Erosion and Sediment Transport Modelling in Shallow Waters: A Review on Approaches, Models and Applications

The erosion and sediment transport processes in shallow waters, which are discussed in this paper, begin when water droplets hit the soil surface. The transport mechanism caused by the consequent rainfall-runoff process determines the amount of generated sediment that can be transferred downslope. Many significant studies and models are performed to investigate these processes, which differ in terms of their effecting factors, approaches, inputs and outputs, model structure and the manner that these processes represent. This paper attempts to review the related literature concerning sediment transport modelling in shallow waters. A classification based on the representational processes of the soil erosion and sediment transport models (empirical, conceptual, physical and hybrid) is adopted, and the commonly-used models and their characteristics are listed. This review is expected to be of interest to researchers and soil and water conservation managers who are working on erosion and sediment transport phenomena in shallow waters. The paper format should be helpful for practitioners to identify and generally characterize the types of available models, their strengths and their basic scope of applicability.


Introduction
Soil erosion and its degradation of soil productivity and environment effects on the productivity of land and water quality (of rivers, estuaries and lakes) comprise one of the major concerns of watershed managers and decision makers. Temporal and spatial information of soil erosion processes is required to reflect the pattern of sediment transport during storm events. Erosion is a process of detachment and transport of soil materials by erosive agents from any part of the Earth's surface [1]. Generally, natural erosion is divided into two main categories: water erosion and wind erosion. Water erosion occurs as different forms of splash, sheet and interrill erosion, rill erosion, gully erosion, river banks or channel erosion, tillage erosion and glacial erosion. Factors affecting water erosion are climate, topography, soil structure, vegetation and anthropogenic activities such as tillage systems and soil conservation measures [2]. Sheet and interrill erosion is considered one of the first steps of erosion in catchments, which is widely observed on bare or almost bare soils in agricultural lands, pasturage and open areas. In this type of erosion, the process begins by rain drops hitting the soil surface, and their effect of detaching the soil structure is an important factor in particulate matter transport. Generally, soils, vegetation maps, etc. [17][18][19][20][21]. Much information such as canopy leaf area index, slope, aspect, contributing drainage area, soil texture or hydraulic conductivity assigned by soil series, and so on, can be automatically imported into the models using remote sensing and GIS techniques. cover, soils, vegetation maps, etc. [17][18][19][20][21]. Much information such as canopy leaf area index, slope, aspect, contributing drainage area, soil texture or hydraulic conductivity assigned by soil series, and so on, can be automatically imported into the models using remote sensing and GIS techniques. The structure of this paper is to review most of the available literature concerning sediment transport modelling in shallow waters and to make a classification based on the representational process of the model adopted, and the commonly-used models and their characteristics are listed. Model types are categorized in terms of how the processes of soil detachment, transport and deposition are represented by the model. It provides descriptions of a number of available models that are widely used in the market. The review is expected to be of interest to researchers, decision makers and water quality managers who are concerned with erosion and sediment transport phenomena in shallow waters. This paper will conclude with the major issues of the introduced erosion and sediment transport models, including discussions about the models' complexity and accuracy, data availability and models' uncertainties. This review is prepared to provide an overview of the wide range of issues related to the erosion and sediment transport processes in shallow waters. For a detailed analysis of these components, the reader is required to refer to the appropriate references throughout this text prior to modelling.

Soil Erosion and Sediment Transport Models
A wide range of soil erosion models has been developed in the past few decades, each differing in terms of complexity, accuracy, inputs and outputs, approaches and their spatial and temporal scales. Generally, based on the physical processes simulated by the model, approaches to generate the data and data dependence, different kinds of models can be categorized into four widely-used models including: (1) Empirical models, (2) Conceptual models, (3) Physically-based models, (4) Hybrid models. The structure of this paper is to review most of the available literature concerning sediment transport modelling in shallow waters and to make a classification based on the representational process of the model adopted, and the commonly-used models and their characteristics are listed. Model types are categorized in terms of how the processes of soil detachment, transport and deposition are represented by the model. It provides descriptions of a number of available models that are widely used in the market. The review is expected to be of interest to researchers, decision makers and water quality managers who are concerned with erosion and sediment transport phenomena in shallow waters. This paper will conclude with the major issues of the introduced erosion and sediment transport models, including discussions about the models' complexity and accuracy, data availability and models' uncertainties. This review is prepared to provide an overview of the wide range of issues related to the erosion and sediment transport processes in shallow waters. For a detailed analysis of these components, the reader is required to refer to the appropriate references throughout this text prior to modelling.

