Topology Aligned Least Cost Routing Model for Canals

Abstract

In developing the infrastructure facilities such as irrigation canals and road networks, topography acts as a significant enabler or constraint. Contour maps and low resolution DEMs have been used by Irrigation engineers and planners to assess the canal routing options which is time consuming and requires repeated evaluations. So, there is a need to develop robust path planning algorithms, including least cost routing, that takes the topographic and engineering constraints while providing potential canal routing paths. Some recent works have attempted to develop algorithms on synthetic data sets but have not been scaled up on high-resolution data sets, limiting their practical use. This article discusses the problem of canal route analysis and proposes a least-cost route model (LCRM) for canals between two points, given the grid-based Digital Elevation Models (DEMs), a unit cost of construction per length, cost of lift to raise water along the surface of the terrain up to a height of 10 meters, set of coordinates the resultant flow needs to pass-through. This work develops two generic models namely, Gravitational Flow Model (GFM) where the flow is unidirectional and under the force of gravity; and Lift Based Flow Model (LBFM) where antigravitational force or pumping is used to lift the water along the surface of the terrain. We present an optimised version of Lift based flow model as well to reduce the number of computations. By implementing and verifying the algorithms on real-world data sets, the correctness of these algorithms will be based on the Digital Chart of the World (DCW) data sets. The algorithm correctness values for 1KM resolution stand at 82.10%, whereas for 90 meters resolution stands at 82.08%. The average value stands out to be 82.09% proving that both the GFM and LBFM algorithms are very effective in practice. The study also advances the problem of LCRM by introducing a more complex problem that balances cost and distance considerations that is a trade-off between the cost and the distance. Multiple use-cases will be examined to explore this problem and establish its boundaries. The results of the trade-off between the cost and the distance show that for various cases of the terrain and the spatial scale of the data, the patterns tend towards the elliptical bounds, though they can have different patterns at some other parametric combinations.