Chapter 5.Expect, Macroweather

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Tuesday, May 16, 2017

Chapter 5.Expect, macroweather

5.1

“Expectthe cold weather to continue for the next ten days followed by a warm spell”; this was the extended range 14 day weather for Montreal on the 31st of December, 2006, (fig. 5.1a). But imagine what it might have been if the earth rotated about its axis ten times more slowly; with the length of the day coinciding with the 10 day weather-macroweather transition time scale. In that case (fig. 5.1b), we might have heard: “expect mild weather on Monday, followed by freezing temperatures until a warm spell on Thursday followed by a brisk Friday and Saturday, a warming on Sunday and Monday followed by freezing on Tuesday, then a four day warm period followed by freezing and then warming…”. Whereas long term trends in weather can persist for up to ten days or more, in macroweather the upswings tend to be immediately followed by downswings (and visa versa) and longer term trends are much more subtle, being the result of imperfect cancellation of fluctuations.

The fact that a series of fluctuations tend to cancel rather than – as in the weather regime - “wandering” up and down with prolonged increasing or decreasing swings in either direction is the defining feature of macroweather. Quantitatively, it implies that the exponent H in time is negative rather than positive. Whereas the weather with H>0 is a metaphor for instability, in macroweather, due to the cancelling, the temperature appears to be stable, with averaging over longer and longer times reducing the variability so that it appears to converge to a well defined value, the “climate”. In more prosaic terms, the “macroweather is what you expect, the weather is what you get”.

But what about in space? Fig. 5.2 left (weather) and right (macroweather) appear somewhat different[1]. As usual, we could explain the forecast with recourse to weather and macroweather maps. For example, fig. 5.2 (left) shows the day to day evolution of the corresponding daily temperatures over the globe over the next four days. Focusing on the North American continent (within the green ellipses), we would have been told that “a mass of warm air will be gradually displaced by colder arctic air descending from the north west, covering the continent by Thursday.” In the macroweather planet (right column fig, 5.2), the explanation might be: “The mass of unusuallycold air currently over the continent will shrink on Tuesday, spread to the northeast on Wednesday and by Thursday will expandcovering most of Canada and the United States”.

While the appearance of the temperature maps forweather(Fig. 5.2 left) and macroweather (right) appear to be a bit different, it turns out that they both have fairly similar, smooth behaviour in space (positive spatialH’s with comparable values) so that they are mostly distinguished by the way that they evolve in time: the sign of the temporal H. ButH only characterizes typical, average fluctuations;recall that in ch. 1 we saw how a fairly innocent looking aircraft transect hid very strong variability, “spikiness”, “intermittency”. To bring this out, consider fig. 5.3 that compares the spikiness of weather and macroweather, both inspace (bottom row) and in time (top row). To make the comparisons as fair as possible, we have presented 360 points for each (corresponding to a spatial resolution of 1o longitude and 1 hour, one month in time). Following fig. 1?, we have taken the absolute differences (so that the minimum is zero), then normalized them by their means (so that they all fluctuate around the value 1), finally we used a common vertical scale. By inspection, we can see that the macroweather time series is the odd one out with only small,nonintermittentfluctuations; indeed, the maximum is quite close to what would be expected if the process were Gaussian. On the contrary, in both time and in space (left column), the weather is highly spiky as is macroweather in space. Indeed, if any of these three were produced by a Gaussian process, their maxima would correspond to probabilities of less than one in a trillion.

The strong intermittency of the weather regime is unsurprising and is due to its turbulent nature discussed earlier. Similarly, the averaging (here, over a month) to obtain the macroweather series greatly reduces (nearly eliminates) the temporal intermittency. However, it completelyfails to reduce the spatial intermittency:the intermittency of the spatial macroweather transect actuallyquantitatively a bit stronger than the weather regime intermittency! This turns out to bethe statistical consequence of the existence of “climate zones”: the fact that huge spatial variability persists over long periods of time characterizing fairly stable “climate states”. Indeed, due to this long term persistence of stable atmospheric conditions[2], the maps shown are for “anomalies”; not for the temperatures themselves andthe use of anomalies highlights the relatively small changes. Just as the daily maps (fig. 5.2 left) defined anomalies as differences of the daily temperatures with the current “macroweather state” (one month average), the macroweather series and mapsare for anomalies obtained as the differences of the actual macroweather temperatures with the deseasonalized thirty year averages that thus implicitly define “climate states”[3].