Soil Erosion and Sediment Transport Models
A wide range of soil erosion models has been developed in the past few decades, each differing in terms of complexity, accuracy, inputs and outputs, approaches and their spatial and temporal scales. Generally, based on the physical processes simulated by the model, approaches to generate the data and data dependence, different kinds of models can be categorized into four widely-used models including: (1) Empirical models, (2) Conceptual models, (3) Physically-based models, (4) Hybrid models.
The accuracy of soil erosion measurement depends on model type and the considered parameters. For example, Kinnell [22,23] pointed out that both conceptual and empirical models have some inadequacy in characterizing the soil loss in comparison to observed erosion values in bare soils. Models may also be described as hybrids between two or more of these classes. For example, the Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow-Water Quality (IHACRES-WQ) model [24] and European SEDiment NETwork (SEDNET) model [25] are hybrid metric-conceptual models. The structure of the models consists of a number of storages and is basically conceptual, while statistical identification procedures are used to determine the number and configuration of storages in each catchment [9].
Most of the studies are performed on bare soils and in some cases on tilled soils covered by grass or mulch. However, natural systems are more complex and represent many variations in terms of spatial and temporal scales, transport media and dimensions and the interactions between detached sediment and attached chemicals. Jakeman et al. [26] stated that environmental modeling is limited by natural complexity, spatial heterogeneity and the lack of available data. As an example, in forested areas, high variability in the spatial and temporal distribution of vegetation and soil properties may be seen. In such areas, different types of surface cover, runoff-generating mechanisms and various spatial and temporal patterns of hydraulic conductivity, infiltration capacity and surface erodibility are experienced [27][28][29][30][31][32][33][34][35][36][37][38][39][40]. These factors can cause different values of sediment generation and deposition.
It should be noted that it is impossible to choose the 'best' model among those available, because each model has been developed for a particular purpose and is unable to solve the problem in every situation. A number of factors that should be considered in order to choose an appropriate model for a particular purpose include:

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Dataset requirements of the model, • Fundamental assumptions of the model, • The accuracy and validity of the model, • Model capabilities and susceptibilities, • The components of the model, • User-friendliness of the model, • The objectives of the model, • The scales of the model outputs, • Hardware requirements of the model.

Empirical Models
Empirical models are a simulation of natural processes, mostly based on statistical observations, and rely on developed regression relationships. The computational processes of empirical models are simple, and their data requirements are less than those that are required for conceptual and physically-based models. In this way, it can be said that empirical models are the simplest approach to measure soil erosion and sediment transport when compared to the other three types of models. The difficulty with using empirical models is the inability to be accurately used outside of the geographical area where their relationships were derived. Empirical models also may utilize unrealistic assumptions about the physics of the catchment system and, therefore, ignore the heterogeneity of some catchment inputs such as rainfall and soil types. In addition, it should be noted that the inherent non-linear relations in the catchment system are ignored in empirical models [41].
Morgan [42] introduced three types of analyses for empirical models: (1) black-box analysis, where only the main inputs and outputs are studied; (2) grey-box analysis, where the system's procedure is explained in more detail; and (3) white-box analysis, where the elements of the system are represented in detail. An advantage of empirical models is their ability to be employed in catchments with limited data, and also the lack of a requirement for complex inputs; thus, they can be considered preferable to more complex conceptual and physically-based models. Empirical models are valuable as a first step in identifying sources of sediment and nutrient generation. At regional scales, with the recognition of sediment residence time and delivery patterns, empirical methods can be applied uniformly to predict the sediment delivery [25]. In the empirical models, the parameter values can be obtained from local calibrations, although sometimes transferred from calibrations at experimental sites [9].

