Tuesday, November 30, 2010

Topping 700 mm - rainfall and inflow update

I have been holding off for a little while waiting for rainfall to top 700 mm for the year. And it has done so with a bang: we have now had 744.6 mm of rainfall this year, which is a very good year indeed, and we still have a month to go, which means that 800 mm looks to be well within reach. And it is possible that we will top 850 mm, blowing my statistical predictions out of the water, so to speak. But we will see.

Regarding inflow, the full inflow from the last two days rain has not yet been measured, but we are currently sitting at around 122500 megalitree for the year. This is still below what we would have expected from such an amount for rain, but it is still almost triple what we had last year.

Wednesday, November 24, 2010

Statistical immortality

Okay: first up, statistical immortality does not mean that you will live forever. But it does open up the possibility for people to live very long lives indeed.

What is statistical immortality? Statistical immortality, as I define it, is where the pace of increase in life expectancy reaches parity - in other words, life expectancy increases by a year every year.

At present, life expectancy is increasing by around one year every three years for those in rich Western nations like Australia. Most of this increase *not* in reduction in infant mortality - we have almost reached the limit of improvement there. Rather, most of it is coming at the other end of life: we are not dying when we used to.

To illustrate exactly what I mean, I will go through an example. Imagine a person who is 60. They have a life expectancy of a further 22.9 years. What this means is that some people of their age will die prior to 82.9 (and some will die before reaching 61!) and some will live longer, but that the average age of death for the group as a whole will be 82.9.

Looking at the table from the ABS, around 53 per cent would still be alive at 82.9. However, let us assume that by the time this cohort was 65, their life expectancy had increased five years to 87.9. Only around 3 per cent of them would be dead at this point. If we take them through five year steps, this pattern repeats, with a small per cent of them dying and the life expectancy of the rest extending further and further into the future.

Even with this small death rate, however, eventually the whole cohort would be dead. But this would take a significant amount of time. From an original cohort of 100,000 at age 60, there would still be around 50,000 alive after 23 steps - 115 years. So we are looking at a median age (the age by which half of them will be dead) of death for this cohort of 197.9.

Now, 197.9 is not immortality. So why would I call it statistical immortality? For two reasons: firstly, if you had an infinitely sized population (mathematicians like infinity) some of that cohort would be expected to survive forever (in fact, an infinite number of them :)); and secondly, this is so far beyond the usual life of a human being that it moves significant numbers of the population (50 per cent of this particular cohort) into a world that we can barely begin to imagine - one in which all sorts of other pathways would almost certainly open up for them.

Returning to climate change, the rapid increases in life expectancy that we are experiencing in the West at present makes it almost certain that, if you are reading this, you will be alive to see some of the worst effects. And then life expectancy may start to drop again ...

Tuesday, November 23, 2010

Life expectancy

One of the interesting things - to me - about the climate change debate is how many people seem to think that the effects of climate change will not be experienced by them but rather by their children or grandchildren.

These statements are even made, perhaps rhetorically, perhaps not, by people who are authorities on the science. Storms of my grandchildren is a book written by James Hansen, the head of the Goddard Institute and the man who runs one of the five major global temperature data sets, GISSTemp. While I am sure that James Hansen is aware of what climate change is doing to the world now, the emphasis is on what will occur many decades into the future. (To be fair, Hansen is 69, so his grandchildren are likely around 10 or so).

However, even someone who is 69 and who lives in the wealthy west has a reasonable chance of living for another 20 years.

And that leads me to the point of this post: examining life expectancy.

Let us examine the life expectancy by age tables published by the ABS here:


What they show us is that an Australian male (and James Hansen is American, but the difference will not be all that great) aged 69 has a life expectancy of a further 15.7 years.

The tables towards the bottom of the page show something even more interesting. They show that as you get older the age at which you are expected to die increases quite signficantly.

For example, someone who was 40 in 1989 was expected to die at age 75.9. Those members of that demographic who reached the age of 60 in 2009 were expected to die at age 82.9, an increase of seven years in a 20-year period.

If you think about, this is at least partly to be expected. If you survive from age 40 to age 60, the most obvious conclusion is that you have not died. Thus, you have successfully avoided the dangers that have taken the lives of others in your demographic. Those who died were taken into account in working out the expected age of death of 75.9. They no longer exist, and so the expected age of death for the survivors must be higher than 75.9.

However, an increase of seven years seems quite large. Think about it this way: once we reach a point where our average age of death increases by one year for every year that goes by, we will have reached statistical immortality (in a way - there will still be deaths, but they will be compensated for, in the statistical sense, by faster and faster increases in life expectancy). Seven in 20 is a reasonable step towards that mark. And the figures for those aged 60 in 1989 who survived to 80 in 2009 are even more interesting: the expected age at death increased by 10 years in those 20 years.

What is going on here? Well, apart from death winnowing out people from the second set of statistics (ie, not everyone is making it to 80), medical technology is improving quite rapidly. This is expanding life expectancy, and it is particularly doing so for those aged 40 or above.

Having done some calculations based on these tables, it is my conclusion that someone who is aged approximately 40 today has a 25 per cent chance of living to 120. These calculations assume the continuation of the steady increase in life expectancies, with no spectacular breakthroughs.

It is also my calculation that 'statistical immortality' will be acheived in 100 years, with those aged around 20 today having about a 30 per cent chance of reaching that point.

And I will write a more detailed post about what I mean by 'statistical immortality' in the near future.