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Event-Based Hydrological Signatures to Quantify Soil Moisture Parameters in Agricultural Soils Under Contrasting Irrigation Practices in Humid Climates
Suman Budhathoki1,*, Julie E. Shortridge1
Published in Journal of the ASABE 68(3): 379-395 (doi: 10.13031/ja.15999). Copyright 2025 American Society of Agricultural and Biological Engineers.
1 Department of Biological Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA.
* Correspondence: szb0153@vt.edu
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 11 March 2024 as manuscript number NRES 15999; approved for publication as a Research Article by Associate Editor Dr. Zhiming Qi and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 10 March 2025.
Citation: Budhathoki, S., & Shortridge, J. E. (2025). Event-based hydrological signatures to quantify soil moisture parameters in agricultural soils under contrasting irrigation practices in humid climates. J. ASABE, 68(3), 379-395. https://doi.org/10.13031/ja.15999
Highlights
ABSTRACT. Accurate estimation of soil moisture parameters, such as field capacity and permanent wilting point, is essential for improved irrigation management. However, these parameters can be challenging to accurately estimate in production conditions, and literature reference values are not always accurate for field-specific management. This study presents a technique for quantifying soil moisture parameters based on the identification of event-based hydrologic signatures in volumetric water content (?) data. The data were collected from corn and cotton fields under different irrigation treatments (non-irrigated, full irrigation, precision irrigation) in Virginia during 2020 and 2021. The proposed method identifies various hydrologic events, including infiltration, gravity drainage, evapotranspiration, and rewetting, and estimates of field capacity and plant extraction limit values based on transitions and occurrence periods of these events. The results of the event-based analysis were compared to two existing hydrologic signature methods in terms of classification accuracy (determining whether soil moisture levels reached field capacity or plant extraction limit values for a given sensor) and estimation error (difference between signature and reference values). The event-based method resulted in higher classification accuracy (75.0%–79.2%) and lower estimation error (1.69%–1.87%) for field capacity determination across all sensors tested when compared to existing methods. Additionally, the event-based approach exhibited superior classification accuracy for plant extraction limit estimation, except for deep sensors (>30 cm) in 2021. By more accurately estimating hydrologic parameters using temporal patterns in volumetric water content data, this approach can ultimately support more efficient irrigation water management. More broadly, it contributes to a more thorough understanding of which signature methods are most suitable for different types of hydrologic, climatic, and analytical contexts.
Improved irrigation efficiency can contribute greatly to reducing costs of agricultural production. It can also minimize environmental impacts caused by excess water and subsequent chemical transport and leaching. Precise monitoring and understanding of soil moisture content and its dynamics are critical to improved irrigation water use. Soil moisture has an impact on hydrological processes, such as infiltration, runoff, and percolation, thereby influencing the evapotranspiration patterns and crop-water uptake (Hupet and Vanclooster, 2002). It also influences nutrient uptake and losses, influencing crop production and environmental water quality impacts (Ballester et al., 2021; Lu et al., 2021; Malhotra et al., 2024; Sangha et al., 2023). Data from soil moisture sensors allow growers and agronomists to understand how much water is being consumed by crops and thereby can inform decisions about when and how much to irrigate (Figueroa and Pope, 2017).
Irrigation scheduling can be accomplished by monitoring soil water content in the plant root zone, tracking plant evapotranspiration (ET), and monitoring plant response to water stress (Sui, 2017). Monitoring plant response to water stress involves observing the physiological responses in plants, such as stomatal closure, leaf wilting, and reductions in photosynthesis rate that occur when they are experiencing water shortage (Ihuoma and Madramootoo, 2017). However, these approaches are typically labor-intensive, destructive, or time-consuming, and do not account for variability in plant reactions to water stress (Ihuoma and Madramootoo, 2017). Similarly, ET-based scheduling requires crop-specific ET models that can be challenging to parameterize (Khanal and Barber, 2023; Kimball et al., 2019; Pereira et al., 2020) and that typically rely on a simplified representation of soil hydrology, rarely accounting for infiltration and drainage limitations. The use of soil moisture sensing data can address these limitations (Irmak and Irmak, 2005; Kukal et al., 2020). Irrigation based on real-time monitoring of the soil water status has been shown to increase water use efficiency by 16% to 25% for vegetable crops (Rekika et al., 2014), 7% to 15% for strawberries (Létourneau et al., 2015), and 7% for tomatoes (Muñoz-Carpena et al., 2003), compared to conventional irrigation management. Sensor-based irrigation promotes efficient water use by reducing runoff and deep percolation (Zamora Re et al., 2020) and reducing energy consumption for pumping, thereby resulting in a reduction of greenhouse gas emissions (Trost et al., 2013).
Realizing the benefits of soil moisture sensing in irrigation management requires quantifying certain soil hydrologic parameters (SHPs), including field capacity (FC) and permanent wilting point (PWP), that are challenging to accurately estimate in production conditions. While multiple methods for estimating FC have been proposed (e.g., Assouline and Or, 2014; Chandler et al., 2017; Soil Science Society of America, 2008; Twarakavi et al., 2009), in irrigation scheduling FC is typically used to represent the upper bound of water that can be stored within the root zone soil. PWP is the point at which plants can no longer extract sufficient water from the soil and is treated as the lower limit on plant-available water in irrigation scheduling. Typically, irrigation scheduling is determined using FC and PWP values based on soil texture that are widely available in the literature (Datta et al., 2017). However, published values for FC and PWP based on soil texture may not accurately reflect actual field conditions (Vories and Sudduth, 2021). For example, Vories and Sudduth (2021) observed FC values for sand and loamy sand that were twice as high as published literature values in irrigated crop fields. Furthermore, while FC is traditionally considered to be a static value, the true values can vary across a dynamic range depending on the antecedent moisture conditions of the soil (Bean et al., 2018; Hardie et al., 2011). For instance, prolonged droughts can reduce the water-holding capacity of the soil, resulting in different FC values than those observed under normal conditions.
The most commonly used irrigation scheduling approach involves initiating irrigation when the soil water content falls below a specific threshold relative to FC and PWP. However, if the estimated FC and PWP values are inaccurate, irrigation could have a negative impact on crop yield and water use efficiency due to either over-irrigation or under-irrigation. This is especially important in humid climates, where rainfall is abundant but highly irregular and unpredictable (Takhellambam et al., 2023, 2022). In these regions, a fine balance between the water supply and demand needs to be maintained, and irrigation scheduling methods must be accurate and responsive to rapidly changing and highly variable soil moisture conditions. Additionally, the risk of nutrient leaching in these climates, particularly when irrigation coincides with frequent precipitation, underscores the need for precise soil moisture management (Zurweller et al., 2019; McCann and Starr, 2007). To ensure that crops receive the proper amount of water at the right time, an accurate benchmark is required to start and stop irrigation, minimizing the risk of water stress or excessive watering.
Recognizing the importance of accurate estimation of SHPs relevant for irrigation, including FC and PWP, several recent studies have developed novel approaches that integrate soil moisture sensing data with computational models to assess how FC estimation methods impact irrigation recommendations. Lena et al. (2022) demonstrated how different drainage flux definitions of FC (e.g., 0.1 cm/day, 0.01 cm/day, etc.) and quantification methods (laboratory or empirically-derived) impacted irrigation thresholds and efficiency, finding that irrigation recommendations were particularly sensitive to FC estimation methods in coarse-textured soils. More recent research has leveraged soil tension monitoring data to optimize SHPs through inverse modeling in the HYDRUS-1D model and found that the use of irrigation thresholds derived from optimized SHPs resulted in improved irrigation efficiency compared to those derived from laboratory-determined SHPs (Kumar et al., 2022). The inverse modeling approach has also been used to quantify pressure head values of FC based on drainage flux criterion and optimized SHPs and was shown to result in greater irrigation efficiency in computational simulations when compared to the use of FC values based on soil texture or laboratory analyses (Kumar et al., 2023).
