Sea Surface Temperatures (SSTs) measured by the AMSR-E instrument on NASA’s Aqua satellite continue the fall which began several months ago. The following plot, updated through yesterday (July 29, 2010) shows that the cooling in the Nino34 region in the tropical east Pacific continue to be well ahead of the cooling in the global average SST, something we did not see during the 2007-08 La Nina event (click on it for the large, undistorted version; note the global SST values have been multiplied by 10):

(UPDATED: 3:10 p.m. July 29, 2010 with temperature difference plot)

As promised, here are the first results from my little backyard experiment to investigate the role of downwelling infrared (IR) sky radiation on air temperature. (High school students looking for a science experiment, pay attention).

It’s a heavily insulated box that — theoretically — should chill air at night to a temperature below that of the outside air. The following is a conceptual design of The Box before I built it, along with the key components:

This all came about because I got tired of being asked about the theory behind global warming, specifically, how can downwelling infrared sky radiation from greenhouse gases (mostly water vapor, to a lesser extent CO2) cause global warming of the Earth surface, when the emitting temperature of the sky is colder than the surface?

Some people are convinced that this cannot happen, since the 2nd Law of Thermodynamics says energy naturally flows from higher temperature to lower temperature. In contrast, the mainstream science community, while agreeing the NET energy flow is from warm to cold, you can still cause warming by adding more greenhouse gas to the colder atmosphere. This happens even though the IR emitting temperature of the sky “causing” that warming is 10’s of degrees colder than the surface.

[NOTE: the direct warming effect of more atmospheric CO2 is small; its the resulting indirect warming (positive feedbacks) from clouds and water vapor that has most scientists worried. But not me…I think the net feedbacks are negative.]

The Box

So, since I have two automated weather stations in my backyard, I decided to build a heavily insulated box that would contain a small amount of air, and try to reduce all the other kinds of energy exchange between that air sample and the environment to a minimum EXCEPT for the influence of the downwelling sky radiation.

The air sample and the sky would be allowed to exchange IR radiation, and the colder the infrared emitting temperature of the sky is, the colder the air in the box should become compared to the air outside of the box. More about that later.

While we might not put the debate to rest with such an experiment, we can build some intuition about the energy flows that cause day and night air temperatures to be what they are. Of course, one could simply buy a hand-held infrared radiometer and take the sky’s “temperature” directly. But since everyone (myself included) has at least some trouble conceptualizing the role of infrared radiation in weather and climate (after all, we can’t see IR radiation), I thought that letting the IR effect be measured through its influence on temperature would make a bigger impact.

So, here’s a picture of the real thing that I took this morning, after collecting data since about noon yesterday:

The wireless data processor for the cavity temperature data is the little unit on the top. It sends a new temperature measurement every 5 minutes to my desktop computer in the house.

Here’s a close-up of the cavity. There is an insulating layer of air trapped between the two thin sheets of polyethylene, which are nearly transparent to infrared energy. The temperature sensor itself can be seen below that, in the cavity, the walls of which are painted with high emissivity paint (Krylon 1502 Flat White, IR emissivity = 0.99; Note that in the infrared, black is not necessarily more emissive than white…it depends on what the paint is made of, and whether the surface is rough or smooth).

Meanwhile, my regular weather station is about 20 feet away, and it is collecting air temperature and dewpoint data on the same schedule as The Box cavity temperatures are taken:

First Data from The Box
The first 17 hours of data, from midday yesterday until 8:05 a.m. this morning, are plotted below:

When I first closed up the box with the thermometer placed in the cavity, I was surprised how hot the cavity became. The maximum temperature recorded yesterday afternoon was 158 deg. F, and that must have been the limit for the sensor, because the temperature then flatlined for about an hour.

The reason for the high temperature was some direct sunlight reflecting off of one wall of the airspace, above the cavity. Even though the cavity was painted white, it still absorbed enough energy to make the air very hot. From what I have been able to gather, it is very difficult to get the solar reflectance of white paint above about 0.9.

It is interesting to calculate what rate of energy input would be required to cause this rapid rate of warming, which was about 3 deg. F per minute. If the cavity is initially in energy equilibrium, and we start reflecting 20 Watts per sq. meter more onto the cavity walls, about 10% of that (2 Watts per sq. meter) would be heating the paint, and so the air in the cavity.

According to my calculations, that would be more than enough to explain the initial rapid rise of temperature in the cavity on its way to 158+ deg. F. My calculations are only approximate, though, since I did not take into account the heat capacity of the cavity walls (painted aluminum foil), or the increased loss of IR as the cavity warmed, or conductive losses to the styrofoam and air space above the cavity.

But what we are really interested in is what happens when the overwhelming influence of solar radiation subsides. In the above plot, look at what happens as sunset approaches. Despite diffuse solar radiation still entering The Box from the blue sky, the cavity air cools to a couple of degrees below the ambient air temperature by sunset. Then, during the night, the cavity air averages about 4 deg. F colder than the outside air. This is easier to see in the next plot of the temperature difference between the cavity and the outside air, which we see remains pretty constant during the night:

To see how even a little diffuse sunlight from the sky can cause warming of the cavity, note what happened just after sunrise this morning…even though our yard does not see direct sunlight till close to 11 a.m. (very tall trees in the way), the blue sky started warming the cavity almost immediately after sunrise.

Then, after a short while, I put a white cover from a plastic cooler over the cavity to minimize the daytime heating of the cavity. At the end of the data plot you can see this solar cover caused the cavity to cool back down to the same temperature as the ambient air.

So, we already can see the cooling effect of infrared radiation in the data…in the form of cavity temperatures colder than the air. This happens from just before sunset, until sunrise — the period when there is little or no sunlight, either direct, or diffuse from the sky. But what, exactly, is the reason for this chilling effect?

Why Was the Cavity Colder than the Outside Air Temperature?
The temperature of virtually anything is the result of a balance between (1) energy gained and (2) energy lost. As long as the energy gained exceeds that lost, the temperature will rise. This was clearly seen when I closed up The Box, and the rate of sunlight absorption in the cavity exceeded the rate of energy lost by infrared emission (and any — hopefully small — conductive losses). The temperature skyrocketed.

But once the rate of energy loss exceeds that gained, then the temperature will fall, as was seen when The Box entered the shade. Then, then rate of IR energy lost (which increases rapidly with temperature) exceeded that gained from diffuse solar radiation, and the cavity temperature fell.

