The fertile Anatolian lands in Turkey, supporting about 80 million people, rely on abundant water resources. The Kızılırmak River basin in Anatolia is vulnerable to global warming, mainly due to snowmelt in its headwaters. Quantifying the upper watershed’s climate sensitivity is crucial for assessing water availability. Instead of using Global Climate Model (GCM)-driven projections, a sensitivity-based approach was employed with the Variable Infiltration Capacity (VIC) hydrologic model to assess the region’s hydrological vulnerability to potential future climatic changes. Considering the consistent projections of increasing temperature (T) over this region in GCMs, the system was perturbed to examine gradients of a more challenging climate, characterized by warming and drying conditions. The sensitivity of streamflow, snowpack water equivalence, and evapotranspiration to T and Precipitation (P) variations under each perturbation or “reference” climates was quantified. Results indicate that streamflow responds to T negatively under all warming scenarios. Streamflow responding to P increases nonlinearly as P decreases in the reference climates. These results suggest that there will be heightened difficulty in managing water resources in the region if it undergoes both warming and drying due to the following setbacks: 1) water availability will shift away from the summer season of peak water demand due to the warming effects on the snowpack, 2) annual water availability will likely decrease due to a combination of warming and lower precipitation, and 3) streamflow sensitivity to hydroclimatic variability will increase, meaning that water managers will likely need to plan for a system that is more sensitive to weather variations.

Scenarios have emerged as valuable tools in managing complex human-natural systems, but the traditional approach of limiting focus on a small number of predetermined scenarios can inadvertently miss consequential dynamics, extremes, and diverse stakeholder impacts. Exploratory modeling approaches have been developed to address these issues by exploring a wide range of possible futures and identifying those that yield consequential vulnerabilities. However, vulnerabilities are typically identified based on aggregate robustness measures that do not take full advantage of the richness of the underlying dynamics in the large ensembles of model simulations and can make it hard to identify key dynamics and/or narrative storylines that can guide planning or further analyses. This study introduces the FRamework for Narrative Scenarios and Impact Classification (FRNSIC; pronounced “forensic’): a scenario discovery framework that addresses these challenges by organizing and investigating consequential scenarios using hierarchical classification of diverse outcomes across actors, sectors, and scales, while also aiding in the selection of narrative storylines, based on system dynamics that drive consequential outcomes. We present an application of this framework to the Upper Colorado River Basin, focusing on decadal droughts and their water scarcity implications for the basin’s diverse users and its obligations to downstream states through Lake Powell. We show how FRNSIC can explore alternative sets of impact metrics and drought dynamics and use them to identify narrative drought storylines, that can be used to inform future adaptation planning.

Storage and release of surface water by reservoirs can alter the natural streamflow pattern of rivers with negative impacts on the environment. Such reservoir-driven river regulation is poorly understood at a global scale due to a lack of publicly available in-situ data on reservoir operations. However, with rapid advancements in satellite remote sensing-based tracking of reservoir state, this gap in data availability can be bridged. In this study, we modeled regulated flow of rivers using only satellite-observed reservoir state and hydrological modeling forced also with satellite precipitation data. We propose a globally scalable algorithm, ResORR (Reservoir Operations driven River Regulation), to predict regulated river flow and tested it over the heavily regulated basin of the Cumberland River in the US. ResORR was found able to model regulated river flow due to upstream reservoir operations of the Cumberland River. Over a mountainous basin dominated by high rainfall, ResORR was effective in capturing extreme flooding modified by upstream hydropower dam operations. ResORR successfully captured the peak of the regulated river flow altered by hydropower dam and flood control operations during the devastating floods of 2018 in the South Indian state of Kerala. On average, ResORR improved regulation river flow simulation by more than 50% across all performance metrics when compared to a hydrologic model without a regulation module. ResORR is a timely algorithm for understanding human regulation of surface water as satellite-estimated reservoir state is expected to improve globally with the recently launched Surface Water and Ocean Topography (SWOT) mission.

