Water is essential for agricultural productivity. Assessing water shortages and reduced yield potential is a critical factor in decision-making for ensuring agricultural productivity and food security. Crop simulation models, which align with physical processes, offer intrinsic explainability but often perform poorly. Conversely, machine learning models for crop yield modeling are powerful and scalable, yet they commonly operate as black boxes and lack adherence to the physical principles of crop growth. This study bridges this gap by coupling the advantages of both worlds. We postulate that the crop yield is inherently defined by the water availability. Therefore, we formulate crop yield as a function of temporal water scarcity and predict both the crop drought stress and the sensitivity to water scarcity at fine-scale resolution. Sequentially modeling the crop yield response to water enables accurate yield prediction. To enforce physical consistency, a novel physics-informed loss function is proposed. We leverage multispectral satellite imagery, meteorological data, and fine-scale yield data. Further, to account for the uncertainty within the model, we build upon a deep ensemble approach. Our method surpasses state-of-the-art models like LSTM and Transformers in crop yield prediction with a coefficient of determination ($R^2$-score) of up to 0.82 while offering high explainability. This method offers decision support for industry, policymakers, and farmers in building a more resilient agriculture in times of changing climate conditions.

Regarding problems like reduced precipitation and an increase in population, water resource scarcity has become one of the most critical problems in modern-day societies, as a consequence, there is a shortage of available water resources for irrigation in arid and semi-arid countries. On the other hand, it is possible to utilize modern technologies to control irrigation and reduce water loss. One of these technologies is the Internet of Things (IoT). Despite the possibility of using the IoT in irrigation control systems, there are complexities in designing such systems. Considering this issue, it is possible to use agent-oriented software engineering (AOSE) methodologies to design complex cyber-physical systems such as IoT-based systems. In this research, a smart irrigation system is designed based on Prometheus AOSE methodology, to reduce water loss by maintaining soil moisture in a suitable interval. The designed system comprises sensors, a central agent, and irrigation nodes. These agents follow defined rules to maintain soil moisture at a desired level cooperatively. For system simulation, a hybrid agent-based and system dynamics model was designed. In this hybrid model, soil moisture dynamics were modeled based on the system dynamics approach. The proposed model, was implemented in AnyLogic computer simulation software. Utilizing the simulation model, irrigation rules were examined. The system's functionality in automatic irrigation mode was tested based on a 256-run, fractional factorial design, and the effects of important factors such as soil properties on total irrigated water and total operation time were analyzed. Based on the tests, the system consistently irrigated nearly optimal water amounts in all tests. Moreover, the results were also used to minimize the system's energy consumption by reducing the system's operational time.

Reference Evapotranspiration (ET0) is a key parameter for designing smart irrigation scheduling, since it is related by a coefficient to the water needs of a crop. The United Nations Food and Agriculture Organization, proposed a standard method for ET0 computation (FAO56PM), based on the parameterization of the Penman-Monteith equation, that is widely adopted in the literature. To compute ET0 using the FAO56-PM method, four main weather parameters are needed: temperature, humidity, wind, and solar radiation (SR). One way to make daily ET0 estimations for future days is to use freely available weather forecast services (WFSs), where many meteorological parameters are estimated up to the next 15 days. A problem with this method is that currently, SR is not provided as a free forecast parameter on most of those online services or, normally, such forecasts present a financial cost penalty. For this reason, several ET0 estimation models using machine and deep learning were developed and presented in the literature, that use as input features a reduced set of carefully selected weather parameters, that are compatible with common freely available WFSs. However, most studies on this topic have only evaluated model performance using data from weather stations (WSs), without considering the effect of using weather forecast data. In this study, the performance of authors' previous models is evaluated when using weather forecast data from two online WFSs, in the following scenarios: (i) direct ET0 estimation by an ANN model, and (ii) estimate SR by ANN model, and then use that estimation for ET0 computation, using the FAO56-PM method. Employing data collected from two WFSs and a WS located in Vale do Lobo, Portugal, the latter approach achieved the best result, with a coefficient of determination (R2) ranging between 0.893 and 0.667, when considering forecasts up to 15 days.

Current hydrological modeling methods combine data-driven Machine Learning (ML) algorithms and traditional physics-based models to address their respective limitations incorrect parameter estimates from rigid physics-based models and the neglect of physical process constraints by ML algorithms. Despite the accuracy of ML in outcome prediction, the integration of scientific knowledge is crucial for reliable predictions. This study introduces a Physics Informed Machine Learning (PIML) model, which merges the process understanding of conceptual hydrological models with the predictive efficiency of ML algorithms. Applied to the Anandapur sub-catchment, the PIML model demonstrates superior performance in forecasting monthly streamflow and actual evapotranspiration over both standalone conceptual models and ML algorithms, ensuring physical consistency of the outputs. This study replicates the methodologies of Bhasme, P., Vagadiya, J., & Bhatia, U. (2022) from their pivotal work on Physics Informed Machine Learning for hydrological processes, utilizing their shared code and datasets to further explore the predictive capabilities in hydrological modeling.

