A Chain Of Results – Watts Up With That?

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Guest Post by Willis Eschenbach

In looking at the climate I’m often reminded of Sufi stories. The Sufis are an ancient mystical sect. They are often associated with Islam, and many were Muslims, but the sect preceded Islam.

The Sufis often taught their knowledge by means of most curious stories about life. The Sufis said that every story had seven different meanings.

Often the stories involved a “Mulla”, a holy man, named Nasrudin. He’s either a total fool or a wise saint depending on which end of the telescope you’re looking through. Here’s a story exposing both sides:

Hardly anyone could understand Nasrudin, because sometimes he snatched victory from defeat, sometimes things seemed to go astray because of his blundering. But there was a rumor that he was living on a different plane from others, and one day a young man decided to watch him, to see how he managed to survive at all, and whether anything could be learned from him.

He followed Nasrudin to a riverbank and saw him sit down under a tree. The Mulla suddenly stretched out his hand and a cake appeared in it which he ate. He did this three times. Then he put his hand out again, picked up a goblet, and drank deeply.

The youth, unable to contain himself, rushed up to Nasrudin and caught hold of him. “Tell me how you do these wonderful things, and I will do anything you ask,” he said.

“I will do that,” said Nasrudin, “but first you have to get into the right state of mind. Then time and space have no meaning, and you can be reaching out to the Sultan”s chamberlain to hand you sweetmeats. There is only one proviso.”

“I accept it!” shouted the young man.

“You will have to follow my way.”

“Tell me about it.”

“I can only tell you one thing at a time. Do you want the easy exercise, or the difficult one?”

“I will take the difficult one.”

“This is your first mistake. You have to start with the easy one. But now you cannot, for you have chosen. The difficult one is this: Make a hole in your fence so that your chickens can get into your neighbor’s garden to peck—large enough for that. But it must also be so small that your neighbor’s chickens cannot get into your own garden to feed themselves.

The young man was never able to work this one out, and so he never became a disciple of Nasrudin. But when he told people about what Nasrudin could do, they thought he was mad.

“This is a good start,” said Nasrudin; “one day you will find a teacher.”

So with that as an introduction to the mad Mulla and my own less-than-normal self, I’ll leave you to consider what the seven meanings in that story might be … and in the meantime, let me wander back to the world of the climate. Here are some graphs showing various aspects of atmospheric water vapor and its relationship to temperature. Atmospheric water vapor is often described as “total precipitable water”, or “TPW”. It is measured as the amount of water in a one-metre-square column extending from the surface to the top of the atmosphere, in units of kilograms per square metre of surface. 

The water vapor information I’m using is a new dataset to me. It’s reanalysis results from ECMWF, the European Centre for Medium-Range Weather Forecasts. So to start with I know little about it. I generally begin by looking at the global map of the average values.

Here’re the long-term global average values.

Figure 1. Total precipitable water, long-term average.

What’s of note here? Well, the poles have little water in the air. In part this is because cold air holds less water, and in part because the water is freezing out as snow, sleet, graupel, and the like.

The ocean has about 50% more water vapor than the land because there is a constant source of evaporation. The greatest concentration is in the line above the Equator known as the ITCZ, the inter-tropical convergence zone. This is where the two great hemispheric atmospheric air masses meet. It’s an area of nearly constant thunderstorms.

And on average, there’s much more precipitable water in the tropics than in the temperate or polar regions. 

Also, mountains like the Himalayas are drier than the surrounding regions, because the air up there is colder.

My next step with a variable that’s new to me is generally to take a look at how it changes over time. Figure 2 shows those results

Figure 2. Annual changes in total precipitable water, and the residual after the seasonal variations are removed.

First, there is a strong annual cycle. It varies every year from a low of about 23 kg/m2 to a high of nearly 27 kg/m2. Next, the TPW has changed over time. In this time period, it was dropping for the first twenty years, and has been rising for the last 20 years. Why? No clue.

Then when looking at a variable that’s new to me, I often look to see if there are any cyclical variations longer than one year. For that, I usually use a technique called CEEMD, which is short for Complete Ensemble Empirical Mode Decomposition. I describe the method in a post called “Noise Assisted Data Analysis“. It breaks the data into “empirical modes”, frequency bands that contain cycles with different periods. Here is a result of that analysis.

Figure 3. Periodograms of the various empirical modes of the cycles inherent in the TPW

The only large signal is at about 3 – 4 years. I suspect this is related to the QBO. The “quasi-biennial oscillation” is a roughly periodic change of the equatorial stratospheric wind between easterlies and westerlies. However, that’s just a guess. There are no sunspot-related or other longer inherent cycles.

Now, I got this TPW dataset so that I could better understand the relationship between temperature and water vapor. In general it’s said that a warmer world is a wetter world. However, it’s also true that water vapor is a greenhouse gas. So a wetter world would also be a warmer world.

