The timing of cool changes in Melbourne

Melbourne – what a place to live! If you don’t like the weather, just wait a while and it will change. Positioned in the southeast of Australia, the most dramatic changes occur when summer north-westerly winds that channel over the country’s baking interior are replaced by south-westerlies coming roughly from Antarctica.

A typical headline in Melbourne after days of sweltering heat in summer.

A typical headline in Melbourne after days of sweltering heat in summer.

These cool changes can be dramatic. Temperatures can drop from around 40 °C to 25 °C in a matter of an hour. That’s a drop of 25-30 °F for those working in Fahrenheit. Maximums can be more than 20 °C different from one day to the next. Cool changes often arrive in Melbourne after many days of sweltering heat; you can almost hear the city of 4 million sigh.

Predicting the timing of summer cool changes is important for various reasons regarding public safety, including bushfire management. The winds before and after a cool change are often strong, so bushfires can be extremely intense at this time. The worst fire events in Victoria are typically associated with these wind changes. Fires that might have spread along quite narrow fronts under north-westerlies can have massive fronts when the wind switches to the south west. The Kilmore East fire of 7 February 2009 (“Black Saturday”) is one example.

The effect of the windchange on the Kilmore East fore on Black Saturday from the Royal Commission's report.

The effect of the windchange on the Kilmore East fore on Black Saturday from the Royal Commission’s report.

If you need to know when a change will occur, you should ask a weather forecaster. Weather systems in Melbourne typically move from west to east, and cold fronts that bring the change certainly match this pattern. While weather forecasters use models of atmospheric dynamics to predict the passage of these cold fronts, most of us don’t have access to the necessary computer power, data and expertise to solve the equations required to analyze these models.

So what should we do if we want to DIY? Thanks to the Australian Bureau of Meteorology (BoM), we can access data for a range of weather stations to the west of Melbourne. These weather stations record the wind direction and temperature, and the BoM displays these data every half hour via their website, and sometimes more frequently. So we can watch the cool change approach.

But can we do more? If we wanted to model the passage of a cold front to predict the timing of a wind change, how might we do that without the aid of numerical weather forecasting?

Let’s overlay a model of a cold front at Aireys Inlet on the map of weather stations. Cold fronts are usually aligned at an approximate 45 degree angle. Imagine it sweeping from west to east. What would be the simplest model for this cold front? Well, we might represent the cold front as a straight line and have it progressing at a constant speed to the east. Let’s assume the cold front is currently at Aireys Inlet (dark line), and we are interested in predicting where it will be at some time in the future (grey line).

Weather Stations to the west of Melbourne, and the modelled cold front moving from west (black) to east (grey).

Weather Stations to the west of Melbourne, and the modelled cold front moving from west (black) to east (grey).

This model has two parameters that we need to estimate. We need to know the slope of the cold front and its speed. Thinking of the model in this way helps us realise how it might be wrong – the cold front might not be a straight line (it might be curved), and it might not move at a constant velocity (it might change speed or direction). For example, a curved front slipping away to the south east might take longer to arrive than anticipated.

Bearing these simplifications in mind, we will plough on with our simple model, and leave more realistic ones to the experts. We can define the model geometrically. Think of the location of Aireys Inlet as being the origin of an x-y graph, so Aireys Inlet has coordinates (0, 0). Melbourne is approximately 76 km east of Aireys Inlet and 72 km north, so Melbourne has coordinates (76, 72). We can define the coordinates of all the other weather stations (and all other locations) in a similar way. A negative value for the x-value of the coordinate indicates that the site is to the west of Aireys Inlet and a negative y-value indicates the site is to the south of Aireys Inlet.

When the front is at Aireys Inlet, the equation defining its location is y = −bx (with b, a positive number, defining the backward slope of the front). If the front is moving eastward at a speed of v km/hour, then after t hours, the front will be vt kilometres to the east. So, the equation defining the location of the front at some other time is y = −b(xvt).

I've switched the model of the cold front onto an X-Y coordinate system. I've chosen the origin to be Airey's Inlet, so all locations are measured relative to there.

I’ve switched the model of the cold front onto an X-Y coordinate system. I’ve chosen the origin to be Airey’s Inlet, so all locations are measured relative to there.

The location and time in this equation is relative to a reference location; in this case I chose Aireys Inlet. So a negative value for time t indicates the passage of the front at a particular location prior to it arriving at Aireys Inlet.

