Monday, November 28, 2011

Weekend downpour and inflow update

On the weekend, 26-27 November, we received a very nice downpour of 53 mm. This has pushed November well above average in terms of rainfall. However, we have still had less than 500 mm of rainfall this year, which means that we need a wet Christmas to reach Canberra's average.

The inflow since the start of this year has been, by my calculations, 47,175 megalitres, with an error margin of 2,000 megalitres. The megalitre per millimetre ratio is around 98, but that should improve some as we are due more inflow from the downpour - probably 2,000 to 3,000 more.

If we have a few years without drought, it might be possible for us to return to something closer to the average megalitre per millimetre ratio of 300. But I do not think that we will ever get back to that level.

Oh, and a word on consumption: ACTEW releases annual figures, but for financial years. This financial year, we have used 17,142 megalitres thus far, an average of close to 3,500 per month. This points to another year of 40,000 megalitre consumption. This is good: lowest ever consumption was last year's 40,923 megalitres. While we get more than that on average, we will be fine.

Monday, November 14, 2011

Good rainfall to start November; la nina confirmed

We have had a good start to November, with 27 mm thus far, putting us on track for the average of around 60 mm. However, ACTEWAGL have been slow updating their dam level numbers and so I will have to estimate the inflow for the year thus far. My calculation put it around 44,000 megalitres, with probably a little more to come from last week's rain. However, we are having hot weather for November, which increases evaporation and transpiration, so there might not be much more to come. We will see.

La Nina has been confirmed as present in the Pacific, so above average rainfall is projected for the summer. If above average rainfall eventuates, it will be interesting to see the inflow figures. The heavy rainfall that we had from February 2010 and February 2011 did not bring us back to average inflow levels, but perhaps a few further months of good rain will go some way towards doing so.

Wednesday, November 2, 2011

Poor start to spring

Spring is when the rain should fall in Canberra, although in recent years the rain has been coming more in the summer months. Thus far this year, we have had below average rainfall for the first two months of the season. Our yearly total has not yet crested 400 mm, which means that in the last eight weeks or so  of the year we need more than 210 mm to reach the annual average.

The 13 months from February 2010 to February 2011 were months of extremely good rain. Since then, however, only around 210 mm have fallen, leaving the ground parched even though the dams are still full.  The megalitres per mm rate has dropped from a high of 120 early in the year (still low) to a low of 101. And in the past three months we have had less than 7,000 megalitres of runoff.

While I do not think that permanent drought will come upon Canberra in the next decade, which is what I was predicting previously, I think that we are heading in that direction. Large rainfall every few years may make us relatively secure, especially with the new dam. But I am still very concerned.

Monday, September 19, 2011

Rainfall and inflow update after a lengthy absence

I have been on my second teaching prac for a month and thus have not had time to keep this updated.

I overestimated the expected inflow from the good rain that we received in August. As of 19 September, we are only up to about 38,000 megalitres of inflow from yearly rain totalling close to 340 mm. Below average rainfall so far for this year and below average inflow. It does not appear that last year's huge amount of rain changed the dynamics significantly: megalitres per mm has dropped to 113.

La Nina has rolled in officially, so it is probable that we will get some good rain over the remaining four months of the year. We need it to push as to the average or above. I admit that I am concerned that we could be heading into another period of drought. At least our dams are full, though.

Thursday, August 18, 2011

August Rain

We had some great rain yesterday: 34.2 mm. This brings the yearly total to around 320 mm, which is still below average for the year. However, we are heading into spring and if ENSO conditions remain neutral or extend to a La Nina we could catch up.

Inflow total thus far is 37,500 megalitres, well below average. There should still be around 3,000 to come from this good rain, but even so we are looking at getting less than 75,000 megalitres of inflow for the year. While this is way better than some recent years, it would be a significant drop on last year. Further, the ratio for inflow to rainfall is 120 megalitres of inflow per mm of rain. This is still a very low ratio, even with last year's very high amount of rain. Remember that the long-term average is 300 megalitres per mm and that inflow declines greater than linearly with decline in rainfall.

This seems to show that the relationship between low rainfall and even lower inflow is still holding. If we get a very bad year or enter drought conditions once more, I would not be surprised to see the inflow to rainfall ratio decline a hell of a lot further in a very short period.

