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 Testing the analog method in reconstructing the global mean annual temperature during the Common Era

2016 ◽  
Author(s):  
Juan José Gómez-Navarro ◽  
Eduardo Zorita ◽  
Christoph C. Raible ◽  
Raphael Neukom
Keyword(s):  
Missing Values ◽  
Mean Annual Temperature ◽  
Test Bed ◽  
Analog Method ◽  
Proxy Records ◽  
The Common ◽  
Reduced Space ◽  
Worldwide Network ◽  
Common Era ◽  
Global Mean

Abstract. This study addresses the possibility to carry out global gridded mean annual temperature reconstructions using a worldwide network of proxy records and a method based on the search of analogs (AM-CFR). Several variants of the method are evaluated, and their performance is analysed. As test bed for the reconstruction, the PAGES2K proxy database (version 1.9.0) is employed as predictor, the HadCRUT4 dataset is the set of observations used as predictand and target, and a set of simulations from the PMIP3 are used as pool to draw analogs and carry out Pseudo Proxy Experiments (PPE). The performance of the variants of the analog method is evaluated through a series of PPEs in growing complexity, from a perfect scenario to a realistic one where the pseudo-proxy records are contaminated with noise and missing values mimicking the limitations of actual proxies. From all the tests carried out, we can conclude that the analog pool provided by PMIP3 ensemble is large enough to reconstruct global annual temperatures during the Common Era. Further, the search of analogs based on a metric that minimises the RMSE outperforms other evaluated metrics, including the search of analogs in the range-reduced space expanded by the leading EOFs. We show how the method is able to extrapolate the information of the proxy network to produce a homogeneous gap-free climate field reconstruction with valuable information in areas barely covered by proxies. Finally, the method is applied to reconstruct the HadCRUT4 observed temperature based on the calibration of the proxies. The reconstructed fields reproduce the observed decadal temperature variability. The AM-CFR is a suitable tool which is able to deliver valuable climate field reconstructions for the Common Era.

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 Extratropical cyclone statistics during the last millennium and the 21st century

2018 ◽  
Vol 14 (10) ◽  
pp. 1499-1514 ◽  
Author(s):  
Christoph C. Raible ◽  
Martina Messmer ◽  
Flavio Lehner ◽  
Thomas F. Stocker ◽  
Richard Blender
Keyword(s):  
21St Century ◽  
Internal Variability ◽  
Extratropical Cyclone ◽  
Strong Increase ◽  
Dynamical Processes ◽  
Proxy Records ◽  
Extreme Wind ◽  
The Common ◽  
Common Era ◽  
Fully Coupled

Abstract. Extratropical cyclones in winter and their characteristics are investigated in depth for the Atlantic European region, as they are responsible for a significant part of the rainfall and extreme wind and/or precipitation-induced hazards. The analysis is based on a seamless transient simulation with a state-of-the-art fully coupled Earth system model from 850 to 2100 CE. The Representative Concentration Pathway 8.5 (RCP8.5) scenario is used in the 21st century. During the Common Era, cyclone characteristics show pronounced variations on interannual and decadal timescales, but no external forcing imprint is found prior to 1850. Thus, variations of extratropical cyclone characteristics are mainly caused by internal variability of the coupled climate system. When anthropogenic forcing becomes dominant in the 20th century, a decrease of the cyclone occurrences mainly over the Mediterranean and a strong increase of extreme cyclone-related precipitation become detectable. The latter is due to thermodynamics as it follows the Clausius–Clapeyron relation. An important finding, though, is that the relation between temperature and extreme cyclone-related precipitation is not always controlled by the Clausius–Clapeyron relation, which suggests that dynamical processes can play an important role in generating extreme cyclone-related precipitation – for example, in the absence of anomalously warm background conditions. Thus, the importance of dynamical processes, even on decadal timescales, might explain the conundrum that proxy records suggest enhanced occurrence of precipitation extremes during rather cold periods in the past.

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.

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.

The Word of God in One’s Hand: Touching and Holding Pendant Koran Manuscripts

2020 ◽  
Vol 25 (2) ◽  
pp. 338-357
Author(s):  
Cornelius Berthold
Keyword(s):  
Haptic Feedback ◽  
The Body ◽  
Word Of God ◽  
Rare Occurrence ◽  
Recent Scholarship ◽  
Solid Objects ◽  
Cylindrical Form ◽  
The Common ◽  
Common Era

AbstractKoran manuscripts that fit comfortably within the palm of one’s hand are known as early as the 10th century CE.For the sake of convenience, all dates will be given in the common era (CE) without further mention, and not in the Islamic or Hijra calendar. Their minute and sometimes barely legible script is clearly not intended for comfortable reading. Instead, recent scholarship suggests that the manuscripts were designed to be worn on the body like pendants or fastened to military flag poles. This is corroborated by some preserved cases for these books which feature lugs to attach a cord or chain, but also their rare occurrence in contemporary textual sources. While pendant Korans in rectangular codex form exist, the majority were produced as codices in the shape of an octagonal prism, and others as scrolls that could be rolled up into a cylindrical form. Both resemble the shapes of similarly dated and pre-Islamic amulets or amulet cases. Building on recent scholarship, I will argue in this article that miniature or pendant Koran manuscripts were produced in similar forms and sizes because of comparable modes of usage, but not necessarily by a deliberate imitation of their amuletic ‘predecessors’. The manuscripts’ main functions did not require them to be read or even opened; some of their cases were in fact riveted shut. Accordingly, the haptic feedback they gave to their owners when they carried or touched them was not one of regular books but one of solid objects (like amulets) or even jewellery, which then reinforced this practice.

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.

Identifying VIV Vibration Modes by Use of the Empirical Orthogonal Functions Technique

2002 ◽  
Author(s):  
Gudmund Kleiven
Keyword(s):  
Model Test ◽  
Vibration Mode ◽  
Multivariate Data ◽  
Empirical Orthogonal Functions ◽  
Mode Shapes ◽  
Data Sets ◽  
Vibration Modes ◽  
Ocean Engineering ◽  
Orthogonal Functions ◽  
Related Technique

The Empirical Orthogonal Functions (EOF) technique has widely being used by oceanographers and meteorologists, while the Singular Value Decomposition (SVD being a related technique is frequently used in the statistics community. Another related technique called Principal Component Analysis (PCA) is observed being used for instance in pattern recognition. The predominant applications of these techniques are data compression of multivariate data sets which also facilitates subsequent statistical analysis of such data sets. Within Ocean Engineering the EOF technique is not yet widely in use, although there are several areas where multivariate data sets occur and where the EOF technique could represent a supplementary analysis technique. Examples are oceanographic data, in particular current data. Furthermore data sets of model- or full-scale data of loads and responses of slender bodies, such as pipelines and risers are relevant examples. One attractive property of the EOF technique is that it does not require any a priori information on the physical system by which the data is generated. In the present paper a description of the EOF technique is given. Thereafter an example on use of the EOF technique is presented. The example is analysis of response data from a model test of a pipeline in a long free span exposed to current. The model test program was carried out in order to identify the occurrence of multi-mode vibrations and vibration mode amplitudes. In the present example the EOF technique demonstrates the capability of identifying predominant vibration modes of inline as well as cross-flow vibrations. Vibration mode shapes together with mode amplitudes and frequencies are also estimated. Although the present example is not sufficient for concluding on the applicability of the EOF technique on a general basis, the results of the present example demonstrate some of the potential of the technique.

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