A note on the climatic factors controlling the global distribution of vegetation

Geographical Reports of Tokyo Metropolitan University, 35, 21 -- 30 (2000).

                               Kooiti MASUDA


Major climatic factors that control the global distribution of vegetation are reviewed. They are summarized into three factors, namely the energy factor, the moisture factor and the chill factor.

Using the gridpoint data sets of climate (temperature and precipitation) and vegetation, the vegetation types are plotted on the two-dimensional plane composed of the energy factor and the moisture factor.

Key words: Vegetation, energy factor, moisture factor, chill factor, gridpoint climate data

1. General discussion

Energy factor

How climate controls the distribution of vegetation is a classical subject of physical geography. To explain it, Japanese scientists often employ the `warmth index' (WI) conceived by Jiro Kawakita (see Kawakita, 1999) and elaborated and published by Tatuo Kira (1949). WI is accumulated degree-months above 5o C. Holdridge (1947) defined the `average biotemperature', that is the annual average of climatological monthly temperature with values less than 0o C substituted by 0o C. He also considered that this variable is proportional to annual total potential evaporation. Potential evaporation at a certain location is the amount of evaporation from a hypothetical wet surface with other near-surface meteorological condition being equal as it is. This definition is, however, not complete. Since the `condition' to be equated may be various, there are many variants of the definition.

Budyko (1971) considered that the annual mean surface net radiation is one of critical variables. Since in the annual average the surface energy balance over land is essentially,

  net radiation = sensible heat flux + latent heat flux,
and the two terms in the right-hand side are positive in most cases, the net radiation may be considered as a kind of potential evaporation.

As Nogami (1990) demonstrated in the case of the Japanese islands, potential evaporation as defined by Thornthwaite's formula (Thornthwaite and Mather, 1955) is very well correlated with WI. Thus, potential evaporation, net radiation and accumulated temperature in the growing season may indicate essentially the same factor, namely the energy factor in the growing season.

Moisture factor

It is obvious that the form of vegetation depends on how much water is available as well as the energy factor. Usually, scientists employ observational data of precipitation. It does not seem to be the best variable, since if there is excessive precipitation most of water runs off quickly and it is not useful for plants in the neighborhood. However, data of other variables, such as soil moisture content, are not available globally.

It seems that the distinction of major types of vegetation (forest, grassland and desert) does not correspond to the absolute value of precipitation, but its ratio with potential evaporation (or some other index of the energy factor). Water is abundant if precipitation exceeds potential evaporation, and it is deficit otherwise.

This concept was already evident to climatologists around 1900. Many formulas were proposed (see Yazawa, 1989 for review). For example, Köppen (as summarized in Köppen 1936) equated the boundary between his arid (B) climate and other climates with a line of P = a T + b where P is annual precipitation, T is annual mean temperature and a and b are constants. Here, a T + b can be considered as the index of energy factor.

The climatic diagram of Walter and Lieth (Walter, 1973) compares 20 mm / month of precipitation with 10o C of monthly mean temperature on the same axis (origin set at 0 mm and 0oC).

Budyko (1971) defined the `radiative index of dryness' (RDI), that is the non-dimensionized ratio between net radiation and precipitation. He positioned types of vegetation on a two-dimensional plot composed of RDI and net radiation.

Holdridge (1947) made a honeycomb-like diagram, composed of two logarithmic axes of his `average biotemperature' and precipitation intersected with 60o angle. The third side of the equilateral triangle is the ratio between the two variables. In determining vegetation types, this axis seems to more important than the axis of precipitation.

Kira also introduced an index of dryness like P / (a T + b) when he discusses vegetation in the continental interior in his papers written in 1945 and reviewed by Yazawa (1989).

In summary, the index of moisture factor effective to determine vegetation types is something like the ratio between precipitation and potential evaporation.

Evaporation and productivity

Though the absolute amount of available water does not critically matter to the types of vegetation, it does matter to their growth rate.

According to Lieth and Box (1972), the net primary productivity (NPP, production rate of organic matter by plants except its own consumption) can be empirically explained by actual evaporation. The actual evaporation was calculated by Thornthwaite's formula, which is bucket-like water budget calculation with precipitation and Thornthwaite's potential evaporation as inputs. Uchijima and Seino's (1987) results may be explained similarly, though their formula is based on net radiation and RDI.

