1. Introduction

Agricultural water management is a pressing issue globally, driven by increasing water scarcity, climate change, and population growth. Currently, agriculture accounts for approximately 70% (from FAO AQUASTAT database) of worldwide freshwater withdrawals, with irrigation consuming the majority of this amount. As demand for sustainable water use intensifies, precision agriculture has gained prominence as a means of optimizing agricultural inputs based on site-specific data[1].Precision agriculture employs advanced technologies to monitor and manage variables such as soil moisture, aiming to apply water only as needed, thereby reducing waste and improving yield quality.

Wireless Sensor Networks (WSNs) are foundational in precision agriculture, providing continuous monitoring of environmental parameters, including soil moisture, temperature, and humidity. These networks, composed of distributed sensor nodes, facilitate real-time data collection essential for irrigation and other agricultural practices. However, conventional WSN systems are limited to reactive responses based on immediate environmental readings, which limits the efficiency of irrigation management. Without predictive capabilities, current WSNs lack the foresight to adjust irrigation schedules based on anticipated soil moisture variations due to weather changes or crop demand [2].

Integrating predictive models with WSNs presents a potential solution to these limitations, enabling proactive water management strategies. Among various predictive modeling techniques, the Markov chain model has proven effective for forecasting in stochastic environments where states transition probabilistically. Markov chain models are particularly suited for predicting soil moisture fluctuations due to their adaptability to time-series data and environmental variability. By forecasting future soil moisture levels, a WSN enhanced with a Markov chain model could provide actionable insights, optimizing irrigation schedules to align with projected water needs[3].

This study proposes an innovative approach that integrates a Markov chain-based predictive model within a WSN framework tailored for precision irrigation. This system anticipates changes in soil moisture and generates informed irrigation schedules, aiming to improve water-use efficiency, reduce unnecessary water application, and support sustainable agricultural practices. Such an approach holds considerable promise, especially in regions facing severe water scarcity, where efficient irrigation is essential for maintaining productivity without overusing limited water resources [4].

This paper is structured as follows. Section 2 reviews the current state of soil moisture monitoring technologies, WSN applications in precision agriculture, and Markov chain models in environmental prediction. Section 3 outlines the proposed methodology, detailing the construction of the Markov chain model, the design of the WSN architecture, and the integration of predictive and monitoring capabilities. Section 4 presents the results and discusses the system’s efficiency in enhancing irrigation management. Finally, Section 5 summarizes the study’s findings and offers directions for future research.

2. Literature Review

2.1. Soil Moisture Monitoring Techniques

Effective soil moisture monitoring is fundamental to irrigation management. Traditional approaches, such as gravimetric analysis, provide accurate measurements but are time-consuming and lack real-time capabilities. The introduction of sensor-based systems, particularly WSNs, transformed soil moisture monitoring by enabling continuous data collection and remote access. WSNs deploy sensor nodes across agricultural fields to capture soil moisture, temperature, and other environmental parameters, transmitting this data to a central gateway for analysis. These systems facilitate real-time monitoring and scalable field coverage, but they often struggle with energy consumption, connectivity, and predictive capabilities, limiting their proactive potential in irrigation[5].

2.2. Application of WSNs in Precision Agriculture

In precision agriculture, WSNs are primarily used to gather environmental data that supports precise irrigation, nutrient management, and crop health monitoring. Typical WSNs in agriculture consist of sensor nodes that record data on soil moisture, temperature, and other variables critical for crop growth. The real-time data from WSNs allows farmers to make informed decisions, though the reactive nature of these systems remains a challenge. Limitations include energy constraints, data transmission issues, and the need for consistent maintenance. Integrating predictive capabilities could address these challenges by enabling WSNs to forecast environmental conditions and optimize resource allocation[6].

2.3. Markov Chain Models in Agricultural Prediction

Markov chains are valuable in agricultural prediction due to their probabilistic state-transition capabilities, which are well-suited for time-series data like soil moisture. By defining discrete states (e.g., “dry,” “moderate,” “wet”), the Markov model captures soil moisture dynamics over short periods, providing forecasts that can support proactive irrigation decisions. Despite challenges in adapting Markov models to variable agricultural environments, they are increasingly recognized for their utility in short-term forecasting, particularly when combined with real-time data from WSNs[3].

