Kd(443) were realistically lower than values derived using GIOP and QAA, in agreement with radiative transfer modeling. This signified that the benthic reflectance correction was performing as expected. However, in more optically complex waters, SWIM had difficulty converging to a solution, a likely consequence of internal IOP parameterizations. Whilst a comprehensive study of the SWIM algorithm's behavior was conducted, further work is needed to validate the algorithm using in situ data.

Great Barrier Reef↗

SWIM: A Semi-Analytical Ocean Color Inversion Algorithm for Optically Shallow Waters

Ocean color remote sensing provides synoptic-scale, near-daily observations of marine inherent optical properties (IOPs). Whilst contemporary ocean color algorithms are known to perform well in deep oceanic waters, they have difficulty operating in optically clear, shallow marine environments where light reflected from the seafloor contributes to the water-leaving radiance. The effect of benthic reflectance in optically shallow waters is known to adversely affect algorithms developed for optically deep waters [1, 2]. Whilst adapted versions of optically deep ocean color algorithms have been applied to optically shallow regions with reasonable success [3], there is presently no approach that directly corrects for bottom reflectance using existing knowledge of bathymetry and benthic albedo.To address the issue of optically shallow waters, we have developed a semi-analytical ocean color inversion algorithm: the Shallow Water Inversion Model (SWIM). SWIM uses existing bathymetry and a derived benthic albedo map to correct for bottom reflectance using the semi-analytical model of Lee et al [4]. The algorithm was incorporated into the NASA Ocean Biology Processing Groups L2GEN program and tested in optically shallow waters of the Great Barrier Reef, Australia. In-lieu of readily available in situ matchup data, we present a comparison between SWIM and two contemporary ocean color algorithms, the Generalized Inherent Optical Property Algorithm (GIOP) and the Quasi-Analytical Algorithm (QAA).

QAA↗

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗

A Three-Step Semi Analytical Algorithm (3SAA) for Estimating Inherent Optical Properties Over Oceanic, Coastal, and Inland Waters From Remote Sensing Reflectance

We present a three-step inverse model (3SAA) for estimating the inherent optical properties (IOPs) of surface waters from the remote sensing reflectance spectra, Rrs(). The derived IOPs include the total (a()), phytoplankton (aphy()), and colored detrital matter (acdm()), absorption coefficients, and the total (bb()) and particulate (bbp()) backscattering coefficients. The first step uses an improved neural network approach to estimate the diffuse attenuation coefficient of downwelling irradiance from Rrs. a() and bbp() are then estimated using the LS2 model (Loisel et al., 2018), which does not require spectral assumptions on IOPs and hence can assess a() and bb() at any wavelength at which Rrs() is measured. Then, an inverse optimization algorithm is combined with an optical water class (OWC) approach to assess aphy() and acdm() from anw().The proposed model is evaluated using an in situ dataset collected in open oceanic, coastal, and inland waters. Comparisons with other standard semi-analytical algorithms (QAA and GSM), as well as match-up exercises, have also been performed. The applicability of the algorithm on OLCI observations was assessed through the analysis of global IOPs spatial patterns derived from 3SAA and GSM. The good performance of 3SAA is manifested by median absolute percentage differences (MAPD) of 13%, 23%, 34% and 34% for bbp(443), anw(443), aphy(443) and acdm(443), respectively for oceanic waters. Due to the absence of spectral constraints on IOPs in the inversion of total IOPs, and the adoption of an OWC-based approach, the performance of 3SAA is only slightly degraded in bio-optical complex inland waters.

ocean color↗