So, at night when there is no solar energy available, what is to prevent the cavity from getting very cold? Outer space is supposed to emit near absolute zero, 3 K. The Box’s cavity enters the hours of darkness at something like 300 K temperature. At 300 K, and assuming an IR emissivity of 0.99, the cavity is emitting IR at a rate of just over 400 Watts per sq. meter. Assuming the box is very well insulated, and is not leaking air, what is to prevent the cavity temperature from dropping well below freezing (273 K)?

The answer is downwelling IR from the sky. During the day in the summer, the broadband infrared sky temperatures viewed from the ground generally runs about 10 – 20 deg. F cooler than the near-surface air temperatures. This source of energy must exist, because without it the temperature of a cavity in a well insulated box at night would plunge even faster than we saw it heat up when exposed to indirect sunlight. And that rapid rate of temperature rise was due to only about 2 Watts per sq. meter! Imagine what in imbalance of 400 Watts per sq. meter would do.

Instead, the sky emits at only a slightly lower temperature than the surface, so the cavity cools only a little at night: about 4 deg. F cooling out of a “potential cooling” of 15 deg. F, assuming the IR emissivity of the cavity is 1.0.

By the way, I calculate that, if the cavity emissivity was only 0.90 rather than the advertised 0.99 (we really don’t know), we could explain the entire 4 deg. F drop based upon the cavity coming to a radiating temperature equal to that of the sky.

Presumably, once drier air arrives here in Alabama in another couple months, I should see larger temperature falls in the cavity, since water vapor is the Earth’s main greenhouse gas. In the meantime, I’m open to suggestions regarding simple ways to make The Box more efficient at rejecting all sources of energy except downwelling infrared radiation from the sky.

…a radiation source which some say, does not exist. 😉

As a follow-up to my controversial post on the effect of infrared “back radiation” downwelling from the colder sky to the warmer surface, the existence of which some dispute (despite the real-time availability of such data), I’ve come up with an experimental setup to see how IR radiation from the sky influences air temperature near the ground. (Yes, I know some of you think there is no such thing, but please indulge my fantasy as if it was true, ok?)

The design is pretty simple and inexpensive, and looks a little like the blackbody radiators that are used as calibration sources. The following cartoon shows the main components:

The idea is to isolate a sample of air and control its environment so that it’s main source of energy gain or loss is through an opening that looks at the sky. You have probably noticed that on a clear evening, dew forms first on the tops of cars and other surfaces. This is because these surface are losing IR energy faster than the air and other surfaces are, so their temperature falls below the dewpoint temperature first.

If we can isolate that effect sufficiently from other sources and sinks of energy, we should be able to get air temperature drops within the cavity in the direction of the colder, effective sky temperature. (We use air since it is very hard to measure the temperature of a cold surface accurately, so we let the cold surface inside the cavity chill the air in contact with it).

The cavity will be lined with aluminum foil, which has very high reflectivity in the infrared, painted on the inside only with high-emissivity paint (Krylon flat white, #1502 if I can find it…apparently, black paint isn’t as good an emitter in the IR.)

The 2 thin polyethylene sheets are in the upward-looking cavity opening to trap a layer of air for thermal conductive insulation, while at the same time passing most IR radiation (something polyethylene is apparently quite good at). The thermal conductivity of the trapped air is a little better (less) than that of Styrofoam, but since convection can occur in an air cavity, I’m sure the actual rate of heat transfer will be more than that for Styrofoam.

SO WHAT KIND OF SIGNALS CAN WE EXPECT?

(…assuming the experiment isn’t a complete failure because of something important I haven’t thought of…)

If you search around on the internet you will find that those who have made such broadband IR measurements of the sky (from what I can tell, usually with instruments that measure between 8 and 14 microns wavelength) report that the effective sky temperature in the infrared is usually 10 to 30 deg. C lower than the near-surface air temperature. Ten deg. C is more typical during humid conditions or cirrus cloud cover, while 30 deg. C would be during clear, low humidity conditions.

Low clouds produce a downwelling sky temperature nearly the same as the upwelling temperature. The sky temperature increases as you scan from the zenith down in elevation, due to the greater path length through the atmosphere.

As an example of the theoretically-expected difference in IR energy flows in and out of the cavity, at an emissivity of 1, a cavity at 300 K temperature should emit a broadband IR flux of 459 Watts/m2, while a downwelling apparent temperature of 290 K (10 deg. lower than the cavity) would produce 401 Watts/m2, the difference being 58 Watts per sq. meter.

In a perfect setup with a cavity emissivity of 1 and no other losses of energy under these conditions, the inside of the cavity would then cool to 10 deg. C less than the surrounding air temperature as the insulated cavity comes into radiative equilibrium with the sky. (I am currently monitoring 2 temperatures in my back yard, with the data sent to my computer by wireless. My first design failed due to large conductive energy loses, which led to the 2nd design, above).

Of course, a “perfect” experimental setup is not possible. I’ve run some numbers based upon the thermal conductivity of Styrofoam and I think I can keep the energy loses to about 20% of the signal being sought, but this is uncharted territory for me.

OK, TIME FOR YOUR PREDICTIONS

So, for all of you who think you know what will happen in this experiment, come on and tell the rest of us. Will the temperature of the air in the cavity stay the same? Will it cool? By how much?

I especially want to hear an answer to 2 questions:

(1) If you think the cavity will be the only source of IR radiation, and there is no downwelling IR radiation from the sky, then what will keep the air temperature inside from falling dramatically lower than the air temperature outside of the box?

(2) If you think the temperature in the cavity will not change, then what is keeping the IR radiation flowing out of the cavity toward the sky from causing a temperature fall? Wouldn’t want to violate the 1st Law of Thermodynamics, ya know.

Let the thinking begin.

Probably as the result of my recent post explaining in simple terms my “skepticism” about global warming being mostly caused by carbon dioxide emissions, I’m getting a lot of e-mail traffic from some nice folks who are trying to convince me that the physics of the so-called Greenhouse Effect are not physically possible.

More specifically, that adding CO2 to the atmosphere is not physically capable of causing warming.

These arguments usually involve claims that “back radiation” can not flow from the cooler upper layers of the atmosphere to the warmer lower layers. This back radiation is a critical component of the theoretical explanation for the Greenhouse Effect.