The idea of macroweather states and using them to define weather anomalies is a natural consequence of the weather-macroweather transition and physically it corresponds to averages over several lifetimes of planetary structures. But what about climate states and the justification for effectively using them to definethe macroweather anomalies in fig. 5.2? Although it is nearly always used, this macroweather anomaly definition ispurely conventional - being codified by the World Meteorological Organisation. For example, the January anomalies used in fig. 5.2 are the differences between the January monthly averaged temperature and the average of all the Januaries over the previousthirty year reference period (by convention updated every decade), similarly for the other months of the year. Whereas at one month[4] and at 1- 2o spatial resolution, the anomalies typically vary in the range of a few degrees whereas over the globe the absolute reference temperature may vary by 70oC from one region to another. Had we shown the monthly variation of the actual temperatures rather than the anomalies, we wouldn’t have seen much beyond the seasonal temperature variation.

Fig. 5.1a: The mean daily temperatures in Montreal, Canada for Jan. 1- 14, 2006.

Fig. 5.1b: Macroweather temperatures for Montreal obtained by rescaling Montreal macroweather temperature anomalies from monthly resolution data from January 2000 through February 2001. The mean (-1 oC) was adjusted to be the same as in fig 5.1a and it was scaled so that the spread about the mean (the standard deviation, 4.9 oC) was also the same.

Fig. 5.2: Left column:Average daily temperatures for January 1 - 4 (top to bottom) from the ECMWF reanalysis for the month of January 2006 (used in fig. 5.1a), at 1.5o spatial resolution. To bring out the small changes, the anomaly with respect to the overall January average temperature is shown. The data are from ±60o latitude (this avoids much of the map projection distortion).

Right: Average monthly temperatures for the twentieth century reanalysis for the first four months of 2000 (used in fig. 5.1b), at 2o spatial resolution. To bring out the small changes, the anomaly with respect to the average temperature for the previous 30 Januaries is shown.

Blue indicates negative anomalies, red positive anomalies the green circlearound North American is discussed in the text.

Fig. 5.3: “Climate states” using the 28 year period 1871-1898 as the reference, data from the 20CR, ±60o latitude. Blue shows little change, red shows much change (increase) in temperatures. The regions most sensitive to global warming are the most red.

Why 30 years? In chapter 1, we traced its origin to the original “climate normal” defined by the International Meteorological Organization as the period from 1900-1930. As it became clear that the climate was changing, the reference period was changed - at first every thirty years, now every decade - but keepingwithout scientific justification the thirty year duration. Then, in ch. 2, using spectral and fluctuation analysis (figs. ?, ?), we saw that - at least in the instrumental period (roughly 1850 - present[5]) and for globally averaged temperatures, that there is a new regime at around 20- 30 years. Using fluctuation analysis (fig. ?) we saw that at longer times, the fluctuations started to increase again marking the end of the macroweather regime and the beginning of the climate regime. Fig. 5.4 shows the transition time scale estimated directly from the 1871-2010 20CR reanalysis data at 2o resolution. Although the transition varies somewhat with latitude, at least in the industrial epoch, a value of 30 years is a reasonable overall characterization.

