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Estimating the microbiological risks associated with inland flood events: Bridging theory and models of pathogen transport Philip A. Collender 1 , Olivia C. Cooke 2 , Lee D. Bryant 2 , Thomas R. Kjeldsen 2 and Justin V. Remais 1 1 Environmental Health Sciences, School of Public Health, University of California, Berkeley, Berkeley, CA 94720 2 Department of Architecture and Civil Engineering, University of Bath, Bath, UK BA2 7AY 1 1 2 3 4 5 6 7 8 9 10 11 12
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Estimating the microbiological risks associated with inland flood events: Bridging theory and models of pathogen transport
Philip A. Collender1, Olivia C. Cooke2, Lee D. Bryant2, Thomas R. Kjeldsen2 and Justin V. Remais1
1 Environmental Health Sciences, School of Public Health, University of California, Berkeley, Berkeley, CA 94720
2 Department of Architecture and Civil Engineering, University of Bath, Bath, UK BA2 7AY
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Abstract:
Flooding is known to facilitate infectious disease transmission, yet quantitative research on microbial
risks driven by floods has been limited. Pathogen fate and transport models provide a framework for
examining impacts of landscape characteristics and hydrology on infectious disease, but have not been
widely developed for flood conditions. We critically examine capacities of existing hydrological models
to represent the unusual flow paths, non-uniform flow depths, and unsteady flow velocities accompanying
flooding. We investigate theoretical linkages between hydrodynamic processes and spatio-temporally
variable suspension and deposition of pathogens from soils and sediments, pathogen dispersion in flow,
and concentrations of constituents that influence pathogen transport and persistence. Identifying gaps in
knowledge and modeling practice, we propose a research agenda to strengthen microbial fate and
transport modeling applied to inland floods: 1) development of models incorporating pathogen discharges
from flooded latrines, effects of transported constituents on pathogen persistence, and supply-limited
pathogen transport; 2) studies assessing parameter identifiability and comparative performance of models
with varying degrees of process representation in various settings; 3) development of remotely sensed
datasets for models of vulnerable, data-poor regions; and 4) collaboration between modelers and field-
based researchers to expand the collection of useful data in situ.
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1. Floods and infectious disease transmission
Floods are a major, recurring source of harm to global economies and public health. In the past decade,
floods have caused US$185 billion in economic losses and have been responsible for 65,000 deaths
globally, accounting for nearly half of the mortality associated with natural disasters (EM-DAT 2014).
Future changes to the global climate and increasing urbanization may exacerbate the impact of floods.
Projected increases in the frequency and intensity of heavy precipitation events in some areas, for
instance, may expose larger populations to more frequent and severe flooding in future decades (Jonkman
2005, United Nations 2012, IPCC 2013). Flood-related mortality is greatest in populations with poor
infrastructure and limited economic resources; thus, the impact of flooding in developing countries in
particular is set to remain a major source of morbidity, mortality and economic loss in the coming
decades (Ahern, et al. 2005). Improved flood risk management is therefore essential to support global
development, protect infrastructure, and improve public health.
When considering the public health impact of floods in a risk management framework, most analyses
consider only a subset of the direct pathways linking flood events to mortality and morbidity (e.g.,
injuries, drowning), neglecting more subtle and sometimes delayed impacts such as those resulting from
infectious diseases (Jonkman, et al. 2008). At the same time, it is well known that flood conditions—
defined in detail below—can exacerbate the spread of infectious diseases through various mechanisms
affecting the transport and persistence of pathogenic microorganisms. Microbial contamination of surface
water can result from flood conditions following heavy rainfall when high flow volumes and suspended
solids overwhelm water treatment systems, or when fecal material is flushed from sources on the land
surface due to runoff or inundation by an overflowing channel (Ahern, et al. 2005, Hunter 2003,
Alderman, et al. 2012). High flow velocities in flooded channels may lead to resuspension of pathogens
persisting in channel bed sediments, which may then be transported over long distances in rapidly flowing
surface water (Hunter 2003, McBride and Mittinty 2007). Furthermore, increased transport of suspended
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solids in flooded channels may affect microbial persistence, potentially allowing pathogens to remain
infectious as they reach locations far from their original sources (Walters, et al. 2014).
1.1 Models for characterizing flow and microbial dynamics during flooding
Integrated modeling platforms are available to characterize the timing and extent of flooding during
heavy rainfall events; these generally consist of rainfall-runoff models for estimating channel flows in
response to precipitation inputs, followed by hydrodynamic modeling to simulate the movement of water
through channels and floodplains. Rainfall-runoff models provide a quantitative representation of the
interaction between meteorology and channel flows, and of the partitioning of water between
environmental compartments (e.g., surface storage, subsurface storage, and channel storage), and may
take into account topology, soil type, vegetation and other land-surface characteristics of entire upstream
drainage areas. Rainfall-runoff models may also be used to examine the effects of changes in climate and
land management on the frequency and magnitude of flood events as reflected by their hydrograph
outputs (Singh and Woolhiser 2002, Miller, et al. 2014). Hydrodynamic models are used to route flood
waves (i.e., track water depth and velocity of flow through space and time) through channels and
floodplains based on principles of conservation of mass and, in many applications, momentum (Singh
1996){Singh, 1996 #80;Singh, 1996 #12}.
In most practical applications, a modeler will initially choose a model system deemed suitable for the task
at hand. Next, model parameters are calibrated by tuning the parameter values until as good a fit between
observed and simulated flows, water levels, and/or inundation extents can be obtained. Ideally, some
observed data are withheld from the calibration process and used for subsequent model validation to
ensure that the model performs as expected outside the range of the calibration data (Klemeš 1986). In
practice, rainfall-runoff and hydrodynamic models are affected by uncertainty, parameter non-
identifiability, and model equifinality (a phenomenon in which multiple structurally distinct models
perform similarly well after calibration to observed data) (Beven 2006). These issues are unavoidable in
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hydrological modeling, stemming from the complexity of the factors at play in determining hydrological
responses, the non-linear relationships between them, their spatiotemporal heterogeneity, mismatches in
scale between process descriptions and empirical equations derived from lab experiments, data available
from local or remote sensing, and model spatial discretization, and the limited availability, reliability, and
spatiotemporal coverage of observations used to parameterize or calibrate model process descriptions
(Beven 2006, Beven 2001). Despite these practical difficulties, hydrological and hydrodynamic models
provide a necessary framework for integrating knowledge on the many factors determining regional
hydrology and flood risk.
To estimate microbial hazards alongside physical hazards of floods, additional subcomponents can be
incorporated into hydrological and hydrodynamic models representing the mobilization, transport, and
fate of pathogens in runoff, channels and inundated areas. Microbial transport has been incorporated into
a number of rainfall-runoff and hydrodynamic models, as reviewed by Jamieson et al. (Jamieson, et al.
2005) and de Brauwere et al. (de Brauwere, et al. 2014). These models have primarily been developed for
and applied in agricultural settings in order to assess and attribute microbial pollution of receiving waters.
Issues of parameter non-identifiability and equifinality are exacerbated for fate and transport models, due
to the large number of additional parameters that may be incorporated into the model calculations, as well
as to the scarcity of spatially distributed measurements of microbial concentrations within a catchment
(Sommerfreund, et al. 2010). Issues of data scarcity are even more severe when analyzing flood events:
Gauge data is usually confined to channels (Neal, et al. 2009), leading to difficulty in obtaining data for
calibration of flow parameters in inundated areas, and microbiological measurements are especially
scarce during high flows (Ghimire and Deng 2013). This is probably why integration of microbial
transport modeling into analysis of flood events, especially the analysis of flows in inundated areas, is
notably sparse in the literature. In one example linking transport modeling to flood conditions, Wu et al.
(2009) used the Waterloo flood system distributed hydrological model (WATFLOOD) to predict the
temporal and spatial distribution of E. coli in the Blackstone River (USA) during a series of wet weather
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events in 2005-06. They attained correlation between modeled and observed in-stream bacterial
concentrations within an order of magnitude upstream of a wastewater treatment plant and combined
sewer overflow (CSO) discharge, though the model did not perform well downstream of the plant and
CSO. Ghimire and Deng (2013) augmented the Variable Residence Time (VART) model for bacterial
transport in stream flows to account for transient storage in permeable banks and sediment, and applied it
to several high flow events in the Motueka River, New Zealand. Estimates of in-stream E. coli
concentrations produced by their model matched observed concentrations reasonably well (r2 range: 0.36
- 0.9) over 12 storm events. Kazama et al. (2012, 2007) used a hydrodynamic model to perform a
quantitative microbial risk assessment for monsoon-driven flooding of the lower Mekong River,
Cambodia, considering transport in both channels and inundated areas. Notably, they found that areas
with heightened exposures to fecal coliforms simulated by their model also displayed elevated infant
mortality from diarrheal disease; these results suggest that pathogen transport modeling for flood events
can be used to understand waterborne disease risks.
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1.2 Unique features of microbial fate and transport during flood events
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Microbial fate and transport during flood events is affected by unusual flow paths taken through complex
topography by overbank flows, and by variations in flow depth and velocity over time and space that may
be more complex than those experienced under nominal flow conditions. Flow paths that extend across
inundated areas may mobilize pathogens from soils, feces, or flooded sanitation facilities (e.g., latrines)
on the land surface that might not be considered as sources of contamination under nominal runoff
conditions. Furthermore, areas affected by overbank flows or heavy rainfall may exhibit markedly altered
pathogen mobilization and transport, due to the activation of preferential flow pathways and decreased
retention of transported pathogens in the surface layers of saturated soils (Bradford, et al. 2013).
Meanwhile, flooding can give rise to variations in flow depth and velocity beyond what would be
experienced under normal conditions as a result of increased in-channel flow volume relative to the
wetted perimeter, variable depth, width, and direction of flow across inundated areas, and complex
transfers of momentum between areas of deeper and shallower flow (Costabile, et al. 2013, Ikeda and
McEwan 2009, Nittrouer, et al. 2011). In addition, backwater effects can occur along flooded channels or
across inundated areas, where alterations of upstream flow characteristics are induced by downstream
obstructions (e.g., rising waters become partially obstructed by a bridge), or transitions to sub-critical
flow regimes (Ikeda and McEwan 2009). In turn, flow depth and velocity directly impact the kinetic
energy available for pathogen mobilization (Wu, et al. 2009, Schulz, et al. 2009), mechanical dispersion
of pathogens along primary and secondary axes of flow (Elder 1959, Fischer 1975, Kashefipour and
Falconer 2002), and the mobilization of solids and organic matter from bed sediments and the land
surface. Increased transport of organic matter and suspended solids in flood waters may affect microbial
persistence and transport in complex ways: transported colloids may prolong microbial persistence by
partially blocking UV radiation and increasing nutrient concentrations in the water column (Walters, et al.
2014), dissolved organic carbon (DOC) and other nutrients may provide a favorable environment for
bacterial survival and regrowth – or decrease survival by promoting the growth and/or activity of
antagonistic microbes, and organic matter and surfactants may compete with microbes for binding sites in
soils and sediments, enhancing microbial mobility (Bradford, et al. 2013).
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In this manuscript, we review specific aspects of hydrodynamic models that impact the simulation of flow
paths (Section 2), flow depths and flow velocities (Section 3) under flood conditions. In Section 4, we
examine key aspects of pathogen transport models that affect model performance under flood conditions.
In tables presented throughout the review, and in our discussion section (Section 5), we critically examine
a representative set of rainfall-runoff and flow-routing models adapted for microbial transport estimation
with respect to their capacities to represent key processes affecting pathogen movement and persistence
under flood conditions. Additionally, we discuss key knowledge gaps relevant to fate and transport during
floods, tradeoffs between detailed process representation and model uncertainty, and the importance of
emerging data sources and enhanced collaboration between modelers and researchers in the field for
advancing understanding of microbial risks associated with flooding. We do not attempt a discussion of
all processes relevant to microbial fate and transport (for comprehensive reviews, see Jamieson et al
(2005), Bradford et al. (2013), and de Brauwere et al. (2014)), but limit our focus to aspects of fate and
transport that seem especially relevant to flood conditions.
2. Modeling flow paths during floods
During flood events, runoff and overbank flows pass through areas that are not wetted under normal
conditions as a result of surface water volumes exceeding the capacity of soils, channel banks, and
hydraulic structures to absorb or contain them. The capability of rainfall-runoff models to represent paths
taken by overland flow is determined at a fundamental level by their spatial resolution, while the
dimensionality of hydrodynamic models affects the routing of overbank flows.