Sometimes the Second Law of Thermodynamics, or Kirchoff’s Law of Thermal Radiation, are invoked in these arguments against back radiation and the greenhouse effect.

One of the more common statements is, “How can a cooler atmospheric layer possibly heat a warmer atmospheric layer below it?” The person asking the question obviously thinks the hypothetical case represented by their question is so ridiculous that no one could disagree with them.

Well, I’m going to go ahead and say it: THE PRESENCE OF COOLER OBJECTS CAN, AND DO, CAUSE WARMER OBJECTS TO GET EVEN HOTTER.

In fact, this is happening all around us, all the time. The reason why we might be confused by the apparent incongruity of the statement is that we don’t spend enough time thinking about why the temperature of something is what it is.

How Cooler Objects Make Warmer Objects Even Hotter

One way to demonstrate the concept is with the following thought experiment, which I will model roughly after the Earth suspended in the cold of outer space. Even my oldest daughter, a realtor who has an aversion to things scientific, got the right answer when I used this example on her.

Imagine a heated plate in a cooled vacuum chamber, as in the first illustration, below. These chambers are used to test instruments and satellites that will be flown in space. Let’s heat the plate continuously with electricity. The plate can lose energy only through infrared (heat) radiation emitted toward the colder walls of the chamber, since there is no air in the vacuum chamber to conduct the heat away from the plate. (Similarly, there is no air in outer space to conduct heat away from the Earth in the face of solar heating.)

The plate will eventually reach a constant temperature (let’s say 150 deg. F.) where the rate of energy gain by the plate from electricity equals the rate of energy loss by infrared radiation to the cooled chamber walls.

Now, let’s put a second plate next to the first plate. The second plate will begin to warm in response to the infrared energy being emitted by the heated plate. Eventually the second plate will also reach a state of equilibrium, where its average temperature (let’s say 100 deg. F) stays constant with time. This is shown in the next illustration:

But what will happen to the temperature of the heated plate in the process? It will end up even hotter than it was before the cooler plate was placed next to it. This is because the second plate reduced the rate at which the first plate was losing energy.

(If you are unconvinced of this, then imagine that the second plate completely surrounds the heated plate. Will the heated plate remain at 150 deg., and not warm at all?)

Since the temperature of an object is a function of both energy gain AND energy loss, the temperature of the plate (or anything else) can be raised in 2 basic ways: (1) increase the rate of energy gain, or (2) decrease the rate of energy loss. The temperature of everything is determined by energy flows in and out, and one needs to know both to determine whether the temperature will go up or down. This is a consequence of the 1st Law of Thermodynamics involving conservation of energy.

Note that the above example involving 2 plates, one hotter than the other, is apparently where the greenhouse effect deniers (sorry, I couldn’t help myself) would claim the “physically impossible” has occurred: The presence of a colder object has caused a warmer object to become even hotter. Again, the reason the heated plate became even hotter is that the second plate has, in effect, “insulated” the first plate from its cold surroundings, keeping it warmer than if the second plate was not there.

The only way I know of to explain this is that it isn’t just the heated plate that is emitting IR energy, but also the second plate….as well as the cold walls of the vacuum chamber. The following illustration zooms in on the plates from our previous illustration:

What happens is that the second plate is heated by IR radiation being emitted by the first plate, raising its temperature. The second plate, in turn, cannot cool to the temperature of the vacuum chamber walls (0 deg. F) because it is not in direct contact with the refrigerant being used…it can only lose IR at a rate which increases with temperature, so it achieves some intermediate temperature.

Meanwhile, the cooler plate is emitting more radiation toward the hot plate than the cold walls of the vacuum chamber would have emitted. This changes the energy budget of the hot plate: despite a constant flow of energy into the plate from the electric heater, it has now lost some of its ability to cool through IR radiation. Its temperature then rises until it, once again, is emitting IR radiation at the same rate as it is receiving energy from its surroundings (and the electric heater).

As we will see, below, in the case of the Earth being heated by the sun, the vacuum chamber “wall” (outer space) is close to absolute zero in temperature. Putting anything between that (essentially infinite) heat sink and the Earth’s surface will cause the surface to warm.

Examples are All Around Us

Examples of objects with lower temperatures causing objects with higher temperatures to become even higher still are all around us.

For instance, in terms of these most basic heating and cooling concepts (energy gain and energy loss), the same thing happens when you put a blanket over yourself when it is cold. The blanket stays cooler than your skin, but it nevertheless makes your skin warmer than if the cooler blanket was not there. Even though the direction of flow of heat never changes (it is always from warmer to cooler objects), a cooler object can still make a warm object even hotter.

It doesn’t matter what the mechanisms of energy transfer are….if the presence of a cooler object keeps a warmer object from losing energy as rapidly as before, the warm object will become even hotter.

But if you insist on another real-world example involving infrared radiation, rather than heat conduction, let’s use clouds at night. Almost everyone has experienced the fact that cloudy nights tend to be warmer than clear nights.

The most dramatic effect I’ve seen of this is in the winter, on a cold clear night with snow cover. The temperature will drop rapidly. But if a cloud layer moves in, the temperature will either stop dropping, or even warm dramatically.

This warming occurs because the cloud radiates much more IR energy downward than does a clear, dry atmosphere. This changes the energy budget of the surface dramatically, often causing warming — even though the cloud is usually at a lower temperature than the ground is. Even high altitude cirrus clouds at a temperature well below than of the surface, can cause warming.

So, once again, we see that the presence of a colder object can cause a warmer object to become warmer still.

Extending the Concept to the Atmosphere

As mentioned above, in the case of the cold depths of outer space surrounding the Earth’s solar-heated surface, ANY infrared absorber that gets between the Earth’s surface and space will cause the surface to warm.

This radiative insulating function occurs in the atmosphere because of the presence of greenhouse gases, that is, gases that absorb and emit significant amounts of infrared energy…(mostly water vapor, CO2, and methane). Clouds also contribute to the Greenhouse Effect.

Kirchoff’s Law of thermal radiation says (roughly), that a good infrared absorber is an equally good infrared emitter. So, each layer of the atmosphere is continuously absorbing IR, as well as emitting it. This is what makes the Greenhouse Effect so much more difficult to understand conceptually than solar heating of the Earth. While the sun is a single source, and most of the energy absorbed by the Earth is at a single level (the surface of the ground), in the case of infrared energy, every layer becomes both as source of energy and an absorber of energy.

