Compound Flooding in a Non-Stationary World: A Primer for Practice

Abstract

Compound flooding conditions present a significant challenge for civil engineers in their pursuit to design for and maintain the integrity of a structure’s entire life cycle. Coupled with non-stationary processes due to a changing climate and land use change, risk is a moving target. Through the support of ASCE’s Task Committee on Compound Flooding, the Hydroclimatology Engineering Adaptation (HYDEA) sub-committee is developing a Manual of Practice (MOP) to provide a synthesis of available tools and methods of best practice for civil engineers designing for compound flooding conditions. This paper presents a primer for practicing civil engineers on this work. Hydrodynamic process-based models such as rainfall-runoff, riverine and coastal modeling as well as statistical models including multivariate statistical models will be addressed. In addition, the importance of linking statistical and process-based models and their various approaches is identified. The MOP also discusses addressing nonstationarity due to changing local and regional conditions and tools to assess risk and uncertainty.

Full text

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Compound Flooding in a Non-Stationary World: A primer for practice
Gerarda M. Shields PhD, PE, F.ASCE,1 J. Rolf Olsen, PhD2, Miguel Medina, Jr., PhD,
F.ASCE,3 and Jayantha Obeysekera, PhD, PE4, Poulomi Ganguli, PhD,5 Carlo DeMichele6,
Gianfausto Salvadori7, Mohammad Reza Najafi8, Hamed Moftakhari, PhD, PE,9,
Ferdinand Diermanse10, and Amir AghaKouchak, PhD, PE11
1 New York City College of Technology, The City University of New York, 300 Jay Street,
V806, Brooklyn, NY 11201; e-mail: gshields@citytech.cuny.edu
2 Charlottesville, VA 22911, email: j.rolf.olsen@gmail.com
3 Professor Emeritus of Civil and Environmental Engineering, Duke University, Durham, NC
27708, email: Miguel.medina@duke.edu
4 Florida International University, 11200 SW 8th Street, OE 148, Miami, FL 33199; e-mail:
jobeysek@fiu.edu
5 Indian Institute of Technology Kharagpur, Agricultural & Food Engineering Department,
Kharagpur - 721302, West Bengal, India, email: pganguli@agfe.iitkgp.ac.in
6 Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, Italy
emil: carlo.demichele@polimi.it
7Department of Mathematics and Physics "E. De Giorgi", Università del Salento, Lecce, Italy
email: carlo.demichele@polimi.it
8Department of Civil and Environmental Engineering, Western University, Claudette MacKay-
Lassonde Pavilion, Room 1301, London, ON N6A 5B9; email: mnajafi7@uwo.ca
9University of Alabama, 248 Kirkbride Ln, Tuscaloosa, AL 35401; e-mail:
hmoftakhari@eng.ua.edu
10 Deltares, Department of Flood Risk Management, PO Box 177, 2600MH Delft, The
Netherlands; email:ferdinand.diermanse@deltares.nl
11University of California - Irvine, Irvine, CA 92697; email: amir.a@uci.edu
ABSTRACT
Compound flooding conditions present a significant challenge for civil engineers in their pursuit
to design for and maintain the integrity of a structure’s entire life cycle. Coupled with non-
stationary processes due to a changing climate and land use change, risk is a moving
target. Through the support of ASCE’s Task Committee on Compound Flooding, the
Hydroclimatology Engineering Adaptation (HYDEA) sub-committee is developing a Manual of
Practice (MOP) to provide a synthesis of available tools and methods of best practice for civil
engineers designing for compound flooding conditions. This paper presents a primer for
practicing civil engineers on this work. Hydrodynamic process-based models such as rainfall-
runoff, riverine and coastal modeling as well as statistical models including multivariate
statistical models will be addressed. In addition, the importance of linking statistical and