We shall see later that even by 1930, only about 0.3oC of global anthropogenic warming had occurred[6] - barely above the natural variability (about 0.2 oC) - and the period 1900-1930 would have witnessed only about a 0.1oC change i.e. well below the “signal to noise” detection level[7]. Since then, emissions and other anthropogenic forcings have increased, so that over the last four decades, the same global change (0.1 oC) occurs every 8 - 9 years requiring about double length of time for the warming to exceed the natural variability. In other words, the weather-macroweather transition time is decreasing on the figure 30 years is an average over the entire period since about 1880. In retrospectit is thus fortuitous that the original 30 year climate normalduration coincides so well with this epoch averaged transition time scale. Beyond this tendency for the time scale to be reduced as we approach the present, there is also some geographical variability. Fig. 5.3 shows the result using the 140 years period from 1871-2010 using twentieth century reanalysis data.

Again, in order to bring out the small changes (of the order of a degree or some), the data were divided into five nonoverlapping 28 year periods (nearly 30 years) and the differences with respect to the reference 28 year period (1871-1898) are shown. Unsurprisingly, the figure mostly displays a fairly uniform warming trend that we will show is primarily due to human activities.

Fig. 5.?: Thevariation of the weather-macroweather transition scale (bottom, an extract of the curves in fig. 4.10 where it is described) and the macroweather-climate transition scale[8](top) as functions of latitude[9]. The thick curves show the mean over all the longitudes, and the dashed lines are the longitude to longitude variations[10]. The macroweather regime is the regime between the top and bottom curves. Adapted from1.

that corresponds also to industrialization and increased anthropogenic influences – at first changes in land use and then increasingly fossil fuels

If we lived on a more Mars like planet with weather macroweather transition at about one day instead of 5- 10 days,

“The extended range forecast calls for mild weather Monday, followed by freezing temperatures until a warm spell Thursday followed by cold Friday and Saturday, warming on Sunday and Monday followed by freezing on Tuesday, then a four day warm period followed by freezing and warming…”

Weather: “The extended range forecast calls for cold weather to continue for the next ten days followed by a warm spell

Fig.5.3The spikiness” (intermittency) in time and space of weather and macroweather series, compared. The graphs show absolute differences of east-west spatial transects (bottom) and series (time, top) at weather scales, (left), and macroweather scales (right). The graphs are each from 360 points (in space, at 1o resolution), and show the absolute differences between consecutive values. All the series were normalized by their means. While the spatial intermittencies (bottom) are not too different (at macroweather scales, it is a bit stronger), the temporal intermittencies are totally different, nearly absent from the 4 month (macroweather) series (upper right).

Upper left: Hourly temperature data from January 1 -15, 2006 from a station in Lander Wyoming. The maximum value is 8.23 standard deviations above mean, the process is highly non Gaussian (for a Gaussian process with 360 points, the maximum would be at roughly 2.8 standard deviations above the mean).

Upper right:20CR reanalysis from 1891-2011, each point is a four month average, the data are for a 2ox2o grid point over from Montreal, Canada (45oN). The maximum is 2.53 standard deviations above the mean, close to that of a Gaussian(for a Gaussian process with 360 points, the maximum would be at roughly 2.8 standard deviations above the mean).

Lower left: ECMWF reanalysis for the average temperature of 21stJanuary, 2000, at 45oN; the maximum value is 7.26 standard deviations above mean, the process is highly non Gaussian.

Lowerright: ECMWF reanalysis: the monthly averaged temperature for January 2000 at 45oN. The maximum is 7.66 standard deviations above the mean.

Fig. 5.? The east-west absolutegradients of the temperature climate state obtained by averaging over 140 years from 1871 to 2010. The data arebetween ±60o latitude and were taken from the twentieth century reanalysis at 2o spatial resolution. For each latitude, the gradients are normalized by the mean gradient at that latitude.

Left: The gradients from successive latitudes are offset by 2 units in the vertical; one can roughly make out the, major mountain ranges and coastlines.

Right:specific examples at 45 oNand 45 oS. Note different scales.

Fig. 5.? RMS: 11 control runs

Control runs (top) actually 5500 months=458 years.

