Water Resources Planning Branch, WRA, MOEAWater Resources Planning Branch, WRA, MOEA

MIKE 21 Model

Model Category: Numerical model for coastal waves, currents, and sediment transport

Model Name: DHI MIKE 21

1. Model Introduction

   MIKE 21 is one of the MIKE series software packages developed by the Danish Hydraulic Institute (DHI) to solve numerical simulation problems related to coastal areas. Its modules include the HD Hydrodynamic Model, SW Spectral Wave Model, ST Sediment Transport Model, SM Shoreline Model, BW Boussinesq Wave Model, etc. Users may select appropriate modules according to the purpose of the study and perform coupled calculations simultaneously. For example, nearshore morphological change simulations can be performed using three-way coupling (HD, SW, and ST) or four-way coupling (HD, SW, ST, and SM). The detailed process is shown in Figure 1.

2. Functions and Output Data

   MIKE 21 mainly uses non-uniform triangular meshes (Figure 2) and the finite volume method for computation. The Hydrodynamic Model (HD) is based on the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations under the Boussinesq and hydrostatic pressure assumptions. It consists of the continuity equation and momentum equations integrated over the water depth. The Spectral Wave Model (SW) solves the wave conservation equation using the finite volume method.

   The modules can either be coupled or operated independently to generate spatial distributions of wave fields (Figure 3), spatial distributions of morphological erosion and deposition (Figure 4), etc. These results can serve as references for subsequent engineering design of oceanographic conditions and planning of beach nourishment effectiveness.
   

   Figure 1. Flowchart of the MIKE 21 Four-Way Coupled Model
   Figure 2. Example of Computational Mesh
   Figure 3. Distribution of Simulated Wave Heights and Wave Directions
   Figure 4. Distribution of Morphological Erosion and Deposition

SMC Model

Model Category: Integrated Two-Dimensional Coastal Model

Model Name: SMC

Model Introduction

SMC (Coastal Modeling System) is a coastal simulation system developed by the Coastal Research Group (GIOC) of the University of Cantabria, Spain, under Professors Raul Medina and Mauricio González between 1995 and 2002, commissioned by the Spanish Ministry of Environment. SMC (Coastal Modeling System) is an integrated coastal planning software system developed for Spain by Professors Raul Medina and Mauricio González of the University of Cantabria between 1995 and 2002 under commission from the Spanish Ministry of Environment.

Since the 1980s, recreational beach design and tourism have become increasingly popular in Spain. The development of the SMC software contributed to the subsequent establishment of systematic design guidelines for static equilibrium artificial beaches combined with beach nourishment, making significant contributions to coastal disaster prevention, coastal recreational facilities, and tourism-related economic development in Spain. The system evolved from numerical simulations of the impacts of large structures on coastal changes to detailed planning and design, with the aim of preventing potential negative impacts of the “groin effect” on downdrift coasts.

Since its development, the SMC system has been upgraded to Version 2.5 while retaining its established basic framework. It is currently an integrated coastal planning and coastal change system platform widely used throughout Spain. This model has two major advantages: (1) the interface between numerical calculations and graphical outputs is smooth and well integrated, allowing the entire process to be completed directly without separate plotting; and (2) when planning or expanding various coastal structures, artificial beach nourishment, and dredging works, users can directly select the project coverage area on the screen, and the software can immediately modify the original topographic data for recalculation of waves, currents, and coastal changes. The application modules included in the SMC software and their relationships are shown in Figures 5 and 6.

