Cool look at risk - Part 1: What is climate?

Celebrating the fourth edition of my book

[There is also a Greek version of the post—Υπάρχει και ελληνική έκδοση της ανάρτησης]

Today I have posted the fourth edition of my book Stochastics of Hydroclimatic Extremes - A Cool Look at Risk. I had planned to have it ready by the end of 2024, but I delayed it by a month for reasons that will be easily guessed by those who have followed my previous posts.

I produced edition 0 of the book in 2020 and a new edition in each of the following four years. The entire production is mine, including developing the mathematics, book design, write up, typesetting, pagination, etc. My colleagues and friends have helped me in various ways, as can be seen from the acknowledgements.

The book is in open access and anyone interested can download it for free from my site (click on the link “Full text”). There are no restrictions on downloading and no user information is required (no login, no email, etc.).

Most of the book’s content cannot be found anywhere else as it is mostly original and novel. (In this respect, I can challenge those “friends” who grumble that I often cite myself to suggest alternative citations).

It is unnecessary to repeat the content of the book here. Besides, this would be impossible as it is 400 pages long and contains a lot of math. Yet the first and the last chapter I believe are easy to read. Also, the other chapters contain Digressions some of which are non-mathematical pieces, explanations or applications in real-world problems. To facilitate reading, I have put most mathematical proofs in Appendices in the end of each chapter.

In this and the next couple of Climath posts I will highlight a few issues for illustration. For simplicity, the topics I have chosen for the posts do not contain any mathematical material. However, I would like to invite the interested readers to see the mathematical material and to let me know their comments, suggestions or possible errors they find.

Here I highlight the book’s Digression 1.C: What is climate? Perhaps some may think the issue I highlight is unimportant but, in my approach (which is that taught by Aristotle),¹ there cannot be science without proper definitions of the related concepts. So, here is my take about the definition of climate.

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As is the case with stochastics (Digression 1.A), the concept of climate is an old one. Aristotle in his Meteorologica describes the climates on Earth in connection with latitude but he uses a different term, crasis (κρᾶσις,² literally meaning mixing, blending of things which form a compound, temperament).³ The term climate (κλίμα, plural κλίματα) was coined as a geographical term by the astronomer Hipparchus⁴ (190 –120 BC). He was the founder of trigonometry but is most famous for his discovery and calculation of the precession of the equinoxes (μετάπτωσις ἰσημεριών) by studying measurements on several stars. In the 20^th century, this precession would be found to be related to the climate of Earth and constitutes one of the so-called Milankovitch cycles. The term climate originates from the verb κλίνειν, meaning ‘to incline’ and originally denoted the angle of inclination of the celestial sphere and the terrestrial latitude characterized by this angle (Shcheglov, 2007)⁵.

Hipparchus’s Table of Climates is described by Strabo the Geographer (63 BC – AD 24), from whom it becomes clear that the Climata of that Table are just latitudes of several cities, from 16° to 58°N (see Shcheglov, 2007, for a reconstruction of the Table). However, Strabo himself uses the term climate with a meaning close to the modern one.⁶ Furthermore Strabo, defined the five climatic zones, one torrid, two temperate and two frigid, as we use them to date.⁷

The term climate was used with the ancient Greek geographical meaning until at least 1700 as imprinted in a dictionary of that era.⁸ A search on old books⁹ reveals that the term climatology appears after 1800. With the increasing collection of meteorological measurements, the term climate acquires a statistical character as the average weather. Indeed, the geographer A.J. Herbertson (1907)¹⁰ in his book entitled “Outlines of Physiography, an Introduction to the Study of the Earth”, gave the following definition of climate, based on, but also distinguishing it from, weather:

By climate we mean the average weather as ascertained by many years’ observations. Climate also takes into account the extreme weather experienced during that period. Climate is what on an average we may expect, weather is what we actually get.¹¹

Herbertson also defined climatic regions of the world based on statistics of temperature and rainfall distribution, a work that was influential for the famous and most widely used Köppen (1918)¹² climate classification; this includes six main zones and eleven climates which are on the same general scale as Herbertson’s (Stamp, 1957)¹³. Herbertson’s definition has been kept without major changes till now; for example, Lamb (1972)¹⁴ states:

Climate is the sum total of the weather experienced at a place in the course of the year and over the years. It comprises not only those conditions that can obviously ‘near average’ or ‘normal’ but also the extremes and all the variations.