Sap flow observations provide a basis for estimating transpiration and understanding forest water use dynamics and plant-climate interactions. This study developed a continental modeling approach using Long Short-Term Memory networks (LSTMs) to predict hourly tree-level sap flow across Europe based on the SAPFLUXNET database. We developed models with varying levels of training sets to evaluate performance in unseen conditions. The average Kling-Gupta Efficiency was 0.77 for gauged models trained on 50 % of time series across all forest stands and was 0.52 for ungauged models trained on 50 % of the forest stands. Continental models matched or exceeded performance of specialized and baseline models for all genera and forest stands, demonstrating the potential of LSTMs to generalize hourly sap flow across tree, climate, and forest types. This work highlights hence the potential of deep learning models to generalize sap flow for enhancing tree to continental ecohydrological investigations.

Runoff in natural rivers, commonly termed as streamflow, is a major process in the water cycle and a crucial variable in water resources engineering. While the increase in extreme rainfall events over the Conterminous United States (CONUS) has been well-documented, understanding the variability of streamflow remains challenging due to the nonlinear relationship between rainfall and runoff. In this study, daily streamflow data from 18 USGS gauge stations with the largest drainage area in its respective Hydrologic Unit Code 2-digit (HUC-2) region throughout the CONUS with contiguous records spanning from 2003 to 2022 water years is used to gain insights into streamflow variability over the past two decades. The original Mann-Kendall (MK) Test is employed to assess the potential temporal trends in the basic statistics (maximum, mean, minimum, and standard deviation) of annual streamflow data over the past 20 water years. Additionally, the seasonal MK Test is performed to explore the trends in the same basic statistics of the daily streamflow on a monthly basis. Furthermore, the statistical distributions of the normalized daily streamflow within each decade (2003-2012 and 2013-2022) are compared for each HUC-2 region. The results of the original MK Test indicate that no discernible trend in the annual streamflow and its standard deviation for most of the HUC-2 regions. However, the results of the seasonal MK Test suggest either an increasing or decreasing trend in around 30% of the HUC-2 regions. Moreover, low flows demonstrate a more significant change in frequency compared to high flows between the past two decades. Overall, this study highlights the complexity of the streamflow variability and the potential implications for changes in flood or drought risk under a changing climate.  

Characterizing climate change impacts on water resources typically relies on Global Climate Model (GCM) outputs that are bias-corrected using observational datasets. In this process, two pivotal decisions are (i) the Bias Correction Method (BCM) and (ii) how to handle the historically observed time series, which can be used as a continuous whole (i.e., without dividing it into sub-periods), or partitioned into monthly, seasonal (e.g., three months), or any other temporal stratification (TS). Here, we examine how the interplay between the choice of BCM, TS, and the raw GCM seasonality may affect historical portrayals and projected changes. To this end, we use outputs from 29 GCMs belonging to the CMIP6 under the Shared Socioeconomic Pathway 5–8.5 scenario, using seven BCMs and three TSs (entire period, seasonal, and monthly). The results show that the effectiveness of BCMs in removing biases can vary depending on the TS and climate indices analyzed. Further, the choice of BCM and TS may yield different projected change signals and seasonality (especially for precipitation), even for climate models with low bias and a reasonable representation of precipitation seasonality during a reference period. Because some BCMs may be computationally expensive, we recommend using the linear scaling method as a diagnostics tool to assess how the choice of TS may affect the projected precipitation seasonality of a specific GCM. More generally, the results presented here unveil trade-offs in the way BCMs are applied, regardless of the climate regime, urging the hydroclimate community for a careful implementation of these techniques.

Regional flood mapping poses computational and spatial heterogeneity challenges, exacerbated by climate change-induced uncertainties. This study focuses on creating a state-wide flood mapping solution with enhanced accuracy and computational speed to support regional flooding hazard analysis and the assessment of climate change, using New Jersey as a case study. The Height Above Nearest Drainage (HAND) framework was employed for large-scale flood mapping. The model was validated against high water marks (HWMs) collected after Hurricane Irene. Based on the National Water Model (NWM), synthetic rating curves in HAND were calibrated by tuning Manning’s roughness, aligning the predicted and observed flood depths. The roughness values were generalized across the state from the validated water basins to the ungauged ones, using a multivariate regression with the hydrologic and geographic information. To map the future climate-change-induced flooding, a correlation between NOAA historical precipitation totals and NWM flow data from 2010-2020 was established to link precipitation and runoff. This study also invented a novel method for correcting catchment discontinuities, inherent in the HAND model, based on a computer vision scheme, the Sobel filter. The modeling results show that average and worst-case storm events have the potential to increase 10-50% in the state, where mountain areas and major river banks would be exposed to this impact more significantly.

