Niels Schütze

Although objective functions (OFs) are widely discussed in the literature, many modelling studies still default to a few common metrics, without much consideration of their relative strengths and weaknesses. This paper systematically investigates the impact of OF choice on the representation of various streamflow characteristics across 47 conceptual models and 10 hydro-climatically diverse catchments selected from the CARAVAN dataset. We use eight different OFs for calibration, including the Kling–Gupta efficiency (KGE), Nash–Sutcliffe efficiency (NSE), a variant of each that uses a streamflow transformation, and four more recently proposed metrics. We further account for parameter uncertainty by retaining the top 500 parameter sets for each combination of model, basin and OF. We evaluate the representation of 15 hydrological signatures that capture a relevant selection of streamflow characteristics to determine generalisable strengths and weaknesses of individual OFs across different models and hydroclimatic conditions. A random forest importance analysis showed that OF choice is often more influential than model structure choice in determining signature representation, with catchment characteristics remaining the dominant control. While certain signatures, particularly those related to flow variability, are relatively insensitive to OF choice, other signatures exhibit large performance shifts across different OFs. As other studies have already noted, no single OF performs best across all signatures. Our consistent multi-model and multi-catchment experiment now provides generalisable guidance on which OF best reproduces which aspect of streamflow behaviour. This helps to better select objective functions most appropriate for a specific modelling purpose and provides insights into which metric combinations can cover a broader range of flow characteristics.

The sustainable intensification of agriculture requires precise water management strategies, particularly the adoption of deficit irrigation to cope with increasing global water scarcity. Optimizing the intraseasonal scheduling of limited water supplies represents a complex sequential decision-making problem governed by stochastic climatic boundary conditions and nonlinear crop responses. While deep reinforcement learning has emerged as a powerful paradigm for developing flexible closed-loop control policies, current applications often exhibit instability due to high-dimensional state spaces and the inadequate handling of physical constraints. This research advances the field by proposing and benchmarking a tailored deep reinforcement learning framework based on the Proximal Policy Optimization algorithm, coupled with the AquaCrop-OSPy soil-crop-atmosphere simulation model. The study introduces specific architectural enhancements to the learning agent, including a reduced observation space consisting of five causal biophysical variables, action masking to ensure strict adherence to seasonal water quotas, and a dense reward function based on transpiration efficiency to guide the learning process. To rigorously assess the algorithmic performance and quantify the value of information, the proposed approach is benchmarked against a comprehensive set of baselines, including a standard deep reinforcement learning implementation and a global evolutionary algorithm. Crucially, the evolutionary algorithm is configured with perfect foresight of future weather events, thereby serving as a theoretical oracle that defines the upper bound of achievable crop water productivity. Experimental validation was conducted for maize cultivation under deterministic conditions in Tunis and stochastic climate scenarios in Nebraska. The empirical results demonstrate that the proposed agent effectively navigates the trade-off between water conservation and yield maximization, capturing approximately 93.5 percent of the theoretical yield potential defined by the evolutionary algorithm oracle. This result indicates a minimal performance penalty attributed to the lack of future weather knowledge. In contrast, the reference implementation failed to converge to efficient policies under tight resource constraints. Furthermore, the economic evaluation highlights that the proposed strategy not only stabilizes yields during extreme drought years but also increases mean net profits by up to 66% compared to the reference baseline. These findings confirm that integrating domain knowledge through action masking and feature selection enables deep reinforcement learning to serve as a robust riskminimization tool, yielding near-optimal irrigation scheduling without requiring extensive weather forecasting.

Sustainable agricultural intensification necessitates precise deficit irrigation strategies to address global water scarcity. However, optimizing intra-seasonal scheduling under stochastic climatic conditions remains a complex control problem. While Deep Reinforcement Learning (DRL) offers a promising approach to flexible decision-making, existing applications often exhibit instability due to high-dimensional state spaces and an inability to enforce physical constraints. This study advances state-of-the-art irrigation control by proposing and benchmarking a tailored DRL framework based on Proximal Policy Optimization (PPO), coupled with the AquaCrop-OSPy simulation model. Moving beyond standard implementations, the research introduces specific enhancements to the learning agent: a reduced observation space limited to five causal biophysical variables, action masking to ensure strict adherence to seasonal water quotas, and a dense reward function based on transpiration efficiency. To rigorously quantify the value of information, the proposed approach is benchmarked against both a standard DRL baseline and a global Evolutionary Algorithm configured with perfect foresight of future weather events. This "oracle" defines the theoretical upper bound of achievable crop water productivity. Experimental validation on maize cultivation under deterministic and stochastic scenarios (Tunis and Nebraska) demonstrates that the proposed agent effectively navigates the trade-off between conservation and yield. The enhanced agent captures approximately 93.5% of the theoretical yield potential defined by the oracle, indicating a minimal performance penalty for the lack of future weather knowledge. Conversely, the standard reference implementation failed to converge under tight resource constraints. Economically, the proposed strategy not only stabilizes yields during extreme drought years but also increases mean net profits by up to 66% compared to the baseline. These findings confirm that integrating domain knowledge through action masking and feature selection transforms DRL into a robust tool for near-optimal irrigation scheduling without requiring extensive weather forecasting.

