Beyond the Köppen-Geiger Climate Classification System, Part I: Extensions and Alternatives

For a while now, I've been using the Köppen-Geiger climate classification system for my climate tutorials and explorations, for much the same reason it's commonly used for studies of Earth's climate; it's a flexible and widely-recognized standard that sums up the most important climate distinctions without getting too lost in fine details (for the most part).

Still, some of the climate states we've been exploring are clearly stretching the limits of what the Koppen system can sensibly describe, with extremes of high temperatures or seasonal variability far beyond what we see on Earth. I've had a fair few people ask if I would consider adding new categories to the Koppen system, or propose full alternative systems of of their own, and so far I've generally declined for two reasons:

  • I want these results to be directly comparable to Koppen maps already made for Earth, and not require casual readers to get acquainted with the specifics of any new system I invent.
  • The Koppen system is tuned based on observations of how climate affects vegetation cover on Earth; any modification would presumably be intended to better reflect vegetation cover on other planets, but because we can't actually observe vegetation on any such planets we have no way to tune those modifications.

When I started this post, I thought this would stay my position, but the more I looked into the matter, the more I began to think there are actually some reasonable improvements that could be made. And, unsurprisingly, that line of investigation ballooned a bit in scope, so I'll be tackling the question of alternatives to the Koppen system in three parts: first, we'll explore modifications to the Koppen system or whole alternative climate classification systems proposed by climate researchers throughout the history of the fireld, seeing what lessons we can take in terms of how these systems apply different climate parameters or choose to make different sorts of distinctions; second, I'll attempt to construct my own bioclimate classification system based on these lessons; and third, I'll see how some of the exotic climate states we've explored previously are represented by this new system.

(Quick terminology note: properly it's the Köppen or Köppen-Geiger classification system, but I'll just be saying Koppen because it's shorter and pasting in the umlaut without Blogger's text editor messing up the font is a pain).

Biomes and Climate Classification 

First off, let's clarify our goals: for the most part what we really want to know is what biomes a planet will have, meaning what types of life—vegetation in particular—are dominant within different areas. There have been numerous schemes to classify Earth's biomes, with this being a typical breakdown (that site also includes a more detailed breakdown into ecoregions, which are more geographically constrained such that they contain not just similar types of life, but similar specific species); but see also this approach, which is a bit more detailed in some cases but doesn't attempt to divide areas into exclusive zones. You may have also seen this popular map before, which so far as I can tell was made by one Wikipedia user as a synthesis of various sources (and they did a fair enough job of it, to be clear):

The trouble of course is that these systems are designed to describe the biomes observed on Earth rather than predict the biomes we might see elsewhere (they're also often a bit specifically tuned to the particular varieties of life present on modern Earth, so won't apply well to alien worlds or even past Earth before the Cenozoic).

Climate classification systems are based on the assumption that biome distribution is (for the most part) controlled by climate, and so we should be able to predict the most likely biome in a location based just on some key parameters of its climate; even on an alien planet with life unrelated to that on Earth, we can expect (however tentatively) that similar environmental influences will create similar ecological niches. All the systems we'll discuss today consider two main types of climate factors influencing growing conditions for plants in any area: thermal factors and water factors.

Thermal factors generally means temperature, but this impacts plant growth in two primary ways: first, tolerances: Certain plants can only tolerate certain ranges of temperature before suffering damage. 0 °C is the most important tolerance threshold, as sub-freezing temperatures cause frosts that can damage exposed soft leaves, stems, and shallow roots, though some plants may be able to tolerate brief nighttime frosts but not sustained subfreezing temperatures. To a lesser extent, some tropical plants may not tolerate temperatures below around 10 °C well, and some mildly frost-tolerant trees may be damaged at temperatures well below freezing.
 
Second, temperature informs the growing season: Broadly speaking, plants grow best between about 20 and 30 °C, with very little growth below 10 °C and essentially none below 0 °C. In seasonal climates with winter frosts, leaves and soft stems may have to be lost in winter, or a smaller plant may attempt to complete its entire life cycle in one year and rely on its seeds surviving winter; the longer and warmer the growing season between winters, the more plants can invest in larger leaves and other soft structures, with the expectation that they can recoup the cost of growth before they have to lose those structures to conserve nutrients in winter; a very short and cool growing season inversely encourages more gradual growth between years and more structures that can tolerate the cold without being lost. Hence the general spectrum of Earth from broad-leaved evergreen trees that can keep their leaves all year without fear of frost, to deciduous trees that grow large leaves but then lose them in winter, and coniferous evergreen trees that retain small needle-like leaves through freezing winters (with a parallel gradient in short-lived undergrowth towards smaller varieties that require shorter growing periods and can better tolerate early frosts).
 
The water factor represents availability of water in the soil, also necessary for growth, but with the complication that water level in the soil depends not only on input of water from precipitation (rain and snow) but also loss of water to evapotranspiration (combined surface evaporation and transpiration through the plants' own leaves). Evapotranspiration generally increases with temperature, so warmer areas generally require more precipitation to ensure sufficient water availability, but timing of precipitation also matters: in a climate with substantial temperature variation, more precipitation will be needed in summer than in winter to balance evapotranspiration, and if all precipitation arrives in one short burst, it may all evaporate and leave the ground dry for the rest of the year. Precipitation generally correlates with temperature, offsetting the importance of evapotranspiration variation a bit, but not always, so you'll see that some classification systems essentially try to track a precipitation seasonal cycle separate from the thermal seasons.

Though these mechanical considerations are taken into account to varying extents by different systems, ultimately they're all still based on observational data; climate data is compared to biome distribution and the researchers try to work out what ranges of the former best match up to the latter. They can be extrapolated to other contexts, much as a we can look at observations of star mass and luminosity and create formulas to predict luminosity for fictional stars based on mass. But, much as with those formulas, this approach is only really reliable within an intended range of use. Most of these climate classification systems are intended for use on Earth and so make various assumptions about what range of climates you can expect to encounter, what exact type of climate data you might have available, and what parameters can be assumed to correlate or ignored entirely.
 