Collectively, these studies demonstrate how soil moisture sensing data can be used to accurately quantify in-situ soil hydrologic properties relevant for irrigation management, including FC, without the need for time and labor-intensive laboratory analyses. However, one challenge in the practical implementation of these approaches in irrigation management is the multiple steps involved. In particular, the application of inverse modeling to quantify SHPs requires significant computational expertise and could pose a barrier to grower adoption. Identifying streamlined approaches for quantifying FC and PWP that use soil sensing data directly could help make precision irrigation based on soil sensing data easier to adopt. This ease of use is important, as increased convenience that requires a low level of grower involvement has been found to be a key predictor of precision technology adoption (Thompson et al., 2019; O’Shaughnessy et al., 2016). Precision irrigation technologies in particular are often “information-intensive,” requiring specialized skills and interpretation of large amounts of data (Barnes et al., 2019), making them less appealing than “embedded-knowledge” technologies that do not require specialized skills (Kolady et al., 2021).
Recent studies have introduced an alternative approach for estimating SHPs, including FC and PWP, that uses high-frequency measurements of soil moisture data directly without the need for additional modeling analyses. This approach, known as hydrological signature analysis (McMillan et al., 2017), can provide insights into key hydrologic processes such as water retention, movement, and availability in the soil (Chandler et al., 2017). While there have been some studies on soil moisture signatures in catchment hydrology (McMillan et al., 2014; Scaife and Band, 2017), limited research has been conducted on their application in agronomic soils where soil moisture conditions change rapidly. Branger and McMillan (2020) tested a set of eight soil moisture signatures at regional scales largely based on seasonal transitions in soil moisture. Similarly, Chandler et al. (2017) evaluated the degree to which high-frequency attractor values in soil moisture time series could be used to estimate hydrologic parameters in a snowfed-dominated semi-arid region. However, it is unclear whether the seasonal-scale dynamics assessed in these studies can translate to an irrigation management context focused on soil moisture fluctuations on shorter time scales. Bean et al. (2018) compared automated approaches for estimating FC from soil moisture time series in irrigated orchard and turfgrass areas, showing that automated methods can approximate FC accurately when compared to the manually labeled true values. However, their study focused only on shallow soil layers (7.6–15.2 cm), which may not accurately represent the soil water dynamics in the deeper root zone where conditions are more stable through time (Kumar et al., 2021). Additionally, neither Bean et al. (2018) nor Kumar et al. (2023) included estimation of PWP, which also plays a crucial role in determining the irrigation thresholds and understanding plant water availability.
The objective of this study is to develop an event-based hydrologic signature approach for quantifying FC and PWP in humid agricultural soils that can be used to inform irrigation management without the need for intermediate inverse modeling analyses. We compare our approach to existing methodologies for extracting soil moisture signatures (Branger and McMillan, 2020; Chandler et al., 2017) using hourly volumetric water content data obtained over two years at an agricultural research site in Virginia, U.S.A., under two crops (corn and cotton) and three different irrigation treatments. We assess the performance of both existing and proposed signature analysis methods by comparing them against reference values through two steps. First, we investigate whether the signatures can accurately identify instances of FC and plant extraction limit (PEL) in the time series. Second, we evaluate the agreement between the signature values and the true estimates. By demonstrating how hydrologic signatures can be used to determine hydrologic parameters relevant to irrigation management in humid climates, we ultimately aim to support more effective sensor-based irrigation scheduling that increases water use efficiency.
Materials and Methods
To develop an approach for soil moisture signature extraction in humid agronomic soils, we leveraged two growing seasons of hourly volumetric water content data across two crops and three irrigation treatments. We developed an event-based signature method, which identified the upper and lower bounds of plant-available water content by classifying the volumetric water content time series into periods of infiltration (INF), rewetting (RW), gravity drainage (GD), and evapotranspiration (ET). These periods were used to identify transitions from INF to GD to ET as a signature of FC and a stable period of ET (period of nearly zero root water uptake) as a signature of the plant extraction limit (PEL) as a lower bound of plant-available water.
Chandler et al. (2017) and Seyfried et al. (2009) used the term “plant extraction limit” (PEL) in place of PWP, which represents the threshold below which plants are unable to extract water, and soil water loss primarily occurs through evaporation. Unlike the traditional concept of the PWP, PEL considers variations among soil-plant combinations and recognizes that vegetation may not necessarily wilt even when transpiration decreases or ceases. Additionally, in our irrigated fields, it is important to note that true PWP might rarely occur. Therefore, we will employ the term PEL in our study as a more suitable representative of the lower bound of water availability for plants.
The performance of our event-based approach was compared with two previously developed methods (density and hysteresis) based on its ability to determine whether FC or PEL occurred in the time series (classification accuracy) and the difference between signature values and reference values of FC and PEL (estimation accuracy).
Study Site Description and Data Collection
Volumetric water content data (?) was collected over two growing seasons (2020 and 2021) at the Tidewater Agricultural Research and Extension Center (AREC) of Virginia Tech, in Suffolk, Virginia (fig. 1). The soils at the study site consist of a Nansemond loamy fine sand to approximately 18 inches depth, underlain by a fine sandy loam (USDA-WSS, 2023). This soil is moderately well drained and formed from alluvium and marine deposits. Average annual rainfall at the site between May and October is 750 mm. Average precipitation is fairly evenly distributed across the growing season, with the highest rainfall occurring in September (153 mm) and the lowest rainfall occurring in May (102 mm) (PRISM Climate Group, 2024). However, this can vary significantly from year to year. Table 1 provides a summary of the precipitation events across the growing season in 2020 and 2021. We collected soil moisture data from three different irrigation treatments (non-irrigated, precision irrigation, and full irrigation) and two different crops (corn and cotton). The full-irrigation treatment involved keeping the soil moisture levels above 70% of the plant-available water capacity of the soil and irrigating up to the FC, while the precision irrigation treatment was based on rainfall forecasts and ? readings to avoid both water stress and saturated conditions (Sangha et al., 2023).
Volumetric water content (? ; m3 of water per m3 of soil) was measured using Sentek TriSCAN capacitance probes. These probes measure a change in capacitance caused by the change in dielectric permittivity that stems from increases or decreases in soil water content through time. Several sensors are distributed along the probe, providing ? measurements every hour at 10 cm increments to a total depth of 90 cm. These sensors can detect changes in soil moisture > 0.01 percent. However, a precise installation is necessary with a good soil-sensor contact, especially in coarse-textured soils (i.e., sandy or gravelly soils) in which air surrounds the sensor or the sensor loses contact with the soil and associated water. We estimated soil moisture signatures for all sensor depths up to 80 cm; the deepest sensor was removed from the analysis to ensure the availability of paired depths required for the hysteresis signature extraction analysis. ? was monitored using one probe installed in each irrigation treatment site for each crop, for a total of six monitored locations in each year. The time series plot of ? for a representative site is shown in figure 2.