In this study, we identify the key length and time scales associated with CO2 mineralization in basalt reservoirs. This is achieved through the development and application of a simple yet complete model of the fate and transport of a supersaturated CO2-charged fluid moving unidirectionally through an initially uniform basalt rock. The model consists of three coupled equations describing, (i) the spatiotemporal evolution of porosity with the mineralization reaction, (ii) the resulting temporal and spatially varying fluid discharge, and (iii) the fate and transport of the mineralization reactant(s) in the aqueous phase. A dimensional analysis provides length and time scales that characterize the extent and duration of field-scale carbon mineralization. These scales are applied to a field site to estimate poorly constrained mineralization parameters, notably, the effective first-order reaction rate constant.

The U.S. National Water Model (NWM) is a hydrologic modeling framework that uses the Weather Research and Forecasting Hydrological modeling system (WRF-Hydro) to simulate land surface hydrology and energy fluxes at 1-km spatial resolution. Understanding the performance of the operational NWM in simulating evapotranspiration (ET) is necessary to identify problems and biases in streamflow forecasts that may result from poor partitioning of runoff and ET. In this study, we compared NWM ET fluxes against OpenET, a satellite-driven dataset that provides interpretive or diagnostic information on actual ET at 30-m spatial resolution. Monthly ET simulations from the NWM version 2.1 (NWM V2.1) retrospective analysis over the Bear River Basin (BRB), U.S. were compared against OpenET products from 2017 to 2020 for different months and seasons. Comparisons showed that there was general agreement between the ET assessments at the 1-km scale, but with notable discrepancies for some landcover types, such as irrigated agriculture and riparian areas. The NWM showed less spatial variability and tended to predict lower ET fluxes compared to OpenET, particularly from June to August. In comparison with water balance estimates of ET derived from precipitation and USGS streamflow observations in four sub-watersheds within the BRB, OpenET modeled ET was biased high in two watersheds dominated by evergreen forest. The results from this study provide useful information for both NWM and OpenET developers, demonstrating the power of comparing predictive and interpretive modeling systems. This study serves as a prototype for broader assessment of both NWM and OpenET via intercomparison. Plain Language Summary This study compared the retrospective U.S. National Water Model (NWM) version 2.1 evapotranspiration (ET) fluxes with OpenET, a satellite-driven data product offering actual ET information at 30-m resolution from 2017 to 2020, aggregated to match the 1 km NWM grid. Results indicated that the NWM tends to underpredict ET fluxes when compared against the different OpenET component models used in this study. OpenET showed a high bias in comparison with water balance assessments of ET in two natural sub-watersheds characterized by evergreen forest. Significant spatial discrepancies were observed in NWM results for certain landcover types, including irrigated agricultural lands, riparian areas, and in one watershed that appears to be mis-calibrated. Key Points: • Compared with OpenET, the U.S. National Water Model (NWM) tends to underpredict evapotranspiration (ET) fluxes in all seasons. • OpenET overpredicts ET in comparison to water balance estimates from observed streamflow and precipitation in two forested sub-watersheds. • Spatial discrepancies between NWM ET and OpenET were observed in irrigated lands, riparian areas, and one mis-calibrated watershed.

In various research fields such as hydrogeology, environmental science and energy engineering, geological formations with fractures are frequently encountered. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and the transport of solute and energy within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observed state variables like hydraulic head, concentration, and temperature. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non-Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as PEDL (parameter estimator with deep learning) that harnesses the capabilities of DL to capture nonlinear relationships and extract non-Gaussian features. To evaluate PEDL’s performance, we conduct two numerical case studies with increasing complexity. Our results unequivocally demonstrate that PEDL outperforms three popular DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL-based update (ESDL). Sensitivity analyses confirm PEDL’s validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.

A document by Salam A. Abbas. Click on the document to view its contents.