Predictions of hydrologic variables across the entire water cycle have significant value for water resource management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly-insurmountable performance in modeling rainfall-runoff and other geoscientific variables, yet they cannot predict untrained physical variables and remain challenging to interpret. Here we show that differentiable, learnable, process-based models (called {\delta} models here) can approach the performance level of LSTM for the intensively-observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, enhance, or replace the process-based model modules. Without using an ensemble or post-processor, {\delta} models can obtain a median Nash Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing dataset, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing dataset, the difference is even smaller: 0.715 vs. 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, e.g., soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and later be constrained by their observations. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.

Groundwater level prediction is an applied time series forecasting task with important social impacts to optimize water management as well as preventing some natural disasters: for instance, floods or severe droughts. Machine learning methods have been reported in the literature to achieve this task, but they are only focused on the forecast of the groundwater level at a single location. A global forecasting method aims at exploiting the groundwater level time series from a wide range of locations to produce predictions at a single place or at several places at a time. Given the recent success of global forecasting methods in prestigious competitions, it is meaningful to assess them on groundwater level prediction and see how they are compared to local methods. In this work, we created a dataset of 1026 groundwater level time series. Each time series is made of daily measurements of groundwater levels and two exogenous variables, rainfall and evapotranspiration. This dataset is made available to the communities for reproducibility and further evaluation. To identify the best configuration to effectively predict groundwater level for the complete set of time series, we compared different predictors including local and global time series forecasting methods. We assessed the impact of exogenous variables. Our result analysis shows that the best predictions are obtained by training a global method on past groundwater levels and rainfall data.

The population of the earth is constantly growing and therefore also the demand for food. In consequence, breeding crop plants which most efficiently make use of the available cropland is one of the greatest challenges nowadays. In particular, plants which are resilient and resistant to environmental stresses are desirable. The development of such plants relies on the investigation of the interaction between the plant's genes and the environmental stresses. In order to be able to investigate the interaction a quantitative representation of the environmental stresses is needed. Here, we consider this representation combining state-of-the-art data-driven methods with expert-driven modeling from agriculture. Briefly put, it has been reported that environmental stress such as inappropriate or extreme temperature conditions, lack of sufficient moisture, etc., can significantly impede the life cycle development of corn, thus leading to yield reductions (cf.

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic parameter values in certain instances, ML algorithms establish the input-output relationship while ignoring the constraints imposed by well-known physical processes. While there is a notion that the physics model enables better process understanding and ML algorithms exhibit better predictive skills, scientific knowledge that does not add to predictive ability may be deceptive. Hence, there is a need for a hybrid modeling approach to couple ML algorithms and physics-based models in a synergistic manner. Here we develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India. Our results show the capability of the PIML model to outperform a purely conceptual model ($abcd$ model) and ML algorithms while ensuring the physical consistency in outputs validated through water balance analysis. The systematic approach for combining conceptual model structure with ML algorithms could be used to improve the predictive accuracy of crucial hydrological processes important for flood risk assessment.

