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Integrated Simulation of Interactive Surface-Water and Groundwater Systems

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Advances in Water Resources Engineering

Part of the book series: Handbook of Environmental Engineering ((HEE,volume 14))

Abstract

Effective management of watersheds and ecosystems requires a comprehensive knowledge of hydrologic processes, and the ability to predict and quantify reliably the impacts due to anthropogenic or natural changes in water availability and water quality. For integrated water resources management studies in which both surface water and groundwater are interactive, a technically rigorous and physically based approach is essential. Simulation models have been used increasingly to provide a predictive capability in support of water resources, and environmental and restoration projects. Often, simplified models are used to quantify complex hydrologic and transport processes in surface and subsurface domains. Such models incorporate restrictive assumptions relating to spatial variability, dimensionality, and interactions of components in flow and transport processes. During the past decade, with the advent of high-speed personal computers, a number of rigorous integrated surface-water/groundwater models have been developed to circumvent these limitations. In general, a typical model of an integrated hydrologic system may be divided into three interactive and interconnected domains: subsurface, overland, and channels/streams, in which water flow and transport of constituents can occur. In this chapter, the following are presented and discussed: a description of relevant processes relating to water flow and solute transport in conjunction with governing equations for all domains; procedures for model development and calibration; and two field application examples.

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Abbreviations

A C :

Wetted cross-sectional area of the channel segment (L2)

A GO :

Area at the interface between overland and subsurface (L2)

A IJ :

Area through which mass influx passes from domain J to domain I (L2)

a ijmn :

Dispersivity tensor (L)

B C :

Top width of channel (L)

b :

Thickness of channel bed (L)

b :

Fitting parameter (dimensionless) (Eq. 2.4c)

b IJ :

Distance between two centroids in domains I and J (L)

C 1, C 2 :

Fitting parameters (dimensionless) (Eq. 2.14b)

C 3 :

Fitting parameters (dimensionless) (Eq. 2.14c)

C k :

Solute concentration of component k (M/L3)

C d :

Weir discharge coefficient (dimensionless)

C int :

Canopy storage parameter (L)

\(\hat{C}{}_{k}\) :

Concentration for species k vector for the transport equation

\(C_{\text{B}}^{k}\) :

Specified concentration of solute k at the boundary (M/L3)

\(C_{\text{C}}^{*k}\) :

Solute concentration of component k of the sources (or sinks) within the channel domain (M/L3)

\(C_{\text{G}}^{*k}\) :

Solute concentration of component k of the sources (or sinks) within the subsurface domain (M/L3)

\(C_{{{\text{J}}^{+}}/{{\text{I}}^{-}}}^{k}\) :

Directionally dependent concentration of component k in domain J, if v IJ is positive, in domain I if v IJ is negative (M/L3)

\(C_{\text{O}}^{*k}\) :

Solute concentration of component k of the sources (or sinks) within the overland domain (M/L3)

\(C_{\text{O}}^{i}\) :

Reference solute concentration of species i (M/L3) corresponding to Δo and : o

\(C_{\text{S}}^{i}\) :

Solute concentration of species i (M/L3) corresponding to \(\rho_{\text{S}}^{i}\) and \(\mu_{\text{S}}^{i}\)

\(C_{\text{s}}^{k}\) :

Concentration of component k adsorbed to the soil (M/Msoil)

\(D_{\text{d}}^{k}\) :

Molecular diffusion coefficient for component k (L2/T)

\(D_{\text{IJ}}^{k}\) :

Effective dispersion coefficient of component k between domains I and J (L2/T)

\(D_{ij}^{k}\) :

Apparent hydrodynamic dispersion tensor of component k (L2/T)

D ijB :

Dispersion coefficient tensor at the boundary (L2/T)

d :

Flow depth (L)

d C :

Depth of channel flow (L)

d O :

Depth of overland flow (L)

E can :

Canopy evaporation (L/T)

E P :

Reference evapotranspiration (L/T)

F F :

Forcing vector for the flow equation

F T :

Forcing vector for the transport equation

f Str :

Structure discharge per unit length (L2/T)

g :

Gravitation acceleration (L/T2)

H :

Specified hydraulic head at the boundary at x iB (L)

h :

Reference hydraulic head (or equivalent freshwater head) (L) = \(\frac{p}{{{\rho }_{o}}g}\,+\,{{x}_{3}}\)

h :

Overland hydraulic head or water surface elevation (L) = d O + z LS

h :

Hydraulic head or water surface elevation of the channel (L) = d C + z C

\(\hat{h}\) :

Hydraulic head vector for the flow equation

h C :

Head in the channel domain (L)

h d :

Downstream head between the two systems (L)

h G :

Head in the subsurface domain (L)

h O :

Head in the overland domain (L)

h u :

Upstream head between the channel and overland domains (L)

LAI:

Leaf area index (dimensionless)

L R :

Effective root length (L)

l UStr :