It also helps that our eyes are much more sensitive to solar radiation than they (or even our skin) are to infrared radiation. It’s more difficult to conceptualize that which you can’t see.

Our intuition begins to fail us when presented with this complexity. The following illustration shows some of these energy flows: just the IR being emitted upward and downward by different atmospheric layers. If I included arrows representing the IR energy being absorbed by those layers, too, it would become hopelessly indecipherable.

As a result of the atmosphere’s ability to radiatively insulate the Earth’s surface from losing infrared energy directly to the “cold” depths of outer space, the surface warms to a higher average temperature than it would have if the atmosphere was not there. The no-atmosphere, global average surface temperature has been theoretically calculated to be around 0 deg. F.

This, then, constitutes the basic mechanism of the Greenhouse Effect. Greenhouse gases represent a “radiative blanket” that keeps the Earth’s surface warmer than it would otherwise be without those gases present.

In fact, research published in the 1960s showed that, if the current atmosphere suddenly became still – with no wind, evaporation, and convective overturning transporting excess energy from the surface to the upper atmosphere – the average surface temperature of the Earth would warm dramatically, from 0 deg. F with no greenhouse gases, to about 140 deg. F. That the real world temperature is much lower, around 59 deg. F, is due to the cooling effects of weather transporting heat from the surface to the upper atmosphere through convective air currents.

Weather as we know it would not even exist without the greenhouse effect continuously destabilizing the vertical temperature profile of the atmosphere. Vertical air currents associated with weather act to stabilize the atmospheric temperature profile, but it is the greenhouse effect that keeps the process going by warming the lower atmosphere, and cooling the upper atmosphere, to the point where convection must occur.

What About Kirchoff’s Law?
One of the statements of Kirchoff’s Law is:

At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity.

Many well-meaning people think that one of the consequences of Kirchoffs Law of radiation is that an individual layer of the atmosphere that absorbs infrared energy at a certain rate must also emit energy at the same rate. This is NOT true.

The rate of emission becoming the same as the rate of absorption occurs in the very special case where (1) the temperature has reached thermal equilibrium, and (2) that equilibrium is the result of only those two radiative flows, in and out of the object.

Interestingly, this condition of a layer emitting the same amount of IR as it is absorbing is virtually never met anywhere in the atmosphere. This is because of the vertical, convective flows which are also transporting energy between layers.

In the global average, air below about 5,000 feet in altitude is absorbing more infrared energy than it emits, while air above that altitude (up to the top of the troposphere, the 80% of the atmosphere where weather occurs) is losing infrared energy faster than it is gained.

The reason why these two regions stay at roughly a constant temperature, despite very different rates of infrared loss and gain, is convective heat transport by weather: air heated by sunlight absorbed at the Earth’s surface has its excess energy transported to the upper troposphere, where a lack of water vapor (Earth’s main greenhouse gas) allows that energy to escape more rapidly to space.

The 2nd Law of Thermodynamics: Can Energy “Flow Uphill”?
In the case of radiation, the answer to that question is, “yes”. While heat conduction by an object always flows from hotter to colder, in the case of thermal radiation a cooler object does not check what the temperature of its surroundings is before sending out infrared energy. It sends it out anyway, no matter whether its surroundings are cooler or hotter.

Yes, thermal conduction involves energy flow in only one direction. But radiation flow involves energy flow in both directions.

Of course, in the context of the 2nd Law of Thermodynamics, both radiation and conduction processes are the same in the sense at the NET flow of energy is always “downhill”, from warmer temperatures to cooler temperatures.

But, if ANY flow of energy “uphill” is totally repulsive to you, maybe you can just think of the flow of IR energy being in only one direction, but with it’s magnitude being related to the relative temperature difference between the two objects. The result will still be the same: The presence of a cooler object can STILL cause a warmer object to become even hotter.

Anyway, that’s my story, and I’m sticking to it. Until someone convinces me otherwise.

So, let the flaming begin! No, really, have fun…but if you want your comments to remain available for others to read, please keep it civil.

SUGGESTION FROM ROY (7:50 a.m. Monday, July 26): If you want to add intelligently to this discussion, you need to actually read (1) what I have said, and (2) what others have said. Chances are, your point has already been made and discussed.

There is a new paper in press at the Journal of Climate that we were made aware of only a few days ago (July 14, 2010). It specifically addresses our (Spencer & Braswell, 2008, hereafter SB08) claim that previous satellite-based diagnoses of feedback have substantial low biases, due to natural variations in cloud cover of the Earth.

This is an important issue. If SB08 are correct, then the climate system could be substantially more resistant to forcings – such as increasing atmospheric CO2 concentrations — than the IPCC “consensus” claims it is. This would mean that manmade global warming could be much weaker than currently projected. This is an issue that Dick Lindzen (MIT) has been working on, too.

But if the new paper (MF10) is correct, then current satellite estimates of feedbacks – despite being noisy – still bracket the true feedbacks operating in the climate system…at least on the relatively short (~10 years) time scales of the satellite datasets. Forster and Gregory (2006) present some of these feedback estimates, based upon older ERBE satellite data.

As we will see, and as is usually the case, some of the MF10 criticism of SB08 is deserved, and some is not.

First, a Comment on Peer Review at the Journal of Climate

It is unfortunate that the authors and/or an editor at Journal of Climate decided that MF10 would be published without asking me or Danny Braswell to be reviewers.

Their paper is quite brief, and is obviously in the class of a “Comments on…” paper, yet it will appear as a full “Article”. But a “Comments on…” classification would then have required the Journal of Climate to give us a chance to review MF10 and to respond. So, it appears that one or more people wanted to avoid any inconvenient truths.

Thus, since it will be at least a year before a response study by us could be published – and J. Climate seems to be trying to avoid us – I must now respond here, to help avoid some of the endless questions I will have to endure once MF10 is in print.

On the positive side, though, MF10 have forced us to go back and reexamine the methodology and conclusions in SB08. As a result, we are now well on the way to new results which will better optimize the matching of satellite-observed climate variability to the simple climate model, including a range of feedback estimates consistent with the satellite data. It is now apparent to us that we did not do a good enough job of that in SB08.

I want to emphasize, though, that our most recent paper now in press at JGR (Spencer & Braswell, 2010: “On the Diagnosis of Radiative Feedback in the Presence of Unknown Radiative Forcing”, hereafter SB10), should be referenced by anyone interested in the latest published evidence supporting our claims. It does not have the main shortcomings I will address below.