Modern scientific glossaries also provide similar definitions of climate. We quote a few:

• By the USA National Weather Service:¹⁵

Climate – The composite or generally prevailing weather conditions of a region, throughout the year, averaged over a series of years.

• By the Climate Prediction Center of the latter:¹⁶

Climate – The average of weather over at least a 30-year period. Note that the climate taken over different periods of time (30 years, 1000 years) may be different. The old saying is climate is what we expect and weather is what we get.

• By the American Meteorological Society,¹⁷

Climate – The slowly varying aspects of the atmosphere–hydrosphere–land surface system. It is typically characterized in terms of suitable averages of the climate system over periods of a month or more, taking into consideration the variability in time of these averaged quantities. Climatic classifications include the spatial variation of these time-averaged variables. Beginning with the view of local climate as little more than the annual course of long-term averages of surface temperature and precipitation, the concept of climate has broadened and evolved in recent decades in response to the increased understanding of the underlying processes that determine climate and its variability.

In turn, the climate system is defined as:

The system, consisting of the atmosphere, hydrosphere, lithosphere, and biosphere, determining the earth’s climate as the result of mutual interactions and responses to external influences (forcing). Physical, chemical, and biological processes are involved in the interactions among the components of the climate system.

• By the WMO (1992):¹⁸

C0850 climate – Synthesis of weather conditions in a given area, characterized by long-term statistics (mean values, variances, probabilities of extreme values, etc.) of the meteorological elements in that area.

C0900 climate system – System consisting of the atmosphere, the hydrosphere (comprising the liquid water distributed on and beneath the Earth’s surface, as well as the cryosphere, i.e. the snow and ice on and beneath the surface), the surface lithosphere (comprising the rock, soil and sediment of the Earth’s surface), and the biosphere (comprising Earth’s plant and animal life and man), which, under the effects of the solar radiation received by the Earth, determines the climate of the Earth. Although climate essentially relates to the varying states of the atmosphere only, the other parts of the climate system also have a significant role in forming climate, through their interactions with the atmosphere.

• By the IPCC (2013):¹⁹

Climate – 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 for averaging these variables is 30 years, as defined by the World Meteorological Organization. The relevant 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.

A useful observation is that all definitions use the term “average” (an exception is the definition by Lamb who uses the loose term sum total with the same meaning). Thus, by its definition, climate is a statistical concept. And since climate is not static but dynamic, it is better to think of it as a stochastic concept.

By scrutinizing these definitions, several questions may arise. A first one might be: Why “at least a 30-year period”? Is there anything special with the 30 years? Probably this reflects a historical belief that 30 years are enough to smooth out “random” weather components and establish a constant mean. In turn, this reflects a perception of a constant climate—and a hope that 30 years would be enough for a climatic quantity to get stabilized to a constant value. It can be conjectured that the number 30 stems from the central limit theorem (see section 2.17) and in particular the common (but not quite right) belief that the sampling distribution of the mean is normal for sample sizes over 30 (e.g. Hoffman, 2015)²⁰. Such a perception roughly harmonizes with classical statistics of independent events. This perception is further reflected in the term anomaly (from the Greek ανωμαλία, meaning abnormality), commonly used in modern climatology to express the difference from the mean. Thus, the dominant idea is that a constant climate would be the norm and a deviation from the norm would be an abnormality, perhaps caused by an external agent (a forcing). However, such a belief is incorrect. The examples given in this chapter support the idea of an ever changing climate.

Actually, this was pointed out almost 50 years ago by Lamb (1977):²¹

the view, regarded as scientific, which was widely taught in the earlier part of this century, that climate was essentially constant apart from random fluctuations from year to year was at variance with the attitudes and experience of most earlier generations. It has also had to be abandoned in face of the significant changes in many parts of the world that occurred between 1900 and 1950 and other changes since.

Clearly, however, even the later generations were not able to get rid of this “view regarded as scientific”, which remains dominant as manifested by the popularity of the term climate change (as if change is not inherent to climate) and reflected in the above definitions. It is noted, though, that the changing character of climate is recognized in the definition of the American Meteorological Society, which highlights the “slowly varying aspects of the atmosphere–hydrosphere–land surface system”.

