Return from the universal to the particular

The tool which closely associates the Budyko curve to the maximum power principle, could therefore help to better predict the evaporation from river basins. However, it is not yet operational. Each point on the graph corresponds to the average precipitation and evaporation from a river basin over several years. Resolution in time and space rem    ains imprecise. “Our publication is only a first step. If we succeed in verifying that the maximum power principle is correct, we will be able to apply it on a much smaller scale while taking account of the real dynamic of each region and particular events etc.” A second drawback for the moment is the fact that the model only makes it possible to predict one of the three factors relative to the cycle of precipitation and evaporation. With two unknowns, it is currently impossible to determine the part played by the flow and seepage factors. It is therefore difficult to predict the impact of climate variations on the supply of rainwater to rivers.

Two birds with one stone

Apart from the desire to demonstrate the universal character of the principle, it was precisely to compensate for these two approximations that the researchers carried out a series of very small-scale laboratory experiments. These ground samples offer the possibility of observing their behaviour in detail and therefore water flow, as well as evaporation. The experiment, which is quite simple, is nothing but a hydrological version of the atmospheric transfer of heat between the equator and the poles.

Two reservoirs were placed side by side and were separated by a ground sample a metre and a half in length. Only the left reservoir was supplied with water from the top, in order to simulate rainfall. On the bottom on the external edges of the reservoirs natural water loss (by evaporation and seepage) was simulated by a tap. The equivalent of thermal energy rediffused into space and which is not kept in the atmospheric system. At the start of the experiment, the water strikes a compact ground. A high resistance prevents the deployment of maximum power transfer. As in the atmosphere, mechanisms will ease this resistance. Here it is not a question of winds or properties associated with air. The processes are different. “One of them, which we are trying to simulate in this experiment, is internal erosion. The water will progressively displace the grains of soil and dig channels. The bigger these arteries are, the more rapid the transfer to the other reservoir will be and the more powerful the transfer will be. Conversely, if these channels become too big, the resistance will become almost non-existent. The water level progressively balances out between the two basins and the volume diminishes until it disappears completely. Between the two extremes, at a given moment, there is a situation where the water flow reaches a maximum power level. The objective of the experiment is to verify whether, as the maximum power principle predicts, these erosion mechanisms will stop developing when the system gets close to this state”.

Currently the results are promising, but experiments need to be repeated to avoid all possible biases. If the approach develops in such a way as to systematically involve the predictions of the maximum power principle, the researchers will obtain an extra element of proof that their theory works. More importantly, they will be able to develop a means of analysing very precise facts about river basins in detail on a case-by-case basis, and to combine the evaluation of two of the ways in which water is transferred. Evaporation on one side with the help of the Budyko curve and water flow on the other following laboratory experiments. “We will then be able to predict the evolution of evaporation and flow of rainwater, but also seepage, because we will only need to subtract from the total precipitation evaporation and water flow to obtain the seepage level. The methodological and theoretical work will still be long, but we will then be able to envisage a practical application of the model”.