Feigning literacy, nothin' up my sleeve

Image courtesy of Chris Butler, Big Chris Gallery

I look at various climate related sites, both those who are skeptical of what I'll call climate disruption caused by the products of mankind's burning of fossil fuels and those who accept the theory (using "theory" here as a scientist would use it, analogous to, say, Newton's theory of gravitation). One of the most frustrating things I find is writers who present a veneer of scientific literacy but, upon even cursory investigation by anyone with a reasonable yet far short of specialist knowledge (e.g., myself) are easily revealed to be nonsense. Yet the scientific veneer ("look! charts! equals signs!") can lead people with almost no scientific or mathematical literacy to place credence in this nonsense. And, sadly, that latter group is a very large one.

A good example is to be found here. Those who follow the ebb and flow of the so-called debate around climate disruption will likely have heard of the "hiatus" in warming, that is, a slowing down of the rate of increase of global temperature. Given the demonstrable increase in energy retained by the earth/ocean/atmosphere system (for what is, in my opinion, a silly if not counterproductive "measurement" of this heat, see here) because of our greenhouse gas emissions, scientists have advanced theories for the so-called "missing heat." As best I can determine, the leading theory is that the oceans are heating and doing so to greater depth than had been anticipated.

But Anthony Cox is having none of it. He reproduces the graphic graphic at left. It charts a time series of "Change in Total Heat Content" data from 1955 through (apparently) 2014. As an aside, my pedantry requires that I mention that "heat content," though widely used and accepted, is poor terminology. Heat is an interaction between a system and its surroundings resulting in a change in internal energy of the system. Temperature, in turn, can be (loosely) considered to be a measure of one specific component of average internal energy.

In any case, Mr. Cox objects, and provides charts showing a calculated equivalent temperature rise in degrees celsius. I'm not sure why he bothered to calculate. The source of such data, NOAA's National Oceanographic Data Center, provides a chart with degrees celsius as the ordinate in the same set of charts as that from which the "heat content" chard is reproduced. Such a chart is here and, in fact, the charts showing heat content are computed from temperature measurements.

But what's the difference? Why does one chart show the data in joules and the other in degrees celsius? The joule is a unit of energy. One joule is an extremely small amount of energy in comparison to everyday experience; the heat energy available in a single piece of plain M&M candy is more than 14,000 joules. A gallon of gasoline releases about 125,000,000 joules when completely oxidized. That's why the heat content chart has such huge numbers. What you see on the vertical axis is measured (actually, computed from temperature measurements in the ocean vertical profile) heat content with a reference number subtracted. Accordingly, this is an "anomaly," and each "tick" on the vertical axis represents a 10²² (1 followed by 22 zeros) joules from the reference period. It does not represent the "total heat content" of the oceans. It represents gains and losses in comparison to the reference period.

To the left is the data showing temperature (again, as an anomaly) over the period. Note that this was taken straight from the the NODC web site, no need for the calculations performed by Lucia at the "The Blackboard."

Mr. Cox contends that the heat content anomaly in joules is used because the big numbers look more scary then the same data presented as temperature anomaly in degrees celsius.

This is simply untrue. The amount of energy that will heat a cubic meter of water by 1 degree celsius will heat about 3,100 cubic meters of air (at sea level pressure) by that same degree celsius. This is due in small part to the higher specific heat of water but mostly to water being about 1,000 times as dense as air (again, at sea level pressure). Looked at another way, the amount of energy required to heat the upper 700 meters of ocean worldwide by 1 degree celsius would heat the ENTIRE atmosphere some 170 degrees celsius (assuming that the specific heat of air is constant as temperature changes, which it is not).

Now, is the interaction between incoming solar energy, outgoing long wave radiation, ocean circulation, heat transfer, etc. as simple as this calculation? Of course not. That's why scientists study these things, measure the relevant parameters, seek hypotheses that explain the measurements, etc. Are there significant questions to be answered with respect to the data presented and how it's measured? Yes. Are scientists trying to answer these questions? Yes. That's what science is.