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process-based models and their various approaches is identified. The MOP also discusses
addressing nonstationarity due to changing local and regional conditions and tools to assess risk
and uncertainty.
INTRODUCTION
Compound floods are combinations of multiple drivers and hazards from meteorological,
hydrological, and oceanographic factors contributing to substantial societal or environmental risk
(Zscheischler et al. 2018). The drivers involving compound floods may not be extreme
individually; however, their compound impact may cause significant damage to society. The
primary elements of compound floods are severity of their impact, the interplay of multiple drivers,
and the role of statistical interdependence of underlying drivers. The term compound flooding
qualifies those flood events that result from interacting flood drivers within a concise time window
that spans from hours and often extends to a day or a week due to the effect of the same large-scale
event (Ganguli and Merz 2019); for example, tropical cyclone-induced heavy rainfall and storm
surges at coasts. On the other hand, cascade hazards develop due to the direct or indirect
consequence of a pre-conditioned driver, such as convective rainfall and its sequential impact, e.g.,
flash floods and landslides, endangering natural and built environment systems (Merz et al. 2020).
In both definitions, the time lag is crucial in controlling the overall compounding impact as these
consecutive and co-occurring hazards within a short period are considered part of the same event.
Furthermore, the time window is short enough to respond to such aggregated effects.
Compound flooding in delta areas, e.g., the simultaneous or sequential occurrence of high
coastal water levels and peak river discharge, are of particular challenge for disaster management
and require updating existing flood control structures (Wright et al. 2019; DHS 2022). A few
distinct mechanisms cause such events are as follows: (1) high coastal water levels may affect river
discharge by backwater effects or by reversing the seaward flow of rivers, particularly for low-
lying areas with elevation less than 10 m (Hoitink and Jay 2016). (2) A storm surge can block or
slow the precipitation drainage into the sea, causing flooding along the coasts (Bevacqua et al.
2017). (3) the compound occurrence of high coastal water levels and river flood may stem from a
common large-scale meteorological driver – a severe storm episode may be associated with high
winds triggered by tropical or extratropical cyclones leading to storm surges at the coast, together
with high precipitation followed by inland flooding. Geospatial locations, topographical settings
and the shape of coastlines further affect the frequency and intensity of compound floods (Lai et
al. 2021). (4) Compound flooding may occur when precipitation on already saturated soil is
preceded by fluvial floods (Thieken et al. 2022; Khatun et al. 2022) or storm surges (Bevacqua et
al. 2019). On a climatological time scale, atmospheric teleconnections, such as El Niño Southern
Oscillation (ENSO) and North Atlantic Oscillations (NAO), often influence compound flooding
at regional scales (Ganguli and Merz 2019; Wu and Leonard 2019). While conventional flood risk
assessment tools are often limited to assessing risk from a single driver, understanding drivers
associated with compound flooding, their changing patterns due to relative sea level rise and

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intensification in the water cycle (precipitation and evapotranspiration) due to climate change are
essential for developing resilience to current and projected flood risks.
The ensuing sections cover several key topics associated with compound flooding that are
covered in the MOP.
HYDRODYNAMIC PROCESS-BASED MODELS OF COMPOUND FLOODING
Processes covered in the MOP include rainfall-runoff, riverine models, and coastal hydrodynamic
models (tides, surge, waves). For example, the generation of runoff and eventual streamflow from
rainfall is a complex conveyance issue. The transformation of precipitation into surface runoff is
illustrated in Figure 1: illustrating the relationship between the rainfall process, infiltration to the
subsurface, generation of overland flow, and flow into an urban, man-made drainage system.
Figure 1. Rainfall, Infiltration, Overland Flow and Flow into Drainage System
Among the many variables that describe these processes mathematically are the width,
area, percent imperviousness, ground slope, roughness parameters of the land cover for both

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impervious and pervious fractions, and several infiltration rate parameters that depend upon
methods chosen.
The transport of runoff through both natural and man-made conduits, as well as routing
through a detention structure requires solution of continuity and momentum equations using
numerical methods. Any mathematical model is an abstraction of the actual physical system it
attempts to simulate, and uncertainty in the values of many model parameters requires field
measurements and calibration.
STATISTICAL MODELS OF COMPOUND FLOODING
In engineering practice, the hydrologic design value used to build or assess the behavior of water
infrastructures is mainly determined through univariate approaches, generally based on one single
event, and a single catchment. However, compound events [AghaKouchak et al. 2018;
Zscheischler et al. 2020; Seneviratne et al. 2021] have shown how univariate approaches may
provide a poor and partial representation of the phenomenon under investigation, and/or an
incorrect estimation of the design value, especially when the event that may put in crisis the water
infrastructure can be due to the co-presence or involvement of two or more variables. For example,
the overflooding due to the overtopping of a levee depends on the flood volume above a threshold
(i.e., the height of the levee) which depends on the flood peak, but also on the shape of the flood
hydrograph. Thus, in hydrologic design, it is important to consider compound events, which
requires an adjustment, or a shift, of the engineers’ paradigm from a univariate perspective to the
multivariate one. Compound events are characterized by the joint action of a number of different
events and/or variables, which often are non-independent (statistically and/or physically). Thus, it
may be necessary to model the association/dependence between the variables at play. Among the
available statistical tools, Copulas [Salvadori et al. 2007] are perhaps the most promising one. The
power and versatility of Copula lies in the Sklar’s Theorem. In a bivariate context (X,Y), it states
that if it is the joint distribution function of such variables, with marginals FX and FY, then there
exists a 2-copula C such that:
FXY (x,y) = C(FX (x),FY (y))
Basically, a bivariate Copula can be viewed as a bivariate distribution function of Uniform
marginals in [0,1], and the Sklar’s Theorem states that any joint distribution function can be
obtained by combining together a copula C with suitable marginals, FX and FY. Many families of
bivariate copulas are available in literature. In a multivariate context, the concept of vine Copulas
[Czado 2019] allows to accommodate the constraints associated with the construction of
statistical/probability models in high (>>2) dimensional problems.

