Possible states the earth can evolve to

Bioregional, continental, and global metastable states for the ecohydrological system

Ecological succession is usually considered within the context of a constant climate. So for example traditional ecology might find that a forest may be the climax community, the state the ecosystem evolves to, in a wetter climate. And a grassland may be the climax community, the state the ecosystem evolves to in a slightly dryer climate.

But what happens if we take into account that the ecosystem can affect rain, and that that rain can then affect ecosystem evolution. How does ecological succession then look? As I pondered this last year, it seemed to me that there are different stable states that the ecosystem+hydrological system can evolve to, given large enough perturbations.

For example consider a bioregion with forests. The forests slow the rain when it comes down. The rain gets absorbed into dead logs, which hold a lot of water in their pores, and also in the carbon-rich soil. The canopy keeps the soil wet a lot longer into the dry season. There is thus more water to then evapotranspire back into the air to create rain. Rain is made up of the large water cycle (which is water blowing in from the ocean and then flowing back out), and the small water cycle (which is water cycling between land and atmosphere, aka precipitation recycling). The small water cycle is responsible from 10 to 80% of the rain depending on where you are in the world [ref 1], so changing the amount of evapotranspiration can have a significant impact on the rain. That rain then helps the forests to grow. More rain means more forest. More forest means more rain. It is a self reinforcing loop. It’s a stable ecohydrological state.

Consider the same bioregion was filled with grasslands. The grasslands slow the rain somewhat when it comes down, but a lot less stays around compared to a forest. By dry season the land loses a lot more water. There is less evapotranspiration, and thus less rain. In lower rainfall areas, grasses have a higher fitness function than trees. So less rain reinforces grasses as the dominant biome, and more grasses leads to less rain. So again we have a self-reinforcing loop. Its a stable ecohydrological state.

If we start out with a forest, and chop some small portion of the forest down, ecological succession will grow the forest back. Viewed through the lens of dynamical systems concepts, this means a small perturbation to the system will lead to system to move back to the dynamically stable state of a forest. However if we chop down enough of the forest, i.e. increase the pertubation large enough, then the system will move to a different metastable state, that of the grasslands. This is because there is no longer enough forest to keep the rain falling at a higher amount. The ecosystem then adapts to the lower rainfall, and becomes a grassland.

We can draw diagrams to illustrate this metastability. (Metastable means something is stable, but not necessarily stable for all time). On the y axis we have potential energy, or the fitness function where it gets larger as you go down. And on the x axis we have the amount of trees

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Earlier this week I was happy to stumble upon the work of Martin Claussen, a professor of meteorology at the Max Planck Institute for Meteorology in Germany who I found had done research in this area already. He had researched the different stable states a ecology+climate system can have.

Martin Claussen had been pondering the question “why was the Sahara significantly greener and the Saharan climate significantly wetter during warmer periods of the last millennia than it is today? Why did the Sahara spread very rapidly - quasi-abruptly, geologically speaking - in some regions a few thousand years ago, and more gradually in others?”

He figured that it had to with how the vegetation and climate were affecting each other. Vegetation affects the climate, and in turn the climate affects the vegetation.

Traditionally global climate models do not take into account how the vegetation evolves. In the 1990s Claussen coupled a biome model, which could evolve vegetation, with a global climate model. He applied it to current day Africa. What he found when applied this model to Africa is that there were different stable states that the ecosystem could be in.

In his words - “It is found that – under present-day conditions of solar irradiation and sea-surface temperatures – two solutions of the atmosphere–vegetation system, or more precisely the atmosphere–biome system, are possible: the first solution yields the present-day distribution of vegetation and deserts and the second one shows a northward spread of savanna and xerophytic shrub of some 600 km, particularly in the south-western Sahara. Whether the atmosphere–biome model would attain the first or the second solution depends on the initial conditions. If a bright sand desert (i.e. a desert with a high albedo of some 35%) is prescribed in the area currently occupied by the Sahara desert, then the atmosphere–biome model keeps the desert. If, however, vegetation is initially specified, then some vegetation (savanna, xerophytic shrub, and steppe) remains in the south-western Sahara.” [ref 2-5]

His biome models included variables like leaf cover (which affected shading and surface temperatures), roughness (how much the vegetation slowed the wind via friction). So the vegetation-climate coupling that ensued happened through multiple variables - temperature, wind, energy flux, and water cycle.

In 2021 physicist Giorgio Parisi won the Nobel Physics prize, along with two climate scientists (it was the first time climate scientists had won a physics Nobel). Parisi’s spin glass physics is what the Nobel committee focused on in the Nobel announcement.

Parisi also studied the climate. He researched the multiple metastable states a climate could reside in, and how it was able to bounce between those states.

One metastable state the earth can find itself in, is where it is covered in ice. Ice has a high albedo, and reflects sunlight back to space, lowering the temperature. Ice keeps the earth cold, and the coldness keeps the ice from melting. Its a self-reinforcing loop.

The other metastable state the earth can find itself in is one of more vegetation and less ice. Less ice means more sunlight absorbed, and more sunlight absorbed means less ice. Its another self-reinfocing loop.

The earth flips climate at certain frequency. One frequency has the earth flipping climate states every hundred thousand years. Why it did this was not well understood. A wobble in the earths orbit, called the Milankovitch cycle, had a similar frequency to this hundred thousand year cycle, but it seemed it would not be enough to count for the temperature change of 10 degrees between icy and non icy climates.

[graph from Adamo, Ansari, Sissakian 2021].

Parisi articulated the idea of stochastic resonance, which says that noise/random fluctuations can knock a system from one state to another. These fluctuations could combine with the Milankovitch cycle to knock the earths climate into another metastable state.

