4e534

Environmental Modelling & Software 90 (2017)

Contents lists available ScienceDirec

at t

Environmental Modelling & Software

j o u r n a l h o m e p a g ew: w w. e l s e v i e r. c o m / l o c a t e /e nvts o f

A remote sensing-based tool for assessing rainfall-driven hazards

Daniel B. Wright a, *, Ricardo Mantilla b, Christa D. Peters-Lidard c
a
University of Wisconsin-Madison, Madison, WI, United States b
University of Iowa, Iowa City, IA, United States
c
Article history: RainyDay is a Python-based platform that couples rainfall remote sensing data with Stochastic Storm Transposition (SST) for
Received 16 February 2016 modeling rainfall-driven hazards such as floods and landslides. SST effectively lengthens the extreme rainfall record through
Received in revised form temporal resampling and spatial transposition of observed storms from the surrounding region to create many extreme rainfall
28 December 2016 scenarios. Intensity-DurationFrequency (IDF) curves are often used for hazard modeling but require long records to describe
Accepted 30 December 2016 Available the distribution of rainfall depth and duration and do not provide information regarding rainfall space-time structure, limiting
online 13 January 2017
their usefulness to small scales. In contrast, RainyDay can be used for many hazard applications with 1 e2 decades of data, and
output rainfall scenarios incorporate detailed space-time structure from remote sensing. Thanks to global satellite coverage,
Keywords: RainyDay can be used in inaccessible areas and developing countries lacking ground measurements, though results are
Scenarios impacted by remote sensing errors. RainyDay can be useful for hazard modeling under nonstationary conditions.
Extreme rainfall
© 2016 Elsevier Ltd. All rights reserved.
Remote sensing
Floods
Risk assessment
Nonstationarity
NASA Goddard Space Flight Center, Greenbelt, MD, United States

articleinfo abstract

Software availability 1. Introduction

Name of Software: RainyDay Rainfall Hazard Rainfall-driven hazards such as floods and
landslides are the
Modeling System
Developer: Daniel B. Wright
Contact: Daniel B. Wright; Address: Room * Corresponding author.
1269C Engineering Hall, 1415 Engineering E-mail address: danielb.wright@wisc.edu (D.B. Wright).
Drive, Madison, WI 53706, USA; Email:
dani http://dx.doi.org/10.1016/j.envsoft.2016.12.006
elb.wright@wis 1364-8152/© 2016 Elsevier Ltd. All rights reserved.
most common natural disasters worldwide,
c.edu Year first
and amongst the most devastating. A growing
available: 2015
number of computational hazard models are
Required hardware and software: RainyDay
available to transform extreme rainfall inputs
requires Python 2.7 or newer (not
into hazard predictions, including distributed
tested with Python 3.0 or higher)
hydrologic models for the movement of
with Numpy and Scipy. The Netcdf4
water into and through river systems (e.g.,
and GDAL APIs are also required.
Smith et al., 2004); hillslope stability and
RainyDay will run on Macintosh,
run-out models for landslide initiation and
Linux, and Windows machines
subsequent motion (e.g. Brenning, 2005;
Cost: Free. RainyDay is currently available by
Preisig and Zimmermann, 2010;
request. Open-source release under
respectively); and hydraulic models for flood
version 3.0 of the GNU General
Public License wave propagation in channels and floodplains
(http://www.gnu.org/licenses/gpl- (e.g., Horritt and Bates, 2002). These models
3.0.en.html) is planned have seen significant advances in recent
decades, and have become key components
in probabilistic hazard and risk assessment in
35 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54

fields such as natural catastrophe risk rainfall space-time structure has traditionally
insurance, infrastructure design, and land-use been less well understood than intensity and
planning. The hazard predictions produced duration, and its representation in hazard
by these models tend to be highly sensitive to modeling has been less sophisticated.
the amount, timing, and spatial distribution The probability distribution of rainfall
of rainfall inputs. Unfortunately, progress on depth or intensity for a given duration is
developing realistic rainfall inputs for usually derived from rain gages and distilled
probabilistic hazard and risk assessment has into Intensity-Duration-Frequency (IDF)
been relatively limited. This paper introduces curves, such as those provided by the
RainyDay, a Python-based platform that National Oceanic and Atmospheric
addresses this shortcoming by coupling Administration's (NOAA) Atlas 14 (Bonnin
rainfall remote sensing data from satellites or et al., 2004). Records spanning many
other sources with a technique for temporal decades are generally needed to define the
resampling and spatial transposition known extreme tail of such distributions. The
as Stochastic Storm Transposition (SST) to challenge of measuring extreme rainfall over
generate highly realistic probabilistic rainfall long time periods and over large areas using
scenarios. rain gages has hindered IDF estimation in
Rainfall inputs for long-term hazard and many developed countries, while the lack of
risk assessment require a probabilistic data in poor countries and in inaccessible
description of three interrelated components: terrain means that IDF estimation using such
duration, intensity, and space-time structure. methods is virtually impossible in many
Efforts to jointly model these components are locations. Furthermore, measurements of
usually referred to as rainfall frequency rainfall space-time structure at a high level
analysis, a simple term that belies the of detail using dense networks of rain gages
complexity of the physical phenomena and are nonexistent outside of a handful of
analytical methods involved. The probability wealthy cities and research-oriented efforts.
structure of the first two components, rainfall “Regionalization,”dthe pooling of hazard
duration and intensity, has been a focus of information over a larger area in order to
research and application for decades (see U.S. inform analyses at particular locations (see,
Weather Bureau, 1958 and Yarnell, 1935 for e.g. Alexander, 1963 for an early discussion
early examples). These two components are of rainfall regionalization and Stedinger et
strongly linked and together they determine al.,1993 for a review)dhas helped with IDF
the probability distribution of rainfall volume estimation in areas where rain gage densities
(or depth) at a point or over an area. The third are moderate or high. These techniques offer
component, space-time structure, describes the little help, however, in parts of the world
spatial and temporal variability of rainfall and where rain gages are few or nonexistent, and
is determined by storm size, velocity, and do not offer a framework for incorporating
temporal evolution of spatial rainfall coverage. rainfall space-time properties into hazard
Space-time structure can thus be understood as estimation. Even where long rainfall records
describing the “when” and “where” of extreme do exist, nonstationarity due to climate
rainfall, whereas intensity and duration change may mean that earlier portions of the
describe “how much.” record are no longer representative of current
Rainfall space-time structure can be an or future IDF properties.
important hazard determinant. For example, Several techniques, which generally fall
a rainstorm that is short-lived and small in under the term of design storm methods, are
spatial extent may pose a significant flash used in long-term hazard estimation to link
flood threat in a narrow mountain valley or IDF properties to space-time structure for
urban area, but may not represent a hazard probabilistic flood hazard assessment
on a larger river system. Conversely, a (commonly referred to as flood frequency
month-long rainy period could lead to analysis). Design storm methods include
flooding on a major river due to the gradual linking rainfall duration to rainfall intensity
accumulation of water in soils, river via a measure of flood response time, such as
channels, and reservoirs, but may never the time of concentration (e.g. McCuen,
feature a short-lived “burst” of rainfall 1998), deriving estimates of areaaveraged
sufficiently intense to cause flash flooding at rainfall from point-scale rainfall estimates
smaller scales. Similarly, a storm that covers using area reduction factors (ARFs; U.S.
a large area or passes over a series of valleys Weather Bureau, 1958), and using
could lead to more widespread landslide or dimensionless temporal disaggregation such
debris flow occurrences than a smaller or as the family of U.S. Soil Conservation
stationary storm. Rainfall space-time Service 24-h rainfall distributions (e.g.
structure and its importance as a hazard McCuen, 1998). Each is highly empirical,
trigger, therefore, must be understood within laden with assumptions (see Wright et al.,
the context of the particular geography and 2014a; Wright et al., 2014b; Wright et al.,
scale in question. Due to its complexity, 2013), valid only in certain contexts, and
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
36
often misunderstood or misused (K. Potter, distributed hydrologic model in Wright et al.
personal communication, May 6, 2015). (2014b). These two papers, along with Wright et
SST explicitly links IDF to rainfall space- al. (2014a) show that commonly-used design
time properties, providing certain advantages storm practices (ARFs, dimensionless time
over design storm methods. Similar to other distributions) have serious shortcomings in
regionalization techniques, SST aims to representing the multiscale space-time structure
effectively “lengthen” the period of record by of extreme rainfall and critical interactions with
using nearby observations, albeit using a of this structure with watershed and river
fundamentally different approach involving network features. Wright et al. (2014b) also
temporal resampling and spatial transposition of show that when SST is coupled with rainfall
rainstorms drawn from a catalog of observed remote sensing data and a distributed hydrologic
rainfall events from the surrounding region. The model, it can reproduce the role that this
inclusion of nearby storms at least partially structure plays in determining multi-scale flood
addresses the difficulty of accurately estimating response. The RainyDay software described in
rainfall hazards using short records. SST can be this paper was developed to facilitate the use of
used to estimate rainfall IDF properties and also SST in conjunction with rainfall remote sensing
to facilitate modeling of interactions of rainfall data.
space-time structure with geographic features Though SST was developed in the context of
(such as hillslopes and river networks) at the flood hazard estimation, it may prove useful for
appropriate spatial and temporal scales. It rainfall-triggered landslides and other mass
accomplishes this by generating large numbers movements, subject to the oftentimes poor
of extreme rainfall “scenarios,” each of which accuracy of remote sensing data in steep terrain
has realistic rainfall structure based directly on as well as other limitations that will be
observations. discussed subsequently. Rainfall space-time
Alexander (1963), Foufoula-Georgiou structure governs the temporal distribution of
(1989), and Fontaine and Potter (1989) describe rainfall volume onto individual hillslopes, as
the general SST framework, while Wilson and well as the number of hillslopes subject to
Foufoula-Georgiou (1990) use the method for rainfall. In addition, steep landslide-prone
rainfall frequency analysis and Gupta (1972) terrain often has poorer rain gage coverage than
and Franchini et al. (1996) use it for flood lowland areas due to limited accessibility,
frequency analysis. In those days, however, the suggesting that remote sensing rainfall estimates
method was of limited practical use due to the are potentially useful in such regions,
lack of detailed rainfall datasets with large areal particularly if improvements in accuracy can be
coverage. Those studies also did not focus realized (e.g. Shige et al., 2013).
explicitly on the aspects of SST related to Section 2 provides a description of the SST
rainfall space-time structure nor its implications methodology used in RainyDay. Section 3
for hazard modeling. discusses the specific implementation of SST in
The recent advent of satellite-based remote RainyDay and some of the software's important
sensing provides a relatively low-cost means of features. Section 4 provides sample results from
measuring extreme rainfall over large parts of RainyDay and sensitivity analyses using
the globe at moderately high spatial and different input rainfall datasets for rainfall and
temporal resolution (30 mine3 h, 4e25 km), flood frequency analysis in order to illustrate its
while ground-based weather radar offers higher- capabilities and some of its limitations,
resolution estimates (5e60 min, typically 1e4 including for flood frequency analysis in
km) over smaller regions. While the accuracy of nonstationary conditions. Section 5 includes
rainfall remote sensing can be poor (particularly discussion and concluding remarks.
for satellite-based estimates, e.g. Mehran and
AghaKouchak, 2014; and in mountainous 2. The SST methodology
regions, e.g. Nikolopoulos et al., 2013;
Stampoulis et al., 2013), such data nonetheless In this section, we provide a step-by-step
offer unprecedented depictions of rainfall over methodology for SSTbased rainfall frequency
large areas, offering opportunities for hazards analysis for a user-defined geographic “area of
research and practice at various scales, ranging interest,” A of arbitrary shape. Higher-level
from forecasting and post-event analysis to description of software features is left to Section
long-term hazard assessment. 3, but it merits mention that in RainyDay, A can
In the context of SST, the ongoing be a single remote sensing pixel, a rectangular
accumulation of remote sensing data to lengths area containing multiple pixels, or a contiguous
of 10e20 years or more “unlocks” many of the area defined by a usersupplied polygon in
as-yet unrealized opportunities offered by SST. shapefile format.
Wright et al. (2013) demonstrated the coupling The following five steps describe the SST
of SST with a 10-year high resolution radar methodology, as implemented in RainyDay:
rainfall dataset for IDF estimation, and the
method was extended to flood frequency 1. Identify a geographic transposition
analysis for a small urban watershed using a domain A0 that encompasses the area of
37 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54

