Marit Gitte Andrea Hendrickx

Field-scale soil moisture retrieval from Sentinel-1 synthetic aperture radar (SAR) is rather well established for bare soils, winter crops, and grasslands, but its applicability during summer cropping periods remains uncertain due to dense vegetation and complex vegetation structure. This study evaluates the potential and limitations of the Sentinel-derived soil moisture product (S²MP, El Hajj et al. (2017)), based on a neural network that uses Sentinel-1 VV backscatter and Sentinel-2 NDVI, for surface soil moisture estimation during summer cropping.The first part of this study evaluates S²MP against in situ measurements at 10 cm depth over several winter and summer crops in a Mediterranean context (Bazzi et al., 2023). Results show that Sentinel-1 mainly senses the top few centimetres of soil, leading to strong underestimation in dry conditions (up to ~20 vol.%) and smaller biases under moderately wet conditions, while performance degrades again in very wet soils. Reliable soil moisture retrievals are limited to low–moderate vegetation cover (NDVI < 0.7), with crop-dependent biases under dense canopies, and accuracy improves at lower radar incidence angles (< 35°).The second part analyses summer vegetable case studies in Flanders, comparing S²MP with in situ observations across irrigated and rainfed fields. S²MP successfully captures rainfall and irrigation signals during early growth stages and differentiates irrigated from non-irrigated areas, but performance under dense canopies strongly depends on crop type. Crops with complex canopy structures (e.g. beans podding stage, pumpkins) show reduced or inconsistent sensitivity, while onions and carrots retain detectable soil moisture dynamics even at high NDVI. These results demonstrate that NDVI alone is insufficient to characterise vegetation effects on SAR soil moisture retrievals and highlight the need for crop-specific parameterisation and complementary longer-wavelength SAR observations.References:El Hajj, M., Baghdadi, N., Zribi, M., & Bazzi, H. (2017). Synergic Use of Sentinel-1 and Sentinel-2 Images for Operational Soil Moisture Mapping at High Spatial Resolution over Agricultural Areas. Remote Sensing 2017, Vol. 9, Page 1292, 9(12), 1292. https://doi.org/10.3390/RS9121292Bazzi, H., Baghdadi, N., Nino, P., Napoli, R., Najem, S., Zribi, M., & Vaudour, E. (2023). Retrieving Soil Moisture from Sentinel-1: Limitations over Certain Crops and Sensitivity to the First Soil Thin Layer. Water 2024, Vol. 16, Page 40, 16(1), 40. https://doi.org/10.3390/W1601004

Observations of soil states obtained from in-situ or remote sensors have various sources of errors. A crude way to represent these errors is to assume that part of the error is purely random whereas another part persists and does not change over time. Since the persistent part does not cancel out when more data become available over time whereas the random part does, the partitioning of the error into a persistent and random part is important to assess the uncertainty of model parameters and model predictions that are derived from these observations. Two approaches can be followed to represent these systematic errors in model parameter estimation. The first approach represents the systematic error as an additional parameter representing the bias that is estimated using additional unbiased observations, which we assumed to have only random errors. A second approach represents the systematic error as a covariance in the error-covariance matrix. The uncertainty of the model predictions in the first approach consists of a term that represents the uncertainty of the bias estimation, which is independent of the magnitude of the bias and depends only on the uncertainty of the unbiased additional observations. When additional unbiased measurements are included in the second approach, which represents bias as error covariance, smaller model prediction uncertainty is obtained than using the first approach. This is especially the case when the covariance representing the bias is smaller than the variance of the average error of the random observations. Including prior knowledge about the bias in the error covariance, reduces the model parameter and prediction uncertainty.

The SWIM² framework (Hendrickx et al., 2025) integrates a soil water balance model with in situ sensor data and soil moisture samples through Bayesian inverse modelling. The calibrated model then generates probabilistic 10-day soil moisture forecasts, enabling real-time, site-specific irrigation advice. SWIM² was validated in a real-time setup for 18 vegetable cropping cycles on agricultural fields in Flanders, Belgium, with reliable precipitation data. Although using minimal prior knowledge and despite sensor bias, SWIM² achieves robust soil moisture predictions for a 7-day horizon, with accuracies comparable to sensor measurements. We also assessed the impact of model parameter and weather forecast uncertainty on SM prediction uncertainty, water stress prediction and irrigation advice by integrating the calibrated model ensemble with ensemble-based probabilistic weather forecasts, resulting in high detection rate and accuracy in predicting water stress triggering the irrigation threshold.Time series of vegetation indices such as NDVI and LAI from Sentinel-2 optical remote sensing as well as LST from Sentinel-3 contain much information on crop growth and crop evapotranspiration. Additionally, the new NISAR mission is promising for high-resolution surface soil moisture observations. We assess relations between in situ measurements and model outputs (crop growth curve, actual ET and SWC), and the remote sensing data, and we discuss opportunities of these data to improve soil moisture and ETa predictions.Reference: Hendrickx, M.G.A., Vanderborght, J., Janssens, P., Laloy, E., Bombeke, S., Matthyssen, E., Waverijn, A., Diels, J. (2025). Field-scale soil moisture predictions in real time using in situ sensor measurements in an inverse modeling framework: SWIM². Authorea Preprints, doi:10.22541/ESSOAR.175103915.57413983/V1.

