Modelling of Nutrient Pollution Dynamics in River Basins: A Review with a Perspective of a Distributed Modelling Approach

Nutrient pollution is one of the major issues in water resources management, which has drawn significant investments into the development of many modelling tools to solve pollution problems worldwide. However, the situation remains unchanged, even likely to be exacerbated due to population growth and climate change. Effective measures to alleviate the issues are essential, dependent upon existing modelling tools’ capacities. More complex models have been developed with technological advancement, though applications are mainly limited to academic reach. Hence, there is a need for a paradigm shift in policymaking that looks for a reliable modelling approach. This paper aims to assess the capacity of existing modelling tools in the context of process-based modelling and provide a future direction in research. The article has categorically divided models into plot scale to basin-wide applications for evaluation and discussed the pros and cons of conceptual and process-based modelling. The potential benefits of distributed modelling approach have been elaborated with highlights of a newly developed distributed model and its application in catchments in Japan and Australia. The distributed model is more adequate for predicting the realistic details of pollution problems in a changing environment. Future research needs to focus on more process-based modelling.

Stream discharge depends more on the temporal distribution of water inputs than on yearly snowfall fractions for a headwater catchment at the rain-snow transition zone

Climate warming affects snowfall fractions and snowpack storage, displaces the rain-snow transition zone towards higher elevations, and impacts discharge timing and magnitude as well as low-flow patterns. However, it remains unknown how variations in the spatial and temporal distribution of precipitation at the rain-snow transition zone affect discharge. To investigate this, we used observations from eleven weather stations and snow depths measured in one aerial lidar survey to force a spatially distributed snowpack model (iSnobal/Automated Water Supply Model) in a semi-arid, 1.8 km2 headwater catchment at the rain-snow transition zone. We focused on surface water inputs (SWI; the summation of rainfall and snowmelt) for four years with contrasting climatological conditions (wet, dry, rainy and snowy) and compared simulated SWI to measured discharge. We obtained a strong spatial agreement between snow depth from the lidar survey and model (r2: 0.88), and a median Nash-Sutcliffe Efficiency (NSE) of 0.65 for simulated and measured snow depths for all modelled years (0.75 for normalized snow depths). The spatial pattern of SWI was consistent between the four years, with north-facing slopes producing 1.09 to 1.25 times more SWI than south-facing slopes, and snow drifts producing up to six times more SWI than the catchment average. We found that discharge in a snowy year was almost twice as high as in a rainy year, despite similar SWI. However, years with a lower snowfall fraction did not always have lower annual discharge nor earlier stream drying. Instead, we found that the dry-out date at the catchment outlet was positively correlated to the snowpack melt-out date. These results highlight the heterogeneity of SWI at the rain-snow transition zone and emphasize the need for spatially distributed modelling or monitoring of both the snowpack and rainfall.

Genetic programming for hydrological applications: to model or forecast that is the question

Genetic programming (GP) is a widely used machine learning (ML) algorithm that has been applied in water resources science and engineering since its conception in the early 1990s. However, similar to other ML applications, the GP algorithm is often used as a data fitting tool rather than as a model building instrument. We find this a gross underutilization of the GP capabilities. The most unique and distinct feature of GP that makes it distinctly different from the rest of ML techniques is its capability to produce explicit mathematical relationships between input and output variables. In the context of theory-guided data science (TGDS) which recently emerged as a new paradigm in ML with the main goal of blending the existing body of knowledge with ML techniques to induce physically sound models. Hence, TGDS has evolved into a popular data science paradigm, especially in scientific disciplines including water resources. Following these ideas, in our prior work, we developed two hydrologically informed rainfall-runoff model induction toolkits for lumped modelling and distributed modelling based on GP. In the current work, the two toolkits are applied using a different hydrological model building library. Here, the model building blocks are derived from the Sugawara TANK model template which represents the elements of hydrological knowledge. Results are compared against the traditional GP approach and suggest that GP as a rainfall-runoff model induction toolkit preserves the prediction power of the traditional GP short-term forecasting approach while benefiting to better understand the catchment runoff dynamics through the readily interpretable induced models.