The spatial resolution of rainfall-runoff models (Table 1) determines the specificity with which runoff and
transported pathogens may be routed from land surface and subsurface compartments into channels.
Spatially lumped models average landscape and climate characteristics and estimate a single set of
outputs over an entire drainage area. As a result, it is not straightforward to assess the reliability with
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which lumped models partition precipitation between runoff, interflow, and base flow components across
the region of interest, all of which have different implications for pathogen mobilization and transport.
Furthermore, no information on the actual path taken by runoff is generated within lumped models. As a
result, the path taken by pathogens in overland flow from sources to channels and spatial heterogeneity of
pathogen sources, runoff generation, and key processes of pathogen release, transport, and retention
across the basin cannot be explicitly represented. Rather, the total runoff generated is applied to the total
pathogens available for transport even if these parameters do not spatially coincide. Semi-distributed
models capture key aspects of a catchment’s hydrological response and land-surface processes, without
relying on a fully explicit spatial representation, and by lumping spatial elements into response units that
are thought to share common hydrological characteristics. Each response unit is treated as homogenous
with respect to processes generating runoff and transported pathogens (Bormann, et al. 2009). Semi-
distributed models can differentiate between the contributions of various land types within a catchment,
allowing for more realistic matching of runoff generation with pathogen mobilization. Fully distributed
models may either function similarly to semi-distributed models, applying empirical formulae to simulate
the amount of runoff generated from each spatial element (e.g., grid cells of a Digital Elevation Model),
or may represent overland flow between adjacent spatial elements using hydrodynamic equations. In the
latter case, the generation and routing of runoff and mobilized pathogens may be estimated across
overland flow paths.
While distributed hydrological models with flow routing between spatial elements may seem superior
because of the detail with which they represent the land surface and runoff generation processes, they are
prone to issues of parameter non-identifiability and equifinality. This is in large part due to the large
number of additional parameters which may be necessary to represent spatial heterogeneity, many of
which cannot be measured directly or at the scale relevant to the model, particularly the parameters of
subsurface processes (Beven 2001). Furthermore, it is widely acknowledged that the use of mathematical
models of open, complex and large-scale real-world environmental systems involves a range of necessary
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simplifications which introduce uncertainty into the modelling process (Beven 2010a). Thus, despite the
appearance of being more theoretically rigorous, complex distributed models do not necessarily guarantee
more reliable descriptions of hydrological systems, even when accompanied by an increase in the quality
of observational data available for calibration (Beven 2006, Beven 2001, Beven 2010a).
In the case of hydrodynamic models (Table 2), spatial dimensionality may constrain the representation of
flow paths in inundated areas. One-dimensional (1D) models perform best in areas with high volume and
narrow width of flow, as in most river reaches (Tayefi, et al. 2007). Two-dimensional (2D) models
usually provide an improved simulation of floodplain flows (Tayefi, et al. 2007) but require significantly
more computational resources (Pilotti, et al. 2014). Three-dimensional (3D) model formulations are
normally reserved for flow simulations in lakes, estuaries, and coastal waters. In many cases, modelers
have coupled 1D models for channel flow with 2D floodplain models, allowing for realistic routing of
floodplain flows while foregoing high computational costs associated with gridded 2D solutions for
channel flows (Bladé, et al. 2012). In 1D models, inundation is typically represented by a compound
channel in which water levels in overbank and channel areas are set as equivalent, with overbank flow
following the direction of channel flow but at a different velocity. Conversely, in fully 2D or coupled 1D
channel - 2D floodplain models, flow in inundated areas may be routed in any cardinal direction.
3. Modeling depth and velocity of flow during floods
Section 3 nomenclatureh Depth of flow
(m)t Time (continuous)
(units range from seconds to days)Q Discharge (rate of flow)
(L ∙ time-1)x Distance along primary axis of flow
(m)v Flow velocity
(m ∙ time-1)g Acceleration due to gravity
(m2 ∙ time-1)s0 Bed slope
(unitless)sf Friction slope (energy head loss)
(unitless)I Inflow
(L ∙ time-1)O Outflow
(L ∙ time-1)S Storage
(L)∆ t Time step (discrete)
(units range from seconds to days)
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α General term for user-defined or calibrated coefficient
β General term for user-defined or calibrated exponent
θ Muskingum weighting factor(unitless)
K s Ratio of storage to discharge in Muskingum equation(time)
During flood events, flow depth and velocity may vary substantially across time and space, which can
significantly influence microbial transport. Flow depth and velocity are key determinants of many
transport processes, including net mobilization of free and sediment-associated pathogens from surface
layers of soils and channel sediments; dispersion of entrained pathogens; and aspects of pathogen
persistence mediated by suspended solids and dissolved nutrients. Thus, various properties of rainfall-
runoff and flow-routing models that affect the estimation of flow parameters may impact simulations of
microbial transport. The temporal resolution of rainfall-runoff models (Table 1) used to generate
boundary conditions for flow models of flood-affected areas is important, as peak flow may be transient,
and models run at coarser time steps are known to provide less-accurate estimates of even daily discharge
during time periods encompassing storm events (Borah, et al. 2007). In open-channel hydrodynamic
models (Table 2), the dimensionality and physical fidelity of the equations for conservation of mass and
momentum that are used to simulate the movement of water across the model domain, as well as
techniques to simulate exchanges of flow between channels and inundated areas, and a modeler’s
implementation of spatial heterogeneities in roughness (a quantity representing losses of momentum to
friction or turbulence) may impact estimates of flow depth, velocity, and direction; we detail these in the
next section.
Table 1: Spatial and temporal resolution of rainfall-runoff microbiological transport
models
Hydrological model Minimum time step Spatial discretization References
HSPF 1 minute Semi-distributed (Bicknell, et al. 1996)
WATFLOOD 1 hour Semi-distributed (Wu, et al. 2009, Kouwen 2014, Dorner, et al. 2006)
IHACRES 1 day Lumped (Croke, et al. 2005, Ferguson, et al. 2007)
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SWAT 15 minutes Semi-distributed (Neitsch, et al. 2011, Jeong, et al. 2010)
KINEROS2 /STWIR 1 hour
Fully-distributed hydrodynamic
(kinematic wave routing)(2000, Guber, et al. 2014)
COLI 1 hour Lumped (Walker, et al. 1990)
WAMVIEW 1 day Fully-distributed conceptual (Soil & Water Engineering Technology Inc. , Tian, et al. 2002)
WEPP 1 secondFully-distributed hydrodynamic
(kinematic wave routing)
(Flanagan and Nearing 1995, Yeghiazarian, et al. 2006, Bhattarai, et al.
2011)
GIBSI 1 hour Semi-distributed (Simon, et al. 2013)
3.1 Hydrodynamic equations for conservation of mass and momentum
Many hydrodynamic models track the depth and velocity of flow through space and time using variations
of the de Saint Venant shallow-water equations for conservation of mass (eqn 1) and momentum (eqn 2),
presented here in 1D form (Singh 1996):
∂ h∂ t
+ ∂ Q∂ x
=0 (1 )
∂ v∂ t
+v ∂ v∂ x
+g ∂ h∂ x
+g(s0−sf )=0 (2 )
where h is water depth; t is time; Q is discharge; x is a positional coordinate in the direction of flow; v is
flow velocity; g is acceleration due to gravity; s0 is the channel bed slope; and sf is the friction slope.
Within the momentum equation (eqn 2), the terms account for local acceleration and unsteady flow ( ∂ v∂ t ),
convective acceleration (v ∂ v∂ x ), water pressure gradient (g ∂ h
∂ x ), gravitational acceleration along the
channel slope ( g s0 ) ,and momentum lost to friction (−g sf ), respectively. The complete form of the
momentum equation given above (eqn 2), also known as the dynamic wave equation, is capable of
modeling fully unsteady (time-varying), non-uniform (space-varying) flows, including the effect of
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downstream conditions on upstream depth and flow velocity (i.e., backwater effects). The dynamic wave
equation is considered the standard of physical fidelity for conservation of momentum, especially when
modeling overbank flows and sediment transport using high-resolution topographical data (Costabile, et
al. 2013).
Simplified approaches to conservation of momentum assume that one or more terms within the dynamic
wave equation may be considered negligible, resulting in model formulations that may assume space- or
time-invariant flows with varying capacity to represent backwater effects. Typically, the diffusive wave
(eqn 3) or kinematic wave (eqn 4) approximations may be used in place of the dynamic wave equation
(Miller 1984):
g ∂ h∂ x
+g (s0−s f )=0 (3 )
g(s¿¿0−s f )=0¿ (4 )
The diffusive wave approximation (eqn 3) conserves momentum by balancing the water pressure
gradient, acceleration due to gravity, and resistance due to friction along the boundaries of the channel.
By including the water pressure gradient, the diffusive wave equation allows the energy of the wave to
diffuse, via lengthening and flattening, as the wave propagates downstream (Novak, et al. 2010). The
pressure gradient also gives diffusive wave models some ability to account for backwater effects. Since it
neglects terms for local and convective acceleration, the diffusive wave approximation is best suited to
slow flows on gentle slopes without rapid changes in flow (Novak, et al. 2010). The kinematic wave
approximation (eqn 4) assumes that the wave is long and flat enough that the pressure gradient and local
and convective acceleration are negligible in comparison to gravitational acceleration along the channel
slope (Miller 1984). Kinematic waves propagate downstream only and thus cannot represent backwater
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effects; these waves are best suited for representation of shallow flows over steep slopes (Novak, et al.
2010) in the absence of highly super-critical flows (Miller 1984).
Some models further simplify flood-wave routing by using storage routing (also termed hydrological
routing), which considers only conservation of mass. By neglecting the conservation of momentum
altogether, storage routing relates inflows, outflows, and volumes of water in a channel reach directly;
see, for example, the flow routing equation (eqn 5) implemented in WATFLOOD (Kouwen 2014):
I 1+ I 2
2−
O1+O2
2=
S2−S1
∆ t(5 )
where I , O, and S are the inflow and outflow and storage (volume) of water in the channel; subscripts 1
and 2 denote quantities at the beginning and end of time interval ∆ t , respectively. In order to determine
I 2 and O2, Q may be estimated from rating curves (eqn 6) or by employing methods such as the
Muskingum equation (eqn 7) which relates the movement of a flood wave to conceptual storages for
steady (prism) and transient (wedge) flows.
Q=α hβ (6 )
Q=θI +(1−θ )O= 1K s
∗S (7 )
where α and β are derived constants; θ is a weighting factor representing the relative effects of inflows
and outflows on storage within the reach; and K s is the ratio of storage to discharge and approximates the
travel time of the flood wave through the reach (Martin and McCutcheon 1998). The Muskingum method
can be shown to be a discretization of the kinematic wave equation. The related Muskingum-Cunge
method, in which numerical dispersion is controlled by channel hydraulic characteristics (Miller 1984),
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can be shown to be a discretization of the diffusive wave equation (Koussis 2009). Importantly, storage
routing methods provide no information on variability of flow between the considered inflow and outflow
locations (Koussis 2009). The number of spatial dimensions in any hydrodynamic equation may affect
estimates of flow depth and velocity. For instance, secondary lateral flows assumed to be negligible in 1D
models are accounted for in 2D formulations; hence, differences in the spatial distribution of flows
simulated by either approach result in different simulated flow depths and velocities.
Momentum losses to friction and turbulence often vary dramatically across flow domains, and
implementations of hydrodynamic models may vary in their spatial discretization of roughness
parameters. The problem of calibrating roughness across the spatial domain of a hydrodynamic model is
analogous to issues with subsurface parameters in rainfall-runoff models, in that these parameters are not
directly measurable at the scales used in models. Similar to the case of distributed rainfall-runoff models,
while it seems intuitive that allowing roughness to vary at the scale of spatial discretization would offer
more realistic simulations, observational data are rarely, if ever, capable of identifying roughness
parameters at fine spatial resolutions. Hence, many modelers simply apply distinct roughness parameter
values to floodplains and channels (Beven 2007). Hydrodynamic model approaches to simulating flow
are summarized in Table 2.
Table 2: Hydrodynamic model approaches to routing flow through channels and
floodplains
Model Routing in channel
Channel dimensionality
Routing in floodplain
Floodplain dimensionality References
DIVAST Dynamic wave 2D Dynamic wave 2D(Falconer, et al. 2001, Gao, et al.