Forests as natural reservoirs and filters can store, release, and purify water through their interactions with hydrological processes. For humans, a clean, stable, and predictable water supply is one of the most valuable ecosystem services provided by forests. Yet, globally, forests have undergone many changes driven by human activities (logging, reforestation, afforestation, agriculture, and urbanization) and natural disturbances (wildfires and insect infestations). From 2010 to 2015, tropical forests declined by 5.5 million ha year −1 , whereas temperate forests expanded by 2.2 million ha year−1 ([ 1 ][1]). The effects of both deforestation and forestation (reforestation and afforestation) on water supply have generated serious concerns and debates ([ 2 ][2], [ 3 ][3]), particularly after recent catastrophic fires in Australia and the western United States. However, hydrological consequences of forest changes are never simple, and future research and watershed management require a systematic approach that considers key contributing factors and a broad spectrum of response variables related to hydrological services. Zhang et al. showed the consistent tendency of deforestation to increase annual streamflow ([ 4 ][4]). More than 80% of deforested watersheds had annual streamflow increases ranging from 0.4 to 599.1%, mainly owing to reduced evapotranspiration after 1.7 to 100% forest cover loss ([ 4 ][4]). The large variations in the magnitude of changes depend on the scale, type, and severity of forest disturbance, climate, and watershed properties ([ 4 ][4], [ 5 ][5]). Larger-scale disturbance tends to cause greater increase in annual streamflow. Hydrological response to fire is similar to the response to logging, but the severity of the impact varies with climate, fuel accumulation, fire intensity, overstory tree mortality, and climate. Fires often cause hydrophobic soils, with reduced soil infiltration and acceleration of surface runoff and soil erosion. In a recent national assessment of the contiguous United States, forest fires had the greatest increase in annual streamflow in semiarid regions, followed by warm temperate and humid continental climate regions, with insignificant responses in the subtropical Southeast ([ 6 ][6]). The hydrological impact of insect infestation is likely less pronounced than those of other disturbances. Large-scale beetle outbreaks in the western United States and British Columbia, Canada, over recent decades were predicted to increase streamflow, with reduced evapotranspiration because of the death of infested trees ([ 5 ][5]). However, further evidence showed negligible impacts of beetle infestation on annual streamflow, owing to increased evapotranspiration of surviving trees and understory vegetation ([ 7 ][7]). Forestation can either reduce annual streamflow or increase it ([ 4 ][4], [ 8 ][8]). Zhang et al. ([ 4 ][4]) found that 60% of the forestation watersheds had annual streamflow reduced by 0.7 to 65.1% with 0.7 to 100% forest cover gain, whereas 30% of them (mostly small watersheds) had annual streamflow increased by 7 to 167.7% with 12 to 100% forest cover gain. Variations in annual streamflow response to forestation are even greater than those caused by deforestation, possibly owing to site conditions prior to forestation and tree species selected. Planting with a single fast-growing exotic species can have greater reduction in annual streamflow than with native species ([ 8 ][8]). Streamflow reductions after forestation are more common in semiarid and arid regions than in the humid subtropics and tropics ([ 4 ][4], [ 5 ][5]). Large-scale reforestation programs in the semiarid Loess Plateau in China caused substantial streamflow reductions that consequently approached water resource limits ([ 9 ][9]). Dry-season low flow is critical for water supply, particularly in the face of more severe droughts under climate change. Low-flow response to forest change can be positive, neutral, or negative ([ 5 ][5], [ 10 ][10]). The variable low-flow responses are mainly attributed to low-flow generation processes, forest characteristics (age, species, and regeneration), forestry practices (retention of riparian buffers, logging methods, and silviculture), changes in soil conditions, and choice of low-flow metrics (daily or 7-day minimum flow). Nevertheless, negative low-flow response is commonly expected if soil water storage and infiltration capacities are impaired by forest disturbances (soil compaction and erosion from logging, and soil water repellency following severe fires), and their recovery through reforestation could take much longer, because of the difficulty in restoring damaged soils ([ 10 ][10]). Generally, climate, watershed properties, forest characteristics, and their interactions are the major drivers for large variations in hydrological responses to forest change ([ 2 ][2], [ 4 ][4]). Zhou et al. assessed global land-cover effects on annual streamflow, based on a general theoretical framework ([ 11 ][11]). They found that hydrological sensitivity to land-cover change was determined by watershed properties (watershed size, slope, configuration, and soil), climate (precipitation or potential evaporation), and their interactions, where land cover and watershed properties jointly indicate water retention ability. Land cover or forest change can cause greater hydrological responses in drier watersheds or those with low water retention capacity. Similarly, McDonnell et al. ([ 12 ][12]) recommended studying watershed storages and water movements in the vertical zone that includes forest canopy, soil, fresh bedrock, and the bottom of groundwater ([ 13 ][13]), to further reveal the mechanisms for variable hydrological response to forest change. The feedback between forests and climate may also introduce complexity. Forests can supply atmospheric moisture through evapotranspiration and potentially increase precipitation (precipitation recycling) locally and in downwind directions. Therefore, forest change affects not only downstream river flow, but also precipitation and water supply downwind ([ 5 ][5]). Lawrence and Vandecar revealed variable rainfall responses to tropical deforestation across landscapes, depending on deforestation thresholds, such