1. Pre-stored Data (Sigma): Pre-stored coastal topography (Baco), marine and meteorological data (Odin), coastal inundation information (Altas), coastal engineering application formulas, and the self-practice Tic component.
2. Short-Term Coastal Change Analysis: Includes the planar hydrodynamic calculation module Mopla for wave fields (Oluca), current fields (Copla), and morphological changes (Eros), as well as the Petra module for calculating beach-profile morphological changes during typhoon-induced high waves and storm surges.
3. Long-Term Equilibrium Coastal Analysis: Integrated into the main SMC program, including the long-term equilibrium beach profile model (Perfil de equilibrio) calculated from cross-shore sediment transport and the equilibrium shoreline model (Planta de equilibrio) calculated from wave hydrodynamics.
4. Engineering Field Applications: Integrated into the main SMC program, including dredging, beach nourishment, prevention of downstream coastal impacts caused by breakwater expansion and construction of new coastal structures, and planning of static equilibrium artificial headland bays.
5.  Demonstration Case Module Tic: A wide range of coastal engineering design methods and empirical formulas are included, but this section is available only in Spanish. Tic consists of four parts: (1) dynamic analysis, including wave prediction, wave theory, wave propagation, wave statistical methods, spectral analysis, long waves, and sea-level calculations; (2) littoral sediment transport, including sediment transport, sediment characteristics, beach shoreline changes, and profile change models; (3) structural design, including wave-structure interactions such as wave run-up, permeability, and overtopping; and (4) coastal environmental impacts.
   
   Figure 5. Schematic Diagram of Relationships among Modules in the Spanish SMC Software
   Figure 6. Schematic Diagram of Relationships among Modules in the Spanish SMC System

SRH-Coast Model

SRH-Coast, also known as the SRH-C model, is the Coast module of the SRH-One numerical model jointly developed by the Water Resources Agency, Ministry of Economic Affairs, and the U.S. Bureau of Reclamation (USBR). It is a two-dimensional numerical model coupling hydrodynamics and waves, designed to extend the application scope of the two-dimensional numerical model SRH-2D. Together with the watershed rainfall-runoff and soil erosion model (SRH-Watershed), it is being integrated and developed into a unified watershed-scale hydrodynamic and mobile-bed numerical model (SRH-ONE) to meet analytical needs related to water and watershed issues. The main characteristics and functions of SRH-Coast are as follows:

1. Module Composition: SRH-C contains three major submodules:

   • o    Hydrodynamics (Current): Uses the SRH-2D module and obtains hydrodynamic information by solving the shallow-water equations.

     o    Wave: Solves the wave force balance equation using a solution method similar to the SWAN model and estimates wave information using the spectral method.

     o    Sediment Transport: Solves non-uniform and non-equilibrium sediment equations.

2. Mesh System: SRH-C uses an unstructured mesh system and is capable of coupled calculations of wave-current-sediment interactions.
3. Governing Equations: SRH-C assumes incompressible flow and adopts depth-averaged and wave-averaged computational approaches. Its primary governing equations include:

   • o     Continuity Equation: Describes changes in water depth.

     o     Momentum Equation: Describes changes in the velocity components of the water body in the X and Y directions, considering gravity, total water pressure, Reynolds stress, bed shear stress, wind shear stress, Coriolis force, wave-induced surface roller, radiation stress, and other factors.

     o      Wave Force Balance Equation: Describes changes in the wave action density function (N), considering group velocity, wave-direction turning rate, frequency change rate, and wave generation and dissipation processes, such as wind action, three-wave/four-wave interactions, whitecapping, wave breaking, and energy dissipation caused by bottom friction.

4. Characteristics of the Sediment Transport Module: The SRH-C sediment transport module has the following characteristics:

   • o     Non-equilibrium Transport: Allows the sediment transport rate to gradually develop toward an equilibrium state and is particularly suitable for environments affected by tides and waves, where sediment concentrations vary spatially and temporally under non-equilibrium conditions.

     o     Sediment Treated as a Continuum and Represented by Concentration (Eulerian Framework): Sediment concentration is treated as a field variable similar to thermal diffusion, making it suitable for large-scale hydrodynamic simulations and long-term sedimentation calculations.

