Original papers
Simulation of water distribution under surface dripper using artificial neural networks

https://doi.org/10.1016/j.compag.2017.10.003Get rights and content

Highlights

  • We introduced a new method of determining the wetting pattern under drip irrigation.

  • The method is based on Artificial Neural Networks.

  • The method returns trustful results very similar to HYDRUS 2D model.

  • The developed neural network is freely available for all readers.

  • Sensitivity analyses were performed to all input features that contribute to output variables.

Abstract

Predicting the wetting pattern of a dripper helps in the proper design of the drip irrigation system. An artificial neural network predictor model was developed based on the data from the well-tested model HYDRUS 2D/3D. The simulation data grid from HYDRUS was converted to simpler 3-variables vectors of wetting ellipses. The output vectors contain the radii in x and z directions and the center’s location in the z direction. The simulations were performed for several textural classes, infiltration times, emitter’s discharges, hydraulic models, and other features. After training the neural network, the testing dataset showed a correlation of 0.93–0.99, and the tested patterns showed high similarity to the HYDRUS outputs. Additionally, the paper provided solutions for the problem of simulating larger flow emitters where the flux exceeds the soil’s hydraulic conductivity and the problem of converting HYDRUS outputs to easy-to-use vectors of three parameters representing specific moisture content at a particular time. This work tried a set of 51 input variables’ permutations suggesting the best set of top results. The best trained neural network is freely available for the benefit of researchers and for future development. The sensitivity analysis of the input variables showed that the wetting pattern is mostly affected by time of infiltration, emitter discharge, and the saturated hydraulic conductivity. Future developments of the model are promising by increasing the training data extremes and possibly by adding more features like emitter’s depth for the subsurface drippers.

Introduction

Drip irrigation system offers the highest water conservation among all other irrigation systems. The main reason of such conservation is that it limits the wetted zone to about 30% of that the other systems do, hence, reduces deep percolation, surface runoff, and evaporation from the soil surface (Brouwer et al., 1988). The shape of the wetted part of the soil root zone is called the Wetting Pattern (WP). The WP is a partially saturated region with truncated-ellipsoid shape whose dimensions depend on several factors. These factors depend on the soil (texture, compaction, hydraulic conductivity, etc.), the plant (type, age, roots, etc.), the irrigation system’s features (dripper discharge, application frequency, etc.), and the climatic conditions (temperature, relative humidity, etc.) (Bhatnagar and Chauhan, 2008, Peries et al., 2007). Understanding the wetting pattern features is very important to achieve the reliable design of drip irrigation systems as well as for efficient management of natural resources (Lazarovitch et al., 2009, Lubana and Narda, 2001).

Several approaches to simulate the wetting pattern were performed; these were either empirical, analytical, or numerical (Kandelous and Šimůnek, 2010a). Empirical approaches use regression tools to derive an equation based on the results of well-controlled experiments (e.g. Malek and Peters, 2010). Analytical approaches use mathematical approximations to the modeled phenomena so that the governing equation can be solved with some easy calculations (e.g. Cook et al., 2003, Kandelous et al., 2008). On the other hand, numerical approaches (Arbat et al., 2013; e.g. Šimůnek et al., 2011) use the same governing equation as the analytical approaches, but they solve it numerically (by methods like finite element or finite difference) with almost no approximation or simplification. Unlike numerical approaches, both analytical and empirical approaches are fast and easy to solve, but their results are less precise than the results of the empirical approaches. Additionally, it worth to notice that the analytical models are useful in understanding principles than other approaches, but because of the spread of computers and other smart devices, the numerical methods became much more attractive as they could handle more complex and realistic situations (Kalogirou, 2007).

