scholarly journals On the Sensitivity of Field Reconstruction and Prediction Using Empirical Orthogonal Functions Derived from Gappy Data

2013 ◽  
Vol 26 (22) ◽  
pp. 9194-9205 ◽  
Author(s):  
Marc H. Taylor ◽  
Martin Losch ◽  
Manfred Wenzel ◽  
Jens Schröter
Keyword(s):  
Least Squares ◽  
Missing Values ◽  
Estimation Error ◽  
Computation Time ◽  
Matrix Decomposition ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Galapagos Archipelago ◽  
Novel Approach ◽  
Superior Approach

Abstract Empirical orthogonal function (EOF) analysis is commonly used in the climate sciences and elsewhere to describe, reconstruct, and predict highly dimensional data fields. When data contain a high percentage of missing values (i.e., gappy), alternate approaches must be used in order to correctly derive EOFs. The aims of this paper are to assess the accuracy of several EOF approaches in the reconstruction and prediction of gappy data fields, using the Galapagos Archipelago as a case study example. EOF approaches included least squares estimation via a covariance matrix decomposition [least squares EOF (LSEOF)], data interpolating empirical orthogonal functions (DINEOF), and a novel approach called recursively subtracted empirical orthogonal functions (RSEOF). Model-derived data of historical surface chlorophyll-a concentrations and sea surface temperature, combined with a mask of gaps from historical remote sensing estimates, allowed for the creation of true and observed fields by which to gauge the performance of EOF approaches. Only DINEOF and RSEOF were found to be appropriate for gappy data reconstruction and prediction. DINEOF proved to be the superior approach in terms of accuracy, especially for noisy data with a high estimation error, although RSEOF may be preferred for larger data fields because of its relatively faster computation time.

scholarly journals The Effect of Signal-to-Noise Ratio on the Study of Sea Level Trends

2011 ◽  
Vol 24 (5) ◽  
pp. 1396-1408 ◽  
Author(s):  
B. D. Hamlington ◽  
R. R. Leben ◽  
R. S. Nerem ◽  
K.-Y. Kim
Keyword(s):  
Least Squares ◽  
Sea Level ◽  
Least Squares Method ◽  
Secular Trend ◽  
Signal To Noise Ratio ◽  
Empirical Orthogonal Functions ◽  
Signal To Noise ◽  
Orthogonal Functions ◽  
Geophysical Processes ◽  
Noise Ratio

Abstract Extracting secular sea level trends from the background ocean variability is limited by how well one can correct for the time-varying and oscillating signals in the record. Many geophysical processes contribute time-dependent signals to the data, making the sea level trend difficult to detect. In this paper, cyclostationary empirical orthogonal functions (CSEOFs) are used to quantify and improve the signal-to-noise ratio (SNR) between the secular trend and the background variability, obscuring this trend in the altimetric sea level record by identifying and removing signals that are physically interpretable. Over the 16-yr altimetric record the SNR arising from the traditional least squares method for estimating trends can be improved from 4.0% of the ocean having an SNR greater than one to 9.9% when using a more sophisticated statistical method based on CSEOFs. From a standpoint of signal detection, this implies that the secular trend in a greater portion of the ocean can be estimated with a higher degree of confidence. Furthermore, the CSEOF method improves the standard error on the least squares estimates of the secular trend in 97% of the ocean. The convergence of the SNR as the record length is increased is used to estimate the SNR of sea level trends in the near future as more measurements become available from near-global altimetric sampling.

scholarly journals A singular evolutive extended Kalman filter to assimilate real in situ data in a 1-D marine ecosystem model

2003 ◽  
Vol 21 (1) ◽  
pp. 389-397 ◽  
Author(s):  
I. Hoteit ◽  
G. Triantafyllou ◽  
G. Petihakis ◽  
J. I. Allen
Keyword(s):  
Estimation Error ◽  
Marine Ecosystem ◽  
Ecosystem Model ◽  
Ocean Model ◽  
Empirical Orthogonal Functions ◽  
Error Statistics ◽  
Orthogonal Functions ◽  
In Situ Data ◽  
Marine Ecosystem Model

Abstract. A singular evolutive extended Kalman (SEEK) filter is used to assimilate real in situ data in a water column marine ecosystem model. The biogeochemistry of the ecosystem is described by the European Regional Sea Ecosystem Model (ERSEM), while the physical forcing is described by the Princeton Ocean Model (POM). In the SEEK filter, the error statistics are parameterized by means of a suitable basis of empirical orthogonal functions (EOFs). The purpose of this contribution is to track the possibility of using data assimilation techniques for state estimation in marine ecosystem models. In the experiments, real oxygen and nitrate data are used and the results evaluated against independent chlorophyll data. These data were collected from an offshore station at three different depths for the needs of the MFSPP project. The assimilation results show a continuous decrease in the estimation error and a clear improvement in the model behavior. Key words. Oceanography: general (ocean prediction; numerical modelling) – Oceanography: biological and chemical (ecosystems and ecology)

scholarly journals Pseudo-proxy tests of the analogue method to reconstruct spatially resolved global temperature during the Common Era