But for those who want to get some idea of how we view the specific MF10 criticisms of SB08, I present the following. Keep in mind this is after only three days of analysis.

There are 2 Big Picture Questions Addressed by SB08 & MF10

There are two overarching scientific questions addressed by our SB08 paper, and MF10’s criticisms of it:

(1) Do significant low biases exist in current, satellite-based estimates of radiative feedbacks in the climate system (which could suggest high biases in inferred climate sensitivity)?

(2) Assuming that low biases do exist, did we (SB08) do an adequate job of demonstrating their probable origin, and how large those biases might be?

I will address question 1 first.

Big Picture Question #1: Does a Problem Even Exist in Diagnosing Feedbacks from Satellite Data?

MF10 conclude their paper with the claim that standard regression techniques can be applied to satellite data to get useful estimates of climate feedback, an opinion we strongly disagree with.

Fortunately, it is easy to demonstrate that a serious problem does exist. I will do this using MF10’s own method: analysis of output from coupled climate models. But rather than merely referencing a previous publication which does not even apply to the problem at hand, I will show actual evidence from 18 of the IPCC’s coupled climate models.

The following plot shows the final 10 years of data from the 20th Century run of the FGOALS model, output from which is archived at PCMDI (Meehl et al., 2007). The plot is global and 3-month averaged net radiative flux anomalies (reflected solar plus emitted infrared) versus the corresponding surface temperature anomalies produced by the model.

This represents the kind of data which are used to diagnose feedbacks from satellite data. The basic question we are trying to answer with such a plot is: “How much more radiant energy does the Earth lose in response to warming?” The answer to that question would help determine how strongly (or weakly) the climate system might respond to increasing CO2 levels.

It is the slope of the red regression fit to the 3-month data points in the above figure that is the question: Is that slope an estimate of the net radiative feedback operating in the climate model, or not?

MF10 would presumably claim it is. We claim it is not, and furthermore that it will usually be biased low compared to the true feedback operating in the climate system. SB08 was our first attempt to demonstrate this with a simple climate model.

Well, the slope of 0.77 W m^-2 K^-1 in the above plot would correspond to a climate sensitivity in response to a doubling of atmospheric carbon dioxide (2XCO2) of (3.8/0.77=) 4.9 deg. C of global warming. [This assumes the widely accepted value near 3.8 W m^-2 K^-1 for the radiative energy imbalance of the Earth in response to 2XCO2].

But 4.9 deg. C of warming is more than DOUBLE the known sensitivity of this model, which is 2.0 to 2.2 deg. C (Forster & Taylor, J. Climate, 2006, hereafter FT06). This is clearly a large error in the diagnosed feedback.

As a statistician will quickly ask, though, does this error represent a bias common to most models, or is it just due to statistical noise?

To demonstrate this is no statistical outlier, the following plot shows regression-diagnosed versus “true” feedbacks diagnosed for 18 IPCC AR4 coupled climate models. We analyzed the output from the last 50 years of the 20th Century runs archived at PCMDI, computing average regression slopes in ten 5-year subsets of each model’s run, with 3-month average anomalies, then averaging those ten regression slopes for each model. Resulting climate sensitivities based upon those average regression slopes are shown separately for the 18 models in the next figure:

As can be seen, most models exhibit large biases – as much as 50 deg. C! — in feedback-inferred climate sensitivity, the result of low biases in the regression-diagnosed feedback parameters. Only 5 of the 18 IPCC AR4 models have errors in regression-inferred sensitivity less than 1 deg. C, and that is after beating down some noise with ten 5-year periods from each model! We can’t do that with only 10 years of satellite data.

Now, note that as long as such large inferred climate sensitivities (50+ deg.!?) can be claimed to be supported by the satellite data, the IPCC can continue to warn that catastrophic global warming is a real possibility.

The real reason why such biases exist, however, is addressed in greater depth in our new paper, (Spencer and Braswell, 2010). The low bias in diagnosed feedback (and thus high bias in climate sensitivity) is related to the extent to which time-varying radiative forcing, mostly due to clouds, contaminates the radiative feedback signal responding to temperature changes.

It is easy to get confused on the issue of using regression to estimate feedbacks because linear regression was ALSO used to get the “true” feedbacks in the previous figure. The difference is that, in order to do so, Forster and Taylor removed the large, transient CO2 radiative forcing imposed on the models in order to better isolate the radiative feedback signal. Over many decades of model run time, this radiative feedback signal then beats down the noise from non-feedback natural cloud variations.

Thus, diagnosing feedback accurately is fundamentally a signal-to-noise problem. Either any time-varying radiative forcing in the data must be relatively small to begin with, or it must be somehow estimated and then removed from the data.

It would be difficult to over-emphasize the importance of understanding the last paragraph.

So, Why Does the Murphy & Forster Example with the HadSM2 Model Give Accurate Feedbacks?

To support their case that there is no serious problem in diagnosing feedbacks from satellite data, MF10 use the example of Gregory et al. (2004 GRL, “A New Method for Diagnosing Radiative Forcing and Climate Sensitivity”). Gregory et al. analyzed the output of a climate model, HadSM3, and found that an accurate feedback could be diagnosed from the model output at just about any point during the model integration.

But the reason why Gregory et al. could do this, and why it has no consequence for the real world, is so obvious that I continue to be frustrated that so many climate experts still do not understand it.

The Gregory et al. HadSM3 model experiment used an instantaneous quadrupling (!) of the CO2 content of the model atmosphere. In such a hypothetical situation, there will be rapid warming, and thus a strong radiative feedback signal in response to that warming.

But this hypothetical situation has no analog in the real world. The only reason why one could accurately diagnose feedback in such a case is because the 4XCO2 radiative forcing is kept absolutely constant over time, and so the radiative feedback signal is not contaminated by it.

Again I emphasize, instantaneous and then constant radiative forcing has no analog in the real world. Experts using such unrealistic cases has led to much confusion regarding the diagnosis of feedbacks from satellite data. In nature, ever-evolving time-varying radiative forcings (what some call “unforced natural variability”) are almost always overpowering radiative feedback.

But does that mean that Spencer & Braswell (2008) did a convincing job of demonstrating how large the resulting errors in feedback diagnosis could be in response to such time-varying radiative forcing? Probably not.

Big Picture Question #2: Did Spencer & Braswell (2008) Do An Adequate Job of Demonstrating Why Feedback Biases Occur?