Distributed hydrological water quality models are increasingly being used to manage natural resources at the catchment scale but there are no calibration guidelines for selecting the most useful gauging stations. In this study, we investigated the influence of calibration schemes on the spatiotemporal performance of a fully distributed process-based hydrological water quality model (mHM-Nitrate) for discharge and nitrate simulations at Bode catchment in central Germany. We used a single- and two multi-site calibration schemes where the two multi-site schemes varied in number of gauging stations but each subcatchment represented different dominant land uses of the catchment. To extract a set of behavioral parameters for each calibration scheme, we chose a sequential multi-criteria method with 300.000 iterations. For discharge (Q), model performance was similar among the three schemes (NSE varied from 0.88 to 0.92). However, for nitrate concentration, the multi-site schemes performed better than the single site scheme. This improvement may be attributed to that multi-site schemes incorporated a broader range of data, including low Q and NO3- values, thus provided a better representation of within-catchment diversity. Conversely, adding more gauging stations in the multi-site approaches did not lead to further improvements in catchment representation but showed wider 95% uncertainty boundaries. Thus, adding observations that contained similar information on catchment characteristics did not seem to improve model performance and increased uncertainty. These results highlight the importance of strategically selecting gauging stations that reflect the full range of catchment heterogeneity rather than seeking to maximize station number, to optimize parameter calibration.

Increasing climatic variability has resulted in an unprecedented surge in extreme events, pressing global ecosystems towards systematic breakdown. Yet, the resilience of the soil-vegetation-atmosphere (SVA) system to revert to its natural state indicates the existence of energetic barriers forbidding systems from tipping. Observational and theoretical constraints limit our understanding of these energetic barriers which are crucial for assessing ecosystem sensitivity to atmospheric perturbations. We provide a novel coherent theory on the dissipative energy barriers (𝛥e) which decides the resilience potential of an ecosystem. These barriers are manifestation of lower bounds of entropy produced ( Σ *) for unit anomaly transference from soil moisture (SM) to evapotranspiration (ET). Using remote sensing data, we compute these global entropy bounds by introducing a new metric (Wasserstein distance, dw) for SM-ET coupling. Quantifying these lower bounds from SM-ET coupling, places terrestrial ecosystems in the hierarchy of dissipative energy states spanning from forested regions to barren lands. Furthermore, we show that the optimization of SM-ET coupling translates to entanglement of water potential gradient (∆ω) between land surface and atmospheric boundary layer, and the resulting memory timescale or residence time (τ). This (τ.∆ω) entanglement propels moisture-rich and moisture-deficit systems in complementary evolutionary pathways in responding to imposed anomalies. As a result, we witness an emergence of coupling-aridity tradeoff with temperate climates operating as least efficient systems for unit SM to ET anomaly transfer. Physical basis, and transferability across space and scale makes this theory a potential benchmark for process improvement in the climate and earth system models.  

Climate elasticity of streamflow represents a nondimensional measure of the sensitivity of streamflow to climatic factors. Estimation of such elasticities from observational records has become an important alternative to scenario-based methods of evaluating streamflow sensitivity to climate. Nearly all previous elasticity studies have used a definition of elasticity known as arc elasticity, which measures changes in streamflow about mean values of streamflow and climate. Using observational records in western U.S., our findings reveal that elasticity definitions based on power law models lead to both regional and basin specific estimates of elasticity which are physically more realistic than estimates based on arc elasticity. Evaluating the ability of arc and power law elasticity estimators in reproducing Dooge’s complementary relationship (DCR) between potential evapotranspiration and precipitation elasticities reveal that power law elasticities estimated from at-site, panel and hierarchical statistical models reproduce DCR, whereas corresponding estimators based on arc elasticity cannot reproduce DCR. Importantly, our regional elasticity formulations using either panel and/or hierarchical formulations led to estimates of both regional and basin specific estimates of elasticities, enabling and contrasting streamflow sensitivity to climate across both basins and regions.

Despite advances in hydrological Deep Learning (DL) models using Single Task Learning (STL), the intricate relationships among multiple hydrological components and model inputs might not be comprehensively encapsulated. This study employed a Long Short-Term Memory (LSTM) neural network and the CAMELS dataset to develop a Multi-Task Learning (MTL) model, predicting streamflow and evapotranspiration across multiple basins. An optimal multi-task loss weight ratio was determined manually during the validation phase for all 591 selected basins with streamflow data-gaps under 5%. During test period, MTL showed median Nash-Sutcliffe Efficiency predictions for streamflow and evapotranspiration at 0.69 and 0.92, consistent with two STL models. The MTL’s strength appeared when predicting the non-target variable, surface soil moisture, using probes derived from LSTM cell states—representative of the internal DL model workings. This prediction showed a median correlation coefficient of 0.90, surpassing the 0.88 and 0.89 achieved by the streamflow and evapotranspiration STL models, respectively. This outcome suggests that MTL models could reveal additional rules aligned with hydrological processes through the inherent correlations among multiple hydrological variables, thereby enhancing their reliability. We termed this as “variable synergy,” where MTL can simultaneously predict varied targets with comparable STL performance, augmented by its robust internal representation. Harnessing this, MTL promises enhanced predictions for high-cost observational variables and a comprehensive hydrological model.