as reduced rainfall by large-scale deforestation and increased rainfall by small clearings ([ 14 ][14]). The effects of forest change on precipitation are likely related to topography, prevailing wind, and climate, because they affect moisture residence time, moisture transportation, and precipitation generation. The lack of observational evidence highlights the need for research on the feedback between climate and forest change at regional or continental scales. Time scale is important for understanding these variations. Hydrological effects of forest change can vary with time as forests regrow. Coble et al. reviewed long-term responses of low flows to logging in 25 small catchments in North America ([ 10 ][10]). They identified dynamic low-flow responses over three distinct time periods associated with the development of forest canopy leaf area index and corresponding evapotranspiration: consistent increase in the first 5 to 10 years, variable responses (increase, no change, or decline) during the next 10 to 20 years, and substantial decline in some (16 out of 25) watersheds multiple decades later. However, no decline in low flows was found in nine watersheds during the third period—likely dependent on similar factors previously identified for variations in low-flow response. The dynamic hydrological responses suggest that long-term studies are critical for fully capturing possible trends and variations in the effects of forest change on water supply ([ 5 ][5]). ![Figure][15] The complex influence of forests on water supply Forests in watersheds play a critical role in regulating downstream water supply and associated ecosystem services. GRAPHIC: N. DESAI/ SCIENCE The consistencies and large variations over space and time in streamflow responses to forest change call for a systematic perspective to elucidate both explanatory (factors affecting hydrological functions) and response (hydrological functions) variables in future studies (see the figure). In the systematic context, explanatory variables, including climate, forest, watershed properties, and their interactions and feedback across multiple spatial-temporal scales that jointly control streamflow responses, should all be assessed. To better clarify the response, a more complete spectrum of hydrological variables, including the magnitude, duration, timing, frequency, and variability of flows, which collectively determine river flow conditions, aquatic functions, and thus ecosystem services such as water supply, should be included in an assessment ([ 15 ][16]). Nonetheless, water-supply assessments often use limited hydrological variables (such as annual mean flows), which could underestimate total hydrological functions or even produce misleading conclusions resulting from different or contrasting responses of various flow variables. A systematic assessment of the effects of deforestation and forestation on water supply requires multidisciplinary collaborations. The classic paired watershed experiment (PWE: one watershed as a control and the others as the treatment) ([ 12 ][12]), mainly designed to assess streamflow response to forest change, has limitations to evaluate interactions and feedback among water, forests, climate, and watershed properties. Future PWEs should systematically consider more variables and processes (flow pathways, water storage and retention, and hydrological sensitivity) with various approaches (isotopic tracing, telemetering, and modeling). With long-term in situ monitoring and growing remote-sensing data, the forest-water nexus at larger spatial scales should be explored using advanced analytical tools (machine learning, and coupled climatic-ecohydrological modeling) within a systematic context. Future assessment should also focus on watershed management tools such as payments for ecosystem services, with the inclusion of more representative water variables to support synergies or trade-offs between hydrological and other ecosystem services provided by forests in a changing environment. 1. [↵][17]1. R. J. Keenan et al ., For. Ecol. Manage. 352, 9 (2015). [OpenUrl][18] 2. [↵][19]1. X. Wei et al ., Glob. Change Biol. 24, 786 (2018). [OpenUrl][20] 3. [↵][21]1. K. D. Holl, 2. P. H. S. Brancalion , Science 368, 580 (2020). [OpenUrl][22][Abstract/FREE Full Text][23] 4. [↵][24]1. M. Zhang et al ., J. Hydrol. (Amst.) 546, 44 (2017). [OpenUrl][25] 5. [↵][26]1. I. F. Creed, 2. M. van Noordwijk 1. I. F. Creed et al ., in Forest and Water on a Changing Planet: Vulnerability, Adaptation and Governance Opportunities. A Global Assessment Report, I. F. Creed, M. van Noordwijk, Eds. (International Union of Forest Research Organizations, 2018). 6. [↵][27]1. D. W. Hallema et al ., Nat. Commun. 9, 1307 (2018). [OpenUrl][28] 7. [↵][29]1. K. M. Slinski, 2. T. S. Hogue, 3. A. T. Porter, 4. J. E. McCray , Environ. Res. Lett. 11, 074010 (2016). [OpenUrl][30] 8. [↵][31]1. S. Filoso, 2. M. O. Bezerra, 3. K. C. B. Weiss, 4. M. A. Palmer , PLOS ONE 12, e0183210 (2017). [OpenUrl][32] 9. [↵][33]1. X. Feng et al ., Nat. Clim. Chang. 6, 1019 (2016). [OpenUrl][34] 10. [↵][35]1. A. A. Coble et al ., Sci. Total Environ. 730, 138926 (2020). [OpenUrl][36] 11. [↵][37]1. G. Zhou et al ., Nat. Commun. 6, 5918 (2015). [OpenUrl][38] 12. [↵][39]1. J. McDonnell et al ., Nat. Sustain. 1, 378 (2018). [OpenUrl][40] 13. [↵][41]1. G. Grant, 2. W. Dietrich , Water Resour. Res. 53, 2605 (2017). [OpenUrl][42] 14. [↵][43]1. 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Statistical methods for the analysis and forecasting of time series data have a long history (Tsay, 2000). The well-accepted Box-Jenkins analysis and forecasting methods have been applied in a wide range of applications, from finance to medicine, and the classic book that laid out the theory is now in its fourth edition with over 55,000 citations (Box et al., 2015). In this paper, we focus on the specialized area of time series regression where the goal is to predict one time series with the help of covariates that include elements which also have a time series nature. Some authors refer to this as dynamic regression (Hyndman and Athanasopoulos, 2018), others use the term regARIMA (Gómez and Maravall, 1994; Maravall et al., 2016). Pankratz (2012) provides an excellent overview.