8 Water Quality and Ecosystem Modelling …
175
supporting the protection of water resources date back to the 1950s and were rapidly
developed thanks to advances in information and communication technology [14].
However, origins of mathematical modelling in the hydrology can be traced to works
like the analysis of the biological oxygen demand in the Ohio river by Streeter and
Phelps in 1925 [15]. The model was run with the use of computers in the 1960s, and
it included a first-order linear differential equation and 1-dimensional flow equation
based on the water level and the flow rate. There are various classifications of mathematical models, for example, stochastic and deterministic, steady-state and unsteady,
0-dimensional to 3-dimensional, however, in this chapter we focus on a division of
models into two groups based on the scope of simulated processes, i.e., hydrodynamic models and aquatic ecosystem models. The first type allows simulating the
water flow and the transport of variables taking into account a wide scope of driving
forces and features of the analysed water body (e.g., wind energy, heat transfer, solar
radiation, bathymetry, inflows/outflows, damming level, etc.). Models of aquatic
ecosystems are usually coupled to hydrodynamic models in order to simulate both
the water flow and quality. These models compute equations representing chemical and biological processes, thus enabling the simulation of cycles of individual
elements (e.g., N, P, Si, O 2 , C, metals), chemical compounds and biomass of plankton,
bacteria, fish, macrophytes and other organisms. Taking into account the variability
and complexity of aims, various legal regulations, socio-economic conditions and
unique characteristics of analysed areas (geography, hydrology, geology, climate,
etc.) it is not possible or at least it is unreasonable to develop one, all-purpose and
widely applicable model [16]. At present, there are thousands of mathematical models
dedicated to various components of the environment, for example, Janssen et al. [17]
reported over 1500 aquatic ecosystem models that varied in their complexity. There
are widely used one-dimensional models, like CE-QUAL-R1, DYRESM, DUFLOW,
GLM, GOTM, LIMNMOD, MINLAKE, Mylake, PROTECH, SIMSTRAT, which
are usually applied for the simulation of water mixing and quality in a water column
[17]. Based on such tools, two-dimensional models are often developed (e.g., CEQUAL-W2), which are capable of simulating processes along rivers and streams
or narrow reservoirs/lakes. Two-dimensional models can be used to simulate floods
taking into account the elevation of bed and floodplains. In these models, however,
it is assumed, that the variation of analysed parameters (e.g., water temperature,
concentrations) is negligible in a horizontal plane. It is a considerable limitation
of the use of 2-D models in the analysis of local problems, as the algal blooms
[18, 19]. The most advanced tools have a form of three-dimensional models (e.g.,
AEM3D, ELCOM-CAEDYM, GEMSS, GETM) or systems allowing the user to
choose the number of dimensions appropriately to the goal of application (e.g.,
Delft3D, EFDC, WASP) [17]. Three-dimensional models usually allow to simulate
changes in multiple water quality parameters (even teens or hundreds of parameters simultaneously) and includes non-linear interrelated equations. The water body
is represented as a set of cuboids or polyhedrons, for which output variables are
calculated. Advantages and disadvantages of various model types were a subject of
numerous studies, e.g., [17, 20, 21].
175
supporting the protection of water resources date back to the 1950s and were rapidly
developed thanks to advances in information and communication technology [14].
However, origins of mathematical modelling in the hydrology can be traced to works
like the analysis of the biological oxygen demand in the Ohio river by Streeter and
Phelps in 1925 [15]. The model was run with the use of computers in the 1960s, and
it included a first-order linear differential equation and 1-dimensional flow equation
based on the water level and the flow rate. There are various classifications of mathematical models, for example, stochastic and deterministic, steady-state and unsteady,
0-dimensional to 3-dimensional, however, in this chapter we focus on a division of
models into two groups based on the scope of simulated processes, i.e., hydrodynamic models and aquatic ecosystem models. The first type allows simulating the
water flow and the transport of variables taking into account a wide scope of driving
forces and features of the analysed water body (e.g., wind energy, heat transfer, solar
radiation, bathymetry, inflows/outflows, damming level, etc.). Models of aquatic
ecosystems are usually coupled to hydrodynamic models in order to simulate both
the water flow and quality. These models compute equations representing chemical and biological processes, thus enabling the simulation of cycles of individual
elements (e.g., N, P, Si, O 2 , C, metals), chemical compounds and biomass of plankton,
bacteria, fish, macrophytes and other organisms. Taking into account the variability
and complexity of aims, various legal regulations, socio-economic conditions and
unique characteristics of analysed areas (geography, hydrology, geology, climate,
etc.) it is not possible or at least it is unreasonable to develop one, all-purpose and
widely applicable model [16]. At present, there are thousands of mathematical models
dedicated to various components of the environment, for example, Janssen et al. [17]
reported over 1500 aquatic ecosystem models that varied in their complexity. There
are widely used one-dimensional models, like CE-QUAL-R1, DYRESM, DUFLOW,
GLM, GOTM, LIMNMOD, MINLAKE, Mylake, PROTECH, SIMSTRAT, which
are usually applied for the simulation of water mixing and quality in a water column
[17]. Based on such tools, two-dimensional models are often developed (e.g., CEQUAL-W2), which are capable of simulating processes along rivers and streams
or narrow reservoirs/lakes. Two-dimensional models can be used to simulate floods
taking into account the elevation of bed and floodplains. In these models, however,
it is assumed, that the variation of analysed parameters (e.g., water temperature,
concentrations) is negligible in a horizontal plane. It is a considerable limitation
of the use of 2-D models in the analysis of local problems, as the algal blooms
[18, 19]. The most advanced tools have a form of three-dimensional models (e.g.,
AEM3D, ELCOM-CAEDYM, GEMSS, GETM) or systems allowing the user to
choose the number of dimensions appropriately to the goal of application (e.g.,
Delft3D, EFDC, WASP) [17]. Three-dimensional models usually allow to simulate
changes in multiple water quality parameters (even teens or hundreds of parameters simultaneously) and includes non-linear interrelated equations. The water body
is represented as a set of cuboids or polyhedrons, for which output variables are
calculated. Advantages and disadvantages of various model types were a subject of
numerous studies, e.g., [17, 20, 21].