2.4. Need for Integrated Predictive Systems

Research shows a critical need for systems that combine WSNs with predictive models. Current WSNs are limited by their inability to anticipate changes, resulting in reactive irrigation practices. By integrating models like the Markov chain with WSNs, a proactive approach to irrigation can be achieved, optimizing water use and enhancing system sustainability. Such integration has proven challenging but offers promising potential for creating more adaptive, efficient agricultural systems.

3. Methodology

3.1. A. Markov Chain Predictive Model

3.1.1. Defining state space for soil moisture

The Markov chain model simplifies soil moisture levels by discretizing them into distinct states, which enables the continuous moisture data to be represented as discrete events, making it computationally feasible. The state space, denoted as

\( S=\lbrace {s_{1}},{s_{2}},{s_{3}}\rbrace \)

, includes three primary states: \( {s_{1}} \) (“dry”), \( {s_{2}} \) (“moderate”), and \( {s_{3}} \) (“wet”). Each state corresponds to a specific range of soil moisture values, based on historical data and crop requirements.

Mathematically, let

\( S={s_{1}},{s_{2}},…,{s_{n}} \)

\( \) where \( {s_{i}} \) represents a discrete soil moisture state. In this study, we define the state boundaries for each \( {s_{i}} \) as follows:

\( {s_{i}}=\lbrace \begin{matrix}dry & if moisture ≤{θ_{1}} \\ moderate & if {θ_{1}} \lt moisture≤{θ_{2}} \\ wet & if moisture \gt {θ_{2}} \\ \end{matrix} \)

3.1.2. Constructing the Transition Probability Matrix

The core of the Markov chain model is the transition probability matrix \( P \) , which captures the likelihood of transitioning from one moisture state to another. Let \( P \) be an \( n×n \) matrix where each entry \( {P_{ij}} \) represents the probability of moving from state \( {s_{i}} \) to state \( {s_{j}} \) in the next time step. The transition probabilities are derived from historical data as follows:

\( {P_{ij}}=Pr{({X_{t+1}}={s_{j}} | {X_{t}}={s_{i}})} \)

where \( {X_{t}} \) denotes the soil moisture state at time \( t \) , and \( {P_{ij}} \) satisfies the condition \( \sum _{j=1}^{n}{P_{ij}}=1 \) for all \( i \) .

For example, if the soil moisture level is currently in the “moderate” state ( \( {s_{2}} \) ), the matrix \( P \) will give the probabilities that it will remain in \( {s_{2}} \) or transition to \( {s_{1}} \) (“dry”) or \( {s_{3}} \) (“wet”) in the next period. The probability values in \( P \) are updated periodically to reflect recent changes in weather and soil conditions.

A sample transition probability matrix with three states might look as follows:

\( P=[\begin{matrix}0.6 & 0.3 & 0.1 \\ 0.2 & 0.7 & 0.1 \\ 0.1 & 0.4 & 0.5 \\ \end{matrix}] \)

where each row sums to 1, indicating that the sum of all possible transitions from any given state equals 100%.

3.2. B. Wireless Sensor Network Architecture

3.2.1. Design of Sensor Nodes

Each WSN (Wireless Sensor Network) node in this system is equipped with soil moisture and temperature sensors, a microcontroller, and a wireless communication module, typically using low-power protocols like ZigBee. The choice of sensors and components is crucial to ensure data accuracy, energy efficiency, and operational longevity in outdoor environments. Soil moisture sensors are selected for their sensitivity to moisture variations at different depths, allowing for a comprehensive profile of soil hydration levels across the field. Temperature sensors provide additional environmental context, which can be essential for calibrating moisture readings, as soil temperature affects moisture evaporation rates.

The nodes are solar-powered, using photovoltaic panels to reduce reliance on battery replacements, thus minimizing maintenance costs. This energy-harvesting design is particularly advantageous for remote agricultural settings, where battery replacement could be labor-intensive. To further optimize energy usage, nodes operate in low-power modes during idle periods, and only “wake up” at pre-programmed intervals to collect and transmit data. This sleep-wake cycle is managed by the microcontroller, which is programmed to balance energy efficiency with the need for real-time data updates.

