Downscaling temperature fields with genetic programming

This blog is not called Variable Variability for nothing. Variability is the most fascinating aspect of the climate system. Like a fractal you can zoom in and out of a temperature signal and keep on finding interesting patterns. The same goes for wind, humidity, precipitation and clouds. This beauty was one of the reasons why I changed from physics to the atmospheric sciences, not being aware at the time that also physicists had started studying complexity.

There is variability on all spatial scales, from clusters of cloud droplets to showers, fronts and depressions. There is variability on all temporal scales. With a fast thermometer you can see temperature fluctuations within a second and the effect of clouds passing by. Temperature has a daily cycle, day to day fluctuations, seasonal fluctuations and year to year fluctuations and so on.

Also the fluctuations fluctuate. Cumulus fields may contain young growing clouds with a lot of variability, older smoother collapsing clouds and a smooth haze in between. Temperature fluctuations are different during the night when the atmosphere is stable, after sun rise when the sun heats the atmosphere from below and the summer afternoon when thermals develop and become larger and larger. The precipitation can come down as a shower or as drizzle.

This makes measuring the atmosphere very challenging. If your instrument is good at measuring details, such as a temperature or cloud water probe on an aircraft, you will have to move it to get a larger spatial overview. The measurement will have to be fast because the atmosphere is changing continually. You can also select an instrument that measures large volumes or areas, such as a satellite, but then you miss out on much of the detail. A satellite looking down on a mountain may measure the brightness of some mixture of the white snow-capped mountains, dark rocks, forests, lush green valleys with agriculture and rushing brooks.



The same problem happens when you model the atmosphere. A typical global atmospheric oceanic climate model has a resolution of about 50 km. Those beautiful snow-capped mountains outside are smoothed to fit into the model and may have no snow any more. If you want to study how mountain glaciers and snow cover feed the rivers you can thus not use the simulation of such a global climate model directly. You need a method to generate a high resolution field from the low resolution climate model fields. This is called downscaling, a beautiful topic for fans of variability.

Deterministic and stochastic downscaling

For the above mountain snow problem, a simple downscaling method would take a high-resolution height dataset of the mountain and make the higher parts colder and the lower parts warmer. How much exactly, you can estimate from a large number of temperature measurements with weather balloons. However, it is not always colder at the top. On cloud-free nights, the surface rapidly cools and in turn cools the air above. This cold air flows down the mountain and fills the valleys with cold air. Thus the next step is to make such a downscaling method weather dependent.

Such direct relationships between height and temperature are not always enough. This is best seen for precipitation. When the climate model computes that it will rain 1 mm per hour, it makes a huge difference whether this is drizzle everywhere or a shower in a small part of the 50 times 50 km box. The drizzle will be intercepted by the trees and a large part will evaporate quickly again. The drizzle that lands on the ground is taken up and can feed the vegetation. Only a small part of the heavy shower will be intercepted by trees, most of it will land on the ground, which can only absorb a small part fast enough and the rest runs over the land towards brooks and rivers. Much of the vegetation in this box did not get any water and the rivers swell much faster.

In the precipitation example, it is not enough to give certain regions more and others less precipitation, the downscaling needs to add random variability. How much variability needs to be added depends on the weather. On a dreary winters day the rain will be quite uniform, while on a sultry summer evening the rain more likely comes down as a strong shower.

Genetic Programming

There are many downscaling methods. This is because the aims of the downscaling depend on the application. Sometimes making accurate predictions is important; sometimes it is important to get the long-term statistics right; sometimes the bias in the mean is important; sometimes the extremes. For some applications it is enough to have data that is locally realistic, sometimes also the spatial patterns are important. Even if the aim is the same, downscaling precipitation is very different in the moderate European climate than it is in the tropical simmering pot.

With all these different aims and climates, it is a lot of work to develop and test downscaling methods. We hope that we can automate a large part of this work using machine learning: Ideally we only set the aims and the computer develops the downscaling method.

We do this with a method called "Genetic Programming", which uses a computational approach that is inspired by the evolution of species (Poli and colleagues, 2016). Every downscaling rule is a small computer program represented by a tree structure.

The main difference from most other optimization approaches is that GP uses a population. Every downscaling rule is a member of this population. The best members of the population have the highest chance to reproduce. When they cross-breed, two branches of the tree are exchanged. When they mutate, an old branch is substituted by a new random branch. It is a cartoonish version of evolution, but it works.