Conceptual Models
Conceptual models are basically a combination of empirical and physically-based models and are more applicable to answering general questions [63]. These models were developed on the basis of spatially-lumped forms of water and the sediment continuity equation [64]. The main focus of a conceptual model is to predict sediment yield, basically using the concept of the unit hydrograph. Conceptual models represent a catchment by its internal storage systems, which typically incorporate the inherent physical processes of runoff generation and sediment transport in their conceptual structure. These models usually unify general descriptions of catchment processes without specifying the process of interactions that would require very detailed catchment information [65]. These models therefore provide an indication of the quantitative and qualitative effects of land use changes within a watershed, without taking into consideration the data that are obtained from spatial and temporal input. The value of each parameter in conceptual models is obtained through calibration against observed data, such as stream discharge and sediment concentration measurements [66]. Therefore, due to this requirement, conceptual models tend to suffer from the identifiability problems of their parameter values [67]. Generally, simple conceptual models have fewer problems with model identification than more complex models. Thus, to minimize the problems with model identification, the number of parameters to be estimated through calibration can be reduced where applicable [41,68]. However, this simplification of models may affect the goodness of fit to calibration data.

Physically-Based Models
Physically-based models are generally based on the concept of the conservation of mass, momentum equations and energy as governing equations describing streamflow or overland flow, and conservation of mass equation for sediment [98,99]. Most of the developed physically-based soil erosion models that are being used worldwide to predict erosion and sediment yield are not 100% physically-based because mathematical expressions describing each individual process are developed based on the empirical/conceptual approaches and their assumptions and consideration [100]. Physically-based models, in particular, are often over-parametrized [41,101]. Basically, the parameters of physically-based models are independently measurable. However, due to the existence of a large number of complex parameters and the heterogeneity of critical characteristics, especially in catchments, calibration of these parameters with observed data is inevitable [41]. This procedure creates extra uncertainties in parameter values. In this situation, with the large number of parameter values (in some cases, hundreds) that are required to be measured through the mentioned process, the ability to identify the model parameters will become very difficult, and the non-uniqueness of 'best fit' solutions can be expected [63].
Generally, the governing equations in physically-based models are derived at a small scale and under very specific physical conditions. However, in many cases, these equations are regularly applied to a greater scale with different physical conditions. Continuous spatial and temporal data have been considered for use in these equations, although it is used most often in practice point source data taken to represent an entire grid cell in the catchment. This manner of scaling up is questionable [102], as these small-scale parameters that are assumed for application in small-scale models have the potential to lose their physical significance when they are applied to larger scales [103]. There is not enough theoretical justification to assume that equations can be used identically at the grid scales that represent the lumped aggregate of heterogeneous sub-grid processes [9]. The mathematical expressions in physically-based models, which are derived to describe individual processes, have many assumptions that may not be relevant in most of the natural conditions [104]. Beven [105] notes that by calibration-based model parameterization, physical distributed models are equal to any conceptual model.
The Erosion Kinematic Wave Models [106][107][108], Quasi-Steady State Erosion [109], ANSWERS (Areal Non-point Source Watershed Environment Response Simulation) [110], CREAMS (Chemical Runoff and Erosion from Agricultural Management Systems) [111] and Continuum Mechanics Model [112] are among the first examples of researchers' efforts to develop physically-based models. Table 3 represents the list of commonly-used physically-based models with their characteristics and sources.

