Estimate for the first time the flow of rivers on a planetary scale with the SWOT satellite

The SWOT Satellite (NASA-CNES) launched on Friday 16 December will make it possible to measure the waters of the globe over 90% of its surface: the oceans of course, but also for the first time lakes, reservoirs and rivers. For rivers wider than 100 meters, the measurements will be provided with a spatial density of around 250 meters and a frequency of around 11 days.

From measurements of the height of the water surface of a river, a scientific challenge consists in deducing its flow Q (m3/s). River flows are very poorly known in regions of the world with very few instruments (for example the Amazon basin, the large Asian and African basins and many others throughout the world).

Rivers and rivers act as the veins of our territories. Estimating the flow of the rivers of our planet remains a major scientific challenge but also above all a socio-economic challenge.

Agriculture represents 70% of fresh water consumption worldwide (90% in some countries), industry 19% and domestic use only 12% (of which a large share is due to household uses such as washing machine, dishwasher, watering, bathroom and a very small part is related to the drink). Nowadays, 1 out of 2 inhabitants of our planet lives in areas affected by severe water scarcity for at least one month a year.

Human activities depend on the quantity of water available but 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) may arise. Many examples exist throughout the world (for example in the Middle East or in the south of the United States of America to name only these two regions of the world).

Europe is also experiencing tensions around the use of water; the summer of 2022 has shown it to us again. Of the risks also occur in connection with the opposite extreme, namely the “too much water” which is flowing. Floods represent almost the half the risk natural events with, for 2021 alone, more than 50 major events and more than 80 billion dollars in damage.

These findings are getting worse and will get worse with increasing climate change.

Mathematical models to estimate river flow

The key variable to quantify the water flows of a river is the flow Q (m3/s). We have the simple relation Q=AU, A (m2) being the section across the river, U (m/s) the average water velocity in this section, but these quantities A and U will not be measured from space.

Diagram of the calculation of the flow of rivers. Jérôme Monnier, Provided by the author

Accurate flow measurements are available daily (or even hourly) in industrialized regions only, for example in France via the Vigicrues network. Conversely, in less industrialized regions, the data is often non-existent or at best very approximate: the flows of rivers at a given time are globally very poorly known on a planetary scale.

When the flow velocity of a river U (m/s) and its depth H (m) are unknown, we cannot directly deduce its flow Q (m3/s) in a simple way. On the other hand, the flow can potentially be estimated via more complex mathematical models. This requires an estimation of the shape and depth of its bed and also physical parameterizations such as the coefficient of friction of the flow on the ground.

The difficulty of estimating these flows is increased when the altimetric measurements of the water surface (which therefore does not correspond to the depth H of the river) are only available at a few points on the river.

The revolution of SWOT measurements and the resulting algorithms

the satellite SWOT will therefore make it possible to “map” the water levels of rivers (more than 100 meters wide) of the globe at a frequency of approximately 11 days.

Intense multidisciplinary research was needed to know how to determine the flow of rivers from such measurements. These works (mostly Franco-American) lead to calculation algorithms implemented on computers. Five algorithms with different methodologies have been so far inter-compared based on“synthetic observations” from a SWOT instrument simulator which has just been launched.

The work carried out at the University of Toulouse and especially at INSA – Institute of Mathematics of Toulouse, the Midi-Pyrenees Observatory, in partnership with INRAe and the private group CS (with CNES funding) led to a available algorithm within a research software open to all scientific communities.

The first ingredients of such an algorithm are the Saint-Venant equations dating from the 19e century enriched with equations dedicated to this very particular observational context and resulting from our recent research. The following ingredients are mathematical methods of the optimal control type, similar to those used to control the trajectory of a robot or to determine the initial state of the atmosphere before a weather forecast, combined with probabilistic methods and learning methods machine (“artificial intelligence”).

The results obtained give hope for relatively accurate flow estimates (within 30%) in non-instrumented regions, in near real time.

Estimates based on actual SWOT measurements should be available (if all goes as planned) after a full year of satellite flyby, while the models are being calibrated.

These estimates of river flow on a planetary scale should contribute to improving our knowledge of the water cycle, contribute to the improvement of numerical models of floods but also of droughts, make it possible to better estimate the interaction between large (non-instrumented) rivers and local ocean currents, to better estimate the impact of the different uses of large non-instrumented rivers, including cross-border ones, and also to contribute to the water management policies of many statements based on global and open knowledge.


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This article is part of the series “The great stories of science in open access”, published with the support of the Ministry of Higher Education, Research and Innovation. To find out more, please visit the page Openthescience.fr.The Conversation

Jerome MonnierUniversity Professor, Applied Mathematics, INSA Toulouse

This article is republished from The Conversation under Creative Commons license. Read theoriginal article.

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Estimate for the first time the flow of rivers on a planetary scale with the SWOT satellite


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