interest A. One could confine A0 to in which hazard response is intrinsically

regions with homogeneous extreme sensitive to the user-specified duration,
rainfall properties, (e.g. flat areas far from and this feature is indeed one of the chief
large water bodies and topographic advantages of SST over design storm
features). However, such homogeneity methods for multiscale flood hazard
would likely be difficult to rigorously estimation (see Wright et al., 2014b for
determine in practice and regardless, such analysis and discussion). In the case of
strict interpretation is likely to be overly SST-based flood frequency analysis, t
limiting. RainyDay offers several should be at least as long as the watershed
diagnostic aids, discussed in Section 3.3, time of concentration and preferably
that help the user to understand rainfall somewhat longer.
heterogeneity over the region A 0 and to 3. Randomly generate an integer k, which
improve the performance of the SST represents a “number of storms per year.”
procedure in cases where rainfall In previous SST literature, the assumption
heterogeneities do exist. Additional issues was made that k follows a Poisson
related to the selection of A 0 are explored distribution with a rate parameter l storms
in Section 4.3. per year. The m parent storms are selected
2. Identify the largest m temporally non-
such that an average of l¼ m/n storms per
overlapping storms in A0 from an n-year
year are included in the storm catalog.
rainfall remote sensing dataset, in terms
For example, if m ¼ 100 storms selected
of rainfall accumulation of duration t and
from a ten-year remote sensing dataset,
with the same size, shape, and orientation
of A. For example, the principal axis of then l¼ 100/10 ¼ 10.0 storms per year.
the Turkey River watershed in RainyDay will generate k using either the
northeastern Iowa in the central United Poisson distribution or an empirical
States is oriented roughly northwest- distribution, discussed in Section 3.3. If
southeast and has an area of 4400 km 2. In the Poisson distribution is selected,
this case, the m storms are those RainyDay will automatically calculate l
associated with the m highest t-hour based on user-specified m and the length
rainfall accumulations over an area of of the input dataset.
4400 km2 with the same size, shape, and 4. Randomly select k parent storms from the
orientation as the Turkey River storm catalog. For each selected parent
watershed. We refer to this set of storms storm, transpose all rainfall fields
henceforth as a “storm catalog,” with the associated with that storm by an east-west
same geographic extent as A0 and the distance Dx and a northsouth distance Dy,
same spatial and temporal resolution as where Dx and Dy are drawn from the
the input rainfall data. We refer to the m
distributions DX(x) and DY(y) which are
storms in the storm catalog henceforth as
bounded by the east-west and north-south
“parent storms.” In RainyDay, the user extents of A0, respectively. The motion
can specify whether to exclude certain and structure of the parent storm is
months (such as wintertime) from the unaltered during transposition and only
storm catalog. Previous studies have the location is changed. The distributions
shown that there can be low bias DX(x) and DY(y) were taken to be uniform
introduced in high-exceedance in Wright et al. (2013, 2014b), but
probability (i.e. frequent, low-intensity) RainyDay offers additional options,
events if m is small (e.g. described in Section 3.3. We illustrate this
FoufoulaGeorgiou, 1989; Franchini et al., step schematically in Fig. 1. For each of
1996; Wilson and FoufoulaGeorgiou, the k transposed storms, compute the
1990; see Wright et al., 2013 for a resulting t-hour rainfall accumulation
discussion). The sensitivity of SST results averaged over A.
to the choice of m and A0 is explored in Step 4 can be understood as temporal
detail in Section 4.3, but m z 10n resampling and spatial transposition of
generally minimizes the low bias for observed storm events within a
frequent events, and would likely be a probabilistic framework to synthesize one
good starting point for new analyses. Low year of heavy rainfall events over A 0 and,
exceedance probability (i.e. rare) events by extension, over A. RainyDay and
are less sensitive to the choice of m (see previous SST efforts retain the largest (in
Section 4.3). In RainyDay, duration t is a terms of rainfall intensity) of the k events
user-defined input, and if t is neither very for subsequent steps and discard the k-1
short nor very long relative to the time remaining events, though in principle
scale of hazard response in A, subsequent these events could be retained. The single
hazard modeling results will be relatively retained storm can be understood as a
insensitive to the chosen value. In this “synthetic” annual rainfall maximum,
respect, the duration t in SST differs analogous to those annual rainfall
conceptually from design storm methods,
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
38
maxima that are extracted from rain gage 3. RainyDay software
records for rainfall frequency analysis. It
should be noted that these rainfall events 3.1. Overview of software
do not form a continuous series, meaning
that neither inter-storm periods nor the We wrote RainyDay to render SST more
temporal sequencing of the k storms are accessible and to streamline the code for
considered. speed and ease-of-use using Python. The
5. Repeat steps 3 and 4 a user-specified Tmax, majority of subroutines utilize the Scipy
number of times, in order to create Tmax (Jones et al., 2011) and Numpy packages
(Walt et al., 2011). Fig. 2 shows a schematic
years of t-hour synthetic annual rainfall
of workflow in RainyDay.
maxima for A. RainyDay then assigns
While the ranking of rainfall events
each annual maxima a rank i according to described in Step 5 of the SST methodology
its rainfall intensity relative to all others. in Section 2 is based on rainfall intensity
Each of these ranked maxima can then be averaged over A, RainyDay will create
assigned an annual exceedance NetCDF4 files (http://www.unidata.
ucar.edu/software/netcdf) that contain the
probability i
pe where pe i
≡ i/Tmax.
transposed rainfall scenarios with full
Exceedance probability pe is the depictions of rainfall space-time structure at
probability in a given year that an event the native spatial and temporal resolution of
of equal or greater intensity will occur. the input. This is an important feature
The “return period” or “recurrence because space-time structure, and not just
average rainfall intensity over area A and
interval” Ti, commonly used in hazard
duration t, is important in determining
analysis, is simply Ti ≡ 1/pie, so if Tmax ¼ hazard response. For example, one rainfall
103, it is possible to directly infer scenario may produce a more severe flood
exceedance probabilities of 1.0 pe 103 response than another scenario, even if it has
(recurrence intervals of 1 Ti 103). Each of a lower overall average rainfall intensity
over A and t, due to interactions with
these rainfall events can then serve as one
watershed features (see Section 3.2 of this
datum of an empirical IDF estimate or as paper for discussion and Wright et al., 2014b
a rainfall scenario for hazard modeling. for analysis).
We will provide the RainyDay source
code, examples, and user documentation
upon request, and intend to release it under
version 3 of the GNU General Public
License (http://www.gnu.org/copyleft/
gpl.html) once we have completed sufficient
testing and documentation. The code is
currently not parallelized. Computational
time is determined mainly by the size of the
input dataset (record length n, input
resolution, and geographic size of A and A’),
while other factors, such as m, t, T max, and N
can impact runtime. Computational speed,
even without parallelization, is not
prohibitive on a modern desktop or laptop
computer (several seconds to several hours
for typical configurations and input datasets).
To ensure accessibility for users
inexperienced with Python, all the necessary
Python modules are supported within recent
versions of the Anaconda Python distribution
from Continuum Analytics
(https://store.continuum.io/cshop/anaconda).
The user must install NetCDF4 libraries and any
Fig. 1. Depiction of SST procedure for a single storm requisite dependencies. If the user wishes to use
consisting of four time intervals t 1 … t4. The blue shapefile functionality, necessary for defining A
ellipses illustrate the time evolution of an arbitrary to be a shape other than a rectangle or a single
rainfall isohyet derived from remote sensing
rainfall pixel, the GDAL library
observations, while the green ellipses show the time
evolution of the same isohyets after transposition.
(http://www.gdal.org) and any necessary
Adapted from Wright et al. (2013). (For interpretation dependencies must also be installed.
of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
39 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
3.2. SST internal variability to the confidence intervals of other IDF
estimates. Like virtually all frequency analyses
In RainyDay, the user specifies N, the and IDF estimation methods, the ensemble
number of Tmax-year long “ensemble members” spread generated by RainyDay does not
to be generated. This enables examination of consider measurement error, which can be
“internal variability,” i.e. how much variation in substantial. Since the ensemble spread is
rainfall intensity is possible for a given p e for a characteristic to a given set of user-defined
given input rainfall dataset and set of user- values such as A’ or m, it does not consider
defined parameters. For example, if the user uncertainty associated with these choices.
specifies Tmax ¼ 103 and N ¼ 100, then there will Analyses in Section 4.3 show how such
be 100 intensity estimates for each p e between uncertainties can be assessed, but fundamentally
1.0 and 103. RainyDay will automatically this requires manipulating the size or
generate text file and graphics files containing composition of the storm catalog through the
the results of this rainfall frequency analysis, choice of user-defined values, necessitating
including the rainfall mean, minimum, and multiple distinct runs of RainyDay.
maximum (or, optionally, a quantile interval) for
each pe, computed from the N ensemble
members.
If the scenarios generated by RainyDay are
fed through a hazard model, then the ensemble
spread will propagate through to generate
ensemble hazard estimates. A useful and
interesting feature of SST and RainyDay that is
not examined in this paper, but is discussed at
length in Wright et al. (2014b), is that the
exceedance probability of rainfall and of
subsequent hazards can be decoupled using
SST, particularly if some realistic scheme is
used to account for the initial conditions in A
(such as soil moisture or baseflow). Consider the
example where N ¼ 1 and 103 rainfall scenarios
(Tmax ¼ 103) are created as input to a distributed
flood hydrologic model. One of these rainfall
scenarios has pe ¼ 0.01 (in terms of watershed-
average t-hour rainfall depth over an area A).
Even if initial conditions are kept constant
across all Tmax simulations, the pe of the peak
discharge or volume predicted by the model for
this particular scenario need not be equal to
0.01, since the space-time structure of the
rainfall scenario and its interactions with
watershed and river network features can
dampen or magnify the flood severity. If
variability in initial conditions within the hazard
model are considered, this dampening or
magnification can be even greater. This property
of SST contrasts with design storm methods,
which typically assume a 1:1 relationship
between the pe of rainfall and the resulting
hazard, though variability in initial conditions
could in principle be used with design storm
approaches to produce some degree of
“decoupling” of rainfall and hazard pe.
RainyDay provides one simple scheme for
creating variability in initial conditions,
described in Section 3.5.
It should be pointed out that the ensemble
spread generated in RainyDay is not completely
comparable to the confidence intervals of more
traditional rainfall or flood frequency analyses.
The latter show statistical uncertainty associated
with parameter estimation. Therefore, it might
not be reasonable to expect that the uncertainty
ranges produced by RainyDay to be comparable
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
40

Fig. 2. Flow chart demonstrating the workflow of RainyDay.