MF10 made two changes in our simple climate model which had large consequences: (1) they change the averaging time of the model output to be consistent with the relatively short satellite datasets we have to compare to, and (2) they increase the assumed depth of the tropical ocean mixed layer from 50 meters to 100 meters in the simple model.

The first change, we agree, is warranted, and it indeed results in less dramatic biases in feedbacks diagnosed from the simple model. We have independently checked this with the simple model by comparing our new results to those of MF10.

The second change, we believe, is not warranted, and it pushes the errors to even smaller values. If anything, we think we can show that even 50 meters is probably too deep a mixed layer for the tropical ocean (what we addressed) on these time scales.

Remember, we are exploring why feedbacks diagnosed from satellite-observed, year-to-year climate variability are biased low, and on those short time scales, the equivalent mixing depths are pretty shallow. As one extends the time to many decades, the depth of ocean responding to a persistent warming mechanism increases to 100’s of meters, consistent with MF10’s claim. But for diagnosing feedbacks from satellite data, the time scales of variability affecting the data are 1 to only a few years.

But we have also discovered a significant additional shortcoming in SB08 (and MF10) that has a huge impact on the answer to Question #2: In addition to just the monthly standard deviations of the satellite-measured radiative fluxes and sea surface temperatures, we should have included (at least) one more important satellite statistic: the level of decorrelation of the data.

Our SB10 paper actually does this (which is why it should be referenced for the latest evidence supporting our claims). After accounting for the decorrelation in the data (which exists in ALL of the IPCC models, see the first figure, above, for an example) the MF10 conclusion that the ratio of the noise to signal (N/S) in the satellite data is only around 15% can not be supported.

Unfortunately, SB08 did not adequately demonstrate this with the satellite data. SB10 does…but does not optimize the model parameters that best match the satellite data. That is now the focus of our new work on the subject.

Since this next step was not obvious to us until MF10 caused us to go back and reexamine the simple model and its assumptions, this shows the value of other researchers getting involved in this line of research. For that we are grateful.

Final Comments

While the above comments deal with the “big picture” issues and implications of SB08, and MF10’s criticism of it, there are also a couple of errors and misrepresentations in MF10 that should be addressed, things that could have been caught had we been allowed to review their manuscript.

1) MF10 claim to derive a “more correct” analytical expression for the error in feedback error than SB08 provided. If anything, it is ours that is more correct. Their expression (the derivation of which we admit is impressive) is only correct for an infinite time period, which is irrelevant to the issue at hand, and will have errors for finite time periods. In contrast, our expression is exactly correct for a finite time series of data, which is what we are concerned with in the real world.

2) MF10 remove “seasonal cycles” from the randomly forced model data time series. Why would this be necessary for a model that has only random daily forcing? Very strange.

Despite the shortcomings, MF10 do provide some valuable insight, and some of what they present is indeed useful for advancing our understanding of what causes variations in the radiative energy budget of the Earth.

References
Forster, P. M., and J. M. Gregory (2006), The climate sensitivity and its components diagnosed from Earth Radiation Budget data, J. Climate, 19, 39-52.

Forster, P.M., and K.E. Taylor (2006), Climate forcings and climate sensitivities diagnosed from coupled climate model integrations, J. Climate, 19, 6181-6194.

Gregory, J.M., W. J. Ingram, M.A. Palmer, G.S. Jones, P.A. Stott, R.B. Thorpe, J.A. Lowe, T.C Johns, and K.D. Williams (2004), A new method for diagnosing radiative forcing and climate sensitivity, Geophys. Res. Lett., 31, L03205, doi:10.1029/2003GL018747.

Meehl, G. A., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer, and K. E. Taylor (2007), The WCRP CMIP3 multi-model dataset: A new era in climate change research, Bull. Am. Meteorol. Soc., 88, 1383-1394.

Murphy, D.M., and P. M. Forster (2010), On the Accuracy of Deriving Climate Feedback Parameters from Correlations Between Surface Temperature and Outgoing Radiation. J. Climate, in press. [PDF currently available to AMS members].

Spencer, R.W., and W.D. Braswell (2008), Potential biases in cloud feedback diagnosis: A simple model demonstration, J. Climate, 21, 5624-5628. PDF.

Spencer, R. W., and W. D. Braswell (2010), On the Diagnosis of Radiative Feedback in the Presence of Unknown Radiative Forcing, J. Geophys. Res., doi:10.1029/2009JD013371, in press. [PDF currently available to AGU members] (accepted 12 April 2010)

I receive many e-mails, and a recurring complaint is that many of my posts are too technical to understand. This morning’s installment arrived with the subject line, “Please Talk to Us”, and suggested I provide short, concise, easily understood summaries and explanations “for dummies”.

So, here’s a list of basic climate change questions, and brief answers based upon what I know today. I might update them as I receive suggestions and comments. I will also be adding links to other sources, and some visual aids, as appropriate.

Deja vu tells me I might have done this once before, but I’m too lazy to go back and see. So, I’ll start over from scratch. (Insert smiley)

It is important to understand at the outset that those of us who are skeptical of mankind’s influence on climate have a wide variety of views on the subject, and we can’t all be right. In fact, in this business, it is really easy to be wrong. It seems like everyone has a theory of what causes climate change. But it only takes one of us to be right for the IPCC’s anthropogenic global warming (AGW) house of cards to collapse.

As I like to say, taking measurements of the climate system is much easier than figuring out what those measurements mean in terms of cause and effect. Generally speaking, it’s not the warming that is in dispute…it’s the cause of the warming.

If you disagree with my views on something, please don’t flame me. Chances are, I’ve already heard your point of view; very seldom am I provided with new evidence I haven’t already taken into account.

1) Are Global Temperatures Rising Now? There is no way to know, because natural year-to-year variability in global temperature is so large, with warming and cooling occurring all the time. What we can say is that surface and lower atmospheric temperature have risen in the last 30 to 50 years, with most of that warming in the Northern Hemisphere. Also, the magnitude of recent warming is somewhat uncertain, due to problems in making long-term temperature measurements with thermometers without those measurements being corrupted by a variety of non-climate effects. But there is no way to know if temperatures are continuing to rise now…we only see warming (or cooling) in the rearview mirror, when we look back in time.

