Tipping points and early warning signals - Istituto …...Tipping points and early warning signals...
Transcript of Tipping points and early warning signals - Istituto …...Tipping points and early warning signals...
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Tipping points and early warning signals
Summer School on Biogeodynamics and Earth System Sciences
Venice, June 2011
Luis Cueto-Felgueroso Sebastian Sonntag
GW Advisor: Tim Lenton
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What is a tipping point?
Lenton (2011) BESS Lecture 4
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Where are tipping points?
• Everywhere
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What happens near a tipping point?
Lenton et al. (2008) PNAS 105(6): 1786-1793
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What happens near a tipping point?
• slowing down recovery from perturbations
• increasing memory, i.e. autocorrelation
• shift of power to lower frequencies
• increasing variance
• increasing skewness
Lenton et al. (2008) PNAS 105(6): 1786-1793
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But: Noise induced transition
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But: Noise induced transition
fundamentally
unpredictable
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Can we detect an early warning signal for a greening desert?
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Can we detect an early warning signal for a greening desert?
• model of vegetation dynamics of arid ecosystems
• involves positive feedback between vegetation and soil water availability
Kefi et al. (2010) Theor Ecol 3:257–269
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Model equations
Kefi et al. (2010) Theor Ecol 3:257–269
surface water
soil water
plant density
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Model equations
Kefi et al. (2010) Theor Ecol 3:257–269
surface water depth
soil water
plant density
rainfall
infiltration runoff/evaporation
uptake drainage
mortality
infiltration
uptake
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sample simulation …with noise
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bistability(same parameters, different initial condition)
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hysteresis diagram
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hysteresis diagram, bistability
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hysteresis diagram, bistability
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effect of noise near transition
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R
driving the system over the edge
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driving the system over the edge
R
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hysteresis
time domain
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hysteresis
time domain phase space
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hysteresis
time domain phase space
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noise
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noise
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SlowdownTime to recover 10% reduction in P
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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Time series analysisvariance, autocorrelation…
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
R
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Time series analysisdetrend with moving average
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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Time series analysisdetrend with moving average
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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Time series analysisIs the system moving towards a cliff?
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
autocorrelation
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EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
variance
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EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
skewness
Yes, we can!!!
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…can we?
Looks like a random walk!…be careful
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Can we forecast a regime shift?Maybe…
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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Can we forecast a regime shift?Maybe…
…probably not for this model
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
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Can we forecast a regime shift?Maybe…
…probably not for this model
EARLY WARNING SIGNALS OF CRITICAL TRANSITIONS
Need to develop robust indicators