Controlling soil moisture is crucial in optimizing watering and crop performance, particularly for crops with high water demands such as Kiwi. Monitoring and simulating soil behavior are two key approaches to understand soil behavior. Proximal sensors are the most reliable way to monitor soil moisture. While in the past sensor costs limited their adoption, the progressive cost reduction makes now possible to properly capture moisture dynamics in the soil volume occupied by roots. Physically-based numerical models can be used to further understand soil moisture dynamics, but solely in an of-line manner due to their time-consuming simulations. We introduce PLUTO, a cost-efective solution that, starting from sensor data, leverages both Physically-based and machine learning models to build on-line moisture profiles for long-term watering optimization. PLUTO, relies on bi/tri dimensional sensor grids that proved to largely overcome the accuracy of previous profiles obtained with traditional sensor layouts. Besides, we provide an analysis of sensor importance that takes in consideration the trade-of between accuracy, number, and position in order to suggest a smart placement.
Controlling soil moisture is a crucial factor in optimizing watering and crop performance [
Dripper
Watered volume Alongtherow
Soil volume
Unwatered volume in soil composition, and (iv) exposure to atmospheric agents. The most reliable approach to monitor soil moisture consists of exploiting proximal sensors (i.e., installed below the ground to monitor soil moisture in the plant root zone). Typically, a single (0D) or a line of sensors (1D) are used for cost reasons. This limit the data precision since moisture varies in the soil volume.
Observed moisture data have been historically enhanced with the aid of Physically-based
models (i.e., numerical solutions that encode the physical laws of hydrological fluxes; e.g.,
HYDRUS [
To the best of our knowledge, there is no approach aimed at creating a fine-grained multidimensional representation of soil moisture given a sensor grid. In response, we introduce PLUTO1 [17]: a cost-efective solution that leverage both Physically-based and Machine Learning models to build on-line moisture profiles, whose reference application is monitoring and long-term watering optimization. This is indeed beneficial for preserving optimal soil moisture levels and preventing water waste. We focus on the following contributions. • The concept of 2D/3D moisture profile as a fine-grained representation of a sensor grid. • Two alternative solutions to compute the profile, capturing linear and non-linear patterns. • An analysis of the trade-of between the accuracy, the number, and the position of sensors to smartly place them. 1In Greek mythology, god of wealth, linked to the prosperity of crops.
(a) Actual soil moisture.
(b) Raw sensor grid (c) Soil profile Our work is one of the outcomes of the Agro.Big.Data.Science project [18]. The project, funded by Regione Emilia Romagna, aims at studying and implementing digital solutions to support smart and precision farming.
The remainder of this paper is organized as follows. Section 2 provides a formal introduction to the important domain notions for this work. Section 3 illustrates the approach in detail. Section 4 reports the tests carried out on real data collected over two years and a sensor layout analysis for optimal placement Finally, Section 5 draws the conclusions.
In orchards, where a stable watering system can be built, drip irrigation is widely used as it enables precise watering that, in turn, reduces water waste. Figure 1 shows an example of an orchard watered through a single-pipeline dripper system. The cubes represent the soil volume taken by the roots of each tree. Along the row of trees, a limited distance between drippers ensures a homogeneous watered volume (in blue); while across the rows (i.e., between two lines of trees), the soil volume remains completely unwatered (in orange).
Our goal is to create a moisture profile that represents the whole soil volume. Definition 1 (Soil volume). Given a tree, its soil volume is a parallelepiped of soil that contains most of the tree roots. The soil volume is centered in the tree position.
Definition 2 (Sensor grid). A sensor grid = {1, ..., ||} is an -dimensional layout of || sensors installed in a soil volume. Each sensor is defined by a three-dimensional displacement (.1, .2, .3) with respect to the center of the soil volume, and by a soil moisture value ..
Depending on , the grid resembles a line ( = 1), a rectangle ( = 2) or a parallelepiped ( = 3). The monitored value depends on the sensor technology, typically sensors measure volumetric water content (i.e., the volume of liquid water per volume of soil) or the soil potential (i.e., the energy required by tree roots to extract water from soil particles).