We have multiple aims, we would like the solution to be accurate, we would like the variability to be realistic and we would like the downscaling rule to be small. You can try to combine all these aims into one number and then optimize that number. This is not easy because the aims can conflict.
1. A more accurate solution is often a larger solution.
2. Typically only a part of the small-scale variability can be predicted. A method that only adds this predictable part of the variability, would add too little variability. If you would add noise to such a solution, its accuracy goes down again.

Instead of combining all aims into one number we have used the so-called “Pareto approach”. What a Pareto optimal solution is is best explained visually with two aims, see the graphic below. The square boxes are the Pareto optimal solutions. The dots are not Pareto optimal because there are solutions that are better for both aims. The solutions that are not optimal are not excluded: We work with two populations: a population of Pareto optimal solutions and a population of non-optimal solutions. The non-optimal solutions are naturally less likely to reproduce.


Example of a Pareto optimization with two aims. The squares are the Pareto optimal solutions, the circles the non-optimal solutions. Figure after Zitzler and Thiele (1999).

Coupling atmospheric and surface models

We have the impression that this Pareto approach has made it possible to solve a quite complicated problem. Our problem was to downscale the fields near the surface of an atmospheric model before they are passed to a model for the surface (Zerenner and colleagues, 2016; Schomburg and colleagues, 2010). These were, for instance, fields of temperature, wind speed.

The atmospheric model we used is the weather prediction model of the German weather service. It has a horizontal resolution of 2.8 km and computes the state of the atmosphere every few seconds. We run the surface model TERRA at 400 m resolution. Below every atmospheric column of 2.8x2.8 km, there are 7x7 surface pixels.

The spatial variability of the land surface can be huge; there can be large differences in height, vegetation, soil type and humidity. It is also easier to run a surface model at a higher spatial resolution because it does not need to be computed so often, the variations in time are smaller.

To be able to make downscaling rules, we needed to know how much variability the 400x400 m atmospheric fields should have. We study this using a so-called training dataset, which was made by making atmospheric model runs with 400 m resolution for a smaller than usual area for a number of days. This would be too much computer power for a daily weather prediction for all of Germany, but a few days on a smaller region are okay. An additional number of 400 m model runs was made to be able to validate how well the downscaling rules work on an independent dataset.

The figure below shows an example for temperature during the day. The panel to the left shows the coarse temperature field after smoothing it with a spline, which preserves the coarse scale mean. The panel in the middle shows the temperature field after downscaling with an example downscaling rule. This can be compared to the 400 m atmospheric field the coarse field was originally computed from on the right. During the day, the downscaling of temperature works very well.



The figure below is the temperature field at night during a clear sky night. This is a difficult case. On cloud-free nights the air close to the ground cools and gathers in the valleys. These flows are quite close to the ground, but a good rule was to take the temperature gradient in the lower model layers and multiply it with the height anomalies (height differences from spline-smoothed coarse field).



Having a population of Pareto optimal solutions is one advantage of our approach. There is normally a trade of between the size of the solution and its performance and having multiple solutions means that you can study this and then chose a reasonable compromise.

Contrary to working with artificial neural networks as machine learning method, the GP solution is a piece of code, which you can understand. You can thus select a solution that makes sense physically and thus more likely works as well in situation that are not in the training dataset. You can study the solutions that seem strange and try to understand why they work and gain insight into your problem.

This statistical downscaling as an interface between two physical models is a beautiful synergy of statistics and physics. Physics and statistics are often presented at antagonists, but they actually strength each other. Physics should inform your statistical analysis and the above is an example where statistics makes a physical model more realistic (not performing a downscaling is also a statistical assumption, just less visible and less physical).

I would even argue that the most interesting current research in the atmospheric sciences merges statistics and physics: ensemble weather prediction and decadal climate prediction, bias corrections of such ensembles, model output statistics, climate model emulators, particle assimilation methods, downscaling global climate models using regional climate models and statistical downscaling, statistically selecting representative weather conditions for downscaling with regional climate models and multivariate interpolation. My work on adaptive parameterisation combining the strengths of more statistical parameterisations with more physical parameterisations is also an example.

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Related reading

On cloud structure

An idea to combat bloat in genetic programming

References

Poli, R., W.B. Langdon and N. F. McPhee, 2016: A field guide to genetic programming. Published via Lulu.com (With contributions by J. R. Koza).

Schomburg, A., V.K.C. Venema, R. Lindau, F. Ament and C. Simmer, 2010: A downscaling scheme for atmospheric variables to drive soil-vegetation-atmosphere transfer models. Tellus B, doi: 10.1111/j.1600-0889.2010.00466.x, 62, no. 4, pp. 242-258.