2011)
SOBEK/D-Water Quality Dynamic wave 1D Dynamic wave 2D (Deltares
Systems 2013a)
HSPF Storage routing 1D NA NA (Bicknell, et al. 1996)
WATFLOOD Storage routing 1D Storage routing with simplified
floodplain
1D (Wu, et al. 2009, Kouwen
2014, Dorner, et
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geometry al. 2006)
SWATStorage routing,
Muskingum routing
1D
Storage routing, Muskingum routing
with simplified floodplain geometry
1D (Neitsch, et al. 2011)
KazamaET AL. Dynamic wave 1D
Dynamic wave without convective acceleration term
2D(Kazama, et al. 2012, Kazama,
et al. 2007)
Yakirevich et al. Dynamic wave 1D NA NA (Yakirevich, et al. 2013)
QUAL2K Storage routing 1D NA NA (Chapra, et al. 2012)
WAMVIEW Storage routing 1D NA NA
(Soil & Water Engineering
Technology Inc. , Tian, et al.
2002)
FASTER Dynamic wave 1D NA NA
(Kashefipour and Falconer
2002, Falconer and
Kashefipour 2001)
EFDC Dynamic Wave 1D, 2D, or 3D NA NA(Bai and Lung
2005, Tetra Tech Inc. 2002)
DUFLOW Dynamic wave 1D Dynamic wave 1D(1995,
Manache, et al. 2007)
TELEMAC Dynamic wave 2D or 3D Dynamic wave 2D or 3D(Desombre
2013, Bedri, et al. 2011)
SLIM Dynamic wave 1D NA NA
(de Brye, et al. 2010, de
Brauwere, et al. 2011)
MOBED Dynamic wave 1D NA NA(Krishnappan 1985, Droppo,
et al. 2011)
QUAL2E-GIBSI Storage routing 1D NA NA
(Simon, et al. 2013, Brown and Barnwell
1987, Rousseau, et al. 2000)
HEMAT Dynamic wave 2D Dynamic wave 2D
(Namin, et al. 2002,
Schnauder, et al. 2007)
KINEROS2/STWIR Kinematic wave 1D Kinematic wave 1D (2000, Guber, et
al. 2014)
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WEPP NA NA Kinematic wave 1D
(Flanagan and Nearing 1995,
Yeghiazarian, et al. 2006,
Bhattarai, et al. 2011)
3.2 Exchange of flow between channels and floodplains
During flood events, overbank flows may result in the development of shear layers between slow-moving,
shallow floodplain flows and swifter, deeper channel flows. The transfer of momentum across these shear
layers affects flow velocity and is potentially important for understanding the transport of sediments and
associated pathogens within channels (Ikeda and McEwan 2009). Furthermore, the large-scale turbulent
structures that may result contribute to substantial dispersion of transported constituents into inundated
areas (Besio, et al. 2012). In most compound channel formulations, transfer of momentum between the
channel and floodplain is neglected (Seckin, et al. 2009). Channel-floodplain exchanges in coupled 1D-
2D models are most often estimated using weir or friction slope equations which similarly neglect the
transfer of momentum. Such approaches may be reasonably accurate when there is significant obstruction
(e.g., embankments, levees, etc.) of flow between channels and floodplains. However, for most other
situations numerical 1D-2D coupling techniques conserving both mass and momentum have been shown
to greatly improve the accuracy of modeled velocity fields in floodplains (Bladé, et al. 2012). Methods for
simulating exchanges of flow between channels and floodplains in models that simulate overbank flows
are summarized in Table 3.
Table 3: Hydrodynamic model approaches to simulating exchange of flow between
channels and floodplains
Model Method of exchange between channel and floodplain
Quantities conserved References
DIVAST Floodplains and tidal flats may be modeled on the same finite element mesh as channels. Mass, momentum (Falconer, et al. 2001)
SOBEK/D-Water Quality
Flow above elevation of 2D overland grid cells containing channel elements, or above elevation
Mass (Deltares Systems 2013a)
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of defined embankments enters 2D floodplain model.
WATFLOODCompound channel. Channel and overbank flow
velocities may be affected by separate terrain roughness parameters.
Mass(Wu, et al. 2009,
Kouwen 2014, Dorner, et al. 2006)
SWAT Compound channel. Mass (Neitsch, et al. 2011)
Kazama et al. Weir equations for channel overflow across levees. Mass (Kazama, et al. 2012,
Kazama, et al. 2007)
DUFLOW Compound channel. Mass (1995, Manache, et al. 2007)
TELEMAC Floodplains and tidal flats may be modeled on the same finite element mesh as channels. Mass, momentum (Desombre 2013,
Bedri, et al. 2011)
HEMAT Floodplains and tidal flats may be modeled on the same finite element mesh as channels. Mass, momentum (Namin, et al. 2002,
Schnauder, et al. 2007)
KINEROS2/ STWIRCompound channel. Channel and overbank flow
velocities may be affected by separate terrain roughness, losses to infiltration, and bed slopes.
Mass (2000, Guber, et al. 2014)
4. Modeling pathogen transport during floods
Pathogen transport during flood events can be conceptualized as the result of three general processes:
mobilization of pathogens from sources on the land surface or within channels; transportation of
pathogens within runoff and streamflow; and removal of pathogens from runoff and streamflow via
settling, or die-off. Variations in depth and velocity of flow across flood-affected areas can have a
considerable influence on microbial transport, including on pathogen settling and mobilization, mixing by
mechanical dispersion, and, through the suspension and deposition of solids, die-off mediated by solar
radiation.
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4.1 Source characterization
In order to estimate influxes of pathogens to channels during rainfall events, including those that give rise
to flood conditions, modelers must characterize point sources of pathogens, such as wastewater treatment
plants (WWTPs), and non-point sources, such as previously contaminated channel sediments and diffuse
fecal contamination on the land surface, in their study area. Assessment of sanitation conditions and
sanitary infrastructure for source characterization alone may provide important information regarding
potential microbial risks during flooding (Chaturongkasumrit, et al. 2013, Funari, et al. 2012), including
whether high flows are likely to increase pathogen concentrations in local water, as would be expected in
the event of WWTP or sewer failure (see e.g., Bhavnani, et al. 2014, Baqir, et al. 2012, ten Veldhuis, et
al. 2010, Massoud, et al. 2009, Shimi, et al. 2010); or likely to dilute and flush contamination present in
waterways (see e.g., Bhavnani, et al. 2014).
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For the most part, pathogen source characterization for flood conditions should follow characterization
approaches for typical rainfall-runoff modeling, which have been discussed in detail elsewhere in the
literature (e.g., de Brauwere, et al. 2014, Benham, et al. 2006, Blaustein, et al. 2015). However, it is worth
noting that the efficiency of microbial release from fecal deposits may change with rainfall intensity and
amount, especially for feces with higher liquid content (Blaustein, et al. 2015). Furthermore, saturation of
soils with water and increases in suspended organic matter will tend to decrease retention of microbes in
soil and sediment matrices, adding to effective mobilization in large-scale models (Bradford, et al. 2013).
Therefore, care should be taken to ascertain whether empirical models for microbial release and transport
derived under nominal conditions are suitable for extreme rainfall and floods. Additionally, key sources,
such as channel bed sediments that provide favorable environments for pathogen survival and may
become resuspended in high flows, and flooded latrines, may be significantly more important under flood
conditions than they are under nominal conditions (Wu, et al. 2009, Bhavnani, et al. 2014, Carlton, et al.
2014, Hofstra 2011, Muirhead, et al. 2004, Jamieson, et al. 2004, Coffey, et al. 2010). The effects of
flooding on pathogen sources may also be socially or behaviorally mediated, as in the Ganges Basin in
Bangladesh, where only 3% of toilets and sanitation remain in use during annual floods while a majority
of the population resorts to defecation in hanging latrines that open directly into the environment (Shimi,
et al. 2010).
4.2 Pathogen mobilization
Subsection 4.2 nomenclatureI pat hk
Influx of pathogens to channel reach from source k(organisms)
Nwwtp Population connected to wastewater treatment plant(individuals)
Pi24Number of pathogens excreted per person per time interval(organisms ∙ individuals-1 ∙ time-1)
V exc Volume of effluent exceeding capacity of wastewater treatment plant(L)
∆ t e Rainfall event duration(units range from seconds to days)
V cap Capacity of wastewater treatment plant prior to overflow(L)
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Mobilization of pathogens during flood events can occur via: 1) erosion of fecal matter or contaminated
soil and sediment from the land surface or from channel boundaries; 2) passive diffusion of unattached
pathogens; and 3) direct release of already contaminated water into the environment (e.g., in the case of
WWTP overflows). In many models, pathogen mobilization is presented as analogous to or dependent on
erosion of soil and sediments as a function of the energy available in rainfall, runoff or streamflow. The
quantity of pathogens mobilized in such a fashion may be expressed using physically-based, mechanistic
equations (presented in section 4.4), or simpler empirical or conceptual relationships (presented in section
4.7).
While many models allow input of time-series data characterizing pathogen concentrations in WWTP
effluent, models describing dependence of pathogen mobilization from sanitation facilities on rainfall or
discharge are rare. The sole example identified in the present review was a transport model coupled to
IHACRES that employs a simple expression for discharges of pathogens from wastewater treatment
plants in wet weather (eqn 8) (Ferguson, et al. 2007):
I pat hwwtp=
Nwwtp Pi24V exc ∆ t e
V exc+V cap(8 )
where Nwwtp is the proportion of the population of a subcatchment connected to a WWTP; Pi24 is the
number of microorganisms excreted per person per day; V exc is the volume of effluent exceeding the
capacity of the WWTP during a wet weather event; ∆ t e is the event duration; and V cap is the treatment
capacity of the WWTP before it overflows. While flow parameters play no explicit role in eqn 8, the
concept of capacity exceedance implicit in eqn 8 may be a reasonable way to approach mobilization of
pathogens from inundated WWTPs. A similar model could relate flow volume over spatial elements
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containing rudimentary sanitation infrastructure (e.g., pit latrines) to the release of their microbial
contents; this would be a more relevant approach for estimating pathogen mobilization in many
developing country settings.
4.3 Modeling pathogen transport in flowing water
Subsection 4.3 nomenclatureC path Concentration of pathogens in the water
column(organisms ∙ L-1)
t Time(units range from seconds to days)
v Flow velocity(m ∙ time-1)
x Distance along primary axis of flow(m)
D Diffusion/Dispersion coefficient(m2 ∙ time-1)
G General term for sinks and sources of substances(organisms ∙ time-1 ∙ L-1 or g ∙ time-1 ∙ L-1)
Epath Exported load of pathogens(organisms)
I pat hkInflux of pathogens to channel reach from source k(organisms)
δ 24 Fraction of pathogens surviving after 24 hours
LR lLocal reach length for transport to main channel (square root of sub-catchment area)(m)
Πd Probability of pathogen settling out of flow over 1 km reach
Hydrodynamic models typically simulate pathogen transport processes using the advection-diffusion
equation (ADE; eqn 9) which models the transport of constituents based on conservation of mass:
∂C path
∂ t=−v
∂ C path
∂x+D
∂2C path
∂ x2 +G (9 )
where C pathis the concentration of transported pathogens; v is flow velocity; D is a coefficient describing
the magnitude of passive diffusion, turbulent diffusion, or dispersion. The first term on the right side of
the equation, −v∂ Cpath
∂ x, represents advection of the substance in the direction of flow, the second term,
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D∂2C path
∂ x2 , represents diffusion or dispersion of the substance to areas of lower concentration, and the
final term, G, is a composite term representing source processes adding pathogens to the water column
(e.g., influx in runoff or from upstream channels, suspension from bed sediments, and growth) as well as
sink processes removing pathogens from the water column (e.g., sedimentation along the channel bed and
pathogen die-off). Transport of sediment-associated and free-floating pathogens in the water column may
be modeled separately by using different values for the diffusion coefficient (Jamieson, et al. 2005). The
ADE has been noted to underestimate the spreading of tracer concentrations in many natural rivers, and
attribute this shortcoming to the assumption within the equation that the diffusive or dispersive flux is
proportional to the local concentration of transported material (Beven 2007, Blazkova, et al. 2012).