A second question inspired by Climate Prediction Center’s definition is: Why would the climate taken over 30 or 1000 years be different? The obvious reply is: Because different 30-year periods have different climates. This contradicts the tacit belief of constancy and harmonizes with the perception of an ever-changing climate. With the latter perception, Herbertson’s idea (whose origin the Climate Prediction Center seems not to be aware of, referring to as an “old saying”) that “climate is what we expect, weather is what we get” can be reformulated as “weather is what we get immediately, climate is what we get if we keep expecting for a long time” (Koutsoyiannis, 2011).²²

As many of the above definitions refer to weather, it is useful to clarify its meaning, noting that it represents a popular notion, often used with respect to its effects upon life and human activities, rather than a rigorously scientific one. Interestingly, in its colloquial use in Greek and Romance (Neo-Latin) languages, weather is almost indistinguishable from time (Greek: καιρός; Italian: tempo; French: temps; Spanish: tiempo; Portuguese: tempo). On the other hand, in English and Greek, weather refers to short-scale variations in the atmosphere and is distinguished from climate; note however that in colloquial Spanish and Portuguese there is no such distinction (the term clima is used interchangeably with tiempo and tempo, respectively). In scientific terms, the definition given by the WMO (1992; footnote 18) is this:

W0410 weather – State of the atmosphere at a particular time, as defined by the various meteorological elements.

Based on the above discussion, here we attempt to give a definition of climate, which is used in this book, in a hierarchical manner (avoiding circular logic) starting from the concept of the climatic system, as follows:

• Climatic system is the system consisting of the atmosphere, the hydrosphere (including its solid phase—the cryosphere), the lithosphere and the biosphere, which mutually interact and respond to external influences (system inputs) and particularly those determining the solar radiation reaching the Earth, such as the solar activity, the Earth’s motion and the volcanic activity.

• Climatic processes are the physical, chemical and biological processes, which are produced by the interactions and responses of the climatic system components through flows of energy and mass, and chemical and biological reactions.

• Climate is a collection of climatic processes in a specified area, stochastically characterized for a range of time scales.

According to this latter definition—and given that the term process means change (Kolmogorov, 1931),²³ climate changes by definition. Thus, there is no need to define or use the term climate change; actually, this latter term, which appeared in literature only after the 1970s, serves non-scientific purposes (Koutsoyiannis, 2020a,b, 2021)²⁴. Change occurs at all scales (Koutsoyiannis, 2013)²⁵, and there is nothing particular about any specific one, like the commonly assumed 30-year scale. By studying long observation series of atmospheric and hydrological processes, one would see that the only characteristic scale with clear physical meaning is the annual. Beyond that there is no objective “border scale” that would support a different definition of climate. The above definition includes all scales beyond the annual, thus leaving out the smaller scales (e.g. of several minutes or days) to be associated to weather.

The stochastic characterization, appearing in the definition of climate, includes all statistics used in other definitions, such as averages, variability, extremes, etc., and collectively encompasses all related concepts of the scientific areas of probability, statistics and stochastic processes (Koutsoyiannis, 2021; footnote 24).

The main distinction between weather and climate is this. While weather, according to its definition by WMO (1992; footnote 18) which is kept unchanged here, refers to a particular time, climate refers to the entire climatic process, throughout all times.

As stated in the WMO (1992; footnote 18) definition of climate quoted above, the typical use of the term climate relates to the atmosphere only, leaving out the other parts of the climatic system. However, since the climatic system includes the hydrosphere, there is no reason to exclude the hydrological processes from the climatic processes. Therefore, our definition includes these, and to emphasize their inclusion, the term hydroclimatic has been used even in the title of the book. This provides additional clarity, but it is also a pleonasm since the hydrosphere is already included in the climatic system and water is, in fact, the most important driver of climate (Koutsoyiannis, 2021; footnote 24).

Update 2025-01-31: I received comments from colleagues that their antiviruses block the link to Substack and/or to my web site. Therefore, I provide alternative links below:

• On ResearchGate.

• On Internet Archive.

