Meteorological And Oceanographic

[Kimberly Ballas]

Manyof NOAA's water level stations are equipped with meteorological and additional oceanographic sensors to collect observations such as wind speed and direction, air temperature, water temperature, water conductivity, barometric pressure, relative humidity, and visibility. Meteorological conditions can greatly impact water levels. For example, onshore winds tend to elevate water levels and offshore winds tend to suppress water levels. There are many other factors that affect water levels in various water bodies but changing meteorological conditions such as frontal passages and tropical storms can dramatically change water levels in a very short period of time. In addition, the combination of water temperature and conductivity provides a measurement of the water's salinity, which affects everything from a ship's draft to ecological resources.

NATO cooperation in METOC support for its forces aims to ensure that Allies get the information they need through efficient and effective use of national and NATO assets. This information helps allied forces exploit the best window of opportunity to plan, execute, support and sustain military operations. Furthermore, it helps them optimize the use of sensors, weapons, targeting, logistics, equipment and personnel.

The NATO Meteorological and Oceanographic Military Committee Working Group [MCWG(METOC)] advises the Military Committee on METOC issues. It also acts as a standardization authority by supervising two subordinate panels on military meteorology and military oceanography.

MCWG(METOC), which comprises delegates from each allied country, meets annually to address military METOC policy, procedures and standardization agreements between NATO and partner countries. It relies to a large extent on the resources of NATO members, most of which have dedicated civil and/or military METOC organizations.

The group supports NATO and national members in developing effective plans, procedures and techniques for providing METOC support to NATO forces and ensuring data is collected and shared. In a more general sense, it encourages research and development as well as liaison, mutual support and interoperability among national and NATO command METOC capabilities that support allied forces.

NATO member countries are expected to provide the bulk of METOC information and resources. At the same time, national delegates are able to steer policy, when needed, through the MCWG(METOC) and act as the approval authority for standardization. Among other tasks, nations are expected to:

NATO established a METOC Communications Hub collocated with the Bundeswehr Geo-Information Office in Germany to better enable information-sharing among Allies and partner countries. Other allied nations also contribute to data-sharing capabilities by, for example, sustaining databases of oceanographic information or taking a lead responsibility in supporting specified operations and missions.

The interdependencies and importance of climate change was one of the motivating factors for combining the former oceanography and meteorology groups. NATO nations and partners monitor global situations like climate change that affect security interests. In this respect, it collaborates with international organizations such as the United Nations, the World Meteorological Organization and the International Civil Aviation Organization.

The working group helps NATO members and partner countries look at how, within their national civil or military METOC capabilities, or within a collective capability, they are assessing and preparing for climate change and other national security threats.

The eofs library provides a high-level Python interface for computing empirical orthogonal functions (EOFs) and related quantities, with a focus on correctness and ease of use. The library is implemented in a modular hierarchical fashion, allowing computations using plain arrays, or the inclusion of metadata. The software provides a convenient package for users wanting to perform EOF analysis in Python, and integrates with popular libraries from atmospheric and climate science. The software is available on Github.

Data sets in meteorology, oceanography, and climate are typically very large, containing data covering large spatial areas, observed or modelled over long periods of time. Studying variability in these data sets can be challenging, with coherent modes of large-scale spatial and temporal variability in the atmosphere-ocean system hidden amongst the noise of smaller scale physical processes. An often used technique for examining large-scale patterns of variability in such data sets is the analysis of empirical orthogonal functions (EOFs) [1]. Decomposing a complex data set varying in time and space into a set of EOFs and associated principal component time series (PCs) can allow insight into the most dominant modes of spatial variability, for example El Nio, one of the leading modes of climate variability, is often characterised by the first EOF and PC of sea surface temperature in the tropical Pacific [2].

The EOFs and PCs of a data set describe a new basis, where instead of a series of spatial observations varying in time, the data set is represented as a set of fixed spatial patterns or modes, which represent a given amount of the total variance in the data set, and a set of time series describing how each pattern changes with time. In typical applications the first few EOFs account for a large portion of the total variance, allowing the study of one or two modes to give insight into the variability present in the data set. The method of analysis is purely mathematical and does not depend on any physical properties of the quantity being analysed.

The process of computing and analysing EOFs and related structures is non-trivial, and highly error prone. For example, consider the computation of EOFs from a time-series of sea surface temperature on a latitude-longitude grid. First one must correctly weight the input data to account for spatial variability in the size of grid cells due to convergence of the meridians. The input data must then be reconfigured into a 2-dimensional form, and care taken to remove any missing values (e.g., values of an oceanographic field over land) so that the covariance matrix can be constructed, and the EOFs computed as the (possibly scaled) eigenvectors of the covariance matrix. In order to correctly interpret the EOFs it is necessary to undo the data preparation steps listed above: the eigenvectors must be reformed into 2-dimensional maps, inserting any missing values back into their correct locations, and weighting often needs to be removed. Typically one will not just be interested in the EOFs themselves but also in other derived quantities such as the PC time series associated with each EOF, or the projection of other fields onto the EOFs. Similar data preparation and reconfiguration procedures are required to construct these quantities and great care must be taken to ensure that the application of these procedures is consistent in the computation of each quantity.

There are existing software packages and libraries for computing EOFs and related quantities [3, 4], but this type of data analysis is often done in an ad-hoc manner using un-published code. The publically available tools for EOF analysis are typically libraries that provide separate procedures to compute each required output, a design that cannot automatically ensure the self-consistency of the analysis outputs. Therefore the user is responsible for keeping track of the integrity of the analysis. One of the major motivations behind the development of eofs was to resolve this problem by taking advantage of object-oriented design. Using an object to encapsulate the core information about how the input data set was transformed in order to do the EOF computation allows the construction of method calls to compute any required related quantity in a manner consistent with the original decomposition. This is not only convenient for the programmer as it removes a lot of tedious overheads, but also ensures correctness of the resulting quantities. The eofs library has been used to analyse data in a number of scientific studies [5, 6].

The eofs library is implemented in a hierarchical structure. The core of the library is an EOF solver object. The solver object is a numerical solver constructed by passing a data set to analyse in the form of a NumPy array [7], and optionally an array of weights that apply to that data. Method calls are then used to generate the required outputs, in the form of NumPy arrays (see Table 1). This design allows all methods of the solver object to know exactly what weighting, reconfiguration and scaling has taken place to produce the EOFs, and hence allows derived quantities to be computed in an internally consistent manner. This core solver object does not know (or care) about the meaning or structure of the input data set, and is thus generic.

On top of the core component there are interfaces that can apply the analysis to data structures that contain structured metadata as well as data values, specifically designed for meteorological and oceanographic data sets. These metadata-aware solvers are motivated the desire to improve data provenance and ensure the correctness of scientific results. These issues affect all scientific research, but have been strongly highlighted in the climate science community in recent years [8]. The metadata-aware interfaces provide a layer on top of the core solver that interprets metadata from the input and uses it to determine how the data set is structured. The metadata-aware solvers are able to automatically reconfigure input data sets and generate appropriate weights for them according to pre-defined weighting schemes, and crucially they are able to return objects with correct metadata that can be used to identify the returned field outside the context of the analysis program.

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