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| Figure 1. Location of Tidewater Agricultural Research and Extension Center (AREC) in Suffolk, Virginia. |
| Table 1. Summary of growing season precipitation at the study area. | |||||
| Month | Average Precipitation (mm) | 2020 Precipitation (mm) | 2020 Precipitation Events (n) | 2021 Precipitation (mm) | 2021 Precipitation Events (n) |
| May | 102 | 80 | 15 | 43 | 9 |
| June | 111 | 110 | 10 | 134 | 13 |
| July | 135 | 45 | 7 | 204 | 11 |
| August | 140 | 239 | 14 | 233 | 14 |
| September | 152 | 259 | 12 | 75 | 7 |
| October | 109 | 49 | 12 | 46 | 12 |
Determination of Reference PEL and FC
Testing the performance of different signature analysis methods required a set of reference FC and PEL values for each soil sensor against which the signature FC and PEL values could be compared. The reference values of FC and PEL for all sites in 2020 and 2021 were obtained using manual labeling of the time series of soil moisture data as in previous studies (Bean et al., 2018; Branger and McMillan, 2020; Chandler et al., 2017). Because FC is the threshold between free-draining water and water retained by the soil, we estimated FC by visual analysis as the point of “change of slope” between fast drainage after a rainfall or irrigation event and slower drainage as discussed by Branger and McMillan (2020) and Chandler et al. (2017). Similarly, PEL was estimated using manual labeling of the plateau in time series with a prolonged period of relatively stable soil moisture representing the lower limit of plant-available water (Chandler et al., 2017). In instances where a sensor did not exhibit FC or PEL behavior, then no reference value was recorded, and these sensors were only evaluated in terms of their classification accuracy. While laboratory assessment of soil samples can also be used to estimate FC and PEL reference values, they require extensive fieldwork and laboratory analyses and are often not representative of spatially heterogeneous field conditions (Kumar et al., 2022; Evett et al., 2019). Inverse modeling is another option for reference value estimation, but issues with equifinality, where multiple parameter sets can produce similar model outputs, complicate the identification of unique parameter set solutions (Beven, 1993). For these reasons, and for consistency with prior research on hydrologic signatures, manual labeling of reference values was adopted for this research.
To confirm these manual labels, we used the SWAP (Soil, Water, Atmosphere, and Plant) model—a one-dimensional, physically based, agro-hydrological model that simulates soil water and solute transport based on the Richards equation (Kroes et al., 2017). From the calibrated SWAP model for non-irrigated corn, we developed a soil water retention curve (SWRC) using the Van Genuchten equation, allowing us to evaluate and compare the field capacity (FC) values obtained in our study with the associated soil tension values suggested in established literature. The hourly water content data at 10 cm vertical increments, as well as season-end measures of biomass accumulation, nitrogen uptake, and crop yield for corn during the 2021 growing season, were used for SWAP calibration. SWRCs describe the relationship between ? and soil water tension (SWT) that can be utilized to describe the recharge and depletion behavior of soil water between FC and PWP (Liang et al., 2016). Previous researchers (Dane and Topp, 2020; Kumar et al., 2022; Lena et al., 2022; Liang et al., 2016; Tolk, 2003) have commonly utilized SWT ranging from 10 to 33 kPa as reference FC values. However, it has been observed that for soils characterized by a sandy texture, the FC values tend to be closer to 10 kPa (Hansen et al., 1980; Rivers and Shipp, 1972; Vories and Sudduth, 2021).
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| Figure 2. Time series plot of ? for a representative probe (2021, corn, non-irrigated) showing fluctuations in volumetric water content (?) across different depths in the field. |
Taking this into consideration, in our study focusing on sandy loam soils, we employed two different SWT values, specifically 10 and 15 kPa, to confirm the manually-labeled FC values. Additionally, we also compared our results with the commonly used benchmark SWT of 33 kPa for FC (Kumar et al., 2022; Rawls and Brakensiek, 1989; Saxton and Rawls, 2006). The plot and table showing the SWRCs for different soil depths along with the corresponding SWT-based FC estimates for non-irrigated corn in 2021 are included in the supplementary document. Similarly, the reference values for all the sites in 2020 and 2021 are also included in the supplementary document. This analysis confirmed that the manually identified reference FC values were consistent with SWRCs calibration to observed soil moisture dynamics at the study location.
Soil Moisture Signature Analysis Methods
The effectiveness of soil moisture signature analysis methods is likely to vary based on field and climate conditions (Araki et al., 2022). To understand the effectiveness of previously developed signature analysis methods in agricultural soils, we evaluated two different soil moisture signature analysis methods: density analysis and hysteresis analysis (Branger and McMillan, 2020; Chandler et al., 2017). Chandler et al. (2017) found that the hysteresis analysis approach is the most robust predictor of FC and PEL, while the density analysis approach is the simplest approach to determine those values. We compared these two approaches to an event-based method specifically designed for agricultural soils and irrigation management in conditions of rapidly changing soil moisture in humid climates. A summary of the different soil moisture signatures included in the analyses is presented in table 2. All signature identification and evaluation were conducted using the R programming language (R Core Team, 2022). The codes are available online at https://github.com/sumanager56/ASABE_Signature.
Method 1: Event-Based Signatures
To better identify soil moisture signatures in humid agronomic soils that experience frequent fluctuations in soil moisture, we developed an event-based approach based on the classification of ? data into different soil moisture events: infiltration (INF), rewetting (RW), evapotranspiration (ET), and gravity drainage (GD). INF events indicated the entry of water into the soil, either via irrigation or rainfall. It is important to acknowledge that this classification of hydrological events is intended to identify the dominant process in each period as an intermediate step in the hydrologic signature identification method. It is not meant to represent a precise accounting of hydrologic processes within the time series and does not exclude the concurrent occurrence of other processes.
RW events were classified as relatively small increases in soil moisture due to processes such as capillary action, where soil moisture can move upwards from wetter lower layers to higher dry layers of soil. Particularly in the shallow sensors, we observed diurnal behavior in ?, likely attributed to capillary wicking of moisture from wetter soil layers beneath during nighttime hours. We acknowledge the possibility that some of the nocturnal rewetting observed may be partially attributed to the temperature sensitivity of capacitance sensors, as highlighted by Evett et al. (2006). The range of temperature sensitivity for the probes used for this analysis is approximately 0.10%; this compares to typical nighttime ? fluctuations on the order of 0.01%–3.00%. Thus, at least some of the nocturnal increases in volumetric water content are likely attributable to vertical water movement, although some may be artifacts of nighttime temperature changes. In either case, the primary goal of the classification step was to isolate periods of rapid increases in volumetric water content likely to indicate infiltration. For this purpose, the underlying driver of moderate increases in volumetric water content (rewetting or temperature artifacts) does not impact the outcome of the analysis. ET represented the loss of water from the soil through a combination of soil evaporation and plant transpiration. GD events represented rapid decreases in water content at a given depth that occurred when water moved downward through the soil profile under the influence of gravity. Our preliminary analysis revealed that the distribution of the rate of change of ? at a given time step t (d?t) exhibited bidirectional heavy-tailed behavior. For values of d?t greater than zero (increasing water content), there were generally a small number of very positive values representing rapid soil moisture increase (INF) and a larger number of moderately positive values indicating RW processes. Negative values of d?t displayed similar patterns, with short periods of rapid reduction indicating GD and longer periods of slow reduction corresponding to ET.
| Table 2. Summary of soil moisture signature analysis methods used in this study.[a] | ||
| Signature Name | Description | |
| Event-based signatures | - Compute derivative of ? - Apply classification algorithm to identify instances of INF, GD, RW, and ET - Estimate FC as the value of ? where GD transitions to ET following an INF event - Estimate PEL as the value of ? where daily ET stabilizes. | |
| Density analysis (Branger and McMillan, 2020; Chandler et al., 2017) | - Compute Probability Density Function (PDF) that shows the relative frequency of different values of ? - Classify each PDF into a unimodal, bimodal, or multimodal distribution - Estimate FC from high modal values (peaks in the PDF) and PEL from low modal values | |
| Hysteresis analyses (Chandler et al., 2017) | - Plot paired hysteresis pattern between shallow (10–40 cm) and deep (50–80 cm) values of ? - Estimate FC and PEL using high-density grids representing dominant wet and dry soil moisture states | |
[a] T = volumetric water content, INF = infiltration, GD = gravity drainage, RW = rewetting, ET = evapotranspiration, FC = field capacity, PEL = plant extraction limit. | ||
An overview of the event-based signature analyses is shown in figure 3. The first step of the process was to calculate the change in volumetric water content (d?t) for each reading relative to the prior reading. These values were then categorized into positive (d?t > 0) and negative (d?t < 0) classes. The head-tail (H/T) classification algorithm (Jiang, 2013), specifically designed for heavily right-tailed data, was then applied to differentiate the extreme positive values of d?t(INF) from more moderate positive values (RW). Similarly, the H/T classification algorithm was also used to differentiate extreme negative values (GD) of d?t from more moderate negative values (ET).