The KliWES 3.0 project investigated the historical and future development of the water balance in Saxony under changing climatic conditions. The simulations covered the reanalysis period 1961–2020 as well as the future up to the year 2100 using 21 climate projections. A comprehensive hydrological modeling was carried out for the entire Free State of Saxony (≈22,200 km²), including the opencast mining areas of Lusatia. The water balance of this region is characterized by decades of lignite mining and the associated intensive groundwater management, which led to a cumulative regional deficit of approximately 4 billion m³ by 2020. By flooding of the former opencast mines and the gradual reduction of groundwater drainage a large-scale recovery of groundwater levels shell be achieved within the coming decades, despite the expected reduction in water availability due to climate change.The state-wide water balance calculations for Saxony are based on the ArcEGMO model, which was improved by the integration of a floodplain approach. Furthermore, ERA5 land data were used to determine the potential grass reference evaporation. To evaluate the robustness of the model, a comparison between ArcEGMO, BROOK90, Raven 3, and Raven 4 was carried out in the catchment area of the Spree River in Saxony.BROOK90 is a 1d site model, which was used as validation for actual evaporation due to its detailed description of vertical soil-plant-atmosphere processes. Raven is a modular, object-oriented open-source model that allows flexible combinations of different hydrological process modules – from precipitation-runoff concepts and various snowmelt models to a wide range of evapotranspiration and soil moisture approaches. It can replicate both conceptual and physically based model structures. The current version, Raven 4.1, offers significant enhancements over Raven 3, in particular an integrated optimization module based on a linear solver for water management. This allows operating rules, reservoir target specifications, and water management discharge rules to be embedded directly into the hydrological system model - a functionality that is highly relevant in the context of the Lusatian opencast mining landscape.The results of the model comparison are examined with regard to structural differences, the sensitivity of the models to climatic changes, and the extent to which the choice of model influences the assessment of future water availability and runoff development. Particular focus is placed on the representation of anthropogenically modified systems in which management measures play a central role. The analysis demonstrates how model structure and process understanding shape the interpretation of future hydrological scenarios, and the resulting uncertainties for water management.

Increasing climate variability, more frequent droughts, and growing competition for freshwater resources amplify uncertainty in irrigation water availability and challenge sustainable agricultural water management. Addressing this uncertainty is essential for maintaining crop productivity under changing climatic conditions. This study presents a preliminary, climate-driven assessment of irrigation strategies using numerical irrigation experiments at more than ten climatically representative agricultural sites worldwide.The site selection is based on the second level of the Köppen–Geiger climate classification, with each site representing a distinct agro-climatic zone characterized by contrasting precipitation regimes, evaporative demand, and seasonal variability. By prioritizing climatic representativeness over dense spatial coverage, the analysis enables systematic comparison of irrigation responses across a broad range of hydroclimatic conditions.Crop growth and yield responses are simulated using the FAO AquaCrop model, which provides a robust representation of crop water productivity under water-limited conditions. AquaCrop simulations are coupled with multiple irrigation scheduling strategies implemented through the Deficit Irrigation Toolbox (DIT), an open-source probabilistic simulation–optimization framework developed in MATLAB. This integrated modeling approach explicitly accounts for climate-driven uncertainty by evaluating rainfed conditions, full irrigation, and optimized deficit irrigation strategies under stochastic weather forcing. Model outputs include irrigation water demand, yield response, and water productivity, enabling the assessment of trade-offs between production stability and water use efficiency.The results highlight pronounced climate-dependent differences in irrigation requirements and sensitivity to water availability. In particular, the simulations indicate that deficit irrigation can reduce vulnerability to interannual water scarcity and improve water productivity in arid and semi-arid regions, while offering limited benefits in humid climates.This preliminary analysis establishes a methodological foundation for a future global-scale assessment of irrigation strategies under uncertain water resources and supports the development of climate-adaptive irrigation management approaches.

