Expectation-maximization analysis of spatial time series

© Author(s) 2007. This work is licensed under a Creative Commons License. The definitive version was published in Nonlinear Processes in Geophysics 14 (2007): 73-77, doi: 10.5194/npg-14-73-2007Expectation maximization (EM) is used to estimate the parameters of a Gaussian Mixture Model for spatial time series data. The method is presented as an alternative and complement to Empirical Orthogonal Function (EOF) analysis. The resulting weights, associating time points with component distributions, are used to distinguish physical regimes. The method is applied to equatorial Pacific sea surface temperature data from the TAO/TRITON mooring time series. Effectively, the EM algorithm partitions the time series into El Nino, La Nina and normal conditions. The EM method leads to a clearer interpretation of the variability associated with each regime than the basic EOF analysis.This work was supported by NSF grant DMS-0417845

Analyzing state-dependent model–data comparison in multi-regime systems

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Computational Geosciences 15 (2011): 627-636, doi:10.1007/s10596-011-9229-3.An approach to analyze regime change in spatial time series data sets is followed and extended to jointly analyze a dynamical model depicting regime shift and observational data informing the same process. We analyze changes in the joint model-data regime and covariability within each regime. The method is applied to two observational data sets of equatorial sea surface temperature (TAO/TRITON array and satellite) and compared with the predicted data by the ECCO-JPL modeling system.Funding for this work was provided by Spanish National Program on Space, under contract ESP2005-06823-C05. A. Aretxabaleta has been additionally supported by a Juan de la Cierva grant of the Spanish Government. K. Smith was supported by NSF Grant DMS-0934653

Physical and biogeochemical controls on light attenuation in a eutrophic, back-barrier estuary

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 11 (2014): 7193-7205, doi:10.5194/bg-11-7193-2014.Light attenuation is a critical parameter governing the ecological function of shallow estuaries. In these systems primary production is often dominated by benthic macroalgae and seagrass; thus light penetration to the bed is of primary importance. We quantified light attenuation in three seagrass meadows in Barnegat Bay, New Jersey, a shallow eutrophic back-barrier estuary; two of the sites were located within designated Ecologically Sensitive Areas (ESAs). We sequentially deployed instrumentation measuring photosynthetically active radiation, chlorophyll a (chl a) fluorescence, dissolved organic matter fluorescence (fDOM; a proxy for colored dissolved organic matter (CDOM) absorbance), turbidity, pressure, and water velocity at 10 min intervals over 3-week periods at each site. At the southernmost site, where sediment availability was highest, light attenuation was highest and dominated by turbidity and to a lesser extent chl a and CDOM. At the central site, chl a dominated followed by turbidity and CDOM, and at the northernmost site turbidity and CDOM contributed equally to light attenuation. At a given site, the temporal variability of light attenuation exceeded the difference in median light attenuation between the three sites. Vessel wakes, anecdotally implicated in increasing sediment resuspension, did not contribute to local resuspension within the seagrass beds, though frequent vessel wakes were observed in the channels. With regards to light attenuation and water clarity, physical and biogeochemical variables appear to outweigh any regulation of boat traffic within the ESAs.Funding was provided by the New Jersey Department of Environmental Protection and the U.S. Geological Survey Coastal and Marine Geology Program

Estimating time-dependent connectivity in marine systems

This paper is not subject to U.S. copyright. The definitive version was published in Geophysical Research Letters 43 (2016): 1193–1201, doi:10.1002/2015GL066888.Hydrodynamic connectivity describes the sources and destinations of water parcels within a domain over a given time. When combined with biological models, it can be a powerful concept to explain the patterns of constituent dispersal within marine ecosystems. However, providing connectivity metrics for a given domain is a three-dimensional problem: two dimensions in space to define the sources and destinations and a time dimension to evaluate connectivity at varying temporal scales. If the time scale of interest is not predefined, then a general approach is required to describe connectivity over different time scales. For this purpose, we have introduced the concept of a “retention clock” that highlights the change in connectivity through time. Using the example of connectivity between protected areas within Barnegat Bay, New Jersey, we show that a retention clock matrix is an informative tool for multitemporal analysis of connectivity.New Jersey Department of Environmental Protectio

