Sunday, June 10, 2018

May global surface TempLS down 0.038 °C from April.

The TempLS mesh anomaly (1961-90 base) fell a little, from 0.716°C in April to 0.678°C in May. This is less than the 0.09°C fall in the NCEP/NCAR index, while the satellite TLT indices fell by a similar amount (UAH 0.03°C).

It was very warm in much of N America, except NE Canada (cold), and very warm in Europe. Cold in E Siberia, but warm in East Asia generally. Again a pattern of warm blobs around 40-50 °S, though less marked than in recent months. Quite warm in Antarctica (relatively).

Here is the temperature map. As always, there is a more detailed active sphere map here.

Data from Canada delayed this report by a couple of days. Following my recent post on the timing of data arrival, I kept a note of how the TempLS estimates changed day by day as May data came in. The TempLS report is now first posted when the SST results are available, but I wait until all large countries are in before writing a post about it. Here is the table (Melbourne time):
DateNumber stations (incl SST)Temperature
June 0545160.676
June 0648290.723
June 0752940.709
June 0853720.708
June 0953810.709
June 1054740.678

Canada (late) did have a cooling effect.

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Sunday, June 3, 2018

May NCEP/NCAR global surface anomaly down by 0.09°C from April

In the Moyhu NCEP/NCAR index, the monthly reanalysis anomaly average fell from 0.377°C in April to 0.287°C in May, 2018. This cancels out the last two months of increase, and matches the February average.

It was for once warm in both in North America (except far N) and Europe especially Scandia. Russia was cold in the W, warm in the East. Nothing special at either pole. Probably the main contributor to the drop was a chill in the N Atlantic region, including Greenland. Active map here.

I had thought that the gradual warming might be associated with the decline of La Niña. But the changes are small, so shouldn't be over-interpreted. The BoM still says that ENSO is neutral, and likely to stay so for a few months.

Thursday, May 31, 2018

To see the month's GHCN coverage, patience is needed.

I often see on contrarian sites graphs, usually from NOAA, which are supposed to show how sparse is GHCN-M's coverage of land sites, as used by the major US temperature indices. The NOAA monthly reports usually show interpolated plots, but if you go to some legacy sites, you can get a plot like this:

It is a 5x5° grid, but it does look as if there are a lot of empty cells, particularly in Africa. But if you look at the fine print, it says that the map was made April 13. That is still fairly early in the month, but NOAA doesn't update. There is a lot of data still to come. Station coverage isn't ideal, but it isn't that bad.

I took issue with a similar graph from SPPI back in 2010. That was quite a high visibility usage (GISS this time). Fortunately GISS was providing updates, so I could show how using an early plot exaggerated the effect.

The issue of spread out arrival of data affects my posting of monthly TempLS results. I calculate a new monthly average temperature each night, for the current month. I post as soon as I can be reasonably confident, which generally means when the big countries have reported (China, Canada etc). I did comment around January that the temperatures were drifting by up to about 0.04°C after posting. I think that was a run of bad luck, but I have been a little more conservative, with stabler results. Anyway, I thought I should be more scientific about it, so I have been logging the arrival date of station data in GHCN-M.

So I'll show here an animation of the arrival of March 2018 data. The dates are when the station data first appears on the posted GHCN-M file. Click the bottom buttons to step through.

The colors go from red when new to a faded blue. The date is shown lower left.

The behaviour of the US is odd, and I'll look into it. About 500 stations post numbers in the last week of February. I presume these are interim numbers, but my logging didn't record changing values. Then another group of stations report mid April.

Otherwise much as expected. The big countries did mainly report by the 8th. A few medium ones, like South Africa, Mongolia, Iran and Sudan, were quite a lot later. But there is substantial improvement in overall coverage in the six weeks or so after April 1. Some of it is extra stations that arrive after a country's initial submission.

There certainly are parts of the world where more coverage would be useful, but it doesn't help to exaggerate the matter by showing incomplete sets. The good news from the TempLS experience is that, even with an early set, the average does not usually change much as the remaining data arrives. This supports the analysis here, for example, which suggests that far fewer stations, if reasonably distributed, can give a good estimate of the global integral.