We can manipulate the equation y = −b(xvt) to determine the time of arrival of the front for any location x and y by solving for t. Thus:

xvt = y / b

vt = y / b x

t = y / bv + x / v

This tells us that the time of arrival of the front at a particular location depends on the coordinates of the location (x, y), and the speed (v) and slope (b) of the front. So to determine the arrival time, we must estimate the two parameters b and v. If the front is at Aireys Inlet, then it will have passed at least some of the other weather stations, so we will know when it arrived at those locations. Therefore, we can fit the observed times and locations of the passage of the front to the equation t = y / bv + x / v to estimate b and v.

A simple way to estimate b and v is to construct the model as a linear regression. Manipulating the equation (by dividing both sides by x), we have:

t/x = y/xbv + 1/v,

in which the variable t/x is proportional to the variable y/x (with a constant of proportionality 1/bv) plus a constant 1/v.

This is simply a linear regression of the form Y = mX + c, based on the transformed variables Y = t/x and X = y/x. The speed and slope of the front are defined by the regression coefficients, and are v = 1/c and b = c/m.

Let’s apply that to some data on the passage of a cold front. Melbournians might remember the front that arrived on 17 January 2014 after a few days with maximums above 40°C. I’m sure tennis players in the Australian Open remember it – seeing Snoopy anyone?

Here are recorded times for the passage of the cold front at weather stations prior to them arriving at Aireys Inlet. The column t is the number of hours relative to arrival at Aireys Inlet. For example, the front arrived at Mount Gellibrand 15 minutes (0.25 hours) prior to its arrival at Aireys Inlet.

Location

x

y

Time

t

y/x

t/x

Port Fairy

−162.77

0.99

10:46

−2.77

−0.00611

0.01700

Warrnambool

−144.09

13.07

11:10

−2.37

−0.09072

0.01643

Hamilton

−182.00

82.39

11:48

−1.73

−0.45269

0.00952

Cape Otway

−48.93

−46.16

12:03

−1.48

0.94350

0.03032

Mortlake

−117.20

38.83

12:09

−1.38

−0.33131

0.01180

Westmere

−104.02

79.46

13:08

−0.40

−0.76391

0.00385

Mount Gellibrand

−27.07

24.66

13:17

−0.25

−0.91092

0.00924

Aireys Inlet

0.00

0.00

13:32

0.00

The linear regression of t/x versus y/x yields m = 0.0133 and c = 0.0171. Therefore, v = 58.5 km/hour and b = 1.28. The value of v means the front was estimated to be moving eastward at 58.5 km/hour, and the value of b implies it was approximately aligned at an angle of tan−1(1.28) = 52° above the horizontal (b = 1 would imply an angle of 45°).

The regression for the cool change on 17 January 2014. Note that the cool front took longer than predicted to reach both Geelong and Melbourne (blue dots; these were not used to construct the regression).

The regression for the cool change on 17 January 2014. Note that the cool front took longer than predicted to reach both Geelong and Melbourne (blue dots; these were not used to construct the regression).

Using those parameters, the time at which the front is expected to arrive at a location with coordinates (x, y) is t = 0.0133y + 0.0171x (relative to the time it arrived at Airey’s Inlet). Different fronts will have different alignments and move at different speeds, so these parameters only apply to the passage of this particular front.

But let’s look at the regression relationship more closely; it has some interesting attributes. Firstly, the relationship is approximately linear, although clearly imperfect. The approximate linearity might encourage us to have some faith in our rather bold assumptions.

Also, one of the points, corresponding to Cape Otway, has a potentially large influence on the regression. Being to the right of the other data, it has “high leverage”; the regression line will tend to always pass quite close to that point.

Whether that high leverage is important will depend on where we wish to make predictions. It turns out that Melbourne is located very close to that point. Now, that might seem surprising at first because, compared to Cape Otway, Melbourne is in the opposite direction from Aireys Inlet. In fact, that is why Cape Otway and Melbourne have similar values for y/x (the “x-value” of the regression model) – the two locations are in opposite directions from Aireys Inlet.

This dependence of the regression on when the front reaches Cape Otway actually means we can very much simplify the model. We can use t/x for Cape Otway to predict t/x for Melbourne because they have very similar values of y/x. For Cape Otway, x = −48.93, and for Melbourne x = 76.14. If the front arrived at Cape Otway (relative to Aireys Inlet) at tCO, then the time it arrives at Melbourne, tM, is predicted from the expected dependence:

tCO / −48.93 = tM / 76.14.

Thus, tM = −tCO 76.14/48.93 = −1.56tCO.

That is, the time it takes for the front to arrive in Melbourne from Aireys Inlet is approximately the time it takes the front to travel between Cape Otway and Aireys Inlet multiplied by 1.56. The accuracy of this method can be assessed by comparing it to data on the passage of two fronts (17 Jan 2014 and 28 Jan 2014).

