Myten om nye miljøvennlige fly

Luftfartens representanter hevder ofte at nye fly er miljøvennlige. De forteller at drivstoffforbruket per setekilometer har blitt sterkt redusert etter hvert som nye flymodeller har blitt introdusert, noe som isolert sett er riktig. Men det er mye som de ikke forteller. Veksten i flyreiser har vært enorm siden jetflyene ble introdusert omkring 1960, og de årlige utslippene er nesten tidoblet siden da. Jetflyene flyr vesentlig høyere enn propellflyene som de avløste, og utslipp i stor høyde er spesielt skadelige for miljøet. Når vi tar med dette ser vi at luftfarten har blitt et stort miljøproblem, og at selv de nyeste langdistanse jetflyene gir større klimabelastning målt per passasjerkilometer enn propellflyene som de avløste for snart 60 år siden.

Utslipp fra fly i stor høyde er spesielt skadelige

Eksosen fra flymotorer inneholder bl.a. karbondioksid CO₂, vanndamp og nitrogenoksid NO_x. CO₂  er en drivhusgass som blander seg godt i atmosfæren, og CO₂-utslipp i stor høyde påvirker derfor klimaet like mye som tilsvarende utslipp ved bakken. Vanndampen kan i stor høyde kondensere på partikler i avgassene og danne kondensstriper, som igjen kan utvikle seg til fjærskyer. I stor høyde er begge varmende. NO_x kan både føre til dannelse av ozon og til nedbrytning av metan. Ozon i stor høyde er varmende, og nedbrytning av metan er kjølende. Summen av tilleggseffektene forårsaket av vanndamp og NO_x er i stor høyde varmende. De kommer i tillegg til drivhuseffekten av CO₂.

Det er vitenskapelig usikkerhet om størrelsen på tilleggseffektene. Sammenlignet med effekten av CO₂ er tilleggseffektene kortvarige, men de er sterke sålenge de virker. Det er et verdivalg å bestemme hvor stor vekt vi skal legge på kortvarige effekter i forhold til langvarige effekter. Dette innlegget vil diskutere hvor store tilleggseffektene er ved å vise til vitenskapelige artikler og til annen litteratur.

Et kort sammendrag er at tilleggseffektene må tas hensyn til for jetflyene som flyr høyt, men ikke for propellflyene som flyr vesentlig lavere. Tilleggseffektene blir tatt hensyn til ved å multiplisere de direkte CO₂ utslippene fra en flyreise med en faktor som kalles EWF, Emission Weighting Factor. Produktet angir CO₂ mengden som måtte ha blitt sluppet ut på bakkenivå for å gi det samme bidraget til global oppvarming som flyreisen gjorde. EWF lik 3 er et fornuftig valg. Dvs. at brenning av en viss mengde flybensin i stor høyde gir tre ganger så stort bidrag til global oppvarming som om den samme mengden hadde blitt brent på bakkenivå.

Luftfart og klima

For mange nordmenn er flyreiser en betydelig del av våre bidrag til global oppvarming. I dette innlegget vil jeg først referere til noen forsknings-artikler. Deretter vil jeg beregne hvor store utslippene er for fire typiske flyreiser beregnet med britiske retningslinjer og med fire utslippskalkulatorer på nettet. Disse resultatene vil jeg så sammenligne med annen litteratur. Til slutt vil jeg sammenligne dette med bilkjøring. Et veldig kort sammendrag er at på korte reiseavstander gir fly og privatbil sammenlignbare bidrag til global oppvarming per passasjerkilometer. Men på lange avstander, der tilleggseffektene pga. stor høyde slår tungt inn for flyreiser, gir fly større bidrag enn privatbil. Hovedproblemet med flyreiser er imidlertid ikke at utslippet per passasjerkilometer er så stort, men at det så lett blir så mange kilometer. Flyene oppmuntrer til lange reiser som det ellers ikke ville vært praktisk å gjennomføre.

S-curve shows transition to disruptive technology

The two previous blog posts show that the transition to wind and solar energy in the electricity production has started, both globally and in China, the largest emitter of greenhouse gases. It is now cheaper to build new electricity plants based on wind and solar than based on nuclear and fossil fuels. Wind and solar are therefore often regarded as disruptive technologies.

Generally, a disruptive technology will replace the older technology, and the transition will follow an S-curve.

