Climate

For any coefficient matrix A(t), the equation

y’ = A*y + f’ – A*f

has y=f as a solution. A perfect emulator. But as I showed above, the error propagation is given by the homogeneous part y’ = A*y. And that could be anything at all, depending on choice of A. Sharing a common solution does not mean that two equations share error propagation. So it’s not OK.

  1. A post elsewhere that highlights the problem Nick is trying to address
    “how is it that we can reasonably accurate calculate GMST with only about 60 gauges? I know that ATTP has had at least one blog post in that regard. Now, I think that error improves as the (inverse) square root of the number of gauges. The average is twice as accurate for N = 3,600, not proportional to the square root of N but proportional to the inverse square root of N.”

    GMST is such a fraught concept.
    Problem one is the definition of the surface on a mixed changing atmospheric world (variable water vapour) plus a mixed solid/liquid “surface of variable height and depth on top of an uneven shape with long term variability in the spin and torque and inclination of the world plus the variation in distance from the heating element plus variation in the shade from the satellite at times and albedo variation from clouds and volcanic emissions and ice and dust storms and heating from volcanic eruptions and CO2 emmision and human CO2 emissions.
    Phew.

    We could get around this partly by measuring solar output, albedo change and earth output from space by satellites and just using a planetary emmision temperature as a substitute for GMST.
    You could actually compute what the temperature should be at any location on earth purely by it’s elevation, time of year and orientatation in space to the sun without using a thermometer.

    In a model world, barring inbuilt bias, one only ever needs one model thermometer. There can be no error. Using 3600 does not improve the accuracy.
    In a model world allowing a standard deviation for error will lead to a possible Pat Frank scenario. The dice can randomly throw +4W/m-2 for ever. Having thrown one head is no guarantee that the next throw or the next billion throws will not be a head.
    Using 3600 instead of 60 does not improve the accuracy at all. It improves the expectation of where the accuracy should be is all. While they look identical accuracy and expectation of accuracy are two completely different things. Your statement on probability is correct.

    Finally this presupposes a model world and temperature and reasonable behaviour. Thermometers break,or degrade over time, people enter results wrongly,or make them up or take them at the wrong time of day or average them when missing ( historical). The accuracy changes over time. They only cover where people can get to easily, like looking for your keys under the streetlight, spacial, height, sea, polar, desert, Antarctica etc. Collating the information in a timely manner, not 3 months later when it all comes in. Are 3600 thermometers in USA better than 60 scattered around the world.

    60 is a good number adequately sited for an estimation. 3600 is a lot better. As Paul said any improvement helps modelling tremendously.
    Not having a go at you, just pointing out the fraughtness

Chapter 12 reflections

the man on the stair who was not there.

How did America come to this sad impasse?
The same pastiche of our own personal lives is to blame.
We all want to succeed in life, have friends and control our lives.
On the largest scale America, Russia and China are no different from squabbling families.
They push their own interests first and only if all is going well can they afford to be magnanimous.

On the grand scale Russia an America have been friends in the past, One brought Alaska from the other. Both fought in the first world war against a common foe 100 years ago.
Both threw off monarchist systems for individual rights but there a giant gulf developed.
Both advocated for better lives for people under their systems of democracy and communism. equal rights for people to vote and have a say but with a fundamental twist.
Democracy does not specify a heart, Communism does not specify a soul.

Communism has been a dirty word in America since the 1950’s with McCarthy.
Worse both nations have nuclear weapons. For many years the worst insult that could be used in America, and their are some choice ones, was to be called a communist.
While this attitude has changed somewhat with the 70’s. with information technology and TV  there is still a deep fundamental distrust in the American soul which can be and is manipulated when needed.
Christianity is also large in America. Recognised in the Constitution. With this comes a decent serving of morality. Which also died a part death in the 70’s. Still breaking sexual mores is often a death sentence to any political or business career. Made worse by the recent #Metoo movement.
Business is big. Ruthless. Money talks. Yet behind it all is the notion, a notion onlty, that Business should be fair. Robbing the bank is still robbing the bank. Fiddling the books, defrauding people is still a major nono.

There is a two party system in America which has a similar struggle on a more local scale for political sway. Both have been staunchly anticommunist but the Democratic Party has been the more progressive with allowing some freedom of choice and  and expression of alternative views over the last 30 years, moving to the left towards a more socialistic, dare one say communistic way of doing things, without openly saying it.

Hence the choice of tactics, to accuse an American citizen, of being a secret Communist agent is on the surface all the more surprising coming from the Democratic Party but not when you are trying to throw mud.
Accusations of sexual impropriety  are the icing on the cake.
Finally throw in the idea that the fix is in, that money is being made illegay and the Tax Office gets you.
It got Al Capone.
It got MADDOX

Most of us are prepared to believe bad things, particularly about people we do not like.

Democrats believe bad things about Republicans on the surface which look ridiculous, and vice versa.We want to believe because they appeal to our identity in that the other side has to be bad.
So a few home truths need to be set out. In reverse order.

1, Donald Trump files tax returns.
The Tax office looks at them closely. Since the election they have looked at them even more closely. Everyone in the know in America has seen every last bit of dirty laundry in those tax returns even if the general public has not. Every business dealing he has had, every disgruntled partner has had years and years to come forward. Every investigative journalist knows how much he earned, how he earned it and who he did business with.

2 Donald Trump has had affairs. He has been married 3 times. He has said, off the record, crass things. At the same time he was admired for his bling and lionised by people when doing his TV show.