Water level response in back-barrier bays unchanged following Hurricane Sandy

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Geophysical Research Letters 41 (2014): 3163–3171, doi:10.1002/2014GL059957.On 28–30 October 2012, Hurricane Sandy caused severe flooding along portions of the northeast coast of the United States and cut new inlets across barrier islands in New Jersey and New York. About 30% of the 20 highest daily maximum water levels observed between 2007 and 2013 in Barnegat and Great South Bay occurred in 5 months following Hurricane Sandy. Hurricane Sandy provided a rare opportunity to determine whether extreme events alter systems protected by barrier islands, leaving the mainland more vulnerable to flooding. Comparisons between water levels before and after Hurricane Sandy at bay stations and an offshore station show no significant differences in the transfer of sea level fluctuations from offshore to either bay following Sandy. The post-Hurricane Sandy bay high water levels reflected offshore sea levels caused by winter storms, not by barrier island breaching or geomorphic changes within the bays

The dynamics of digits: Calculating pi with Galperin's billiards

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number $\pi$. This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of $\pi$ in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be $\pi$ itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls' positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of $\pi$ with Galperin billiards, including curious cases with irrational number bases.Comment: 30 pages, 13 figure

Observations and a linear model of water level in an interconnected inlet-bay system

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 2760–2780, doi:10.1002/2016JC012318.A system of barrier islands and back-barrier bays occurs along southern Long Island, New York, and in many coastal areas worldwide. Characterizing the bay physical response to water level fluctuations is needed to understand flooding during extreme events and evaluate their relation to geomorphological changes. Offshore sea level is one of the main drivers of water level fluctuations in semienclosed back-barrier bays. We analyzed observed water levels (October 2007 to November 2015) and developed analytical models to better understand bay water level along southern Long Island. An increase (∼0.02 m change in 0.17 m amplitude) in the dominant M2 tidal amplitude (containing the largest fraction of the variability) was observed in Great South Bay during mid-2014. The observed changes in both tidal amplitude and bay water level transfer from offshore were related to the dredging of nearby inlets and possibly the changing size of a breach across Fire Island caused by Hurricane Sandy (after December 2012). The bay response was independent of the magnitude of the fluctuations (e.g., storms) at a specific frequency. An analytical model that incorporates bay and inlet dimensions reproduced the observed transfer function in Great South Bay and surrounding areas. The model predicts the transfer function in Moriches and Shinnecock bays where long-term observations were not available. The model is a simplified tool to investigate changes in bay water level and enables the evaluation of future conditions and alternative geomorphological settings.New York State Department of Environmental Conservation Grant Number: (NYS-DEC); U.S. Geological Survey (USGS

Physical response of a back-barrier estuary to a post-tropical cyclone

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 5888–5904, doi:10.1002/2016JC012344.This paper presents a modeling investigation of the hydrodynamic and sediment transport response of Chincoteague Bay (VA/MD, USA) to Hurricane Sandy using the Coupled Ocean-Atmosphere-Wave-Sediment-Transport (COAWST) modeling system. Several simulation scenarios with different combinations of remote and local forces were conducted to identify the dominant physical processes. While 80% of the water level increase in the bay was due to coastal sea level at the peak of the storm, a rich spatial and temporal variability in water surface slope was induced by local winds and waves. Local wind increased vertical mixing, horizontal exchanges, and flushing through the inlets. Remote waves (swell) enhanced southward flow through wave setup gradients between the inlets, and increased locally generated wave heights. Locally generated waves had a negligible effect on water level but reduced the residual flow up to 70% due to enhanced apparent roughness and breaking-induced forces. Locally generated waves dominated bed shear stress and sediment resuspension in the bay. Sediment transport patterns mirrored the interior coastline shape and generated deposition on inundated areas. The bay served as a source of fine sediment to the inner shelf, and the ocean-facing barrier island accumulated sand from landward-directed overwash. Despite the intensity of the storm forcing, the bathymetric changes in the bay were on the order of centimeters. This work demonstrates the spectrum of responses to storm forcing, and highlights the importance of local and remote processes on back-barrier estuarine function.Department of Interior Hurricane Sandy Recovery progra

