Statistical methods

Feliks Y, Ghil M, Ziona I, Dynamique M. Long-range forecasting and the scientific background in Joseph's interpretation to Pharaoh’s dreams, in Proc. 16th Conf. Research Judaea & Samaria. in press ; 2006.Abstract

Long-range forecasting is today a major area of climate research. Such forecasts affect socioeconomic planning in many fields of activity. There are essentially two approaches to longrange forecasting: one is based on solving the equations that govern atmospheric and ocean dynamics, the other on the statistical properties of past climate records. The present talk is based on the latter, statistical approach. Joseph’s interpretation of Pharaoh’s dreams provides a striking example of long-range planning based on a climate forecast. Joseph interpreted the two dreams as a forecast for seven years of plenty, followed by seven of famine. Based on this forecast, he proposed to Pharaoh a plan for running the agriculture and economy of Egypt. It is not clear from the Biblical story why Pharaoh trusted Joseph’s forecast and appointed him to implement the plan. Our answer to this question is based on ancient and medieval Egypt’s being entirely dependent on the Nile River’s seasonal flooding: when the highest water levels did not cover the arable areas of the river valley, crops were insufficient to feed the population. When successive years of hunger weakened the economy and the state, change of rulers could, and sometimes did ensue. Extreme examples were the fall of the Old Kingdom in 2185 B.C. and the Fatimid conquest of Egypt in 969 A.D. Hence the Egyptians measured the high-water mark of the Nile River for over 5000 years, using different tools. The most advanced of these tools was the nilometer; typical nilometers appear in several mosaics from the Roman and Byzantine period around the Mediterranean, such as the “Nile Festival” mosaic in Zippori (Upper Galilee), Fig. 1. The measurements had a twofold purpose: first to set the annual taxes, which were a function of the high-water mark, for obvious reasons; and second, to provide information for water management, with a view to reduce drought damage. Our analysis of high- and low-water levels for 622–1922 A.D. shows that oscillations with a period of several years occur, with a 7-year oscillation being dominant. We suspect that the origin of this 7-year swing lies in the same periodicity being present in the North Atlantic’s sea-surface temperatures and sea-level pressures. This North Atlantic Oscillation affects the climate of Europe, North America and the Middle East, and might be the ultimate reason for Joseph’s successful climate forecast.

Walwer D, Calais E, Ghil M. Data-Adaptive Detection of Transient Deformation in Geodetic Networks. Journal of Geophysical Research: Solid Earth. 2016;121 (3) :2129-2152 .Abstract

The recent development of dense and continuously operating Global Navigation Satellite System (GNSS) networks worldwide has led to a significant increase in geodetic data sets that sometimes capture transient-deformation signals. It is challenging, however, to extract such transients of geophysical origin from the background noise inherent to GNSS time series and, even more so, to separate them from other signals, such as seasonal redistributions of geophysical fluid mass loads. In addition, because of the very large number of continuously recording GNSS stations now available, it has become impossible to systematically inspect each time series and visually compare them at all neighboring sites. Here we show that Multichannel Singular Spectrum Analysis (M-SSA), a method derived from the analysis of dynamical systems, can be used to extract transient deformations, seasonal oscillations, and background noise present in GNSS time series. M-SSA is a multivariate, nonparametric, statistical method that simultaneously exploits the spatial and temporal correlations of geophysical fields. The method allows for the extraction of common modes of variability, such as trends with nonconstant slopes and oscillations shared across time series, without a priori hypotheses about their spatiotemporal structure or their noise characteristics. We illustrate this method using synthetic examples and show applications to actual GPS data from Alaska to detect seasonal signals and microdeformation at the Akutan active volcano. The geophysically coherent spatiotemporal patterns of uplift and subsidence thus detected are compared to the results of an idealized model of such processes in the presence of a magma chamber source.

Groth A, Ghil M, Hallegatte S, Dumas P. The Role of Oscillatory Modes in U.S. Business Cycles. Fondazione Eni Enrico Mattei (FEEM) [Internet]. 2012;26 :1. Publisher's VersionAbstract

We apply the advanced time-and-frequency-domain method of singular spectrum analysis to study business cycle dynamics in a set of nine U.S. macroeconomic indicators. This method provides a robust way to identify and reconstruct shared oscillations, whether intermittent or modulated. We address the problem of spurious cycles generated by the use of detrending filters and present a Monte Carlo test to extract significant oscillations. Finally, we demonstrate that the behavior of the U.S. economy changes significantly between episodes of growth and recession; these variations cannot be generated by random shocks alone, in the absence of endogenous variability.

Kondrashov D, Shprits Y, Ghil M. Gap Filling of Solar Wind Data by Singular Spectrum Analysis. Geophysical Research Letters. 2010;37 :L15101.Abstract

Observational data sets in space physics often contain instrumental and sampling errors, as well as large gaps. This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation. For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994. Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth “signal” that captures coherent modes, while “noise” is discarded. In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time continuous, and generalizing it to multivariate geophysical data consisting of gappy “driver” and continuous “response” records. The reconstruction error estimates provide information on the physics of co variability between particular solar wind parameters and geomagnetic indices.

Feliks Y, Ghil M, Robertson AW. Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation. Journal of Climate. 2010;23 (15) :4060–4079.Abstract

Oscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights. The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization. A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.