Ensemble spread is shown throughout costs associated with large numbers of
Section 4 to illustrate various aspects of SST- simulations, which can be substantial depending
based rainfall and flood frequency analysis. If on the particular hazard model. To help manage
the user is only interested in examining internal the number of simulations required, the user can
variability of SSTbased rainfall IDF, then the specify a rainfall return period threshold, below
number of ensemble members can be large (e.g. which output scenarios will not be created. For
N 100). If the user wishes to perform hazard example, if the user specifies a 5-year threshold,
simulations, however, N should be selected with no rainfall scenarios with a rainfall depth less
consideration of the computational and storage than the 5-year return period depth will be
41 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
written, which reduces the number of hazard remote sensing estimates or of randomness
simulations by 80% for a given value of N while in the climate system over the relatively
still retaining the most extreme scenarios. short remote sensing record, rather than from
“true” heterogeneity in the underlying
3.3. Rainfall heterogeneity and non-uniform rainfall hydroclimate.
spatial transposition Additional optional diagnostic outputs
include static and animated rainfall maps for
A common criticism of SST is that its each storm in the storm catalog (not shown).
validity is restricted to regions with These storm rainfall maps are useful for
homogenous extreme rainfall properties. As diagnosing “bad data,” particularly in rainfall
previously mentioned, depending on how datasets that use ground-based weather radar
rigidly this criterion is enforced, the method contaminated by radar beam blockage and
would be limited to small, flat regions far other artifacts. Anomalous storm periods
from topographic features, water bodies, etc. must be identified by the user (i.e. no
It is unclear how homogeneity would be automatic data quality checking is provided),
determined, particularly given the paucity of but such periods can be excluded from
rainfall data in most regions. Instead, steps subsequent analyses.
can be taken to use SST in more varied The two-dimensional PDF of spatial
geophysical settings. Regardless of the storm probability of storm occurrence can
setting, the selection of A’ requires an optionally be used as the basis for non-
understanding of regional rainfall patterns uniform spatial transposition (providing the
and of the intrinsic assumptions of SST. DX(x) and DY(y) described in Step 4 and Fig.
Though more work is needed to understand 1 in Section 2) so that the spatial distribution
the geographic limits of the applicability of of storm occurrences will be preserved
RainyDay in complex terrain, the work of between the input data and output rainfall
England et al. (2014) provides an example of scenarios and IDF estimates. Section 4.3
SST usage in complex terrain. examines the impact of this optional feature
RainyDay provides several tools to help on results for the Iowa study region, along
understand the issue of rainfall with potential implications.
heterogeneity, and, to some extent, to It is important to note that this approach
mitigate it. First, RainyDay produces a map only addresses the spatial heterogeneity of
showing the location of the rainfall centroids storm occurrences, not of spatial variations
for all storms in the storm catalog, overlaid in the climatology of rainfall intensity (due
on a smoothed field of the spatial probability to topography or other
of storm occurrence within A’. This spatial
probability of occurrence map is generated
by applying a two-dimensional Gaussian
kernel smoother to the (x,y) locations of the
rainfall centroids for all the storms in the
storm catalog. This smoothed field is then
normalized such that the sum of all grid cells
in A equals 1.0, thus creating a two-
dimensional probability density function
(PDF) of storm occurrence. A second plot
shows these rainfall centroids overlaid with
the average rainfall per storm across A’.
These diagnostic plots assist in
understanding regional variations in storm
occurrences and rainfall over A’. Examples
of these diagnostic plots for a region A’
encompassing most of the state of Iowa in
the central United States are shown in Fig. 3.
The top panel suggests that storms are
somewhat more frequent in the southernmost
third or so of the transposition domain (top
panel), along with slightly elevated activity
in the northeast quadrant. The bottom panel
shows somewhat higher average storm
rainfall in these two areas. Caution should be
taken when drawing firm conclusions from
these diagnostic plots, however, since
rainfall heterogeneities evident in both storm
occurrences and average storm rainfall may
be the result of spatial biases in rainfall
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
42
3.4. Empirical temporal resampling

As mentioned in Step 3 of the SST

procedure described in Section 2, previous SST
work has employed the assumption that the
annual number of storm counts follows a
Poisson distribution, which in turn serves as the
basis for the temporal resampling of storms (i.e.
for generating the number of storms per year k
that will be spatially transposed). RainyDay
supports Poisson-based resampling, but also
allows the use of an empirical distribution. This
distribution is derived from the number of
storms that enter into the storm catalog from
each calendar year in the rainfall input dataset.
Then, during the temporal resampling step, k is
obtained by randomly selecting one of these
values. This feature may be useful in regions
where storm occurrences exhibit strong
clustering (i.e. where there is strong evidence
for more storms in some years and fewer in
other years for persistent climatological reasons;
e.g., Villarini et al., 2013). Section 4.3 examines
the impact of this choice on SST results. Other
discrete probability distributions, such as the
two-parameter negative binomial (Pascal)
distribution, can also be used to model clustered
storm occurrences. RainyDay does not currently
use such distributions, however, since short
(typically 10e20 year) remote sensing records
may yield poor parameter estimates stemming
from the limited number of statistical degrees of
freedom.

3.5. “Spin-up” of initial conditions

A key issue in the modeling of rainfall

Fig. 3. Example of diagnostic plots produced by RainyDay driven hazards is to adequately represent initial
for 24-h duration rainfall from the Stage IV rainfall dataset conditions. In many flood and landslide
(described in Section 4.1) over a region encompassing the modeling efforts, the most critical of these is
state of Iowa, United States. Top: shading indicates spatial antecedent soil moisture, while other states such
probability of storm occurrence. Bottom: shading indicates
as snowpack, river baseflow, and water table
the average rainfall per storm from the same storm catalog.
Black dots show the rainfall centroids for each storm in the position may also be relevant. Many hydrologic
storm catalog. Dot size in both panels indicates relative models allow for the specification of such initial
rainfall storm total rainfall depth. Key RainyDay conditions, and thus many design storm-based
parameters: m ¼ 150 storms, A’ ¼ 2[40 to 44 N, 90 to 96 W]. hazard modeling efforts rely on an assumed soil
A is a single Stage IV rainfall pixel (approximately 16 km ) moisture state, such as an average or fully
and t ¼ 24 h.
saturated condition. Such approaches have
previously been used with SST (Wright et al.,
2014b), and could be combined with the rainfall
scenarios generated via RainyDay. This
factors). For example, if A0 contains a flat plain
approach has the downside, however, that the
and an adjacent mountain range, the probability
true variability antecedent soil moisture is not
of storm occurrence will vary across A’. This
captured in hazard predictions. This is
variation will be captured in the two-
particularly important in regions in which heavy
dimensional PDF of spatial storm probability
rainfall does not necessarily occur in the same
and, using the optional nonuniform spatial
season as high soil moisture conditions. A
transposition scheme, will be reflected in
second approach that can capture this variability
RainyDay outputs. In this example, however,
would be to derive a distribution of antecedent
rainfall intensity from these storms will also
soil moisture from previous long-term (ideally
vary according to the underlying topography.
continuous multidecadal) model simulations.
The current transposition scheme in RainyDay
Since there can be substantial variation in how
cannot explicitly account for this variation,
soil moisture is represented in different hazard
which is likely to be a serious constraint in some
models, the same model should be used for
regions.
43 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
these long-term simulations and for the hazard then applied to the output rainfall scenarios
scenario modeling. RainyDay offers an via a normalization procedure that assumes
alternative option, however, in which initial soil that the supplied distribution corresponds to
moisture can be “spun up” within the hazard the annual maximum t-hour rainfall intensity
model to represent seasonally realistic initial for a single rainfall grid cell. Rainfall space-
conditions without the need for long-term time structure is still derived from the remote
simulations. sensing data. It should be noted, however,
The spin-up procedure is described for a that when the resolution of the input remote
single rainfall scenario. The month of sensing dataset is coarse relative to the
occurrence of the rainfall scenario is identified spatial coverage of the rainfall measurement
based on the “parent storm” that created it. Then device upon which the parametric
RainyDay identifies the set of X-day periods distribution is based (for example, the
(where X is a user-defined spin-up period) 16e625 km2 footprint of many satellite
preceding all parent storms that occur within a rainfall datasets relative to the 0.1 m2
user-defined number of months from the date of sampling area of a single rain gage), this
occurrence of the parent storm. One of the X- approach may be problematic. This
day periods is randomly selected and prepended procedure is also problematic in regions
to the rainfall scenario. This scheme helps to where such parametric rainfall distributions
ensure that spin-up conditions are reasonable for might be the synthesis of “mixture
the given season. It also helps ensure that spin- distributions” of distinct storm types in
up conditions have realistic temporal which rainfall intensity is intrinsically linked
correlations when pre-pended to the rainfall to rainfall space-time structure (e.g. Smith et
scenario (for example, if there is a historical al., 2011), since RainyDay does not
tendency for several days of moderate rain prior distinguish between different storm types.
to heavy storms but several days of heavy rain Currently only the three-parameter
prior to the main storm doesn't have historical generalized extreme value distribution
precedent, these conditions will be properly (Walshaw, 2013) is supported, though it
represented). It is important to note, however, would be straightforward to add additional
that the 10 to 20year records typical of rainfall options.
remote sensing records may not capture the full
variability of “true” initial conditions. 4. Rainfall and flood case studies
This pre-pending procedure creates rainfall
scenario output files that are of duration X þ t. 4.1. Rainfall IDF
The modeler can then assign an average initial
We used RainyDay to generate IDF
soil moisture condition to initialize each model
results for durations from 3 to 96 h and p e
run, and use the rainfall scenario as input. Soil
ranging from 0.5 to 103 for single rainfall grid
moisture within the model will then evolve over
cells in the vicinity of Iowa City, Iowa (Fig.
the spin-up period based on the rainfall (or lack
4) using rainfall data from Stage IV (Lin and
thereof), evapotranspiration, and other modeled
Mitchell, 2005) and version 7.0 of the
processes. This spin-up procedure has storage
Tropical Rainfall Measurement Mission
and computational costs since it can
Multi-Satellite Precipitation Analysis
substantially increase the size of the rainfall
(TMPA; Huffman et al., 2010). Stage IV is
scenario files generated by RainyDay and
available through the National Weather
increase the length of each hazard simulation.
Service (NWS) National Center for
The importance of these limitations depends on
Environmental Prediction and provides
the size of A, the resolution of the input rainfall
hourly, 4 km resolution rainfall estimates by
dataset, and the computational burden of the
merging data from the NWS Next-
hazard model. In Section 4.2, for example, X ¼
Generation Radar network (NEXRAD; Crum
6 days and t ¼ 4 days. This spin-up period is
and Alberty, 1993) with rain gages and, in
likely sufficient to spin up moisture in the upper some instances, satellite rainfall estimates.
soil layers, but not to fully establish baseflow or Stage IV has been extensively used in studies
deeper groundwater flow. The modeler should of extreme rainfall and flooding. All Stage IV
evaluate the tradeoffs between longer X and the analyses in this paper use data from 2002 to
associated storage and computational costs. 2014. TMPA merges passive microwave,
active radar, and infrared observations from
3.6. Parametric rainfall intensity multiple satellites to create a near-global
(±50 latitude) rainfall dataset with 3-hourly,
Instead of relying on the rainfall intensity 0.25 (approximately 25 km) resolution.
derived from a remote sensing input dataset, Unless otherwise noted, TMPA analyses this
a user might prefer to use a parametric
study use the final “research version” of
distribution to impose rainfall depths on the
TMPA from 1998 to 2014, which includes a
rainfall output scenarios. RainyDay supports
monthly rain gage-based bias correction. For
this option. The user can supply a t-hour
the results in Fig. 4, and most subsequent
rainfall depth distribution. This distribution is
analyses in this study, A’ is the rectangular
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
44
area shown in Fig. 3. A is set to a single rainfall pixel and each run