Upstream reference location of the structure (L)

l DStr :

Downstream reference location of the structure (L)

K :

Leakance (1/T)

K C :

Conductance term along the length of the channel (L3/T)

K ij :

Hydraulic conductivity or conductance (L/T) in Eqs. (2.1), (2.5a), and (2.6a)

\(K_{ij}^{\text{G}}\) :

Hydraulic conductivity tensor (L/T) = \(\frac{{{k}_{ij}}{{\rho }_{\text{o}}}g}{{{\mu }_{\text{o}}}}\)

\(K_{ij}^{\text{O}}\) :

Overland conductance tensor (L/T)

K F :

Conductance matrix for the flow equation

\(K_{\text{GC}}^{\text{eff}}\) :

Effective leakance across the interface area between channel and subsurface (1/T)

K GO :

Leakance across the interface area between overland and subsurface (1/T)

K T :

Conductance matrix for the transport equation

k ij :

Intrinsic permeability tensor (L2)

k n :

Manning’s conversion factor (L1/3/T)

k rC :

Relative channel conductance (dimensionless)

k rG :

Relative permeability (dimensionless) which is a function of water saturation as provided by the relative permeability curve

k rGC :

Relative leakance at the interface between channel and subsurface (dimensionless)

k rGO :

Relative leakance at the interface between overland and subsurface (dimensionless)

k rO :

Relative overland conductance (dimensionless)

k Str :

Structure operation coefficient (dimensionless)

L C :

Length of channel segment (L)

l :

Length along the direction of flow (L)

\(M_{\text{B}}^{k}\) :

Dispersive mass flux of species k per unit area (M/L3 T)

M F :

Mass matrix for the flow equation

M T :

Mass matrix for the transport equation

\(m_{\text{IJ}}^{k}\) :

Mass influx rate per unit area from domain J to domain I of component k (M/L2 T)

N P :

Number of parent chemicals or solute k (dimensionless)

n C :

Manning’s roughness coefficient for channel (dimensionless)

n i :

Unit vector (dimensionless), positive inward

n ij :

Manning’s roughness coefficient tensor for overland flow (dimensionless)

n R :

Number of cells that contribute to the total root zone for each areal location (dimensionless)

n RT :

Number of cells that lie within the depth interval from 0 to L R at any areal location (dimensionless)

n s :

Number of solutes (dimensionless)

P C :

Wetted perimeter of the channel segment (L)

P P :

Precipitation rate (L/T)

p :

Fluid pressure (M/LT2)

p o :

Reference fluid pressure (M/LT2)

Q B :

Volumetric water flux per unit area (L)

Q CG :

Flux across the area of the interface from subsurface to channel (L3/T)

Q GC :

Flux across the area of the interface from channel to subsurface (L3/T)

Q GO :

Flux across the area of the interface from overland to subsurface (L3/T)

Q OC :

Flux across the total length of channel banks to/from the overland flow domain (L3/T)

Q i :

Discharge per unit width normal to the flow direction (L2/T)

Q OG :

Flux across the area of the interface from subsurface to overland (L3/T)

Q Str :

Discharge rate (L3/T) of the structure as a function of head, h

q C :

Volumetric flux per unit volume (1/T) of the overland domain and represents sources and/or sinks of water

q CO :

Flux per unit volume of channel flow domain from the overland flow domain (1/T)

q CG :

Flux per unit volume of channel flow domain from the subsurface (1/T)

q G :

Volumetric flux per unit volume (1/T) of the subsurface domain and represents sources and/or sinks of water

q GC :

Flux per unit volume of subsurface from the one-dimensional channel domain = − q CG (1/T)

q GO :

Flux per unit volume of subsurface from the two-dimensional overland flow domain (1/T)

q O :

Volumetric flux per unit volume (1/T) of the overland domain and represents sources and/or sinks of water

q OC :

Flux per unit volume of overland flow domain from channel (1/T) = –q CO

q OG :

Flux per unit volume of overland flow domain from groundwater (1/T) = –q GO

r F(z):

Root extraction function (dimensionless) which typically varies logarithmically with depth

S b :

Bed slope (dimensionless) at the zero-depth gradient boundary

S e :

Effective water saturation (dimensionless)

S G :

Degree of water saturation (dimensionless) and is determined by the moisture retention curve as a function of the pressure head

S Gr :

Residual water saturation (dimensionless)

S int :

Canopy storage (L)

\(S_{\text{int}}^{\max}\) :

Canopy storage capacity (L)

\(S_{\text{int}}^{\text{o}}\) :

Previous time step canopy storage (L)

\(S_{\text{int}}^{\text{*}}\) :

Intermediate canopy storage (L)

S O :

Equivalent sediment depth (L)

S Str :

Structure unit function (dimensionless), equals unity along the length when a hydraulic structure is present, 0 otherwise

s :

Length along the direction maximum local slope (L)