So … which one is the cause here, and which one is the effect? This brings me to my next Nasrudin story:

“What is Fate?” Nasrudin was asked by a Scholar.

“An endless succession of intertwined events, each influencing the other.”

“That is hardly a satisfactory answer. I believe in cause and effect.”

“Very well,” said the Mulla, “look at that.” He pointed to a procession passing in the street.”

“That man is being taken to be hanged. Is that because someone gave him a silver piece and enabled him to buy the knife with which he committed the murder; or because someone saw him do it; or because nobody stopped him?”

Me, I’ve mostly given up trying to decide which is cause and which is effect in many matters climatical. In that regard, here’s a scatterplot of TPW and temperature, using CERES and ECMWF results.

Figure 4. Scatterplot, monthly precipitable water versus monthly temperature.

Clearly, there’s a strong relationship between the two. However, as mentioned above, this could either mean that a warmer world is wetter, or that a wetter world is warmer … or some combination of the two.

So, for a final look at this relationship, here is a scatterplot of the gridcell-by-gridcell variation shown in Figure 1, versus the corresponding graphic of surface temperature (not shown). I’ve split it up into land and sea to see what difference there is between the two.

Figure 5. Scatterplot, gridcell by gridcell average temperature versus gridcell average total precipitable water.

Now, this is showing something very interesting. First, almost nowhere on earth, and nowhere on the ocean, is the long-term average surface temperature above about 30°C.

Next, the closer the temperature gets to 30°C, the faster the total precipitable water vapor rises. Eventually, it seems that any additional energy goes into evaporation rather than into increasing the temperature.

Now, does this put a hard limit on the global temperature? Well, clearly not on the mean temperature … but it does seem to put a limit on the maximum temperature.

Can this maximum temperature limit change under modern conditions? Unknown. The oceanic temperature limit is a function of things like downwelling radiation, evaporation, and thunderstorms. The relation with thunderstorms is most clearly seen in the following movie. It shows cloud top altitude (as a proxy for deep tropical convective thunderstorms) versus sea surface temperature.

As you can see, the thunderstorms closely follow the warmest parts of the sea surface through all of their changes and variations.

In my post entitled “Air Conditioning Nairobi, Refrigerating The Planet“, I elucidated how thunderstorms function as giant refrigerators, cooling the surface in a host of ways. So clearly, they are a very large part of whatever combination of physical phenomena are involved in keeping a lid on the sea surface temperature. 

Thus, the maximum sea surface temperature could change from anything that changes evaporation, incident energy, or clouds. The number of things that could do that is limited—natural or anthropogenic surfactants on the ocean affecting evaporation, natural or anthropogenic aerosols that change cloud properties, changes in average wind speed, things like that.

So … at the end of the day, does a warmer world cause a wetter world, or does a wetter world cause a warmer world?

I can only echo what the incomparable Mulla Nasrudin said:

“Only children and fools seek both cause and effect in the same story.”

My very best to all, stay strong, stay healthy, stay crazy …

w.

PS—In this discussion of causes and effects, I would be remiss to close without mentioning the idea of “Granger Causality”. A variable X is said to “Granger-cause” variable Y if knowing the history of X improves our ability to predict variable Y. Curiously, there are four possibilities of Granger causation. The first three are similar to normal causation:

• Neither X nor Y Granger-causes the other. They are independent variables.

• X Granger-causes Y

• Y Granger-causes X

However, in Granger Causality, there is a fourth possibility:

• X and Y each Granger-causes the other.

And as you might expect in this most perplexing of worlds, when we analyze total precipitable water and temperature, we find that they are in the fourth case—each one Granger-causes the other one … go figure.

This in turn reminds me of Godel’s Incompleteness Theorem, which states that for any formal system of logic, there always are statements whose truth value simply cannot be determined. No matter what we do, in that logical system, we can’t determine whether some statements are true or not.

Of course, Mulla Nasrudin knew about Godel’s Theorem centuries ago, so if you’ll excuse me one final story …

A king, disenchanted with his subjects’ dishonesty, decided to force them to tell the truth. When the city gates were opened one morning, gallows had been erected in front of them. A royal guard announced, “Whoever will enter the city must first answer a question which will be put to them by the captain of the guard.”

Mulla Nasrudin stepped forward first. The captain spoke, “Where are you going? Tell the truth…the alternative is death by hanging.”

“I am going,” said Nasrudin, “to be hanged on those gallows.”

“I don’t believe you!” replied the guard.

Nasrudin calmly replied, “Very well then. If I have told a lie, hang me!”

“But that would make it the truth!” said the confused guard.

“Exactly,” said Nasrudin, “your truth.”

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