In particular, a lot of these systems, especially the older ones, assume that direct observations of factors like minimum temperature or evapotranspiration are not available, and so rely on proxies: other parameters that are assumed to correlate to these factors well enough to be taken as direct indicators of them. The assumed correlations are, again, tuned based on observational data on Earth, so may not apply well to other planets. One common issue we'll see is that average annual temperatures are used as a proxy for overall temperature range based on some assumed seasonal pattern, or monthly temperature averages are used as proxies for maximum and minimum temperatures based on assumed daily variation, but these assumptions won't hold particularly well for planets with very different seasons or days.

But even that issue aside, biomes are not actually solely determined by climate; soil quality, topography, fire frequency, and herbivory by animals all influence vegetation distribution as well (though many of these factors do correlate to climate to some extent, but often not perfectly). Thus no climate classification system will perfectly match biome distribution (and many biomes are divided by gradual gradients rather than hard boundaries anyway), which has led to something of a division in the philosophy of how climate classification systems are developed and what each climate zone is meant to represent:
  • What we might call boundary systems still attempt to correlate climate directly to biomes, with each zone taken to correspond directly to a specific biome and predict its distribution, such that the boundaries seen on the climate map represent real boundaries between biomes in reality—even if we have to accept a certain margin of error and "fuzziness" to these boundaries in practice.
  • Alternatively, what I'll call gradient systems abandon any such direct correspondence and instead use zones as indicators of the overall gradient in major thermal and water factors; there's still some correlation to biomes in that, for example, areas indicated as wetter might be expected to be lusher, but an individual zone doesn't correspond to a single biome, and the boundaries between zones aren't assigned any particular importance either; instead, zone boundaries are used to show the progression from drier to wetter or colder to warmer areas with a bit more visual clarity than something like a color gradient might provide, much as a topographic map might use contour lines to show elevation.
Much has been said over the years of the relative advantages of each; boundary systems may sometimes be misleading where their boundaries don't match well to actual biomes, but gradient systems may be less intuitive to read and fail to give us a clear picture of what to expect specific areas to actually look like.

Beyond that, it's perhaps best to compare these approaches by seeing them in practice; so with all that in mind, let's go through a few of these systems and see how they approach these challenges and what limitations that imposes:

Köppen-Geiger Climate Zones 

The Koppen system was developed over a series of papers from 1884 to 1961, the final couple papers published after Koppen's death based on his notes by his colleague Geiger, hence the double-barreled name. It determines all climate zones based on monthly averages of temperature (typically taken to be near-surface air temperature at about 2 meters height) and precipitation, using combinations of these factors to define 5 main climate groups split into 31 individual zones—though various simplified schemes with ~14 main subgroups are fairly common. It is, of course, a boundary system, and easily the most famous of the type, though it's not hard to find areas on Earth where the boundaries don't align terribly well with actual observed biomes. This has given it something of an ambiguous double-identity over time, where even though it was constructed based on observed correlations between climate and biomes, it is not always presented or used solely as a system for predicting biomes, but sometimes as a system for classifying general climate conditions that is conveniently related to biomes but not necessarily bound to replicate them.

A fairly familiar map, though I think this uses the 18 °C average threshold for thermal arid zones. Wikimedia
 
But if we are primarily concerned with its performance in predicting biomes, there is a logic to how it classifies climates, though not always a wholly intentional one; the system was originally constructed with a largely empirical approach, where zone definitions were chosen based on how well they correlated to biomes, even if the reasons for that correlation weren't clearly known at the time (there was also some ambiguity in how some zones were defined in Koppen's original papers, but a consensus on standard interpretations has emerged over time). But with the benefit of modern knowledge, we can see clear functional relationships in retrospect:

First, the distinction between arid (B) and non-arid zones is determined by essentially using temperature as an evapotranspiration proxy, calculating an aridity threshold that represents a total precipitation level low enough relative to evapotranspiration for the region to be dry most of the year, with adjustments for distribution of precipitation throughout the year to account for greater evapotranspiration in summer. Arid zones are then subdivided into steppe (BS) zones, which might still get enough water for widespread vegetation of some kind, and true deserts (BW), too dry for much growth.
 
The remaining groups and many of the subdivisions are defined by thermal limits, using monthly temperatures as proxies both for tolerances and the overall shape of the growing season, in particular relative to the 10 °C threshold below which most growth is assumed to stop:
  • Tropical (A) zones have all months above 18 °C, warm enough both to ensure that even brief nighttime frosts are unlikely and that good growth is sustained year-round.
  • Temperate (C) zones have their coldest month between 0 and 18 °C, such that winters are cold enough for growth to slow and for winter frosts to be possible, but sustained freezing temperatures are unlikely.
  • Continental (D) zones have at least one month below 0 °C, such that there will be sustained frosts and potentially temperatures low enough to damage some moderately frost-tolerant plants.
  • Polar (E) zones have all months below 10 °C, such that there is essentially no growing season.
Then, within C and D zones:
  • Hot-summer (Xxa) zones have at least one month above 22 °C and 4 above 10 °C, indicating a long, warm growing season.
  • Warm-summer (Xxb) zones have cooler summer peaks but still at least 4 months above 10 °C, so a more moderate but still reasonably long growing season.
  • Cold-summer (Xxc) zones have no more than 3 months above 10 °C, so only a brief growing season which may thus not sustain deciduous plants and tall grasses.
  • D zones then also have extremely cold (Dxd) zones, with no more than 3 months above 10 °C and 1 below -38 °C, cold enough to damage even some hardy trees, such that even conifers must drop their needles in winter.
Arid B zones are generally assumed to have too little water for sustained growth anyway, so growing season concerns are ignored, but a 0 °C threshold for the coldest month is still used to divide hot (BXh) and cold (BXk) varieties to reflect different frost tolerances. Some sources still use an 18 °C threshold of annual average temperature for this division, which is perhaps intended to include some indication of growing season intensity as well, or the point where desert plants with C4 photosynthesis, which is advantageous in hot, dry conditions, dominate over those with more common C3 photosynthesis.

E zones are also subdivided into tundra (ET) zones, with at least one month above 0 °C, allowing for some slow growth, and ice cap (EF) zones, below 0 °C in all months and thus having effectively no growth and likely becoming covered in ice.