On 17 January, the front took 1.48 hours to travel between Cape Otway and Aireys Inlet, so our simplified model predicts the front’s arrival in Melbourne 2.3 hours after it passed through Aireys Inlet. The observed time was 3.2 hours, so the front took about 55 minutes longer than predicted. Thus, the data point for Melbourne is above that of Cape Otway.

On 28 January, the front took 1.56 hours to travel between Cape Otway and Aireys Inlet, so our simplified model predicts the front’s arrival in Melbourne 2.1 hours after it passed through Aireys Inlet. The observed time was 1.7 hours, so the front arrived about 25 minutes sooner than predicted. Thus, the data point for Melbourne is below that of Cape Otway.

CoolChange28Jan

The regression for the cool change on 28 January 2014. Note that the cool front arrived than predicted in both Geelong and Melbourne (blue dots; these were not used to construct the regression).

Interestingly, errors in the predictions could have been anticipated once the front arrived in Geelong. Because the front on 17 January took longer than predicted (by the regression) to arrive in Geelong, it seems to have travelled slower than anticipated. In contrast, the front on 28 January arrived in Geelong earlier than predicted, so its passage might have accelerated.

The simplification tM = −1.56tCO only works for predicting arrival of the front at Melbourne. If you want to predict the passage of the front at other locations, you might need to do the linear regression (or better still, ask a numerical weather forecaster).

The diversity of science careers

Many different scientific career opportunities exist. Sometimes a “traditional” science career is portrayed as students travelling from undergrad, to postgrad, a post-doc research position or two, and then an academic position at a university.

myscicareer_greyscale_232x130px_transp_bg

First-person science career stories

Of course, such a career trajectory is atypical. Most scientists end up in other professions, branching out at various points from this academic path, and sometimes even veering back onto it. The variety of paths is almost as great as the variety of people on them.

It is not always easy to see examples of this diversity of career paths. That makes the website MySciCareer all the more useful. There you can read first-hand accounts of people who have followed various career paths in science.

So, if you are wondering about the options available in science, hop on over to MySciCareer, and browse around. You could even consider contributing a story.

How many surveys to demonstrate absence?

In the lecture today in Environmental Monitoring and Audit, I mentioned the model examining how much search effort is required to be sufficiently sure of the absence of a species at a site. This was based on a paper by Brendan Wintle et al. (2012).

You can read more about this topic here, with an attempt at an intuitive interpretation of the model, and some links to other examples where the prior probability (base rate) matters.

If you are particularly keen, you can read a copy of the manuscript here.

Reference

Wintle, B.A. Walshe, T.V., Parris, K.M., and McCarthy, M.A. (2012). Designing occupancy surveys and interpreting non-detection when observations are imperfect. Diversity and Distributions 18: 417-424.

Is the temperature rising?

In 2009, Senators Penny Wong and Steven Fielding debated the issue about whether the Earth’s temperature was increasing. Senator Wong was the minister for climate change at the time, and Senator Fielding was on the cross benches in the senate; the government was hoping for his support for action on climate change.

Senator Fielding’s position was basically that the Earth was no longer warming based on data over the last 10 years. Senator Wong argued that using data over a few decades, the Earth was clearly still warming.

The question about whether the Earth’s temperature is increasing is rather simple – one would hope that data might help answer it. In a previous post on my research site, I looked at how much data would be required to answer this question with confidence. This analysis suggested that more than 15 years of data would be required to be sure that the rate of temperature increase had slowed, even when the observed trend was flat. This was because the temperature record is noisy – measured global temperatures fluctuate.

Here we are, a few years later – where does the evidence lie? Well, let’s examine the relationship between global temperature and atmospheric concentrations of CO2. This might be the world’s most mindless climate model, but let’s assume that temperature is related linearly to CO2 concentration. Using HadCRUT3 data and CO2 measured at Mauna Loa (data downloaded in July 2013), the relationship looks like this:

Annual average global temperature anomaly as measured by HadCRUT3 versus annual average carbon dioxide concentration measured at Mauna Loa.

Annual average global temperature anomaly as measured by HadCRUT3 (relative to the average for the period 1961-1990) versus the annual average carbon dioxide concentration measured at Mauna Loa. Data are shown for the period up to 2008, which were the data available at the time of the debate between Senators Fielding and Wong.

