Prey and predator model of clouds

From the Weizmann Institute of Science – Eat, Prey, Rain


Photo: Tamar Deutsch

What do a herd of gazelles and a fluffy mass of clouds have in common? A mathematical formula that describes the population dynamics of such prey animals as gazelles and their predators has been used to model the relationship between cloud systems, rain and tiny floating particles called aerosols. This model may help climate scientists understand, among other things, how human-produced aerosols affect rainfall patterns. The research recently appeared in the Proceedings of the National Academy of Sciences (PNAS).

Clouds are major contributors to the climate system. In particular the shallow marine stratocumulus clouds that form huge cloud decks over the subtropical oceans cool the atmosphere by reflecting part of the incoming solar energy back to space. Drs. Ilan Koren of the Weizmann Institute’s Environmental Sciences and Energy Research Department (Faculty of Chemistry) and Graham Feingold of the NOAA Earth System Research Laboratory, Colorado, found that equations for modeling prey-predator cycles in the animal world were a handy analogy for cloud-rain cycles: Just as respective predator and prey populations expand and contract at the expense of one another, so too rain depletes clouds, which grow again once the rain runs out. And just as the availability of grass affects herd size, the relative abundance of aerosols – which “feed” the clouds as droplets condense around them – affects the shapes of those clouds. A larger supply of airborne particles gives rise to more droplets, but these droplets are smaller and thus remain high up in the cloud rather than falling as rain.

In previous research, Feingold and Koren had “zoomed in” to discover oscillations in convective cells in marine stratocumulus. Now they returned to their data, but from a “top down” angle to see if a generalized formula could reveal something about these systems. Using just three simple equations, they developed a model showing that cloud-rain dynamics mimic three known predator-prey modes. Like gazelles and lions, the two can oscillate in tandem, the “predator” rain cycle following a step behind peak cloud formation. Or the two can reach a sort of steady state in which the clouds are replenished at the same rate as they are diminished (as in a light, steady drizzle). The third option is chaos – the crash that occurs when predator populations get out of hand or a strong rain destroys the cloud system.

The model shows that as the amounts of aerosols change, the system can abruptly shift from one state to another. It also reveals a bifurcation – two scenarios at different ends of the aerosol scale that lend themselves to stable patterns. In the first, relatively low aerosol levels lead to clouds in which development depends heavily on aerosol concentrations. In the second, high levels produce saturation; these clouds depend solely on the initial environmental conditions.

Using this so-called systems approach, says Koren, “can open new windows to view and understand the emergent behavior of the complex relationships between clouds, rain and aerosols, giving us a more useful view of the big picture and helping us to understand how shifting aerosol levels can lead to different climate patterns.”

Dr. Ilan Koren’s research is supported by the Yeda-Sela Center for Basic Research. Dr. Koren is the incumbent of the Benjamin H. Swig and Jack D. Weiler Career Development Chair in Perpetuity.

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July 25, 2011 9:16 am


jack morrow
July 25, 2011 9:21 am

I can’t accept this. It’s just seems like too much modeling going on with really no hard proof, only conjecture.

July 25, 2011 9:24 am

Seems to be a fairly reasonable notion. I’d hope that some more academics might follow the equations through to check the (interim?) conclusions. It would be far beyond me :-((

July 25, 2011 9:37 am

“In previous research, Feingold and Koren had “zoomed in” to discover oscillations in convective cells in marine stratocumulus. Now they returned to their data, but from a “top down” angle … ”
Model run results are not data.

July 25, 2011 9:50 am

Predators and prey undergo natural, psuedo periodic cycles where one is out of great in number and the other is not. If clouds of different types similarly cycle in an out of balance with one another, that might explain apparent periodicities in weather and climate.

July 25, 2011 9:51 am

“high levels produce saturation; these clouds depend solely on the initial environmental conditions”
is apparently derived from “high levels of food produce saturation in gazelle; these herd sizes depend solely on initial number of lions” – which doesn’t sound plausible.

July 25, 2011 10:02 am

My BS monitor went crazy when I read this.

July 25, 2011 10:09 am

A larger supply of airborne gazelles gives rise to more droplets, but these droplets are smaller and thus remain high up in the cloud rather than falling as gazelles.
Can I have my grant money now?

July 25, 2011 10:15 am

Is this what happens when all a post-doctoral researcher has is time, grant money, and a hankering to play around with John Conway’s Game of Life?

July 25, 2011 10:48 am

Exactly my thoughts!