Figure 1: The S-curve shows how the market share of a disruptive technology evolves. The curve flattens when the market share reaches its saturation level.

The curves showing the electricity production in the recent years by both wind and solar resemble the start of an S-curve. But there are topics for wind and solar that may cause the further evolution to differ from the S-curve. China, as the rest of the world, wants to phase out fossil fuels in its electricity production as fast as possible due to both global warming and local pollution. This may cause the transition to be even faster than the S-curve.

Wind and solar both have intermittency problems. We need electricity also when the wind does not blow and the sun does not shine. The intermittency problems become more and more serious as the shares of wind and solar increase. This may cause the transition to be slower than the S-curve.

There are some solutions to the intermittency problems, and new solutions will certainly be developed. Chris Goodall discusses these problems in his latest book The Switch. He writes that various solutions have to be applied, in part simultaneously. Many of the solutions are technical, but not all of them. A technical solution is to produce hydrogen and gas for later use when there is a  surplus of solar and wind electricity. A non-technical solution is to control the demand for electricity using varying prices so that demand better matches production.

Solar, wind, hydro and the other renewables have different properties. Their saturation levels measured in percent of the total market will therefore vary around the world. The S-curve in Figure 1 may represent the electricity production by solar and wind, and the saturation level may be the production needed to totally phase out the electricity produced by fossil fuels.

The rest of the blog post deals with mathematical details about S-curves.

China's electricity transition

This blog post shows that the transition to wind and solar energy in China's electricity production has started.

China is the world's largest emitter of greenhouse gases, and its inhabitants are suffering from air pollution caused by the burning of fossil fuels. China is determined to improve on these topics, and it is interesting to see how this has affected the country's electricity production. China publishes both its capacity and its production of electricity on the China Energy Portal. The portal is updated with data up to and including 2016. All plots in this blog post are based on data from that portal.

The Great Transition

This blog post comments on Lester Brown's book The Great Transition, Shifting from Fossil Fuels to Solar and Wind Energy.

I start with a micro-summary of Lester Brown's view on the alternatives to fossil fuels.

Lester Brown is skeptical about nuclear power, mainly due to cost, long planning and construction time to build new nuclear power plants, problems with nuclear waste, and the probability for accidents like those in Chernobyl in 1986 and Fukoshima in 2011. The share of nuclear power in the global electricity production has fallen from 18 percent in 1996 to 11 percent in 2013.

Lester Brown is also skeptical to increase the use of biomass for energy, mainly because cropland should be used for food production and because intact woods are important for biodiversity.

Lester Brown argues that wind and solar energy is the best alternative to fossil fuel energy. He presents many cases where solar or wind accounts for a significant share of the electricity production. Examples of such cases are wind in Denmark and wind and solar in Germany.

Based on what I have read in other sources I fully agree with Lester Brown's viewpoints on the alternatives to fossil fuels.

Detect serial correlation in data with outliers

This is the sixth post in a series of six that describes mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Correlation when outliers in the data.
Post 3  Trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added. Example.
Post 5  Compare Kendall-Theil and OLS trends.            Simulations.
Post 6  Detect serial correlation when outliers.          Simulations.

The posts are gathered in this pdf document.

Start of post 6:    Detect serial correlation in data with outliers

This chapter deals with Monte Carlo simulations that calculate the serial correlation coefficients in noisy data. They are calculated with two different approaches. One uses the noise values, and the other uses the ranks of the noise values. Both approaches work well when the noise is white and when there is serial correlation in the noise. The approach that uses the ranks works much better than the other when there are outliers in the noise. The results are presented as probability density plots.

Compare Kendall-Theil and OLS trends

This is the fifth post in a series of six that deals with mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Correlation when outliers in the data.
Post 3  Trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added. Example.
Post 5  Compare Kendall-Theil and OLS trends.        Simulations.
Post 6  Detect serial correlation when outliers.               Simulations.

The posts are gathered in this pdf document.

Start of post 5:  Compare Kendall-Theil and OLS trends

This blog post deals with Monte Carlo simulations that calculate trends. The calculations use both the Kendall-Theil (K-T) methodology and the Ordinary Least Squares (OLS) methodology. The post compares the results. Both methodologies work well when the noise in the dependent variable is white. They are about equal when there is serial correlation in the dependent variable. K-T is much more robust against outliers than OLS is. The results are presented in probability density plots.