One of the most famous two-dimensional numerical models is the HYDRUS (2D/3D) software package (Šimůnek et al., 2011). The model is a finite element model for simulating the two- or three-dimensional movement of water, heat, and multiple solutes in variably saturated media. The model numerically solves the Richards equation for saturated–unsaturated water flow and convection–dispersion type equations for heat and solute transport. HYDRUS was well-tested by many investigators for surface or subsurface drip irrigation simulation (Skaggs et al., 2004, Cook et al., 2006, Arbat et al., 2008, Kandelous and Šimůnek, 2010a, Kandelous and Šimůnek, 2010b, Ramos et al., 2012, Abou-Lila et al., 2013, Elnesr et al., 2013, Liu et al., 2013). The good results of HYDRUS validation increases its reliability and trustfulness especially for no-plant simulation (Mmolawa and Or, 2003, Zhou et al., 2007)

Despite the benefits of the numerical solutions, they are not always easy-to-use approaches. They are, however, very sensitive to the boundary and initial condition, they may be unstable if over-relaxation occur, they may have difficulties with speed and possibility of convergence, the precision is directly-proportional to the required hardware resources, and it needs a higher level of human skills than the analytical models (Neufeld, 2010, Toombes and Chanson, 2011). Hence, we need a more robust approach that leads to more realistic and fast simulations; this might be achieved by the artificial intelligence approaches. In these approaches, the models attempt to act like the human brain that collects several input features that frequently appear together, and link them to the result or output through a complex nervous system that learns and improves its efficiency over time. This imitation to the human brain is called the artificial neural networks (ANN). Several works were published showing attempts to simulate the in-soil flow of water and solutes.

One of the earliest attempts was the work of Li et al. (2004) who combined laboratory experiments with the ANN in simulating the distribution of nitrate fertigated by a dripper; they concluded that the ANN models are reasonably accurate and can provide an easy and efficient means of estimating nitrate distribution. Lazarovitch et al. (2009) used the ANN approach in predicting water distribution around subsurface drip irrigation. They used HYDRUS simulations (Šimůnek et al., 2011) as the reference to water distribution, and they tested three scenarios of input-output combinations concluding that prediction using moment analyses is probably the most robust and gives an adequate picture of the subsurface dripper water distribution. Later, Hinnell et al. (2010) used this approach to develop a Microsoft Excel’s model that depends on moment analysis to draw contours that are a close representation of the actual wetting pattern.

The objective of this work is to develop a different neural network’s approach to simulating the wetting pattern from a surface dripper, with the various timings of infiltration and redistribution, different soil textural classes, different soil-water retention models, etc. Additionally, we aimed to use the developed model to evaluate the contribution of each variable to the drip wetting pattern.

Section snippets

Governing equations of water movement in soil

We used HYDRUS (2D/3D) package to simulate soil-water distributions under a dripping point source. The model numerically solves the Richards equation for variably-saturated water flow in soils. The Richards governing equation in two-dimensional coordinates is as follows (Tian et al., 2011):θt=xK(h)hx+zK(h)hz-K(h)z-S(h)where θ is the volumetric water content [L3 L−3], t is the time [T], h is the soil water pressure head [L], x is the horizontal coordinate [L], z is the vertical

The predictions of the artificial neural networks

After training all the neural networks, the best networks were selected as indicated in Sections 2–4, Section 5, Section 6. The trained network for MFG 9 is illustrated in Fig. 7; where the lines between neurons indicate weights, and the line’s thickness is directly proportional to the weight value, while the color of the line shows the sign of the weight (blue = positive, red = negative). This is a quick method to know the importance of each of the input variables, a more descriptive method is

Conclusions

An innovative solution for predicting the dimensions of wetting contours of surface drippers was introduced. The solution used artificial neural network method as a reliable and robust method for predicting the complex nonlinear systems. Our data were gathered from a well-verified numerical model which is HYDRUS 2D/3D model. In this paper, we showed our solution to some simulation problems using HYDRUS, like the instability problem when the emitter’s flux is higher than the soil’s saturated

Acknowledgements

The work was financially supported by King Saud University, vice deanship of research chairs.

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