by Judith Curry
Everybody talks about climate feedbacks, but what are they, really? And where did the expression ΔTs = λRF actually come from?
All of this originated in a loose way from control theory developed in the context of engineered systems. It is certainly an appealing idea to look at the climate as a control system, where we only need to keep track of the energy entering and leaving the system, and through some basic thermodynamic assumptions, relate changes in the flux of energy in/out of the system to a change in surface temperature. The application of linear control theory to this problem assumes a very small perturbation to the system. The following thermodynamic feedbacks are typically separated out in this analysis to be additive: water vapor, lapse rate, cloud, and ice albedo.
Since I don’t have time at the moment to develop extensive new content, here are some resources to kick off the discussion, I will add others as they are suggested in the comments.
Here are some of the references that I regard to be seminal in framing how to think about climate feedbacks. AFAIK, Hansen et al. and Schlesinger were the first to frame the problem in this way. The best overall discussion is given by Roe.
Roe 2009: Feedbacks, timescales, and seeing red
Hansen, J., A. Lacis, et al., 1984: Climate sensitivity: Analysis of feedback mechanisms.
Schlesinger, M 1985, 1986 (unavailable on the web, contact me if you want a copy).
Stephens, 2005: Cloud feedbacks in the climate system: A critical review.
Aires and Rossow, 2003: Inferring instantaneous, multivariate and nonlinear sensitivites for the analysis of feedback sensitivities for the analysis of feedback processes in a dynamical system: Lorenz model case study
Bony et al. 2006: How well do we understand and evaluate climate feedback processes?
Bates 2007: Some considerations of the concept of climate feedback.
The NRC in 2003 published a report “Understanding Climate Change Feedbacks”
In my text Thermodynamics of Atmospheres and Oceans, I have written a chapter on Thermodynamic Feedbacks in the System, which is available online (text, figures). If you aren’t ok with partial derivatives, you probably won’t get much out of this.
At a simpler level, here are some explanations of climate feedbacks that I’ve spotted in the blogosphere:
JC’s 2003 feedback presentation
Circa 2003, I gave a presentation on feedbacks at a Search meeting, relevant excerpts from the presentation is appended below:
The nature, measurement, and modeling of feedbacks: Some thoughts on framing the feedback issues/strategies for SEARCH
Feedback is an interaction among processes in a system in which a change in one process triggers a secondary process that influences the first one. A positive feedback intensifies the change in the original process, and a negative change reduces it. A feedback is NOT a forcing (e.g. clouds influencing sea ice is a forcing rather than a feedback). “Feedback process” is ambiguous; a single arrow is not a feedback process, and a collection of processes is not a feedback unless they contribute to a closed feedback “loop”.
Observing feedbacks: A feedback cannot be observed. Variables are observed. Correlation between variables says nothing about causality. Direction(s) of causality between variables can (at best) be inferred probabilistically.
Evaluating feedbacks using models: Some causation processes are represented explicitly in models; others are indirect results of nonlinear processes. In a chaotic, nonlinear climate model with 107 –109 degrees of freedom, we do not know how to evaluate the feedbacks. It is not possible to unambiguously separate individual feedback loops. Estimating feedback through equilibrium simulations of GCMs, linear analysis, or analysis of vastly simplified models can be misleading. It is not possible to identify the “most important” feedbacks.
Example – cloud feedback. Cloud feedback is regarded as a very important climate feedback. This evaluation is tied to the magnitude of “cloud radiative forcing.” In a complex nonlinear system, a large forcing does not necessarily translate into a large and “important” feedback. Evaluation of cloud feedback in GCMs using a simple linear analysis shows model disagreement in both magnitude and sign. If plausible projections can be made with different signs of the cloud feedback, it is possible that cloud feedback is not “important”. LESSON: Do not confuse forcing with feedback.
Example – snow/ice albedo feedback. Snow/ice albedo feedback is regarded as a positive feedback. The sign depends on the time scale under consideration. On glacial time scales, there is a period that follows the onset of warming where snow/ice extent increases, owing to an increase in snowfall. LESSON: The magnitude and sign of a feedback can be frequency dependent or associated with a substantial time lag.
Example – water vapor feedback. Water vapor feedback is generally regarded as being positive. However, one study of tropical convection suggests a negative water vapor feedback. While this study is very controversial, the relevant point is that we do not know how to unambiguously discriminate between the two opposing theories. LESSON: The sign and strength of a feedback can vary regionally.
How can we productively use the concept of feedback to understand and model climate variations?
1. Use our understanding of physics, chemistry, biology to construct feedback diagrams or causal graphs. Such diagrams aid our conceptual understanding of the climate system and its subsystems.
2. The concept of feedback can help guide effective design of process studies and use of observations to evaluate models
Using observations to evaluate models. Examine the evolution of model processes over short-term modes of variability (e.g. the annual cycle) and compare with a carefully constructed set of observations. Compare model results with observations in the context of the covariance of variables that are related in a feedback loop. Hypothesis: current parameterizations of sea ice albedo are too simple to accurately simulate the ice albedo feedback mechanism. Method to test hypothesis: conduct model experiments with i) the simple parameterizations; and ii) a more complex parameterization. Criterion for accepting simple parameterization: feedback gain ratio for simulations is essentially the same as that for the more complex parameterizations
Conclusions regarding the appropriateness of one parameterization vs another depend on the model that is used to evaluate it. Investigation of the parameterization in a hierarchy of different models is needed to understand the impact of the parameterization and its role in the modeled feedbacks. Coupling of two subsystem models will introduce additional nonlinearities into the coupled model. Nonlinearities arising from the coupling requires additional attention to both the modeling aspects of the coupling and observations with which to evaluate the coupling.
Use the annual cycle and any other short modes of variability to explore interactions and feedbacks. When comparing models with observations, examine the covariance among variables related in feedback loops. Be patient, the system is complex and the answers won’t fall out easily or unambiguously.
So what are the outstanding issues?
After two decades of wrestling with this issue, I’m not sure how useful the concept of “feedback” is in the context of the climate system. We already saw what kind of trouble we can get into on the thread on CO2 no feedback sensitivity, which is supposed to be the easy part of the problem. The problem flat out isn’t linear, and attempting to do a nonlinear control theory analysis is pretty hopeless, as illustrated by the Aires and Rossow paper. At best, it seems like the concept is useful as a conceptual aid in thinking about a complex system. Various metrics like ΔTs = λRF or the partial derivatives may have some use in comparing climate models with each other or with observations, but it may not say much about feedback. So is this concept useful? If not, can it be salvaged? I find the conclusion in the Roe paper to be very insightful.
And finally, are there better ways to try to understand the whole system, something from dynamical systems theory, entropy extremals, etc?
Note: this is a technical thread, comments will be moderated for relevance.