Definition 3 (Moisture profile) . Given an -dimensional sensor grid , the moisture profile is an -dimensional grid = {1, ..., | |} that approximates, in each , the soil moisture measured by . is fine-grained with respect to since | | > ||.
Building the moisture profile, based on raw sensor measurements, requires to estimate soil moisture of the whole soil volume at a fine-grained resolution.
Example 1. Given a 2D sensor grid covering an area of 0.62 (i.e., a rectangle with a width of 1 and a height of 0.6), we employed a sensor grid with 12 sensors (i.e., || = 12) and a moisture profile with 1000 points (i.e., | | = 1000). As a result, we obtained a moisture profile having a granularity of 62 (i.e., 0.62/1000) while the sensor grid granularity is 5002 (i.e., 0.62/12). For the sake of clarity, Figure 2b shows a sensor grid with || = 9 and Figure 2c shows a moisture profile with | | = 25.
The transformation of raw sensor measurements into a fine-grained moisture profile is achieved through a profiling function.
Definition 4 (Profiling function) . Given an -dimensional sensor grid and a moisture profile , a profiling function : → approximates the moisture profile starting from the grid .
The role of a profiling function is approximating the soil moisture values in those positions of the moisture profile where a sensor is not present. A profiling function is based on sensor grid measurements and can optionally exploit further information about the behavior of the soil. Several profiling functions can be adopted. We propose two alternative approaches that difer in the information exploited.
• Soil-feature unaware - FU: exploits the sensor measurements only. The most obvious choice is to carry out a linear interpolation between pairs of sensor values. • Soil-feature aware - FA: exploits the knowledge about soil hydrological dynamics to keep into account non-linearities and to get a more accurate estimation.
Sample profiles created through the two profiling functions are reported in Figure 3. It is apparent that the FA one encodes complex non-linearities deriving from the combined efect of the multiple factors that characterize the soil and the plant. PLUTO data processes for the two alternative profiling functions are sketched in Figure 4. The FU function does not require to be fitted to a specific field and only gets sensor data as input, while the FA function is trained ofline to capture non-linear behaviors due to specific plant and soil behaviors at hand.
As to the FU profiling function, we rely on the well-known -linear interpolation, where is the profile grid dimensionality. Although this regression approach is bounded to linear behavior between sensor pairs, we highlight that the composition of several linear strokes approximate a non-linear trend. For the sake of conciseness, in the following, we describe the 2-linear case. Given a 2D sensor regular grid , this technique carries out a linear interpolation in each dimension independently from each other. The approach consists of two phases (Figure 5). For each point ∈ of the moisture profile to be computed: (i) we find the four sensors that determine the minimum bounding rectangle enclosing (Figure 5a), then (ii) we compute . (Figure 5b) by interpolating along the 1 axis first. Then, exploiting the obtained points (blue dots), interpolation is performed along the 2 axis and the value . is finally determined. The trilinear procedure is analogous: it just has three steps instead of two.
As to the FA function, we rely on a machine learning model to capture non-linear soil moisture
behaviors; in particular we built an Artificial Neural Network (ANN) that learns the moisture
dynamics from a physically-based model (i.e., CRITERIA [
(a) Bounding rectangle for (b) Bilinear interpolation
Value # Hidden Layers 1 # Neurons per layer 100 Activation function Tanh Normalization Z-score # Training epochs 50 Batch size 30 Reduce learning rate factor=2, patient=10
We tested PLUTO one of the Agro.Big.Data.Science project installations [18] located in Faenza (Emilia Romagna, Italy). This orchard is watered through a single pipeline of drippers (distance between drippers 40cm) and Kiwifruit vines were spaced 2m along the row and 4.5m across the rows. Soil moisture is monitored through two installations, specifically 2D and 3D sensor grids of – respectivelly – 12 and 15 gypsum block sensors. We monitored the soil water potential, hence the profile values are in unit of pressure (namely, in cbar).