To ensure effective coverage, nodes are strategically deployed based on a spatial sampling strategy that considers crop type, field layout, and soil heterogeneity. Each node temporarily stores data in its onboard memory, using a FIFO (First-In-First-Out) mechanism, until it is transmitted to the central gateway. This temporary data storage prevents data loss in case of communication delays, thus enhancing data reliability for predictive modeling. The deployment strategy is planned to maximize data collection accuracy while minimizing redundancy, ensuring that each node captures unique and relevant data points that contribute to a holistic understanding of soil conditions[7].

3.2.2. Network Communication Protocol

A TDMA (Time-Division Multiple Access) protocol is implemented to coordinate data transmission across nodes, reducing data collisions and conserving energy. In a TDMA-based system, each sensor node is assigned a specific time slot for data transmission, which eliminates the possibility of simultaneous transmissions that can cause interference and packet loss. By organizing transmissions in sequential slots, the protocol minimizes idle listening and retransmission costs, which are typically major energy drains in wireless networks.

In this system, the gateway serves as the central coordinator, assigning time slots to each node and managing communication schedules. The gateway is equipped with preprocessing capabilities, such as data aggregation and filtering, to reduce redundant information before forwarding data to a cloud server for long-term storage and advanced analytics. The TDMA protocol, combined with selective data aggregation, significantly extends node battery life, making the network sustainable for extended periods.

Additionally, the communication protocol is designed to be resilient in the face of node failures. If a node fails or its battery is depleted, the gateway dynamically reallocates time slots to active nodes to maintain network functionality. This adaptive feature enhances the robustness of the network, ensuring consistent data flow even under challenging field conditions. By minimizing power consumption and maximizing data reliability, the protocol design supports the long-term operational sustainability of the WSN[8].‬‬‬‬‬‬

3.3. C. Integration of Predictive Model and WSN

3.3.1. Data Collection and Preprocessing

Data preprocessing is a critical step to ensure that the data fed into the predictive model is both reliable and consistent. Raw data collected from sensor nodes often contain noise or errors due to environmental factors, sensor limitations, or transmission issues. Therefore, preprocessing includes several key techniques:

• Outlier Detection: Identifies and removes data points that deviate significantly from typical values. Techniques such as Z-score analysis or interquartile range (IQR) filtering are applied to detect outliers that may result from sensor errors or temporary environmental disturbances.

• Interpolation: Addresses missing values by estimating intermediate data points based on known values. For instance, linear interpolation is used when data from certain time intervals is missing, ensuring continuity and preventing gaps in the time series.

• Normalization: Standardizes the data to a common scale, especially important when combining moisture and temperature data from different nodes. This process involves rescaling data to fall within a specified range, making it compatible with the Markov chain model and reducing the influence of extreme values.

These preprocessing steps produce a cleaned dataset \( \widetilde{D}(t) \) , which is then transmitted to the Markov chain model for forecasting. This real-time data flow ensures that the predictive model operates on high-quality inputs, enabling it to generate accurate irrigation recommendations that are aligned with current field conditions[9].

3.3.2. Model Deployment and Execution

The Markov chain predictive model is deployed on a hybrid system, capable of running either on the gateway or on a cloud-based platform, depending on the scale and requirements of the agricultural field. For small to medium-sized fields, local deployment on the gateway is feasible and cost-effective, as it minimizes data transfer to external servers, thus reducing latency and dependency on internet connectivity. For larger deployments, a cloud-based setup is preferable, as it offers scalability and the ability to handle more extensive datasets.

The model forecasts soil moisture levels over a short-term horizon, typically 24-48 hours, based on current and historical data. This short forecasting window is chosen to balance model accuracy with computation efficiency, as soil moisture levels can change rapidly due to environmental factors. The Markov chain model operates in a rolling-update mode, where it continuously recalculates transition probabilities based on the latest preprocessed data. This allows the model to adapt to real-time field changes, maintaining its relevance and accuracy in dynamic agricultural conditions.

To improve the model’s robustness, it is periodically calibrated with new field data to capture seasonal changes or anomalies due to unexpected weather events. Calibration is essential in areas with high climate variability, as it adjusts the model’s parameters to reflect recent trends, thus enhancing forecast reliability. By combining local and cloud-based processing, the system achieves flexibility and can scale across diverse agricultural scenarios[10].