Here is what Nature, a leading scientific journal wrote about Parisi’s work.

“Usually, the concept of noise is associated with something negative, that one might want to reduce as much as possible. However, in the early 1980s, Parisi and collaborators discovered that when it comes to nonlinear physical systems such as the Earth’s climate, noise might play a positive role. This is due to a phenomenon known as stochastic resonance, observed in nonlinear systems where a characteristic frequency is present, for example in the form of a periodic perturbation. The right amount of noise can amplify the signal-to-noise ratio, favouring the emergence of a behaviour which would not be observed with a lower or higher noise level.

Stochastic resonance has been used to explain an apparent climatological paradox. For the last few million years, the average temperature on Earth has been strongly correlated with the flux of energy coming from the Sun, mostly due to the eccentricity of our planetary orbit. The variation of the energy flow is approximately periodic, with a characteristic period of about 100,000 years, but is too small to account for temperature variations of the order of 10 °C, such as those that can be reconstructed from the paleoclimatic record.

However, let’s also consider the internal dynamics of the ocean and the atmosphere (with periods of a few months and a few thousand years, respectively), which can be viewed as noise. It is possible to show that such noise, combined with periodic changes in the energy flow from the Sun, induces large variations of the global temperature which are roughly periodic. If one of those two ingredients, noise or periodic forcing, is absent, the phenomenon cannot hold.” [ref 6]

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Parisi’s stochastic resonance work may have some relevance to the metastable states we see in the vegetation-climate system like those that come out of Claussen’s simulations. Its possible that noise in the earth system can combine with climate forcings like deforestration, to knock an ecosystem from one biome to another.

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Giorgio Parisi main work was the study of spin glasses, a type of disordered system with many metastable states. Glasses have a random-ish arrangement of atoms, and physicists had been having a hard time understanding their behavior, especially when compared with orderly solids like crystals. Parisi gave clarity to the field by inventing some interesting fractal concepts to describe the multiple metastable stable states the glasses could be in. Local atoms could rearrange themselves into configurations that were energetically favorable that would also be coupled with longer range configurations.

Spin glasses has found a lot of uses in the field of complexity science. Its been used as an analogical model to understand computational complexity, protein folding, immune response, social networking, economics. The Santa Fe Insitute has in particular pioneered the usage of spin glasses to understand a wide variety of complex phenomena.

I have some tentative ideas on how Parisi’s work on spin glasses can help us understand the climate, which I will outline below.

In glassy systems, local groups of atoms can flip to find a more stable local configuration on short time scales. However those local groups of atoms may not be in the stable state in relation to atoms further away. It takes longer for a local group of atoms to come into correlation with a group of atoms further away. There are metastable states at different length scales. These larger supergroups flip to different metastable states on longer time scales.

By analogy think of college students in a dorm finding roommates. Each student has certain people it wants to live with, and others they don’t. Finding the best configuration (a small group metastable state) for a group of 6 students can happen more quickly. But when that group has to coordinate with other groups of students to find the best configuration in the dorm ( a large group metastable state), it will take a lot longer.

We can think of a bioregion as being in certain metastable states. Each bioregion is also correlated with other bioregions through the hydrological cycle, energy fluxes, and atmospheric circulations. For a group of bioregions to flip to another more stable metastable state takes much longer.

There are also correlations between continents. Scientists have found ecoclimate teleconnections, where what you do one continent affects another continent through large scale atmospheric circulations like the jet stream. Chopping down forests in the Amazon affects the weather and hydrological cycle in the USA. The metastable ecoclimate states of one continent are correlated with those on another climate. For the global system to find a lower metastable state will take even longer.

In this multiscale view of our ecosystem, we have tipping points on many size scales. There are bioregional, continental, and global tipping points. A tipping point is what takes a system from one metastable state to another.

Restoring a bioregional area ( see for example my essay “Regreening the Sinai”) can change the metastable state it is in, which then impacts the possible metastable states the continent can move into, which then impacts the possible metastable states the globe can be in. Each successively larger size scale is associated with larger time scales. This fractal view gives us a picture of how local bioregional restoration work is tied to into the global climate picture, coupled together via different cycles like the hydrological cycle and large scale atmospheric circulation patterns, which themselves are impacted by the local metastable states.

References

1. van der Ent, R. J., Savenije, H. H. G., Schaefli, B., and Steele-Dunne, S. C. (2010), Origin and fate of atmospheric moisture over continents, Water Resour. Res., 46, W09525 https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2010WR009127

2.Brovkin, V., Claussen, M., Petoukhov, V. & Ganopolski, A. (1998). On the stability of the atmosphere-vegetation system in the Sahara/Sahel region. Journal of Geophysical Research-Atmospheres, 103(D24), 31613-31624. doi:10.1029/1998JD200006 [ Fulltext]

3.Claussen, M., Brovkin, V., Ganopolski, A., Kubatzki, C. & Petoukhov, V. (1998). Modelling global terrestrial vegetation climate interaction. Philosophical Transactions of the Royal Society of London Series B-Biological Sciences, 353(1365), 53-63. doi:10.1098/rstb.1998.0190

4.Claussen, M. (1998). On multiple solutions of the atmosphere-vegetation system in present-day climate. Global Change Biology, 4(5), 549-559. doi:10.1046/j.1365-2486.1998.00122.x

5.Claussen, M. & Esch, M. (1994). Biomes computed from simulated climatologies. Climate Dynamics, 9, 235-243. doi:10.1007/BF00208255 [ Fulltext]

6.“Understanding climate and turbulence; the mark of Giorgio Parisi” https://www.nature.com/articles/d43978-021-00128-0