2) Why Do Some Scientists Say It’s Cooling, while Others Say that Warming is Even Accelerating? Since there is so much year-to-year (and even decade-to-decade) variability in global average temperatures, whether it has warmed or cooled depends upon how far back you look in time. For instance, over the last 100 years, there was an overall warming which was stronger toward the end of the 20th Century. This is why some say “warming is accelerating”. But if we look at a shorter, more recent period of time, say since the record warm year of 1998, one could say that it has cooled in the last 10-12 years. But, as I mentioned above, neither of these can tell us anything about whether warming is happening “now”, or will happen in the future.

3) Haven’t Global Temperatures Risen Before? Yes. In the longer term, say hundreds to thousands of years, there is considerable indirect, proxy evidence (not from thermometers) of both warming and cooling. Since humankind can’t be responsible for these early events, this is evidence that nature can cause warming and cooling. If that is the case, it then opens up the possibility that some (or most) of the warming in the last 50 years has been natural, too. While many geologists like to point to much larger temperature changes are believed to have occurred over millions of years, I am unconvinced that this tells us anything of use for understanding how humans might influence climate on time scales of 10 to 100 years.

4) But Didn’t the “Hockey Stick” Show Recent Warming to be Unprecedented? The “hockey Stick” reconstructions of temperature variations over the last 1 to 2 thousand years have been a huge source of controversy. The hockey stick was previously used by the IPCC as a veritable poster child for anthropogenic warming, since it seemed to indicate there have been no substantial temperature changes over the last 1,000 to 2,000 years until humans got involved in the 20th Century. The various versions of the hockey stick were based upon limited amounts of temperature proxy evidence — primarily tree rings — and involved questionable statistical methods. In contrast, I think the bulk of the proxy evidence supports the view that it was at least as warm during the Medieval Warm Period, around 1000 AD. The very fact that recent tree ring data erroneously suggests cooling in the last 50 years, when in fact there has been warming, should be a warning flag about using tree ring data for figuring out how warm it was 1,000 years ago. But without actual thermometer data, we will never know for sure.

5) Isn’t the Melting of Arctic Sea Ice Evidence of Warming? Warming, yes…manmade warming, no. Arctic sea ice naturally melts back every summer, but that meltback was observed to reach a peak in 2007. But we have relatively accurate, satellite-based measurements of Arctic (and Antarctic) sea ice only since 1979. It is entirely possible that late summer Arctic Sea ice cover was just as low in the 1920s or 1930s, a period when Arctic thermometer data suggests it was just as warm. Unfortunately, there is no way to know, because we did not have satellites back then. Interestingly, Antarctic sea ice has been growing nearly as fast as Arctic ice has been melting over the last 30+ years.

6) What about rising sea levels? I must confess, I don’t pay much attention to the sea level issue. I will say that, to the extent that warming occurs, sea levels can be expected to also rise to some extent. The rise is partly due to thermal expansion of the water, and partly due to melting or shedding of land-locked ice (the Greenland and Antarctic ice sheets, and glaciers). But this says nothing about whether or not humans are the cause of that warming. Since there is evidence that glacier retreat and sea level rise started well before humans can be blamed, causation is — once again — a major source of uncertainty.

7) Is Increasing CO2 Even Capable of Causing Warming? There are some very intelligent people out there who claim that adding more carbon dioxide to the atmosphere can’t cause warming anyway. They claim things like, “the atmospheric CO2 absorption bands are already saturated”, or something else very technical. [And for those more technically-minded persons, yes, I agree that the effective radiating temperature of the Earth in the infrared is determined by how much sunlight is absorbed by the Earth. But that doesn’t mean the lower atmosphere cannot warm from adding more greenhouse gases, because at the same time they also cool the upper atmosphere]. While it is true that most of the CO2-caused warming in the atmosphere was there before humans ever started burning coal and driving SUVs, this is all taken into account by computerized climate models that predict global warming. Adding more “should” cause warming, with the magnitude of that warming being the real question. But I’m still open to the possibility that a major error has been made on this fundamental point. Stranger things have happened in science before.

8 ) Is Atmospheric CO2 Increasing? Yes, and most strongly in the last 50 years…which is why “most” climate researchers think the CO2 rise is the cause of the warming. Our site measurements of CO2 increase from around the world are possibly the most accurate long-term, climate-related, measurements in existence.

9) Are Humans Responsible for the CO2 Rise? While there are short-term (year-to-year) fluctuations in the atmospheric CO2 concentration due to natural causes, especially El Nino and La Nina, I currently believe that most of the long-term increase is probably due to our use of fossil fuels. But from what I can tell, the supposed “proof” of humans being the source of increasing CO2 — a change in the atmospheric concentration of the carbon isotope C13 — would also be consistent with a natural, biological source. The current atmospheric CO2 level is about 390 parts per million by volume, up from a pre-industrial level estimated to be around 270 ppm…maybe less. CO2 levels can be much higher in cities, and in buildings with people in them.

10) But Aren’t Natural CO2 Emissions About 20 Times the Human Emissions? Yes, but nature is believed to absorb CO2 at about the same rate it is produced. You can think of the reservoir of atmospheric CO2 as being like a giant container of water, with nature pumping in a steady stream into the bottom of the container (atmosphere) in some places, sucking out about the same amount in other places, and then humans causing a steady drip-drip-drip into the container. Significantly, about 50% of what we produce is sucked out of the atmosphere by nature, mostly through photosynthesis. Nature loves the stuff. CO2 is the elixir of life on Earth. Imagine the howls of protest there would be if we were destroying atmospheric CO2, rather than creating more of it.

11) Is Rising CO2 the Cause of Recent Warming? While this is theoretically possible, I think it is more likely that the warming is mostly natural. At the very least, we have no way of determining what proportion is natural versus human-caused.

12) Why Do Most Scientists Believe CO2 is Responsible for the Warming? Because (as they have told me) they can’t think of anything else that might have caused it. Significantly, it’s not that there is evidence nature can’t be the cause, but a lack of sufficiently accurate measurements to determine if nature is the cause. This is a hugely important distinction, and one the public and policymakers have been misled on by the IPCC.

13) If Not Humans, What could Have Caused Recent Warming? This is one of my areas of research. I believe that natural changes in the amount of sunlight being absorbed by the Earth — due to natural changes in cloud cover — are responsible for most of the warming. Whether that is the specific mechanism or not, I advance the minority view that the climate system can change all by itself. Climate change does not require an “external” source of forcing, such as a change in the sun.

