Approach for Propagating Radiometric Data Uncertainties Through NASA Ocean Color Algorithms

Abstract

Spectroradiometric satellite observations of the ocean are commonly referred to as "ocean color" remote sensing. NASA has continuously collected, processed, and distributed ocean color datasets since the launch of the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) in 1997. While numerous ocean color algorithms have been developed in the past two decades that derive geophysical data products from sensor-observed radiometry, few papers have clearly demonstrated how to estimate measurement uncertainty in derived data products. As the uptake of ocean color data products continues to grow with the launch of new and advanced sensors, it is critical that pixel-by-pixel data product uncertainties are estimated during routine data processing. Knowledge of uncertainties can be used when studying long-term climate records, or to assist in the development and performance appraisal of bio-optical algorithms. In this methods paper we provide a comprehensive overview of how to formulate first-order first-moment (FOFM) calculus for propagating radiometric uncertainties through a selection of bio-optical models. We demonstrate FOFM uncertainty formulations for the following NASA ocean color data products: chlorophyll-a pigment concentration (Chl), the diffuse attenuation coefficient at 490 nm (K d,490), particulate organic carbon (POC), normalized fluorescent line height (nflh), and inherent optical properties (IOPs). Using a quality-controlled in situ hyperspectral remote sensing reflectance (R rs,i) dataset, we show how computationally inexpensive, yet algebraically complex, FOFM calculations may be evaluated for correctness using the more computationally expensive Monte Carlo approach. We compare bio-optical product uncertainties derived using our test R rs dataset assuming spectrally-flat, uncorrelated relative uncertainties of 1, 5, and 10%. We also consider spectrally dependent, uncorrelated relative uncertainties in R rs. The importance of considering spectral covariances in R rs , where practicable, in the FOFM methodology is highlighted with an example SeaWiFS image. We also present a brief case study of two POC algorithms to illustrate how FOFM formulations may be used to construct measurement uncertainty budgets for ecologically-relevant data products. Such knowledge, even if rudimentary, may provide useful information to end-users when selecting data products or when developing their own algorithms.

Development and Validation of an Empirical Ocean Color Algorithm with Uncertainties: A Case Study with the Particulate Backscattering Coefficient

“…In a similar style to work of McKinna et al. (2019), the model skill assessments we present may be repeated or expanded to other models provided one has reasonable knowledge (or estimate) of observation and model uncertainties.…”

“…Following McKinna et al. (2019), we have used the first‐order first‐moment formulations to estimate uncertainties due to random radiometric error. This approach is valid when the uncertainty is small relative to the measurement.…”

“…From these relative uncertainties, we computed the standard uncertainty for each quantity. Standard uncertainties in GIOP-derived b bp (555) were estimated following McKinna et al (2019) while standard uncertainties in Huot-derived b bp (555) were also estimated using a first-order analytical methodology (see Appendix A for detail).…”

“…The standard uncertainties of model coefficients was estimated by dividing the 95% confidence intervals values reported in . Uncertainty in chlorophyll-a pigment concentration, u(Chla), was estimated per McKinna et al (2019) with relative uncertainties in R rs (λ) set to 5%. We have not considered covariance terms for Equation A1 as there are unreported.…”

Living up to the Hype of Hyperspectral Aquatic Remote Sensing: Science, Resources and Outlook

“…Some algorithms are less sensitive to uncertainties in atmospheric correction such as those focused on narrowband features, and others may require highly calibrated data across the spectrum. While uncertainties can be quantified directly with some techniques, like so-called Optimal Estimation (Rodgers, 1998), techniques have been proposed for propagating uncertainties through other types of algorithms (McKinna et al, 2019).…”