River flows are far from being well estimated on a planetary scale and the task is absolutely not easy, according to our partner The Conversation.
The SWOT satellite, which will be launched in the fall of 2022, will make it possible to measure the height of the water surface of rivers for the first time, for rivers wider than 100 meters and over 90% of the globe.
This analysis was conducted by Jerôme Monnier, professor of applied mathematics at the National Institute of Applied Sciences in Toulouse.
Fresh water is vital for life, for our societies and cannot be substituted.
Economic developments, agriculture, industries and growing demography are creating tensions around this limited resource, all the more so because of climate change.
Agriculture accounts for 70% of freshwater consumption worldwide (90% in some countries), industry 19% and domestic use only 12% (much of which is due to household uses such as washing -linen, dishwasher, watering, bathroom and a very small part is related to the drink).
To date, 1 in 2 inhabitants of our planet live in areas affected by severe water shortage for at least one month a year.
France is also experiencing tensions around the use of water on its own scale.
Following the dry and hot winter and then spring of 2022, the prefecture of the Alpes-Maritimes, for example, had to place two thirds of its municipalities (including several large cities) on "drought alert" for several months, from the end of Winter.
Seen from the angle of natural risks (which overall are three times more frequent in 2020 than in the 1975s), “too much water” also represents a significant danger.
Floods represent almost half of the risks with, for the year 2021 alone, more than 50 major events and more than 80 billion dollars in damage.
These findings are worsening and will continue to worsen with climate change.
The water cycle is still poorly understood and the flows poorly quantified, including surface flows (runoffs) that flow towards the seas via hydrographic networks (rivers).
Rivers and rivers act as the veins of our territories.
Human activities greatly depend on the amount of water available and also modify the resource.
Typically, the policy of managing a dam to develop agriculture in a region can cause a shortage in a region further downstream.
Tensions between regions or users (agriculture, industry, populations) can then arise.
Examples include the various conflicts between Israel and the Arab states which are exacerbated by water scarcity (e.g. the disputes around the Litani in Lebanon or the small Yarmouk river in the Golan Heights), tensions between the countries bordering the Nile or the tensions between Mexico and the United States around the Rio Grande and the Colorado.
Estimating the flow of our planet's rivers is a major challenge both from a scientific point of view and from a socio-economic point of view.
Contrary to what we might think at first sight, flows are far from being well estimated on a planetary scale and the task is absolutely not obvious.
Mathematical measurements and models
The key variable to quantify surface water flows is the river flow Q (m3/s), Q = AU, A (m2) being the section across the river, U (m/s) the average speed In this section.
Flow measurements are available daily or even hourly in industrialized or densely populated regions of the world, for example in France via the Vigicrues network.
Conversely, in the less developed regions, the data are non-existent;
the flows are therefore very poorly estimated.
The estimation of the flow of a river is possible via mathematical models and numerical calculations.
On the other hand, to do this, you must know the depth of the river (h in the figure), the shape and nature of its bed and the topography of the surrounding terrain.
Without field measurement, the depth of a river remains unknown (how deep is the bottom?).
In addition, physical parametrizations such as the coefficient of friction of the flow on the ground are required to be able to use these numerical models.
A challenge then consists in knowing how to estimate mathematically, numerically the depth of the river h, its physical parameterizations and finally its flow Q, from the available measurements which are generally only the height of the water surface (and not its depth) at some points of the river.
Measuring water levels from space
To make up for our lack of field measurements, which is the case in the vast majority of regions of the globe, the spatial observation of rivers should soon be a solution.
The SWOT satellite, which will be launched in the fall of 2022, will make it possible to measure the height of the water surface of rivers for the first time, for rivers wider than 100 meters and over 90% of the globe, i.e. 213,500 sections. about ten kilometers.
The frequency of measurements will be around ten days (depending on the latitude of the river).
The spatial density of the measurement points will be approximately 250 meters.
From these measurements of water surface heights H (m), the scientific challenge consists in transforming these measurements into values of flow Q (m3/s), knowing that in non-instrumented areas, the speed of the flow and the depth of the river are unknown!
The multidisciplinary research carried out in applied mathematics, computational sciences, hydraulics and hydrology, at INSA – Institut de Mathématiques de Toulouse, INRAe, the University of Strasbourg – ICUBE and the CS group (CNES funding) aims to meet this scientific challenge: determine the depth of rivers and their flow from satellite measurements of water levels.
This challenge is about to be taken up on the basis of mathematical models of fluid mechanics (for example, the 19th century Saint-Venant equations) revisited in this particular multi-scale and observational context, mathematical methods of the optimal control type similar to those used to control the trajectory of a robot or determine the initial state of the atmosphere before a weather forecast,
These scientific advances are then implemented to obtain calculation algorithms.
Our algorithm called HiVDI for
Hierarchical Variational Discharge Inference
is available within our calculation software, which is certainly technical, but open to everyone (DassFlow research software).
The estimates currently obtained are based on purely numerical measurements from a CNES-NASA simulator of the future SWOT instrument and also three comparative algorithms (including two from the United States) with different methodologies.
Our "WATER" file
The results of the calculations make it possible to hope for obtaining an approximate estimate of the depth of non-instrumented rivers and above all a relatively precise estimate of the flow (to within about 30%), in near real time.
Such estimates should be available after a full year of satellite overflight, time for model calibration and learning.
Will these global river flow estimates help improve our knowledge of the water cycle?
On the interaction between large non-instrumented rivers and local ocean currents?
Will we be able to better estimate the impact of the different uses of certain large rivers (poorly or not at all instrumented to date) and therefore better manage them in the future?
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This analysis was written by Jerôme Monnier, university professor in applied mathematics at the National Institute of Applied Sciences (INSA) in Toulouse.
The original article was published on
The Conversation website
.
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Declaration of interests
● Jérôme Monnier has received funding from CNES to develop a flow calculation algorithm based on satellite measurements.
Its results are published in open peer-reviewed scientific journals;
the algorithm is available in open-source computing software.
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