2017 ◽  
Vol 13 (6) ◽  
pp. 629-648 ◽  
Author(s):  
Juan José Gómez-Navarro ◽  
Eduardo Zorita ◽  
Christoph C. Raible ◽  
Raphael Neukom
Keyword(s):  
Missing Values ◽  
Real Space ◽  
Empirical Orthogonal Functions ◽  
Test Bed ◽  
Orthogonal Functions ◽  
Proxy Records ◽  
Spatially Resolved ◽  
Analogue Method ◽  
The Common ◽  
Common Era

Abstract. This study addresses the possibility of carrying out spatially resolved global reconstructions of annual mean temperature using a worldwide network of proxy records and a method based on the search of analogues. Several variants of the method are evaluated, and their performance is analysed. As a test bed for the reconstruction, the PAGES 2k proxy database (version 1.9.0) is employed as a predictor, the HadCRUT4 dataset is the set of observations used as the predictand and target, and a set of simulations from the PMIP3 simulations are used as a pool to draw analogues and carry out pseudo-proxy experiments (PPEs). The performance of the variants of the analogue method (AM) is evaluated through a series of PPEs in growing complexity, from a perfect-proxy scenario to a realistic one where the pseudo-proxy records are contaminated with noise (white and red) and missing values, mimicking the limitations of actual proxies. Additionally, the method is tested by reconstructing the real observed HadCRUT4 temperature based on the calibration of real proxies. The reconstructed fields reproduce the observed decadal temperature variability. From all the tests, we can conclude that the analogue pool provided by the PMIP3 ensemble is large enough to reconstruct global annual temperatures during the Common Era. Furthermore, the search of analogues based on a metric that minimises the RMSE in real space outperforms other evaluated metrics, including the search of analogues in the range-reduced space expanded by the leading empirical orthogonal functions (EOFs). These results show how the AM is able to spatially extrapolate the information of a network of local proxy records to produce a homogeneous gap-free climate field reconstruction with valuable information in areas barely covered by proxies and make the AM a suitable tool to produce valuable climate field reconstructions for the Common Era.

scholarly journals Technical Note: A novel approach to estimation of time-variable surface sources and sinks of carbon dioxide using empirical orthogonal functions and the Kalman filter

2011 ◽  
Vol 11 (1) ◽  
pp. 1367-1384
Author(s):  
R. Zhuravlev ◽  
B. Khattatov ◽  
B. Kiryushov ◽  
S. Maksyutov
Keyword(s):  
Carbon Dioxide ◽  
Kalman Filter ◽  
Carbon Dioxide Emissions ◽  
Transport Model ◽  
Technical Note ◽  
Empirical Orthogonal Functions ◽  
Computationally Efficient ◽  
Orthogonal Functions ◽  
Novel Approach ◽  
Variable Surface

Abstract. In this work we propose an approach to solving a source estimation problem based on representation of carbon dioxide surface emissions as a linear combination of a finite number of pre-computed empirical orthogonal functions (EOFs). We used NIES transport model for computing response functions and Kalman filter for estimating carbon dioxide emissions. Our approach produces results similar to these of other models participating in the TransCom3 experiment, while being more advantageous in that it is more computationally efficient, produces smooth emission fields, and yields smaller errors than the traditional region-based approach. Additionally, the proposed approach does not require additional effort of defining independent self-contained emission regions.

Empirical Orthogonal Functions

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Missing Values ◽  
Original Data ◽  
Empirical Orthogonal Functions ◽  
Basis Set ◽  
Data Matrix ◽  
Multidimensional Data ◽  
Data Sets ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Multidimensional Data Sets

This chapter focuses on empirical orthogonal functions (EOFs). One of the most useful and common eigen-techniques in data analysis is the construction of EOFs. EOFs are a transform of the data; the original set of numbers is transformed into a different set with some desirable properties. In this sense the EOF transform is similar to other transforms, such as the Fourier or Laplace transforms. In all these cases, we project the original data onto a set of functions, thus replacing the original data with the set of projection coefficients on the chosen new set of basis vectors. However, the choice of the specific basis set varies from case to case. The discussions cover data matrix structure convention, reshaping multidimensional data sets for EOF analysis, forming anomalies and removing time mean, missing values, choosing and interpreting the covariability matrix, calculating the EOFs, projection time series, and extended EOF analysis.