The H/T method (Jiang, 2013) follows a recursive four-step process with a stopping condition to identify a series of break points (H/T break) that separate the head of the distribution from the tail. Initially, the mean value (µ) of the input vector of d?t is computed. The vector is then split into two parts: the tail, consisting of values below µ, and the head, consisting of values above µ. To determine if further partitioning is required, the proportion of values in the head relative to the entire vector is compared to a threshold value. If the proportion is less than or equal to the threshold, the process is repeated using the head values as the new vector and identifying a new H/T break as the mean of the head values. This continues until the condition is false or until no further partitions are possible due to the head having fewer than two elements. Hence, the approach iteratively selects different breaks in the dataset with the goal of providing the smallest in-class variance and largest between-class variance. In terms of stopping criteria, we selected the H/T break value that resulted in the head containing at least 35% of the observations for the negative class and 30% for the positive class. These percentages, although slightly below the recommended threshold of 40% by Jiang (2013), were used as indicators of even distribution between the classes. This threshold level was chosen after evaluating the 2020 and 2021 ? data to ensure that the head-tail algorithm could effectively identify different events.
In our analysis, the H/T algorithm was applied separately to the time series of d?t from each sensor and applied independently to the positive (wetting) and negative (drying) d?t values. Because the H/T algorithm assumes a positive heavy-tailed distribution, negative values of d?t were multiplied by negative one prior to implementing the H/T algorithm. An additional criterion was set while applying the H/T algorithm to the negative d?t values to account for the fact that the frequency of GD should be proportionate to the occurrence of INF. The extreme break corresponding to the GD class was selected such that it resulted in at least as many head values classified as GD as the head records in extreme positive d?t classified as INF.
After the ? time series was partitioned into INF, RW, GD, and ET, these sequences of processes and their magnitudes were used to identify FC and PEL signature values. FC was determined as the soil moisture value when the gravity drainage (GD) ceases, and ET just begins to occur after an infiltration (INF) event. The FC estimates for each sensor were determined by first identifying sequences of infiltration – gravity drainage – evapotranspiration (INF-GD-ET). For each valid INF-GD-ET sequence, FC was estimated as the ? value where gravity drainage transitioned to ET. The final estimates of FC were identified following a cross-checking process with recent rainfall or irrigation events. This was done to ensure that the identification of FC was backed up by actual water inputs in the field. By confirming that FC determinations occurred only after rainfall or irrigation within the preceding three days, we achieved a more accurate representation of the soil’s water holding capacity post-infiltration events. In cases where more than one FC value was identified, the mean of these values was used as the final FC signature value. If no FC values were identified, then FC was assumed to have not occurred in the time series from that sensor.
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| Figure 3. Diagram overview of event-based approach to identify different hydrologic events using soil moisture time series. T = volumetric water content, H/T = head-tail, INF = infiltration, GD = gravity drainage, RW = rewetting, ET = evapotranspiration. |
For PEL estimation, we first filtered the derivative values (d?t) to include only data from daylight hours between 6AM and 6PM. Next, we calculated the sum of d?t for each two-day window where no INF and GD events were identified while excluding any periods of time when RW events accounted for more than 25% of observations in each window. The selection of this window was based on the criterion of maintaining a stable soil moisture condition during daylight hours for a minimum of two consecutive days. To identify the events where the reduction in ? was negligible, we identified periods where the total ET losses over a two-day period were less than 0.1% and considered those points as PEL. Similar to FC, the final estimates of PEL were identified following a cross-checking process with recent rainfall or irrigation events. By confirming that PEL determinations occurred only on periods devoid of rainfall or irrigation for at least five days, a final check was done to make sure that all the PEL estimates were below the FC estimates and the average ? values.
Method 2: Density Analysis
The density analysis signature method uses the probability density function (PDF) of the time series ? to capture information on the shape of the soil moisture distribution, including modal values (peaks in the PDF) and the number of peaks. Soil moisture data commonly exhibit a bimodal distribution indicating two dominant soil moisture states (Branger and McMillan, 2020; Penna et al., 2009) that have been used to estimate FC (wet peaks) and PEL (dry peaks). While FC is an attractor value that prevails under wet, low flux conditions, Chandler et al. (2017) and Seyfried et al. (2009) described ? at PEL as an attractor value under extended dry periods at which existing vegetation does not extract soil water by transpiration. Branger and McMillan (2020) used an automated approach where the detected peaks were sorted in a descending order of their probability value and then used to classify the PDF as “unimodal,” “bimodal,” or “multimodal.” Chandler et al. (2017), on the other hand, used a simpler visual approach to determine the extreme peaks corresponding to the attractor values.
In our analysis, we made several adjustments to the processes presented in Chandler et al. (2017) and Branger and McMillan (2020) to automate attractor value identification and make the process compatible with ? data characterized by high in-season variability. Peaks were determined as points of transition in the probability density function from a positive to a negative slope that met two threshold requirements to select only distinct and dominant peaks. The first threshold was fulfilled when a peak was at least 33% higher than the height of the next adjacent valley. This threshold ensures that the selected peak stands out prominently compared to the surrounding valleys, indicating a significant increase in data frequency. The second threshold ensured that each selected peak was within 30% of the value of the highest peak. Both the threshold values were determined based on manual calibration and trial and error by evaluating what values successfully resulted in distinct peaks being chosen. When a sensor’s distribution was bimodal, the greater of the two peak values was selected as FC, while the lesser of the two was selected as PEL. For unimodal distributions, the peak was classified as FC if it was located above the mean soil moisture or PEL if it was located below the mean. In multi-modal distributions, the soil moisture values corresponding to the greatest and lowest peaks were classified as FC and PEL, respectively.
Method 3: Hysteresis
The hysteresis signature analysis method uses plots of paired VWC readings across two depths to provide a visualization of how ? varies with respect to depth during the drying and wetting cycles. Although the usage of the term ‘hysteresis’ in this study differs from its classical meaning, we intentionally retained this term to maintain consistency with previous studies using hydrologic signature approaches. This choice aids in aligning our methodology and findings directly with the established literature, facilitating a clearer comparison and understanding for readers familiar with these studies. In previous analyses, hysteresis produces a clockwise or counterclockwise pattern of ? indicating progression of drying or wetting fronts across two depths in a vertical soil profile, typically comparing the near-surface and deep soil layers (Chandler et al., 2017). The observed delay in time between wetting and drying events at the near-surface and deep soil layers increases the occurrence of wet and dry attractors, especially in the vicinity of the intersection point where the wetting and drying limbs of the hysteresis loop meet.
In our study, we conducted hysteresis analyses between shallow soil sensors (10-40 cm) and the deeper sensors located 40 cm beneath each shallow sensor (e.g., 10 vs. 50 cm). The FC value, representing the wet attractor, was estimated near the intersection of the wetting and drying limbs of the hysteresis loop. This was achieved by identifying the position of the high-density cell furthest from the origin of the hysteresis graph. The x-coordinate of this cell corresponded to the FC value of the near-surface sensors, while the y-coordinate corresponded to the FC values of the deep sensors. Similarly, the PEL value, representing the dry attractor, was estimated at the intersection of the drying and wetting limbs of the hysteresis loop. This was achieved by identifying the position of the high-density cell closest to the origin.