     o     Total Load Approach: Incorporates both suspended load and bed load into the sediment transport flux calculation, providing simulation of overall sedimentary changes.
     o    Newtonian Fluid Behavior under the Low-Concentration Assumption: When the volumetric concentration is below 0.1, the water-sediment mixture can be approximated as a Newtonian fluid for computation, avoiding high-concentration nonlinear viscous effects and instability.
     o     Independent Solution for Each Grain-Size Class: An independent partial differential equation is used for each grain-size class in the system to simulate the total sediment transport rate.
     o      Sediment Exchange Flux: The key parameter Se,kS_{e,k} in the non-equilibrium equation represents the sediment exchange flux between the water body and riverbed. Its calculation considers the theoretical total sediment transport capacity and adaptation length.
     o     Methods for Calculating Total Sediment Transport Capacity: Three calculation methods are provided: van Rijn (2007), Camenen and Larson (2007), and Soulsby-van Rijn (1997). These methods consider the combined effects of waves and currents.
     o     Adaptation Length: Controls the distance required for sediment to approach equilibrium from a non-equilibrium state and directly affects the sediment exchange rate between the water body and riverbed. The model provides both constant and variable adaptation-length methods. The variable adaptation length can be divided into the sum of the adaptation lengths for suspended load and bed load.
     o     Bed Change Simulation: Uses a modified non-equilibrium bed-change equation and divides the bed structure into an active layer and subsurface layer. The thickness of the active layer is variable and directly exchanges sediment with the water body, while the subsurface layer serves as a sediment source or storage layer.
     o     Gravity Sliding Effect: The SslideS_{slide} term can be optionally used to simulate gravity-induced bed sliding on steep slopes, such as collapse or embankment sliding.
     o     Wave Effects: Supports consideration of the effects of radiation stress on water levels and velocity fields, thereby reflecting sediment transport and offshore sediment transport within nearshore breaking zones.
     
     

5.  5.    Applications: Because wave-driven conditions affect the selection of sediment transport capacity and the correction of shear stress, the SRH-C model can be applied to coastal environments such as intertidal zones, beaches, and lagoons. Under the pressures of climate change and human development, coastal erosion, barrier breaching, lagoon sedimentation, harbor and navigation-channel migration, and other significant morphological changes may occur. The development of coastal numerical models such as SRH-C is therefore crucial for scientifically predicting these evolutionary processes and effectively supporting coastal disaster prevention and land-use planning.
   Figure 7. Schematic Diagram of the Operation of Each Module in the SRH-C Numerical Model

Microscale modeling of submarine geomorphology trends

1. SWMM model

   Calculate the amount of change in local erosion or siltation. Predictive analysis for local submarine geomorphology trends, they are generally 3-D modeling.

   	Features
   MIKE3 FM (Danish Hydraulic Institute, DHI)	Widely applied to estuaries, harbors and coastal areas. Simulate 3D flow phenomenon of free surface, including : advection-dispersion, water quality, heavy metal pollution, water eutrophication, sediment transport of hydrodynamic.
   FLOW-3D (Dr. C.W. Hirt)	Applied to aerospace engineering, machine casting, river regulation, ship simulation, inkjet and smear, electrical engineering and coastal engineering, etc.
   Delft 3d-wave (Delft hydraulics, Netherlands)	Fluid mechanics, wave mechanics, sediment transport, geomorphology, water quality, particle tracking and ecology.
   CMS-M3D (US Army Corps of Engineers)	Simulation of wave and flow field at coastal construction, sand bar, inlet, diversion dike.

Mesoscale modeling of submarine geomorphology trends

Larger local submarine geomorphology trends is feasible，the calculations of flow field are governed by numerical model of 2-D depth average velocity and 3-D geomorphology trends, they are generally 2-D modeling.

Figure.1 Architecture of SMC

Large-scale modeling of submarine geomorphology trends

Mainly consider the submarine geomorphology trends in large space and long-term scale, they are generally 1-D modeling.