An N-dimensional space representation of the problem of initial values with ensemble forecasting

We are all familiar with the concepts of 2 dimensional graphs with an x and y axis. It is not too difficult to understand how we might add a third and have a z axis. On such graphs a point represents a combination of 2 or 3 parameters (x,y) or (x,y,z). For orthogonal variables of equal scale we can use an analogy of distance between points in that the distance is √(x2 + y2 + z2). As such we can refer to any set of parameters where this relationship is expected to exist using the concept of “space”. This concept can be extended beyond three dimensions to 4, 5 or even much higher.

A digital model of the atmosphere consists of a large array cells. Each cell contains a set of parameters. If these are linear and can be scaled, then they can be represented by a distance. For n cells, each with m parameters, these can be represented by n.m dimensional space, and the set of parameters characterising the atmosphere can be plotted as a point in n.m space.

When an ensemble forecast is run using a ray of initial values, these initial values correspond to a set of points in the n.m space and in order to explore this space they are chosen to be widely dispersed.

The butterfly effect

A_Trajectory_Through_Phase_Space_in_a_Lorenz_AttractorThe butterfly effect is a phenomenon whereby small perturbations in the atmosphere tend to grow to become larger and larger. This means that if we go back far enough, these perturbations will be so small that they are smaller than the highest precision that can be reasonably used in a model. These perturbations are represented in n.m space by points, but just as phenomenon like the flap of a butterfly’s wings can grow in the atmosphere, so within n.m space, starting conditions that are so close together that they cannot be distinguished tend to grow to expand more and more space.

However, because n.m.space is constrained by what is physically possible, if some parts of the space being to expand, then other parts must shrink.

PrintThe effect is that whilst the initial set of conditions of a ensemble forecast may be reasonable well spaced in n.m space, as small areas of the space expand due to the butterfly effect, the space occupied by the initial perturbations destroys and no longer becomes evenly spread. The result, is that fairly quickly the initial perturbations are no longer exploring a well spread area of n.m.space but are instead bunched and at the extreme they become denser and denser areas leaving large unexplored areas of potential futures.

Thus in order to explore new spaces that open up, it is necessary to have a mechanism to redistribute the model points in n.m space.

One mechanism, is to add small perturbations – in the manner that a molecule in a heated gas is constantly knocked out – so that the ensemble forecast points tend to redistrubute themselves more evenly in n.m space.

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Simple 1/f noise generator

It’s often useful to be able to play around with things to get a feel for how they work. One of these is 1/f noise. There’s a very simple algorithm for generating this type of noise.

We set up n storage locations. To start a random value (-1 to 1) is stored in each location, Then every 2nd step, the first one changes to a new random value (-1 to +1), every 4th step the second changes, every 8th step the third, every 16th the fourth, etc. until the last one change in the middle of the run.

If we then set it so that at each step only one storage location is changing, then if we sum all the locations we have a random value that changes only by a random value between (-1 to +1) at each step.

For the equivalent of 10 years of daily readings we need ~4000 steps and when graphed for a scale of years we should have something like this:

1-fgeneratorI’ve included a openoffice calc file and xls

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It’s snowing again – again!

A while back I wrote an article saying it was the snowiest winter we had had. We then got the so called “beast from the east”. That brought Scotland to a standstill. For a few days it looked like it might melt away.

It’s now snowing and settling again.

I will be spending some serious money preparing for next winter.

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Small but significant risk of major loss of life in Scotland

Before the snow deluge, this winter had been worse than any in the 20 years we’ve lived in this location. It arrived earlier it remained cold and we had frequent period of snow that lay for a few days. But we had had deeper snow one year. That’s now changed and we’ve still got at least 3 more days of colder weather.

That is not the problem, like most people we stocked up on food and toilet rolls before the roads shut. And having bought snow chains (everyone laughed as we live in a suburb of Glasgow), it would take just five minutes to get to roads that are “drivable”.

The problem is that there is no way on earth the global warming obsessed Scottish government or local government could ever conceive of the amount of snow we’ve already had. They weren’t prepared for the last few winters when people were stuck up to 8 hours of motorways, they aren’t prepared for this. We have certainly got a few more days of this snow, but whilst there’s a couple of days has a maximum of 4C, that may be no where near enough to melt the snow. If people cannot restock their larders, cannot do minor repairs, and then there is even more snow as forecast … Continue reading

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BBC Newsnight hit by PIW (Politically Incorrect Water)

For years the BBC have carried what seemed to be an endless propaganda campaign on global warming. I gave up complaining when they falsely called us “deniers” but I can never forgive them for likening those of us who are rightly sceptical of “data” coming from the eco-zealots running NASA to paedophiles. Even for the Biased Broadcasting Company that has become a beacon of bigotry on subjects as wide ranging as Global warming to Scottish Independence (which I disagree with) and Brexit (which I agree with), that was a new low.