Signature Evaluation Criteria
Two criteria were used to evaluate the performance of the different soil moisture signatures. Firstly, we assessed whether each method could correctly identify instances where FC and PEL occur in ? time series data. In agricultural soils, especially those under irrigation, soil moisture levels are ideally maintained at moderate levels that provide sufficient water for plant growth while avoiding excess moisture that could result in nutrient leaching, runoff, or oxygen stress. This is particularly true in irrigated fields, where soil moisture levels should be maintained above PEL, and deeper soils where soil moisture levels are more stable through the growing season. Because of this, there may be sensors where FC and PEL never occur.
Thus, each signature method was first evaluated based on whether the method was able to identify an FC value for a sensor that exhibited FC behavior, as well as identifying a PEL value for a sensor that exhibited PEL behavior. To evaluate the classification accuracy of the different soil moisture signature methods, a binary representation was used to classify whether an FC value was identified for a signature method (eq. 1) and whether an FC value occurred in the time series (eq. 2). These values were then used to quantify the FC classification accuracy for each signature method across all probes and sensor depths (eq. 3):
(1)
(2)
(3)
where
E_FC?,d = signature outcome of FC at depth (d) and probe location (p)
E_FC*?,d = reference (true) occurrence of FC at depth (d) and probe location (p)
CA_FC = classification accuracy for FC
E_PEL?,d = signature outcome of PEL at depth (d) and probe location (p)
E_PEL*?,d = reference (true) occurrence of PEL at depth (d) and probe location (p)
CA_PEL = classification accuracy for PEL
The classification accuracies for FC and PEL were calculated using equations 3 and 6, respectively.
(4)
(5)
(6)
Hence, the overall classification accuracy (CA) of a particular method was determined by calculating the ratio of total number of correct classifications across all depths and probe locations to the total number of probes and depths evaluated. For example, the CA for FC values reported as 0.75, indicated that 75% of the sensors were correctly labeled as FC occurring or not occurring by a particular signature method.
Secondly, we assessed whether the numerical values of FC and PEL obtained from each signature method were consistent with the reference FC and PEL values estimated by manual labeling of the VWC time series. To quantify the consistency between the identified (signature) and reference values, we calculated the root mean square error (RMSE) between the signature and reference values (equations 7 and 8):
(7)
(8)
where
FCp,d = signature values [%] for FC at a particular depth (d) and probe location (p)
FC*p,d = true reference values [%] for FC at a particular depth (d) and probe location (p)
PELp,d = signature values [%] for PEL at a particular depth (d) and probe location (p)
PEL*p,d = true reference values [%] for PEL at a particular depth (d) and probe location (p).
Results
Reference Values of FC and PEL
The reference FC and PEL values obtained from the manual labeling of time series of ? are summarized in table 3. There is a clear pattern of increasing FC and PEL with depth, consistent with the transition from sandy shallow soils to increasing loam and clay content at depths greater than 30 cm. The percentages of sensors exhibiting FC tend to decrease with depth, with 100% of the sensors exhibiting FC behavior at near-surface depths (10 and 20 cm). This reflects the presence of distinct occasions of wetting and gravity drainage events near the soil surface throughout the time series. As we move deeper into the soil profile, soil sensors experience less fluctuation in ? values, resulting in FC behavior being observed in less than or equal to 50% of the total sensors beyond the 50 cm soil depth. Across all depths, 69% (66 out of 96) of the sensors exhibited FC events. A comparatively small number of sensors, approximately 22% (21 out of 96), exhibited PEL events across the entire soil profile. This is consistent with meteorological conditions that provided regular rainfall throughout most of the growing season and the use of irrigation across two of the treatment groups. The higher percentage of sensors exhibiting FC behavior provides greater confidence in estimating reference values and evaluating the performance of signature methods. Conversely, the lower percentage of sensors exhibiting PEL events increases uncertainty in reference values and evaluations of the performance of different signature methods.
| Table 3. Mean reference values and the percentage of sensors that exhibited FC and PEL behavior. Reference values are the mean across all sensors at a given depth, with the standard deviation in parentheses. NA values indicate depths where no sensors demonstrated PEL behavior, and missing SD values indicate instances where only a single sensor from that depth exhibited PEL and thus no standard deviation could be calculated. | ||||
| Depth (cm) | Reference FC Values Mean (SD) | Percentage of Sensors Exhibiting FC | Reference PEL Values Mean (SD) | Percentage of Sensors Exhibiting PEL |
| 10 | 19.7 (5.74) | 100.0 | 4.50 (2.12) | 16.7 |
| 20 | 23.5 (2.47) | 100.0 | 17.0 (-) | 8.30 |
| 30 | 25.4 (2.20) | 91.7 | NA | 0.0 |
| 40 | 25.3 (3.43) | 83.3 | 16.3 (1.53) | 25.0 |
| 50 | 29.1 (3.30) | 91.7 | 20.6 (4.34) | 41.7 |
| 60 | 29.7 (3.33) | 50.0 | 22.8 (1.71) | 33.3 |
| 70 | 28.0 (1.41) | 16.7 | 22.3 (1.15) | 25.0 |
| 80 | 31.5 (0.71) | 16.7 | 23.5 (1.32) | 25.0 |
Density Analysis
The density analysis revealed the presence of unimodal, bimodal, and multimodal distributions from the volumetric water content data, as shown in table 4. The analysis indicated that unimodal distributions were typically identified at near-surface depths (=30 cm), while bimodal distributions were more common at depths greater than 30 cm. The presence of a bimodal distribution signifies the existence of two distinct soil moisture regimes, which facilitated the identification of FC as the higher side peak and the PEL as the lower side peak. This finding aligns well with the results presented in table 5, which indicate a higher percentage of sensors identifying both the FC and PEL at deeper depths (>30 cm). However, this could lead to the identification of FC signatures in instances where actual FC behavior did not occur, as the density method led to 100% FC identification at depths of 70 cm and 80 cm (table 5), even though only 16.7% of the sensors at these depths exhibited true FC behavior (table 3). Similarly, the identification percentage of PEL using the density analysis method was unexpectedly high compared to the reference values, which indicated infrequent occurrence of PEL at most depths. This resulted in high variability in PEL estimates between the reference and the density-identified values, especially at depths beyond 30 cm. Non-irrigated plots showed a higher percentage of bimodal distributions (58.3%) at the near-surface depths (=30 cm), whereas the majority of shallow sensors in irrigated plots were unimodal (70.8%). This observation suggests that the more prominent drying and wetting regimes in non-irrigated plots may reveal more distinct FC and PEL estimates than is possible in irrigated plots, likely due to few if any occurrences of PEL.
