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Velocity and celerity - studying the invisible

“…The invisible is not the opposite of the visible:

the in-visible is the secret counterpart of the visible”


Maurice Merleau-Ponty. Visible and invisible, 1964



When it rains, we can follow water drops until they reach different surfaces, and keep checking out water movement on the surface. But what happens to water when it moves through the soil?

Much of our work in hydrology is focused on the movement of rainfall through a watershed – and we have explained the apparently contradictory quick rise of streams after rainfall and the long time (months, years even!) that water resides in catchments using the concepts of velocity and celerity. The difference between velocity and celerity and their relationship is one of the ultimate challenges of modern hydrology. Velocity and celerity are both linked to the concept of “speed”, but the terms are quite specific. In hydrology, we borrow the “hydraulic” definition of celerity, which goes somewhat like this: it is a measure of the impact of a perturbation on a channel. When it rains, in the soil we have a similar effect: water residing in the soil gets “pushed” by the “new” water coming in rain form. The result of this is that we can quantify the “push” with which water infiltrates in the soil during a rainfall event. This is called celerity, and it depends on how much water resides in the soil in the first place, and how much space there is yet to be filled during such “pushing”. Now, the measure of the movement of this new water entering the soil is different. Such new water will have a range of velocities depending not only on the amount of water that already occupies the space, but also how big the pores are, and how easy it is for water to move through them.

Ultimately, we can say that celerity is responsible for increases and decreases in stream discharge (the hydrograph), while velocity controls how old is the water reaching the stream at a given time.

So why do we need to keep these measures separate? Predicting the hydrograph response (celerity), given a certain amount of rainfall, can be done quite easily with modern modelling frameworks. However, equifinality is always around the corner: models can be parameterised in many ways to make a good approximation of the hydrograph, so which parameterisation is actually happening? I think of equifinality as a number of possibilities. From A I can reach B by taking different paths. Now, each path is different as some may be longer than others, some nicer than others, etc., but the point is that there is more than one way to get from one point to the other, they are all possible. In the same way, the water that contributes to the rise of a stream can come from different parts of the area conveyed to that stream.

When we are interested in measuring water in the soil, we have an additional issue to solve: water “disappears” to our eyes when it infiltrates in the soil. The invisibility of water inside the soil makes measuring things more difficult, but also more interesting.

To measure how much water comes from which part of the catchment, we need to design good experiments that allow us to measure velocities as well as possible, to try to understand which is the path that is taken by water. In order to do this, we can artificially apply water, but we need to know how to track the water we are adding. This is usually done by means of substances that can be dissolved in water, in particular salt tracers.

We performed experiments in this way, and as often happens, we found out that all our efforts brought little (that was 2014, my heart-breaking Experiment 1). Experiment 2, in 2015, one year of experiences later, produced a dataset to work with.

My PhD work has a lot to do with the invisibility of water moving through the soil.






















One-dimensional sketch of a schematic soil box showing the difference between celerity and velocity estimated in this paper. The response to the sprinkling event using traced water (a) is shown. A wetting front is generated as a consequence to the pressure given by the water input (b). A process of displacement moves the water stored in the soil until reaching the measurement point (c1). Bypassing flow occurs when traced water moves through preferential flow reaching the measurement point in correspondence with, or even “before”, the wetting front (c2).

From: Scaini, A., Audebert, M., Hissler, C., Fenicia, F., Gourdol, L., Pfister, L., Beven, K.J., 2017. Velocity and celerity dynamics at plot scale inferred from artificial tracing experiments and time-lapse ERT. Journal of Hydrology 546, 28–43. doi:10.1016/j.jhydrol.2016.12.035

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