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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

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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

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2 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Young Investigators Group CoSy‐CC2 @ PIK

  • 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

Complex systems methods for understanding causes and consequences of past, present and future climate change

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3 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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

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4 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

  • 1. Extremes – why are they so important?
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5 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Relevance of extreme events

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6 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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

  • f values
  • f 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.

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7 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

  • 2. Quantile

trends as proxies for time‐dependent extremes

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8 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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

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9 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Example: Monthly tide gauge data from the Baltic Sea

(Barbosa, 2008)

Result: higher quantiles rise faster, lower ones slower than the mean (in entire Baltic Sea)

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10 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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)

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11 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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)

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12 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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)

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13 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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)

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14 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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? Question: Is there any systematic acceleration/deceleration of trends?  Statistical tests (t‐test and Mann‐Kendall test for (in)/dependent data)

(Donner et al., 2012)

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15 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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
  • r 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

  • f time‐dependent

extreme value theory?

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16 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Example: Daily tide gauge data from the Baltic Sea

(Ribeiro et al., 2014)

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17 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Example: Daily tide gauge data from the Baltic Sea

(Ribeiro et al., 2014)

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18 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Examples for

  • ther

climate variables

Daily temperatures (max/min/mean) – station data

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19 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Examples for

  • ther

climate variables

Daily temperatures (max/min/mean) – station data

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20 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Examples for

  • ther

climate variables

Daily mean temperatures DJF – ERA‐Interim

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21 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Examples for

  • ther

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

  • …
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22 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

  • 3. Spatial patterns of extremes: Complex network analyses
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23 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

The starting point…

(Bull. Amer. Meteor. Soc., 2006)

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24 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

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

Networks are everywhere!

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25 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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 Aij =1  nodes i and j are connected by a link Aij =0  nodes i and j are not connected by a direct link  binary matrix containing connectivity information of the graph  undirected graph: A symmetric

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26 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 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

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27 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Starting point: Spatially distributed climate time series (e.g. reanalysis data)  Consider spatial locations as “nodes” (vertices) of a network  Compute mutual correlations between time series = “weights”

  • f links

(edges) in a weighted network representation based on statistical associations (functional network!)  Remove all links with “weak” correlations = unweighted network representation  Apply measures from complex network theory for studying the topological properties of the resulting graphs and their evolution Refinement: replace correlations by other more sophisticated interdependency measures (mutual information, event synchronization,…)

Climate networks: Basic algorithm

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28 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Climate network analysis for running windows in time: evolving climate networks Global network characteristics show distinct temporal variability profile strongly related to ENSO

Evolving global surface air temperature network

(Radebach et al., Phys. Rev. E, 2013)

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29 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Interesting observation: peaks in global network characteristics do not coincide 1:1 with El Nino episodes Reason: peaks indicate the formation of “localized structures”

  • f high connectivity, which may also

arise in some La Nina periods as well as after strong volcanic eruptions (common regional cooling trend – increase of correlations) In turn, not all El Ninos are accompanied by peaks: functional discrimination between classical and Modoki El Ninos!

Evolving global surface air temperature network

(Radebach et al., Phys. Rev. E, 2013) Transitivity, NINO3.4, strat. opt. depth

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30 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Investigation of spatio‐temporal structure of South American moisture divergence (E‐P) from MERRA Simplified view:

  • Positive extrema: strong evapo‐transpiration
  • Negative extrema: heavy rainfall

(Boers et al., Clim. Dyn., in revision)

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31 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Special interest: spatio‐temporal organization of extremes (i.e., moisture divergence above/below certain thresholds)  Use event synchronization as similarity measure: normalized fraction of temporally close extremes observed at different grid points

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32 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Mean daily moisture divergence

(Boers et al., Clim. Dyn., in revision)

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33 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

10% quantile

  • f daily moisture divergence (extreme precipitation)

(Boers et al., Clim. Dyn., in revision)

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34 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

90% quantile

  • f daily moisture divergence (extreme evapotranspiration)

(Boers et al., Clim. Dyn., in revision)

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35 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Local clustering coefficient for networks of extreme evapotranspiration events

(Boers et al., Clim. Dyn., in revision)

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36 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Average size of connected components of contemporaneous evapotranspiration extremes

(Boers et al., Clim. Dyn., in revision)

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37 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Networks of extreme moisture divergence

Differences between classical (1) and Modoki (2) El Ninos

(Boers et al., Clim. Dyn., in revision)

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38 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Spatial backbone of Indian summer monsoon revealed by event synchronization of heavy rainfall (Malik et al., Climate Dyn., 2012)

Regional climate networks

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39 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

  • 4. Do climate

extremes determine extreme ecosystem responses?

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40 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Coincidence analysis

  • Related concept with rigorous statistical framework
  • Uncorrelated events: analytical expressions for the probability distribution
  • f number of co‐occurrences

(Donges, Donner, et al., PNAS, 2011)

  • Correlated events: analytics approximately valid for short‐term

correlations – work in progress

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41 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Coincidence analysis

  • Uncorrelated events: analytics vs. numerics

(N=10 reference events)

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42 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Definition of events

Classical definition: fixed thresholds – only valid for stationary signals with constant background (e.g., no seasonal cycle) Possible solution: Determine time‐varying threshold according to a given quantile conditioned to the phase of the seasonal cycle 1. Filtering / decomposition (SSA, wavelets, EMD,…) – corrects only for non‐ stationarity in mean, not in higher‐order moments 2. Quantile regression – determines time‐varying quantile threshold for event detection (accounts for trends and cycles) 3. Double‐kernel approach in time and magnitude (MSc thesis Eva Hauber)

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43 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Definition of events

  • Multivariate extremes (e.g. heat and water stress to plants)?

 alternative definition of events (e.g. based on copula concept) – work in progress  more than just two types of extremes (cluster analysis)?!

(Schölzel & Friedrichs, NPG, 2008)

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44 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Application: Yearly extreme tree ring widths

 Tree ring width as a proxy for annual net primary production (Rammig et

  • al. 2014): Do bad years correspond to extreme climatic conditions?
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45 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Next steps

 Extension of this approach to much shorter time‐scales (PhD project Jonatan Siegmund):

  • Remote sensing data (faPAR, NDVI)
  • Eddy covariance measurements (FLUXNET)
  • Ecosystem models (validation)
  • (sub)seasonally

resolved tree ring data?  Spatially resolved coincidence analysis between two variables: (coupled) complex network approach?!  Necessary modifications: time lags, causality,…

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  • 5. Take home messages
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47 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

Take home messages

  • Statistical analysis of extremes provides new insights into their potential

impacts on human societies and ecosystems

  • Trend analysis for extremes: quantile

regression methods

  • Spatial patterns of extremes: event synchronization and complex

networks

  • Statistical relationships between extremes in more than one variable:

coincidence analysis

  • Many open points currently being addressed: temporal aggregation

effect, time‐dependent baseline states, multivariate extremes,…

  • Further applications/collaborations are welcome!
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48 Reik V. Donner, RD IV Transdisciplinary Concepts & Methods reik.donner@pik‐potsdam.de

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