I am still predicting an inevitable collapse of Canberra's water resources that requires urgent action to forestall. However, last year's high rainfall leads me to believe that this will take longer than my initial modelling suggested.

Monday, July 11, 2011

New figures

I am probably going to have to change the way I look at rainfall and runoff to a financial year model, as it seems that that is the main way that ACTEWAGL are reporting data.

However, as of this date we have had 270.6 mm of rainfall for the calendar year and - by a revised calculation that removes the 130 megalitres per day of overflow that ACTEWAGL reported for March and April from my May, June and July figures - 33,000 megalitres of inflow. We have had 23,000 megalitres of water usage over that period also, which is sitting at slightly above last year, but - give the uncertainties - is basically the same.

Friday, July 8, 2011

June/July update

I haven't posted for over a month, as I have been elsewhere.

Unfortunately, so has ACTEWAGL's daily usage data while they switched to a new website design ...

This means that I am having to estimate the amount of runoff that we have received. That estimate is currently at around 41,000 megalitres from rainfall of not much more than 280 mm. This estimate is at the high end--we may have received closer to 30,000 megalitres. Rainfall thus far this year has been low, with very low April, May and June. We have already had some rain in July, but it is not yet enough to counter the previous low months. Spring will be all important in determining annual rainfall.

Tuesday, May 31, 2011

Rainfall and runoff: year to date

The last two months have seen low levels of rainfall in Canberra and thus a decline in runoff. However, we have still had 246 mm of rainfall for the year, about average, and runoff of close to 33,000 megalitres.

The runoff total needs to be explained, however, as it is likely that we have had significantly less than this - perhaps as low as 28,000 megalitres. The reason is that I have factored in releases of 130 megalitres a day from Canberra dams over the last month or so. ACTEWAGL were definitely making releases of that magnitude over some of that period, and there were additional releases from smaller dams over one weekend. However, I am pretty certain that these releases stopped a couple of weeks or so ago. To ensure that I overestimate rather than underestimate runoff, I am working on the assumption that releases ceased as of 31 May.

It should be pointed out that even this overestimated runoff total is well below Canberra's average runoff for the first five months of the year. But it is better than last year: at the same point, we had had 21,000 megalitres of runoff.

Thursday, May 19, 2011

Arctic ice volume

I have been doing some work on Arctic sea ice volume, trying to determine whether a second order polynomial function had a physical basis. And I have discovered that it does. While others have obviously already worked this out, it is new to me, and thus at least a little bit exciting. :)

To look at this, what I did was sit and think about what would happen in an Arctic that was melting, and write down a few things.

The first thing that I thought of was that there are two significant parts to the Arctic year - the melt and the freeze. Using the values generated by Frank, I determined that over the period of the model (and, yes, PIOMAS is *not* data, but a model, but it does not matter for the purposes of this exercise) there was an increase in the amount of ice melting each year and a decrease in the amount of ice freezing each year. This increase and decrease were each moving in a linear fashion. It was difficult for me to see how a second order polynomial function could emerge from these linear functions. Silly me, as we will see.

So I set up a model that mirrored these linear changes in melt and freeze, and then looked at the yearly totals at maximum and minimum that resulted. Graphing these totals, I found that the declines in each perfectly followed a second order polynomial function ... What an earth was going on here?

I tried various values for the change constants in both the melt and the freeze periods, but always ended up with second order polynomial functions. So I decided to investigate this function a little more by differentiating it and seeing if the resultant function related in any way to the change constants.

And, of course, it did. What I found was that the differentiated function for the decline in ice volume at the end of the melt season was  - with X years - always:
- (Melt Constant + Freeze Constant)* X + (Melt Constant + Freeze Constant)/2

The differentiated function for the decline in ice volume at the end of the freeze season was  - with X years - always:
- (Melt Constant + Freeze Constant)* X + (3*Melt Constant + Freeze Constant)/2

Why these particular functions? The constants in them result from the 1/2 years offset between the two seasons. The Melt Constant + Freeze Constant is simply the total yearly change - the two constants added.

So integrating this returns us to our second order polynomial. And why do we integrate? Because the reductions in ice volume in any year are *summed* to the reductions in ice volumes of all previous years. And a sum function is an integral.