But the conclusion is that energy (referred to by NOAA as "Heat Content" and tracked as an anomaly) is an entirely appropriate way to picture one component of the effect of greenhouse gases on our ocean/atmosphere system. It is NOT a nefarious way to be able to insert scary large numbers into a chart. And, to reemphasize for yet the third time, the same set of NOAA charts that shows the energy anomaly in joules shows its effect in degrees celsius as well. So who really has deception as their goal?

More on fuel saved by regenerative braking

I published a post regarding how much energy is captured in the regenerative braking system in my Lexus CT200h hybrid. After some discussion with commenter Gabriel Grosskopf, I estimated that about 59% of the energy available (after subtracting the energy used to overcome aerodynamic drag, rolling resistance, and internal friction) was recaptured and used to charge the battery.

Since I (and others) have represented that the regenerative braking system is among the key reasons that hybrids achieve superior fuel economy, I decided to check the actual impact.

My round trip commute, generally downhill in the morning and uphill in the evening, is 62.46 miles and, for the last 10 fill ups, my average m.p.g. has been 52.47. So, to make my commute, I use, on average 62.46/52.47=1.190 gallons of gasoline. My display showed me today that my regenerative braking system added 700 watt hours or 2,520,000 joules to my battery that I could use for accelerating, hill climbing, etc. If I assume my electric motor is 90% efficient, I put 2,268,000 of these joules to work.

A gallon of gasoline (reformulated blend in this case) has an energy upon oxidation of 111,836 btu or 117,993,000 joules. I estimate that my internal combustion engine is about 25% efficient, so I put about 29,498,000 of these joules to work. My 1.19 gallons thus provide 35,103,000 joules that propel my vehicle (the remainder being lost as waste heat in myriad ways).

If I assume that I used all of the energy my brakes provided, then 35,103,000 + 2,268,000 = 37,371,000 joules of work were done to propel my car. Then, dividing by 0.25, I can estimate that 149,484,000 joules of oxidized gasoline would have been necessary to do this work. This is the energy in 1.267 gallons. Dividing this into 62.46, I find that the fuel economy without the regenerative braking would have been about 49.30 m.p.g. The regenerative braking thus upped my m.p.g. by 3.17.

As I've often said, it's much more intuitively informative to discuss gallons per mile, or gallons per 100 miles. So, the regenerative braking took me from 2.03 gallons per 100 miles to 1.91 gallons per 100 miles. So it takes me 5.9% less fuel to go a given distance, ceteris parabus.

There's no question that I'm carrying a lot more significant figures (apologies to John Denker) than are warranted by the precision of my data, but I think that the figure I've determined is probably in the ballpark.

Rates vs. quantities - more unit confusion

It's widely accepted (though not universally) in the renewable energy/clean tech/green community that one of THE major problems in the widespread adoption of such renewable sources of electricity as solar and wind is their intermittent character. It's further believed that the ability to store the energy from these sources will enable their intermittency to be smoothed out, thus making them a reliable source of energy and enabling them to become much more easily integrated into the grid, possibly even a source of baseload power.

I read today that my state, California, has, through our Public Utilities Commission, set a goal of "1.3 gigawatts of energy storage by 2020." My state is certainly at the leading edge of sustainability with AB32, the Global Warming Solutions Act of 2006, the Cap and Trade Program, and many others. But I worry about people who make laws write regulations and yet aren't able to distinguish between rates and quantities.

Here's a link to the Assigned Commissioner's Ruling on this. Throughout the document, Carla Peterman discusses storage in megawatts. But a "watt" is a rate of energy utilization, or rate of performing work. A megawatt is a million joules per second. Certainly, the rate at which a storage system can deliver energy is important, but the key is the quantity that can be stored. This would be measured in watt hours, kilowatt hours, megawatt hours, gigawatt hours, terawatt hours, etc. Or, equivalently, in joules, megajoules, etc. Saying "we need 1.3 gigawatts of storage" is analogous to saying San Francisco is 80 miles per hour away from Los Angeles.