Instead, transport time distributions in many river systems are dominated by the effects of retention in
areas of low flow velocity near channel boundaries, so-called ‘dead zones’, which depend primarily on
turbulence structures developing from the geometry of the flow domain and the volume of flow (Beven
2007, Blazkova, et al. 2012). The ADE can be augmented to describe these effects (see e.g. (Bencala and
Walters 1983, Romanowicz, et al.)), but doing so requires the addition of local parameters that must be
calibrated and may exacerbate problems of identifiability and equifinality (Blazkova, et al. 2012).
Alternatively, Blazkova et al. (2012) (Blazkova, et al. 2012) proposed using a simple linear transfer
function, originally suggested by Beer and Young (1983) (Beer and Young 1983), to capture the effect of
dead-zone retention on the transport time distribution of suspended constituents, although this approach
has not been validated for flood conditions.
Simplified transport models may neglect the diffusion term or may use mixing cell techniques. The
relationship of mixing cell techniques to the advection-diffusion equation is analogous to the relationship
between the Muskingum wave routing technique to the kinematic wave shallow-water equations, in that
they may be regarded as finite-difference numerical solutions to the advection-diffusion equation (Barry
and Bajracharya 1996). However, dispersion/diffusion processes are not explicit in mixing cell models.
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Instead, the mixing cell models that attempt to represent dispersion/diffusion do so by controlling
numerical dispersion through varying the size of spatial and temporal intervals for calculation (Barry and
Bajracharya 1996). All mixing cell approaches assume pathogen concentrations to be homogenous
throughout a channel reach. Hydrodynamic model approaches to simulating pathogen transport in
channels and floodplains are summarized in Table 4.
Table 4: Hydrodynamic model approaches to pathogen transport
Hydrodynamic model Approach to pathogen transport References
DIVAST 2D advection-diffusion equationSeparate terms for particle-associated and free-floating pathogens (Gao, et al. 2011)
SOBEK/D-Water Quality 1D advection-diffusion equation (Deltares Systems 2013b)
HSPF 1D mixing cell approachSeparate terms for particle-associated and free-floating pathogens (Bicknell, et al. 1996)
WATFLOOD/ DORNER/ WU
1D mixing cell approachSeparate terms for particle-associated and free-floating pathogens
(Wu, et al. 2009, Dorner, et al. 2006)
Kazama et al. 2D advection equation with numerical diffusion
(Kazama, et al. 2012)(S. Kazama,
personal communication,Feb. 3, 2016)
YAKIREVICH ET AL.
1D advection-diffusion equationTerms for exchange of pathogens between channel flow, groundwater,
and transient storage (stagnant pools, eddies, etc.)(Yakirevich, et al. 2013)
QUAL2K 1D mixing cell approach (Chapra, et al. 2012)
WAMVIEW 1D mixing cell approach (Tian, et al. 2002)
FASTER 1D advection-diffusion equation (Falconer and Kashefipour 2001)
EFDC 3D advection-diffusion equationSeparate terms for particle-associated and free-floating pathogens (Bai and Lung 2005)
DUFLOW 1D advection-diffusion equation (Manache, et al. 2007)
TELEMAC 2D advection-diffusion equation (Bedri, et al. 2011)
SLIM 1D advection-diffusion equation (de Brye, et al. 2010, de Brauwere, et al. 2011)
MOBED 1D mixing cell approachExplicitly models particle-associated pathogens (Droppo, et al. 2011)
QUAL2E-GIBSI 1D advection-dffusion equation(Simon, et al. 2013, Brown and Barnwell
1987)
KINEROS2 / STWIR 1D advection-diffusion equation (Guber, et al. 2014)
HEMAT 2D advection-diffusion equation (Schnauder, et al. 2007)
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In addition to the approaches outlined above, it is worth noting the possibility of augmenting semi-
distributed rainfall-runoff models with simplified conceptual pathogen transport. For instance, Ferguson
et al. (2007) modeled in-channel transport alongside a semi-distributed implementation of IHACRES by
expressing pathogen export for each sub-catchment as a function of steady flow velocity and static
probabilities of pathogen removal by sedimentation or inactivation (eqn 10):
Epath=∑k=1
Nk
I pat hkδ 24
LR l
v ( 1−Π d )LR l (10 )
where Epath is the exported load of pathogens from the sub-catchment; I pat hk is the input of pathogens to
the stream from source k; δ 24 is the fraction of pathogens surviving in water after 24 hours; LR l is the
local reach length (for transport to the main channel, assumed equal to square root of sub-catchment
area); v is flow velocity over the reach; and Π d is the probability of pathogens settling out over a 1-km
reach. Unfortunately, the authors did not compare model estimates with measured pathogen
concentrations, and the extent to which this approach is capable of representing pathogen transport under
real conditions is not readily apparent.
4.4 Hydrodynamic calculation of pathogen suspension and settling during floods
Section 4.4 nomenclatureGmob Net source or sink of substance to water
column from deposition and suspension(organisms ∙ time-1 ∙ L-1 or g ∙ time-1 ∙ L-1)
Rrl Rate of suspension of substance l(organisms ∙ time-1 ∙ L-1 or g ∙ time-1 ∙ L-1)
Rd l Rate of deposition of substance l(organisms ∙ time-1 ∙ L-1 or g ∙ time-1 ∙ L-1)
ce Entrainment coefficient(g ∙ m-2 ∙ time-1)
τ b Shear stress along bed(Pa)
τ crCritical shear stress for net suspension(Pa)
τ cdCritical shear stress for net deposition(Pa)
ω Particle settling velocity(m ∙ time-1)
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Psus Number of pathogens suspended(organisms)
C pathsed Concentration of pathogens in bed sediments(organisms ∙ g-1)
C sed maxMaximum concentration of sediment channel can transport(g ∙ L-1)
C sed Concentration of sediment in channel(g ∙ L-1)
cse Channel erodibility factor(unitless)
cveg Vegetative cover factor(unitless)
Sch Storage (volume) of water in channel(L)
Pdep Number of pathogens deposited(organisms)
t Time(units range from seconds to days)
t cr Time at which critical shear stress for suspension is exceeded(time)
K e Enhanced mass transfer rate from sediments to water after biofilm sloughing(g ∙ time-1)
ρ sed Bed sediment density(g ∙ L-1)
ρ Water density(g ∙ L-1)
g Acceleration due to gravity(m ∙ time-2)
vx , v y Flow velocity in x and y dimensions(m ∙ time-1)
C Chezy roughness coefficient(m1/2 ∙ time-1)
τ c Pivot point critical shear stress -suspension dominates above, deposition dominates below(Pa)
s0 Channel bed slope(unitless)
R Hydraulic radius(m)
Q Discharge (rate of flow)(L ∙ time-1)
α General term for user-defined or calibrated coefficient
vpk Peak flow velocity(m ∙ time-1)
β General term for user-defined or calibrated exponent
t res Residence time in reach(time)
W Channel width(m)
W b Bottom width of channel(m)
v Mean flow velocity(m ∙ time-1)
V c h24Daily flow volume(L)
V c h24cr Critical daily flow volume determining dominance of suspension or deposition(L)
mme Dry sediment mass per unit area(g ∙ m-2)
∆ t Length of time step(time)
Av Vertical turbulent viscosity(Pa ∙ time)
z Vertical coordinate within water column(m)
sf Friction slope (energy head loss)(unitless)
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Net mobilization of pathogens (i.e., the total number entering the water column less the number leaving
through settling or retention) from sources in channels and on land surfaces (included within the G term
in eqn 9) depends on flow velocity, which determines the amount of energy available to mobilize
particles, and flow depth, which influences the time it takes suspended particles to settle. The physical
mechanisms involved include entrainment and settling of particles mediated by shear stresses along the
boundaries of flow, as well as loss of suspended pathogens infiltrating into the soil column or channel
bed. Additionally, pathogens trapped in sediment or soil near the surface-subsurface interface may be re-
mobilized during high flows independent from sediment suspension (Ghimire and Deng 2013,
Yakirevich, et al. 2013, Grant, et al. 2011); however, this hyporheic transport process is rarely accounted
for in fate and transport models (Piorkowski, et al. 2014).
Mobilization of channel bed sediments is an important source of suspended pathogens during high flow
events (Wu, et al. 2009). Physically based models often calculate net mobilization of particle-associated
pathogens as a piecewise function of bed shear stresses (e.g., eqns 11-13; Yakirevich, et al. 2013):
Gmob=Rr path−Rdpath (11)
Rr path={ce( τb
τ c r
−1) for τ b> τcr
0 for τ b≤ τ cr
(12 )
Rd path={ω (1−τb
τ cd) for τb< τcd
0 for τb ≥ τcd
(13 )
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where Gmob is the net flux of pathogens into or out of the water column via suspension and sedimentation;
Rr path is the rate of pathogen resuspension; Rd path is the rate of pathogen deposition; ce is an entrainment coefficient; τ b is the shear stress along the channel bed; τ cr
and τ cd are empirically
determined critical shear stresses for erosion and deposition, respectively; and ω is the particle settling
velocity (calculated via Stokes’ law or other means). Depending on each model’s approach to
hydrodynamics, turbulent shear stresses may be calculated as a function of either temporally and spatially
varying quantities, such as flow depth and velocity, or spatially varying but temporally invariant factors
such as channel slope and width, hydraulic radius, and friction coefficients. Critical shear stresses for
erosion or deposition may be empirically determined or estimated based on sediment properties.
Less physically oriented models for pathogen mobilization and deposition rely, respectively, on power
laws relating suspension to discharge or flow velocity, or expressions relating settling rates to particle
settling velocity, which may or may not incorporate flow depth or pathogen concentrations (Wu, et al.
2009, de Brauwere, et al. 2011, de Brye, et al. 2010, Chapra, et al. 2012). Additionally, many models
which implement storage routing invoke a concept of sediment transport capacity. Settling and
suspension are specified as mutually exclusive conditions resulting when the concentration of transported
sediment is above or below the channel’s transport capacity, respectively (e.g., eqn 14; Neitsch, et al.
2011), or in a roughly equivalent specification, the critical daily flow volume for erosion (Tian, et al.
2002):
{Psus=Cpat h sed∗(C se dmax
−C sed )∗cse∗c veg∗Sch
for C sed<C sed max
Pdep=(C sed−C se dmax )∗Sch
for C sed>C sed max
(14 )
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where Psus is the number of pathogens suspended; C sed max is the capacity of the channel reach to transport
sediment (which may be determined as a function of peak flow velocity, average flow velocity, depth of
flow, channel slope, or shear stresses); C pat hsed is the concentration of pathogens in bed sediments; C sed is
the concentration of sediment currently transported by the channel; cse is a coefficient representing the
erodibility of the bed material; cveg is a coefficient representing the effect of vegetation on bed erodibility;
Sch is the storage (volume) of water in the channel; and Pdep is the number of pathogens deposited.
Some investigators have reported evidence that sloughing of biofilms during high flows may contribute to
enhanced mobilization of pathogens from bed sediments (Yakirevich, et al. 2013, Droppo, et al. 2007,
Droppo, et al. 2009). To date, this mechanism has yet to be incorporated into a fate and transport model,
though a piecewise function has been proposed (eqn 15; Yakirevich, et al. 2013):
Psus (t> tcr )=Rr sedC pat hsed
+ K e ρ sed Cpat hsedH ( t−tcr ) (15 )
where Rr sed is the rate of resuspension of sediment prior to sloughing of biofilms; C pat hsedis the
concentration of bacteria in bed sediments; K e is the mass transfer rate due to enhanced erosive exchange;
ρ sedis the density of bed sediments; H (t ) is the Heaviside step function; and t cr is the time at which
critical bed shear stress for suspension is exceeded (Yakirevich, et al. 2013). Table 5 summarizes
hydrodynamic model approaches for calculating net pathogen mobilization from bed sediments.