In real-world applications, the number of sensors is by far less than those we used in our research project. Section 4.1 leverages an incremental number of sensors to compute the profile and the remaining as ground truth to evaluate the performance. Section 4.2 conducts an analysis of the sensor importance according to the trade-of between accuracy and position.
Figure 7 and Figure 9 show the system performance for – respectivelly – the 2D and 3D cases, varying the number of input sensors. In each test, the performance is calculated as the RMSE (i.e., Root Means Square Error, the less the better) between the ground truth and the estimated values by the profile. To better understand the advantage provided by PLUTO, we also report the performance of profiling based on a single sensor — 0D setting — (i.e., the de facto standard) or a column of 3 sensors at diferent depths — 1D setting.
To extend the soil moisture value of the single sensor to the entire soil volume, we must assume the soil moisture to be constant in the whole volume. Similarly, when a column of sensors is available, we assume that soil moisture is constant at the same depth in the soil. Since the accuracy varies based on the sensor location, we choose the single sensor position (or the sensor line) that minimizes the RMSE as a fair comparison baseline. The same methodology was adopted to displace the sensors used to calculate the profile with our approach. Specifically, 2D profiles assume soil moisture to be constant along the row, while 3D profiles have no assump
In both cases, the 0D setting estimations are by far less accurate than the ones obtained by our profiling functions. The 1D settings achieve slightly better results since it captures soil moisture at diferent soil depths, but fails in capturing longitudinal variations. The extent of these errors is not negligible since the optimal range for soil moisture for kiwi cultivation is [− 100; − 300) cbar [20].
RMSE for FA and FU gradually decreases as the number of sensors increases. Note that the linear profiling function can be computed only for some sensor layouts, due to the intrinsic geometrical constraints (i.e., the profile region must be partitioned in bounding rectangles/cubes). The ANN profiling function always outperforms the bilinear one due to its capability to better model non-linear behaviors.
As shown in Figures 7 and 9, accuracy varies with the number of sensors. Given a regular grid
with sensors, several layouts are possible when < sensors are used. In particular, while
the bilinear FU function implies some geometric constraints, in the ANN-based FA one all the
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SM80
R60
layouts are feasible. To compare diferent layout performances and suggest the smart one, we
considered the five profiles that achieve the best performances when ∈ [
We presented PLUTO [17], an original approach to compute fine-grained moisture profiles. PLUTO relies on a grid of soil moisture sensors and it largely outperforms previous approaches based on a single or a column of sensors. We have shown that three sensors, properly placed in the soil, are suficient to efectively obtain the profile.
We are currently turning our monitoring system into a forecasting one. We are testing ANNs to create a solution that initially (i.e., before the deployment of the sensors) learns from a soil simulator and then improves its accuracy by exploiting real sensor samples collected during operations. The overall goal is to create a prescriptive analytics system that automatically activates the watering system based on a soil moisture prediction module fed with weather forecasts. using artificial neural networks, arXiv preprint arXiv:1303.1868 (2013). [16] E. Babaeian, S. Paheding, N. Siddique, V. Devabhaktuni, M. Tuller, Estimation of root zone soil moisture from ground and remotely sensed soil information with multisensor data fusion and automated machine learning, Remote Sensing of Environment 260 (2021). doi:10.1016/j.rse.2021.112434. [17] M. Francia, J. Giovanelli, M. Golfarelli, Multi-sensor profiling for precision soil-moisture monitoring, Computers and Electronics in Agriculture 197 (2022) 106924. [18] A.B.D.S., The Agro.Big.Data.Science project, http://agrobigdatascience.it/, 2021. Last accessed: 2021-10-18. [19] J. Bergstra, B. Komer, C. Eliasmith, D. Yamins, D. D. Cox, Hyperopt: a python library for model selection and hyperparameter optimization, Computational Science & Discovery 8 (2015) 014008. [20] S. Miller, G. Smith, H. Boldingh, A. Johansson, Efects of water stress on fruit quality attributes of kiwifruit, Annals of botany 81 (1998) 73–81.