Tuesday, May 29, 2018

Updating the blog index.

I wrote late last year about improving the blog topic index, which is top on the page list, to right. I've now tinkered a bit more. The main aim was to automate updates. This should now work, so the index should always be up to date.

The other, minor improvement was to add a topic called "Complete listing" This does indeed give a listing of all posts, with links, back to the beginning of the blog in 2009. It includes pages, too (at the bottom), so there are currently 751 in the list, organised by date.

Friday, May 25, 2018

New interactive updated temperature plotting.

As part of the Moyhu latest data page, I have maintained a daily updated interactive plotter. I explained briefly the idea of it here. There is a related and more elaborate annual plotter kept as a page here, although I haven't kept that updated.

I think interactive plotting is a powerful Javascript capability. You can move the curves around as you wish - expanding or contracting the scales. You can choose which of a large set of data offerings to show. You can smooth and form regression lines.

But the old version, shown with that old post, looks a bit raw. I found I was using it more for display graphs, so I have cleaned up the presentation, using PrintScreen on my PC, and pasting the result into Paint. I have also simplified the controls. I had been using draggable popup windows, which are elegant, but not so straightforward, and don't make it easy to expand facilities. So I have reverted to an old-fashioned control panel, in which I can now include options such as writing your own headings and y-axis label. There is now also the option of changing the anomaly base, and you can choose any smoothing interval. Here is how it looks, in a working version:

You can choose data by clicking checkboxes on the left. Dragging in the main plot area translates the plots; dragging the pointer under the x-axis changes the time scale, and dragging vertically left of the y-axis changes the y-scale. At bottom left (below the checkboxes), there is a legend, only partly visible. This reflects the colors and choice of data, and you can drag it anywhere. The idea is that you can place it on the plot when you want to capture the screen for later presentation.

The control panel has main rows for choosing the regression, smoothing and anomaly base. When you want to make a choice, first tick the relevant checkbox, and then enter data in the textboxes. Then yo make it work, click the top right run button. The change you make will apply either to all the curves, or just to one nominated on the top row, depending on the radio buttons top left. The nominated curve is by default the last one chosen, but you can vary this with the arrow buttons just left of the run button. However, the anomaly base can only be altered for all, and the color selection only for one.

Choosing regression over a period displays the line, and also the trend, in the legend box, in °C/century units. You can only have one trend line per dataset, but possibly with different periods. If you want to make a trend go away, just enter a date outside the data range (0 will do). You could also deselect and reselect the data.

Smoothing is just moving average, and you enter the period in months. Enter 1 for no smoothing (also the default).

There are two rows where you can enter your own text for the title and y-axis label. Click run to make it take effect. The title can include any HTML, eg bold, text-size etc. You can use heading tags, but that takes up room.

Color lets you choose from the colored squares. A choice takes effect immediately, for the nominated data only.

Generally keep the checkboxes in the control panel unchecked unless you are making a change.

For anomaly base, you can also enter an out of range year to get no anomaly modification at all. The plots are shown each with the suppliers base. I don't really recommend this, and it tends to get confused if you have already varied base choices.

There are two more buttons, on the right of the control panel. One is Trendback. This switches (toggles) to a style which was in the old version, and is described here, for example. It shows the trend from the time on the x-xis to present (last data) in °C/century. In that mode, it won't respond to the regression, smooth, or anomaly base properties. The other button is "Show data". This will make a new window with the numbers graphed on the screen. This can be quite handy for the trendback plots, for example. You can save the window to a file.

Here is how the plot might look if you drag the legend into place:

Thursday, May 17, 2018

GISS April global down 0.02°C from March.

The GISS land/ocean temperature anomaly  fell 0.02°C last month. The April anomaly average was 0.86°C, down slightly from March 0.88°C. The GISS report notes that it is still the third warmest April in the record. The fall is very similar to the 0.016°C fall, of TempLS Mesh, although the NCEP/NCAR index showed a slight rise.