Spatial distribution of water level impacting back-barrier bays

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Aretxabaleta, A. L., Ganju, N. K., Defne, Z., & Signell, R. P. Spatial distribution of water level impacting back-barrier bays. Natural Hazards and Earth System Sciences, 19(8), (2019): 1823-1838, doi: 10.5194/nhess-19-1823-2019.Water level in semi-enclosed bays, landward of barrier islands, is mainly driven by offshore sea level fluctuations that are modulated by bay geometry and bathymetry, causing spatial variability in the ensuing response (transfer). Local wind setup can have a complementary role that depends on wind speed, fetch, and relative orientation of the wind direction and the bay. Bay area and inlet geometry and bathymetry primarily regulate the magnitude of the transfer between open ocean and bay. Tides and short-period offshore oscillations are more damped in the bays than longer-lasting offshore fluctuations, such as a storm surge and sea level rise. We compare observed and modeled water levels at stations in a mid-Atlantic bay (Barnegat Bay) with offshore water level proxies. Observed water levels in Barnegat Bay are compared and combined with model results from the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system to evaluate the spatial structure of the water level transfer. Analytical models based on the dimensional characteristics of the bay are used to combine the observed data and the numerical model results in a physically consistent approach. Model water level transfers match observed values at locations inside the bay in the storm frequency band (transfers ranging from 50 %–100 %) and tidal frequencies (10 %–55 %). The contribution of frequency-dependent local setup caused by wind acting along the bay is also considered. The wind setup effect can be comparable in magnitude to the offshore transfer forcing during intense storms. The approach provides transfer estimates for locations inside the bay where observations were not available, resulting in a complete spatial characterization. An extension of the methodology that takes advantage of the ADCIRC tidal database for the east coast of the United States allows for the expansion of the approach to other bay systems. Detailed spatial estimates of water level transfer can inform decisions on inlet management and contribute to the assessment of current and future flooding hazard in back-barrier bays and along mainland shorelines.This work was supported by the US Geological Survey, Coastal and Marine Hazards/Resources Program

Spatiotemporal variability of light attenuation and net ecosystem metabolism in a back-barrier estuary

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ganju, N. K., Testa, J. M., Suttles, S. E., & Aretxabaleta, A. L. Spatiotemporal variability of light attenuation and net ecosystem metabolism in a back-barrier estuary. Ocean Science, 16(3), (2020): 593-614, doi:10.5194/os-16-593-2020.Quantifying system-wide biogeochemical dynamics and ecosystem metabolism in estuaries is often attempted using a long-term continuous record at a single site or short-term records at multiple sites due to sampling limitations that preclude long-term monitoring. However, differences in the dominant primary producer at a given location (e.g., phytoplankton versus benthic producers) control diel variations in dissolved oxygen and associated ecosystem metabolism, and they may confound metabolic estimates that do not account for this variability. We hypothesize that even in shallow, well-mixed estuaries there is strong spatiotemporal variability in ecosystem metabolism due to benthic and water-column properties, as well as ensuing feedbacks to sediment resuspension, light attenuation, and primary production. We tested this hypothesis by measuring hydrodynamic properties, biogeochemical variables (fluorescent dissolved organic matter – fDOM, turbidity, chlorophyll a fluorescence, dissolved oxygen), and photosynthetically active radiation (PAR) over 1 year at 15 min intervals at paired channel (unvegetated) and shoal (vegetated by eelgrass) sites in Chincoteague Bay, Maryland–Virginia, USA, a shallow back-barrier estuary. Light attenuation (KdPAR) at all sites was dominated by turbidity from suspended sediment, with lower contributions from fDOM and chlorophyll a. However, there was significant seasonal variability in the resuspension–shear stress relationship on the vegetated shoals, but not in adjacent unvegetated channels. This indicated that KdPAR on the shoals was mediated by submerged aquatic vegetation (SAV) and possibly microphytobenthos presence in the summer, which reduced resuspension and therefore KdPAR. We also found that gross primary production (Pg) and KdPAR were significantly negatively correlated on the shoals and uncorrelated in the channels, indicating that Pg over the vegetated shoals is controlled by a feedback loop between benthic stabilization by SAV and/or microphytobenthos, sediment resuspension, and light availability. Metabolic estimates indicated substantial differences in net ecosystem metabolism between vegetated and unvegetated sites, with the former tending towards net autotrophy in the summer. Ongoing trends of SAV loss in this and other back-barrier estuaries suggest that these systems may also shift towards net heterotrophy, reducing their effectiveness as long-term carbon sinks. With regards to temporal variability, we found that varying sampling frequency between 15 min and 1 d resulted in comparable mean values of biogeochemical variables, but extreme values were missed by daily sampling. In fact, daily resampling minimized the variability between sites and falsely suggested spatial homogeneity in biogeochemistry, emphasizing the need for high-frequency sampling. This study confirms that properly quantifying ecosystem metabolism and associated biogeochemical variability requires characterization of the diverse estuarine environments, even in well-mixed systems, and demonstrates the deficiencies introduced by infrequent sampling to the interpretation of spatial variability.This study was funded by the USGS Coastal and Marine Geology Program and the Department of the Interior Hurricane Sandy Recovery program (GS2-2D)