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Figure 2. Decomposing the non-stationarity issue in compound events problem using
the Sklar’s Theorem. Example of nonstationarity both in the marginals and the association.
The upper panel shows how the marginals of X and Y change passing from a sample to the
other; similarly, the association between the variables is different in the two samples, evident
in the X-Y plane and also in the U-V plane (lower panel).
Furthermore, in engineering practice, the hydrologic design is usually assessed under the
umbrella of stationarity. This assumption entails the time invariance of the probability
distributions of the variables at play (strong stationarity), which implies that the distribution and
its parameters are fixed and constant, or the time invariance of the statistical moments (weak
stationarity). However, natural and anthropogenic forcings, including climate and/or land use
changes can put this assumption of stationarity at risk [Milly et al. 2008]. These forcings may lead
to changes in the frequency, intensity, spatial extent, duration, and timing of extreme weather-
related and climate-related events and can result in unprecedented extreme events [Seneviratne et
al. 2021]. According to the Sklar’s Theorem, the nonstationarity issue in compound events and in
general multivariate problems can be decomposed in assessing separately the presence of
nonstationarity in the marginals and in the Copula model as firstly illustrated in Vezzoli et al.
[2017]; see also Salvadori et al. [2018], and Villalobos-Herrera et al. [2021] for additional
applications. Three possible cases can happen in the analysis: Case 1 when there is non-stationarity
in the marginals but not in the association/copula model; Case 2 when there is stationarity in the

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marginals but not in the association/copula model; and Case 3 the general one, when the non-
stationarity is in both the marginals and the association/copula model. Figure 2 exemplifies case
3, in the bivariate setting, using two synthetic samples (indicated with different colors). In the
upper panel, the marginals of X and Y , given by the empirical densities, change by changing the
sample, as well as the association. In the lower panel, showing the unitary square representing the
domain of bivariate Copulas, the two samples present a different placement, where the sample
indicated in red has a wider spread (and thus a lower association) in the copula plane.
LINKING STATISTICAL AND PROCESS BASED MODELS
Multivariate risk assessment considers the simultaneous or integrative impact of multiple factors,
including the (statistical) interdependence and (physical) interrelation of different risk factors,
resulting in more reliable estimates of compound flood risks. Statistical and process-based models,
while offering complementary skills, have limitations. Statistical methods require a sufficiently
large and spatially distributed record of flood intensity, which is usually unavailable, while
process-based models require extensive computational resources and suffer from a lack of
comprehensive records for volition purposes. Integrating and linking these models can result in a
more reliable estimation of compound flood risk while keeping the computational cost reasonable
and providing valuable insights for resilience assessment and planning.
In the process of linking the statistical and process-based models there exist challenges
including identifying proper boundary conditions. Compound coastal flooding risk assessment
requires accounting for multiple interrelated stochastic variables (for example rainfall, and sea
level) that vary both in time and space. The choice of the most suitable set of variables to represent
a flood driver depends on the system under consideration. For a comprehensive flood hazard and
risk assessment, it may be necessary to consider as many variables as possible, which yields in the
dilemma of ambient scenarios to simulate to cover the widest range of possible combinations. The
choice of the number of model simulations is a trade-off between accuracy and simulation time.
In order to make an informed choice on the number of variables and model simulations, it is
important to understand the relationship between the flood drivers and flood response.
Furthermore, the aspect of relative timing of flood drivers can be very relevant and is often
overlooked. For example, the probability of the exact 5-year rainfall depth occurring in
combination with the exact 10-year tailwater level or within a timeframe comparable to the time
of concentration for the coastal watershed of interest. In all these cases, a sensitivity analysis is
recommended to determine the number of realizations per variable for which model simulations
need to be carried out.
Multivariate flood risk analysis approaches can be classified into three categories: structure
variable approaches, impact-based approaches, and joint density approaches (Zheng et al., 2015).
Structure variable approaches transform the multivariate input data into equivalent structure
variable values, the distribution of which is extrapolated to extreme values. Impact-based