Orthogonal to these thermal divisions are a set of divisions based on seasonal precipitation patterns, essentially reflecting the degree to which water is available during the growing season:
  • Monsoon (Xw) zones have wet summers, ensuring plentiful moisture levels during the growing season, even to the point of being hazardous, encouraging adaptations to tolerate flooding or avoid collecting water on leaves.
  • Mediterranean (Xs) zones have wet winters but dry summers, such that there's little rain during the growing season but plants may still have sources of groundwater, flowing water, or internally stored water to rely on, allowing for more substantial growth than arid zones but still causing patchier vegetation cover and encouraging adaptations to conserve water.
  • Humid (Xf) zones have some but not excessive rainwater available during growth.
The exact definitions vary (as do naming conventions), but though Xw and Xs zones are often defined in seemingly symmetric ways (usually comparing the wettest month in one thermal season to the driest in the other), they're really reflecting different phenomena and so have different thresholds, and Mediterranean adds an extra requirement that summers also be dry in absolute terms (otherwise it doesn't matter that winters are wetter, because vegetation can still rely on immediate sources of water from precipitation through summer rather than having to conserve water from winter).

Tropical zones essentially lack substantial thermal seasons (on Earth anyway), so the relative timing of rains isn't too important—it's always warm enough to grow—and they can be divided into a simpler system based on the regularity of the rains:
  • Rainforest (Af) with year-round rains.
  • Monsoon (Am) with some dry periods that must be tolerated but still enough overall rain to allow for substantial forests.
  • Savanna (As/Aw) with too little rain for dense tropical forests, but still more vegetation than seen in arid climates. This can be subdivided into dry-summer (As) and dry-winter (Aw) varieties, but again the distinction is usually unimportant when all months are warm enough for growth.
All in all, this scheme pretty well suits our purposes for a number of reasons:
  • Monthly average data for precipitation and temperature aren't too hard to produce; basically any GCM like ExoPlaSim or ROCKE-3D should be able to do it, and even if you can only do the hottest and coldest month of the year this is usually good enough to estimate zones if you're willing to make a lot of assumptions about how representative these months are of the whole seasonal cycle.
  • The system specifically checks seasonal extremes of temperature and precipitation rather than assuming their variation based on annual averages or other proxies, so it's somewhat flexible in allowing for different ranges and "shapes" of seasons.
  • The number and specificity of zones is fairly well tuned to show us a lot of detail without digging too deep into distinctions only important for the particular species of modern Earth.
Still, the system was simply not designed with application to other planets in mind, which leaves us with a number of quandaries in its application, several of which I've mentioned before:
  • The use of monthly averages makes it a bit ambiguous how different year lengths should be approached; if a planet has years half as long as Earth, should we split that year into 6 months to preserve month length or 12 months to preserve number of months per year? When testing for tolerances, my inclination would be to maintain month length, presuming that the relationship between monthly average and the actual extreme conditions depends to some extent on month length, or that brief excursions to extreme conditions may be tolerable—but when testing for type of growing season, I'm unsure if it would be more sensible to assume plants will adapt around different year lengths (a shorter year may mean less time to grow but also a shorter winter to survive) or if the absolute length of each growing season is always the most important. There's also presumably some minimum year length below which we should consider there to effectively be no seasons, but again it's hard to say where exactly that should be.
  • The system makes no distinctions in temperature above 22 °C and marks all areas with a coldest month above 18 °C as tropical or arid. On Earth this is fine as few non-arid regions have months much over 30 °C, but we've seen a few cases in our explorations of climates with summers reaching to 60 °C or more, which is high enough to be a serious hazard for Earthlike life, while still having more hospitable periods of year.
  • Similarly, defining the aridity threshold using temperature as an indirect proxy for evaporation works well enough within the intended range of temperature, but the formula used may not be tuned as well for very hot planets outside the original intended range of the Koppen system—and flat precipitation thresholds for Mediterranean and tropical zones may similarly not extend well to some extremes.
  • Though the system is fairly flexible in terms of the exact shape and range of seasonal variation, it still assumes a single seasonal cycle per year: one warm summer and one cold winter, as well as one wet period which will mostly align with one or the other of these thermal seasons. Planets with very high obliquity seem to show much more complicated seasonal patterns, with some areas having two warm periods and two cold periods per year, and others having two wet periods between a dry summer and winter. To a lesser extent, the system also tends to assume seasonality for all temperate regions, which may not always be true.
There's also various quibbles to be had about how well the system represents specific biomes or regions. These can often be somewhat subjective, but there's two I'd choose to highlight:
  • Though the driest areas are marked as arid, there's still a range of somewhat wetter semiarid climates not well represented here, which makes the interpretation of some zones fairly ambiguous; D zones in particular tend to cover a broad range from dense forests to open grassland, and Aw/As also covers a fairly diverse set of variously dry to wet or open to densely forested biomes (none of which correlate well to the As/Aw distinction).
  • At the same time, in other areas the D zones are somewhat excessively subdivided based on the overlap of seasonal precipitation and thermal classes, creating a number of rare subtypes that don't correlate to any particular biome distinctions.
At any rate, this hopefully gives us a bit more of a baseline to assess our potential alternatives. To help with that task, I've been working on a substantial rewrite of my koppenpasta script to make it easier to implement different classification systems and incorporate different data outputs. Though the updated script is not quite ready for public release, I can use it with some climate data of modern Earth to produce some maps of these different climate classification systems for easier comparison—note that this is averaged data for only land areas from 1981 to 2010,  and that the dataset included only average daily high and low temperatures for each month, but the average of the two seems to be a good approximation for monthly average temperature. Here is the standard Koppen-Geiger zones to start with, including As and using the 0 °C coldest-month threshold for dividing hot and cold arid zones:
 
I've added a function to the script to auto-generate map keys, which I'll be using for these maps, but it only includes zones which actually appear on the map, hence the lack of Dsd here; though it does manage to pick up a couple patches of Csc in the Rockies.