This strong dependence of NPP on evaporation may be explained from the fact that the plants growing on land must evaporate (transpirate) water in order to perform photosynthesis, and also in order to keep the leaf temperature low enough under sunshine. Over-simply speaking, land plants may be considered as such heat engines that the sole heat sink being evaporation into the atmosphere (Tsuchida, 1978).

It should be noted that in warmer climates (the energy factor being large) the rate of decomposition of organic matter is also high. The form of vegetation largely depends on the amount of organic matter existent at any given moment, which is essentially determined by the balance between the two rates of production and decomposition. Hence the ratio is more important than the absolute values in controlling the forms of plant life.

Chill factor

Woodward (1987) also tried to explain the global distribution of vegetation by means of climatic variables. His emphasis is on the fact that freezing of water in the cells is crucial to plants. Experimental studies have been done by Akira Sakai (see Sakai and Larcher, 1987) among others. To explain the distribution of types of vegetation, Woodward puts this factor (minimum temperature in winter) first, the moisture factor (similar to that discussed above) second. Woodward gives the energy factor in the growth season comes only the third priority, when he needs it to explain the boundary between tundra and taiga (or the tree limit in the cold region).

Prentice et al. (1992) made a scheme of determining types of vegetation based on climatic variables. Though not exactly the same, the concept is very similar to Woodward's. This scheme has been often combined with the atmospheric general circulation model in the assessment of the consequence of global warming as well as in the simulation of Quaternary paleoclimates.

Strictly speaking, both the winter coldness and the energy factor in the growing season should have some effects on plants. Since the two variables are considerably correlated, it may be difficult to decompose the effects of them. Nevertheless, this decomposition seems to be an important step in order to predict changes of vegetation according to those of climate.

Data analysis


Here, I wish to demonstrate to what extent vegetation types can be explained by the two factors, the energy factor and the moisture factor, as conceived by Budyko (1971) and Holdridge (1947). I utilize gridded data sets of both vegetation and climate, where the world is divided into grid boxes.


Selection of variables

For vegetation, such a data set that describe the form (tree or grass, evergreen or deciduous, etc.) of the dominant members of the ecosystem, rather than the taxonomy (species, families, etc.) is chosen.

For climate, two factors are chosen. The moisture factor is represented by annual precipitation. This choice is because of data availability. The energy factor is represented by annual potential evaporation. In this paper, I use the formula of potential evaporation according to Holdridge (1947) as a crude approximation. It is the `average biotemperature' multiplied by 60 (mm / year)/oC. The number is rounded, because this is an approximate formula.


For data analysis, a graphical method is used, following suggestions by Cleveland (1985). The most basic method of multivariate data analysis is the scatter-plot. In this case, we have two quantitative variables (potential evaporation and precipitation) and one qualitative variable (vegetation type). I decided to plot symbols representing the vegetation type on a plane with the two quantities as the axes. However, since potential evaporation and precipitation have considerable correlation, the symbols cluster along a narrow region near the y = x diagonal. It is better to chose the difference or the ratio between the two quantities. In this study, the ratio between potential evaporation and precipitation is chosen, following the discussion in Section 1. This ratio is the reciprocal of the `moisture index' used by Thornthwaite and others, and is equivalent to Budyko's RDI if net radiation can be replaced with potential evaporation. The orientation of plots is chosen to be consistent with Budyko's. The abscissa is the ratio, and the ordinate is potential evaporation. The scaling of the abscissa is made to be logarithmic (base 2), unlike the linear scale used by Budyko, in order to have relatively uniform density of points. In this plot, $x$ means the logarithm (base 2) of potential evaporation divided by precipitation; x = +1, +2, +3, etc. means that potential evaporation is twice, four times, eight times etc. as large as precipitation, and x = -1, -2, -3, etc. means that that it is one half, one fourth, one eighth, etc.



For vegetation, the data set compiled by Matthews (1984) is used. It is included in the Global Ecosystem Database Disc A published by the U. S. National Geophysical Data Center in 1992. Though this is not the only such data set, its merit is that the method of compilation is relatively well described (Matthews, 1983). One out of 31 natural vegetation types (except water surfaces) is specified for the each of 1 degree latitude / longitude grid boxes. The system of classification follows UNESCO (1973), somewhat simplified, and augmented with `desert' and 'ice'. The left part of Table 1 shows this classification. Also, for each type, the count of grid boxes and the area relative to the whole surface of the earth are shown.

