Siddik Barbhuiya

Distributed land-surface models require parameters at every grid cell, yet calibration data are unevenly informative, streamflow is measured directly but only at sparse gauges, while satellite evapotranspiration and soil moisture cover the domain indirectly. We present SCALE, a three-stage framework for learning, refining, and regionalizing parameters across continental domains . Stage A trains multivariable differentiable parameter learning (MdPL) from attributes to parameters through a frozen neural surrogate, jointly constrained by evapotranspiration, soil moisture, and streamflow and anchored to a pedotransfer prior. Stage B refines the resulting field with the original process model at gauged locations, calibrating precipitation phase against snow water equivalent before correcting discharge with explicit routing. Stage C transfers these corrections to unobserved locations through attribute-based donor similarity. Applied to VIC 4.2d at 6 km over 104,841 cells of the Indian subcontinent, Stage A matched per-cell optimizers for evapotranspiration and exceeded them for soil moisture (median KGE 0.795 versus 0.640-0.675) but reproduced discharge poorly. Sparse refinement raised teacher-basin median KGE from 0.10 to 0.63 and reduced median absolute bias from 49.5% to 3.58%; transfer improved 94% of held-out basins. Resolution sensitivity proved variable-specific and non-monotonic. SCALE delivers spatially complete, physically anchored parameter fields for large-scale distributed modelling in data-sparse regions.

Distributed land-surface models require parameters at every grid cell, yet calibration data are unevenly informative, streamflow is measured directly but only at sparse gauges, while satellite evapotranspiration and soil moisture cover the domain indirectly. We present SCALE, a three-stage framework for learning, refining, and regionalizing parameters across continental domains . Stage A trains multivariable differentiable parameter learning (MdPL) from attributes to parameters through a frozen neural surrogate, jointly constrained by evapotranspiration, soil moisture, and streamflow and anchored to a pedotransfer prior. Stage B refines the resulting field with the original process model at gauged locations, calibrating precipitation phase against snow water equivalent before correcting discharge with explicit routing. Stage C transfers these corrections to unobserved locations through attribute-based donor similarity. Applied to VIC 4.2d at 6 km over 104,841 cells of the Indian subcontinent, Stage A matched per-cell optimizers for evapotranspiration and exceeded them for soil moisture (median KGE 0.795 versus 0.640-0.675) but reproduced discharge poorly. Sparse refinement raised teacher-basin median KGE from 0.10 to 0.63 and reduced median absolute bias from 49.5% to 3.58%; transfer improved 94% of held-out basins. Resolution sensitivity proved variable-specific and non-monotonic. SCALE delivers spatially complete, physically anchored parameter fields for large-scale distributed modelling in data-sparse regions.

Land surface models (LSMs) are crucial tools for simulating the coupled water, energy, and carbon exchanges between the land surface and the atmosphere, yet their high computational cost limits their applicability for large-scale analyses, parameter uncertainty quantification, and real-time hydrological assessment. This study introduces LandFormer, a Swin Transformer-based deep learning surrogate framework designed to emulate the Variable Infiltration Capacity (VIC) model across the Indian subcontinent at 0.0625° (~6 km) spatial resolution, covering approximately 3.77 million km² and 104,841 grid cells. LandFormer is the first temporal adaptation of the Swin Transformer architecture to continental-scale land surface surrogate modelling, simultaneously emulating evapotranspiration, streamflow, and soil moisture within a unified framework. The architecture integrates a hierarchical temporal Swin Transformer encoder with a Spatial Graph Attention Network (GAT) module and task-specific dual-path regression heads, trained using the Kling–Gupta Efficiency (KGE) as the primary loss function. Training data were generated from VIC simulations using 150 random parameter combinations of 13 soil parameters per grid. LandFormer consistently outperforms LSTM-based surrogates across all three variables, with autoregressive conditioning yielding median KGE values of 0.947 for ET, 0.870 for streamflow, and NSE of 0.989 for soil moisture. The surrogate generalises effectively from sparse training data, achieving acceptable skill from as little as 1.9% spatial coverage, with performance saturating near 59%. Training at 0.5° coarse resolution maintains equivalence with native-resolution performance for ET and soil moisture, reducing data requirements by 98.9%. These results establish LandFormer as a computationally efficient and physically grounded emulator for continental-scale hydrological applications.

The development of hyper-resolution land surface modelling poses significant computational challenges. Detailed water balance assessments, ensemble-based uncertainty quantification, and climate scenario exploration all require running physics-based models like VIC, Noah-MP, and CLM at continental scales with high spatial resolution, long temporal spans, and multiple parameter configurations. The computational cost becomes prohibitive. Machine learning surrogates have recently emerged as potential solutions; however, existing LSTM and CNN approaches have fundamental architectural problems. Sequential processing prevents parallel computation, limited receptive fields miss long-range dependencies, and most approaches only predict single variables, which restricts comprehensive hydrological analysis.We present a shifted-window transformer framework that simultaneously predicts multiple land surface fluxes (runoff, evapotranspiration, and soil moisture) while maintaining computational efficiency at continental scales. The hierarchical attention mechanism captures both local temporal patterns through windowed self-attention and global temporal context through shifted-window operations. This eliminates recurrent bottlenecks. We adapt vision transformers for hydrological regression by tokenizing meteorological sequences temporally, using relative position biases to encode lag-dependent hydrological relationships, and designing multi-task regression heads that preserve both nonlinear interactions and direct physical drivers.We demonstrate the approach by emulating the VIC model across India's 76,390 land grid cells at 6 km resolution, spanning diverse climate regimes. Training uses sparse spatial sampling with only a small fraction of available locations. This allows us to evaluate how well the surrogate generalizes VIC's process behaviors to the newer, unseen regions and parameter configurations. We test multiple variants, including autoregressive formulations that incorporate previous timestep outputs, and benchmark everything against LSTM baselines to isolate the contributions of the architecture.