| Table 4. Percentage of sensors demonstrating unimodal, bimodal, and multimodal distributions from the density analysis signature method. | ||||
| Depth | % of Sensors Revealing Certain Distribution | |||
| Unimodal | Bimodal | Multimodal | ||
| All treatments | =30 cm | 55.6 | 36.1 | 8.30 |
| >30 cm | 13.9 | 61.1 | 25.0 | |
| Irrigated treatments | =30 cm | 70.8 | 25.0 | 4.20 |
| >30 cm | 12.5 | 65.0 | 22.5 | |
| Non-Irrigated treatments | =30 cm | 25.0 | 58.3 | 16.7 |
| >30 cm | 20.0 | 55.0 | 25.0 | |
| Table 5. Density analysis signature values of FC and PEL and the percentage of sensors where the density analysis signature method identified FC and PEL across all sensors at each depth. Signature values are the mean across all sensors at a given depth, with the standard deviation in parentheses. | ||||
| Depth (cm) | Estimated FC Values Mean (SD) | Percentage of Sensors with Identified FC | Estimated PEL Values Mean (SD) | Percentage of Sensors with Identified PEL |
| 10 | 19.0 (3.76) | 66.7 | 10.3 (3.51) | 91.7 |
| 20 | 23.6 (2.93) | 75.0 | 18.0 (3.22) | 50.0 |
| 30 | 25.7 (4.09) | 100.0 | 19.1 (5.59) | 50.0 |
| 40 | 26.9 (4.30) | 100.0 | 19.9 (5.04) | 83.3 |
| 50 | 31.0 (2.77) | 91.7 | 26.7 (3.95) | 83.3 |
| 60 | 33.4 (2.62) | 83.3 | 30.0 (3.08) | 91.7 |
| 70 | 33.3 (2.01) | 100.0 | 29.5 (3.48) | 100.0 |
| 80 | 31.3 (2.90) | 100.0 | 26.4 (3.51) | 91.7 |
Figure 4 presents the density analysis for a representative treatment site, demonstrating a multimodal distribution, in comparison to the frequency analysis performed by Chandler et al. (2017). While a multimodal distribution allows identification of FC and PEL estimates based on extreme peak values, this raises concerns as it does not provide sufficient evidence of the occurrence of a distinct soil moisture regime. The presence of multiple peaks in the distribution is likely associated with greater short-term variability in soil moisture conditions typically found in irrigated crop fields. Consequently, the identification of FC and PEL values based on these multiple peaks may not accurately reflect the true underlying soil moisture dynamics. Similarly, the presence of unimodal distributions indicates situations where FC and PEL values may not be easily distinguishable. The difficulty in identifying FC and PEL estimates in the presence of unimodal and multimodal distributions highlights the limitations of the density analysis method in capturing the true soil moisture characteristics.
 |
| Figure 4. Schematic diagram demonstrating frequency/density analysis to represent the wet (FC) and dry (PEL) soil attractor values from this study (2021, corn, non-irrigated, 50 cm). |
Hysteresis Analysis
Table 6 summarizes the outcomes of the hysteresis analysis, revealing certain discrepancies when compared to the reference values. The mean FC values obtained through the hysteresis analysis were consistently overestimated across all soil depths. Additionally, except for the 60 cm soil layer, the estimated FC values displayed greater variability in comparison to the reference values. Similarly, the hysteresis analysis resulted in overestimation of PEL values at depths greater than 30 cm, with high variability observed when compared to the reference values. The identification percentages of FC and PEL were consistently 100% at all depths, highlighting a limitation of the hysteresis analysis in classifying high-density cells as either FC or PEL based solely on their location within the hysteresis loop. While the percentages of sensors exhibiting PEL remained below 50% throughout the soil profile, the frequent identification of PEL estimates in the hysteresis analysis may lead to more frequent irrigation than is necessary.
| Table 6. Hysteresis analysis signature values of FC and PEL and the percentage of sensors where the hysteresis analysis signature method identified FC and PEL across all sensors at each depth. Signature values are the mean across all sensors at a given depth, with the standard deviation in parentheses. | ||||
| Depth (cm) | Estimated FC values Mean (SD) | Percentage of Sensors with Identified FC | Estimated PEL Values Mean (SD) | Percentage of Sensors with Identified PEL |
| 10 | 20.6 (6.83) | 100.0 | 7.1 (4.73) | 100.0 |
| 20 | 29.2 (4.92) | 100.0 | 12.2 (3.90) | 100.0 |
| 30 | 29.2 (4.15) | 100.0 | 14.5 (3.23) | 100.0 |
| 40 | 28.1 (4.33) | 100.0 | 17.3 (4.46) | 100.0 |
| 50 | 30.2 (3.58) | 100.0 | 25.5 (4.68) | 100.0 |
| 60 | 33.5 (2.38) | 100.0 | 27.7 (4.24) | 100.0 |
| 70 | 33.5 (1.97) | 100.0 | 27.7 (4.86) | 100.0 |
| 80 | 31.9 (2.86) | 100.0 | 25.3 (3.50) | 100.0 |
 |
| Figure 5. Schematic diagram demonstrating hysteresis analysis to represent the soil attractor values (FC and PEL estimates) from this study (2021, corn, full irrigation, 40 vs. 80 cm). |
In figure 5, a hysteresis analysis of ? is presented for a representative sensor to make a comparison with the hysteresis analysis conducted by Chandler et al. (2017). This plot demonstrates how soil moisture at our study location exhibited numerous indistinct patterns of drying and wetting cycles through time. This lack of clear patterns can be attributed to rapid oscillation of the time series data caused by highly fluctuating events of drying and wetting within the fields. While the high-density cells provided some estimations of FC and PEL, they were not dense enough to capture the variability in soil moisture regimes. Additionally, figure 5 demonstrates that simultaneous occurrences of drying and wetting events were observed at the two soil depths, further highlighting the complexity of soil moisture conditions within the soil profile. Intermittent or light rainfall may wet only the surface soil, especially in our sites where finer soils dominate the deeper profile. Conversely, heavy rainfall can saturate the deeper soils for extended periods, causing the surface soils to dry out more rapidly while deeper soils remain wet. This is particularly true given the rainfall patterns in the humid climates of our study site. Similarly, transpiration by plants primarily affects the root zone, which might be deeper, causing drying at those depths while surface layers might still retain moisture. These findings suggest that in humid agricultural fields, the conditions are less likely to facilitate long periods of stable drying or wetting cycles, making it challenging to identify distinct patterns across two depths in a hysteresis analysis.
Event-Based Analysis
A summary of the outcomes of the event-based signature analysis is presented in table 7. The mean FC values estimated using the event-based method are generally in agreement with the reference values (table 3), especially at shallow depths such as 10 cm and 20 cm. The high percentage of sensors where the method identified an FC value at these depths reflects the reliability of the event-based method to identify FC events. Although the estimated FC values show relatively greater variability at depths below 20 cm compared to the reference FC values, the mean estimates of FC still remain close to the reference values. The method also captures the general pattern of increasing FC values with depth. As for the estimated plant extraction limit (PEL) values, they align well with the reference values until a soil depth of 40 cm. However, beyond 40 cm, the event-based PEL estimates exhibit higher mean values and a greater degree of variability compared to the reference PEL values. The accurate detection of FC and PEL estimates, particularly at shallow sensors, likely stems from the frequent occurrence of excess and low water conditions in shallow soil. The increasing complexity in estimating FC and PEL at deeper sensors highlights the challenges associated with the less frequent occurrence of these events.