In other words, we do not start from scratch each year: each year, we are melting from a lower volume of ice and freezing from a lower volume of ice.

Basically, what it means is that if melting and freezing change in a linear fashion then we get a second order polynomial function for the ice volume totals.

And is there a physical basis for such a linear increase and decrease? Of course: the linear increase in energy, as measured through linear temperature change, in the Arctic due to rising CO2.

Which points to a dramatic crash in Arctic ice volume, and thus area and extent, over the next few years. Indeed, using PIOMAS, further modelling suggests that zero volume will be reached at the end of the melt period in 2018 at the latest, with it occurring possibly as early as 2013.

My projections are:
Year      Volume (cubic kilometres)
2011 ->  3744
2012 ->  2853
2013 ->  1935
2014 ->    990
2015 ->      18
2016 ->   -981
2017 -> -2007
2018 -> -3060

(all values have a two deviation error range of +/- 2445)

Tuesday, May 10, 2011

Aerosol evolution: two scenarios

This is a post inspired by SteveF's work at Lucia's blog here:

The above table from excel uses (I hope) SteveF's method to look at the evolution of aerosol forcings over time. In his simple analysis of equilibrium climate sensitivity, SteveF looked at the situation now and worked out what aerosol forcing would have to be if forcing caused an increase of .4207 degrees per watt per square metre and if forcing caused an increase of .81 degrees per square metre (and another higher scenario).

I have extended his analysis to cover the period 1970 to 2010. One of the thing that I noted in the comments to that thread was that the aerosol forcings under the higher sensitivity scenario are currently the same as they were after the Mount Pinatubo eruption. This seems unlikely. More reasonable is the lower sensitivity scenario, in which current sensitivity is about half of that after Mount Pinatubo erupted.

One interesting fact is that under the higher sensitivity scenario there is quite an upward trend over time in aerosol forcings. This does to some extent seem reasonable, imo, as the increase in CO2 emissions is directly associated with an increase in sulphur emissions. In fact, the correlation between well mixed greenhouse gas (WMGHG) forcings is high (r^2 value of 0.81). This makes sense to me.

Still not sure what it all means, but it is interesting to play with. :)

And I have realised that I may have missed one important component: solar forcings. I will check into that.

*Done a little checking. SteveF seems to simply use one value, but that could be because he is only looking at one year - he might change that value for each year.

*Re correlation, the lowest value for a statistically significant correlation, ignoring possible autocorrelation, which is relatively small, is 0.55 degrees per watt per square metre.

Tuesday, May 3, 2011

Hansen by logarithm

As I have been unable to find the linear graphs that I thought Hansen was using, I have recreated his numbers using the logarithmic model I described previously. After some fiddling around with the parameters, I have managed to create a reasonable match with observed temperatures and the observed rate of warming over the last 40 years using a climate sensitivity of 3.3 degrees per doubling. I homed in on this number because of a priori knowledge that Hansen's model E matches observations the best when such a sensitivity is used, so this is not an independent test.

I should again point out here that lower sensitivities require a faster response time and higher sensitivities require a lower response time.

My model predicts a rate of warming of .0187 degrees per year for the next 25 years, which equates to a bit less than half a degree of warming. At that point, we would be committed to a further one degree of warming, most of which would occur this century. If all human greenhouse gas emissions ceased at that point, total warming from preindustrial would be around 2.3 degrees by the time warming ceased.

I will be interested to see how my model compares with reality over the next little while.

Thursday, April 28, 2011

Using Hansen's linear response times

Testing my model using Hansen's linear response times (which leaves me with only one variable to play with, climate sensitivity) I need to use a climate sensitivity somewhere between five and 5.5 to get a match with the observed temperature trend between 1970 and 2010.

This could indicate that my model is wrong in other respects - I will need to read Hansen's paper carefully to check this, as he does mention a long-term sensitivity of around six degrees.

I should also note here that I am aware that my model is attributing all of the temperature increase between 1970 and 2010 to CO2, making the assumption that other forcings cancel out over that period. This is likely true for things like solar forcings, ENSO and so forth. However, aerosols are still an issue.

More on my temperature model

My temperature model - which is really a test of the climate sensitivity, as it is looking backwards over the last 50 years of data - has two basic variables.