Fig. 4. Comparison of IDF curves from Atlas 14 and RainyDay using the Stage IV and TMPA rainfall datasets for 3-, 6-, 12-,
24-, 48-, and 96-h durations. Shaded areas for RainyDay estimates denote the ensemble spread. Bars on the NOAA Atlas 14
IDF estimates denote the 90% confidence intervals. Key RainyDay parameters: m ¼ 150 storms, A’ ¼ [40 to 44 N, 90 to 96 W].
A is a single rainfall pixel (approximately 16 km 2 for Stage IV, 625 km 2 for TMPA), N ¼ 100, Tmax ¼ 1000. Spatially-uniform
45 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
transposition and Poisson-based temporal resampling are selected. Stage IV period of record is 2002 e2014, TMPA period of
record is 1998e2014. Analyses are restricted to AprileNovember period.

consists of 100 ensemble members (i.e. N ¼ includes the 60-min, approximately 4 km

100). We compare these results with rain gage- version of Precipitation Estimation from
based IDFs from NOAA Atlas 14. Atlas 14 uses Remotely Sensed Information Using Artificial
L-moment regionalization techniques to Neural Networks Global Cloud Classification
combine observations from large number of rain System (PERSIANN-GCCS; Sorooshian et al.,
gages. The Atlas 14 analysis for Iowa uses 369 2000), which does not use gage-based bias
rain gages, many of which have records correction. The results in the top panel of Fig. 5
beginning in the late 19th century. show relatively good agreement between point-
The range of IDF durations shown in Fig. 4 scale NOAA Atlas 14 IDFs and single-pixel
emphasizes that RainyDay is flexible in terms of RainyDay-based IDFs for bias-corrected TMPA
the selection of duration t. RainyDay-based IDF and PERSIANN-GCCS, particularly
estimates using Stage IV exhibit slight considering the spatial sampling mismatch
systematic underestimation relative to Atlas 14 between the remote sensing data and Atlas 14
across a range of pe except for at the 96-h mentioned previously, while results based on
duration, where there is a close match. CMORPH Corrected show systematic
RainyDay-based IDF estimates using TMPA, underestimation.
meanwhile, closely match Atlas 14 for high p e The middle panel of Fig. 5 shows how
(except at the 3-h scale) and underestimates for RainyDay can be used to examine the effect of
low pe for all durations. Underestimation using rain gage-based bias correction on satellitebased
RainyDay may be attributed to the mismatch in IDF estimates. In the case of CMORPH, the
spatial resolution of the remote sensing data Raw version overestimates rainfall intensity at
(approximately 16 km2 for Stage IV and 625 all pe, while results for the Corrected version
km2 for TMPA) and the rain gages shows that the daily-scale bias correction
(approximately 0.1 m2). We have refrained from scheme leads to systematic underestimation.
using ARFs to convert the Atlas 14 point IDF The TMPA-RT also overestimates at all p e,
estimates into area-averaged IDFs due to though not as severely as CMORPH Raw, while
practical and conceptual limitations of the ARFs the monthly bias correction scheme used in the
(see Wright et al., 2014a). Both the slight final version of TMPA appears to offer superior
overestimation of rainfall depth from TMPA performance to the daily-scale routine used by
(relative to Stage IV) for more frequent events CMORPH Corrected. It is not immediately clear
and the underestimation for more rare events
using both datasets could potentially be
explained by conditional bias (i.e. bias that is
dependent on rain-rate; Ciach et al., 2000; see
Habib et al., 2009 for evidence of conditional
biases in TMPA). The convergence between
Stage IV-based RainyDay IDFs and Atlas 14
with increasing duration is consistent with both
conditional bias and spatial mismatch effects,
both of which diminish with increased temporal
aggregation. Thus, while not definitive, Fig. 4
does not clearly point to shortcomings
associated with the SST procedure itself.
In order to highlight both the potential for
IDF estimation and probabilistic hazard
assessment in data-sparse regions using
RainyDay with satellite remote sensing and
some of the associated challenges, we compare
24-h IDF curves generated using RainyDay for
various satellite rainfall datasets for the vicinity
of Iowa City (Fig. 5). This comparison includes
two versions of TMPA: the aforementioned final
version which includes monthly rain gagebased
bias correction, and TMPA-RT, which is
produced in near real-time, does not feature bias
correction, and runs from 2000 to 2014. It also
includes two versions of the 30-min resolution,
8 km Climate Prediction Center (CPC)
Morphing Technique (CMORPH; Joyce et al.,
2004): CMORPH Corrected, which uses a daily
rain gage-based bias correction scheme, and
CMORPH Raw, which does not. Finally, it
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
46
encouraging in the context of Integrated
Multi-satellitE Retrievals for GPM
(IMERG), a state-of-theart rainfall dataset
that combines various elements from TMPA,
CMORPH, and PERSIANN, including
TMPA's monthly bias correction (Huffman et
al., 2014). The IMERG dataset is not
analyzed in this study since the full
retrospective dataset is not yet available.
The bottom panel of Fig. 5 shows results
similar to those in the top panel, but with A
set to a 0.5 by 0.5 (approximately 2500 km2)
box centered on Iowa City. The results
demonstrate that RainyDay can easily
generate spatially aggregated rainfall IDF
curves. This is not achievable using standard
gage-based IDF curves without the use of
ARFs, which, as previously mentioned, have
been shown to have limitations. We omit
gage-based IDF curves from the bottom
panel of Fig. 5 for this reason.
The results shown in Figs. 4 and 5 have
implications for using RainyDay for IDF and
hazard estimation in data-sparse regions
using satellite remote sensing. First, there
can be substantial differences in extreme
rainfall estimates between satellite rainfall
datasets, and these differences will propagate
through to IDF estimates (and to
probabilistic hazard estimates, as will be
shown in Section 4.2). Furthermore, while
comparison with gage-based IDFs (when
available) can be used to understand these
differences, spatial sampling mismatches
complicate comparisons. Findings may not
be transferable across regions since the
Fig. 5. Comparison of IDF curves. Top: 24-h duration
IDF curves at the point scale from NOAA Atlas 14 and performance of satellite rainfall retrievals
at the pixel scale from RainyDay using TMPA Final, vary with region and latitude (e.g. Ebert et
PERSIANNGCCS, and CMORPH Corrected rainfall al., 2007) and because the quality of the
datasets. Middle: 24-h duration IDF curves at the point gage-based bias correction schemes that
scale from NOAA Atlas 14 and at the pixel scale from some of satellite datasets employ will vary
RainyDay using TMPART, TMPA Final, CMORPH
regionally with the density of rain gage
Raw, and CMORPH Corrected rainfall datasets.
Bottom: 24-h duration IDF curves at the 0.5 by 0.5 observations that are available.
scale from RainyDay using TMPA, PERSIANNGCCS,
and CMORPH Corrected rainfall datasets. Shaded areas 4.2. Flood frequency analysis
for RainyDay estimates denote ensemble spread. Bars
on the NOAA Atlas 14 IDF estimates denote the 90% In this section, we present flood peak
confidence intervals. Key RainyDay parameters: m ¼
frequency analyses for the 4400 km2 Turkey
150 storms, A’ ¼ [402 to 44 N, 90 to 96 W]. A is a single
River watershed in northeastern Iowa using
Stage IV rainfall pixel (approximately 625 km for
TMPA, 64 km2 for CMORPH, 16 km2 for PERSIANN),
rainfall scenarios from RainyDay as inputs to
N ¼ 100, Tmax ¼ 1000, t ¼ 24 h. Spatiallyuniform the Iowa Flood Center (IFC) Model, a
transposition and Poisson-based temporal resampling calibration-free distributed hydrologic
are selected. TMPA Final and CMORPH period of modeling framework designed primarily for
record is 1998e2014, TMPA RT period is 2000e2014, multi-scale flood research and applications
PERSIANN GCCS period of record is 2004e2014.
(see Cunha et al., 2012; Demir and
Analyses are restricted to AprileNovember period.
Krajewski, 2013; Mantilla and Gupta, 2005;
Moser et al., 2015; Small et al., 2013). Moser
et al. (2015) provides a detailed model
why this is the case, but relevant
description and Cunha et al. (2012)
considerations include the effect of rainfall
performed validation for flood events in
detection errors on bias correction (Tian et
al., 2007) and the challenge of correcting for Iowa, showing that performance of the IFC
conditional biases at short time scales Model is generally comparable to that of the
(Wright et al., 2014c). The apparent strong more heavily-calibrated operational SAC-
performance of the monthly bias correction is SMA flood forecast model (Burnash, 1995).
47 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
This study aims only to demonstrate basic bank,” meaning the flood magnitude is large
features of RainyDay for flood hazard enough to exceed the normal confines of the
analysis and so does not provide detailed river channel and spill into the floodplain.
discussion of the IFC Model or comparisons The left panel of Fig. 7 shows that, while
with other available platforms. For a there is modest scatter in the Stage IVbased
discussion of the value of calibration-free, flood peak simulations, there is no obvious
distributed hydrologic models for multi-scale systematic bias with watershed scale or event
flood modeling, the reader is directed to magnitude. The TMPA-based simulations in
Wright et al. (2014b) and, in particular, the right panel of Fig. 7 exhibit greater
Cunha et al. (2012). The full multi-scale scatter, generally poor performance, and
hazard estimation capabilities of SST and show some low bias across a range of event
RainyDay can, in principle, be harnessed magnitudes. While not exhaustive, the
using any distributed hydrologic or mass validation shown in Figs. 6 and 7 suggests
wasting model, while some of the that streamflow prediction accuracy in the
capabilities can be achieved through the use IFC model is driven primarily by the
of lumped models. accuracy of the input rainfall rather than by
A limited set of model hydrograph model structure, consistent with Cunha et al.
validation is provided in Fig. 6 for the 2008 (2012), and that the limited accuracy of
and 2014 AprileJuly periods, during which satellite rainfall inputs, even with gage-based
major flooding occurred throughout Iowa bias correction, can translate into poor model
(see Smith et al., 2013 for a detailed performance.
examination of the hydrometeorology of the We performed IFC model simulations using
2008 floods). The model is run both with RainyDay rainfall scenarios developed from
Stage IV and gage-corrected TMPA. both the Stage IV and final gagecorrected TMPA
Comparisons with U.S. Geological Survey rainfall datasets. For each rainfall dataset, we
(USGS) stream gage observations are ran ten ensemble members (i.e. N ¼ 10), each
provided at four locations, with upstream consisting of 500 rainfall scenarios (i.e. T max ¼
drainage areas ranging from 900 to 4000 500). At any point along the modeled river
km2. All hydrographs are normalized by the system, therefore, flood peak exceedance
median annual flood (pe ¼ 0.5), taken from probabilities as low as 0.002 (500-year return
the USGS StreamStats system period) could be directly derived from the IFC
(http://water.usgs.gov/osw/streamstats/) to Model predictions. The Stage IV and TMPA-
facilitate comparison across watershed based storm catalogs for the Turkey River
scales. Model performance varies from event include 150 storms, drawn from the
to event but there is no clear evidence of AprileNovember rainfall record (2002e2014 for
systematic bias in the streamflow predictions Stage IV, 1998e2014 for TMPA). A’ is an area
as a function of event magnitude or drainage covering most of Iowa, southwestern Wisconsin,
area. Predictions based on Stage IV are and southeastern Minnesota in the United
generally better than TMPA and several time States.
periods show serious problems with the t ¼ 96 h for all simulations in this section.
timing of TMPA-based simulations. In the Each simulation was initialized with a spatially
2008 flood season, for example, TMPA uniform initial soil moisture value found to be
incorrectly identifies the late April event as typical for the region. Rainfall from a
the largest for that year. seasonally-based six-day “spin-up” period was
We compare observed and simulated then prepended to each storm scenario as per
flood peaks for the 2008e2014 Section 3.5, for a total rainfall input time period
AprileNovember period (Fig. 7). All of ten days. Spatial variations in both soil
observed flood peaks that exceed 100 m 3 s1 moisture and river flow were therefore allowed
are extracted from the four USGS stream to develop in each simulation prior to the arrival
gaging records. Then the corresponding flood of the main storm. It should be noted that
peaks predicted by the IFC model are restricting the rainfall record to
extracted from simulated hydrographs based AprileNovember, in addition to the lack of
on Stage IV and TMPA rainfall (left panel snowfall functionality in RainyDay and
and right panels of Fig. 7, respectively). To snowpack functionality in the IFC model, means
allow for modest errors in flood peak timing, that snowmelt-driven flooding is not considered
a window of 48 h centered around the in the analyses. In Iowa, snowmelt is generally a
observed peak is used to identify the minor though non-negligible flood mechanism.
corresponding simulated peaks. All peaks in We do not evaluate the accuracy of spin-up soil
Fig. 7 are normalized by the median annual moisture and river flow, and in fact such
flood for to facilitate comparison across evaluation is relatively challenging due to the
basin scales. As a rule of thumb, peaks below paucity of long-term soil moisture observation
the median annual flood can be considered records that would be needed. As discussed in
“within bank,” while peaks above the median Section 3.2, SST and RainyDay facilitates
annual flood can be considered “out-of- “decoupling” of discharge pe from rainfall pe.
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
48
Though not demonstrated explicitly, the effect km2), and above French Hollow (2338 km2),
of this decoupling is embedded in the while 63 years are reported for Volga River at
RainyDay-based frequency analyses in this Littleport (901 km2) and 45 years for Turkey
section, in that the combination of stochastic River at Spillville (458 km2). It should be noted
spun-up initial conditions and rainfall space- that these record lengths refer to “historic record
time structures may produce discharge pe that length” described in Section V.B.10 of Bulletin
are different from the p e of the input rainfall 17B and do not correspond to length of the
scenarios. USGS annual maxima streamflow timeseries
RainyDay-based frequency analysis results available on the USGS National Water
are shown for five subwatersheds of the Turkey Information System
River, ranging in drainage area from (http://nwis.waterdata.usgs.gov/nwis), which are
approximately 460 to 4000 km2 (Fig. 8). Also much shorter. All available USGS streamflow
included in Fig. 8 are two types of frequency observations for the five sites are also shown,
analyses derived from USGS stream gage where pe is estimated using the Cunnane plotting
observations and taken from Eash et al. (2013) position (Cunnane, 1978; pie ¼ [i - 0.4]/ [X þ
and retrieved from