| Table 7. Event-based signature values of FC and PEL and the percentage of sensors where the event-based signature method identified FC and PEL across all sensors at each depth. Signature values are the mean across all sensors at a given depth, with the standard deviation in parentheses. NA values indicate instances where the event-based method did not detect any instances of PEL at sensors from the specified depth. | ||||
| Depth (cm) | Estimated FC Values Mean (SD) | Percentage of Sensors with Identified FC | Estimated PEL Values Mean (SD) | Percentage of Sensors with Identified PEL |
| 10 | 20.1 (4.71) | 100.0 | 6.1 (2.81) | 25.0 |
| 20 | 23.6 (1.95) | 100.0 | NA | 0.0 |
| 30 | 25.3 (2.36) | 91.7 | 22.7 (NA) | 8.3 |
| 40 | 23.9 (3.73) | 83.3 | 15.6 (2.10) | 16.7 |
| 50 | 27.9 (3.32) | 83.3 | 24.7 (1.50) | 16.7 |
| 60 | 30.2 (3.28) | 83.3 | 26.5 (4.99) | 41.7 |
| 70 | 30.9 (1.69) | 58.3 | 28.7 (3.11) | 91.7 |
| 80 | 29.8 (1.85) | 50.0 | 26.7 (3.29) | 83.3 |
Representative plots demonstrating the outcome of the event-based analysis are shown in figures 6 and 7. Figure 6 demonstrates the event-based approach in two contrasting treatment plots (full irrigation vs. non-irrigated) at a depth of 10 cm. Full irrigation plots show higher short-term variability in ? resulting from frequent occurrence of distinct wetting and drying events, enabling the capture of the dynamic nature of FC estimates from the time series. In contrast, the non-irrigated plot exhibits less temporal variability in ?, resulting in relatively fewer representative estimates of the FC values. However, the more frequent occurrence of dry conditions provided increased opportunities for estimating the PEL; three of our 12 sensors at 10 cm soil depth had PEL values identified, 2 of which were in the non-irrigated plots (table 7). Figure 7 illustrates the application of the event-based signature analysis method at two contrasting soil depths (10 cm vs. 60 cm) for the precision irrigation and non-irrigated treatments of corn in 2020. While ? at 10 cm soil depth exhibits more variability and higher occurrences of FC events, ? at 60 cm remains relatively static, leading to the absence of FC estimates. Nonetheless, the stable soil moisture conditions at 60 cm depth in late July facilitated the identification of PEL.
Signature Evaluation Results
To compare the accuracy of different soil moisture signature methods, we calculated the CA and RMSE for each method across different soil depths and irrigation treatments. The classification accuracies (CA) and root mean square errors (RMSE) of FC signature values estimated by the different methods are presented in table 8. Across all sensors, the event-based method demonstrated the highest CA (75.0%–79.2%) and minimum RMSE (1.69%–1.87%) for determining FC in both the 2020 and 2021 data compared to the density and hysteresis methods. For all signature methods, classification accuracies were higher in the shallow sensors (=30 cm depth) compared to the deeper sensors. Across both the shallow and deep sensors, the event-based method had the highest CA and lowest RMSE in all cases except in the shallow sensors in 2020, when the CA was highest (94.44%) in the hysteresis method. The event-based approach also resulted in the highest CA and lowest RMSE when looking at results across irrigated and non-irrigated treatments separately. In general, the CA of hysteresis analysis was higher than the density analysis for all depths, irrigation treatments, and years; however, the RMSE of the hysteresis method was always higher than the density approach.
For PEL estimation, the event-based approach demonstrated higher CA than the other methods in both growing seasons, across all depths and irrigation treatments except for the deep sensors (>30 cm) in 2021 (table 9). While the hysteresis analysis consistently led to 100% identification of PEL events at all depths (table 6), its CA was generally lower compared to the other methods. This suggests that the hysteresis analysis tends to overestimate the occurrence of PEL events in the field relative to their actual occurrence. Although the hysteresis analysis exhibited the lowest RMSE in most cases, the low CA associated with false identification of PEL events raises concerns about its application in fields where over-irrigation could pose a threat to crops. Likewise, the density analysis had the highest RMSE in 80% of the cases (8 out of 10) across different depths, years, and treatment combinations (table 9). While the event-based approach did not consistently outperform the density and hysteresis analysis in terms of RMSE for PEL estimation, its consistently higher CA and better performance in irrigated treatments provide confidence in its ability to detect fluctuations in dynamic field conditions.
 |
| Figure 6. Representative plots of the event-based method demonstrating different events (ET, INF, RW, GD) and illustrating the identification of FC (blue circle) estimates using volumetric water content (?) measurements for 2020, corn with full irrigation [top] and corn 2020 with non-irrigated [bottom] treatment plots at 10 cm soil depth. Blue dashed line represents reference FC estimate for the sensor. Neither of the sensors plotted demonstrated PEL behavior. INF = infiltration, GD = gravity drainage, RW = rewetting, ET = evapotranspiration. |
Discussion
To support irrigation management, hydrologic signatures for soil moisture should ideally be able to identify instances when FC and PEL occur and accurately estimate the values associated with those instances. Our findings highlight the feasibility of using the event-based method to identify periods of INF, GD, ET, and RW. By analyzing the transitions and occurrence periods of these events across multiple depths and irrigation treatments, the event-based approach provides an effective framework for estimating FC and PEL that outperforms other signature methods, particularly at shallow soil depths. Our comparison found that at shallow depths (=30 cm), sensors often exhibited unimodal distributions of soil moisture, which contrasts with the assumption of a bimodal soil moisture distribution, implies more soil water stored in the fields (Araki et al., 2022), and is indicative of the challenges of applying density-based soil moisture signatures in well-drained soils due to the faster rate of change of ? (Chandler et al., 2017). Density and hysteresis approaches are likely to perform better under different seasonal conditions and longer timescales (Branger and McMillan, 2020); for example, hysteresis analyses perform best in conditions where periods of cool-season rainfall are followed by a period of several days without evaporation (Chandler et al., 2017). Similarly, Bean et al. (2018) found that the performance of different automated methods for estimating FC in shallow soil varied significantly across soil types and cropping systems. These findings collectively demonstrate that the effectiveness of any signature method will depend on the soil type and climate conditions at the site in which it is applied. Additional research that provides guidance on which signature approaches are most appropriate in different soil types, land uses, and climatic conditions would be valuable in translating these results into practice.
While this study demonstrates the potential for using event-based signature analysis for estimating FC and PEL, there are several limitations and areas for future research and methodological refinement. Our approach does require tuning some steps within the analytical process; for example, we adjusted the stopping criteria in the H/T algorithm (30% for positive and 35% for negative class) slightly below the recommended threshold of 40% by Jiang (2013) to improve the classification of the soil moisture events. We recognize that this threshold might vary in different datasets and may require tuning for effective event identification and identifying algorithmic steps that can reduce the need for manual tuning could result in a more easily transferable process. Additionally, previous studies have highlighted the influence of antecedent ? values on FC estimation, suggesting the presence of dynamic FC (Bean et al., 2018; Hardie et al., 2011). However, our event-based method, along with the existing hydrological signature methods, estimates one single value for FC and PEL, which may not reflect actual conditions. Further research should focus on capturing dynamic FC and PEL estimates to provide a better representation of the total plant-available water for irrigation management at different periods throughout the growing season. One final limitation of our study is that we admittedly focused only on the delineation of FC and PEL values, rather than quantifying their impacts on irrigation recommendations and efficiency. This would be a valuable area of additional research using computational modeling (as in Kumar et al., 2023) and field studies (as in Sangha et al., 2023).
 |
| Figure 7. Representative plots of the event-based method comparing identification of different events (ET, INF, RW, GD) and the FC (blue circle) and PEL (red circle) estimates using volumetric water content (?) measurements at shallow (10 cm) [top] vs. deep (60 cm) soil depth [bottom] for corn 2020, precision and 2020, corn, non-irrigated, respectively. Blue dashed line represents reference FC estimate, while red dashed line represents the reference PEL estimate for the sensor. The absence of red circles on the top plot indicates that the method did not detect any PEL estimates for this sensor. Absence of blue or red dashed lines indicates that no reference values (FC or PEL) were detected for the sensor. INF = infiltration, GD = gravity drainage, RW = rewetting, ET = evapotranspiration. |
Even with methodological refinements, any event-based signature approach will likely rely on distinct fluctuations in ? to identify these events accurately. However, in situations where soil moisture fluctuations are not pronounced, the applicability of the event-based signature approach may be limited, and other approaches will be necessary. These could be contexts where more sophisticated analyses, such as the inverse modeling approach adopted by Kumar et al. (2023), could be particularly valuable. There is potentially a tradeoff where more sophisticated analyses can achieve greater accuracy in determining optimal irrigation recommendations but require additional time, data, and analytical steps to achieve this. Because of this tradeoff, we think that hydrologic signature analyses and inverse modeling present two complementary approaches to SHP quantification, and collectively point towards multiple potentially fruitful areas of additional research. In particular, computational modeling and field studies that quantify the yield and financial benefits of increasingly accurate SHP estimation would be a valuable area for future research. Optimal approaches to using sensor data for irrigation management will likely depend on grower objectives (e.g., maximizing yield versus maximizing profit), the labor and equipment available to implement irrigation management, crop values and water sensitivities, and soil conditions. Thus, there could be great benefit in developing a suite of different management approaches that could be implemented under different contexts. We acknowledge that the need for specialized knowledge is a barrier to grower’s adoption, and our method in its current form requires specialized skills and is not a simple “click-of-a-button” solution. The development of user-friendly tools and algorithms that automate the event-based signature analysis process, as well as methods for integrating SHP estimation into existing data storage and automated irrigation management platforms, will enhance its accessibility and practicality for irrigators.