The first is the climate sensitivity. I imput that against the Manua Loa CO2 data since 1959, which then generates the set of temperatures that we would expect were the climate response time instantaneous.

The second variable is the climate response time. As I stated previously, I have set this up as a logarithmic function that can be 'stretched' or 'squeezed'.

I have chosen to ignore the first 10 years of data and thus the absolute temperature value for the whole time period. The reason for this is that the first CO2 level seemingly makes the earth have a sudden jump above 280 ppm, instead of the slow rise that there was in reality. I believe that this must distort the temperature data, although I have not yet investigated as to in what fashion it does so.

This means that I cannot directly compare measured historical temperatures with the temperatures outputted by my model. I do not think that this is a problem, however, as what I can do is compare trends (which is another way of saying that I am measuring the difference, or anomaly, between the temperature my model shows for 1970 and the temperature my model shows for 2010).

Using GISS data, the trend between 1970 and 2010 is .0163 per year. I can fiddle with the response time parameter to make any climate sensitivity provide a match for this trend. However, the response times required for any particular sensitivity to do so are give us an interesting picture of the realistic sensitivities.

Using my model, a sensitivity of two degrees requires 70 per cent of the expected total temperature increase from a given rise in CO2 to occur in the first 10 years. Further, as we move past 30 years, more than 100 per cent must occur. This would seem to rule out two degrees as a viable sensitivity value under this model. (I am not yet claiming that my model is of use).

If we examine a sensitivity of six degrees, however, we get a different picture. Early on, it seems okay, with a bit over 30 per cent of the expected temperate rise occuring in the first decade. But to get the next 30 per cent takes a further 170 years. And then the next 15 per cent takes close to a further 700 years ... And that leaves a further 25 per cent of the response still to come. That does not seem plausible, either, leaving six degrees as not a viable sensitivity value under this model.

Three degrees sensitivity forces me to use a pretty fast response time to get a match - over 50 per cent in the first decade and 75 per cent after a touch over 30 years.

Four degrees sensitivity requires over 40 per cent in the first decade and around a total of 75 per cent after 85 years.

A sensitivity of 4.5 degrees has just under 40 per cent in the first decade and around 70 per cent after 100 years.

The question then becomes: which is plausible. I would suggest that the last is the most plausible using my model.

However, now the question becomes: is a logarithmic model realistic? Hansen et al use a linear model, with one line for the first decade and another line for the next 90 years, so maybe a logarithmic model is not realistic.

I will test the linear method in my model and report back.

Wednesday, April 27, 2011

Climate sensitivity revisited

I have been working with a simple model for temperature that has the earth responding logarithmically to CO2 forcing (for example, depending on the parameters that I use, it might warm by 40 per cent of the expected total warming in the first 10 years and then by another 30 per cent of the expected total warming in the next 90 years) and then running that model using different climate sensitivities.

Climate sensitivity is commonly defined as the predicted climate response to a forcing and in the case of CO2 it is put as X degrees per doubling.

The values for X that I have tried range from one to 10.

The CO2 data I am taking from Manua Loa.

At the moment I have having some difficulty getting my model to come close to matching observations if I use a low climate sensitivity. I can almost do it if I have a very fast response time. For example, if I choose a climate sensitivity of two degrees per doubling and I have the vast majority (80 per cent) of the temperature response occuring within 50 years, with more than 50 per cent of that in the first decade, I can fit the model to the current observed temperature. But the rate of warming that this produces for the last 50 years is still too low.

However, even here there is a problem: the rate of observed change is still faster than my model shows.

The better fits are with higher climate sensitivities, but even there things are not perfect. (Note: I would not expect them to be so, as my model is leaving out climate variability, but they are still not good enough for my purposes).

This seems reasonable: based on our observations of temperature and atmospheric CO2 concentrations over the last 130 years and the linear fit between the two, a sensitivity of two degrees would seem to be implied. However, this would seem to suggest an almost instantaneous response to CO2. If instead some kind of logarithmic fit was used, I wonder what result we would end up with?

I am assuming that there is a major problem with a model such as this. Hansen seems to use a linear model, with different slopes at different periods of time (for example, four per cent of the response per year for the first decade, followed by about .4 per cent of the response per year for the rest of the century). According to him, other models use much longer response times, at least for the second half of the response.

