Dynamical aspects of extremes in climate and ecosystems: Assessing trends, spatial coherence and mutual interdependence Reik V. Donner with Janna Wagner, Viola Mettin, Susana Barbosa, Eva Hauber, Marc Wiedermann, Jonathan F. Donges, Niklas Boers and others Tomsk, 30 June 2014
Young Investigators Group CoSy ‐ CC 2 @ PIK Complex systems methods for understanding causes and consequences of past, present and future climate change • New methods for studying recent climate and paleoclimate data • Regime shifts / dynamical transitions in climate history • Spatio ‐ temporal pattern of climate and paleoclimate variability • Societal / cultural / ecological consequences of climate change Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 2 reik.donner@pik ‐ potsdam.de
Agenda 1. Extremes – why are they so important? 2. Quantile trends as proxies for time ‐ dependent extremes 3. Spatial patterns of extremes: Complex network analyses 4. Do climate extremes determine extreme ecosystem responses? 5. Take home messages Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 3 reik.donner@pik ‐ potsdam.de
1. Extremes – why are they so important? Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 4 reik.donner@pik ‐ potsdam.de
Relevance of extreme events Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 5 reik.donner@pik ‐ potsdam.de
Relevance of extreme events Human societies and ecosystems are commonly adjusted to certain mean conditions, but exhibit tolerance with respect to certain ranges of values of relevant characteristics (e.g., precipitation – sewage systems, river runoffs – dams, etc.) When such ranges are exceeded, negative response often sets in rather quickly and with a strong impact regarding the system’s functionality (e.g., vegetation depth, faunal migration, economic losses, breakdown of infrastructures,…). Consequence: need better knowledge on future frequencies of extremes, their spatial and temporal organization and consequences for interconnected systems. Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 6 reik.donner@pik ‐ potsdam.de
2. Quantile trends as proxies for time ‐ dependent extremes Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 7 reik.donner@pik ‐ potsdam.de
Quantile regression Traditional trend analysis: trends in the mean What about the rest of the distribution, especially the tails? Classical approach: time ‐ dependent extreme value statistics – data ‐ demanding! Useful tool: quantile regression analysis • Estimates a (parametric or nonparametric) model for the conditional quantile functions of the data distribution as a function of time • Generalization of ordinary least ‐ squares estimator replacing squared difference by asymmetric loss function Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 8 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Result: higher quantiles rise faster, lower ones slower than the mean (in entire Baltic Sea) (Barbosa, 2008) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 9 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Results 1: linear quantile trends (10%/50%/90%) corrected for GIA (Donner et al., 2012) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 10 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Results 2: linear quantile trends (10%/50%/90%) relative to trend in mean (Donner et al., 2012) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 11 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Results 3: average nonparametric quantile trends corrected for GIA (Donner et al., 2012) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 12 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Results 4: average nonparametric quantile trends relative to mean (Donner et al., 2012) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 13 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Nonparametric quantile trends show long ‐ term variability Are quantile trends changing with time? (Donner et al., 2012) Question: Is there any systematic acceleration/deceleration of trends? Statistical tests (t ‐ test and Mann ‐ Kendall test for (in)/dependent data) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 14 reik.donner@pik ‐ potsdam.de
Example: Monthly tide gauge data from the Baltic Sea Intermediate summary: • Heterogeneous long ‐ term trends in the distribution of Baltic sea ‐ level: broadening, potentially stronger extremes • Trends in sea ‐ level quantiles are not constant, but vary with time • Consistent spatial pattern of long ‐ term quantile trends Questions: • Monthly variability does not cover time scales of interest (typically 1 day or below): extremes are contained in short ‐ term variability! • Are trends in daily extremes consistent with those in monthly extremes? (Does temporal aggregation matter?) • Are the results comparable to those of time ‐ dependent extreme value theory? Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 15 reik.donner@pik ‐ potsdam.de
Example: Daily tide gauge data from the Baltic Sea (Ribeiro et al., 2014) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 16 reik.donner@pik ‐ potsdam.de
Example: Daily tide gauge data from the Baltic Sea (Ribeiro et al., 2014) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 17 reik.donner@pik ‐ potsdam.de
Examples for other climate variables Daily temperatures (max/min/mean) – station data Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 18 reik.donner@pik ‐ potsdam.de
Examples for other climate variables Daily temperatures (max/min/mean) – station data Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 19 reik.donner@pik ‐ potsdam.de
Examples for other climate variables Daily mean temperatures DJF – ERA ‐ Interim Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 20 reik.donner@pik ‐ potsdam.de
Examples for other climate variables More results (not shown, mostly unpublished): • Daily precipitation values for Germany • Daily runoff values for Germany (SWIM model) • Daily mean/maximum/minimum temperatures for NCEP/NCAR, ERA ‐ Interim, ERA ‐ 40 and e ‐ Obs (MSc thesis Viola Mettin) Planned: • Effect of temporal aggregation on quantile trends for precipitation • … Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 21 reik.donner@pik ‐ potsdam.de
3. Spatial patterns of extremes: Complex network analyses Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 22 reik.donner@pik ‐ potsdam.de
The starting point… (Bull. Amer. Meteor. Soc., 2006) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 23 reik.donner@pik ‐ potsdam.de
Networks are everywhere! Complex networks appear in various scientific disciplines, including transportation sciences, biology, sociology, information sciences, telecommunication, engineering, economics, etc. Solid theory of statistical evaluation and modeling Efficient numerical algorithms and multiple complementary measures Knowledge of interrelations between structure and dynamics Investigate climate problems by making use of complex network approaches as an exploratory tool for data analysis and modeling Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 24 reik.donner@pik ‐ potsdam.de
Network theory: General terms A graph (network) is described by • a set of nodes (vertices) V • a set of links (edges) E between pairs of vertices • eventually a set of weights W associated with the nodes and/or links Basic mathematical structure: adjacency matrix A A ij =1 nodes i and j are connected by a link A ij =0 nodes i and j are not connected by a direct link binary matrix containing connectivity information of the graph undirected graph: A symmetric Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 25 reik.donner@pik ‐ potsdam.de
Network theory: General terms Degree centrality: number of neighbors of a vertex Local clustering coefficient: relative fraction of neighbors of a vertex that are mutual neighbors of each other Global clustering coefficient: mean value of the local clustering coefficient taken over all vertices Transitivity: relative fraction of 3 ‐ loops in the network Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 26 reik.donner@pik ‐ potsdam.de
Recommend
More recommend