In mountain rivers, sediment from landslides or debris flows can alluviate portions or even full reaches of bedrock channel beds, influencing bedrock river incision rates. Various landscape evolution models have been developed to account for the coevolution of alluvial cover and sediment-flux-dependent bedrock incision. Despite the commonality of their aims, one major difference between these models is the way they account for and conserve sediment. We combine two of the most widely used sediment conservation schemes, an Exner-type scheme and an erosion-deposition scheme, with the saltation-abrasion model for bedrock incision to simulate the coevolution of sediment transport and bedrock incision in a mixed bedrock-alluvial river. We compare models incorporating each of these schemes and perform numerical simulations to explore the transient evolution of bedrock incision rates in response to changes in sediment input. Our results show that the time required for bedrock incision rates to reach a time-invariant value in response to changes in sediment supply is over an order of magnitude faster using the Exner-type scheme than the erosion-deposition scheme. These different response times lead to significantly different time-averaged bedrock incision rates, particularly when the sediment supply is periodic. We explore the implications of different model predictions for modeling mixed bedrock-alluvial rivers where sediment is inevitably delivered to rivers episodically during specific tectonic and climatic events.

Climate projections suggest an increase in drought frequency and intensity in various places over the globe, one of them being Southern Europe, expected to become a hotspot. However, 2018 presented an anomaly with the emergence of a rare “water seesaw” phenomenon, leading to severe drought in Central and Northern Europe while Southern Europe experienced high humidity. This unexpected event resulted in significant agricultural disparities, emphasizing the influence of interannual variability. The commentary underscores the danger of overlooking short-term climate variability, vital for accurate adaptation planning, especially for vulnerable regions, when focusing solely on long-term trends. This case serves as a motivation for exploration of global atmospheric circulation changes, emphasizing the need for nuanced modeling approaches to grasp subtle complexities in climate predictions and considering short-term climate variability alongside long-term trends.

Tectonic and/or climatic perturbations can drive drainage adjustment. The capture events, significantly changing the river network topology, are the major events in river network evolution. While they could be identified through field observations and provenance analysis, reconstructing this evolution process and pinpointing the capture time remain challenging. Following a capture event, the steady-state elevation of the captor river will be much lower than that of the beheaded river. Then, the newly-formed drainage divide will migrate towards the beheaded river, a process also known as river-channel reversal. The migration of the newly-formed drainage divide provides a new perspective for identifying the reorganization of the river network. Here, we employ numerical modeling to reproduce the characteristic phenomena of drainage-divide migration following capture events and analyze the effects of different parameters on the migration rate. We find that (1) the migration of newly-formed drainage divides can last for tens of millions of years, with the migration rate decreasing exponentially over time; (2) larger captured area, higher uplift rate, and lower erosional coefficient, all of which cause a higher cross-divide difference in steady-state elevation, will cause higher migration rate of the newly-formed drainage divide. This insight was further applied to the Dadu-Anning and Yarlung-Yigong capture events. We predict the present Dadu-Anning drainage divide would further migrate ~65–92 km southward to reach a steady state in tens of millions of years. The Yarlung-Yigong capture event occurred in the early-middle Cenozoic, which implies that the late-Cenozoic increased exhumation rate is not related to the capture event.

A document by Yi Yang. Click on the document to view its contents.

Reliable nutrient load estimation of a reservoir is challenging due to inconsistent spatial extent and temporal frequency of water quality and quantity. This study aims to collect consistent spatial extent and temporal frequency of water depths and nitrate concentrations of a reservoir in South Korea using uncrewed surface vehicle (USV). In this study, reservoir nitrate loads were estimated using four methods to examine how spatial variation in water depth and nitrate concentrations affected load estimates. Based on dual measurements of water depth and nitrate concentration, reservoir nitrate loads across 30 sampling dates (0.7 million tons of fresh water on average) ranged from one to four tons. Results showed that a point measurement of water depths and nitrate concentrations can cause up to -17% of underestimation of nitrate loads, particularly after intense rainfall events. This study highlights potential opportunities and  challenges of the USV-based dual monitoring systems for water quality and quantity.