Zerenner, Tanja, Victor Venema, Petra Friederichs and Clemens Simmer, 2016: Downscaling near-surface atmospheric fields with multi-objective Genetic Programming. Environmental Modelling & Software, in press.

Zitzler, Eckart and Lothar Thiele, 1999: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE transactions on Evolutionary Computation 3.4, pp. 257-271, 10.1109/4235.797969.


* Sierpinski fractal at the top was generated by Nol Aders and is used under a GNU Free Documentation License.

* Photo of mountain with clouds all around it (Cloud shroud) by Zoltán Vörös and is used under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license.

Extending the temperature record of southeastern Australia

This is a guest post by Linden Ashcroft. She did her PhD studying non-climatic changes in the early instrumental period in Australia and now works at the homogenization power house, the Centre on Climate Change (C3) in Tarragona, Spain. She weekly blogs on homogenization and life in Spain.

This guest post was originally written for the Climanrecon blog. Climanrecon is currently looking at the non-climatic features of the Bureau of Meteorology’s raw historical temperature observations, which are freely available online. As Neville Nicholls recently discussed in The Conversation, the more the merrier!

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Southeastern Australia is the most highly populated and agriculturally rich area in Australia. It’s home to our tallest trees, our highest mountains, our oldest pubs and most importantly, our longest series of instrumental weather observations. This makes southeastern Australia the most likely place to extend Australia’s instrumental climate record.

The official Australian Bureau of Meteorology was formed in 1908, bringing standard observing practices into effect across the country. Before this time, Australian weather station coverage was not as dense as today’s network, and there was no nationally-standard procedure for recording temperature.

The uncertain quality of the pre-1910 data and the lack of readily available information about observation techniques is why the current high-quality temperature dataset available for Australia does not begin until 1910. However, this does not mean that valuable observations were not taken in the 19th century, or that the spatial coverage of these data is too poor to be useful for studies of regional climate. Here, I explain what colleagues and I did to extend the temperature record of southeastern Australia.

When is the temperature not the temperature?

First of all, it’s important to know what ‘non-climatic’ influences can affect temperature observations. Some influences are fairly obvious: if you move a thermometer 20km down the road, change the time of day that the temperature is recorded, or replace the screen the thermometer is housed in, that will most likely cause changes in the data recorded at that station which are not caused by actual changes in the surrounding air.

Other non-climatic influences are more subtle. The slow growth of a tree next to a thermometer for example, or changes to the irrigation system in nearby paddocks can cause gradual changes to temperature observations that are not a reflection of the temperature in the wider area.

Three thermometer screens used in Adelaide, South Australia, in 1890: a Stevenson screen (left), a thermometer shed (centre), and a Glaisher stand (right). Charles Todd famously recorded the temperature in each of these screens for around 40 years, giving us invaluable information about the effect of different screens on temperature observations. Image: Meteorological Observations Made at the Adelaide Observatory, Charles Todd (1907).

Finding and reducing the impacts of these non-climatic influences is an important part of any climate change research. A multitude of statistical methods have been developed over the last 30 or so years to do this, ranging from the beautifully simple to the mind-bogglingly complex. Most of these methods rely on reference series, or a version of the truth with which you can compare data from the station you’re interested in. Reference series are often made using data from neighbouring weather stations that experience a similar climate. Of course this is much harder if you don’t have many neighbouring stations, or if a change in observation method happens at all stations at once! This is another reason why Australia’s national temperature record does not extend before 1910.

As well as these statistical tests, it’s also really useful to have information, or metadata, about the maintenance and changes that occur at a weather station. Metadata help you understand why a non-climatic influence might occur in the climate data, and how big it could be. In reality though, metadata can be hard to find.

Extending southeastern Australia’s temperature record

My work with the South Eastern Australian Recent Climate History project (SEARCH) set out to explore the quality and availability of climate data for Australia before 1908. Our aim was not to look at extreme events, or the exact temperature value at a particular location in a particular month, but to see how the average temperature across southeastern Australia varied over years and decades. This is important to note because if we were studying extremely hot months for example, or only the climate of Wagga, we might have used different methods.

The first step was looking for long-term temperature stations in southeastern Australia. Although the Bureau of Meteorology only started in 1908, a number of weather stations were set up in capital cities and key country towns from the late 1850s, thanks to the dedication of Australia’s Government Astronomers and Meteorologists

My colleagues and I also uncovered some sources of pre-1860 instrumental climate data for southeastern Australia that we painstakingly digitised and prepared for analysis. You can read more about that here.