Hybrid Models
Hybrid models are a mixture of dynamic and empirical soil erosion evaluation techniques. The structure of hybrid models is usually physical or conceptual at the core, while the configuration of the model in the spatial and temporal scales is based on statistical observations and relies on developed regression relationships. For example, in an empirical-conceptual hybrid model, the structure is conceptualized as a set of storages, and effective rainfalls are modelled at these scales to generate runoff values. In the empirical phase, the statistical identification procedure is applied to determine the metric component of the model, the storage number and configurations per catchment.
Hybrid models developed as soil erosion and sedimentation modelling systems can be used to predict the water erosion vulnerability, soil productivity reduction at hillslopes, catchments and farms and can also assess the optimal management strategies for agricultural or soil and water conservation practices. The list of commonly-used hybrid models and their characteristics and sources are summarized in Table 4.   Note: Gen. * = Generation; Trans. * = Transportation; Dep. * = Deposition. Note: Gen. * = Generation; Trans. * = Transportation; Dep. * = Deposition.

Criteria for the Selection of a Proper Model for Study
Most of the soil erosion and sediment yield and transport models have their own capabilities and limitations based on their complexities, uncertainties, data availability and accuracy, objectives and spatial and temporal scales of study. There are still many difficulties in the understanding and description of event-based procedures that cause erosion, and this may lead to exaggeration of the erosion and sediment yield when combined with the insufficiency and inaccuracy in the interpretation of data. Due to the limitations and difficulties in fully understanding the complexity of natural systems, especially over large watersheds, empirical models are more widely used than physically-based models to solve specific problems in large-scale ecosystems. Furthermore, the large database required by physically-based models is not always easily accessible and available for all watersheds, especially in developing countries.
Many successes and failures derived from different widely-used models that are reported in the literature should be considered precisely by modelers and the agencies that support the models' development to promote and enhance the usefulness of existing models. Simulated results should be validated and calibrated by comparing with the field-measured data. However, the limitations, capacities and capabilities of the model, sensitivities, uncertainties, assumptions, required inputs and expected results, license costs and other determined physiographic and climatic conditions of models must be studied and considered by users. Based on these criteria, to select a proper model to obtain the desired results, a user should first know what the simulation outputs of the model are. Furthermore, special attention should be given to the spatial (field, catchment, hillslope and regional) and temporal (continuous, event, daily, monthly, seasonal and annual) scales of the model, which are important factors in the selection of a proper tool for a specific study. It is highly recommended to use accredited and validated models that have been previously used to simulate erosion and sediment processes in similar physiographic and climatic conditions. In addition, accurate data are required to obtain reliable results from erosion and sediment prediction models.