In this study, the classification is tentatively generalized into 10 types, as shown in the right part of Table 1. This basically follows the principal classes of UNESCO (1973). Though the classification generally corresponds to the common sense of present geographers, one thing should be noted: Matthews classified the larch forest (needleleaved deciduous forest) in eastern Siberia as No. 16, `cold-deciduous woodland'. Accordingly, I included it in the generalized class (e), `woodland' (see following Figure 2 (e)). Since the density of trees is smaller there than in evergreen taiga in western Siberia, this classification may be justified.

Matthews's data set additionally contains the intensity of cultivation expressed in five classes.

Temperature and precipitation

For temperature and precipitation, the data set of New et al. (1999) is used. It is available from the Climatic Research Unit, University of East Anglia through the Internet http://ipcc-ddc.cru.uea.ac.uk/). It contains climatological monthly values at grid-points over land except Antarctica on a 0.5 degree latitude / longitude grid. The grid-point values are obtained from observations at stations, with smooth `surface' fitting in a three-dimensional space (longitude, latitude and elevation). Therefore, the regionally and seasonally variable lapse rate is taken into account realistically where enough data is available. This is (theoretically) better than those which do not take elevation into account explicitly (such as Legates and Willmott, 1991), or those which assume a constant lapse rate (such as Leemans and Cramer, 1990). The period of observation is 1961 -- 1990 as long as appropriate data are available. From this data set, I sub-sampled every other row and every other column in order to obtain the same resolution as the vegetation data set of Matthews (1984).

Further screening

It is difficult to assign natural vegetation to places where the land is totally cultivated or urbanized. Therefore, the grid boxes where the intensity of cultivation is the highest degree (5) according to Matthews (1984) are excluded for further analysis.

In mountainous areas, both climate and vegetation information may have been interpolated from samples of observations not fully representative of the ensemble of vertical distribution. Therefore, such grid boxes where the standard deviation of 5-minute grid elevation in a 1-degree box is larger than 200 m are excluded for further analysis. The elevation values of the 5-minute grid has been calculated from those of the 30-second grid of the `GLOBE' data set (Hastings and Dunber, 1999). Of course, it is desirable to discuss the relationship between vegetation and climate in the vertical distribution. It seems to be, however, out of scope of the approach utilizing global-scale gridded data sets.


Figure 1 shows the scatter-plots for 10 generalized vegetation types. The abscissa is truncated at x = 4, though some points in frames (i), (h) and (f) actually have larger values. Figure 2 shows the geographical distribution of the grid-points in each type for reference.

The distribution of points are mutually overlapping. Nogami and Ohba (1991) showed histograms of vegetation types along the axis of WI, and defined `dominant types' by using relative abundance. Such analysis in a one-dimensional space may be extended to a two-dimensional space like Figure 1, if the two-dimensional plane is divided into cells and the density of points in the cells are compared. It will be a subject of near future study.

Here, some characteristics of the scatter-plot is described subjectively.

The scatter of points can be divided into relatively warm climate (potential evaporation greater than about 200 mm / year) and cold climate. The former may be divided into humid climate (x < 0) and dry climate (x > 0). The distribution of points for woodland (e), shrubland (f) and desert (i) vegetation are each clearly separated into two groups: one in cold region, the other in dry and relatively warm region. Grassland (h) seems to fill the gap between the two (cool, dry region).

In humid climate, forests are abundant. Tropical rain forest (a), other evergreen forest (b), deciduous forest (d) and needleleaved forest (c) exist in the decreasing order of potential evaporation.

In dry climate, as it gets drier (x larger), deciduous forest (d), woodland (e), shrubland (f) and desert (i) appears in that order. The region of grassland (h) overlaps woodland (e) and shrubland (f), but if the climate is cool (potential evaporation around 500 mm / year) grassland is more abundant than woodland.

In cold climate, as it gets colder (potential evaporation smaller), woodland (e) and shrubland (f), tundra (g), desert (i) and ice (j) appear in that order. The distinction is not good, probably because potential evaporation (at least its approximate formula of Holdridge) is not a measure of the critical climatic factor here. Winter chill factor should also be taken into account in the future study.


Prof. Michio Nogami gave me the opportunity to join the project `Geographic Information Systems for Environmental Change in Modern Japan' in FY 1990 -- 1992. The present paper is an entirely revised version of my report for that project (Masuda, 1992).


*: in Japanese. **: in Japanese with English abstract.

[Table 1] [Figure 1] [Figure 2] [index of published text of Masuda]