Modern Statistical Methods in Oceanography: A Hierarchical Perspective

Processes in ocean physics, air-sea interaction and ocean biogeochemistry span enormous ranges in spatial and temporal scales, that is, from molecular to planetary and from seconds to millennia. Identifying and implementing sustainable human practices depend critically on our understandings of key aspects of ocean physics and ecology within these scale ranges. The set of all ocean data is distorted such that three- and four-dimensional (i.e., time-dependent) in situ data are very sparse, while observations of surface and upper ocean properties from space-borne platforms have become abundant in the past few decades. Precisions in observations of all types vary as well. In the face of these challenges, the interface between Statistics and Oceanography has proven to be a fruitful area for research and the development of useful models. With the recognition of the key importance of identifying, quantifying and managing uncertainty in data and models of ocean processes, a hierarchical perspective has become increasingly productive. As examples, we review a heterogeneous mix of studies from our own work demonstrating Bayesian hierarchical model applications in ocean physics, air-sea interaction, ocean forecasting and ocean ecosystem models. This review is by no means exhaustive and we have endeavored to identify hierarchical modeling work reported by others across the broad range of ocean-related topics reported in the statistical literature. We conclude by noting relevant ocean-statistics problems on the immediate research horizon, and some technical challenges they pose, for example, in terms of nonlinearity, dimensionality and computing.Comment: Published in at http://dx.doi.org/10.1214/13-STS436 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatio-Temporal Hierarchical Bayesian Modeling: Tropical Ocean Surface Winds

This is the author's version of the article found in the Journal of the American Statistical Association. The publisher's version can be found at http://pubs.amstat.org/loi/jasa.Spatio-temporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and large number of observation/prediction locations preclude the use of traditional covariance-based space-time statistical methods. Alternatively, we focus on conditionally-specified (i.e., hierarchical) spatio-temporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints are easily incorporated into the conditional formulation, so that the series of relatively simple, yet physically realistic, conditional models leads to a much more complicated space-time covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models are computable with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial resolution but are limited in global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The goal is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research as no complete high resolution surface wind datasets exist over the world oceans. High resolution datasets of this kind are crucial for improving our understanding of: global air-sea interactions affecting climate, tropical disturbances, and for driving large-scale ocean circulation models.Support for this research was provided for CKW, DN, and LMB by the NCAR Geophysical Statistics Project, sponsored by the National Science Foundation (NSF) under Grant DMS93-12686. Support for RFM and CKW is provided by the NCAR NSCAT Science Working Team cooperative agreement with NASA JPL. NCAR is supported in part by the NSF

LANDSAT-D investigations in snow hydrology

Work undertaken during the contract and its results are described. Many of the results from this investigation are available in journal or conference proceedings literature - published, accepted for publication, or submitted for publication. For these the reference and the abstract are given. Those results that have not yet been submitted separately for publication are described in detail. Accomplishments during the contract period are summarized as follows: (1) analysis of the snow reflectance characteristics of the LANDSAT Thematic Mapper, including spectral suitability, dynamic range, and spectral resolution; (2) development of a variety of atmospheric models for use with LANDSAT Thematic Mapper data. These include a simple but fast two-stream approximation for inhomogeneous atmospheres over irregular surfaces, and a doubling model for calculation of the angular distribution of spectral radiance at any level in an plane-parallel atmosphere; (3) incorporation of digital elevation data into the atmospheric models and into the analysis of the satellite data; and (4) textural analysis of the spatial distribution of snow cover

Hierarchical Bayesian Approach to Boundary Value Problems with Stochastic Boundary Conditions

This is the pre-print version of the article found in the Monthly Weather Review (http://journals.ametsoc.org/toc/mwre/138/10).Boundary value problems are ubiquitous in the atmospheric and ocean sciences. Typical settings include bounded, partially bounded, global and limited area domains, discretized for applications of numerical models of the relevant fluid equations. Often, limited area models are constructed to interpret intensive datasets collected over a specific region, from a variety of observational platforms. These data are noisy and they typically do not span the domain of interest uniformly in space and time. Traditional numerical procedures cannot easily account for these uncertainties. A hierarchical Bayesian modeling framework is developed for solving boundary value problems in such settings. By allowing the boundary process to be stochastic, and conditioning the interior process on this boundary, one can account for the uncertainties in the boundary process in a reasonable fashion. In the presence of data and all its uncertainties, this idea can be related through Bayes' Theorem to produce distributions of the interior process given the observational data. The method is illustrated with an example of obtaining atmospheric streamfunction fields in the Labrador Sea region, given scatterometer-derived observations of the surface wind field