The emission potential, which represents the total leachable mass in landfill waste body, is hard to measure directly. Therefore we propose to quantify it by assimilating available measurements. The leachate production rate is influenced by the total water storage in the waste body, while both total chloride mass and total water storage in the waste body influence the chloride concentration in the leachate. Thus assimilating leachate volume and chloride concentration simultaneously will help quantify the uncertainties in emission potential. This study investigated the feasibility of using particle filter in a concentration-volume coupled travel time distribution model to estimate the emission potential. Leachate production rates and chloride concentrations were assimilated simultaneously by a weakly coupled data assimilation(WCDA) method. The time lag issue in the travel time distribution model was solved by adding a daily model error to cover layer states. The proposed method was tested in synthetic experiments firstly to investigate the performance. The results show that the uncertainties in chloride mass and waste body total water storage were quantified and reduced. The predictions of chloride concentrations were also improved.

Increasing wildfire frequency and severity in high-elevation seasonal snow zones presents a considerable water resource management challenge across the western U.S. Wildfires can affect snowpack accumulation and melt patterns, altering the quantity and timing of runoff. While prior research has shown that wildfire generally increases snow melt rates and advances snow disappearance dates, uncertainties remain regarding variations across complex terrain and the energy balance between burned and unburned areas. Utilizing multiple paired in-situ data sources within the 2020 Cameron Peak burn area during the 2021–2022 winter, we found no significant difference in peak snow water equivalent (SWE) magnitude between burned and unburned areas. However, the burned south aspect reached peak SWE 22 days earlier than burned north. During the ablation period, burned south melt rates were 71% greater than unburned south melt rates, whereas burned north melt rates were 94% greater than unburned north aspects. Snow disappeared 7 to 11 days earlier in burned areas than unburned areas. Net energy differences at the burned and unburned AWS sites were seasonally variable, with the burned area losing more energy during the winter but gaining significantly more energy during the spring. Net shortwave radiation was 56% greater at the burned area during the winter and 137% greater during the spring driving a ~60% greater cumulative net energy at the burned site during May. These findings emphasize the need for post-wildfire water resource planning that accounts for aspect-dependent differences in energy and mass balance to accurately predict snowpack storage and runoff timing.

Integrated hydrologic models can simulate coupled surface and subsurface processes but are computationally expensive to run at high resolutions over large domains. Here we develop a novel deep learning model to emulate continental-scale subsurface flows simulated by the integrated ParFlow-CLM model. We compare convolutional neural networks like ResNet and UNet run autoregressively against our novel architecture called the Forced SpatioTemporal RNN (FSTR). The FSTR model incorporates separate encoding of initial conditions, static parameters, and meteorological forcings, which are fused in a recurrent loop to produce spatiotemporal predictions of groundwater. We evaluate the model architectures on their ability to reproduce 4D pressure heads, water table depths, and surface soil moisture over the contiguous US at 1km resolution and daily time steps over the course of a full water year. The FSTR model shows superior performance to the baseline models, producing stable simulations that capture both seasonal and event-scale dynamics across a wide array of hydroclimatic regimes. The emulators provide over 1000x speedup compared to the original physical model, which will enable new capabilities like uncertainty quantification and data assimilation for integrated hydrologic modeling that were not previously possible. Our results demonstrate the promise of using specialized deep learning architectures like FSTR for emulating complex process-based models without sacrificing fidelity.

The permeability coefficient of seepage is an important factor that is widely used in various engineering fields. There are numerous issues that influence the permeability coefficient, among which the porosity, particle size, particle size distribution and Reynolds number are of great importance. In this paper, a C++ code based on the three-dimensional lattice Boltzmann method (LBM) was developed and used to investigate the effects of the abovementioned factors on the permeability coefficient. A multiple relaxation time (MRT) collision scheme of the LB equations was used in the simulation. Porous media were prepared using the random packing method. Laminar flow and turbulent flow were simulated separately for particle Reynolds numbers in a range from 0.001 to 3,000. It was proven that in addition to the influence of porosity and particle size distribution on the permeability, the influence of the Reynolds number was obvious and could not be ignored. As the Reynolds number increased, the permeability of porous media decreased gradually. Based on the numerical simulation results, a modified formula for the permeability coefficient is proposed.