Deep learning models, particularly LSTMs, have transformed large-sample hydrology by achieving high streamflow predictive performance, yet they remain largely black-box approaches with limited physical interpretability and no explicit representation of multiphysical hydrological processes. Differentiable, learnable process-based models (or δ-models) overcome these limitations by embedding neural networks within differentiable physics frameworks. While existing benchmarks like HBV-δ have proven this concept across 671 US basins, they rely on conceptual foundations (e.g., empirical beta-functions) that approximate, rather than resolve, underlying soil physics. This study introduces MILC-δ (Modular Differentiable Physic-Informed Learning), designed to bridge this gap. The MILC model utilizes continuous soil water retention curves and physically derived drainage laws, which can aid in more accurate hydrological flux simulation. Thus, we developed a MILC-δ - a hydrologic model embedded with neural networks and trained in a differentiable programming framework. Consequently, MILC-δ is anticipated to match or exceed HBV-δ by leveraging neural networks to map static catchment attributes directly to physically measurable properties (e.g., pore size distribution, hydraulic conductivity) rather than abstract calibration parameters. Initial testing of the developed model shows that the model performs at par in some basins and better than HBV-δ in other basins. This approach gives LSTM-level accuracy and generalizability as well as the clear physical story stakeholders actually need to explain the decline in baseflow, threats to the groundwater recharge, etc.

Future streamflow projections are vital for the formulation of effective water resource management strategies and policies for the water‐dependent sectors. Reliable streamflow projections are critical for efficient water resources planning to facilitate better mitigation measures for extreme hydrological hazards such as floods and droughts. Cascading uncertainties in climate and hydrological models due to incorporation of different parametrization, boundary conditions, hydrological processes, model structures, erroneous data and so forth, adds complexity in the adaptation planning. Hence, testing of more than one climate and hydrological models becomes critical. The research provides improved projections of future streamflow, essential for water resource management in various basins throughout the Indian subcontinent. Best‐performing hydrological model and general circulation model (GCM) were identified for 128 river basins of India. Further, impact of climate change on future streamflow were assessed under altered climatic regimes represented by SSP2‐4.5 and SSP5‐8.5 scenarios. Uncertainty in the flow regimes were examined using four hydrological models—MILC, GR4J, HYMOD and HBV along with 12 GCMs and their ensemble mean. Furthermore, 13 hydrological indicators representing flow regime characteristics were used to analyse the changes in the future streamflow. MILC was found to be the best‐performing model for 43.71% of the basins, followed by GR4J, HBV and HYMOD, for 22.52%, 19.87% and 13.90% of the basins, respectively. Among all the analysed GCMs, BCC‐CSM2‐MR, TaiESM1, CMCC‐ESM2, NorESM2‐MM and NESM‐3 were found to be five top performing models. The future hydrological indicators projected an increase in the high flow frequency and duration, highlighting greater flood risks, whereas uncertainty existed for the low flow events, with some basins experiencing prolonged dry spells, whereas others faced shorter and intermittent droughts. Most basins are projected to have an increase in the runoff ratio and zero‐flow events with a decrease in the baseflow index and delay in the half‐flow date.

Runoff estimation in India faces challenges due to diverse climate zones, complex physiographic conditions, and variable rainfall patterns, limiting traditional hydrological models and prompting exploration of advanced deep learning methods for improved streamflow prediction. Existing deep learning hydrological models struggle to estimate discharge at ungauged sites. In this study, we tested eight different deep learning models—four recurrent neural networks (GRU, CudaLSTM, EALSTM, ARLSTM) and four attention-based architectures (Transformer, Informer, Reformer, Linformer)—across 144 watersheds in the Indian subcontinent (ISC). Our training and testing datasets combined meteorological forcing, catchment attributes, and observed discharge records. According to the results, ARLSTM improved prediction accuracy, achieving a median Nash–Sutcliffe Efficiency (NSE) of 0.71 on test basins. ARLSTM performs exceptionally well in specific regions: tropical monsoon areas (median NSE = 0.849), semi-arid regions (median NSE = 0.586), monsoon-influenced subtropical zones (NSE = 0.688), and tropical wet–dry climates (NSE = 0.539), especially in arid zones where traditional hydrological models often struggle. The assessments of high- and low-flow frequencies and durations, mean discharge, and runoff ratios underscore ARLSTM's capability to capture both extreme and average flow conditions. ARLSTM’s reliance on lagged streamflow limits its use in ungauged basins. To address this issue, we developed a novel deep learning architecture, Ungauged Basin LSTM (UBLSTM), to predict the runoff values for any ungauged basin in India. UBLSTM matches the performance of ARLSTM, making it a better choice for areas in India that lack sufficient data or have ungauged basins across various climate zones.