14) So, What Could Cause Natural Cloud Changes? I think small, long-term changes in atmospheric and oceanic flow patterns can cause ~1% changes in how much sunlight is let in by clouds to warm the Earth. This is all that is required to cause global warming or cooling. Unfortunately, we do not have sufficiently accurate cloud measurements to determine whether this is the primary cause of warming in the last 30 to 50 years.

15) How Significant is the Climategate Release of E-Mails? While Climategate does not, by itself, invalidate the IPCC’s case that global warming has happened, or that humans are the primary cause of that warming, it DOES illustrate something I emphasized in my first book, “Climate Confusion”: climate researchers are human, and prone to bias.

16) Why Would Bias in Climate Research be Important? I thought Scientists Just Follow the Data Where It Leads Them When researchers approach a problem, their pre-conceived notions often guide them. It’s not that the IPCC’s claim that humans cause global warming is somehow untenable or impossible, it’s that political and financial pressures have resulted in the IPCC almost totally ignoring alternative explanations for that warming.

17) How Important Is “Scientific Consensus” in Climate Research? In the case of global warming, it is nearly worthless. The climate system is so complex that the vast majority of climate scientists — usually experts in variety of specialized fields — assume there are more knowledgeable scientists, and they are just supporting the opinions of their colleagues. And among that small group of most knowledgeable experts, there is a considerable element of groupthink, herd mentality, peer pressure, political pressure, support of certain energy policies, and desire to Save the Earth — whether it needs to be saved or not.

18) How Important are Computerized Climate Models? I consider climate models as being our best way of exploring cause and effect in the climate system. It is really easy to be wrong in this business, and unless you can demonstrate causation with numbers in equations, you are stuck with scientists trying to persuade one another by waving their hands. Unfortunately, there is no guarantee that climate models will ever produce a useful prediction of the future. Nevertheless, we must use them, and we learn a lot from them. My biggest concern is that models have been used almost exclusively for supporting the claim that humans cause global warming, rather than for exploring alternative hypotheses — e.g. natural climate variations — as possible causes of that warming.

19) What Do I Predict for Global Temperature Changes in the Future? I tend to shy away from long-term predictions, because there are still so many uncertainties. When pressed, though, I tend to say that I think cooling in our future is just as real a possibility as warming. Of course, a third possibility is relatively steady temperatures, without significant long-term warming or cooling. Keep in mind that, while you will find out tomorrow whether your favorite weather forecaster is right or wrong, no one will remember 50 years from now a scientist today wrongly predicting we will all die from heat stroke by 2060.

Concluding Remarks

Climate researchers do not know nearly as much about the causes of climate change as they profess. We have a pretty good understanding of how the climate system works on average…but the reasons for small, long-term changes in climate system are still extremely uncertain.

The total amount of CO2 humans have added to the atmosphere in the last 100 years has upset the radiative energy budget of the Earth by only 1%. How the climate system responds to that small “poke” is very uncertain. The IPCC says there will be strong warming, with cloud changes making the warming worse. I claim there will be weak warming, with cloud changes acting to reduce the influence of that 1% change. The difference between these two outcomes is whether cloud feedbacks are positive (the IPCC view), or negative (the view I and a minority of others have).

So far, neither side has been able to prove their case. That uncertainty even exists on this core issue is not appreciated by many scientists!

Again I will emphasize, some very smart people who consider themselves skeptics will disagree with some of my views stated above, particularly when it involves explanations for what has caused warming, and what has caused atmospheric CO2 to increase.

Unlike the global marching army of climate researchers the IPCC has enlisted, we do not walk in lockstep. We are willing to admit, “we don’t really know”, rather than mislead people with phrases like, “the warming we see is consistent with an increase in CO2”, and then have the public think that means, “we have determined, through our extensive research into all the possibilities, that the warming cannot be due to anything but CO2”.

Skeptics advancing alternative explanations (hypotheses) for climate variability represent the way the researcher community used to operate, before politics, policy outcomes, and billions of dollars got involved.

YR MON GLOBE NH SH TROPICS
2009 1 0.251 0.472 0.030 -0.068
2009 2 0.247 0.564 -0.071 -0.045
2009 3 0.191 0.324 0.058 -0.159
2009 4 0.162 0.316 0.008 0.012
2009 5 0.140 0.161 0.119 -0.059
2009 6 0.043 -0.017 0.103 0.110
2009 7 0.429 0.189 0.668 0.506
2009 8 0.242 0.235 0.248 0.406
2009 9 0.505 0.597 0.413 0.594
2009 10 0.362 0.332 0.393 0.383
2009 11 0.498 0.453 0.543 0.479
2009 12 0.284 0.358 0.211 0.506
2010 1 0.648 0.860 0.436 0.681
2010 2 0.603 0.720 0.486 0.791
2010 3 0.653 0.850 0.455 0.726
2010 4 0.501 0.799 0.203 0.633
2010 5 0.534 0.775 0.292 0.708
2010 6 0.436 0.552 0.321 0.475

The global-average lower tropospheric temperature remains warm, +0.44 deg. C for June, 2010, but it appears the El Nino warmth is waning as a La Nina approaches.

For those keeping track of whether 2010 ends up being a record warm year, 1998 still leads with the daily average for 1 Jan to 30 June being +0.64 C in 1998 compared with +0.56 C for 2010. (John Christy says that the difference is not statistically significant.) As of 30 June 2010, there have been 181 days in the year. From our calibrated daily data, we find that 1998 was warmer than 2010 on 122 (two-thirds) of them.

As a reminder, four months ago we changed to Version 5.3 of our dataset, which accounts for the mismatch between the average seasonal cycle produced by the older MSU and the newer AMSU instruments. This affects the value of the individual monthly departures, but does not affect the year to year variations, and thus the overall trend remains the same as in Version 5.2. ALSO…we have added the NOAA-18 AMSU to the data processing in v5.3, which provides data since June of 2005. The local observation time of NOAA-18 (now close to 2 p.m., ascending node) is similar to that of NASA’s Aqua satellite (about 1:30 p.m.). The temperature anomalies listed above have changed somewhat as a result of adding NOAA-18.

[NOTE: These satellite measurements are not calibrated to surface thermometer data in any way, but instead use on-board redundant precision platinum resistance thermometers (PRTs) carried on the satellite radiometers. The PRT’s are individually calibrated in a laboratory before being installed in the instruments.]