John Stover
July 25, 2011 11:26 am

As both a sailor and a glider pilot I have had a lifelong interest in clouds and I find them to be much more dynamic than perhaps most persons who only occasionally observe their activities. Fair weather cumulus have a very interesting and complex life cycle from when they are born about ten o’clock in the morning as the rising air from the sunshine heating up the earth’s surface readches the dew point altitude and, poof, you have a cloud, through their surly teens as billowing clouds at lunch time to afternoon maturity as black-bottomed, horizontal clouds lined up in characteristic “cloud streets” that let you thermal up just below them, jump the gap losing altitude to the next street, and then thermal back up to the next cloud’s base. When they reach old age at about an hour before sundown the lessening of the sun’s rays severs their life connection to the rising air and they become increasingly ragged and can die very rapidly indeed.
Woe betides the glider pilot who is miles away from the field when the clouds die and the sustaining lift suddenly collapses. 3000 feet agl to the 900 feet you need for an approach only about 3 minutes when you lose the lift so you had better be picking out a safe landing area. That is also when you become acquainted with the cows and get to practice your interpersonal skills trying to convince a suspicious farmer to let your trailer into his field so you can recover your glider without damaging his crops.
“I have looked at clouds from all sides now” are not just the words to a song.

July 25, 2011 11:27 am

Not one mention of model validation. And do “human-produced” aerosols behave differently from volcanic, oceanic and continental aerosols? Is that like comparing gazelles and cape buffalo?

Brian H
July 25, 2011 11:43 am

No, grant refused. The raindrops are well-fed lions, not falling gazelles.
This has interesting implications for GCR theories, and suggests that more nuclei don’t directly lead to more rain. They do, however, at least lead to more cloudiness, hence cooling.

July 25, 2011 11:47 am

I believe the classic problem in making this research practical is that we don’t have enough meters inside the clouds to tell you which way a particular cloud zone is going to jump. Just from a visual observation you know that yep, you have spied a cloud in the wild all right. But what is going to happen next? We don’t know enough about internal conditions to say. Temperature, pressure, humidity, winds, aerosols, and existing droplets, and all of them dynamic. Now if some kind of radar could spell that out, we could move this out of the lab.

Christoph Dollis
July 25, 2011 11:54 am

“I can’t accept this. It’s just seems like too much modeling going on with really no hard proof, only conjecture.”

They seem to be building the model from the ground up, just noticing how similar it is to the observed data. They are obviously not claiming this is literally a predator-prey relationship.
I have no problem with this work. I wouldn’t “accept” it without further study and observations, but I do like working from data first, then devising the model.

Karen D
July 25, 2011 12:27 pm

How about the relationship between rain, clouds and volcanic ash? Why must the study be limited to “human-produced aerosols”?
I live in the Northwest USA where we are having an unusually cool and rainy summer, just like last summer, and I blame it on the volcano activity in Finland over the past two years. I think that would make a good study. Or maybe a good story, maybe. One about mountain lions and deer … something like that..

Doug S
July 25, 2011 12:43 pm

This is interesting to me. The idea that there is some level of aerosol concentration where maximum cloud formation occurs while lower and higher concentrations from this “ideal” yields less clouding certainly sounds plausible. Another reminder that the science is far from settled and much more interesting than simple trace gas concentrations.

Ed Hahn
July 25, 2011 12:45 pm

Setting up a system of differential equations like this is a perfectly legitimate way of approaching this type of problem. I haven’t read the paper in detail, but, like Dollis at 12:54, feel it’s a valid approach to modeling the problem.
A lot of people here seem to have problems with models, Per se.
There really isn’t any other way to approach problems like this.
The real “trick” for modelers’ is to not fall in love with their model, to use real world data to evaluate the parameters (dials), and to be honest about the applicability of the model output and it’s error bars.

July 25, 2011 1:09 pm

Makes sense. There’s another similarity between clouds and populations. A relatively ‘lonely’ cloud that reaches a certain minimum size can’t sustain itself and disappears quickly.
We used to take advantage of this in hippie days. Under the influence of our own cloud-forming aerosols, we’d lay on the ground and try to “think a cloud out of existence.” If you picked a small enough and lonely enough cloud, disappearance was guaranteed in a few minutes.

July 25, 2011 1:15 pm

I would add that the predator-prey relationship here is based on Lotka-Volterra equations (, and the particular equations they use in their model are equations 3 (cloud depth), 8 (cloud drop concentration), and 10 (predator population) from their paper. Not an expert in any of these fields, but the approach looks very interesting for understanding the overall dynamics. (Not sure that they take John Stover’s observations — in particular the change in clouds throughout the day — into account, though.)

July 25, 2011 1:24 pm

I too have been watching clouds a lot, killing time in intercontinental flights, wondering why sheepy clouds grow into bigger ones, and gradually I began to see that they canibalise one another (not predator/prey). The slightly bigger ones outrun the smaller ones and then ‘eat’ them, in the process growing bigger and running faster still. It also creates empty ‘streets’ for others to occupy. Fastest of all are the anvil-shaped rain clouds. But understanding how their internal energies merge is still problematic. Has anyone observed something like this?
Another question I’d like to raise is that of condensation creating a vacuum. When water vapour condensates, it occupies a smaller volume such that the partial pressure in air decreases, thus making a slight vacuum (5% of 1000mbar?) for air to move in to. Where a large volume of air turns into cloud, the air around is sucked in. In this manner it may well be that winds chase rains and in doing so cause more rain, etc. Any ideas?

