the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Sep 2024
Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics
Abstract. Understanding the resilience and stability of vegetation patterns under changing environmental conditions is crucial for predicting ecosystem responses to climate change. This study investigates the dynamics of vegetation patterns in response to a spatially homogeneous decrease in rainfall across the entire domain. Starting from high-rainfall with a stable homogeneous vegetated state, we applied various rates of rainfall reduction to observe system transitions. We find that rainfall decrease may cause transitions to two or three pulse states, or abrupt shifts to bare soil depending on the rate of change, highlighting the significance of rate-induced tipping (R-tipping) in open dynamical systems.
We identified the pulse creation and destruction timescale (τpulse) and the rearrangement timescale (τrear) as the critical timescales which govern the system response to gradual environmental changes. The rearrangement timescale, significantly longer than τpulse, is relevant for characterising the system behavior under slow perturbations. Dimensional analysis and sensitivity analysis with numerical experiments further validate the fundamental connections between these timescales.
Additionally, we examined the impact of spatially and temporally structured noise on vegetation pattern resilience. Perturbations modeled as Gaussian stochastic processes with specific autocorrelation structures were applied to the system. We find that increased spatial autocorrelation in noise reduces pattern formation, while temporal autocorrelation at critical timescales significantly influences biomass mean and variance. The co-existence of multiple equilibria and unstable states, combined with the presence of ghost attractors enhances system resilience by providing alternative stable configurations under fluctuating conditions.
These findings underscore the importance of considering slow timescales and structured noise in analyzing vegetation dynamics. Understanding these factors is essential for predicting ecosystem resilience and developing strategies to manage vegetation systems under climate variability.
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RC1: 'Comment on egusphere-2024-2830', Anonymous Referee #1, 10 Oct 2024
The manuscript "Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics" by Lilian Vanderveken and Michel Crucifix presents a very interesting investigation on understanding the resilience and stability of vegetation patterns in response to changing environmental conditions, particularly decreased rainfall. The key result is the identification of two critical timescales governing the system’s response to slow changes in the environment. Additionally, the authors also explored how spatially and temporally structured noise impacts vegetation resilience. Overall, the manuscript is clear, well written, and the research emphasizes how simple models can be helpful in identifying critical transitions for predicting ecosystem resilience. I only have some points to be clarified, before the manuscript can be accepted for publication.
1. It would be useful to assess the stability of the results with respect to the intensity of the noise. I mean finding, if it exists, a relation and how it is robust between the critical transitions with varying noise amplitude. This would provide more information on the assessment of the role of noise-driven processes.
2. I find the results in Figure A2 very interesting and maybe suitable for description after considering my previous point. Indeed, it would be interesting to show directly a k-ω spectrum as a function of the noise intensity and how temporal/spatial covariance is captured through the noise process.
3. My last point is on Figure 3. Would be possible to make an exponential fit of the black line to be compared with the resulting scaling?
4. As a minor point I would suggest a careful reading of the text to fix some typos, as below:
- please fix units (g.m-2 should be written as g m-2, etc)
- please check missing spaces in lines 71, 72, 91, 106
- Line 114: Figure 2 should be Figure 3
- Line 154: Figure 5 should be Figure 6
Citation: https://doi.org/10.5194/egusphere-2024-2830-RC1 -
RC2: 'Comment on egusphere-2024-2830', Anonymous Referee #2, 23 Nov 2024
Based on an idealized model, the manuscript titled "Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics" analyzes the responses of vegetation pattern dynamics to rainfall reduction with different rates and noises with different spatial and temporal structures. Intriguing outcomes are presented, including two critical timescales governing the system response to gradual environmental changes, and different behaviors under the impact of spatially and temporally structured noise. The results are insightful for understanding the specific characteristics of response of vegetation to climate change and ecosystem resilience. The manuscript are convincing and well-organized and worth to be published.
Specific comments:
1. The responses of vegetation to reduced rainfall rates is discussed in the manuscript. How about the responses in an increased rainfall scenario? Do these two inverse scenarios induce anti-symmetric responses? In other words, are the changes of vegetations due to increased and decreased rainfall reversible?
2. Noises are applied to two variables--- the biomass B and surface water W. What if the noises are applied to only one variables or all three variables?
Typos:
1. L91: "It is is linked"
2. L114: Figure 2 should be 3
3. L153: Figure 5 should be 6
4. In the caption of Figure 6: "On the top-bottom panel"
Citation: https://doi.org/10.5194/egusphere-2024-2830-RC2 - AC1: 'Comment on egusphere-2024-2830', Lilian Vanderveken, 24 Jan 2025
Status: closed
-
RC1: 'Comment on egusphere-2024-2830', Anonymous Referee #1, 10 Oct 2024
The manuscript "Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics" by Lilian Vanderveken and Michel Crucifix presents a very interesting investigation on understanding the resilience and stability of vegetation patterns in response to changing environmental conditions, particularly decreased rainfall. The key result is the identification of two critical timescales governing the system’s response to slow changes in the environment. Additionally, the authors also explored how spatially and temporally structured noise impacts vegetation resilience. Overall, the manuscript is clear, well written, and the research emphasizes how simple models can be helpful in identifying critical transitions for predicting ecosystem resilience. I only have some points to be clarified, before the manuscript can be accepted for publication.
1. It would be useful to assess the stability of the results with respect to the intensity of the noise. I mean finding, if it exists, a relation and how it is robust between the critical transitions with varying noise amplitude. This would provide more information on the assessment of the role of noise-driven processes.
2. I find the results in Figure A2 very interesting and maybe suitable for description after considering my previous point. Indeed, it would be interesting to show directly a k-ω spectrum as a function of the noise intensity and how temporal/spatial covariance is captured through the noise process.
3. My last point is on Figure 3. Would be possible to make an exponential fit of the black line to be compared with the resulting scaling?
4. As a minor point I would suggest a careful reading of the text to fix some typos, as below:
- please fix units (g.m-2 should be written as g m-2, etc)
- please check missing spaces in lines 71, 72, 91, 106
- Line 114: Figure 2 should be Figure 3
- Line 154: Figure 5 should be Figure 6
Citation: https://doi.org/10.5194/egusphere-2024-2830-RC1 -
RC2: 'Comment on egusphere-2024-2830', Anonymous Referee #2, 23 Nov 2024
Based on an idealized model, the manuscript titled "Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics" analyzes the responses of vegetation pattern dynamics to rainfall reduction with different rates and noises with different spatial and temporal structures. Intriguing outcomes are presented, including two critical timescales governing the system response to gradual environmental changes, and different behaviors under the impact of spatially and temporally structured noise. The results are insightful for understanding the specific characteristics of response of vegetation to climate change and ecosystem resilience. The manuscript are convincing and well-organized and worth to be published.
Specific comments:
1. The responses of vegetation to reduced rainfall rates is discussed in the manuscript. How about the responses in an increased rainfall scenario? Do these two inverse scenarios induce anti-symmetric responses? In other words, are the changes of vegetations due to increased and decreased rainfall reversible?
2. Noises are applied to two variables--- the biomass B and surface water W. What if the noises are applied to only one variables or all three variables?
Typos:
1. L91: "It is is linked"
2. L114: Figure 2 should be 3
3. L153: Figure 5 should be 6
4. In the caption of Figure 6: "On the top-bottom panel"
Citation: https://doi.org/10.5194/egusphere-2024-2830-RC2 - AC1: 'Comment on egusphere-2024-2830', Lilian Vanderveken, 24 Jan 2025
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