| Table 8. Classification accuracy (CA) and root mean square error (RMSE) of FC values estimated using density, hysteresis, and event-based analyses compared to the reference values for 2020 and 2021. | |||||||||||||
| Signature Method | Sensors | 2020 | 2021 | ||||||||||
| CA (%) | RMSE (%) | CA (%) | RMSE (%) | ||||||||||
| All depths and irrigation treatments | Density | all | 54.2 | 2.66 | 62.5 | 3.36 | |||||||
| Hysteresis | all | 62.5 | 4.83 | 75.0 | 4.82 | ||||||||
| Event | all | 75.0 | 1.87 | 79.2 | 1.69 | ||||||||
| Results by depth | Density | =30 cm | 72.2 | 2.58 | 83.3 | 3.32 | |||||||
| Hysteresis | =30 cm | 94.4 | 6.20 | 100.0 | 5.73 | ||||||||
| Event | =30 cm | 88.9 | 1.44 | 100.0 | 1.90 | ||||||||
| Density | >30 cm | 43.3 | 2.68 | 50.0 | 2.82 | ||||||||
| Hysteresis | >30 cm | 43.3 | 3.09 | 60.0 | 3.19 | ||||||||
| Event | >30 cm | 70.0 | 1.99 | 66.7 | 1.14 | ||||||||
| Results by treatment | Density | Irrigated | 46.9 | 2.60 | 62.5 | 3.91 | |||||||
| Hysteresis | Irrigated | 56.3 | 4.55 | 78.1 | 5.15 | ||||||||
| Event | Irrigated | 81.3 | 1.58 | 78.1 | 2.04 | ||||||||
| Density | Non-irrigated | 68.8 | 2.78 | 62.5 | 2.26 | ||||||||
| Hysteresis | Non-irrigated | 75.0 | 5.39 | 68.8 | 4.16 | ||||||||
| Event | Non-irrigated | 75.0 | 2.45 | 81.3 | 1.00 | ||||||||
Table 9. Classification accuracy (CA) and root mean square error (RMSE) of PEL values estimated using density, hysteresis, and event-based analyses compared to the reference values for 2020 and 2021. RMSE could not be calculated for shallow sensors in 2020 or for the event-based method on irrigated sensors in 2020 because no sensors demonstrated PEL behavior either in the time series or using the event-based method. | |||||||||||||
| Signature Method | Sensors | 2020 | 2021 | ||||||||||
| CA (%) | RMSE (%) | CA (%) | RMSE (%) | ||||||||||
| All depths and irrigation treatments | Density | all | 37.5 | 7.28 | 29.2 | 4.94 | |||||||
| Hysteresis | all | 25.0 | 2.56 | 18.8 | 2.78 | ||||||||
| Event | all | 68.8 | 3.90 | 72.9 | 2.47 | ||||||||
| Results by depth | Density | =30 cm | 44.4 | - | 33.3 | 8.08 | |||||||
| Hysteresis | =30 cm | 0.00 | - | 16.7 | 3.68 | ||||||||
| Event | =30 cm | 77.7 | - | 88.9 | 3.79 | ||||||||
| Density | >30 cm | 33.3 | 7.28 | 26.7 | 1.15 | ||||||||
| Hysteresis | >30 cm | 40.0 | 2.56 | 76.7 | 1.81 | ||||||||
| Event | >30 cm | 60.0 | 3.90 | 63.3 | 1.80 | ||||||||
| Results by treatment | Density | Irrigated | 28.1 | 10.65 | 34.4 | 4.80 | |||||||
| Hysteresis | Irrigated | 6.25 | 6.40 | 25.0 | 3.70 | ||||||||
| Event | Irrigated | 62.5 | - | 75.0 | 1.80 | ||||||||
| Density | Non-irrigated | 56.2 | 5.59 | 18.8 | 5.23 | ||||||||
| Hysteresis | Non-irrigated | 62.5 | 0.64 | 6.25 | 0.93 | ||||||||
| Event | Non-irrigated | 81.2 | 3.90 | 68.8 | 3.79 | ||||||||
While the event-based approach is generally suitable for most agricultural fields, caution should be exercised when applying it to determine PEL in fields with energy-limited conditions and during periods of extensive rainfall events. For instance, our study fields experienced frequent rainfall and irrigation events, resulting in rare occurrences of PEL events. Additionally, care should be taken when estimating FC values at deeper sensors, as they may not exhibit clear signs of drainage and ET losses. To ensure reliable and accurate estimation of FC and PEL, it is recommended to assess the applicability of the event-based approach in specific contexts and complement these estimates with literature values and expert judgement where required. By addressing these considerations, we can improve irrigation management practices and maintain a fine balance between water supply and demand under rapidly changing soil moisture conditions in humid agricultural fields.
Conclusion
Hydrologic signatures, which can identify soil moisture parameters such as FC and PEL from time series data, can have the potential to make precision irrigation more accurate and efficient. This study presented an event-based signature method aimed at capturing the complex soil moisture dynamics that occur in humid agricultural soils, while also contributing to a broader understanding of which signature methods are most suitable for different hydrologic contexts. Our study revealed that existing soil moisture signature methods face limitations in such dynamic soil moisture conditions and that the event-based method exhibited higher classification accuracy for both the field capacity (75.0%–79.2%) and plant extraction limit (68.8%–72.9%) across all tested sensors. Similarly, the estimation error for field capacity was lowest for the event-based method (1.69%–1.87%) compared to the other existing methods. However, it is important to acknowledge that the event-based approach may encounter challenges in accurately identifying different events in situations involving deeper soil depths and non-agricultural fields with less pronounced short-term fluctuations in volumetric water content. We therefore recommend further efforts to refine the event-based signature approach to enhance the detection of different events and obtain more precise estimates of field capacity and plant extraction limit values for more efficient irrigation water management across a wider field and climatic conditions.
Supplemental Material
The supplemental materials for "Event-Based Hydrological Signatures to Quantify Soil Moisture Parameters in Agricultural Soils Under Contrasting Irrigation Practices in Humid Climates" are available from the ASABE Figshare repository:
https://doi.org/10.13031/26075179 (General Supplemental information)
https://doi.org/10.13031/25371220 (R code)
https://doi.org/10.13031/25371214 (Data)
https://doi.org/10.13031/25371202 (Graph)
Acknowledgments
This work was financially supported by the Virginia Agricultural Council (grant #765) and USDA Agriculture and Food Research Initiative (AFRI; Grant #2023-67019-39703). This support is gratefully acknowledged. The authors would also like to thank Laljeet Sangha and the field managers and staff at Tidewater Agricultural Research and Extension Center in Suffolk.
References
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