\(T_{ij}^{\text{*}}\) :

Tortuosity tensor (dimensionless)

T pI :

Rate of transpiration for computational cell I (L/T)

t :

Time (T)

V :

Magnitude of the velocity vector (L/T)

V G :

Subsurface elementary volume (L3)

V I :

Normalization volume in domain I (L3)

v IJ :

Water flow rate per unit area from domain J to domain I (L/T)

v i :

Darcy velocity along the ith direction (L/T)

v iB :

Specified fluid velocity at the boundary (M/L3)

x i :

Cartesian coordinate along the ith direction (L) with x 3 being vertically upward

x iB :

Boundary coordinates (L)

Z BANK :

Bank elevation (L) which may be at or above the overland flow surface elevation

z :

Depth coordinate from the soil surface (L) (Eq. 2.14d)

z C :

Channel bottom elevation (L)

z LS :

Land surface elevation (L)

∀ :

Fitting parameter (1/L), (Eqs. 2.4a and 2.4b)

∀ G :

Bulk compressibility of aquifer (L2T2/M)

∃ :

Fitting parameter (dimensionless) (Eqs. 2.4a and 2.4b)

∃ w :

Fluid compressibility (LT2/M)

\( I_{{CInt}}^{k}\) :

Mass transfer rate of component k between the channel and other domains (1/T)

\( I_{{GInt}}^{k}\) :

Mass transfer rate of component k between subsurface and other domains (M/L3 T)

\( I_{{OInt}}^{k}\) :

Mass transfer rate of component k between overland and other domains (1/T)

γ :

1–1/β (dimensionless; Eqs. 2.4a and 2.4b)

δ :

Total density factor (dimensionless) \( =\,\frac{{{\rho }_{\text{f}}}-{{\rho }_{\text{o}}}}{{{\rho }_{\text{o}}}}\)

\(\delta ({{l}_{\text{UStr}}})\) :

Kronecker delta, equals unity at the upstream location of the structure (dimensionless)

\(\delta ({{l}_{\text{DStr}}})\) :

Kronecker delta, equals unity at the downstream reference location of the structure (dimensionless), zero elsewhere

ζ :

Distance along submerged channel cross section (L)

θ an :

Moisture content at anoxic limit (dimensionless)

2 C :

Effective porosity in the channel domain (dimensionless)

θ C :

Channel porosity (dimensionless)

θ e1 :

Moisture content at the end of the energy-limiting stage (above which full evaporation can occur; dimensionless)

θ e2 :

Limiting moisture content below which evaporation is zero (dimensionless)

2 eG :

Effective porosity in groundwater domain (dimensionless)

θ fc :

Moisture content at field capacity (dimensionless)

θ G :

Subsurface porosity (dimensionless)

θ O :

Overland porosity (dimensionless)

2 C :

Channel porosity (dimensionless)

θ o :

Moisture content at oxic limit (dimensionless)

θ wp :

Moisture content at wilting point (dimensionless)

\(g_{s}^{k}\) :

First-order decay coefficients for component k in soil (1/T)

\(g_{w}^{k}\) :

First-order decay coefficients for component k in water (1/T)

μ f :

Fluid dynamic viscosity (M/LT)

: o :

Reference fluid dynamic viscosity (M/LT) corresponding to \(C_{\text{o}}^{i}\)

\(\mu_{\text{S}}^{i}\) :

Fluid dynamic viscosity of species i (M/LT) corresponding to \(C_{\text{S}}^{i}\)

>  kj :

Fraction of parent component j transforming into component k (dimensionless)

\(\rho_{\text{B}}^{\text{C}}\) :

Bulk density of sediment in the channel domain (M/L3)

\(\rho_{\text{B}}^{\text{G}}\) :

Bulk density of soil in the subsurface domain (M/L3)

\(\rho_{\text{B}}^{\text{O}}\) :

Bulk density of sediment in the overland domain (M/L3)

ρ f :

Fluid density (M/L3)

ρ o :

Reference fluid density (M/L3)

Δo :

Reference fluid density (M/L3) corresponding to \(C_{\text{o}}^{i}\)

\(\rho_{\text{S}}^{i}\) :

Fluid density of species i (M/L3) corresponding to \(C_{\text{S}}^{i}\)

P :

Pressure head (L)= p/(Δo g)

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  1. HydroGeoLogic, Inc., 11107 Sunset Hills Road, Suite 400, 20190, Reston, VA, USA

    Varut Guvanasen PhD,PE & Peter S. Huyakorn PhD

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    Chih Ted Yang

  2. Rutgers University, New Brunswick, New Jersey, USA

    Lawrence K. Wang

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Guvanasen, V., Huyakorn, P. (2015). Integrated Simulation of Interactive Surface-Water and Groundwater Systems. In: Yang, C., Wang, L. (eds) Advances in Water Resources Engineering. Handbook of Environmental Engineering, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-11023-3_2

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