As the most popular climate classification system in use for near a century now, the system has accrued a lot of what we might call "Koppen apocrypha" over the the years, alternate interpretations of the somewhat inconsistent original texts or attempts to tweak the system to better address some of its shortfalls either globally or specifically tuned to the conditions of a particular region. The original papers themselves sometimes suggested a somewhat more complex system of water availability classifiers, including options for an autumn wet season or two distinct wet seasons, and a "fog" zone for deserts where frequent fog provides some moisture despite the lack of rain, but failed to provide strict standard for these and so they've rarely been used in practice. There are, however, a few more comprehensive attempts to overhaul the system that are worth noting here.

Köppen-Trewartha Climate Zones

This is a modification of the Koppen system, first published in 1966 but with various later refinements. It mostly focuses on increasing its detail in temperate and continental areas; the details vary by source (I'm mostly going by this one), but typically the main difference is the rearrangement of Koppen's C and D groups into 3 groups:
  • Subtropical (C), with at least 8 months above 10 °C.
  • Temperate (D), with 4-7 months above 10 °C.
  • Boreal (E), with no more than 3 months above 10 °C.
  • (Polar then gets bumped over to F.)
So essentially it's a scheme to get an even more detailed breakdown of growing season length to better reflect some biome distinctions within the mild climates, with the Xxb/Xxc distinction in Koppen also promoted to a group boundary along the way.

Comparison of the main subdivisions of the Koppen (top) and Trewartha (bottom) systems applied to Earth (note that the former uses the old -3 °C threshold for dividing C and D zones). Belda et al. 2014
 
Temperate zones are then subdivided into oceanic (Do) and continental (Dc) based on whether the coldest month drops below 0 °C, corresponding to Koppen's C/D division. The same distinction could also be applied to C and E zones, but on Earth at least Cc and Eo zones are fairly rare, though the latter is still sometimes included when coastal or highland patches of it are relevant. C and D can also be be divided into Xxa and Xxb zones with the same 22 °C threshold for the hottest month as in Koppen, though some authors go further and classify all zones based on their warmest and hottest months—10 levels of each, for 55 possible combinations (however many total zones that works out to after accounting for the reasonable temperature ranges that can be applied to each major type, I leave as an exercise for the reader).
 
Sometimes an additional highland (G or H) group is included, indicating areas where the main thermal grouping is different to what it would be at sea level, assuming a lapse rate of 5.6 °C, but a lot of recent applications exclude this; broadly speaking, plants don't care much what altitude they're at independent of the effect it has on thermal and water factors or soil quality.

The Xw/Xs/Xf zones are also applied from the Koppen scheme, but comparing rainfall over the entirety of the warm and cold halves of the year rather than just the extremes of each, and usually only applied to C zones, largely just because Earth's circulation patterns make heavily seasonal rain patterns rarer towards high latitude but also because the cold temperatures and thus low evaporation makes seasonal water availability less of an issue generally. This does, notably, make both Cs and Cw zones fairly rare, with the former excluding large areas usually considered Mediterranean biomes.
 
Trewartha also often includes a different aridity threshold for B zones (using a more continuous adjustment of the aridity threshold to seasonal precipitation rather than sharp categories) and sometimes excludes the Am zone, but really this is all just down to divergent evolution; these modifications could easily be applied back into Koppen, or some of the recent modifications of Koppen brought into Trewartha.
 
For my part, I've implemented Trewartha in koppenpasta with a simple 14-zone scheme, mostly following my main source above but I've added the Eo/Ec distinction and tweaked some of the colors for better legibility. I'll also add various options to apply elements of the Trewartha algorithm to Koppen or vice-versa.


Ultimately, if we don't bother with the numerous thermal subtypes then the overall picture it's showing us isn't all that different from what we get using Koppen, with the C/D line being the only genuinely new piece of information, but the greater emphasis on growing season length might be useful for some purposes, and trimming of the various continental subtypes makes for a cleaner result. Some of the minor improvements might be worth bringing into Koppen, though the difference they make is probably less than the inherent error in ExoPlaSim (and it looks like this might exacerbate ExoPlaSim's bias towards aridity in the tropics).

FAO Global Ecological Zones

This is a system developed by the UN Food and Agricultural Organization around 2010 to classify global forests which is mostly derived from Trewartha but with some oddities. The given definitions are a bit ambiguous in some places and the distinction between boreal forest and tundra is defined by direct observation of vegetation rather than climate data, so overall it doesn't quite constitute a functional climate classification system I could easily apply elsewhere.
 
But I thought it worth noting for its approach to aridity; rather than a single annual threshold for aridity, months are individually defined as dry if precipitation in cm is less than twice the temperature in °C—a common rule of thumb for dry conditions that roughly aligns with Koppen's aridity threshold if averaged over a year. Areas that are dry all year are defined as deserts (with a separate desert zone for the tropical, subtropical, and temperate groups rather than a separate arid group); areas with some wet months but where total annual evaporation still exceeds total precipitation (exactly how evaporation is determined isn't specified) are semiarid steppe; other tropical areas are divided based on the number of wet and dry months, similar to the division of colder areas based on growing season; and Mediterranean (or "subtropical dry forest") zones are defined by having a wet winter and dry summer, though exactly how that's determined is particularly ambiguous.

Paleoclimate Modified Köppen

This comes from a study investigating how well prehistoric Koppen climate zones can be reconstructed based on geological data. This data is usually insufficient to reconstruct the details of seasonal temperature and precipitation variation, as would be necessary to properly apply Koppen zones. As we've seen, climate models can be tuned to match geological data to attempt to reconstruct this data, but aren't fully reliable. This study attempts to create new definitions that best match the existing Koppen zones based only on the data that can be most reliably estimated for the past: average annual temperature, average annual precipitation, and temperature of the warmest month.

Modified Koppen definitions applied to modern climate data (top) compared to classical Koppen definitions (bottom); see the paper for zone definitions. Zhang et al. 2016

The result isn't a particularly close match, and they have to abandon the Xw/Xs/Xf categories for lack of good data on seasonal precipitation patterns, but it's an interesting attempt to rebuild these patterns from such limited data. It's not particularly relevant to our case, though; it relies heavily on assumptions about how annual averages relate to seasonal variation, and though publicly available climate model data is sometimes quite limited, I've yet to see a dataset that included temperature on the warmest month but not the coldest and with no associated monthly precipitation data.