A typical gasoline pump will pump, conservatively, around five gallons per minute. Each gallon of gasoline has a chemical potential energy through oxidation of about 132 megajoules. Thus, when you fill your tank, you're delivering energy at the rate of 132*10^6 joules/gallon * 5 gallons per minute/60 seconds per minute or 11 megawatts. About 120 people filling their tanks are delivering energy at about the 1.3 gigawatts mentioned by the PUC. But this doesn't tell you a thing about how many miles these 120 drivers can travel. To know that, you need to know the capacity of the 120 tanks in gallons (along with the rate of fuel consumption of the vehicles).

To provide a bit of orientation as to the rates being discussed, in 2011, California generated or imported a total of about 292,454 gigawatt hours of electricity. This is a rate of about 33.36 gigawatts so the storage being discussed could deliver a bit under 4% of the average California rate of electricity usage.  Of course, the planned storage is divided between different utilities and geographical locations and would be deployed locally. But key to the discussion is FOR HOW LONG? A second? A minute? An hour? A day? Nothing in the document tells us.

Addendum, June 15, 2013: It's bad blog form to edit a posted blog without saying so. In reviewing the above, I realize that, while it's quite true that capacity is a fundamental metric of the viability and practicality of storage, rate is also important. I alluded to that above but I want to make it clear that I realize that vast capacity is not relevant if the rate at which it can be delivered isn't matched to the demand present in the area served.

This merits a bit of analysis of what sort of capacity might "match" a delivery rate of 1.3 gigawatts. For a starting point, let's take a look at the 4% calculated above. And I'll arbitrarily assume that we'd like to be able to "even out" the output from intermittent sources over a 24 hour period with a reserve capacity (no wind, cloud covered sky, whatever) for three days. In three days, on average, California might use (3/365)*29,2454 or about 2,400 gigawatt hours of electrical energy. 4% of this is 96 gigawatt hours.

Arguably, the storage method with the best combination of capacity, dispatchability, delivery rate, and efficiency is pumped hydro storage. If we assume a round trip efficiency of 75%, we'll need to store 128 gigawatt hours of energy. Hoover Dam delivered, at its 1984 peak, 10.348 terawatt hours so, in an average three day period in 1984, it delivered 10348*(3/365) = 85 gigawatt hours. So we're talking about something like one and a half Lake Mead/Hoover Dam storage schemes.

By the way, this goes to show just what an amazing resource gasoline is. 3032 gasoline pumps can deliver the energy equivalent to the entirety of California's average electrical consumption.

Update: The Blenheim-Gilboa Power Station in New York can deliver electricity at the rate of 1.6 gigawatts and, per a comment in a post on pumped hyrdo storage at one of my favorite sites, Do the Math, can deliver this for 16 hours for a total of 25.6 gigawatt hours. Another site says 1,000 megawatts for eight hours, or 8 gigawatt hours. In any case, storage of the magnitude specified is certainly achievable.

Also, as seen here, it's clear that pumped hydro plants are typically rated in rate in watts rather than capacity and, in fact, it's difficult to find the energy capacity in megawatt hours or gigawatt hours. In a comment in the article linked above, Ben K. say that this is because generating plants are rated in this way. But I don't see that this is a valid reason. A generating plant generates continuously as long as coal, natural gas, uranium, etc. is delivered - the amount of source material is not the issue. In a storage facility, the amount of source material (compressed air, battery chemical potential energy, water, flywheel rotational energy, capacitor electrical charge energy, whatever) is THE issue. After all, we look at battery storage capacity in terms of amp-hours which, at a fixed voltage, is a measure of quantity of energy.