Table 5: Hydrodynamic model approaches to net pathogen mobilization from bed sediments
Hydrodynamic model General approach Suspension determinants
Settling determinants
Shear stress / capacity
formulation
References
DIVASTPiecewise functions
of shear stressesτ b , τ cr
ω ,C sed , τb , τ c ❑d
τ b=¿
ρg ( v x+v y )C2
(Falconer, et al. 2001,
Gao, et al. 2011)
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512
HSPFMutually exclusive piecewise functions
of shear stressescse , τb , τc ω ,C sed , τb , τc τ b=s0 ρR
(Bicknell, et al. 1996)
WATFLOOD/ WU
Power law for suspension, deposition
dependent only on settling velocity
Q ω NA (Wu, et al. 2009)
SWAT
(OPTION 1)
Mutually exclusive piecewise functions of sediment carrying
capacity
C sed max, C sed , cse ,cveg
C sed max,C sed C sed max
=α∗v pkβ (Neitsch,
et al. 2011)
SWAT
(OPTIONS 2-5)
Piecewise function of sediment carrying capacity, calculated from various stream power formulations,
with constant deposition. Erosion
is calculated separately for banks
and bed.
cse , τb , τ c , ρb ,C sed max
, C sedω ,t res , h
τ b=ρh s0( W2W b
+0.5)(Neitsch, et al. 2011)
Yakirevich et al.Piecewise functions
of shear stressesτ b, τ cr s
ω ,τb , τ cr d τ b=ρ cd v2(Yakirevich, et al.
2013)
QUAL2KNo suspension,
simple deposition NA ω, h NA(Chapra,
et al. 2012)
WAMVIEW
Mutually exclusive piecewise functions
of daily flow volume
V c h24,V c h24cr
V c h24,V c h24cr
NA (Tian, et al. 2002)
EFDCPiecewise functions
of shear stresses
Mode 1: Gradual Erosion
ρb , τb , τc ❑r
Mode 2: Mass Erosion
ρb , τb , mme ,∆ t
ω ,C sed , τb , τcd τ b=
Av
h∗dv
dz
(Bai and Lung 2005, Tetra
Tech Inc. 2002)
SLIMNo suspension,
simple deposition NA C path, ω, h NA
(de Brye, et al.
2010, de Brauwere
, et al. 2011)
MOBED
Non-exclusive piecewise functions for suspension and
deposition, dependent on shear
stresses
τ b , τ c τ b , τ c τ b=ρgR sf
(Droppo, et al. 2011,
Krishnappan
1981)
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4.5 Transport via mechanical dispersion during floods
Section 4.5 nomenclatureD Dispersion coefficient
(m2 ∙ time-1)h Depth of flow
(m)v¿
Shear velocity - √ τb
ρ(m ∙ time-1)
v Flow velocity(m ∙ time-1)
W Channel width(m)
g Acceleration due to gravity(m ∙ time-2)
cd Dispersivity or diffusion constant(m2 ∙ time-1)
n Manning roughness coefficient(time ∙ m-1/3)
v Mean flow velocity(m ∙ time-1)
Variations in the velocity profile along horizontal and vertical axes of flow, such as those that develop
between channels and inundated areas during flooding, result in mechanical dispersion, in which uneven
flow velocities mix and distribute transported constituents along the flow’s longitudinal and/or transverse
axes (Fischer, et al. 1979). The effect of mechanical dispersion is calculated within the advection-
diffusion equation (eqn 8) through the parameter D. In 1D formulations, D represents longitudinal
dispersion along the axis of flow while, in 2D formulations, separate variables account for longitudinal
dispersion and transverse dispersion. The values of the dispersion coefficients are affected by a large
number of flow and channel geometry parameters and several investigators have proposed empirical
formulae to relate dispersion to other quantities. These quantities typically include various combinations
of flow and shear velocities, channel width, and water depth, e.g., as in models proposed by Elder (1959)
(eqn 16), Fischer (1975) (eqn 17), and Kashefipour and Falconer (2002) (eqn 18):
D=5.93 h v¿
(16 )
D=0.011 v2W 2
hv¿(17 )
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D=(7.428+1.775( Wh )
0.620
( v¿
v )0.572)hv ( v
v¿ ) (18 )
where W is channel width; v is flow velocity along the primary axis of flow;v¿ is shear velocity; and h is flow depth. The model proposed by Elder (1959) follows from assumptions of a logarithmic velocity profile across the depth of an infinitely wide open channel.
However, in actual channels, the effect of the lateral shear velocity profile between the two banks can
increase D by up to three orders of magnitude (Fischer, et al. 1979). Thus, the models developed by
Fischer (1975) and Kashefipour and Falconer (2002) incorporate channel width to account for the effects
of friction along the banks. Following the publication of Kashefipour and Falconer’s model (2002), which
was derived empirically, another group of authors (Toprak, et al. 2004) raised questions about the validity
of some of the methods underlying the model. Nonetheless, eqn 18 has been found to outperform other
simple formulations for longitudinal dispersion, though neural network models have been used to arrive at
even more accurate predictions (Toprak and Cigizoglu 2008). In more complex 2D and 3D models,
dispersion may be more accurately accounted for by explicit representation of secondary currents and
turbulence propagation (Wallis and Manson 2005). The approaches of existing microbial fate and
transport models for characterizing dispersion are summarized in Table 6.
Table 6: Hydrodynamic model approaches to estimating dispersion in channels and floodplains
Hydrodynamic model Approach to pathogen dispersion References
DIVAST
Calculated from flow velocity in 2 dimensions, total water depth, and Chezy roughness coefficient:
D xx=√g h (5.93 vx
2+0.23 v y2 )
C √vx2+v y
2
D xy=D yx=√ g h (5.93−0.23 ) vx v y
C √v x2+v y
2
D yy=√g h (5.93 v y
2 +0.23 vx2 )
C √vx2+v y
2
(Falconer, et al. 2001)
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529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
Yakirevich et al.Calculated from flow velocity:
D=cd v (Yakirevich, et al. 2013)
QUAL2K
Calculated from water depth, channel slope, channel width, and flow velocity using Fischer’s model:
D=0.011∗v2W 2
h v¿
(Chapra, et al. 2012)
FASTER
Calculated from water depth, channel width, flow velocity, and shear velocity using Kashefipour and Falconer model:
D=(7.428+1.775( Wh )
0.62
( v¿
v )0.572)hv ( v
v¿ )(Falconer and Kashefipour
2001)
EFDC Explicit turbulence modeling (Bai and Lung 2005, Tetra Tech Inc. 2002)
TELEMAC Explicit turbulence modeling (Desombre 2013)
QUAL2E-GIBSI
Calculated from roughness, mean flow velocity, and depth of flow. Estimated with Elder Model with customizable dispersion
constant:
D=3.82∗cd∗n∗v∗h56
(Simon, et al. 2013, Brown and Barnwell 1987,
Rousseau, et al. 2000)
4.6 Pathogen persistence during floods
Subsection 4.6 nomenclatureC path Concentration of pathogens in the water
column(organisms ∙ L-1)
t Time(units range from seconds to days)
Kd Pathogen die-off rate constant(time-1)
Ra dsnetNet solar radiation (J ∙ cm-2 ∙ day-1)
R Reflectance due to suspended solids (%) Ra ds¿¿Total downward solar radiation(J ∙ cm-2 ∙ day-1)
C ss Concentration of suspended solids in the water column (mg ∙ L-1)
h Depth of flow (m)
34
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545
The persistence of pathogens in natural waters is influenced by a variety of factors including temperature,
salinity, pH, competition and predation from other microorganisms, available nutrients, and sunlight
(Hipsey, et al. 2008). During high flows, mobilization of organic matter and sediments, as well as changes
in the depth of the water column, may alter the balance of nutrients available to support populations of
bacterial pathogens, and influence light penetration and ultraviolet radiation in the water column. The net
mobilization of sediments during flood events is, as described in section 4.4, dependent on depth and flow
velocity. Elevated concentrations of mobilized sediments during artificial flood events have been found to
protect pathogens from ultraviolet radiation, resulting in extended persistence of fecal indicator bacteria
by up to 20 hours (Walters, et al. 2014). Mobilized sediments may thus have a substantial impact on
microbiological risks during flood events.
The impact of flood events on nutrients available to microorganisms within the water column varies
depending on the dominant flow paths under base flow and high water conditions, as well as the
distribution of nutrient sources within a catchment. Periods of high flow have been linked to increased in-
channel concentrations of dissolved organic carbon (DOC) in temperate and subtropical climates (Leff
and Meyer 1991, Royer and David 2005, Tesi, et al. 2013), though in some cases the nutritional quality of
DOC was found to decrease (Leff and Meyer 1991). High water was found to result in enhanced bacterial
growth within certain catchments in the Amazon, which is thought to be linked to the influx of
bioavailable nutrients from inundated floodplains (Benner, et al. 1995). Similarly, in many boreal
catchments, flood events linked to snowmelt have been found to increase bioavailable dissolved organic
nitrogen (Stepanauskas, et al. 2000). While increased nutrient availability tends to promote bacterial
persistence and growth, some researchers have observed that the activities of protozoan species grazing
on bacterial populations may also be enhanced under these conditions, though protozoan grazing shows
marked spatial heterogeneity in the environment (Kinner, et al. 1997, Kinner, et al. 1998, Kinner, et al.
2002). Viral persistence may also be influenced through the transport of organic matter, and enhanced by
35
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decreased binding to and inactivation on certain soils and sediments (Blanford, et al. 2005, Pieper, et al.
1997, Ryan, et al. 1999), or diminished through the production of antiviral compounds by microbial
communities flourishing in nutrient-rich conditions (Deng and Cliver 1995). Thus it is difficult to
generalize the effects of flood events on bioavailable nutrient concentrations, as well as the net effect of
increased nutrient availability on bacterial and viral persistence, though this is clearly an area that merits
further study.
Expressions for the inactivation of pathogens within fate and transport models typically take the form of
an exponential function assuming first order kinetic dependency of the rate of inactivation on pathogen
concentrations (eqn 19):
C path( t )=C path (0 )∗e−K d t (19 )
where C path ( t ) is the concentration of pathogens at time t , and K d is a rate constant describing the
geometric change in pathogen concentration over time. The rate constant Kd may be related to factors
impacting pathogen survival, such as temperature or salinity. Effects of suspended solids have rarely been
incorporated into pathogen inactivation functions within existing fate and transport models, while the
effects of nutrient concentrations are (somewhat understandably) completely absent (Table 7). Among the
reviewed models, Kazama et al. (2012) provide the sole model (eqns 20-22) that incorporates mitigating
effects of water depth and suspended solids on the UV-mediated inactivation of pathogens, based on
empirical relationships between reflectance (R) and suspended solid concentration (C ss ) presented by Oki
et al. (Oki, et al. 2001) and empirical exponential relationships between the die-off ratio (e−Kd ¿ and
average net solar radiation at various depths of flow taken from Gameson and Saxon (Gameson and
Saxon 1967). Presumably eqn. 22 was implemented in some continuous fashion within the model used by
Kazama et al., but its exact implementation is not clear from the text of their study.
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590
591
592
593
594
595
Ra dsnet=1−R
100∗Ra dsmax
(20 )
R=0.0809+0.0146∗C ss (21)
{if h=0.18 m ,e−Kd=117.64∗e−0.0033∗Rad snet
if h=1.00 m,e−Kd=217.33∗e−0.0029∗Rad snet
if h=2.00 m, e−Kd=204.9∗e−0.0021∗Ra dsnet
if h=3.00 m , e−Kd=113.59∗e−0.0010∗Ra d snet
if h=4.00 m ,e−Kd=129.97∗e−0.0007∗Ra ds net
(22)
Table 7: Model approaches to pathogen persistence
Model Inactivation model Rate modifiers Separate rates incorporated References
DIVAST First order decay NA NA (Gao, et al. 2011)
SOBEK/D-WATER QUALITY
First order decay Salinity, temperature, radiation NA (Deltares Systems
2013b)
HSPF First order decay Temperature, radiation (free-floating pathogens)
Free-floating, suspended sediment-associated, and bed sediment-associated
pathogens
(Bicknell, et al. 1996)
WATFLOOD/ DORNER/ WU First order decay NA Winter, spring/fall, summer
months(Wu, et al. 2009,
Dorner, et al. 2006)
SWAT First order decay Temperature
Persistent and less-persistent pathogens
Foliage, soil, soil solution, channel waters.
(Neitsch, et al. 2011)
KAZAMA ET AL. First order decay Solar radiation, water depth, suspended solids NA (Kazama, et al.
2012)
YAKIREVICH ET AL. First order decay NA Pathogens in water column
and bed sediments(Yakirevich, et al.
2013)
QUAL2KFirst order decay, Beer-Lambert law
decay
Temperature, radiation, water depth NA (Chapra, et al.