Algorithmic Köppen-like Climate Zones

I include this more as a curiosity than a real consideration: One 2012 paper uses a computer algorithm to attempt to regroup the world's land area into 5 top-level groups, 13 second-level subgroups, and 30 third-level zones based on temperature and precipitation data, mirroring the breakdown of the Koppen system, but optimized to minimize variation of temperature and precipitation conditions between areas within each zone.

The algorithmically produced classification system; see the paper for definitions. Cannon 2012 

It's a bit interesting to see the way the algorithm placed more focus on tropical and arid regions at the expense of the temperate regions, but ultimately climate classification systems are, again, an attempt to predict biome distribution based on climate, and this study didn't use any vegetation data either as input to its algorithm or for assessing the results, so I feel like it's largely missing the point (though to be fair to the author, they seemed more interested in the potential for such a system to better describe the effects of climate change).
 
A number of other papers have also used similar approaches for classifying climate, most often using k-means clustering, which attempts to divide areas into clusters where each point in the cluster has parameters closer to the average for that cluster than that of any neighboring cluster, but with the same issue that the results tend not to correlate too well to actual biomes and won't apply well to other worlds.

Thornthwaite

Moving on from the direct Koppen derivatives, we'll start with a system that's fairly obscure today but worth starting with because it was conceived from the outset as something of the gradient system antithesis to Koppen's boundary system thesis, developed concurrently in the 30s and 40s in direct response to Koppen's growing popularity.

The main innovation over Koppen is an attempt to better represent the water balance of a region by eschewing any proxies for evapotranspiration and instead attempting to directly measure potential evapotranspiration (PET), the total evapotranspiration that would occur if unlimited groundwater was available. This was originally determined based on monthly averages of temperature and daylight hours, but modern methods based on the Penman equation are generally more reliable and easier to apply to other planets. PET can then be compared directly to precipitation to determine an overall water balance in each month; where a region has higher precipitaiton than PET, there's a surplus of water which will run off into rivers and the sea; where precipitation is lower, there's a deficit of water which will reduce soil moisture.

Without getting too caught up in the thorny (har har) math, monthly measures of surplus or or deficit are used as the system's water factor, while PET on its own is used as the thermal factor (because higher temperatures cause a greater PET). Specific climate zones can then be classified into two main types based on annual averages of these factors, with subtypes based on their seasonal variation:
  • Moisture Index, based on the balance of total annual surplus and deficit.
    • Seasonal Variation of Effective Moisture, based on the total deficit of water in the dry season for wet climates and surplus in the wet season for dry climates—thus giving some sense of how much the climate seasonally diverges from its average conditions implied by the moisture index—as well as which of summer or winter are drier (the seasons presumably determined by temperature or PET).
  • Thermal Efficiency, defined by total annual PET.
    • Summer Concentration of Thermal Efficiency, defined by the portion of annual PET in the 3 hottest months.
Though some of the earliest versions of the system seem to indicate some ambition to correlate these climate types to biomes, ultimately this was abandoned over further refinement in favor of a regular division of the parameter range into zones (e.g. each boundary between thermal efficiency types represents an increase in total annual PET by 142.5 mm), on the argument that this represented a more "rational" approach to classifying climate rather than potentially subjective attempts to link climates to biomes.
 
Considering all the potential types and subtypes, this works out to over 3,000 possible combinations, though not all of them may be terribly likely, and with a bit of grouping together of the more similar types we can perhaps pare that number down to 360. The main idea here is really not so much to divide up the planet into a recognizable few climate zones, but more to have shorthand designations for climates describing their main features. But because of that inability to produce an intuitive map and the somewhat arcane algorithms for determining individual zones (a major drawback before easy access to computers), it simply never gained much popularity. Even within more niche communities of climate research, such specificity never proved particularly useful; broad categories like "mediterranean" or "rainforest" can be useful for stating generalities, but to describe the particular climate of a specific region, it's just easier to directly state ranges of temperature and precipitation rather than having to learn and remember a complex shorthand, and in the internet age we can use intuitive visual charts like this to sum up the patterns of seasonal variation:
 
Note the clear wet-winter, dry-summer pattern of a Mediterranean climate. Wikimedia.

The Thornthwaite-Feddema variant developed in 2005 addresses some of these issues by dropping the many subtypes and simplifying the algorithm, resulting in 36 main types that can be more easily mapped, each a simple combination of a specific range of moisture index and PET. This can optionally be combined with 12 types of seasonal climate variability, indicating both the degree of variability and whether it is primarily caused by thermal or moisture variation.

This does balloon the count of potential individual types to 432, but again the emphasis is on the overlap of different forms of climate variation rather than the importance of individual combinations of factors. A clear way to represent these differences on one map is still an unresolved issue, however; I'm not a big fan of the hatching system attempted in the map above. For my implementation I've just chosen to make the main types and variability types separate output options.

I'm not sure why I got so much more Torrid area than Feddema's map, probably different measures of PET
 
In terms of lessons to take from Thornthwaite, I appreciate the motivation to improve on Koppen's lackluster handling of water balance, but I think this may be an overcorrection; depending on how you interpret the implementation, it either ignores the influence of temperature outside of its impact on water balance or effectively uses PET as a proxy in reverse for temperature, neither of which are ideal. I'm also not quite ready to give up on boundary systems just yet, though there is still more to learn about implementations of gradient systems.