So, you can imagine I have been delighted to read the tweets from a well known Scottish BBC presenter Kirsty Wark who is now stuck on a train going no where.

DXHQ8a2WAAEksiA

DXHBgY2WAAcxkIw

Is that snow I see? No it can’t be snow! According to the BBC, that snow disappeared years ago and anyone denying that is a global warming denier.

No that’s not snow – it’s merely politically incorrect water.

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It’s snow (again)

I’ve already declared this our snowiest winter in the last 20 years living here. The road is covered again. Whilst we don’t get as much snow as some would think (due to prevailing wind off the warm seas), we do usually get one or two snow falls that settle. We once had several weeks of frost – but that was one large snowfall which turned to ice.

This year however, the winter started early and we’ve had repeated snow showers.

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The Anti-Greenhouse Effect (yes it is called that LOL)

This is a little gem I’ve got to share. Apparently not only have academics been daft enough to call the original effect the “Greenhouse effect” – when greenhouses work in completely different ways, but they’ve gone as far as to name something the “anti-greenhouse effect” – thus proving that the name “Greenhouse effect” is a total load of codswallop Continue reading

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Analysis of a joke

It is often said that any joke that has to be explained is ruined. However in this case, that might be the joke. So, to add to the excruciating nature of the joke here is my explanation.

There is another joke that goes:

“There are 10 types of people in the world, those that understand binary and those who don’t”.

That of course is what is being referred to by the “two types of people”. However, note that to accurately reflect the original joke it would need to be 10 types of people. That is why this is such a classic. Because you could use the “10” types of people for any base and have three groups:

“there are those who understand binary, those who don’t, and those who know there are more bases than binary and decimal”.

And of course, the number of possible groups can be extended even further … indeed up to an infinite base.

However a base 1 joke  is unique. Because there is only one number in a base one number system and that number is obviously zero.

So, clearly, we could have the joke of the form:

“There are 10 groups of people in the world: those who don’t understand base 1″.

That then fits the general patten of 10 jokes. Thus the humour in this joke is that “two” spelt out as a word does not work. It is clearly wrong – the teller was so bad at jokes they couldn’t even tell it properly. But then again, the pun on “10” only works when written not when spoken. And “those that don’t understand my humour” is only one group. So, the statement is clearly right, because how can anyone understand a joke that is palpably based on false logic and utterly wrong.

And that is the joke …

Which then, when you get it, makes the statement that there is only one group of people false … and it stops being funny.

No, No, No!
Sorry … just kidding!

The real joke is that’s its a a pun on function and dinner part and that the idea that anyone who thought the joke was funny would be invited to a dinner party in the first place.

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Our snowiest winter

Having lived in our current house for about 20years, like many people who live pretty ordinary lives, I’m able to reasonably accurately judge what has been happening to the weather in our locality.

We’ve had longer periods of ice – that is snow turned to ice and that did not melt, we’ve had a larger single deluge of snow, but there has not been a winter where we have had so many episodes of falling snow throughout the winter. And it is only mid February! AND the Met Office are now warming of “sudden stratospheric warming” which they say tends to lead to colder conditions.

What is different this winter, is that rather than one episode of snow (of varying scale) – which then goes away with no repetition, this winter “normal” amounts of  snow (perhaps just an inch or two) has been a regular feature. And before any alarmists suggest that snow occurs when it’s warmer – we’ve also had numerous days of ice. Instead, what has been happening is that the WARMER days of precipitation have been cooler.

Is that a trend? No. If I ignore what has occurred this winter, I do not think there has been any trend. However if something similar occurs again next winter it may be.

But whether or not it is part of a trend, I am officially declaring this the snowiest winter I have seen in this house (and there’s still a lot of the winter still to go).

(What prompted this post is that it’s start to snow again).

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Ball wins: All it took was a few decent people willing to stand up against tyranny.

When the history of these times are written it will be said that a few decent people stood up to a deluge of delusion and won.

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