2012)
WAMVIEW First order decay NA NA (Tian, et al. 2002)
FASTER First order decay NACoastal waters, rivers, dry
weather, wet weather, daytime, nighttime
(Kashefipour and Falconer 2002)
EFDC First order decay Temperature, solar radiation, salinity, pH
Free-floating, suspended sediment-associated, bed
sediment-associated pathogens
(Bai and Lung 2005)
DUFLOW First order decay NA NA (Manache, et al. 2007)
37
596
TELEMAC First order decay NA NA (Bedri, et al. 2011)
SLIM First order decay Temperature NA (de Brauwere, et al. 2011)
HEMAT First order decay NA Daytime, nighttime (Schnauder, et al. 2007)
IHACRES/ FERGUSON First order decay NA
Cryptosporidium, Giardia, E. Coli
Soil, water
(Ferguson, et al. 2007)
KINEROS2/STWIR First order decay NA Applied manure, soil, soil
solution, runoff water (Guber, et al. 2012)
COLI
First order decay between defecation and mobilization in
runoff
Temperature NA (Walker, et al. 1990)
WAMVIEW/ TIAN ET AL. First order decay Temperature, radiation NA (Tian, et al. 2002)
WEPP First order decay NA NA(Yeghiazarian, et al. 2006, Bhattarai, et
al. 2011)
4.7 Conceptual approaches to pathogen transport in rainfall-runoff modeling systems
Subsection 4.7 nomenclatureE Soil loss / sediment yield
(Mg ∙ m-2 ∙ yr-1)crer USLE rainfall erosivity index
(MJ ∙ mm ∙ m-2 ∙ h-1 ∙ yr-1)cserd USLE soil erodibility index
(Mg ∙ m2 ∙ h ∙ m-2 ∙ MJ-1 ∙ mm-1)c LS USLE Length / slope factor
(unitless)ccrm USLE cropping / management factor
(unitless)ccp USLE conservation practice factor
(unitless)α General term for user-defined or
calibrated coefficientV r o24
24 hour runoff volume(L ∙ day-1)
Qmax Peak discharge during storm event(L ∙ time-1)
Als Land surface area contributing to sediment/pathogen transport(m2)
β General term for user defined or calibrated exponent
Pro Number of pathogens transported in runoff(organisms)
Prf Number of pathogens mobilized by raindrop impact(organisms)
Pof Number of pathogens mobilized by overland flow(organisms)
Rrf Rainfall rate (intensity)(mm ∙ time-1)
c gc Hartley model vegetative cover factor (unitless)
ccan Hartley model canopy factor(unitless)
c perd Hartley model pathogen erodibility factor(organisms ∙ J-1)
c ff Hartley model friction parameter(unitless)
ρ Density of water(g ∙ L-1)
sls Overland slope SEDdetrMass of sediment available for
38
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598
(unitless) transport due to detachment by rainfall(g)
SE Dof Mass of sediment detached and transported in overland flow(g)
cman HSPF supporting management practice factor(unitless)
Sls Water storage on land surface(L)
C sed maxMaximum concentration of sediment runoff can transport(g ∙ L-1)
SE D ro Total sediment mass transported in runoff(g)
cwsh HSPF pathogen washoff factor(mm-1)
While the majority of this review has been devoted to the implications of physical process representation
in hydrodynamic models for modeling pathogen transport during floods, most rainfall-runoff models
represent pathogen mobilization and transport in a conceptual or empirical fashion. In these models, fine-
scale physical processes underlying pathogen transport processes are represented implicitly, if at all.
Watershed-scale pathogen transport modelling is frequently challenging due to lack of site-specific data
on pathogen discharges, the complexity and diversity of pathogen characteristics, and uncertainties
inherent in the underlying environmental models, particularly those related to obtaining averaged, or
effective parameter values at the spatial scale of the model when available theory and measurements
describe these processes at small scale, or in artificially homogeneous settings . Obtaining accurate
estimates of pathogen transport in runoff under extreme rainfall and flooding conditions presents
additional challenges, as common empirical relationships and simplifying assumptions employed by
rainfall-runoff models may not hold.
Characteristics of rainfall and runoff, such as rainfall pattern, effective rainfall volume, and overland flow
velocity, have been identified as some of the most critical factors affecting transport of pathogens from
the land surface (Funari, et al. 2012, Bhavnani, et al. 2014, Jamieson, et al. 2004, Ferguson, et al. 2005,
Jung, et al. 2014, Tsihrintzis and Hamid 1997). However, the relationship of these factors with in-stream
pathogen concentrations across sites is complex. For instance, some investigators have reported dilution
of pathogen concentrations by extreme rainfall (e.g. (Bhavnani, et al. 2014)) while others have noted
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pathogen concentrations several orders of magnitude higher after storm events (Bhavnani, et al. 2014,
Page, et al. 2012). These disparate results likely have to do with pathogen sources and drainage
characteristics of the study area. Other factors used to predict pathogen loading during storms or flood
events include land-use factors, such as the presence of manure-fertilized areas and measures to manage
agricultural runoff, catchment topography, and soil and sediment characteristics (Jamieson, et al. 2004,
Ferguson, et al. 2007, Papanicolaou 2008).
Typically, models for pathogen transport from the land surface involve five components: 1) deposition of
pathogens on the land surface from point or non-point sources (e.g. domestic animals, faulty sanitation);
2) accumulation of pathogens in various reservoirs (e.g. soils, subsurface, foliage); 3) removal of
pathogens via die-off or irreversible infiltration into soils; 4) mobilization of pathogens from
environmental reservoirs by erosion, raindrop impacts, or flowing water; and 5) pathogen transport in
overland and subsurface flows rainwater or overland flow (Figure 1). Here, we restrict our discussion to
mobilization and transport in overland flows, as subsurface flows are rarely incorporated into rainfall-
runoff pathogen transport models, and transport in overland flow is expected to dominate during flood
events; we omit further discussion of environmental reservoirs, pathogen die-off, and influxes to the land
surface from pathogen sources, as these have been discussed in previous sections or are not particularly
relevant to flood conditions.
40
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620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
Figure 1- General components of rainfall-runoff pathogen transport modules.
In many rainfall-runoff modelling systems, pathogen mobilization and transport is conceptualized as
being analogous to or correlated with the mobilization and transport of sediments from the land surface
brought about by raindrop impacts or overland flow (Kouwen 2014, Ferguson, et al. 2003). Thus, many
expressions for pathogen transport in these models are derived from sediment delivery models such as the
Universal Soil Loss Equation (USLE; eqn 23):
E=crer∗c serd∗cLS∗ccrm∗ccp (23 )
where E is sediment yield / soil loss; crer is a rainfall erosivity index (an empirical expression for the
kinetic energy of rainfall as a function of its intensity (Elbasit, et al. 2011)); cserd is a soil erodibility
index; c LS is a composite factor describing the length and gradient of the hillslope; ccrm is a cropping
management factor; and ccp a supporting conservation practice factor (Merritt, et al. 2003, Aksoy and
Kavvas 2005, Renard, et al. 1991). The Revised Universal Soil Loss Equation (RUSLE), a descendant of
the USLE, features refinements to the estimation of the terms of the USLE that increase the level of
process representation and, therefore, the generalizability (Lane, et al. 1992). In contrast to the USLE and
RUSLE, the Modified Universal Soil Loss Equation (MUSLE) was developed for prediction of sediment
41
Influx of pathogens from point and non-point
sources
Accumulation of pathogens in
environmental reservoirs
Removal of pathogens e.g. from die-off,
infiltration
Transport of pathogens in overland flow
Mobilization of pathogens (raindrop or
runoff erosion)
637
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641
642
643
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645
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648
649
650
651
652
653
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656
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658
yield from individual storm events; MUSLE incorporates antecedent soil moisture and erosion by runoff
into its estimations (eqn 24) (Renard, et al. 1991, Williams, et al. 2008):
E=α (V r o24∗Qmax∗A ls)β∗cserd∗cLS∗ccrm∗ccp (24 )
where V r o24 is the daily flow volume; Qmax is the maximum rate of runoff/discharge; Als is the land
surface area from which sediments are being transported; and α and β are calibrated terms to adapt the
equation to local conditions.
Of the models reviewed here for pathogen transport in runoff, COLI and SWAT rely on the MUSLE for
simulation of sediment transport and associated microbiological transport (Neitsch, et al. 2011, Walker, et
al. 1990). The implementations of WATFLOOD by Dorner et al. (2006) and Wu et al. (2009) directly
calculate pathogen mobilization and transport by rainfall impact and overland flow using the Hartley
model, an event-oriented expression that models rainfall-driven erosion using concepts from the USLE
and employs a stream power function to estimate erosion by overland flow (Hartley 1987):
Pro=Prf +Pof (25 )
Prf=R rf∗(11.9+8.7∗log ( R rf ))∗(1−c gc )∗ccan∗c perd (26 )
Pof =
60c ff
∗ρ∗Q
2∗sls
(27 )
where Prois the total number of pathogens transported in runoff; Prf is the number of pathogens
mobilized by raindrop impact; Pof is the number of pathogens mobilized and transported by overland
flow; Rrf is the rate or intensity of rainfall; c gc is a factor accounting for the effect of vegetative ground
42
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662
663
664
665
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667
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669
670
671
672
673
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675
676
677
cover; ccan is a factor accounting for the effect of the canopy layer; c perd is a pathogen erodibility factor;
c ff is an empirical friction coefficient; ρ is the density of water; Q is the overland flow discharge; and sls
is the overland slope.
The treatment of sediment-associated pathogen mobilization in HSPF is based on a physically motivated
conceptual erosion model originating with the work of Negev (1967) and incorporating aspects of models
proposed by Meyer and Wischmeier (1969) and Onstad and Foster (1975) (eqns 28-32):
Pro=C pat h sedls
∗SE Dro=Cpat hse dls
∗( SE Dof +SE Drf ) (28 )
SE D of=αscour∗Qβ scour (29 )
{SE Drf =SE Dd etrfSE Dd etrf
<C se dmax
SE Drf =C sedmaxSE D detrf
≥ C sed max
(30 )
SE Dd et rf=(1−pc tcover )∗cman∗α sdet∗Rrf
β sdet (31 )
C sed max=α cap∗Qβcap (32 )
where C pat hsedls
is the concentration of pathogens in sediments on the land surface; SE D ro is the mass of
sediment transported in runoff; SE Dof is the mass of sediment eroded and transported by overland flow;
SE D rf is the mass of sediment mobilized by rainfall and transported in overland flow; α scour and βscour
are calibrated factors representing the contribution of scour by overland flow to sediment transport (α sdet,
43
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681
682
683
684
685
686
687
688
689
690
βsdet, α cap and βcap are analogous factors for sediment detachment by rainfall and transport capacity of
runoff, respectively); pc t cover represents the fraction of land protected from raindrop impacts by snow,
vegetative, or other cover; and cman is a factor representing land management practices.
Expressions for pathogen transport that do not invoke sediment mobilization are present in the
implementation of IHACRES by Ferguson et al. (2007), which specifies pathogen mobilization as a
function of excess rainfall, and the implementation of WAMVIEW by Tian et al. (2002), which expresses
the proportion of deposited pathogens transported to streams as a function of runoff volume, overland
flow distance, and calibrated coefficients. SWAT also permits simulation of pathogen transport without
consideration of sediment mobilization, using a simple function of runoff and a user-defined partitioning
coefficient (Neitsch, et al. 2011). Meanwhile, HSPF and the implementation of IHACRES by Ferguson et
al. express pathogen transport independent of sediments following assumptions of first-order kinetics
dictated by runoff and effective rainfall, respectively (eqn 33) (Ferguson, et al. 2007, Bicknell, et al.
1996):
dPdt
=−Q∗cwsh∗P ,∫0
∆t dPdt
=P∗(1−e−Q∗cwsh ) (33 )
where cwsh represents the susceptibility of the pathogen to washoff, and all other parameters are as
defined above.