Holdridge Life Zones

This was developed around the same time as Thornthwaite, first published in 1947, and though it's not clear how much influence there was between them or from Koppen, ultimately Holdridge represents a somewhat more successful implementation of some of the same concepts, in terms of gaining widespread recognition and use. So in practice, it is the most popular alternative to Koppen. Definitions vary a bit, but I'll mostly be going by this paper. The system uses three parameters, all averaged across the year:
  • Biotemperature, which is based on average temperature but with all temperatures below 0 °C counted as 0 °C, and all above 30 °C counted as 30 °C, the idea being that photosynthesis largely stops outside this range so further variation beyond it matters little to life (some sources count temperature above 30 °C as 0 °C, but this will have odd results if we consider warmer worlds with regions spending long periods above 30 °C). This was originally sampled based on monthly average temperatures, but some newer studies have used daily averages.
  • Total precipitation, summed across the year.
  • Potential evapotranspiration ratio (PETR): potential evapotranspiration divided by total precipitation; so a PETR under 1 indicates an overall water surplus, and a value over 1 a deficit. Originally PET was estimated as biotemperature * 58.93, making this parameter directly determined by the other two, but again better methods of estimating PET have been developed since.
The main peculiarity (and source of headaches) of the Holdridge system is that it then tries to squash these 3 dimensions of variation into 2, by placing the 3 axes at somewhat odd angles. Each axis is divided into ranges on a log-2 scale (each division is at twice the value of the last) and each overlap of ranges of the 3 parameters roughly defines a life zone. Exactly how to handle cases where different parameters might not line up neatly into these categories is often left a bit ambiguous, but the clearest procedure I've seen is to essentially plot the position first on the PETR/precipitation grid and then project from that point directly up or down to the appropriate level on the biotemperature axis.
 
A typical chart of Holdridge life zones; not that they're classified based on the angled PETR and precipitation lines and the horizontal biotemperature lines, the "humidity provinces" indicated on the bottom don't correspond to any particular axis. Peter Halasz, Wikimedia

If we lump the polar desert zones together into one, this works out to 31 life zones in 6 latitudinal belts. However, the 12-24 °C belt is sometimes subdivided into warm temperate and subtropical belts along the frost line, where minimum temperature drops below 0 °C at least once most years, adding 7 life zones, and much like Trewartha, altitudinal zones due to drop of temperature with elevation are sometimes distinguished from latitudinal zones.
 
 
The result is something of a compromise between boundary and gradient systems; the choice of parameters, naming of individual zones, and use of the frost line for the temperate/subtropical boundary clearly reflect a hope that certain zone boundaries would correspond to specific biomes, but in practice many of the intermediate boundaries don't indicate any actual transition and just serve to show the overall gradient.
 
So far I've usually tended to just choose two axes—biotemperature and either precipitation or PETR depending on whether the latter is conveniently available—and plot life zones based on that, which is often a reasonable approximation given the ways PETR correlates to biotemperature and precipitation.  But for the koppenpasta update I decided to finally implement a 3-parameter approach based on the method I mentioned above: the vertical position of a region in the Holdridge chart is determined based on biotemperature, and then the horizontal position is determined based on the intersection on the oblique PETR and precipitation axes. But rather than trying to work out how this fits in the hexagonal grid usually used for Holdridge zones, I've settled for a more straightforward staggered rectangular grid.
 
Red lines showing the staggered grid used in koppenpasta over the standard hex-grid Holdridge chart, with black lines showing an example of how zones are determined based on biotemperature and the intersection of precipitation and PETR (with the star showing the resulting point, to be classified as warm temperate dry forest).

I also haven't implemented a warm temperate/subtropical distinction yet, as the Earth dataset I'm using doesn't include a convenient measure of the frost line, but there's a few conceivable ways that could be determined for ExoPlaSim data.

 
For our purposes, the main strength and weakness of the system is that, if we exclude the temperate/subtropical distinction, then only annual averages are required to mark zones. On the one hand this heavily relies on assumptions about how these average relate to overall patterns that won't work well for less Earth-like planets and can't distinguish different types of seasonal patterns like Mediterranean and monsoon seasons, but on the other hand it makes this system a convenient option where only annual data is available.

Whittaker Biomes

Not so much a complete classification model as a chart, so far as I can tell first published around 1970. That version was a bit of a rough sketch, but derivatives or charts like it are used fairly often in textbooks and the like to communicate the most basic concepts of climate classification, in particular that:
  • Biomes are determined primarily by the overlap of thermal and water factors of climate.
  • Precipitation requirements to sustain a given biome tend to rise with temperature (due to increased evapotranspiration).
  • Biome variety tends to increase with higher temperatures, partially because the range of precipitation values also typically increases (more evapotranspiration in hotter climates tends to generally increase precipitation).
 
There are many versions of this sort of chart, but most tend to be a bit abstract; the Whittaker biome chart is notable for specifying particular bounds of annual average temperature and total annual precipitation for specific biomes, implying the ability to classify and predict biomes based on these parameters. In practice this is somewhat tricky because I've yet to find a mathematical description of these boundary lines, so classification generally consists of placing data points on a chart and trying to match this to a reference image of the Whittaker biomes chart (and this also makes it unclear to what extent different renderings of the chart are consistent with each other).
 
I managed a rough implementation by taking a version of the chart from here, overlaying an excel chart of temperature and precipitation with axes scaled to match, placing data points as markers along each of the boundary lines, and then fitting a polynomial trendline to those points, which can then be used (along with some reasonably linear extrapolations outside the range of the chart) to classify specific points on Earth.
 
My rough fits overlaid on the reference chart.

The result is somewhat underhelming, generally seeming to underestimate the spread of tropical rainforest and overestimate that of woodland/shrubland. Temperate rainforest also ends up occupying very little space, which makes its inclusion a bit bizarre in this otherwise fairly spare scheme. It is perhaps worth noting that Whitakker's native North America is the continent best represented here, but that may reflect the data conveniently available at the time as much as any cultural bias.
 

Notably, the textbook I sourced the chart from included its own biome map that doesn't much resemble this, which seems to confirm that the chart is meant as more a conceptual guideline than a strict classification system.
 
One odd detail that is borne out, however, is the slight slant in many boundaries that implies that areas with higher precipitation should sometimes be classified into colder zones despite no change in average temperature; this seems to reflect that wetter areas tend to be closer to the sea or at least have more soil moisture, and so have more moderate seasons—and an area with a low average temperature needs more extreme seasons to ensure it has enough of a growing season to support forests rather than tundra.

Two-Parameter Köppen-Alike

Somewhat inspired by the Whitakker chart, I decided to add a feature to the koppenpasta update to chart out all a climate map's points by their average precipitation and temperature, with each point colored by climate zone.
 