Performance and sensitivity of a spatially distributed hydrological conceptual flood model with snow components.

<p>In France, flash floods are responsible for a significant proportion of damages caused by natural hazards, either human or material. Hence, advanced modeling tools are needed to perform effective predictions. However for mountainous catchments snow modeling components may be required to correctly simulate river discharge.</p><p>This contribution investigates the implementation and constrain of snow components in the spatially distributed SMASH* platform (Jay-Allemand et al. 2020). The goal is to upgrade model structure and spatially distributed calibration strategies for snow-influenced catchments, as well as to investigate parametric sensitivity and equifinality issues. First, the implementation of snow modules of varying complexity is addressed based on Cemaneige (Valery et al. 2010) in the spatially distributed framework. Next, tests are performed on a sample of 55 catchments in the French North Alps. Numerical experiments and global sensitivity analysis enable to determine pertinent combinations of flow components (including a slow flow one) and calibration parameters. Spatially uniform or distributed calibrations using a variational method (Jay-Allemand 2020) are performed and compared on the dataset, for different model structures and constrains. These tests show critical improvements in outlet discharge modeling by adding slow flow and snow modules, especially considering spatially varying parameters. Current and future works focus on testing and improving the constrains of snow modules and calibration strategy, as well as potential validation and multiobjective calibration with snow signatures gained from in situ or satellite data. </p><p>*SMASH: Spatially-distributed Modelling and ASsimilation for Hydrology, platform developped by INRAE-Hydris corp. for operational applications in the french flood forecast system VigicruesFlash</p>

Distributed modeling of runoff and soil erosion in vegetated slopes with man-made mountain tracks

<p>Mountain tracks and slope cuts are important sources of runoff and sediment transport in a watershed. Some slope instabilities are also observed nearby mountain roads and tracks. Most of the current literature points out as relevant the modifications of the slope topography, and the concentration of runoff at the bends of the trackways. However, quantitative analysis of runoff generation and sediment delivery are still uncommon. Moreover, the role of vegetation removal or modification along/nearby tracks is not addressed. A physically-based distributed modelling of water runoff, soil erosion and deposition on a natural slope is performed considering the impacts of a mountain track, either in terms slope topography modifications or for the infiltration-runoff patterns. The erosion scenarios for a 30° steep slope are computed with different rainstorms and initial soil suction considered. The numerical analyses provide a comprehensive set of erosion scenarios. Particularly, the numerical results outline the bend of the mountain roads as a major confluence path for water runoff, consistently with the in-situ evidences. The highest loss of soil is found besides and downslope the bends. Very unfavorable combinations of vegetation removal and change in slope topography may finally lead to extensive rill erosions and/or shallow slope failures.</p>

200 years of equilibrium-line altitude variability across the European Alps (1901−2100)

Mountain glaciers are key indicators of climate change. Their response is revealed by the environmental equilibrium-line altitude (ELA), i.e. the regional altitude of zero mass balance averaged over a long period of time. We introduce a simple approach for distributed modelling of the environmental ELA over the entire European Alps based on the parameterization of ELA in terms of summer temperature and annual precipitation at a glacier. We use 200 years of climate records and forecasts to model environmental ELA from 1901 to 2100 at 5 arcmin grid cell resolution. Historical environmental ELAs are reconstructed based on precipitation from the Long-term Alpine Precipitation reconstruction (LAPrec) dataset and temperature from the Historical Instrumental climatological Surface Time series of the greater Alpine region (HISTALP). The simulations of future environmental ELAs are forced with high-resolution EURO-CORDEX regional climate model projections for the European domain using three different greenhouse gas emissions scenarios (Representative Concentration Pathways, RCP). Our reconstructions yielded an environmental ELA across the European Alps of 2980 m above sea level for the period 1901−1930, with a rise of 114 m in the period 1971−2000. The environmental ELA is projected to exceed the maximum elevation of 69%, 81% and 92% of the glaciers in the European Alps by 2071−2100 under mitigation (RCP2.6), stabilization (RCP4.5) and high greenhouse gas emission (RCP8.5) scenarios, respectively.