The Global ocean circulation during 1992-1997, estimated from ocean observations and a general circulation model

We discuss the three-dimensional oceanic state estimated for the period 1992- 1997 as it results from bringing together large-scale ocean data sets with a general circulation model. To bring the model into close agreement with ocean data, its initial temperature and salinity conditions where changed as well as the time-dependent surface fluxes of momentum, heat and freshwater. Resulting changes of those control fields are largely consistent with accepted uncertainties in the hydrographic climatology and meteorological analyses. Our results show that the assimilation procedure is able to correct for the traditional shortcomings of the flow field by changing the surface boundary conditions. Changes of the resulting flow field are predominantly on the gyre scale and affect many features which are often poorly simulated in traditional numerical simulations, such as the strengths of the Gulf Stream and its extension, the Azores Current and the anticyclonic circulation associated with the Labrador Sea. A detailed test of the results and their consistency with prior error assumptions shows that the constrained model has moved considerably closer to those observations which have been imposed as constraints, but also to independent data from the World Ocean Circulation Experiment not used in the assimilation procedure. In some regions where the comparisons remain indeterminate, not enough ocean observations are available. And in such situations, it is difficult to ascribe the residuals to either the model or the observations. We conclude from this experiment that we can find an acceptable solution to the global time-dependent ocean state estimation problem. As the estimates improve through the evolution of numerical models, computer power increases, and better assimilation schemes, improved and routine estimates will become possible

Spatial and seasonal variability of the air-sea equilibration timescale of carbon dioxide

The exchange of carbon dioxide between the ocean and the atmosphere tends to bring waters within the mixed layer toward equilibrium by reducing the partial pressure gradient across the air-water interface. However, the equilibration process is not instantaneous; in general, there is a lag between forcing and response. The timescale of air-sea equilibration depends on several factors involving the depth of the mixed layer, wind speed, and carbonate chemistry. We use a suite of observational data sets to generate climatological and seasonal composite maps of the air-sea equilibration timescale. The relaxation timescale exhibits considerable spatial and seasonal variations that are largely set by changes in mixed layer depth and wind speed. The net effect is dominated by the mixed layer depth; the gas exchange velocity and carbonate chemistry parameters only provide partial compensation. Broadly speaking, the adjustment timescale tends to increase with latitude. We compare the observationally derived air-sea gas exchange timescale with a model-derived surface residence time and a data-derived horizontal transport timescale, which allows us to define two nondimensional metrics of equilibration efficiency. These parameters highlight the tropics, subtropics, and northern North Atlantic as regions of inefficient air-sea equilibration where carbon anomalies are relatively likely to persist. The efficiency parameters presented here can serve as simple tools for understanding the large-scale persistence of air-sea disequilibrium of CO2 in both observations and models

A Southern Hemisphere Sea Level Pressure-Based Precursor for ENSO Warm and Cold Events

Past studies have described large-scale sea level pressure (SLP) variations in the Southern Hemisphere that lead to El Nino-Southern Oscillation (ENSO) warm and cold events (WE and CE). By relying on this description and the importance of the related variability in the lead up to WE and CE, Southern Hemisphere SLP variations in May-June-July (MJJ) are shown here to be excellent predictors for the peak warm/cold events in sea-surface temperatures (SST) and sea level pressure that mark the mature phase of a warm/cold event in November-January of the same year. Cyclostationary empirical orthogonal functions (CSEOFs) are used to extract the variability associated with this description of SLP evolution leading to extreme events, underscoring the importance of this signal in the build-up to ENSO events. Using the CSEOF decomposition, an MJJ precursor is established and shown to precede impending warm and cold events in the past sixty years. Furthermore, the precursor developed in this study would have suggested that a significant WE for the latter half of 2014 was unlikely