If anyone has any advice on this, that would be appreciated. I can obviously provide the full model (which is not very full or large) to anyone who wishes to see it.

Inflow and rainfall for the first four months of the year

As of 27 April 2011, Canberra has received 234 mm of rainfall and, according to my estimates, 28,500 megalitres of inflow into our dams. This has to be an estimate, as it looks as though ACTEWAGL carried out a large release of water over the Easter break from the Cotter and Bendora dams.

This gives a megalitre per millimetre rate of about 120 megalitres per millimetre, still lower than I would have expected after our wet year.

We have had a dry April, bringing down the projections for the year to something just over 700 mm. If things transition to an el nino we may get less, however.

Thursday, April 7, 2011

Yearly inflow to the end of March

The first three months of the year have gone, and we have seen low inflow for the amount of rain that we have received. However, we have still received a large inflow: 23,000 megalitres from 225 mm of rain.

(note: this is assuming that ACTEWAGL are still releasing around 130 megalitres a day to avoid problems with the dams - I suspect that this will not be the case in April, but will continue to track inflow as if that was the case until the end of April or I get more information).

This keeps the runoff per millimetre at just over 100 megalitres, which is odd, given the saturated nature of the soils. What it could mean, however, is that much of the rain is simply not falling in the catchement area, which is something that I was concerned about as a possibility last year.

By the same time last year, we had recieved around 16,700 megalitres in runoff from around the 230 mm of rainfall. This means that there has been a significant improvement, but not near what I expected - I thought that we would have returned to double this, or even higher. (Note that the long-term average is *triple* this rate of megalitres per mm).

Wednesday, February 23, 2011

Information from ACTEWAGL about inflow/outflow

Through the Canberra Times, I have discovered that ACTEWAGL have been releasing 130 megalitres a day for the year so far to keep the main dam at a safe level. This effectively doubles the inflow that I have measured, but I suspect that that is not the full picture. I believe that there must be further significant releases occurring from the other two dams. Why do I think this, even though ACTEWAGL say that these dams do not usually have such releases? Simply because inflows have been relatively low. I think that there must be continuous 'dribble' releases from the smaller two dams that probably again amounts to around 100 megalitres or so.

However, if that is not the case, we have had 14,000 megalitres from 176.2 mm of rainfall. That is again lower than I would have expected. Remember that the average rainfall for Canberra is 612 mm, with the average runoff 180,000 megalitres. Thus, I think that there must be something else going on - either in the hydrology or in the water management system.

Tuesday, February 8, 2011

Canberra rainfall for January

For January, we had around average rainfall, 54 mm.

My usual method of determining inflow will not work, as Canberra dams are sitting at 100 per cent. Thus, while I can set a minimum for the amount of inflow based on water usage and the fact that we briefly dipped below 100 per cent in early January, I cannot know what the real inflow. I will thus make an estimate, based on 300 megalitres of inflow per mm of rainfall - so around 16,000 megalitres.

We have had significant rainfall in the first week of February already - 56 mm. So we are on track for an above average rainfall for the first part of the year at least.

It may be that it will not be until La Nina ends that I will be able to make some more accurate measures of inflow. It will be interesting to see what the ratio of megalitres to mm is, giving me some more information about the hydrology of the Canberra area at the moment. 

Tuesday, January 4, 2011

Yearly wrap

This year, Canberra received 862.2 millimetres of rain, much more than I expected and out of the range for my longer term predictions. I will point out that there was a change over in stations for the last month of the year, which may have contributed to this - for the first 11 months of the year, the original station that I had based my analysis on showed approximately 100 mm less than the replacement station. In December, this station registered 198.4 mm of rainfall - pretty amazing stuff.

The average temperature for Canberra for 2010 was the coolest it has been for a decade, at 20.2 degrees. This continues the correlation of higher rainfall with lower temperatures, but it was still much more rain than my statistical model would have predicted for such a temperature.

The inflow into Canberra's dams will have to be an estimate, with 160,000 megalitres a reasonable one - it was likely slightly less than that, but I will not know until ACTEWAGL publish their figures.

And I have started tracking the rainfall and inflow for 2011.

Where now for my predictions/model? Well, they have been falsified. As such, I am going to require more observations to see if a new model arises or if the trends that I have observed end or continue.