Fig. 6. IFC model validation for 2008 and 2014 flood seasons (left and right panels, respectively) at four USGS stream gaging sites. Hydrographs are normalized by the median
annual flood, which is indicated by dashed horizontal lines. 0.2], where i is the rank of the observation and
X is the number of observations). Other
common plotting position formulae produce
the USGS StreamStats system. The first is similar results (not shown) and do not alter
developed using standardized methods subsequent findings.
described in Bulletin 17B (Interagency For all five locations shown in Fig. 8, the
Advisory Committee on Water Data , 1982) SST-based peak discharge estimates using
using the log-Pearson Type III distribution TMPA are higher than those using Stage IV for
(henceforth referred to as the LP3 distribution) pe < 0.01, generally converging toward the Stage
with a regionalized skew coefficient. The IV estimates as pe decreases, and in some cases
second is based on regional regression yielding lower estimates for p e less than about
equations that consider drainage basin area and 0.005. This is consistent with the rainfall IDF
shape as well as soil properties. Eash et al. results from RainyDay shown in Fig. 4 and are
(2013) report 121 years of data for Turkey River suggestive of conditional biases in the TMPA
at Garber (4002 km2), near Eldorado (1660
49 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54

dataset. This in indeed confirmed in Fig. 9, It should be noted that with the exception of
which shows watershed-specific IDF curves for Turkey River at Garber, the differences between
the entire Turkey River watershed from the RainyDay-based frequency analyses are
RainyDay using TMPA and Stage IV. The roughly similar in magnitude to the differences
USGS streamflow observations shown in Fig. 8 between the two USGS approaches. This, along
agree reasonably well with the Stage IV-based with the underestimation shown by USGS
estimates for pe > 0.5, with the exception of the frequency analyses relative to the USGS peak
smallest subwatershed, Turkey River at discharge observations at several sites, suggests
Spillville, where Stage IV produces low peak that the RainyDay-based frequency analyses
estimates. For pe < 0.5, there is a lack of should not be dismissed out of hand as being
consistency. For example, Turkey River at too high for low p e. In fact, as the next example
Garber shows higher estimates from Stage IV shows, there is observational evidence that
than the streamflow observations, while the supports the validity of the RainyDay-based
reverse is true for Turkey River at French results in light of possible nonstationarity in
Hollow and near Eldorado. Deviations from the flooding. It should be noted that discharge-
USGS observations do not show a systematic based frequency analyses, even in stationary
scale dependency. situations with long records, are not necessarily
Both RainyDay-based frequency analyses superior to hydrologic modeling methods.
and the USGS streamflow observations are Analyses by Smith et al. (2013) suggest that
peak discharge measurement errors may be
generally higher than the USGS frequency
analyses for pe less than about 0.2. One substantial for a recent major flood event in
exception is the set of USGS observations for Iowa. The propagation of discharge
Turkey River at Spillville, which is lower measurement errors through frequency analysis
than both the RainyDay estimates and the is poorly understood (e.g., Petersen-Øverleir
regional regression but generally consistent and Reitan, 2009; Petersen-Øverleir, 2004;
with the Bulletin 17B analysis. The regional Potter and Walker, 1985). Rogger et al. (2012)
regression results for Turkey River at reported significant differences between two
Spillville are greater than the USGS commonly-used flood frequency analysis
regionalized LP3 estimates, while the reverse approaches for ten small alpine watersheds in
is true for the four larger subwatersheds. Austria, one based on a stream gage-based
Interestingly, some of the USGS observations statistical method and the other on design storm
fall outside of the 90% confidence intervals methods combined with a hydrologic model.
of the LP3 analyses for Turkey River near The latter method produced higher discharge
Eldorado, Volga River at Littleport, and values than the former, and the authors discuss
Turkey River at Garber. In the case of the possible explanations and deficiencies in both
latter station, the five most intense floods are approaches, concluding that hydrologic
near or above the upper 95% confidence modeling using rainfall inputs can produce
bound, a finding that is explored in more superior results in certain situations.
detail in the following paragraphs. Of the five USGS stream gage locations
shown in Fig. 8, only the gage at Garber, Iowa
has a long (82-year), unbroken annual peak

Fig. 7. Peak discharge validation for 2008e2014 AprileNovember period at four USGS stream gaging stations. All events for which the USGS observations exceeded 100 m 3 s1 are shown, and peak
discharges are normalized by the median annual flood. Simulated peaks using the IFC model with Stage IV (TMPA Final) rainfall inputs are compared with USGS observed peaks in the left (right)
panel. Straight black lines indicate 1:1 correspondence, while dashed lines indicate the envelope within which the modeled values are within 50% of observed. Grey boxes in the lower lefthand
corners of each panel highlight all events less than the median annual flood.
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
50
discharge record. We use this record to better significant (p-value < 0.05) downward trend was
understand the discrepancies between the found. In contrast, using ordinary least squares,
RainyDay-based results and the USGS an insignificant upward trend is found over the
frequency analyses from Eash et al. (2013), same period. Thus when the influence of the
and in particular to contrast the methods in most extreme values is minimized through
the context of potential nonstationarity in nonparametric methods, there is a tendency
flood processes. The top panel of Fig. 10 toward smaller flood peaks over time that is not
shows the same results as Fig. 8 for Turkey evident with parametric methods, which are
River at Garber, except that the USGS more sensitive to the recent extremes.
observations have been divided into two Fig. 10 shows that the period of apparent
groups: one for all peaks occurring from elevated flood activity is well captured by
1933 to 1989, and the second for all peaks RainyDay, while the preceding period is not,
occurring from 1990 to 2014. The plotting presumably because the IFC model reflects
position-based pe is recalculated for each recent land use changes and because the input
group. The 1933e1989 group shows higher rainfall data are relatively recent. In general,
discharges than either RainyDay Stage IV or whether or not this constitutes a strength or
USGS discharges for pe > 0.5, and lower limitation of RainyDay depends on the
discharges for pe less than about 0.2. The underlying causation of nonstationary flood
1990e2014 group, meanwhile, matches activity. If nonstationarity results from a
closely with the RainyDay-based frequency climate-driven secular trend in extreme rainfall,
analyses with Stage IV. then the results from RainyDay using relatively
Taken together, this suggests a regime shift short and recent rainfall remote sensing records
toward more extreme flooding since 1990 should be understood as more “up-to-date”
accompanied by a reduction in the magnitude of estimates of flood frequency compared to
more average floods. Evidence of this regime approaches, such as the USGS analyses, that use
shift can be seen in the annual peak time series longer stream gage or rain gage records. The
in the bottom panel of Fig.10. We fit a same is true if there is a secular trend in flooding
nonparametric linear regression to the due to urbanization or other land-use changes,
1933e2014 time series using the Theil-Sen so long as these changes are properly
estimator (Sen, 1968) and a statistically incorporated into the hydrologic
51 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54

Fig. 8. Peak discharge analyses using RainyDay with Stage IV and TMPA rainfall remote sensing data and the IFC Model,
compared against USGS stream gage-based analyses for five subwatersheds of the Turkey River in northeastern Iowa. Shaded
areas for RainyDay estimates denote the ensemble spread. Bars on the USGS Bulletin 17B estimates denote the 90%
confidence intervals. Confidence intervals are not available for the USGS regional regression. Key RainyDay parameters: m ¼
150 storms, A’ ¼ [40 to 44 N, 90 to 96 W], A is the watershed upstream of the USGS streamgage at Garber, IA, N ¼ 10, Tmax ¼
500, t ¼ 96 h. Spatially-uniform transposition and Poisson-based temporal resampling are selected. Stage IV period of record
is 2002e2014, TMPA period of record is 1998e2014. RainyDay Analyses are restricted to AprileNovember period.
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
52
Specific topics that are examined include the
optional non-uniform spatial transposition
(Section 3.3), empirically-based temporal
resampling (Section 3.4) and the size of the
transposition domain A’. In all cases, the
specific results pertain to the Iowa study area
and may not be entirely generalizable to
other locations. The intention is to
demonstrate some important concepts and
pitfalls associated with RainyDay, and
provide a possible framework for assessing
performance in different locations and
applications.
A common critique of coupling SST with
rainfall remote sensing datasets is that such
data records are relatively short
(approximately 10e20 years at time of
writing) and thus may not contain sufficient
numbers of extreme events at the regional
scale to leverage “space-for-time
substitution” to accurately recreate the
properties of rare rainfall events. To examine
this critique, we turn to a longer dataset:
Fig. 9. IDF analyses for Turkey River using RainyDay CPC-Unified, a daily rain gage-based
with Stage IV and TMPA rainfall remote sensing data.
gridded rainfall dataset that has a spatial
Shaded areas for RainyDay estimates denote the
ensemble
resolution of 0.25 over the

is the 4400 kmspread. Key RainyDay parameters: 2

watershed upstream of the conm ¼ 150 storms,flAuence

with the Mississippi River.’ ¼ [40 to 44 N, 90 to 96 W],
A

N ¼ 100, Tmax ¼ 500, t ¼ 96 h, and spatially-uniform

transposition and Poisson-based temporal resampling
are selected. Stage IV period of record is 2002e2014,
TMPA period of record is 1998e2014. Analyses are
restricted to AprileNovember period.

model. In the case of Iowa, flooding has been

shown to be affected by land-use change
(Villarini and Strong, 2014) and by climate
change (Mallakpour and Villarini, 2015). If,
on the other hand, flood or rainfall
nonstationarity has a periodic structure due
to a slowlyvarying climate mode, then the
results from SST may adequately reflect the
true flood frequency only for the phase of the
mode that overlaps with the remote sensing
record. It should also be recognized that a
period of higher or lower flood activity at a
particular location could result from pure
randomness (i.e. in absence of both secular
and periodic trends). SST should be
relatively robust to this possibility through
the sampling storms from a larger region.