What's notable is that many of the major boundaries in Koppen do seem to fall fairly close to straight lines on this chart, and so it might be possible to approximate a simplified set of Koppen zones based on annual averages alone. I gave it a go, sticking to straight lines to keep things simple and only including zones with clear regions they near-exclusively occupied.


And this can of course be applied back to the Earth data:
 
 

It's not terrible given the restrictions, but as per usual we're lacking some important distinctions due to the lack of seasonal data, and in general this approach has trouble distinguishing consistently cool climates such as in mountains from highly seasonal climates such as at high latitudes. In applying it to other worlds we'd also have to be wary of losing the assumed correlation between average values and seasonal variation. But it could have some of that same utility I mentioned for Holdridge, allowing you to make some broad guesses at the likely Koppen zones of a world in cases where you only have annual data to work from, so for that reason it's worth holding onto as an option.

IPCC Climate Zones

This is a system devised by the Intergovernmental Panel on Climate Change in 2006 to help estimate soil carbon content, with some slight refinement in 2019. Some of the chosen definitions seem to imply some inspiration from Koppen, but if so the algorithm has been substantially slimmed down, perhaps to make it easier to use for those unfamiliar with climate science and help ensure consistency.
 

It has 12 zones, divided into 5 thermal categories based mostly on Average Annual Temperature, except that the tropical category also requires no more than 7 days with frost and the polar and boreal zones are divided based on the average temperature of the hottest month (the same as tundra in Koppen), and then most categories are divided into a moist and dry zone based on whether Total Precipitation exceeds Total Potential Evapotranspiration. The tropical category is the odd one out, divided into wet, moist, and dry zones based on precipitation alone and then adding an additional montane zone based on elevation.

For my implementation, I've just dropped the tropical montane zone and the frost days requirements, neither of which are easily available in my dataset.
 

It's a somewhat curious result, not aligning particularly well with biomes, but that's not the stated intent so it's hard to judge how successful it is in its actual goals.

World Climate Domains

This one is quite recent, developed in 2020 as a proposed refinement to the IPCC scheme for for use in tracking conservation efforts. It dividedes the tropical category into tropical and subtropical and standardizes the water categories across all zones, with a tweaked moist/dry boundary and an added desert category, coming out to 18 total zones.

The result is a rather better match to biome boundaries. Various other issues I've mentioned for other systems still apply here, like the lack of seasonal data making it difficult to identify areas like Mediterranean or monsoon climates, and it still has somewhat poor resolution in semiarid regions, but regardless it feels proper to have such a straightforward system using this particular combination of parameters, which other systems like Thornthwaite and Holdridge seem to somewhat dance around.
 
I get the feeling some of the intended colors for this scheme lost their saturation in the process, but that's something you can mess with if you like.

The paper does then combine these with 4 terrain categories and 8 land cover categories, both based on direct observation, to assemble a final map of 431 potential ecosystems; but that's of course not much use to us here.

Worldwide Bioclimactic Classification System

Another quite recent system with very little widespread recognition, though not without reason. Though it doesn't appear directly derived from Koppen, it has a broadly similar approach in that attempts to classify climates based of monthly measurements of temperature and precipitation, using calculations that are all individually straightforward. However, in the process of trying to account for various special cases and complexities in the boundaries between biomes, the overall algorithm has become byzantine almost to the point of incomprehensible. Constructing a world map of bioclimate zones may require calculating over 100 different parameters, which are combined in various ways to determine 28 main bioclimate zones, as well as subsidiary classifications of thermotypes (indicating temperature but also latitude as a proxy for day length), continentality (indicating seasonal temperature variation), and ombrotype (indicating the relative prevalance of rain, snow, or drought).
 
The provided map seems to be scaled to work best as a wall poster rather than web image; to see it more clearly, follow the link and look towards the end of the pdf file. Rivas-Martinez et al. 2011
The system uses latitude as part of how it determines the major bioclimate types (and isn't fully symmetric across hemispheres), on the logic that this helps represent day lengths. For use on other worlds one could perhaps attempt to find other measurements of day length or sun exposure that correlate to these latitudes, but I've honestly already given up on any attempt to replicate the algorithm; for all that complexity, the resulting map doesn't appear to be all that better a match to actual biomes compared to the alternatives.

Woodward Vegetation Types

This comes from a 1987 paper that doesn't explicitly construct a climate classification system, but instead talks through an attempt to predict major vegetation types based on climate factors, using the better understanding of ecology developed since the days of Koppen, Thornthwaite, and Holdridge. It particularly highlights absolute minimum temperate encountered on the coldest nights of the year as a measure of thermal tolerances, though also uses month degrees as a measure of growing season to predict tundra distribution; the number of degrees C in each month with a positive temperature, summed across the year.

For the water factor, the paper discusses models of total water balance, but ultimately determines that in most cases grass and shrubland can be divided from forst using single total annual precipitation threshold of 600 mm for most cases and 400 mm for the coldest zones,  but for the hottest, wettest regions , evergreen and drought-decidious forests are divided based on whether total precipitation exceeds total potential evapotranspiration.
The paper assembles these factors to predict the distribution of 6 main vegetation types, though for my implementation I've read between the lines a bit and extended this to 8, and come up with some appropriate colors (which I'll admit maybe came out a bit garish). The minimum temperature data in my dataset doesn't quite correspond well to the absolute minimum Woodward had in mind, so I've borrowed an approach from the next system we'll discuss to estimate minimum temperature from coldest month average temperature.
 

With modern data, it's far from a perfect match—I'm getting the sense that a lot of old datasets may have overestimated precipitation—but paper poses this as a preliminary attempt, waiting on better data on actual vegetation cover to test the central hypothesis—that vegetation cover can be predicted at this level from climate factors alone—and refine the approach.

Prentice et al. BIOME1 Model

This comes from a 1992 paper, with much the same goals as the earlier Woodward paper but benefiting from more detailed data on Earth's biomes collected in the intervening years, and more explicitly constructing a complete set of predicted biomes.  The original paper didn't give this system a particular name; some later papers have referred to it as the BIOME1 model in retrospect because later models would be named "BIOME2", "BIOME3", etc., but that could be a somewhat confusing name so I'll mostly refer to it as the "Prentice et al." model.
 