Hydrologically Informed Machine Learning for Rainfall-Runoff Modelling: Towards Distributed Modelling

Despite showing a great success of applications in many commercial fields, machine learning and data science models in general, show a limited use in scientific fields including hydrology. The approach is often criticized for lack of interpretability and physical consistency. This has led to the emergence of new paradigms, such as Theory Guided Data Science (TGDS) and physics informed machine learning. The motivation behind such approaches is to improve the physical meaningfulness of machine learning models by blending existing scientific knowledge with learning algorithms. Following the same principles, in our prior work (Chadalawada et al., 2020), a new model induction framework was founded on Genetic Programming (GP) namely Machine Learning Rainfall-Runoff Model Induction Toolkit (ML-RR-MI). ML-RR-MI is cable of developing fully-fledged lumped conceptual rainfall-runoff models for a watershed of interest using the building blocks of two flexible rainfall-runoff modelling frameworks (FUSE and SUPERFLEX). In this study, we extend ML-RR-MI towards inducing semi-distributed rainfall-runoff models. This effort is motivated by the desire to address the decreasing meaningfulness of lumped models which tend to particularly deteriorate within large catchments where the spatial heterogeneity of forcing variables and watershed properties are significant. Henceforth, our machine learning approach for rainfall-runoff modelling titled Machine Induction Knowledge-Augmented System Hydrologique Asiatique (MIKA-SHA) captures spatial variabilities and automatically induces rainfall-runoff models for the catchment of interest without any subjectivity in model selection. Currently, MIKA-SHA learns models utilizing the model building components of FUSE and SUPERFLEX. However, the proposed framework can be coupled with any internally coherent collection of building blocks. MIKA-SHA’s model induction capabilities have been tested on the Red Creek catchment near Vestry, Mississippi, United States. The resulted model architectures through MIKA-SHA are compatible with previously reported research findings and fieldwork insights of the watershed and are readily interpretable by hydrologists.

Adaptive clustering: reducing the computational costs of distributed (hydrological) modelling by exploiting time-variable similarity among model elements

In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. Key requirements for the application of adaptive clustering are the existence of (i) many model elements with (ii) comparable structural and functional properties and (iii) only weak interaction (e.g. hill slopes, subcatchments, or surface grid elements in hydrological and land surface models). The clustering of model elements must not only consider their time-invariant structural and functional properties but also their current state and forcing, as all these aspects influence their current functioning. Joining model elements into clusters is therefore a continuous task during model execution rather than a one-time exercise that can be done beforehand. Adaptive clustering takes this into account by continuously checking the clustering and re-clustering when necessary. We explain the steps of adaptive clustering and provide a proof of concept at the example of a distributed, conceptual hydrological model fit to the Attert basin in Luxembourg. The clustering is done based on normalised and binned transformations of model element states and fluxes. Analysing a 5-year time series of these transformed states and fluxes revealed that many model elements act very similarly, and the degree of similarity varies strongly with time, indicating the potential for adaptive clustering to save computation time. Compared to a standard, full-resolution model run used as a virtual reality “truth”, adaptive clustering indeed reduced computation time by 75 %, while modelling quality, expressed as the Nash–Sutcliffe efficiency of subcatchment runoff, declined from 1 to 0.84. Based on this proof-of-concept application, we believe that adaptive clustering is a promising tool for reducing the computation time of distributed models. Being adaptive, it integrates and enhances existing methods of static grouping of model elements, such as lumping or grouped response units (GRUs). It is compatible with existing dynamical methods such as adaptive time stepping or adaptive gridding and, unlike the latter, does not require adjacency of the model elements to be joined. As a welcome side effect, adaptive clustering can be used for system analysis; in our case, analysing the space–time patterns of clustered model elements confirmed that the hydrological functioning of the Attert catchment is mainly controlled by the spatial patterns of geology and precipitation.