4.3. SST sensitivity to record length and

user-defined parameters

In this section, we examine the sensitivity

of SST to the length of the input dataset and
to the different user-defined parameters and
options introduced in Sections 2 and 3.
53 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
Fig. 10. Top paneldfour peak discharge analyses for the full 67-year dataset (Fig. 12). The boxplots
location of the USGS stream gage at Garber, IA: RainyDay show that most deviations in the n-year IDF
with Stage IV and TMPA rainfall and USGS frequency
ensemble means, minima, and maxima are less
analyses using regional regression relationships and
Bulletin 17B methods. Shaded areas for RainyDay
than 10% and that the vast majority are less than
estimates denote the ensemble spread. Bars for the Bulletin 20% for any given p e. For most pe, there are
17Bbased analysis denote the 90% confidence intervals. substantial reductions in deviation when the
Confidence intervals are not available for the USGS records increase in length from n ¼ 10 to n ¼ 20
regional regression. Bottom paneldannual peak discharge years. The reductions in deviation are less when
time series for 1932e2014 for the Garber gage. Linear the record length increases beyond 20 years.
trend lines in the bottom panel use non-parametric Thiel-
Unless the intensity of the rainfall inputs is
Sen regression (Sen, 1968) and ordinary least squares
(OLS). Key RainyDay parameters: m ¼ 150 storms, A’ ¼
perturbed stochastically, SST-based frequency
[40 to 44 N, 90 to 96 W], A is the watershed upstream of the analyses have an upper bound that corresponds
USGS streamgage at Garber, IA, N ¼ 10, Tmax¼ 500, t ¼ 96 to the most intense rainstorm in the storm
h. Spatially-uniform transposition and Poisson-based catalog transposed in such a way that rainfall
temporal resampling are selected. Stage IV period of record over A is maximized. The lack of positive
is 2002e2014, TMPA period of record is 1998e2014. deviations in the ensemble maxima at p e ¼ 103
RainyDay Analyses are restricted to AprileNovember
(middle panel of Fig. 12; also in certain
period.
realizations shown in Fig. 11) show where the
SST procedure “encounters” this upper limit.
conterminous United States (Chen et al., 2008; While the results in this section are by no
Xie et al., 2007). Though the spatial and means exhaustive and the conclusions are
temporal resolution of CPC-Unified is generally specific to the Iowa study region and could vary
insufficient for fine-scale flood modeling, its in different physiographic regions, they
long record (1948 to present) makes it ideal for nonetheless suggest that concerns over the use
evaluating the sensitivity of SST-based IDF of relatively short rainfall remote sensing
estimates to record length. We examined several records with SST may be overstated and that
stationarity measures over the transposition such datasets, many of which are approaching
domain A’ (which, as in Section 4.1, roughly 20 years in length, should provide relatively
encompasses the state of Iowa), including the robust estimates that will improve as these
average number of storm counts per year and datasets continue to grow in length. This
the mean, median, and standard deviation of emphasizes the fact that rainfall events that
storm rainfall depth. None of these measures would be considered rare from the perspective
revealed significant temporal trends (results not of a single location or watershed can occur
shown). This may contradict the apparent flood relatively frequently from a regional
perspective. This is qualitatively consistent with
nonstationarity in the Turkey River watershed
discussed in Section 4.2, or may point to land- the findings of Troutman and Karlinger (2003),
use change as the predominant source of non- who estimate that a flood with pe > 102 occurs on
stationarity in Turkey River, but rigorous average every 4.5 years at least one of the 193
examination is beyond the scope of this paper. USGS stream gage sites in their Puget Sound
We use a bootstrapping approach to examine study region.
variability in IDF estimates derived from the A potentially important issue related to short
CPC-Unified data using RainyDay and how this data records in SST, previously mentioned in
variability evolves as the length of the record Section 3.3, can arise if, instead of assuming
increases. All IDF estimates in this section are that the probability of storm occurrence is
for 1-day rainfall over averaged over a 0.5 by uniform across the transposition domain, non-
0.5 box. We generate n-year long input rainfall uniform spatial transposition is used instead
datasets by randomly selecting n years of CPC- (such as the approach used in Wilson and
Unified data without replacement from the FoufoulaGeorgiou, 1990 or the optional scheme
in RainyDay described in Section 3.3). Using
1948e2014 period. Each of these datasets is then
the bootstrapping approach with the CPCUnified
used as the basis for a single run of RainyDay
dataset described above, visual inspection of
with 100 ensemble members and with m ¼ 10n
storm probability-of-occurrence maps such as
(leading to l¼ 10 storms per year). We repeat
the one shown in Fig. 3 reveal that there can be
this procedure to create 25 datasets for each substantial variations in the spatial distribution
value of n ¼ 10, 20, 30, 40, 50 years. of historical storms when rainfall records are
Greater variability is evident in the ensemble short (results not shown). These variations tend
mean and spread of the IDF estimates using 10 to diminish as the length of record increases, as
years of CPC-Unified data than using 20 years, do their impacts on IDF estimates. More
while change in variability is generally small variation is evident in the median IDFs from
between runs using 20 years and 30 years of independent runs of RainyDay, for example,
data (Fig.11). We also examined the variability using non-uniform transposition than using
of relative deviations in the ensemble IDF uniform transposition when n ¼ 10 years
means, minima, and maxima from RainyDay (Fig.13, left panels). When using non-uniform
between the n-year runs and IDFs based on the transposition, variability diminishes when n ¼
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
54
20 years and a systematic increase in rainfall 3.4. There do not appear to be substantial
intensity for pe > 0.02, relative to the uniform systematic differences between the results
transposition case, emerges from RainyDay using these two schemes
with 10-year records (Fig. 14, left panels),
but like Fig. 13, when 20-year records are
used, there is a tendency toward higher
rainfall estimates for pe > 0.02. Results may
differ in other regions where temporal
clustering of storms is very strong or where
rainstorms are very infrequent. It is
recommended that the modeler assess
clustering using an independent long-term
rainfall data source if available, in addition to
assessing sensitivity to this option in
RainyDay. As with the spatial transposition
schemes, the choice of temporal resampling
scheme does

Fig. 11. The effect of the rainfall record length on daily

rainfall IDF curves estimated using RainyDay with the
CPC-Unified daily rainfall over Iowa, United States.
Each panel shows the ensemble mean (solid lines) for
ten independent runs of RainyDay. The shaded areas
denote the maximum spread across the ten runs. Key
RainyDay parameters: m ¼ 10n storms (where n varies
by specified record length), A’ ¼ [40 to 44 N, 90 to 96
W], A is a 0.5 by 0.5 box, N ¼ 100, Tmax ¼ 1000, t ¼ 1
day, spatiallyuniform transposition and Poisson-based
temporal resampling. Analyses are restricted to
AprileNovember period.

(Fig. 13, right panels). Given these results,

we recommend that the assumption of
uniform transposition be used in the absence
of strong physically-based reasoning and
observational support for non-uniform
transposition. It is possible, however, that
this explains the IDF underestimation by
RainyDay with Stage IV for high p e relative
to Atlas 14 shown in Fig. 4, where uniform
spatial transposition was used.
As mentioned previously, RainyDay
supports either the Poissonbased resampling
that has traditionally been used with SST, or
an empirical scheme described in Section
55 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
Fig. 12. The effect of rainfall record length on variability in daily rainfall IDF estimated using RainyDay with CPC-Uni fied data over Iowa, United States for 0.1, 0.05, 0.01, 0.005, and 0.001
exceedance probabilities. Each boxplot shows the variability of a particular rainfall quantity at a given exceedance probability across 25 independent runs of RainyDay. Speci fic rainfall quantities
shown are the ensemble mean (top panel), ensemble maximum (middle panel), and ensemble minimum (bottom panel). Boxes denote the lower and upper quartiles and whiskers indicate the extent of
the ± 1.5 interquartile range. Key RainyDay parameters: m ¼ 10n storms (where n varies by specified record length), A’ ¼ [40 to 44 N, 90 to 96 W], A is a 0.5 by 0.5 box, N ¼ 100, Tmax ¼ 1000, t ¼ 1
day, spatially-uniform transposition and Poisson-based temporal resampling. Analyses are restricted to

AprileNovember period.

not appear to have a substantial impact on

low pe estimates.
We also examine the sensitivity of
RainyDay results to the size of A’ (Fig. 15).
To do so, we run RainyDay for various
square domains ranging from 1 by 1 up to 10
by 10, while holding A fixed at a 0.5 by 0.5
box. Then the evolution of rainfall intensity
is examined for a range of pe as a function of
A’. This is repeated for a several different
record lengths and for two values of l.
Interestingly, while there is a general
tendency for intensity estimates to stabilize
as A0 grows, the behavior is not asymptotic
(though roughly so for n ¼ 68 years). The
high exceedance probability estimates (p e ¼
0.5) tend to be stable over a large range of A 0
and then decrease for very large values, due
to the tendency for synthetic years to be
created in which no storm is transposed
directly over A. This is the root of potential
low biases mentioned in Step 2 of the SST
procedure described in Section 2. However,
Fig. 15 demonstrates that this tendency for a
decrease in intensity estimates for large A 0
extends to smaller pe values as well, and that
there is a critical value of A0 at which the
estimated intensity is roughly maximized.
This critical value appears to vary more by
the particular period of record than by the
length of record. For example, the 20-year
record from 1976 to 1995 yielded a critical
value of A0 that is lower than the critical
value from 20-year record from 1996 to
2015. This points to the fact that the
existence and number of major storms within
A’ during the record period is very important
(Wright et al., 2014b reached the same
conclusion through different means).
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
56
These results also indicate that increasing by ground-based radar or satellite-based sensors.
m (thus increasing l) can mitigate the This structure can play an important role in
reduction in estimated intensity for values of landslides and floods because the variability in
A0 larger than the critical value. This result the concentration and intermittency of extreme
suggests that, if the modeler is interested in rainfall in space and time can lead to a complex
hazard estimation across a range of p e, she and diverse spectrum of hazard response. This
should choose a relatively large m. A structure is difficult to measure using rain gages
diagnostic framework within the RainyDay due to the high gage densities and sampling
software to identify this critical value of A’ rates required, and so rain gage-based methods
for a given value of m (or vice versa) for for analysis of rainfall-driven hazards, such as
different pe would be useful but does not IDF relations and design storm methods,
currently exist. typically neglect this higher-order variability.
The reader is directed to Wright et al. (2014b)
5. Discussion and conclusions for a deeper examination of this feature of SST
in the context of urban flood
We introduce RainyDay, a Python-based hazards.
platform that couples rainfall remote sensing The second important feature of RainyDay
data with a technique known as Stochastic is that, because of the near-global coverage of
Storm Transposition (SST) that effectively satellite rainfall datasets, it is possible to
“lengthens” the extreme rainfall record through generate realistic representations of extreme
temporal resampling and spatial transposition of rainfall in remote or poorly-instrumented
observed rainstorms. It produces probabilistic regions where rain gage or stream gage records
extreme rainfall scenarios that include realistic are lacking. Such regions are common even in
estimates of rainfall duration, intensity, and wealthy nations and are ubiquitous in
space-time structure that can be used for developing countries, many of which are
probabilistic flood and landslide hazard and risk characterized by rapidly-growing exposure to
assessment at a wide range of scales. rainfall-driven hazards due to urbanization and
The SST technique implemented in climate change. The authors are not aware of
RainyDay has two important features that other approaches that offer the ability to
distinguish it from IDF and design storm generate realistic rainfall inputs for probabilistic
methods for describing the relationships hazard modeling nearly anywhere on the globe
between the intensity, duration, and structure of with minimal computational effort.
extreme rainfall. First, it leverages the detailed Despite the advantages that SST and
picture of rainfall space-time structure offered RainyDay offer over other methods for
assessing rainfall-driven hazards (e.g. design