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approaches, on the other hand, identify coincident or near-coincident values of the flooding drivers
by taking IID extreme events from the response variable, which allows for identification of all the
forcing conditions inducing a threat for critical assets. Joint density approaches use multivariate
distributions and information on the dependence between them to extrapolate the input data to
extreme values. Copulas are commonly used to characterize the correlation structure between
variables for joint density analysis. However, these approaches, as described above, pose
challenges in terms of computational expenses and the need for sufficient realizations that
adequately cover the wide range of compound flood impact possibilities.
As a potential alternative, several ‘hybrid’ approaches, under which multiple statistical and
process-based models are coupled to evaluate the desired impact in a larger complicated system,
have recently been proposed that lays out opportunities to more efficiently overcome these
challenges with the help of reduced physics surrogate modeling and high-performance computing
systems. For example, the dependence-informed sampling hybrid method has shown to have
significant applications in compound flood assessment and inundation analysis (Moftakhari et al.,
2019). The approach is based on selecting a handful of compound scenarios that can cover the
range of possibilities. Without this informed sampling such understanding might require thousands
of simulations. The joint probability method with optimal sampling (JPM-OS) has also shown to
be helpful in reducing the required samples for a comprehensive compound flood assessment (Gori
& Lin, 2022). In this case a relatively small subset of rainfall-surge combinations from a suite of
synthetic TCs could reproduce the compound flood hazard accurately comparable to more
intensive bootstrapping methods. However, this method requires the user to choose the relevant
flood parameters and their relative importance a priori, which may not be known in all locations
and circumstances. There have been recent advances in physics-informed machine learning as a
powerful technique that enables cost-effective compound flood prediction and inundation
mapping. Machine learning models can learn from hidden patterns embedded in time-series and
remote sensing data and can account for nonlinearities resulting from the interaction among flood
drivers and physical settings (Munoz et al., 2021). Additionally, these algorithms can be trained to
incorporate such nonlinearities in short- and long-term flood predictions, frequency analysis, and
damage assessments without the need for modeling the underlying physical processes.
ANALYSIS OF CHANGING CONDITIONS
A challenge for designing and planning for compound flooding is that the climatic drivers
indeed are nonstationary affecting the magnitude and frequency of compound flooding are
changing over time. The rate and magnitude of these future changes are uncertain. For example,
global sea levels are rising due to thermal expansion of the ocean and increased mass of water
from glaciers and the melting ice sheets of Greenland and Antarctica (Oppenheimer et al, 2019).
Future thermal expansion and melting are driven by increasing temperatures, and these are
dependent on future emissions of greenhouse gasses. The Greenland ice sheet is virtually certain
and the Antarctic ice sheet is likely to lose mass this century, but there is uncertainty about some

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of the processes (Fox-Kemper et al 2021). Engineers will need to plan for a range of future
potential sea levels.
Precipitation levels may also increase. The water holding capacity of the atmosphere
increases about 7% for each 1⁰ C of temperature rise. Heavy precipitation events have the
potential to be more intense. The proportion of tropical cyclones that are category 3 or higher
has likely increased over the past forty years and will likely increase in the future (Seneviratne et
al, 2021). One challenge for compound flooding analysis is that the correlation between drivers
may change in the future. For example, as hurricanes become more intense, rain rates and storm
surge may both increase and lead to both increasing means and higher correlations.
In addition to changes in climate, development in coastal regions increases the risk of
economic damage and loss of human life. The population in coastal counties of the United
States increased from 47 million people in 1960 to 87 million people in 2008 (U.S. Census,
2010). The increasing population trend is expected to continue throughout the world (Neumann
et al, 2015). Due to the nonstationary conditions and the uncertainty in future conditions, a risk-
based approach is necessary for compound flooding planning and design.
In order to assess the potential impact of future climate change on compound flooding in
coastal communities, it is essential to consider the projections of both terrestrial and marine
processes. The terrestrial processes mainly include intense precipitation, extreme flows, and
groundwater levels, while the marine processes can consist of storm surges and waves, among
others. Advancements in global and regional climate modeling provide extensive simulations to
assess the nonstationarity of individual flooding drivers and their interrelationships. However,
assessing climate change impacts at local and regional scales requires bias adjustment, and
downscaling of climate model simulations and quantifying the associated uncertainties. Projected
changes in compound floods can be performed at fixed future periods for specific emission
scenarios, associated with specific global warming levels compared to the preindustrial period, or
by pooling realizations from a single large ensemble model simulation, similar to the univariate
analysis of extremes. In addition to projecting individual drivers, research has shown the
significant influence of nonstationary interdependencies between multiple hazards on the
corresponding compound event risks in the future (Singh et al., 2021). The standard bias-
correction and downscaling approaches may fail to capture the true dependencies between flood
mechanisms, as they adjust biases in individual variables independently, without considering
their interrelationships. As a result, multivariate bias adjustment techniques have been developed
to address this issue and improve the representation of concurrent occurrences of multiple factors
(Cannon, 2018; François et al., 2020; Cannon et al., 2022).