July 25, 2011 3:11 pm

Yesterday on the local CBS affiliate here in Houston, the meteorologist had an excellent show of how daytime heating produces strong rain showers (illustrated with up arrows and down arrows over an image of Houston from a highrise building). As the video ran, the clouds darkened significantly, a shower started, turned heavy, which in turn showed a downdraft gust, that in turn flowed out from the rainfall. When the gust visibly reached the area previously indicated to be the updraft area, magically, the rain stopped shortly thereafter as the cool air stopped the updraft.
sarc The topic was well presented, and didn’t involve gazelles at all. /sarc

Ed Hahn
July 25, 2011 4:46 pm

Anthony didn’t say _why_ he posted this, but I’m thinking he saw a connection to Willis E’s Thunderstorm-Thermostat hypothesis.
I imagine Willis will chime in shortly.
I haven’t read it in detail, but so far, what I see I like. The author’s don’t grandstand, and are quite upfront about the simplifications and limitations of what they are doing.

July 25, 2011 6:17 pm

Don’t read too much into these ‘predator-prey’ (aka Lotka-Volterra) models. It’s merely a matter of “model imitates life (more or less)”, not “life imitates model” as some of you seem to be thinking.
‘Negative feedback mechanism’ is another way to look at this. If there are too many lions (or foxes) then the gazelle (or rabbit) population declines. Then the lions/foxes start dying off, which causes the gazell/rabbit population to rebound, which starts the whole cycle over again (oscillation).
Another way to analyze this behavior: solution to a 1st order differential equation where
R(t) = rabbit population as a function of time
F(t) = fox population as a function of time
Then assuming a strict interdependence on each other, it can be shown that the rabbit-fox rates of population growth over time are:
dR/dt = aR – bRF
dF/dt = -cF + dRF
This is a system of 1st order differential equations with oscillatory solutions.
Of course none of this necessarily holds in the real world because predator/prey relationships are far more complex than the simplistic rules suggested by these models: “if all the rabbits die, then all the foxes must die too” etc.

Darren Parker
July 25, 2011 6:32 pm

There’s a blogger who has a theory on cloud formation and earthquakes – she’s using it to predict earthquakes with some sucess

July 25, 2011 6:40 pm

Would really like to see something on clouds and relationships with Cirrus Clouds and the Jetstream. Any pilots out there to help me?

July 25, 2011 10:54 pm

steveta_uk says:
July 25, 2011 at 9:51 am
“high levels produce saturation; these clouds depend solely on the initial environmental conditions”
is apparently derived from “high levels of food produce saturation in gazelle; these herd sizes depend solely on initial number of lions” – which doesn’t sound plausible.

If the “food” requirement is satisfied then the “prey” population is limited solely by the “predator” population. In an actual prey-predator cycle the “saturation” steady state” would be unlikely since the predator population would expand in response to the availability of food. In clouds, “prey” and “predator” are metaphorical, as is “food,” so a potential steady state where moisture, seed, and rain balance out is conceivable.

July 26, 2011 3:22 pm

If you add a third variable, it is time to employ chaos theory. For example, if you attempt to create a “balance of nature,” using green dots for grass plants, brown dots for rabbits, and red dots for foxes, any “balance” you manage is a precarious perfection, and can be knocked out of kilter by the accidental death of a single plant, rabbit or fox. Very swiftly populations explode and then crash, and your model displays either a grassland devoid of both rabbits and foxes, or a total wasteland devoid of all life. (I know about this because I had a friend who worked with such models.)
Nature is very hard to copy. There have been various attempts to create “capsules” cut off from all outside influences except sunshine, to replicate the conditions in a space craft flying to a nearby star, and after a month or so the people in the capsule have to open the hatch and let in some fresh air, because things in the capsule get too out of whack. Even if the plants in the capsule use up the CO2 and make O2 for the people in the capsule to breathe, strange trace gasses build up towards poisonous levels.
Considering people haven’t even learned to mimic what nature does, to claim we understand it is absurd.

July 26, 2011 9:14 pm

Let’s analyze of the Lotka-Voltera equation: it was developed and used to examine population dynamics. It says the populayion of (n + 1) generation depends on the initial population, the birth ratre, death rate, a time factor and “K”- a numerical value describing the carrying capacity (including the interaction of a predator-prey or parasite-host system). By mainpulating the values of these factors and iterating, any number of amazing graphs can be generated including those accurately describing the population spikes of the 17-yr locust, the waxing & waning of deer-wolf populations or the periodic marches to the sea of lemmings, etc.
By cleverly realizing that the cyclic changes in cloud formations ( or even weather) might also be modeled using this equation, these authors substituted values they thought important in cloud dynamics and coincidently found an iteration that accurately reflected observations.
Now the trick is to prove if their assumptions about the important factors are in fact the operative factors or if they just fortuitiously chose numerical values that iterated out to the desired result.

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