An empirical approach to prove the theory

As in the case with analogies made with the atmosphere, there is no question of entering into fine details, into the mechanisms that facilitate or restrict the transfer of water (gradient, ground, erosion, vegetation etc.), but to envisage the dynamic on an overall basis. The angle is very large and the method is empirical. The researchers gathered and compared the average partitioning of rainfall into evaporation and run-off in river basins all over the world (America, Africa, more local data also such as the Ourthe), to search and verify if this distribution corresponded to the maximum or not. The method was backed up by laboratory work. “The principle is meant to be universal”, says Benjamin Dewals. “That it has been verified in large spaces is one thing but it must also be able to be observed on very small scales. We therefore experimented with water flow in small samples over half a cubic metre of ground”. This approach made it possible to observe flow in a very detailed way, while seeking to verify again whether this distribution operates in such a way that the power is at a maximum level.

An enigma that has not been resolved for half a century

At the end of the 1960s, a Russian climatologist by the name of Mikhail Budyko observed the evaporation from a large series of river basins in order to place them on a graph according to two units of measurement. The evaporation was divided by the total precipitation on the vertical axis and the potential for maximum evaporation on the horizontal axis. In other words, if an infinite amount of water was available, this axis would represent what could have been evaporated in accordance with solar radiation. “The scope of possibilities is constrained by two asymptotes. On one hand, the evaporation can be close to an infinitesimal level of the total quantity of precipitation, but would never be able to exceed it. There cannot be more evaporation than the existing water. On the other axis, the evaporation cannot be higher than the thermal energy that the sun allows”.

Mikhail Budyko therefore represented, by points, the average data for each of the river basins studied. These points placed on the graph progressively formed a curve which today bears the name of the researcher. What is astonishing, is that these points aggregate around this curve which is also relatively close to the two asymptotes. As explained above, it is normal that no point should be found beyond the two asymptotes. “But the big question is why there is no point present in the space located between the curve and the horizontal axis. Theoretically, it is quite possible. We could observe all kinds of river basins which would have very heterogeneous evaporation properties that would not be found on this curve”.

To date, nobody has yet succeeded in explaining why the evaporation properties of river basins are so neatly aligned. This is precisely the reason why the young civil engineer suggested the maximum power principle as an answer. “By mathematically imposing the constraints linked to the asymptotes and by applying this maximum power principle, we found that the Budyko curve applied to our river basins. There is therefore a coherence between this principle and our observations which we must continue to prove”, say the two jubilant researchers.

On studying the Budyko graph, the observer notices quite quickly that the points form a cluster rather than an alignment according to a single curve. The theories put forward were up to now based on ground cover. The extent of forests, for example should have an effect on the level of evaporation. But these theories have never been conclusive up to now. “In our mathematical model, we have explored other avenues. First and foremost, we tried to place the asymptotes in a situation of constant rainfall. A diagram of reality to simplify our calculations and already verify whether we were going in the right direction. But there is no such place as a region where it rains all the time. We therefore introduced a seasonal dynamic of rainfall and temperature to simulate rainy and sunnier periods where the evaporation would vary accordingly”. As soon as this dynamic was introduced into the model, the results tended to point toward the cluster. This could signify that the slight variations around the Budyko curve can be explained by changes in precipitation and temperature, implying that soil cover and climate variable are correlated.