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RISK AND UNCERTAINTY ANALYSIS
The Earth has enjoyed a relatively stable or stationary climate during the existence of
humankind. Human-caused climate changes are a result of more than a century of net greenhouse
gas emissions. These emissions were generated by increases in energy use as well as changes to
land use and human lifestyle (IPCC 2023). This has resulted in shifts in climate related to
rainfall, temperature and sea level thus creating a nonstationarity climate now and for the future.
As a result, trends over time prevent historical data from being used to estimate future conditions
(FHWA 2016). Since the historical data may no longer predict future conditions, it becomes
more difficult to assess risk and the associated uncertainty of compound flooding events.
Risk is the product of the probability of an undesirable event and the consequences of the
event (FHWA, 2016). The likelihood of undesirable events such as sea level rise and extreme
events will depend on the extent to which we, as a global community, continue to adopt
mitigation and adaptation strategies. The Intergovernmental Panel on Climate Change (IPCC)
was convened by the United Nations to assess the science of climate change and communicate
the impacts, risks and options to the global community. For example, even with near-term
adoption of very low green-house gas emission scenarios (SSP1), “global warming is more likely
than not (or assessed likelihood between 50%-100%) to reach 1.5°C between 2021 and 2040 and
likely or very likely (or assessed likelihood between 66%-100%) to exceed 1.5°C under higher
emissions scenarios.”
Changes to land use that include increases in transportation development, water usage,
sanitation needs, and energy systems have been impacted by both extreme (ex: flooding) and
slow-onset (ex: sea level rise) events, and these impacts are concentrated in urban areas where
people are economically or socially marginalized. Human influence has likely (or assessed
likelihood between 66%-100%) increased the frequency of compound extreme events since the
1950s (IPCC 2023).
Uncertainty enters the modeling process in three ways:
● through natural parameter variability;
● through measurement error, which also introduces uncertainty in parameter estimation;
and,
● through model error, representing uncertainty introduced by the degree to which the
simplifying assumptions used to develop a model fail to accurately represent the actual
physical, biological, and chemical processes at the site in question.
The first two of these sources of uncertainty can be analyzed separately. However, the data
are often insufficient: in such cases the natural and measurement uncertainty may be combined
into one source of uncertainty for the Monte Carlo-type analysis, through the specification of the
distribution of the parameter value. The third source of uncertainty in the analysis is due to the
degree to which the transport model applied may misrepresent actual processes at the site. This

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source of uncertainty is very difficult to quantify, and indeed may be impossible to quantify for
specific sites unless extensive sampling and monitoring is carried out.
There are available strategies for incorporating uncertainty into planning and design. The
challenge for practicing engineers and policy makers is identifying the most appropriate
approaches, methods and tools based on the scope of work with consideration for the potential
climate change scenarios over the life cycle of the structure.
Methods such as risk-based adaptation, reconsideration of the design life cycle, dynamic
adaptive pathways, cost-benefit analysis under climate uncertainty and multi-criteria decision
making allow for a more fluid response to climate changes. Tools developed by governmental
agencies such as the US Army Corps of Engineers’ Sea Level Change Scenario Analysis or the
Nonstationarity Detection Tool can be utilized to identify and adjust datasets for climate change
(Friedman et al. 2016).
CONCLUSION
The purpose of a Manual of Practice (MOP) is to provide a synthesis of available tools and
methods of best practice for civil engineers. The forthcoming MOP for compound flooding
conditions will provide practical applications, tools and case studies to address hydrodynamic
process-based models such as rainfall-runoff, riverine and coastal modeling as well as statistical
models including multivariate statistical models. In addition, the importance of linking statistical
and process-based models and their various approaches is identified. The MOP also discusses
addressing local and changing conditions and tools to assess risk and uncertainty.
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