Many physical processes are implicit in conceptual and empirical rainfall-runoff model parameters,
optimized values of these parameters often result in acceptable levels of agreement between modelled and
observed discharges or concentrations of indicator organisms. Thus, it is difficult to provide an
overarching assessment of the ability of such models to represent runoff conditions unique to flood
44
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692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
events. In practice, models that rely on calibration of extensive sets of parameters are generally flexible
enough to be adapted to various watersheds and meteorological conditions; however, the data
requirements to do so may be costly or prohibitive, as has been noted for implementations of HSPF and
SWAT (Borah and Bera 2003, Gassman, et al. 2014). Failure to adequately calibrate models such as the
MUSLE, SWAT and HSPF, which include a large number of crucial user-defined parameters, often
results in large errors and very poor predictions of flow and transport (Borah and Bera 2003, Sadeghi, et
al. 2014), especially during periods of high flow (Borah and Bera 2003). Even then, issues of parameter
non-identifiability may prevent such high-dimensional models from generating good predictions outside
of the calibration range, and from providing useful information on the hydrological processes underlying
an area’s response to rainfall (Beven 2006, Freni, et al. 2009). Transport models based off the MUSLE
have been found to perform best when parameterized with directly measured runoff and peak flow data,
raising doubts about the reliability of models which apply the MUSLE using internally calculated
estimates of runoff and streamflow, such as SWAT (Sadeghi, et al. 2014). Properties of models for
pathogen transport in runoff are summarized in Table 8.
Table 8: Rainfall–Runoff Transport Model Characteristics
ModelMethods for
calculating excess rainfall
Sediment transport Pathogen transport
Watershed applications References
COLI SCS curve number MUSLE Sediment-associated transport
Temperate watershed,1153 km2
(Walker, et al. 1990)
IHACRES/ FERGUSON
ET AL.
Empirical non-linear loss module NA
First order kinetic function of
effective rainfall
Temperate watershed,
~90000 km2
(Ferguson, et al. 2007)
WATFLOOD/ DORNER/ WU
Process-based, infiltration excess model Hartley model Sediment-
analogous transport
Temperate, rural
watersheds,130-187 km2
(Dorner, et al. 2006, Wu, et al. 2009)
SWAT
Process-based model, SCS curve number, infiltration excess
options
MUSLESediment-
associated or direct transport
Many applications (Neitsch, et al. 2011)
HSPF Process-based, infiltration excess model
Power laws for rainfall or runoff-
based erosion, limited by supply or transport capacity
Sediment-associated transport or first order kinetic function of runoff
Many applications (Bicknell, et al. 1996)
STWIR Process-based, infiltration excess model
Rainfall splash erosion according to
formula of Meyer
Advection-diffusion equation
Many applications
(Guber, et al. 2012, Meyer and
Wischmeier 1969,
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714
715
716
717
718
719
720
721
722
723
724
725
726
and Wischmeier
Several shear stress-dependent physically
based models for erosion by runoff
Goodrich, et al. 2010)
WAMVIEW/ TIAN
Options include modified SCS curve number, Saturation
excess model, or special cases algorithm with
user-defined parameters
Delivery ratio method incorporating landscape factors and
runoff
Delivery ratio method based on
runoff, distance to stream, and user-
defined coefficients
Temperate agricultural watersheds
0.49-0.95 km2
(Tian, et al. 2002, Soil & Water Engineering
Technology Inc.)
WEPP Process-based infiltration excess model
Shear-stress dependent
physically-based erosion from runoff
Advection equation with stochastic
partition between mobile and
immobile states
Developed for use on fields ~2.6-8.1 km2
(Yeghiazarian, et al. 2006, Bhattarai, et al. 2011, Flanagan and
Nearing 1995)
46
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5. Discussion
5.1 Gaps in pathogen fate and transport modeling practice relevant to flood conditions
Several phenomena relevant to pathogen fate and transport during floods have not been addressed in
current models. These include process descriptions of the mobilization of pathogens from sanitation
facilities in inundated areas, the role of elevated levels of dissolved organic matter in altering pathogen
transport and persistence, and the eventual depletion of pathogen sources that may occur during sustained
or consecutive flood events. Representation of these processes, especially the latter two, within integrated
models may entail greater model complexity than currently available data are capable of supporting.
Nonetheless, mathematical descriptions of these phenomena are a necessary prerequisite to their eventual
incorporation into model frameworks as deterministic processes or sources of uncertainty.
Mobilization of pathogens from inundated facilities, such as pit latrines, may be considered as either a
turbulent diffusion/resuspension process, in which flow over a deep compartment results in passive or
active movement of pathogens from the compartment into the overlying waters, or as the result of
structural damage to the facility caused by sufficiently deep and swift flow, resulting in a rapid release of
pathogens from within the facility. Controlled experiments to measure the release of indicator organisms
from replica latrines in artificial compound channels may provide a suitable baseline for efforts to model
these phenomena.
With respect to the effects of heightened concentrations of dissolved organic matter on pathogen fate and
transport, current knowledge indicates that a decrease in pathogen retention in soils and sediments is
likely, while persistence of bacterial and viral pathogens may be enhanced, or, through the action of
antagonistic microbial communities, diminished (Bradford, et al. 2013). Literature on bacterial die-off
indicates that high nutrient concentrations are associated with extended periods of maintenance or growth
prior to population decline. This maintenance period is not captured by first-order exponential decay
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736
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738
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742
743
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748
749
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equations used in most transport models, although a piecewise model has been proposed to incorporate it
(eqn 31; Darakas 2002):
C path (t )={ C path(0) for t ≤ t d
C path (0 )∗e−Kd∗(t−td ) for t >t d
(31 )
where C path ( t ) is the concentration of organisms at time t ; t d is the duration of the maintenance phase
prior to die-off; Kd is the die-off rate constant. Dissolved Organic Carbon has been suggested as a
suitable indicator for dissolved nutrients (Hipsey, et al. 2008). Where DOC data and, ideally, estimates of
total microbial metabolism (e.g. the biological oxygen demand (BOD)), are available, it may be possible
to represent the maintenance phase as a function of these quantities. Pathogen die-off experiments in
which DOC and BOD are measured and evaluated as determinants of the length of the maintenance phase
will be a prerequisite for its incorporation into fate and transport models.
When flooding or extreme precipitation is sufficiently severe, or occurs frequently, the amount of
pathogens available for transport from the land surface may eventually be exhausted (Muirhead, et al.
2004, Nagels, et al. 2002). While only a few models, such as SWAT (Neitsch, et al. 2011), HSPF
(Bicknell, et al. 1996), and the Dorner et al. model (2006), have incorporated simulation of supply-limited
pathogen transport to date, it is conceptually simple to incorporate rates of pathogen shedding and
persistence in relevant environmental compartments into any rainfall-runoff or land-surface model,
although a major data gathering effort would be necessary to support any such implementation, and
considerable uncertainty regarding appropriate parameter values and their variability would almost
certainly remain. This approach would provide a basis to estimate the total population of pathogens
available for transport from a compartment at any time step. The depletion of pathogens available for
transport from each compartment in response to consecutive flooding events would allow models to
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represent the flushing of fecal contamination by heavy runoff and high flows, which has been advanced as
an important mechanism modulating the effects of precipitation on disease transmission (Carlton, et al.
2014).
Finally, it is worth mentioning that pathogens, which have largely been discussed as an abstract,
monolithic group of suspended constituents in this review, differ with regards to size, density, resilience
to various environmental challenges, and particle affinity. The vast majority of microbial transport
modeling has been conducted using fecal indicator bacteria, which are unlikely to behave similarly to
protozoans and viruses (Ashbolt, et al. 2001). Even within a pathogen class, such as bacteria, there is
considerable heterogeneity with respect to the above mentioned characteristics (Jenkins, et al. 2011,
Schillinger and Gannon 1985). As more robust microbiological fate and transport models emerge, they
should be parameterized and validated using pathogen-specific data, starting with indicator organisms
known to be well-correlated with transport characteristics of important viral, bacterial, and protozoan
pathogens (Ferguson, et al. 2003, Ashbolt, et al. 2001).
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5.2 Where and when should models incorporate increased process complexity?
Models discussed in this review span a range of complexity in process representation, from the almost
entirely empirical, such as IHACRES, to spatially distributed, physically based models, such as
TELEMAC 2D. While increasing model complexity allows for a more comprehensive description of
hydrological and transport processes, it must be acknowledged that the extra parameters entailed by
complex process representation and fine spatial discretization will often result in parameter non-
identifiability and model equifinality, stymying the initial intent of a more detailed process representation,
as there is no guarantee that the ‘optimal’ parameter values of a calibrated model truly represent the
processes driving hydrology and pathogen transport (Beven 2006). This situation is further exacerbated
by issues of data quantity and quality, especially in the developing world, where vulnerability to flood-
related diseases is greatest. Thus, model parsimony is as much a concern as detailed process
representation, and detailed analysis of structural and statistical uncertainties is critical in model
applications.
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The relative effects of parameters and process representations in fate and transport modeling are not well
understood, and are likely to be specific to the pathogen of interest, geographical location, flood event
magnitude, and perhaps even the flow domain (e.g. different relative effects for the channel and the
floodplain) (Sommerfreund, et al. 2010). Some model capabilities, such as mass-and-momentum
conservative exchanges of flow between channels and floodplains, adequate accounting for pathogen
sources in upstream watersheds, and some capacity to represent dispersion and/or retention and release of
transported pathogens, seem likely to improve estimates of pathogen transport associated with floods,
assuming adequate data on channel and floodplain bathymetry/topography and influxes to the flow
domain are available. However, the degree to which more or less detailed process representations of
pathogen suspension, retention, sedimentation, dispersion within flows, and changes in pathogen
persistence due to the effects of suspended solids and dissolved organic matter will affect model skill in
estimating pathogen transport is likely to vary by model application. In order to arrive at parsimonious
model parameterizations, sensitivity analysis techniques can be used to selectively remove parameters
with little impact on model outputs from calibration or randomization processes, or to reduce the
dimensionality of models through principle components analysis and similar techniques (see e.g. Freni et
al. (2009), Sommerfreund et al. (2010)). Alternative model structures and overall uncertainty can be
assessed within Bayesian frameworks, such as the General Likelihood Uncertainty Estimation (GLUE)
method of Beven et al. (Beven 2007, Beven and Binley 1992). To characterize the range of conditions or
research goals for which simplified process representations will be sufficient or preferable, comparative
studies are needed which examine model behaviors over a wide range of rainfall regimes, topography,
soil and land use characteristics, and pathogen source scenarios. While there is still much to be learned
about generalized hydrodynamics and transport during floods, such studies would also ideally utilize time
series of observed indicator organism concentrations as benchmarks for model performance.
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5.3 Summary of properties of reviewed fate and transport models relevant to flood conditions
Existing microbial fate and transport models vary widely in their approaches to simulating the
hydrodynamic flows which drive pathogen transport, with potential consequences for their validity under
flood conditions. Hydrodynamic transport models cover a spectrum of physical complexity, from 1D
steady/uniform flow models (HSPF, WATFLOOD, SWAT, QUAL2K, WAMVIEW, QUAL2E), to 1D
models using the dynamic wave equation (or close approximations of it) to characterize unsteady, non-
uniform flow (SOBEK, Kazama et. al (2012)), to 2D or higher models (HEMAT, TELEMAC, DIVAST,
EFDC) capable of representing secondary flows within channels and inundated areas. SOBEK,
WATFLOOD, SWAT, the Kazama model, and DUFLOW have the capacity to model mass-conservative
exchanges of flow (and therefore pathogens) between channels and floodplains. However, of the reviewed
models, only TELEMAC and HEMAT attempt conservation of momentum in channel-floodplain
exchanges. SWAT and WATFLOOD make simplifying assumptions regarding floodplain topography
which limits their realism in modeling overbank flows.
The parameterization of source, sink, and dispersion terms included in hydrodynamic transport equations
(e.g., eqn 9) also varies widely across existing microbial transport models. Pathogen mobilization from
bed sediments is not accounted for in SOBEK, QUAL2K, FASTER, DUFLOW, TELEMAC 2D, SLIM,
QUAL2E, or HEMAT. Simple models for the mobilization of sediment-associated pathogens are present
in the implementations of WATFLOOD by Dorner et al. (2006) and Wu et al. (2009), while
erosion/deposition models based on concepts of sediment transport capacity are used in WAMVIEW, and
in SWAT’s default configuration. Sediment erosion and deposition is modeled with a higher degree of
physical process representation, based on shear stresses in the model of Yakirevich et al. (2013), as well
as in DIVAST, HSPF, SWAT’s optional configurations, EFDC, and MOBED. Removal of pathogens
from the water column by sedimentation is not accounted for in SOBEK, the Kazama model, FASTER,
DUFLOW, TELEMAC, QUAL2E, or HEMAT. Sedimentation is modeled based on constant pathogen
settling velocity in WATFLOOD, QUAL2K, and SLIM. Variable dispersion parameters are neglected in
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SOBEK, HSPF, WATFLOOD, WAMVIEW, DUFLOW, and MOBED. Simpler formulations relating
dispersion to flow parameters are present in the Yakirevich et al. (2013) model, SLIM, and QUAL2E,
while more complex empirical models are applied in DIVAST, QUAL2K, FASTER, and full turbulence
modeling is available in TELEMAC and EFDC. Regarding the mechanisms through which flood
conditions are likely to affect microbial persistence, only the Kazama model includes parameters to model
the effect of suspended solids on pathogen survival.