Conclusions
Soil erosion caused by water as a natural phenomenon appears in different types and has direct and indirect effects on the environment and human life. It reduces the productivity of lands and decreases the useful storage volume of rivers and reservoirs and the service life of many hydraulic structures, like dams, by deposition of sediments. During the past few decades, a large number of soil erosion and sediment transport models has been developed, focusing on various characteristics and capacities. Based on their underlying concept, these models are categorized into four groups: (I) empirical models, (II) conceptual models, (III) physically-based models and (IV) hybrid models.
Among the empirical models, the Universal Soil Loss Equation (USLE) model is widely described in the literature. Although it was mainly developed based on data from the United States, this model and its latter Revised (RUSLE) and Modified (MUSLE) versions are widely applied all around the world with a large number of subsequently developed models based on this model. Hydrologic simulation Program, Fortran (HSPF), is considered as a conceptual model that is freely available. It is suitable for large watersheds comprised of both urban and rural areas. HSPF can address the sediment and nutrient Total Maximum Daily Load (TMDL) problems, nutrient and pesticide management, urbanization and ponds. It calculates the amounts of deposition or scour of cohesive sediment based on the bed shear stress. The critical shear stress required for the calculation of deposition and scouring is determined by the user, and deposition or scouring of cohesive bed sediments occurs whenever shear stress is less than or greater than the specified critical shear stress, respectively. The simplified Krone's equation [156] is used in this model to measure the rate of deposition based on settling velocity, sediment concentration, shear stress and critical shear stress [157]. The Soil and Water Assessment Tool (SWAT) model is another conceptual model that is continuously under development and largely used worldwide. SWAT is a regional-scale and continuous-time model, which operates on a daily time step at the basin scale. It can be used to predict both overland and in-stream sediment generation, transportation and deposition, as well as rainfall-runoff and sediment-associated transport of chemicals. Prediction of the long-term impacts of erosion in large basins, as well as the timing of agricultural practices within a year are other applications of this model that cause it to be used frequently. Physically-based models are developed on the basis of the physical description of the soil erosion and sediment transport processes. Working with these models is more complex than other models due to their highly detailed representations of the processes and the requirement of the preparation of extensive data. These issues have caused models such as Limburg Soil Erosion Model (LISEM) and Watershed Erosion Prediction Project (WEPP) to be less frequently adopted [9] and has led to efforts to develop physically-based erosion and sediment transport models that are simplified and require less data.
However, physically-based models are more capable of operating either on a continuous basis or in an event-based mode, like MIKE-Systeme Hydrologique Europeen (SHE), CASCade 2-Dimentional SEDimentation (CASC2D-SED), Watershed Erosion Prediction Project (WESP), SEM, SHE-SEDimentation (SHESED) and EUROpe WIthin Storm Erosion (EUROWISE). The Danish Hydraulic Institute (DHI)'s MIKE-SHE is a physically-based watershed model, which also contains several Best Management Practices (BMPs) options, such as wetlands, nutrient and pesticide management. For river hydraulics purposes, MIKE-SHE can be used with MIKE-11. Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) is another model that is used for hydrology, water quality and nutrient analysis, pesticide transport and erosion and sediment yield for field-scale agricultural areas. In this model, the USLE computation methods are used and implemented to measure the rates of erosion and sediment yield. The Kinematic Runoff and Erosion Model-2 (KINEROS-2) is the improved version of KINEROS, which is an event-based model suitable to analyze surface runoff and erosion rates over small natural and urban watersheds. KINEROS-2 can consider both concentrated flow (rill) erosion due to flowing water and splash and sheet (inter-rill) erosion resulting from raindrop energy, separately. This model also can prepare the input data and visualize the results is a GIS format. An important disadvantage of this model is its lack of considering the Evapotranspiration (ET) losses. Furthermore, true soil moisture redistribution for long rainfall intervals cannot be formulated in KINEROS-2.
GSSHA (Gridded Surface/Subsurface Hydrologic Analysis) is a 2D physically-based model, which simulates surface and groundwater hydrology. In previous versions of the model, the erosion and sediment component were semi-empirical; however, in recent versions, the sediment transport formulation is based on the USLE soil parameters. There are also different optional methods to simulate erosion and sediment transport, especially using a specific gravity different from sand. Other optional equations to calculate sediment transport include: Kilinc and Richardson [158], Englund Hanson [8] and Stream power [159]. GSSHA inputs can be driven by land use, soil, vegetation and other physiographic maps in GIS format, and it also links the model results with GIS.
DWSM, the Dynamic Watershed Simulation Model, is a storm event, distributed and physically-based model for simulations of surface and ground water flow, soil erosion and transport of sediment and chemicals (nonpoint-source pollutants) in a watershed during a single or a series of rainfall events. DWSM computes the rates of erosion based on the detachability of user-defined soil particles by raindrop impact and also erodibility of soil by flow characteristics. The sediment transport component and the process of scouring and deposition are computed based on the sediment transport capacity of flow using the approximate analytic solution of the temporally-and spatially-varying continuity equation. Drainage patterns and topographic features are considered to delineate the sub-watersheds.
Hybrid models, which apply both metric and physical processes of soil erosion and sedimentation modelling systems, can be used to predict the water erosion vulnerability and the soil productivity reduction at hillslopes, catchments and farms and are also used to assess the optimal management strategies for agricultural or soil and water conservation practices. IHACRES-WQ, SEDNET, THORNES and Automated Geospatial Watershed Assessment (AGWA), in terms of their characteristics and their outputs, can be mentioned as the strongest models among the hybrid models. The determination of an appropriate model depends on the questions and problems that need to be addressed. Furthermore, the spatial and temporal scales, suitability, accuracy and validity of a model in catchment conditions, model assumptions and data requirements should be considered by the user.