Affordable autonomous soil sensors and IoT technology enable real‐time soil moisture monitoring, which offers opportunities for real‐time model calibration and irrigation optimization. We introduce an irrigation decision support system SWIM ² (Sensor Wielded Inverse Modeling of a Soil Water Irrigation Model), a digital twin that integrates continuous sensor data and unbiased, periodic soil samples with an FAO‐based soil water balance model using a Bayesian inverse modeling algorithm, DREAM _(ZS) (DiffeRential Evolution Adaptive Metropolis). SWIM ² estimates 12 soil and crop parameters and their associated probability distributions and correlations, providing soil moisture predictions with uncertainty estimates. The SWIM ² framework is illustrated and validated in a real‐time setup for 18 vegetable cropping cycles on agricultural fields in Flanders, Belgium, with in situ precipitation data. Although using minimal prior knowledge and despite sensor bias, SWIM ² achieves robust soil moisture predictions for a 7‐day horizon, with accuracies comparable to sensor measurements. Predictions improve substantially in precision within the first 20 calibration days and maintain high predictive power throughout the growing season. The impact of in situ measurements and temporal covariance of the observational errors (“error covariance”) was assessed, indicating that good knowledge of the error covariance and independent soil moisture samples are essential to correct for sensor bias and ensure accurate model calibration, while continuous sensor data ensure accurate and precise estimates of the dynamics. This study demonstrates the use of soil moisture sensor data in a Bayesian inverse modeling framework, offering practical solutions for real‐time soil moisture prediction and irrigation decision‐making, enhancing water management across agricultural fields.

Affordable autonomous soil sensors and IoT technology enable real-time soil moisture monitoring, which offers opportunities for real-time model calibration and irrigation optimization. We introduce an irrigation decision support system SWIM² (Sensor Wielded Inverse Modeling of a Soil Water Irrigation Model), a digital twin that integrates continuous sensor data and unbiased, periodic soil samples with an FAO-based soil water balance model using a Bayesian inverse modeling algorithm, DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis). SWIM² estimates 12 soil and crop parameters and their associated probability distributions and correlations, providing soil moisture predictions with uncertainty estimates. The SWIM² framework is illustrated and validated in a real-time setup for 18 vegetable cropping cycles on agricultural fields in Flanders, Belgium, with reliable precipitation data. Although using minimal prior knowledge and despite sensor bias, SWIM² achieves robust soil moisture predictions for a 7-day horizon, with accuracies comparable to sensor measurements. Predictions improve substantially in precision within the first 20 calibration days and maintain high predictive power throughout the growing season. The impact of in-situ measurements and temporal covariance of the observational errors (“error covariance”) was assessed, indicating that good knowledge of the error covariance and independent soil moisture samples are essential to correct for sensor bias and ensure accurate model calibration, while continuous sensor data ensure accurate and precise estimates of the dynamics. This study demonstrates the use of soil moisture sensor data in a Bayesian inverse modeling framework, offering practical solutions for real-time soil moisture prediction and irrigation decision-making, enhancing water management across agricultural fields.

The rise of affordable, autonomous in-situ sensors and IoT technology has enabled real-time monitoring of soil moisture, opening new opportunities for sustainable irrigation management. We present SWIM² (Sensor Wielded Inverse Modelling of a Soil Water Irrigation Model), a data-driven digital twin designed for field-scale soil moisture predictions, irrigation advice, and quantification of crop water stress, crop water use efficiency, and irrigation efficiency in vegetable production. SWIM² integrates real-time soil moisture sensor data with a soil water balance model using the DREAM(zs) Bayesian inverse modeling approach to estimate 12 key parameters, including soil and crop growth characteristics, along with their uncertainty distributions. This probabilistic framework with integration of weather forecasts allows for dynamic soil moisture predictions with uncertainty estimates, enabling farmers to make informed decisions about irrigation scheduling. By providing an estimate of the water required to mitigate drought risk, SWIM² supports efficient water use while maintaining crop health.We validated and implemented SWIM² in commercial fields and irrigation trials across Flanders to evaluate its performance and demonstrate its utility in predicting soil moisture, scheduling irrigation, and quantifying water use efficiency under diverse conditions. In 2022, SWIM² was used in real-time to guide irrigation decisions during a celery trial, and in 2023, it was applied to celery, chicory, leek, and sweet potato trials. During these irrigation trials, the model was calibrated two times a week, after which soil moisture was predicted, and irrigation scheduling was based on the predicted probability of water stress over the following four days. Retrospectively, model calibration based on the 100% irrigation treatment enabled a comparison of various irrigation treatments, providing insights into crop water stress and irrigation surpluses.Our results show that SWIM² accurately predicts soil moisture and improves irrigation scheduling, while also providing insights into resource optimization, contributing to sustainable agricultural practices. Due to the probabilistic nature of the framework, the irrigation strategy can be tailored to suit a conservative or risk-tolerant approach, depending on the farmer's preferences and water availability. By bridging advanced modeling with practical applications, SWIM² empowers farmers to make data-driven decisions for resilient and efficient crop management.

