Presentation is loading. Please wait.

Presentation is loading. Please wait.

Www.irstea.fr Pour mieux affirmer ses missions, le Cemagref devient Irstea Resilience and vulnerability from a stochastic controlled dynamical system perspective.

Similar presentations


Presentation on theme: "Www.irstea.fr Pour mieux affirmer ses missions, le Cemagref devient Irstea Resilience and vulnerability from a stochastic controlled dynamical system perspective."— Presentation transcript:

1 Pour mieux affirmer ses missions, le Cemagref devient Irstea Resilience and vulnerability from a stochastic controlled dynamical system perspective Charles Rougé, Jean-Denis Mathias and Guillaume Deffuant

2 2 The viability framework for resilience

3 3 Example: The case of lake eutrophication (Carpenter et al., 1999) Lake (Phosphorus concentration P) Inflow Outflow Algae Phosphorus input L Bounded!!! (by U>0)

4 4 Deterministic viability: single trajectories Event Events

5 Pour mieux affirmer ses missions, le Cemagref devient Irstea Part I Resilience of a stochastic controlled dynamical system

6 6 Impact of uncertainty on the viability kernel

7 7 Multiplicity of recovery trajectories Events

8 8 Resilience in a stochastic dynamical system Recovery is defined by getting back to the stochastic viability kernel Centrality of the probability of recovery after a given date: the Probability of resilience No longer a unique measure of recovery but possibility to derive statistics.

9 9 Resilience statistic:expected recovery date

10 10 Resilience statistic: maximal recovery time (99% confidence)

11 11 Resilience statistic: probability of resilience

12 Pour mieux affirmer ses missions, le Cemagref devient Irstea Part II Vulnerability as a measure of future harm

13 13 Harm: a value judgement on a state Economic harm Increases linearly as L decreases Ecological harm Quadratic increase with P Threshold of harm Properties

14 14 Defining vulnerability 1)One associates harm values to a trajectory: Sum of static harm values (cost criterion) Crossing of a threshold (viability criterion) 2)Vulnerability is a statistic on the distribution of harm values: Expected value of the cost Exit probability (crossing of a threshold) Value-at-risk (e.g. worst 1%) of the cost 3)Interest in low-vulnerability kernels.

15 15 Vulnerability as total cost Τ=100

16 16 Vulnerability as exit probability Stochastic viability kernel!!!

17 Pour mieux affirmer ses missions, le Cemagref devient Irstea Part III Towards a resilience-vulnerability framework

18 18 Conceptual definitions Resilience: capacity to keep or recover properties after a hazard, disturbance or change. Probability of recovery at date t Statistic on a recovery time distribution Vulnerability: a measure of future harm (Hinkel, 2011). Statistic on an exit probability Statistic on a cost distribution

19 19 Combining resilience and vulnerability Dynamic safety criterion (or property of interest) Low-vulnerability zone Resilience: capacity to recover Vulnerability: harm experienced (equivalent to a restoration cost) ?

20 20 The proposed framework

21 21 Take home messages Complimentarity of resilience and vulnerability The notion of low-vulnerability kernel generalizes that of viability kernel. Resilience is the ability to get back to this safety set after a disturbance or a change. Vulnerability is a statistic based on the harm values associated to the possible trajectories. Choice of the strategy dependent on the indicator.


Download ppt "Www.irstea.fr Pour mieux affirmer ses missions, le Cemagref devient Irstea Resilience and vulnerability from a stochastic controlled dynamical system perspective."

Similar presentations


Ads by Google