3.3.3. Decision-Making and Irrigation Control

The Decision Support System (DSS) is the final component in the integration of the predictive model and WSN, where it interprets forecast data to make actionable irrigation decisions. Based on the forecasted soil moisture levels, the DSS calculates the optimal irrigation schedule to ensure that crops receive adequate water without waste. If the Markov chain model predicts that soil moisture will fall below a critical threshold within the next 24 hours, the DSS schedules irrigation to maintain optimal levels.

The irrigation amount \( I \) is determined based on the difference between the forecasted soil moisture \( \hat{D}(t+1) \) and the target threshold \( {θ_{target}} \) :

\( I=max{(0,{θ_{target}}-\hat{D}(t+1))} \)

This calculation ensures that water is applied only when necessary, conserving resources and reducing operational costs. The DSS is equipped with both automatic and manual override options; irrigation commands are either sent directly to automated actuators or provided as recommendations to operators for manual execution, depending on system configuration.

Additionally, the DSS includes feedback loops that evaluate the accuracy of each irrigation event. After each irrigation cycle, soil moisture data is re-evaluated to assess whether the DSS’s prediction aligns with actual field conditions. This feedback mechanism enables iterative improvements, where model parameters are adjusted based on observed discrepancies. Over time, this self-learning process refines the system’s predictive accuracy and enhances its adaptability to unique environmental conditions, thus ensuring long-term efficacy in water management [10].

4. Future Directions and Potential Applications

One of the main challenges in implementing a Markov chain predictive model for agricultural applications is the variability in soil and climate conditions, which can impact prediction accuracy. Future research could focus on developing hybrid models that combine Markov chains with machine learning techniques to better capture complex environmental patterns. By leveraging machine learning’s ability to adapt to dynamic data, such hybrid models could enhance the system’s predictive accuracy in diverse agricultural settings. Regular calibration of the model with real-time data is also essential, as it allows the system to adjust to seasonal or unexpected changes in the environment, maintaining relevance and reliability.

In addition to predictive accuracy, energy efficiency remains a priority, especially for large-scale deployments of WSNs in agriculture. Beyond optimizing communication protocols, future studies could explore energy-harvesting methods, such as solar or kinetic energy capture, to provide a sustainable power source for sensor nodes in remote areas. Enhancements to predictive algorithms that reduce the frequency of data transmission could also conserve power without sacrificing system performance. Such improvements would extend the operational life of sensor networks, making the system more feasible for continuous use in resource-limited environments.

While the system described in this study is primarily designed for soil moisture and irrigation management, its flexible architecture has potential for broader applications. For instance, it could be adapted for pest monitoring, nutrient management, and even climate data collection, providing a comprehensive agricultural management tool. Controlled field trials will be essential to validate the system’s real-world performance, offering empirical data on water savings, energy efficiency, and crop yield improvements. Collaborations with agricultural research institutions and pilot programs could accelerate the transition from theoretical models to practical applications, supporting sustainable agricultural practices at a larger scale.

5. Conclusion

This study explored the theoretical integration of a Markov chain predictive model with wireless sensor networks (WSNs) to optimize irrigation management in precision agriculture. The proposed system leverages predictive capabilities to enable proactive irrigation scheduling, potentially transforming traditional water management practices in agriculture. By forecasting soil moisture levels based on historical and real-time data, this model-driven approach allows for resource-efficient irrigation, addressing critical challenges in sustainable water management.

The theoretical analysis suggests that integrating a Markov chain model with WSNs could significantly improve water-use efficiency and reduce the energy consumption typically associated with conventional irrigation systems. The Markov chain model’s ability to represent soil moisture as discrete states, combined with WSN’s real-time data collection, offers a promising framework for agricultural water management. Although limitations such as model accuracy in dynamic environments and the need for frequent recalibration remain, these challenges present valuable areas for further research.

To bridge the gap between theory and practice, future studies should focus on conducting field trials to validate the system’s efficacy under various agricultural conditions. Additionally, exploring hybrid models that combine Markov chains with machine learning algorithms could enhance predictive accuracy, making the system more robust in the face of climate variability. Ultimately, this research contributes to a data-driven approach to sustainable agriculture, aligning with global efforts to conserve water resources and enhance food security.