optimalSensor

Implement optimal sensor analyses

Description

The optimalSensor class provides objects that implement an optimal sensor algorithm and related analyses. These analyses help to evaluate the influence of different observation sites on a Kalman filter assimilation, and can also help determine ideal locations for future proxy record development. Here we implement the optimal sensor algorithm described by Comboul et al., 2015. In this method, potential observation sites are ranked by their ability to constrain a metric. The metric is distributed across an ensemble, and the rankings are determined using each site’s ability to reduce the variance of the metric across the ensemble.

Note that the optimal sensor algorithm does not assimilate observations in order to produce a reconstruction. Instead, the algorithm helps quantify the effects of individual observation on an assimilation. As such, optimal sensor analyses can help characterize recpmstructions produced using Kalman filters. Because they do not produce a reconstruction, optimal sensor analyses do not require observations. Aside from the sensor metric, they only require estimates and uncertainties.

In the classical optimal sensor algorithm, the sites are ranked and the site that most strongly constrains the metric (i.e. most strongly reduces metric variance) is deemed the “optimal sensor”. This observation site is used to update the variance of the metric, and also the observation estimates. After updating, the optimal site is removed from the observation network, and the analysis repeats using the remaining observation sites. This algorithm iterates until the desired number of optimal sites have been selected. This algorithm is implemented using the “run” method.

The optimalSensor class also provides two auxiliary methods for implementing optimal sensors. In many cases, it can be useful to quantify the influence of the observation sites relative to one another without implementing the iterative algorithm. The “evaluate” method provides this analysis. Additionally, the classical optimal sensor algorithm neglects the effects of covarying error uncertainties (R covariances). When observation records do have covarying error uncertainties, the classical algorithm will overestimate the total variance constrained by the proxy network. You can instead use the “update” method to update metric variance in a manner that accounts for these covariances.

Outline

The Following Is A Sketch For Using The Optimalsensor Class

Use the “optimalSensor” method to initialize a new optimalSensor object
Use the “estimates”, “uncertainties”, and “metric” methods to provide essential data inputs for the optimal sensor.
Use the “run”, “evaluate”, and “update” methods to implement optimal sensor analyses.

User Methods

Create

optimalSensor - Initializes a new optimalSensor object

label - Return or apply a label to an optimalSensor

Data Inputs

metric - Provide the metric for an optimal sensor
estimates - Provide the observation estimates for an optimal sensor
uncertainties - Provide the observation uncertainties for an optimal sensor

Analyses

run - Iteratively identify optimal sites and update metric variance
evaluate - Return the variance constrained by each site when assimilated alone
update - Update metric variance for a network of covarying observation records

Console Display

disp - Display an optimalSensor object in the console

Utility Methods

Utility methods that help the class run. They do not implement error checking and are not intended for users.

Misc

name - Return an identifying name for use in error messages
Rvariances - Return the error uncertainty variances for the observation sites
assertFinalized - Throw error if an optimal sensor does not have estimates, uncertainties, and a metric
varianceReduction - Calculate the metric variance reduced by each observation site

Tests

tests - Implement unit tests for the optimalSensor class