scholarly journals Technical Note: A novel approach to estimation of time-variable surface sources and sinks of carbon dioxide using empirical orthogonal functions and the Kalman filter

2011 ◽  
Vol 11 (20) ◽  
pp. 10305-10315 ◽  
Author(s):  
R. Zhuravlev ◽  
B. Khattatov ◽  
B. Kiryushov ◽  
S. Maksyutov
Keyword(s):  
Carbon Dioxide ◽  
Kalman Filter ◽  
Carbon Dioxide Emissions ◽  
Transport Model ◽  
Technical Note ◽  
Empirical Orthogonal Functions ◽  
Surface Fluxes ◽  
Orthogonal Functions ◽  
Novel Approach ◽  
Variable Surface

Abstract. In this work we propose an approach to solving a source estimation problem based on representation of carbon dioxide surface emissions as a linear combination of a finite number of pre-computed empirical orthogonal functions (EOFs). We used National Institute for Environmental Studies (NIES) transport model for computing response functions and Kalman filter for estimating carbon dioxide emissions. Our approach produces results similar to these of other models participating in the TransCom3 experiment. Using the EOFs we can estimate surface fluxes at higher spatial resolution, while keeping the dimensionality of the problem comparable with that in the regions approach. This also allows us to avoid potentially artificial sharp gradients in the fluxes in between pre-defined regions. EOF results generally match observations more closely given the same error structure as the traditional method. Additionally, the proposed approach does not require additional effort of defining independent self-contained emission regions.

Empirical Methods in Short-Term Climate Prediction

2006 ◽  
Author(s):  
Huug van den Dool
Keyword(s):  
Climate Prediction ◽  
Empirical Orthogonal Functions ◽  
Data Sets ◽  
Seasonal Forecasts ◽  
Short Term ◽  
Orthogonal Functions ◽  
Ocean Atmosphere Interaction ◽  
Global Coverage ◽  
Atmosphere Interaction ◽  
Global Data

This clear and accessible text describes the methods underlying short-term climate prediction at time scales of 2 weeks to a year. Although a difficult range to forecast accurately, there have been several important advances in the last ten years, most notably in understanding ocean-atmosphere interaction (El Nino for example), the release of global coverage data sets, and in prediction methods themselves. With an emphasis on the empirical approach, the text covers in detail empirical wave propagation, teleconnections, empirical orthogonal functions, and constructed analogue. It also provides a detailed description of nearly all methods used operationally in long-lead seasonal forecasts, with new examples and illustrations. The challenges of making a real time forecast are discussed, including protocol, format, and perceptions about users. Based where possible on global data sets, illustrations are not limited to the Northern Hemisphere, but include several examples from the Southern Hemisphere.

scholarly journals Spatio-Temporal Patterns of Mass Changes in Himalayan Glaciated Region from EOF Analyses of GRACE Data

2021 ◽  
Vol 13 (2) ◽  
pp. 265
Author(s):  
Harika Munagapati ◽  
Virendra M. Tiwari
Keyword(s):  
Temperature Anomaly ◽  
Mass Gain ◽  
Snow Accumulation ◽  
Empirical Orthogonal Functions ◽  
Total Water ◽  
Orthogonal Functions ◽  
Grace Data ◽  
Grace Satellite ◽  
Spatio Temporal ◽  
Gravity Recovery

The nature of hydrological seasonality over the Himalayan Glaciated Region (HGR) is complex due to varied precipitation patterns. The present study attempts to exemplify the spatio-temporal variation of hydrological mass over the HGR using time-variable gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite for the period of 2002–2016 on seasonal and interannual timescales. The mass signal derived from GRACE data is decomposed using empirical orthogonal functions (EOFs), allowing us to identify the three broad divisions of HGR, i.e., western, central, and eastern, based on the seasonal mass gain or loss that corresponds to prevailing climatic changes. Further, causative relationships between climatic variables and the EOF decomposed signals are explored using the Granger causality algorithm. It appears that a causal relationship exists between total precipitation and total water storage from GRACE. EOF modes also indicate certain regional anomalies such as the Karakoram mass gain, which represents ongoing snow accumulation. Our causality result suggests that the excessive snowfall in 2005–2008 has initiated this mass gain. However, as our results indicate, despite the dampening of snowfall rates after 2008, mass has been steadily increasing in the Karakorum, which is attributed to the flattening of the temperature anomaly curve and subsequent lower melting after 2008.

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