Reliable flood forecasting systems are an important prerequisite for local authorities and flood defence units to prepare for potential flooding at an early stage and to initiate the required measures. Small catchments in mountain ranges pose particular challenges in this regard, as they respond very quickly to rainfall. Furthermore, forecasts of rainfall in terms of their spatial and temporal extent and the associated impact on the areas are subject to a high degree of uncertainty. Ensemble rainfall forecasts as input data for rainfall-runoff (RR) models allow for the evaluation of the uncertainty of the resulting runoff. However, this requires fast-computing RR models to cope with the simulation effort, for which artificial intelligence methods are being used increasingly. Against this background, two hydrologic ensemble forecasting systems (EFS) are compared and evaluated that have been in operational use for small catchments in Saxony, Germany, for two years.System 1, called EFS-howa, was developed in the HoWa-PRO research project, and its predictions can be tracked via the warning platform https://howapro.de/. As an RR model, it includes the event-based, deterministic hydrological model DeHM. DeHM covers the hydrologic processes for runoff formation and concentration, channel routing, and the simulation of flood retention dams. Measured discharge and water level data are assimilated within the forecasting process. For the hydrological ensemble forecast, rainfall data for observation and prediction from established products of the German Weather Service are used (radar-based QPE: RADOLAN-RW, radar-based nowcasting: RADOLAN-RV, ensemble QPF: ICON-D2-EPS). The runoff forecast lead time is 48 hours, and new forecasts are released every half hour if the QPF indicates a potential flood threat.System 2, called EFS-kiwa, was developed in the KIWA research project, and its predictions can be tracked via the web demonstrator http://howa-innovativ.hydro.tu-dresden.de/WebDemoKiwa/. The RR model is a regional AI model (based on LSTMs) that was developed using measured RR data and hydrologic characteristics from 52 small and medium-sized catchments in Saxony, Germany. The current setup of the regional AI-RR model is based on hourly measurements of rainfall (using RADOLAN-RW), runoff, and rainfall forecasts. Thus, it achieves runoff forecasts with a lead time of up to 24 hours. The regional AI-RR model also allows for the fast and robust processing of ensemble rainfall forecasts from ICON-D2-EPS, enabling runoff forecasts with uncertainty/reliability information.Both systems are evaluated in terms of their performance. Across various forecast lead times, different metrics such as KGE or percentage peak error, as well as threshold-based metrics such as false alarm ratio or area under the ROC curve (AUC), are calculated to explore the quality of both forecasting systems. The differences between the two demonstrators are highlighted by means of the selected metrics and specific simulation results. The associated benefits, advantages, and disadvantages for flood early warning are discussed.

The development of transparent and trustworthy hydrological modes requires careful attention to the choices made throughout the modeling process, including the assumptions made about the model structure. However, the structures of conceptual models are often defined indirectly through equations and the code implementation. This limits reproducibility, comparability and transparency of its structural assumptions. Moreover, the is currently no consistent unifying framework that represents the multitude of conceptual model structures found in hydrological modeling literature, making systematic analysis and comparison difficult. We introduce a graph-theory based framework for explicitly and coherently representing conceptual model structures, where model compartments are represented as nodes and fluxes as directed edges. This allows mode structures to be defined independently of specific process formulations, while mass balance equations are derived directly from the graphs topology, ensuring consistent balances across all model compartments.Representing conceptual model structures in an algebraic graph form, also allows to compare, analyze and manipulate in a ways that is difficult to achieve with pure equation-based representations. Graph and matrix encoding allows us to enumerate, compare and modify model structures in a controlled way, enforcing explicit constraints like hydrological plausibility, connectivity and closure. This representation forms a theoretical foundation for flexible and multi-model hydrological frameworks, allowing for the construction, testing and communication of different model hypotheses in a consistent way. Additionally, the graph-based representation support harmonious and unambiguous visual depictions of conceptual model structures, strengthening communication of modelling assumptions alongside their mathematical formulation. Using examples of watershed models, we illustrate how conceptual models correspond to specific graph and matrix configurations and how structural differences are reflected in the resulting system of ordinary differential equations. In particular, we show that the incidence matrix provides a direct algebraic mapping between hydrologic model structure and the governing system of ordinary differential equations, where state derivatives are obtained as the balance of incoming and outgoing fluxes associated with each node. Moreover, we demonstrate how the graph–matrix representation can be used to systematically sample a space of candidate model structures by permuting adjacency matrices under predefined structural constraints. Invalid or implausible structures are excluded through rule-based filtering, yielding a structured yet unconstrained exploration of the admissible model space.