• On the publisher’s (Kallipos) official site (doi: 10.57713/kallipos-1) [Currently it contains edition 3 and it may take a couple of months before they update it with edition 4].

Those who prefer a hard copy may feel free to print the pdf file, or alternatively order a print copy in colour through my web site if they can afford the cost of colour printing.

1. See Digression 2.A: What is sapheneia? in the book for details.

2. The same root has the modern Greek word κρασί for wine. Yet the term is still in use today in Greek for derivative names related to climate such as εύκρατος (well-tempered, temperate) and ευκρασία (eucracy).

3. [Aristot. Mete., 362b.17] «…ὅ τε γὰρ λόγος δείκνυσιν ὅτι ἐπὶ πλάτος μὲν [τὴν οἰκουμένην] ὥρισται, τὸ δὲ κύκλῳ συνάπτειν ἐνδέχεται διὰ τὴν κρᾶσιν, -οὐ γὰρ ὑπερβάλλει τὰ καύματα καὶ τὸ ψῦχος κατὰ μῆκος, ἀλλ’ ἐπὶ πλάτος, ὥστ’ εἰ μή που κωλύει θαλάττης πλῆθος, ἅπαν εἶναι πορεύσιμον, —καὶ κατὰ τὰ φαινόμενα περί τε τοὺς πλοῦς καὶ τὰς πορείας·»

“… theoretical calculation shows that [inhabited Earth] is limited in breadth, but could as far as climate is concerned, extend round the Earth in a continuous belt; for it is not difference of longitude but of latitude that brings great variation of temperature, and if were not for the ocean which prevent it, the complete the complete circuit could be made. And the facts known to us from journeys by sea and land also confirm the conclusion…” (English translation by H.D.P. Lee, Harvard University Press, Cambridge, Mass. USA, 1952).

4. In his Commentary on Aratus (Ιππάρχου των Αράτου και Ευδόξου φαινομένων εξηγήσεως; Shcheglov, 2007).

5. Shcheglov, D., 2007. Hipparchus’ table of climata and Ptolemy’s geography. Orbis Terrarum, 9.

6. [Strab. 1.1] «πάντες, ὅσοι τόπων ἰδιότητας λέγειν ἐπιχειροῦσιν, οἰκείως προσάπτονται καὶ τῶν οὐρανίων καὶ γεωμετρίας, σχήματα καὶ μεγέθη καὶ ἀποστήματα καὶ κλίματα δηλοῦντες καὶ θάλπη καὶ ψύχη καὶ ἁπλῶς τὴν τοῦ περιέχοντος φύσιν.»

“Every one who undertakes to give an accurate description of a place, should be particular to add its astronomical and geometrical relations, explaining carefully its extent, distance, degrees of latitude, and ‘climate’—the heat, cold, and temperature of the atmosphere.” (English translation by H.C. Hamilton, and W. Falconer, M.A., 1903)

7. [Strab. 2.3] «αὕτη δὲ τῷ εἰς τὰς [πέντε] ζώνας μερισμῷ λαμβάνει τὴν οἰκείαν διάκρισιν: αἵ τε γὰρ κατεψυγμέναι δύο τὴν ἔλλειψιν τοῦ θάλπους ὑπαγορεύουσιν εἰς μίαν τοῦ περιέχοντος φύσιν συναγόμεναι, αἵ τε εὔκρατοι παραπλησίως εἰς μίαν τὴν μεσότητα ἄγονται, εἰς δὲ τὴν λοιπὴν ἡ λοιπὴ μία καὶ διακεκαυμένη.»

“In the division into [five] zones, each of these is correctly distinguished. The two frigid zones indicate the want of heat, being alike in the temperature of their atmosphere; the temperate zones possess a moderate heat, and the remaining, or torrid zone, is remarkable for its excess of heat.” (English translation by H.C. Hamilton, and W. Falconer, M.A., 1903). Notice the use of the Aristotelian crasis (κρᾶσις) in the term εὔκρατοι (temperate) zones.