With the rise of affordable, autonomous sensors and IoT (Internet-of-Things) technology, it is possible to monitor soil moisture in a field online and in real time. This offers opportunities for real-time model calibration for irrigation scheduling. A framework is presented where realtime sensor data are coupled with a soil water balance model to predict soil moisture content and irrigation requirements at field scale. SWIM², Sensor Wielded Inverse Modelling of a Soil Water Irrigation Model, is a framework based on the DREAM inverse modelling approach to estimate 12 model parameters (soil and crop growth parameters) and their uncertainty distribution. These parameter distributions result in soil moisture predictions with a prediction uncertainty estimate, which enables a farmer to anticipate droughts and estimate irrigation requirements.The SWIM² framework was validated based on three growing seasons (2021-2023) in about 30 fields of vegetable growers in Flanders. Kullback–Leibler divergence (KLD) was used as a metric to quantify information gain of the model parameters starting from non-informative priors. Performance was validated in two steps, i.e. the calibration period and prediction period, which is in correspondence with the real-world implementation of the framework. The RMSE, correlation (R, NSE) and Kling-Gupta efficiency (KGE) of soil moisture were analyzed in function of time, i.e. the amount of available sensor data for calibration.Soil moisture can be predicted accurately after 10 to 20 days of sensor data is available for calibration. The RMSE during the calibration period is generally around 0.02 m³/m³, while the RMSE during the prediction period decreases from 0.04 to 0.02 m³/m³ when more calibration data is available. Information gain (KLD) of some parameters (e.g. field capacity and curve number) largely depends on the presence of dynamic events (e.g. precipitation events) during the calibration period. After 40 days of sensor data, the KGE and Pearson correlation of the calibration period become stable with median values of 0.8 and 0.9, respectively. For the validation period, the KGE and Pearson correlation are increasing in time, with median values from 0.3 to 0.7 (KGE) and from 0.7 to 0.95 (R). These good results show that, with this framework, we can simulate and predict soil moisture accurately. These predictions can in turn be used to estimate irrigation requirements.Precipitation radar data was primarily considered as an input without uncertainty. As an extension, precipitation forcing error can be treated in DREAM by applying rainfall multipliers as additional parameters that are estimated in the inverse modelling framework. The multiplicative error of the radar data was quantified by comparison of radar data to rain gauge measurements. The prior uncertainty of the logarithmic multipliers was described by a Laplace distribution and was implemented in DREAM. The extended framework with rainfall multipliers shows better convergence and acceptance rate compared to the main framework. The calibration period shows better performance with higher correlations and lower RMSE values, but a decrease in performance was found for the validation period. These results suggest that the implementation of rainfall multipliers leads to overfitting, resulting in lower predictive power.

Accurately quantifying errors in soil moisture measurements from in situ sensors at fixed locations is essential for reliable state and parameter estimation in probabilistic soil hydrological modeling. This quantification becomes particularly challenging when the number of sensors per field or measurement zone (MZ) is limited. When direct calculation of errors from sensor data in a certain MZ is not feasible, we propose to pool systematic and random errors of soil moisture measurements for a specific measurement setup to derive a pooled error covariance matrix that applies across different fields and soil types. In this study, a pooled error covariance matrix was derived from soil moisture sensor measurements and soil moisture sampling campaigns conducted over three growing seasons, covering 93 cropping cycles in agricultural fields with diverse soil textures in Belgium. The MZ soil moisture estimated from soil samples, which showed a small standard error (0.0038 m³ m^‑3) and which was not correlated between different sampling campaigns since soil samples were taken at different locations, represented the ‘true’ MZ soil moisture. First, we established a pooled linear recalibration of the TEROS 10 (Meter Group, Inc., USA) manufacturer's sensor calibration function. Then, for each individual sensor as well as for each MZ, we identified systematic deviations and temporally varying residual deviations between the calibrated sensor data and sampling data. The autocovariance of the individual or the MZ-averaged sensor measurement errors was represented by the variance of the systematic deviations across all sensors or MZs whereas the random error variance was calculated from the variance of the pooled residual deviations. The total error variance was equal to the sum of the autocovariance and random error variance. Due to spatial sensor correlation, the variance and autocovariance of MZ-average sensor measurement errors could not be derived from the individual sensor error variances and covariances. The pooled error covariance matrix of the MZ-averaged soil moisture measurements indicated a significant sensor error autocorrelation of 0.518, as the systematic error standard deviation (σ_α- = 0.0327 m³ m^‑3) was similar to the random error standard deviation (σ_ε- = 0.0316 m³ m^‑3). These results demonstrate that the common assumption of uncorrelated random errors to determine parameter and model prediction uncertainty is not valid when measurements from sparse in situ soil moisture sensors are used to parameterize soil hydraulic models. Further research is required to assess to what extent the error covariances found in this study can be transferred to other areas, and how they impact parameter estimation in soil hydrological modeling.