Reliable identification of agro-hydrometeorological change in developing countries is hindered by sparse and declining monitoring networks as well as limited data-management capacity. Increasing access to accurate, high-resolution agro-hydrometeorological data would improve hydrological model predictions and ultimately support better decision-making. One promising strategy to address data scarcity is model inversion of crop simulation models, where time-resolved crop growth information at the field scale can act as a proxy for soil moisture and, by extension, irrigation amounts.In this study, we evaluate a yield-based inversion approach within AquaCrop, in which the observed final crop yield is used as the inversion target to retrospectively estimate seasonal irrigation. Under uniform, continuously applied irrigation, inferred irrigation amounts were generally accurate, with errors within ±10%. Model performance was strongly affected by the soil’s available water storage capacity, which is governed by texture. Incorporating information on soil texture, irrigation pattern (continuous vs. non-continuous), and rainfall substantially improved inversion accuracy. In contrast, under non-uniform or non-continuous irrigation regimes, the method tended to overestimate irrigation substantially. These findings suggest that yield-constrained inversion can reliably estimate irrigation in controlled settings but is less robust under intermittent or spatially heterogeneous irrigation. As a next step, we will invert AquaCrop using temporally resolved vegetation data rather than final yield to better constrain soil-moisture dynamics and reduce bias under complex irrigation patterns.

Agricultural Drought Risk constitutes one of the most significant and long-term damaging impacts of climate change, primarily contributing to food insecurity. Despite the large number of previous research activities on drought risk management, some countries remain excluded from the global drought studies while vulnerable communities are still exposed to famine and livelihood loss. This critical gap prove that the applied drought assessment techniques faced successive refinements over time including dataset and methodologies but exhibit notable limitation regarding both spatial assessment and theoretical consistency.The present study examines a comparative analysis of agricultural drought risk across two Tunisian watersheds, Medjerda and Merguellil, which are characterized by distinct climatological conditions. The analytical framework integrated the three core components of agricultural drought risk: hazard, vulnerability, and exposure while adopting a resource nexus perspective to capture the interdependencies among the selected indicators of each component. Drought indicators were collected from remotely sensed data over the period 2016-2024 considered as the latest drought period in Tunisia. The hazard indicators were represented by Precipitation condition index (PCI), Temperature condition index (TCI), Vegetation condition index (VCI) and Soil moisture condition index (SMCI). The vulnerability indicators included Runoff, Ground Water (GW), Primary Productivity (NPP) and Nighttime Light (NL). The exposure indicators were cropping area and population density. All indicators were normalized to ensure integration within drought analysis framework. This study employed two temporal lags initially addressing the short-term dynamics of drought hazard on a monthly scale followed by yearly assessment of drought risk components. The combination process of drought indicators was conducted by three objective weighting techniques: Principal Component Analysis (PCA), Gaussian Mixture Model (GMM) and Entropy to create time series of drought risk maps.The spatial structure of obtained drought risk maps was analyzed using spatial pattern indices, including the Gini Index, along with four landscape metrics: Number of Patches (NP), Landscape Shape Index (LSI), Shannon’s Diversity Index (SHDI), and Contagion Index (CONTAG). These indices were considered as objective functions within multiple Pareto optimization scenarios to identify the most relevant spatial configuration of drought risk maps. The optimization results provided robust evidence indicating that the entropy-based approach was the most effective method in drought risk monitoring. The Medjerda watershed, which is characterized by sub-humid regime, faced strong drought variability with a severe drought period recorded in 2023, while drought risk trend remained gradual in the semi-arid watershed, Merguellil, showing slight change in 2022 and 2023.The drought assessment determined the contribution of drought indicators in creating each component, the highest weight was assigned to VCI within monthly and yearly hazard component. Considering the vulnerability component, NPP exhibited the highest contribution followed by GW in the case of Medjerda and NL in the case of Merguellil. The cropping area had highest weight within exposure component. The results offer an objective and reliable assessment of the temporal drought risk variability and quantitatively reveal the climate–water–food nexus shaping drought risk. Overall, the study confirms the viability of using integrated risk assessment for sustainable water-use in agriculture.

Although objective functions (OFs) are widely discussed in the literature, many modelling studies still default to a few common metrics, without much consideration of their relative strengths and weaknesses. This paper systematically investigates the impact of OF choice on the representation of various streamflow characteristics across 47 conceptual models and 10 hydro-climatically diverse catchments selected from the CARAVAN dataset. We use eight different OFs for calibration, including the Kling–Gupta efficiency (KGE), Nash–Sutcliffe efficiency (NSE), and their respective logarithmic variants, as well as four more recently proposed metrics. We evaluate the representation of 15 hydrological signatures that capture a relevant selection of streamflow characteristics to determine generalizable strengths and weaknesses of individual OFs across different models and catchments. Results show that the choice of OF can significantly affect a model's capability to simulate different hydrological signatures such as runoff ratios, extreme flow percentiles, and certain baseflow characteristics. While certain signatures, particularly those related to flow variability, are relatively insensitive to OF choice, others exhibit large performance shifts across different OFs. Generally, no single OF simultaneously achieved high performance across all tested signatures, highlighting that a single-objective calibration is unlikely to lead to an all-purpose model. Our results reinforce calls to choose objective functions deliberately and in line with the objectives of a study. They also provide initial guidance on which metrics highlight particular facets of streamflow behaviour.