Correlation and trend when an outlier is added

This is the fourth blog post in a series of six that deals with mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Correlation when outliers in the data.
Post 3  Trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added. Example
Post 5  Compare Kendall-Theil and OLS trends.                  Simulations.
Post 6  Detect serial correlation when outliers.                     Simulations.

The posts are gathered in this pdf document.

Start of post 4:
Correlation and trend when an outlier is added.

This blog post contains an example that demonstrates the shortcomings of the mostly used methods to calculate trends and correlations when an outlier is added to the data. It demonstrates that alternative methods based on medians and ranks are more robust against outliers.

Trend when outliers in the data

This is the third post in a series of six that deals with mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Correlation when outliers in the data.
Post 3  Trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added.    Example.
Post 5  Compare Kendall-Theil and OLS trends.              Simulations.
Post 6  Detect serial correlation when outliers.                 Simulations.

The posts are gathered in this pdf document.

Start of post 3: Trend when outliers in the data

The method most commonly used in linear regression analysis is to calculate the trend based on the data values. But it is more robust against outliers to calculate it based on the ranks of the data. This blog post discusses the mathematics behind both methods.

Correlation when outliers in the data

This is the second post in a series of six that deals with mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Correlation when outliers in the data.
Post 3  Trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added.   Example.
Post 5  Compare Kendall-Theil and OLS trends.             Simulations.
Post 6  Detect serial correlation when outliers.                Simulations.

The posts are gathered in this pdf document.

Start of post 2: Correlation when outliers in the data

The method most commonly used to estimate the correlation between two datasets is to calculate the correlation coefficient based on the values in the two data sets.. But it is more robust against outliers to calculate it based on the ranks of the data. This blog post discusses the mathematics behind both methods.

Introduction to Statistical analysis of data with outliers

This is the first blog post in a series of six that deals with mathematics for calculation of correlation and trend in data with outliers. The posts are numbered 1 to 6. They should be read consecutively. This first post is just an introduction.

Post 1  Introduction to Statistical analysis of data with outliers
Post 2  Calculate correlation when outliers in the data.
Post 3  Calculate trend when outliers in the data.
Post 4  Correlation and trend when an outlier is added.   Example.
Post 5  Compare Kendall-Theil and OLS trends.             Simulations.
Post 6  Detect serial correlation when outliers.                Simulations.

The posts are gathered in this pdf document.

Start of post 1 Introduction to Statistical analysis of data with outliers

Five blog posts in June 2014 deal with the mathematics that is most commonly used when analysing global temperature series. That mathematics is not well suited when there are large outliers in the data. The first blog post in that series gives an overview of those five posts.

Ordinary least square (OLS) error mathematics is the most commonly used method to calculate trends. It is based on data values, and it therefore performs poorly when there are large outliers in the data. Global temperatures do not have large outliers due to both the inertia in the global climate system and due to the thorough processing before the temperature data is released. Other climate data, such as precipitation, snow depth and skiing conditions at specific locations, have large outliers, and the OLS mathematics is not suitable for those data.

The calculation of the Pearson correlation coefficient is also based on data values. This is the most commonly used method to calculate correlation between variables. It too performs poorly when there are large outliers in the data.

Mathematics based on data ranks performs better than mathematics based on data values when analysing data with large outliers. In this series of blog posts I will describe the rank mathematics which I use to calculate the Kendall tau-b correlation coefficient and the Kendall-Theil robust trend line. For comparison I also shortly describe the Pearson and the OLS mathematics.

As will be seen, the mathematics that is used to calculate the Kendall tau-b correlation coefficient and the Kendall-Theil robust trend line is rather simple and easy to explain. But the mathematics that is used to quantify their uncertainties, which are p-values and confidence intervals, is more complicated.

Next post in the series

Rekalkulere trender og korrelasjoner rundt skiforholdene i Nordmarka med metoder som er robuste mot slengere.

Det forrige innlegget, Fremskrivninger for skiforholdene i Nordmarka er for optimistiske, baserte seg på de vanligste metodene for å beregne trendlinjer og korrelasjonskoeffisienter. Innlegget som du leser nå, gjentar beregningene med alternative metoder som kan være mer velegnet for de aktuelle dataene. Resultatene varierer noe, men hovedbildet er det samme. De alternative beregningsmetodene støtter konklusjonene i det forrige innlegget.