We can characterize Senator Wong’s position as there being a linear relationship between temperature and CO2 that will continue in the future. Thus, we can fit a linear regression to the data up to 2008, predict an interval in which we would expect the data to fall (e.g., a 95% prediction interval), and check for departure from that. Here is that prediction and the subsequent data:

A linear regression of the the global temperature anomaly as measured by HadCRUT3 versus the annual average carbon dioxide concentration. The regression was fitted to data up to 2008, and the data for the next 4 years are shown in blue. These data points fall within the 95% prediction interval, which is given by the dashed line.

A linear regression of the the global temperature anomaly as measured by HadCRUT3 versus the annual average carbon dioxide concentration. The regression was fitted to data up to 2008, and the data for the next 4 years are shown in blue. These data points fall within the 95% prediction interval, which is given by the dashed line.

Code for fitting this linear regression in OpenBUGS is here.

The data remain within the bounds predicted, even if they are slightly on the low side of the trend. But we cannot be sure that the temperature has departed from its previous increasing trend.

Now, let’s characterize Senator Fielding’s position as there being a previous increase in temperature with CO2, but that plateaued after 1998. We fit a linear regression to the data up to 1998, and then a flat line after 1998, with these two lines joining in 1998. Note, in this case I excluded the observed temperature in 1998 because it reduces the influence of cherry picking. Code for fitting this relationship in OpenBUGS is here.

A regression of the the global temperature anomaly as measured by HadCRUT3 versus the annual average carbon dioxide concentration using data up to 2008. The linear relationship up to 1998 was estimated, while the trend was assumed to be flat after that year. To reduce the influence of cherry picking the change point as 1998 (the year with the highest temperature), this year was excluded from the analysis.  The data for the next 4 years are shown in blue. These data points fall within the 95% prediction interval, which is given by the dashed line.

A regression of the the global temperature anomaly as measured by HadCRUT3 versus the annual average carbon dioxide concentration using data up to 2008. The linear relationship up to 1998 was estimated, while the trend was assumed to be flat after that year. To reduce the influence of cherry picking the change point as 1998 (the year with the highest temperature), this year was excluded from the analysis. The data for the next 4 years are shown in blue. These data points fall within the 95% prediction interval, which is given by the dashed line.

The data remain within the bounds predicted, even if they are slightly on the high side of the prediction. But we cannot be sure that the temperature does not conform with a flat relationship since 1998.

What does all this mean? Well, as in my previous post, it shows that several years (e.g., >15 years) of temperature data (or very large and clear changes in temperature) are required to distinguish between these two points of view. It is unfortunate that the number of years of data are considerably longer than the election cycle; while politicians might debate the issue, definitive evidence to support or refute their positions will not arise in typical political lifetimes.

It is also unfortunate that the data used in this debate represent only a small fraction of the heat content of the planet. Thus, while the heat content of the planet seems to be rising consistently, the surface temperature, which is measured by HadCRUT3 and experienced by most people, is noisy. Because the temperature data are equivocal over timescales of a decade or so, the other evidence about increases in the heat content of the Earth (e.g., melting of ice caps, warming of sub-surface of the ocean) become more important, but less tangible to people.

Further debate about this topic also includes whether it is plausible that temperatures might increase with CO2 over some periods and not others. Such debates become much more subtle than simple measures of the temperature at the Earth’s surface.

Yet the noisy data (and subtle changes relative to that noise) cloud the debate about whether the Earth’s temperature is continuing to increase, let alone what are appropriate responses to human-caused climate change.

Species’ responses to climate change

Yesterday in Graduate Seminar: Environmental Science, we discussed the paper by Sinclair et al. (2010) that critiqued the use of species distribution models for helping inform management of species under climate change. A few recent papers related to this topic are worth considering. One is discussed in The Conversation (Moritz and Agudo 2013), part of a special section of Science, and another is in press in PNAS (Blois et al. in press). In particular, the latter paper suggests that species distribution models can indeed help to predict response of species to climate change. These models are not perfect (that’s the thing about models – they are not meant to be perfect), but they seem helpful.

As an aside, a commentator in The Conversation suggested that the last paragraph of The Conversation piece was not appropriate for scientific commentary. What do you think? Is it appropriate for scientists to make such statements? This question is relevant to the second discussion we had about the role of science in public debate.

References

Blois, J. L., J. W. Williams, M. C. Fitzpatrick, S. T. Jackson, and S. Ferrier (in press). Space can substitute for time in predicting climate-change effects on biodiversity. Proceedings of the National Academy of Sciences of the United States of America.

Moritz, C., and R. Agudo, (2013) The future of species under climate change: resilience or decline? Science 341 (6145): 504-508.

Sinclair, S. J., M. D. White, and G. R. Newell. (2010). How useful are species distribution models for managing biodiversity under future climates? Ecology and Society 15 (1): 8.