Fig. 13. The effect of the spatial transposition scheme on daily rainfall IDF curves estimated using RainyDay with the CPC-Uni fied daily rainfall over Iowa, United States. Each panel shows the
ensemble mean (solid lines) for ten independent runs of RainyDay. The shaded areas denote the maximum spread across the ten runs. The speci fic years that comprise the input dataset vary. Key
RainyDay parameters: m ¼ 10n storms (where n varies by specified record length), A’ ¼ [40 to 44 N, 90 to 96 W], A is a 0.5 by 0.5 box, N ¼ 100, Tmax ¼ 1000, t ¼ 1 day. Poisson-based temporal
resampling is used. Analyses are restricted to AprileNovember period.
57 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
storms, discharge frequency analysis), a number landslide forecasting and monitoring, which
of issues remain. Perhaps the biggest limitation require accurate rainfall estimates in real-time.
to coupling SST with rainfall remote sensing is These issues may be somewhat less critical in
the uncertain accuracy of the input rainfall data. the SST framework or in long-term hazard
Significant efforts have been made to better assessment more generally, since the rainfall
understand and minimize the errors in remote estimates need only have fidelity in the
sensing estimates of rainfall, both from satellites statistical sense. SST will be somewhat robust to
(e.g. Petty and Krajewksi,1996; Tian and Peters- random errors in rainfall data, as the
Lidard, 2007; Tian et al., 2009) and from underestimation of rainfall intensity from some
ground-based radar (e.g. Villarini and storms in the storm catalog can be compensated
Krajewski, 2010). Such studies demonstrate that by overestimation of rainfall intensity from
remote sensing estimates can vary significantly others. In contrast, SST is not robust to
from reference observations in terms of rainfall systematic rainfall biases, as demonstrated in
intensity and differentiation between rainy and several examples in this paper. IMERG,
non-rainy areas, with important implications for NASA's newest satellite multi-sensor dataset,
hazard applications. In the case of satellite- will feature improved accuracy and relatively
based rainfall estimates, heterogeneities in the high resolution (0.1, 30-min), thus addressing
underlying land or water surfaces can be some of these issues once the full retrospective
difficult to distinguish from variations in cloud dataset becomes available.
and rainfall properties (e.g. Ferraro et al., 2013), In the case of flood hazard modeling
while both ground-based radar and space-based using SST, a practical upper limit on the size
sensors tend to suffer in mountainous areas due of the area of interest A can arise. The sizes
to dramatic variations in rainfall physical of A and A0 can be limited due to the
properties over short time and length scales. challenges posed by transposition in the
Furthermore, the spatial and temporal resolution presence of complex terrain features.
of remote sensing estimates, particularly from Furthermore, as A becomes larger, the
satellites, can be too coarse for modeling at very rainfall duration t needed to properly model
small scales, especially in urban areas and hazard response becomes longer. While
fastresponding mountain or desert catchments RainyDay does not restrict the choice of t,
where surface runoff generation from intense, practical limitations exist. In large
short-duration rainfall on sub-hourly, sub- watersheds, floods are usually the result of
kilometer scales can be a key driver of hazards. specific space-time arrangements of multiple
The uncertainties associated with rainfall remote distinct storm systems over the span of
sensing data pose serious challenges for flood or perhaps a week to several months, often

Fig. 14. The effect of the temporal resampling scheme on daily rainfall IDF curves estimated using RainyDay with the CPC-Uni fied daily rainfall over Iowa, United States. Each panel shows the
ensemble mean (solid lines) for ten independent runs of RainyDay. The shaded areas denote the maximum spread across the ten runs. The speci fic years that comprise the input dataset vary. Key
RainyDay parameters: m ¼ 10n storms (where n varies by specified record length), A’ ¼ [40 to 44 N, 90 to 96 W], A is a 0.5 by 0.5 box, N ¼ 100, Tmax ¼ 1000, t ¼ 1 day. Spatially uniform transposition
is used. Analyses are restricted to AprileNovember period.
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
58
linked to persistent large-scale atmospheric simple, while IDF databases and design storm
phenomena. One could specify a long t (a methods are generally updated through slow and
month, for example) in RainyDay to costly procedures (Y. Zhang, personal
“capture” multiple storm systems within a communication, May 14, 2015).
single storm catalog entry. Such long t, As highlighted in Section 4.2, SST and
however, means there could only be RainyDay have important features in the context
relatively few entries in the storm catalog, of nonstationary hazards. Extreme rainfall
given the limited record length of the input scenarios from RainyDay are generally based on
dataset. Such an approach would be more recent
constrained by the few space-time
configurations of these storm systems that
were observed, while many other non-
observed configurations are hypothetically
possible. A tradeoff thus emerges as A (and
thus t) increases relative to the area of the
transposition domain A’. If A is a large
fraction of A0, then there is little opportunity
to leverage the “space-for-time” substitution
that is at the core of the SST approach. If the
user instead decides to increase the size of
A’, she must ensure that this transposition is
performed in a realistic manner. This
effectively precludes modeling of regions
that approach continental scales. The
maximum scale at which SST can be feasibly
used is an open question with no simple
answer. It should be noted that IDF and
design storm methods face similar and
perhaps even more acute limitations in terms
of an upper area limit, though for different
reasons (e.g. conceptual and practical
shortcomings of point-based IDF, temporal
rainfall distributions, and area reduction
factors).
As mentioned in Section 4.3, a common
critique of the methodology presented in this
study is that the relatively short remote sensing
records may not contain enough truly extreme
rainfall events. Sensitivity to record length is
not unique to SST; frequency estimates of rare
hazards will be driven by the largest several
events in the historical record, regardless of the
chosen analysis technique. The results in
Section 4.3 demonstrate that this concern may
be somewhat exaggerated in the case of SST
since very extreme rainfall events that are
considered rare from a local viewpoint can
occur much more frequently when viewed
regionally. Like more commonly-used
regionalization techniques, SST leverages this
fact to improve hazard analysis. As the rainfall
remote sensing record grows, the robustness of
estimates produced by SST and RainyDay
should increase as additional extreme storms are
observed (and as their accuracy improves due to
technological advances). Estimates of rainfall
intensity will improve more per unit of
additional observational period using SST than
using pointbased techniques due to SST's
regional nature, while new patterns of rainfall
space-time structure will add to the realism of
SST-based flood and landslide hazard estimates
since a broader spectrum of hazard outcomes
will be possible. RainyDay makes such updating
59 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54

Fig.15. The effect of the size of the transposition domain A 0 on daily rainfall IDF curves estimated using RainyDay with the
CPC-Unified daily rainfall over Iowa, United States using a range of record lengths. Key RainyDay parameters: m ¼ 10n
storms (where n varies by specified record length), A0 is a square of varying size, A is a 0.5 by 0.5 box, N ¼ 100, Tmax ¼ 1000, t
¼ 1 day, spatially-uniform transposition and Poisson-based temporal resampling. Analyses are restricted to April eNovember
period.