8. The following definition appears in Moxon (1700)*: “Climate, From the Greek word Clima. of the same signification; it is a portion of the Earth or Heaven contained between two Parallels. And for distinction of Places, and different temperature of the Air, according to their situation; the whole Globe of Earth is divided into 24 Northern, and 24 Southern Climates, according to the half-hourly encreasing of the longest days; for under the Equator we call the first Climate: from thence as far as the Latitude extends, under which the longest day is half an hour more than under the Equator, viz. 12 hours and an half, is the second Climate: where it is encreased a whole hour, the third Climate: and so each Northerly and Southerly Climate respectively hath its longest day half an hour longer than the former Climate, till in the last Climate North and South, the Sun Sets not for half a year together, but moves Circularly above the Horizon.”

*Moxon, J., 1700. Mathematicks Made Easie: Or, a Mathematical Dictionary: Explaining the Terms of Art, and Difficult Phrases Used in Arithmetick, Geometry, Astronomy, Astrology, and Other Mathematical Sciences … J. Moxon, at the sign of Atlas in Warwick Lane.

9. https://books.google.com/ngrams/graph?content=climatology.

10. Herbertson, A.J., 1907. Outlines of Physiography, an Introduction to the Study of the Earth, Arnold, London, UK.

11. Thus, Herbertson appears to be the father of the famous quotation “climate is what we expect, weather is what we get”, often attributed to Mark Twain. What Twain has actually written, attributing it to an anonymous student, is “Climate lasts all the time and weather only a few days”; see https://quoteinvestigator.com/2012/06/24/climate-vs-weather/.

12. Köppen, W., 1918. Klassifikation der Klimate nach Temperatur, Niederschlag und Jahreslauf, Petermanns Geogr. Mitteilungen, 64, 103-203.

13. Stamp, L.D., 1957. Major natural regions: Herbertson after fifty years. Geography, 42(4), 201-216.

14. Lamb, H.H., 1972. Climate: Past, Present, and Future, Vol. 1: Fundamentals and Climate Now. Methuen, London, UK.

15. https://w1.weather.gov/glossary/index.php?letter=c

16. https://www.cpc.ncep.noaa.gov/products/outreach/glossary.shtml#C

17. http://glossary.ametsoc.org/wiki/Climate

18. WMO (World Meteorological Organization), 1992. International Meteorological Vocabulary. WMO, No. 182, Geneva, Switzerland, https://library.wmo.int/doc_num.php?explnum_id=4712.

19. IPCC (Intergovernmental Panel on Climate Change), 2013: Annex III: Glossary [Planton, S. (ed.)]. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [ed. by Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley]. Cambridge University Press, Cambridge, UK, and New York, NY, USA.

20. Hoffman, J.I., 2015. Biostatistics for medical and biomedical practitioners. Academic Press, London, UK.

21. Lamb, H.H., 1977. Climate: Past, Present, and Future, Vol. 2: Climatic History and the Future. Methuen, London, UK.

22. Koutsoyiannis, D., 2011. Hurst-Kolmogorov dynamics and uncertainty, Journal of the American Water Resources Association, 47 (3), 481–495, doi: 10.1111/j.1752-1688.2011.00543.x.

23. Kolmogorov, A.N., 1931. Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann., 104, 415-458. (English translation: On analytical methods in probability theory, In: Kolmogorov, A.N., Selected Works of A. N. Kolmogorov - Volume 2, Probability Theory and Mathematical Statistics, ed. by A.N. Shiryayev, Kluwer, Dordrecht, The Netherlands, 62-108, 1992).

24. Koutsoyiannis, D., 2020a. Revisiting the global hydrological cycle: is it intensifying?. Hydrology and Earth System Sciences. 24, 3899–3932, doi: 10.5194/hess-24-3899-2020.

Koutsoyiannis, D., 2020b: Rebuttal to review comments on “Revisiting global hydrological cycle: Is it intensifying?” (Interactive comment on “Revisiting global hydrological cycle: Is it intensifying?” by Demetris Koutsoyiannis). Hydrol. Earth Syst. Sci. Discuss., doi: 10.5194/hess-2020-120-AC1.

Koutsoyiannis, D., 2021. Rethinking climate, climate change, and their relationship with water. Water, 13 (6), 849, doi: 10.3390/w13060849.

25. Koutsoyiannis, D., 2013. Hydrology and Change. Hydrological Sciences Journal, 58 (6), 1177–1197, doi: 10.1080/02626667.2013.804626.