The validity of models for the transport of pathogens in runoff under flood conditions is difficult to assess
from a theoretical standpoint. Many rainfall-runoff models, including the implementation of IHACRES
by Ferguson et al. (2007), WATFLOOD by Dorner et al. (2006) and Wu et al. (2009), COLI, GIBSI,
SWAT, HSPF, and WAMVIEW, rely on empirical or conceptual functions to relate pathogen loading of
receiving streams to total runoff or effective rainfall. As a result, the accuracy of estimates for pathogen
transport in runoff will depend on the spatial and temporal resolutions at which these models are run, and
the selection of appropriate parameters for the regional and meteorological conditions for which they are
implemented. Spatially distributed rainfall-runoff transport models, such as WEPP and STWIR, explicitly
account for transient exchanges of pathogens between overland flow, the land surface, and the subsurface
via calibrated rate parameters incorporated into hydrodynamic equations. However, these equations are
designed for implementation in relatively small areas and require extensive collection of data on
catchment characteristics in order to produce accurate results. Properties of the reviewed models are
briefly summarized in Table 9.
Table 9: Summary of capabilities of reviewed models
ModelLand surface simulation
Streamflow simulation
Floodplain simulation
Channel-floodplain exchange
DownstreamPathogen routing
Pathogen settling and resuspension
Pathogen dispersion
Persistencefactors
HSPF Semi-distributed
1D storage routing NA NA Mixing cell
Simplified shear stress formulation
NA
Temperature and radiation, particle association, deposition
WATFLOOD/ DORNER/ WU
Semi-distributed
1D storage routing
1D storage routing (simplified geometry)
Mass conserved
Mixing cell Power law suspension based on discharge,
NA Season
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constant deposition at particle settling velocity
IHACRES/ FERGUSON Lumped NA NA NA NA NA NA Pathogen type
SWAT Semi-distributed
1D storage or Muskingum routing
1D storage or Muskingum routing (simplified geometry)
Mass conserved NA
Sediment carrying capacity formulation, various degress of physical rigor available
NA
Temperature, pathogen type, environmental compartment
KINEROS2 /STWIR
Fully distributed hydrodynamic
1D kinematic wave
1D kinematic wave
Mass conserved
Advection-diffusion equation
NA
Time-invariant calibrated parameter
Deposition, environmental compartment
COLI Lumped NA NA NA NA NA NA Temperature
WAMVIEWFully distributed conceptual
1D storage routing NA NA Mixing cell
Simple function of daily flow volume
NA Temperature, radiation
WEPP
Fully distributed hydrodynamic
NA NA NA NA NA NA None
DIVAST NA2D dynamic wave
2D dynamic wave
Mass and momentum conserved
Advection-diffusion equation
Shear stress formulation
Calculated from depth, flow velocities, and roughness coefficient
None
SOBEK/D-WATER QUALITY
NA1D dynamic wave
2D dynamic wave
Mass conserved
Advection-diffusion equation
NA NASalinity, temperature, radiation
KAZAMA ET AL. NA
1D dynamic wave
2D dynamic wave without convective acceleration
Mass conserved
Advection equation NA NA
Radiation, water depth, suspended solids
Yakirevich et al. NA
1D dynamic wave
NA NAAdvection-diffusion equation
Shear stress formulation
Calculated from flow velocity
Deposition
QUAL2K NA 1D storage routing NA NA Mixing cell
No suspension, deposition dependent on depth and particle settling velocity
Calculated from water depth, channel slope, channel width, and flow velocity
Temperature, radiation, water depth
FASTER NA 1D dynamic NA NA Advection-
diffusion NA Calculated from
Day and night, coastal or fresh
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wave equation
water depth, channel width, flow velocity, shear velocity
waters, dry or wet weather
EFDC NA1, 2, or 3D dynamic wave
NA NAAdvection-diffusion equation
Shear stress formulation
Explicit turbulence modeling
Temperature, radiation, salinity, pH, particle association, deposition
DUFLOW NA1D dynamic wave
1D dynamic wave
Mass conserved
Advection-diffusion equation
NA NA None
TELEMAC NA2 or 3D dynamic wave
2 or 3D dynamic wave
Mass and momentum conserved
Advection-diffusion equation
NA
Explicit turbulence modeling
None
SLIM NA1D dynamic wave
NA NAAdvection-diffusion equation
No suspension, deposition dependent on depth, particle settling velocity, and pathogen concentration
NA Temperature
MOBED NA1D dynamic wave
NA NA Mixing cellSimplified shear stress formulation
NA NA
QUAL2E-GIBSI
Semi-distributed
1D storage routing NA NA
Advection-diffusion equation
NA
Calculated from roughness, mean flow velocity and depth of flow
NA
HEMAT NA2D dynamic wave
2D dynamic wave
Mass and momentum conserved
Advection-diffusion equation
NA NA Day and night
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5.4 Improving data availability and integrating modeling and field efforts for vulnerable regions
Parameterizing pathogen fate and transport models, especially those with more complex representation of
transport processes, requires extensive environmental data (Aksoy and Kavvas 2005). Unfortunately,
many areas at heightened risk of flood-related infectious disease transmission are resource poor, and
unlikely to have extensive high-quality environmental datasets, and in situ collection of data during flood
events may be impossible. As a result, researchers may seek to produce adequate models for vulnerable
areas without extensive in situ data on soils, channel morphology, and/or streamflow records, not to
mention the regular measurements of pathogen or sediment concentrations needed to calibrate fate and
transport models (Coffey, et al. 2010). Remotely sensed Synthetic Aperture Radar (SAR) and LIDAR
images of flood extent and topographical features have proven useful for parameterizing and validating a
number of flood inundation models at high spatial resolutions (Bates 2004, Horritt and Bates 2002, Bates,
et al. 2003, Straatsma and Baptist 2007, Smith 1997, Patro, et al. 2009, Bates, et al. 1997). However, the
use of such image-based techniques to describe the dynamics of inundation over the duration of a flood
event, and thus establish credible estimates of flow velocities and other transport-relevant parameters,
requires high resolution imagery, both spatially and temporally (Bates 2012, Di Baldassarre and
Uhlenbrook 2012). In addition to inundation extent, it may also be possible to identify proxies for
pathogen concentrations and transport that can be measured remotely, such as turbidity (Bradford and
Schijven 2002, Schijven, et al. 2004). Researchers have also proposed methods for imputing channel
geometry and bathymetry, crucial parameters for hydrodynamic models that are often difficult to obtain in
developing countries (Wood, et al. 2016). Given pervasive limitations on obtaining in situ data, especially
in developing country settings, further advances are needed in methods for integrating remote sensing
data and models to impute missing environmental data. These activities should be accompanied by firm
advocacy for the expansion of reliable ground-based environmental monitoring stations in vulnerable
global settings.
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Data collected by environmental field studies can be an important source of information for those
developing models of flood-related infection risks, particularly in areas where standardized, routine
monitoring is limited or absent. There is often poor linkage, however, between parameter and validation
data needed by modelers and the data typically collected in environmental field studies. To a certain
extent, a disconnect is unavoidable, since many model parameters and outputs are ‘effective’ parameters
representing some averaging of characteristics over a spatiotemporal discretization, whereas field
measurements are generally taken as point measurements (Beven 2010b). Other issues arise because the
design and corresponding data collection protocols for field studies are motivated by highly specific
research questions, and the intensity and scope of data collection are often limited by sparse sampling
equipment and constrained study logistics. Yet both field-based researchers and the modeling community
stand to benefit from greater coordination of field studies with modeling efforts. Focusing in situ data
collection on key parameters that underlie hydrological and microbial transport models would be of great
benefit for advancing model capabilities, while also providing information useful for the design of future
field experiments. Moreover, strengthening collaborations between modelers and field researchers can
further the development of models capable of providing mechanistic validation of associations discovered
in the field, and can thus increase the interplay between theory, observation and experimentation.
5.5 Perspective for risk-based engineering design
The application of hydrological and hydrodynamic pathogen fate and transport models to risk assessment
may be viewed as an example of a decision-making processes involving engineering design. In this sense,
fate and transport estimation is analogous to the design of hydraulic structures such as flood defenses and
drainage systems, in that the frequency and severity of future events is inherently uncertain. Design flood
events used in hydraulic engineering are derived either from direct statistical analysis of long-term
records (typically in excess of 20 years) or by considering the joint probability of several factors involved
in flood generation such as rainfall and antecedent soil moisture conditions coupled with a deterministic
watershed model (Svensson, et al. 2013). As long-term observations of pathogens are rare and unlikely to
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be available for most practical applications, particularly in developing countries, it seems that the best
way forward for providing risk-based estimates of pathogen concentrations is to include the deterministic
and random components known to control pathogen concentrations into the joint probability approach.
However, as discussed in Section 4.7, there is still insufficient scientific evidence available to reliably
link, for example, pathogen mobilization to rainfall intensity and watershed characteristics.
Consequently, a quantitative tool for providing risk-based estimates of pathogen concentrations must still
be considered a future ambition.
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6. Conclusion
Given the computational expense, often severe mismatches between data requirements and data
availability, and at least partially irreducible uncertainties associated with microbial fate and transport
modeling in the context of flood events, one might well ask what is to be gained in the endeavor. It is
clear that, once implemented, flood and microbial fate and transport models should not be taken as
deterministic predictions of risk, especially in the contexts of rare and extreme events and hydrological
non-stationarity due to climate change. Despite the aforementioned difficulties, fate and transport models,
as platforms for knowledge integration and synthesis, have the potential to provide much-needed
information to guide research and risk mitigation efforts. In this context, flood and microbial transport
modeling should be viewed as an iterative project, where initial applications may help distinguish
between processes to which model outputs are more or less sensitive in various contexts, as well as
geographical areas estimated to be at high or low risk regardless of model specification, and others for
which uncertain or poor predictions may motivate directed data collection or modifications to existing
theory or model structures (Sommerfreund, et al. 2010).
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Initially, advancing models of microbial risks associated with flood events will require addressing several
areas of incomplete knowledge. New modeling techniques should be developed and validated for
processes that have not previously received attention in the hydrological modeling literature, including
the mobilization of pathogens from flooded sanitation facilities. In order to reduce sizable uncertainties
due to existing data limitations, especially for developing countries, it will be necessary to support and
incorporate multiple sources of information, including continuing to pair and enhance existing models
with more reliable and comprehensive field measurements, as well as new and more extensive remotely
sensed data, and innovative measurement techniques, especially for measuring the properties of overbank
flows. Finally, incorporation of probabilistic model structures (e.g. hierarchical models to specify
distributed roughness coefficients from a common distribution (Rode, et al. 2010)), parameter
identifiability analysis, and ensemble modeling techniques, such as GLUE, will be critical, allowing
researchers to incorporate and refine prior knowledge, distinguish irreducible and reducible uncertainties
in transport parameters, and test various models as alternative hypotheses.
7. Acknowledgements
This work was supported in part by the Chemical, Bioengineering, Environmental, and Transport Systems
Division of the National Science Foundation under grant no. 1249250, by the Division of Earth Sciences
of the National Science Foundation under grant nos. 1360330 and 1646708, by the National Institute for
Allergy and Infectious Disease (K01AI091864) and by the National Institutes of Health/National Science
Foundation Ecology of Infectious Disease program funded by the Fogarty International Center (grant
R01TW010286). Financial support for OC’s contributions to this publication come from the UK
Engineering and Physical Sciences Research Council’s (EPSRC) Water Informatics Science &
Engineering (WISE) Centre for Doctoral Training program (Grant Reference EP/L016214/1) and the
University of Bath International Mobility fund.
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The authors would like to thank Wen Yang, Jedidiah Snyder, Marc Stieglitz, and Kevin Zhu for their
input on early drafts of this manuscript.
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