observations than existing rain gage or as Atlas 14 IDF relations, which contain
stream gage-based frequency analyses such older records that may not be representative
 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
60
of the current state of the climate. In this Chen, M., Shi, W., Xie, P., Silva, V.B.S., Kousky, V.E.,
Wayne Higgins, R., Janowiak, J.E., 2008.
respect, hazard analyses based on RainyDay Assessing objective techniques for gauge-based
can be understood as relatively current analyses of global daily precipitation. J. Geophys.
“snapshots” based on recent climate. The Res. Atmos. 113.
Ciach, G.J., Morrissey, M.L., Krajewski, W.F., 2000.
performance of RainyDay is very dependent Conditional bias in radar rainfall estimation. J.
on major storms having occurred one or Appl. Meteor 39, 1941e1946.
more times within the transposition domain, Crum, T.D., Alberty, R.L., 1993. The WSR-88D and the
WSR-88D operational support facility. Bull. Am.
however, meaning that spatial transposition Meteorol. Soc. 74, 1669e1687.
is not a perfect remedy for short data records. Cunha, L.K., Krajewski, W.F., Mantilla, R., Cunha, L.,
Furthermore, if the rainfall remote sensing 2011. A framework for flood risk assessment under
nonstationary conditions or in the absence of
record deviates significantly from the true
historical data. J. Flood Risk Manag. 4, 3e22.
longterm properties of extreme rainfall over Cunha, L.K., Mandapaka, P.V., Krajewski, W.F.,
the region of interest due to random chance, Mantilla, R., Bradley, A.A., 2012. Impact of radar-
decadal-scale climate variability, or rainfall error structure on estimated flood
magnitude across scales: an investigation based on
systematic measurement bias, then caution a parsimonious distributed hydrological model.
must be taken when using RainyDay. It can Water Resour. Res. 48.
be challenging in practice to diagnose such Cunnane, C., 1978. Unbiased plotting positions d a
review. J. Hydrol. 37, 205e222. Demir, I., Krajewski,
nonstationarities and biases due to a lack of W.F., 2013. Towards an integrated Flood Information
long-term independent observational data, System: centralized data access, analysis, and
particularly in remote or underdeveloped visualization. Environ. Model. Softw. 50, 77e84.
Eash, D.A., Barnes, K.K., Veilleux, A.G., 2013.
regions. Meanwhile, as discussed in Wright Methods for Estimating Annual Exceedance-
et al. (2014b), combining SST (or other probability Discharges for Streams in Iowa, Based
rainfall-based approaches, e.g. Cunha et al., on Data through Water Year 2010: U.S. Geological
Survey Scientific Investigations Report
2011) with a distributed hazard model allows
2013e5086.
the analyst to incorporate changes in land use Ebert, E.E., Janowiak, J.E., Kidd, C., 2007.
and land cover into nonstationary hazard Comparison of near-real-time precipitation
estimates. estimates from satellite observations and
numerical models. Bull. Am. Meteorol.
Soc. 88, 47e64.
Acknowledgments England, J.F., Julien, P.Y., Velleux, M.L., 2014. Physically-
based extreme flood frequency with stochastic storm
transposition and paleoflood data on large watersheds.
This work was made possible through the J. Hydrol. 510, 228e245.
fellowship support of the NASA Ferraro, R.R., Peters-Lidard, C.D., Hernandez, C., Turk,
F.J., Aires, F., Prigent, C., Lin, X., Boukabara, S.-A.,
Postdoctoral Program, administered by Oak
Furuzawa, F.A., Gopalan, K., Harrison, K.W., Karbou,
Ridge Associated Universities, Oak Ridge, F., Li, L., Liu, C., Masunaga, H., Moy, L., Ringerud,
Tennessee. We also acknowledge the support S., Skofronick-Jackson, G.M., Tian, Y., Wang, N.-Y.,
2013. An evaluation of microwave land surface
of the University of Wisconsin-Madison, the
Emissivities over the continental United States to
Wisconsin Alumni Research Foundation, and benefit GPM-Era precipitation algorithms. IEEE Trans.
the Iowa Flood Center and the Geosci. Remote Sens. 51, 378e398.
University of Iowa. We would also like to Fontaine, T.A., Potter, K.W., 1989. Estimating probabilities
of extreme rainfalls. J. Hydraul. Eng. 115, 1562e1575.
thank Scott Small, Chi Chi Choi, and Tibebu Foufoula-Georgiou, E., 1989. A probabilistic storm
Ayalew at the University of Iowa for their transposition approach for estimating exceedance
support in configuring and troubleshooting probabilities of extreme precipitation depths. Water
Resour. Res. 25, 799e815.
the IFC Model. Computing resources Franchini, M., Helmlinger, K.R., Foufoula-Georgiou, E.,
supporting the hydrologic modeling were Todini, E., 1996. Stochastic storm transposition
provided by the NASA High-End Computing coupled with rainfalldrunoff modeling for estimation
of exceedance probabilities of design floods. J. Hydrol.
Program through the NASA Center for 175, 511e532.
Climate Simulation at Goddard Space Flight Gupta, V.K., 1972. Transposition of Storms for Estimating
Center. We would also like to thank the Flood Probability Distributions. Colorado State
University.
editor and the two anonymous reviewers
Habib, E., Henschke, A., Adler, R.F., 2009. Evaluation of
whose constructive criticisms contributed TMPA satellite-based research and real-time rainfall
greatly to the study. estimates during six tropical-related heavy rainfall
events over Louisiana, USA. Atmos. Res. 94,
373e388.
References Horritt, M.S., Bates, P.D., 2002. Evaluation of 1D and 2D
numerical models for predicting river flood inundation.
Alexander, G.N., 1963. Using the probability of storm J. Hydrol. 268, 87e99.
transposition for estimating the frequency of rare Huffman, G.J., Adler, R.F., Bolvin, D.T., Nelkin, E.J., 2010.
floods. J. Hydrol. 1, 46e57. The TRMM multi-satellite precipitation analysis
Bonnin, G.M., Martin, D., Lin, B., Parzybok, T., Riley, (TMPA). In: Hossain, F., Gebremichael, M. (Eds.),
D., 2004. NOAA Atlas 14: Precipitation-frequency Satellite Rainfall Applications for Surface Hydrology.
Atlas of the United States. Springer Verlag, pp. 3e22.
Brenning, A., 2005. Spatial prediction models for Huffman, G.J., Bolvin, D.T., Braithwaite, D., Hsu, K.,
landslide hazards: review, comparison and Joyce, R.J., Xie, P., 2014. Algorithm Theoretical Basis
evaluation. Nat. Hazards Earth Syst. Sci. 5, Document (ATBD) Version 4- NASA Global
853e862. Precipitation Measurement (GPM) Integrated Multi-
Burnash, R.J.C., 1995. The NWS river forecast system:
satellitE Retrievals for GPM (IMERG), PMM Website.
catchment modeling. Comput. Model. Watershed
Hydrol. 311e366.
61 D.B. Wright et al. / Environmental Modelling & Software 90 (2017) 34e54
Interagency Advisory Committee on Water Data (IACWD), Stampoulis, D., Anagnostou, E.N., Nikolopoulos, E.I.,
1982. Guidelines for Determining Flood Flow 2013. Assessment of highresolution satellite-based
Frequency, Bulletin 17B. Reston, VA. rainfall estimates over the Mediterranean during heavy
Jones, E., Oliphant, T., Peterson, P., Walt, S. van der, precipitation events. J. Hydrometeor 14, 1500e1514.
Colbert, S.C., Varoquaux, G., 2011. SciPy: open Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E., 1993.
source scientific tools for Python. Comput. Sci. Eng. Frequency analysis of extreme events. In: Maidment,
13. D.R. (Ed.), Handbook of Hydrology. McGraw-Hill,
Joyce, R.J., Janowiak, J.E., Arkin, P.A., Xie, P., 2004. New York.
CMORPH: a method that produces global Tian, Y., Peters-Lidard, C.D., 2007. Systematic anomalies
precipitation estimates from passive microwave and over inland water bodies in satellite-based
infrared data at high spatial and temporal resolution. J. precipitation estimates. Geophys. Res. Lett. 34,
Hydrometeorol. 5, 487e503. L14403.
Lin, Y., Mitchell, K.E., 2005. The NCEP Stage II/IV hourly Tian, Y., Peters-Lidard, C.D., Choudhury, B.J., Garcia, M.,
precipitation analyses: development and applications. 2007. Multitemporal analysis of TRMM-based
In: Preprints, 19th Conf. on Hydrology. American satellite precipitation products for land data
Meteorological Society, San Diego, CA, pp. 2e5, 9-13 assimilation applications. J. Hydrometeorol. 8,
January 2005, Paper 1.2. 1165e1183.
Mallakpour, I., Villarini, G., 2015. The changing nature of Tian, Y., Peters-Lidard, C.D., Eylander, J.B., Joyce, R.J.,
flooding across the central United States. Nat. Clim. Huffman, G.J., Adler, R.F., Hsu, K., Turk, F.J., Garcia,
Chang. 5, 250e254. M., Zeng, J., 2009. Component analysis of errors in
Mantilla, R., Gupta, V.K., 2005. A GIS numerical satellite-based precipitation estimates. J. Geophys.
framework to study the process basis of scaling Res. 114, D24101.
statistics in river networks. Geosci. Remote Sens. Lett. Troutman, B.M., Karlinger, M.R., 2003. Regional flood
IEEE 2, 404e408. probabilities. Water Resour. Res. 39, 1095.
McCuen, R.H., 1998. Hydrologic Analysis and Design. U.S. Weather Bureau, 1958. Rainfall Intensity-frequency
Mcgraw- Hill. Regime. Part 2-Southeastern United States, Technical
Mehran, A., AghaKouchak, A., 2014. Capabilities of Paper No. 29.
satellite precipitation datasets to estimate heavy Villarini, G., Krajewski, W.F., 2010. Review of the
precipitation rates at different temporal accumulations. different sources of uncertainty in single polarization
Hydrol. Process 28, 2262e2270. radar-based estimates of rainfall. Surv. Geophys. 31,
Moser, B.A., Gallus Jr., W.A., Mantilla, R., 2015. An initial 107e129.
assessment of radar data assimilation on warm season Villarini, G., Smith, J.A., Vitolo, R., Stephenson, D.B.,
rainfall forecasts for use in hydrologic models. 2013. On the temporal clustering of US floods and its
Weather Forecast 30, 1491e1520. relationship to climate teleconnection patterns. Int. J.
Nikolopoulos, E.I., Anagnostou, E.N., Borga, M., 2013. Climatol. 33, 629e640.
Using high-resolution satellite rainfall products to Villarini, G., Strong, A., 2014. Roles of climate and
simulate a major flash flood event in Northern Italy. J. agricultural practices in discharge changes in an
Hydrometeorol. 14, 171e185. agricultural watershed in Iowa. Agric. Ecosyst.
Petersen-Øverleir, A., 2004. Accounting for Environ. 188, 204e211.
heteroscedasticity in rating curve estimates. J. Hydrol. Walshaw, D., 2013. Generalized extreme value
292, 173e181. Distribution Based in part on the article
Petersen-Øverleir, A., Reitan, T., 2009. Accounting for “Generalized extreme value distribution” by Jan
rating curve imprecision in flood frequency analysis Beirlant and Gunther Matthys, which appeared in
using likelihood-based methods. J. Hydrol. 366, the Encyclopedia of Environmetrics. In:
89e100. Encyclopedia of Environmetrics. John Wiley &
Petty, G.W., Krajewksi, W.F., 1996. Satellite estimation of Sons, Ltd, Chichester, UK.
precipitation over land. Hydrol. Sci. J. 41, 433e451. Walt, S. van der, Colbert, S.C., Varoquaux, G., 2011. The
Potter, K.W., Walker, J.F., 1985. An empirical study of NumPy array: a structure for Efficient numerical
flood measurement error. Water Resour. Res. 21, computation. Comput. Sci. Eng. 13.
403e406. Wilson, L.L., Foufoula-Georgiou, E., 1990. Regional
Preisig, M., Zimmermann, T., 2010. Two-phase free- rainfall frequency analysis via stochastic storm
surface fluid dynamics on moving domains. J. Comput. transposition. J. Hydraul. Eng. 116, 859e880.
Phys. 229, 2740e2758. Wright, D.B., Smith, J.A., Baeck, M.L., 2014b. Flood
Rogger, M., Kohl, B., Pirkl, H., Viglione, A., Komma, J., frequency analysis using radar rainfall fields and
Kirnbauer, R., Merz, R., Blo€schl, G., 2012. Runoff stochastic storm transposition. Water Resour. Res.
50, 1592e1615.
models and flood frequency statistics for design flood
Wright, D.B., Smith, J.A., Baeck, M.L., 2014a. Critical
estimation in Austria e do they tell a consistent story?
examination of area reduction factors. J. Hydrol. Eng.
J. Hydrol. 456e457, 30e43.
19, 769e776.
Sen, P.K., 1968. Estimates of the regression coefficient
Wright, D.B., Smith, J.A., Villarini, G., Baeck, M.L.,
based on Kendall's tau. J. Am. Stat. Assoc. 63,
2013. Estimating the frequency of extreme rainfall
1379e1389.
using weather radar and stochastic storm
Shige, S., Kida, S., Ashiwake, H., Kubota, T., Aonashi, K.,
transposition. J. Hydrol. 488, 150e165.
2013. Improvement of TMI rain retrievals in
Wright, D.B., Smith, J.A., Villarini, G., Baeck, M.L.,
mountainous areas. J. Appl. Meteorol. Climatol. 52,
2014c. Long-term high-resolution radar rainfall
242e254.
fields for urban hydrology. JAWRA J. Am. Water
Small, S.J., Jay, L.O., Mantilla, R., Curtu, R., Cunha, L.K.,
Resour. Assoc. 50, 713e734.
Fonley, M., Krajewski, W.F., 2013. An asynchronous
Xie, P., Yatagai, A., Chen, M., Hayasaka, T.,
solver for systems of ODEs linked by a directed tree
Fukushima, Y., Liu, C., Yang, S., 2007. A gauge-
structure. Adv. Water Resour. 53, 23e32.
based analysis of daily precipitation over East
Smith, J.A., Baeck, M.L., Villarini, G., Wright, D.B.,
Asia. J. Hydrometeorol. 8, 607.
Krajewski, W., 2013. Extreme flood response: the June
Yarnell, D.L., 1935. Rainfall Intensity-Frequency Data.
2008 flooding in Iowa. J. Hydrometeorol. 14, Washington, D. C.
1810e1825.
Smith, J.A., Villarini, G., Baeck, M.L., 2011. Mixture
distributions and the hydroclimatology of extreme
rainfall and flooding in the Eastern United States. J.
Hydrometeorol. 12, 294e309.
Smith, M.B., Seo, D.-J., Koren, V.I., Reed, S.M., Zhang, Z.,
Duan, Q., Moreda, F., Cong, S., 2004. The distributed
model intercomparison project (DMIP): motivation and
experiment design. J. Hydrol. 298, 4e26.
Sorooshian, S., Hsu, K.-L., Gao, X., Gupta, H.V., Imam, B.,
Braithwaite, D., 2000. Evaluation of PERSIANN
system satellite-based estimates of tropical rainfall.
Bull. Am. Meteorol. Soc. 81, 2035e2046.