Next, we spent a lot of time collecting information from the Bureau of Meteorology and previous studies about possible changes in station locations and other things that might affect the quality of the observational data. For some stations we found a lot of photos and details about changes to the area around a weather station. For others, particularly in the pre-1860 period, we didn’t find much at all.

After getting all this information and removing some outlying months, we tried to identify the non-climatic features of the temperature observations, and remove their influence. For the pre-1860 data this was particularly difficult, because we did not have a lot of metadata and there were no nearby stations to use as a ‘truth’. In the end we looked for large changes in the data that were supported by metadata and by the behaviour of other variables.

For example, a drop in temperature in the 1840s at some stations occurred at the same time as an increase in rainfall, suggesting that the temperature change was real, not due to some non-climatic influence. We also noted any other issues with the data, such as a bias towards rounding temperature values to the nearest even number (a common issue in early observations).

For the post-1860 data, we applied a 2-stage process of removing the non-climatic factors, using the statistical RHtest developed by members of the international Expert Team on Climate Change Detection and Indices (ETCCDI). The first stage looked for absolute non-climatic features: big jumps in the data that were clearly instrument problems or station changes, and that were supported by the metadata.

The second stage used reference series made from the average of data from up to five highly correlated neighbouring stations. Both stages involved carefully comparing the statistical results with the metadata we had, and making a decision on whether or not a non-climatic feature was present. You can read more about the methods here.

An example of the non-climatic features, or jumps, found in Newcastle maximum temperature data from 1860–1950 using the RHtest method. The supporting metadata are also shown. Image supplied by author.

So what did we find?

Our results for the 1860–1950 period found 185 non-climatic features in the maximum temperature data, and 190 in the minimum temperature data over the full network of 38 stations. Over 50% of these non-climatic features identified were supported by metadata, and most of them occurred from 1880 to 1900, when the thermometer shelters that were used in Australia were changed from Glaisher stands to Stevenson screens.

You can see in the figures below that removing the non-climatic features had a big impact on the variance of the observations, making the spread of temperatures across the region much more similar to the post-1910 period, when observations are more reliable. Our results also agreed very well with southeastern Australia data from the Bureau of Meteorology’s monthly and daily temperature datasets that have been tested for non-climatic features using different methods.

This good agreement allowed us to combine the area-average of my data with that of the Bureau’s best temperature dataset (ACORN-SAT), building a monthly temperature record for southeastern Australia from 1860 to the present. Combining the two series showed that the current warming trends in Australia are the strongest and most significant since at least 1860.

Area-averaged SEA annual anomalies (°C, relative to the 1910–1950 base period) of original data from the historical sources (1860–1950, dashed line), adjusted data from historical sources (1860–1950, solid red line) and data from ACORN-SAT, the Bureau of Meteorology’s daily temperature data over SEA (1910–1950, solid blue line) for maximum and minimum temperature over 1860–1950. The maximum and minimum anomalies for each year across the network are also plotted for the original historical data (grey shading with black outline), adjusted historical data (pink shading with red outline) and ACORN-SAT data (blue dotted lines). Adapted from Ashcroft et al. 2012.

The 1788–1860 data had some non-climatic influences as well, but these were much harder to untangle from the true climate signal because there is not as much ‘truth’ to compare to. We identified five clear non-climatic features of the pre-1860 temperature data from three stations, and found that the year-to-year temperature changes of the adjusted data matched up pretty well with rainfall observations, and newspaper reports at the time. The quality and distribution of the pre-1860 data made it impossible to accurately combine the pre- and post-1860 observations, but hopefully in the future we will uncover more observations and can look more closely at the 1788–1860 period.

Our work is one of the first projects to tackle Australia’s pre-1910 temperature data, shedding more light on Australia’s climatic past. This research also makes use of the hard work that was done by some of the country’s scientific pioneers, which is very rewarding to me as a scientist.

But science is always moving forwards, and our work is just one link in the chain. As more statistical methods are developed and additional data uncovered, I’m sure that we, professional and citizen scientists alike, will be able to build on this work in the future.

More information and references:

Ashcroft, L., Gergis, J. and Karoly, D.J., 2014. A historical climate dataset for southeastern Australia. Geosciences Data Journal, 1(2): 158–178, DOI: 10.1002/gdj3.19 (html and PDF). You can also access the 1788–1860 data at https://zenodo.org/record/7598.

Ashcroft, L., Karoly, D.J. and Gergis, J., 2012. Temperature variations of southeastern Australia, 1860–2011. Australian Meteorological and Oceanographic Journal 62: 227–245. Download here (PDF).