2 multifractal simulations (2^17X2^5)= resolution, 1 day, 340 years

Top slope=-0.15, bottom, -0.32 (muotifractal simulations)

( ranges normalized (seperately for time and space), note that the lower left is the 21 Jan, 2000 ECMWF,Lander, hourly: 8.23 sd' s above the mean

20CR four month averages:, max is 2.53 sd’s above the mean

1/360 corresponds to 2.78 sd' s

Ecmwf, jan. 2000 in space max is 7.6606842 sd' s above mean

Meteorological and climatological sciences have become increasingly distinct yet there is still no generally accepted definition of the climate – or what is nearly the same thing – what precisely is the distinction between the weather and the climate? And if our notion of the climate is vague, what do we mean by climate change?

While atmospheric scientists routinely use the expressions “climate scales” and “meteorological scales” the actual boundary between them is not clear and most improve little upon the dictum:

“The climate is what you expect, the weather is what you get”.

-Farmer’s Almanac

This is actually quite close to the principal definition given by the US National Academy of Science:

“Climate is conventionally defined as the long-term statistics of the weather...”

-2.

Which improves on the Almanac only a little by proposing:

“…to expand the definition of climate to encompass the oceanic and terrestrial spheres as well as chemical components of the atmosphere”.

Another official source attempts to quantify the issue of the exact meaning of “long term” by tentatively suggesting a month as the basic “inner” climate time scale… but ultimately it seems to yield to a higher authority:

“Climate in a narrow sense is usually defined as the "average weather," or more rigorously, as the statistical description in terms of the mean and variability of relevant quantities over a period of time ranging from months to thousands or millions of years. The classical period is 30 years, as defined by the World Meteorological Organization (WMO). These quantities are most often surface variables such as temperature, precipitation, and wind. Climate in a wider sense is the state, including a statistical description, of the climate system.”

-Intergovernmental Panel on Climate Change AR4, Appendix I: Glossary, p. 942, 3.

At first sight, the last sentence is an interesting addition but is ultimately tautological since it defines the climate as the statistics of the “climate system”, which itself is left undefined.

Finally, an attempt at a more comprehensive definition is only a little better:

Climate encompasses the statistics of temperature, humidity, atmospheric pressure, wind, rainfall, atmospheric particle count and numerous other meteorological elements in a given region over long periods of time. Climate can be contrasted to weather, which is the present condition of these same elements over periods up to two weeks... Climate … is commonly defined as the weather averaged over a long period of time. The standard averaging period is 30 years, but other periods may be used depending on the purpose.also includes statistics other than the average, such as the magnitudes of day-to-day or year-to-year variations… The difference between climate and weather is usefully summarized by the popular phrase "Climate is what you expect, weather is what you get."

-Wikipedia

What is new here is the explicit attempt to distinguish weather (periods less than two weeks) and climate (30 years or more). However, as with the IPCC definition, these time periods are simply suggestions, with no attempt at physical justification. In any case they leave the intervening factor of 1000 or so in scale (literally!) up in the air.

An obvious problem with these definitions is that they fundamentally depend on subjectively defined averaging scales. This fuzziness is also reflected in numerical climate modelling since Global Climate Models (GCM’s) are fundamentally the same as weather models but at lower resolutions, with a different assortment of subgrid parametrisations and they are coupled to ocean models and – increasingly – to carbon cycle, cryosphere and land use models. Consequently, whether we define the climate as the long-term statistics of the weather, or in terms of the long-term interactions of components of the “climate system”, we still need an objective way to distinguish it from the weather. These problems are clearly compounded when we attempt to objectively define climate change.

However, there is yet another difficulty with this and allied definitions: they imply that climate dynamics are nothing new: that they are simply weather dynamics at long time scales. This seems naïve since we know from numerous examples in physics that when processes repeat over wide enough ranges of space or time scale they typically display qualitatively new features so that over long enough time scales we expect that new climate laws should emerge from the higher frequency weather laws. These qualitatively new emergent laws could simply be the consequences of long range statistical correlations in the weather physics in conjunction with qualitatively new climate processes – due to either internal dynamics or to (external) orbital, solar, volcanic or anthropogenic forcings - their nonlinear synergy giving rise to emergent laws of climate dynamics.