The overall pattern was similar to that in TempLS. Cold in most of N America, and contrasting warmth in Europe. Warm in East Asia, especially arctic Siberia. Polar regions variable. Warm in S America and Australia, and for at least the third month, a curious pattern of warm patches along about 40°S.

As usual here, I will compare the GISS and previous TempLS plots below the jump.

Tuesday, May 15, 2018

Electronic circuit climate analogues - amplifiers and nonlinearity

This post is a follow-up to my previous post on feedback. The main message in that post was that, although talking of electronic analogues of climate feedback is popular in some quarters, it doesn't add anything mathematically. Feedback talk is just a roundabout way of thinking about linear equations.

Despite that, in this post I do want to talk more about electronic analogues. But it isn't much about feedback. It is about the other vital part of a feedback circuit - the amplifier, and what that could mean in a climate context. It is of some importance, since it is a basic part of the greenhouse effect.

The simplest feedback diagram (see Wiki) has three elements:

They are the amplifier, with gain AOL, a feedback link, with feedback fraction β, and an adder, shown here with a minus sign. The adder is actually a non-trivial element, because you have to add the feedback to the input without one overriding the other. In the electronic system, this generally means adding currents. Adding voltages is harder to think of directly. However, the block diagram seems to express gain of just one quantity, often thought of as temperature.

In the climate analogue, temperature is usually related to voltage, and flux to current. So there is the same issue, that fluxes naturally add, but temperature is the variable that people want to talk about. As mentioned last post, I often find myself arguing with electrical engineers who have trouble with the notion of an input current turning into an output voltage (it's called a transimpedance amplifier).

If you want to use electronic devices as an analogue of climate, I think a fuller picture of an amplifier is needed. People now tend to show circuits using op amps. These are elaborately manufactured devices, with much internal feedback to achieve high linearity. They are differential, so the operating point (see below) can be zero. I think it is much more instructive to look at the more primitive devices - valves, junction transistors, FETs etc. But importantly, we need a fuller model which considers both variables, voltage and current. The right framework here is the two port network.

I've reached an awkward stage in the text where I would like to talk simultaneously about the network framework, junction transistors, and valves. I'll have to do it sequentially, but to follow you may need to refer back and forth. A bit like a feedback loop, where each depends on the other. I'll go into some detail on transistors, because the role of the operating point, fluctuations and linearity, and setting the operating point are well documented, and a good illustration of the two port treatment. Then I'll talk about thermionic valves as a closer analogue of climate.

Two Port Network

Wiki gives this diagram:

As often, engineer descriptions greatly complicate some simple maths. Many devices can be cast as a TPN, but all it means is that you have four variables, and the device enforces two relations between them. If these are smooth and can be linearised, you can write the relation for small increments y as

Wiki, like most engineering sources, lists many ways you could choose the variables for left and right. For many devices, some coefficients are small, so you will want to be sure that A is not close to singular. I'll show how this works out for junction transistors.

This rather general formulation doesn't treat the input and output variables separately. You can have any combination you like (subject to invertible A). For linearity, the variables will generally denote small fluctuations; the importance of this will appear in the next section.

The external circuitry will contribute extra linear equations. For example, a load resistor R across the output will add an Ohm's Law, V₂ = I₂R. Other arrangements could provide a feedback equation. With one extra relation, there is then just one free variable. Fix one, say an input, and everything else is determined.

Junction transistors

I'm showing the use of a junction transistor as amplifier because it is a well documented example of:
  • a non-linear device which has a design point about which fluctuations are fairly linear
  • a degree of degeneracy, in that it is dominated by a strong association between I₁ and I₂, with less dependence on V₂ and little variation in V₁. IOW, it is like a current amplifier, with amplification factor β.
  • there is simple circuitry that can stably establish the operating point.
Here from Wiki, is a diagram of a design curve, which is a representation of the two-port relation. It takes advantage of the fact that there is a second relation which is basically between I₁ and V₁, with V₁ restricted to a narrow range (about 0.6V for silicon).