Building on much the same concepts as Woodward, the authors identify three main parameters which directly influence patterns of vegetation growth and competition between plants:
  • Coldest month temperature as a measure of thermal tolerance, though explicitly as a proxy for minimum temperature, with the assumed correlation noted, so if minimum temperature data is available, it can be used directly. Warmest month temperature is also used to distinguish warm and cold deserts.
  • Growing Degree-Days (GDD) as a measure of growing season, similar to month degrees in Woodward: Each day is given a number of GDD equal to its average temperature in °C above some minimum base temperature (so with a base of 5 °C, a day averaging 20 °C would have 15 GDD), and this is summed across the year, excluding any negative results (so all days below 5 °C would just be 0 GDD). The idea is that the base temperature is the minimum temperature for growth, and then growth rate is assumed to increase linearly with temperature, such that the GDD sum represents the total possible growth during the growing season; which isn't quite true for individual plants but a reasonable approximation for whole ecosystems. This more direct measure of the growing season avoids having to juggle different measures of hottest month temperature or months with sufficient growing temperature as proxies, any of which are unreliable for different "shapes" of seasonal temperature change. This model measures GDD relative to a base temperature of 5 °C for most plants and 0 °C for some desert and tundra shrubs.
  • An aridity factor defined as the ratio of actual evapotranspiration (AET) to potential evapotranspiration (PET): Compared to Holdridge's PETR, this is somewhat more reliable indicator of water availability across different patterns of seasonal precipitation; PETR cannot distinguish between a climate with sufficient year-round rains and one with very heavy rains well above PET in one season but none in another, but AET can never exceed PET (excess precipitation above PET will store in groundwater or runoff into rivers rather than evaporate), so a dry season will always lower the average AET/PET ratio regardless of how much precipitation exceeds PET in the wet season. This also potentially accounts for water sources other than precipitation, like stored groundwater or river flow. The trouble is that AET may be difficult to measure on Earth, but various estimation methods are possible and climate models more typically include it.
(The paper also refers to soil data but only as part of how they estimate AET).

Rather than directly linking these factors to biomes, the paper instead focuses on plant functional types; groupings of plants with similar adaptations to particular climatological niches. The model estimates tolerable ranges for these parameters for 13 different functional types, with a sorting order to decide which types can coexist or will be outcompeted in cases where their ranges overlap (mostly favoring plants with more stringent tolerances requiring high temperatures and long growing seasons, on the assumption that these plants are more efficiently taking advantage of these conditions when they're available because they don't have to spend resources or make compromises developing tolerance to harsh conditions). This results in 17 possible combinations (9 dominated by a single plant type, 7 featuring more even mixes, and 1 ice/polar desert zone where all plant types are excluded), defining the predicted biomes.
 
Predicted biome distribution (the scan has not been kind to the colors but it was the only version I could find). Prentice et al. 1992

The result compares pretty favorably to real biome distribution, though still with a few oddities. Compared to Koppen, the system lacks a few finer distinctions such as between Mediterranean and other semiarid regions based on seasonal precipitation patterns, and the authors do suggest that better accounting for these patterns might improve accuracy in some areas. Some biomes like "Cold Mixed Forest" also end up covering a rather eclectic mix of different parameter ranges, essentially filling the gaps between other biomes. More broadly, this system is perhaps a tad overtuned to the specific plant types of modern Earth; though it might be a bit more flexible in reflecting different plant combinations that might appear in different climates of the recent past or near future, some of the divisions between different mixes of deciduous and coniferous forests or warm and cold desert shrubs may reflect particular evolutionary adaptations of modern plants, some of which are quite recent.
 
The choice of parameters also makes it a tad tricky to implement with other datasets, because measures of PET and particularly minimum temperature can vary depending on the exact methodology. To keep things simple, here I've stuck with using coldest month average temperature rather than absolute minimum, as in the original paper, and I've adjusted all aridity factor thresholds down by 0.05, as that seemed to give a better match to the original results. I may play around with some reference ExoPlaSim data to see if I can find a set of minimum temperature thresholds that work well there for any future use.

 
Still, I decided to discuss this system last because it seems to offer the best model to work from in terms of potential improvements over the Koppen system. It still draws that link between broad climate parameters and specific biomes, but it better identifies the parameters that have the most direct impact based on our modern understanding of plant ecology—and will be the most likely to have that same impact under the different circumstances of an alien world.
 
As mentioned, some later studies would iterate on the model, reducing the number of plant functional types but modelling their growth dynamics in more detail and choosing dominant vegetation type based on their success in maximizing growth rather than a proscribed sorting order. This is a more direct representation of how different biomes arise through the competition of different plant types, and might be intriguing to implement based on ExoPlaSim data at some point (though the in-built SIMBA vegetation system already works on fairly similar principles, but a bit simplified and with a single vegetation type), but it also requires many parameters tuned to the specific behavior of plants on Earth, which may or may not translate well to other worlds with their own evolutionary histories. In particular, how plant productivity might be affect by substantially higher CO2 levels is not clear. It may also be hard to adapt such intensive modelling of photosynthesis to different potential data sources.
 
So, though these later models ultimately gained more widespread use and recognition within academic circles, for our purposes this first version of the model is the one we should draw inspiration from, balanced well between models that are over-complex to the point of inscrutability or rely on detailed modeling assumptions, and simple system that try to reduce classification complexity but lose a lot of important information in the process.

Next Steps

If I dug deeper I could probably find a few more classification systems—I've skipped over several I encountered that were designed only for a specific region, and so can't be generalized to cover whole planets—but I think the sample we've found is sufficient to work from. In Part II, we'll finally put some of the lessons gained here into practice.

Comments

  1. AnonymousDecember 11, 2024 at 7:00 PM

    Great post! What would be the best climate system for a slow rotating planet (more than a month long days), especially if the planet also were to have an obliquity and/or eccentricity that is asynchronous with the day length? Also, what about planets in S-type binaries where the other star causes significant temperate differences to the overall climate?

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    Replies
    1. AnonymousDecember 11, 2024 at 7:01 PM

      *temperature

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    2. AnonymousDecember 11, 2024 at 8:12 PM

      Will you continue using the koppenscript moving forward?

      Delete

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