The top corner shows the transistor with variables labelled; the three pins are emitter E, base B and collector C. In TPN terms, I₁ is the base current IB; I₂ is the current from collector to emitter IC, and V₂ is the collector to emitter voltage VCE. The curves relate V₂ and I₂ for various levels of I₁. Because they level off, the dependence is mainly between IC and IB. The load line in heavy black shows the effect of connecting the collector via a load resistor. This constrains V₂ and I₂ to lie on that line, and so both vary fairly linearly with I₁.

The following diagrams have real numbers and come from my GE transistor manual, 1964 edition, for a 2N 1613 NPN transistor. The left is a version of the design curves diagrammed above, but with real numbers. It shows as wavy lines a signal of varying amplitude as it might be presented as base current (top right) and appear as a collector voltage (below). The load resistor line also lets you place it on the y axis, where you can see the effect of current amplification, by a factor of about 100. The principal purpose of these curves is to show how non-linearity is expressed as signal clipping.

I have included the circuit on the right, a bias circuit, to show how the design operating point is achieved. The top rail is the power supply, and since the base voltage is near fixed at about 0,6V, the resistor RB determines the base current curve. The load RL determines the load line, so where these intersect is the operating point.

So let's see how this works out in the two-port formulation. We have to solve for two variables; the choice is the hybrid or h- parameters:

Hybrid suggests the odd combination; input voltage V₁ and output current I₂ are solved in terms of input current I₁ and output voltage V₂. The reason is that the coefficients are small, except for h₂₁ (also β). There is some degeneracy; there isn't much dependence at all on V₂, and V₂ is then not going to vary much.So these belong on the sides they are placed. I₂ and I₁ could be switched; that is called inverse hybrid (g-). I've used the transistor here partly as a clear example of degeneracy (we'll see more).

Thermionic valve and climate analogue

From Wiki comes a diagram of a triode

The elements are a heated cathode k in a vacuum tube, which can emit electrons, and an anode a, at positive voltage, to which they will move, depending on voltage. This current can be modulated by varying the voltage applied to the control grid g, which sits fairly close to the cathode.

I propose the triode here because it seems to me to be a closer analogue of GHGs in the atmosphere. EE's sometimes say that the circuit analogue of climate fails because they can't see a power supply. That is because they are used to fixed voltage supplies. But a current supply works too, and that can be seen with the triode. A current flows and the grid modulates it, appearing to vary the resistance. A FET is a more modern analogue, in the same way. And that is what happens in the atmosphere. There is a large solar flux, averaging about 240 W/m² passing through from surface to TOA, much of it as IR. GHGs modulate that flux.

A different two-port form is appropriate here. I₁ is negligible, so should not be on the right side. Inverse hyprid could be used, or admittance. It doesn't really matter which, since the outputs are likely to be related via a load resistor.

Climate amplifier

So thinking more about the amplifier in the climate analogue, first as a two port network. Appropriate variables would be V₁,I₁ as temperature and heat flux at TOA, and V₂, I₂ as temperature, upward heat flux at the surface. V₂ is regarded as an output, and so should be on the LHS, and I₁ as an input, on the right. One consideration is that I₂ is constrained as being the fairly constant solar flux at the surface, so it should be on the RHS. That puts V₁ on the left and pretty much leads to an impedance parameters formulation - a two variable form of Ohm's Law.

The one number we have here is the Planck parameter, which gives the sensitivity before feedback of V₂ to I₁ (or vice versa). People often think that this is determined by the Stefan-Boltzmann relation, and that does give a reasonably close number. But in fact it has to be worked out by modelling, as Soden and Held explain. Their number comes to about 3.2 Wm⁻²/K. This is a diagonal element in the two port impedance matrix, and is treated as the open loop gain of the amplifier. But the role of possible variation of the surface flux coefficient should alos be considered.

As my earlier post contended, mathematically at least, feedback is much less complicated than people think. The message of this post is that if you want to use circuit analogues of climate, a more interesting question is, how does the amplifier work?