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\begin{document}

\title{A Multi-sensor Evaluation of Precipitation Uncertainty for
Landslide-triggering Storm Events}



\author[1]{Elsa Culler}%
\author[2]{Andrew Badger}%
\author[1]{J. Minear}%
\author[1]{Kristy Tiampo}%
\author[1]{Spencer Zeigler}%
\author[1]{Ben Livneh}%
\affil[1]{University of Colorado Boulder}%
\affil[2]{USRA}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\selectlanguage{english}
\begin{abstract}
Extreme precipitation can have profound consequences for communities,
resulting in natural hazards such as rainfall-triggered landslides that
cause casualties and extensive property damage. A key challenge to
understanding and predicting rainfall-triggered landslides comes from
observational uncertainties in the depth and intensity of precipitation
preceding the event. Practitioners and researchers must select among a
wide range of precipitation products, often with little guidance. Here
we evaluate the degree of precipitation uncertainty across multiple
precipitation products for a large set of landslide-triggering storm
events and investigate the impact of these uncertainties on predicted
landslide probability using published intensity-duration thresholds. The
average intensity, peak intensity, duration, and NOAA-Atlas return
periods are compared ahead of 228 reported landslides across the
continental US and Canada. Precipitation data are taken from four
products that cover disparate measurement methods: near real-time and
post-processed satellite (IMERG), radar (MRMS), and gauge-based
(NLDAS-2). Landslide-triggering precipitation was found to vary widely
across precipitation products with the depth of individual storm events
diverging by as much as 296 mm with an average range of 51 mm. Peak
intensity measurements, which are typically influential in triggering
landslides, were also highly variable with an average range of 7.8 mm/hr
and as much as 57 mm/hr. The two products more reliant upon ground-based
observations (MRMS and NLDAS-2) performed better at identifying
landslides according to published intensity-duration storm thresholds,
but all products exhibited hit-ratios of greater than 0.56. A greater
proportion of landslides were predicted when including only
manually-verified landslide locations. We recommend practitioners
consider low-latency products like MRMS for investigating landslides,
given their near-real time data availability and good performance in
detecting landslides. Practitioners would be well-served considering
more than one product as a way to confirm intense storm signals and
minimize the influence of noise and false alarms.%
\end{abstract}%



\sloppy


Elsa S. Culler \textsuperscript{1,2}, Andrew M.
Badger\textsuperscript{3,4}, J. Toby Minear \textsuperscript{2}, Kristy
F. Tiampo \textsuperscript{2,5}, Spencer D. Zeigler \textsuperscript{5},
and Ben Livneh \textsuperscript{1,2}

\textsuperscript{1} Department of Civil, Environmental, and
Architectural Engineering, University of Colorado Boulder, Boulder, CO
80309, USA

\textsuperscript{2} Cooperative Institute for Research in Environmental
Science (CIRES), University of Colorado Boulder, Boulder, CO 80309, USA

\textsuperscript{3} Universities Space Research Association, Columbia,
MD, 21046 USA

\textsuperscript{4} Hydrological Sciences Laboratory, NASA Goddard Space
Flight Center, Greenbelt, MD, 20771 USA

\textsuperscript{5} Department of Geological Sciences, University of
Colorado Boulder, Boulder, CO 80309, USA

\textbf{Corresponding Author} : Elsa Culler, 216 UCB, University of
Colorado Boulder campus, Boulder, CO 80309, elsa.culler@colorado.edu

\textbf{Acknowledgements}

This research was supported by funding from the National Aeronautics and
Space Administration's Interdisciplinary Research in Earth Science (IDS)
program grant 16-IDS16-0075, The Interaction of Mass Movements with
Natural Hazards Under Changing Hydrologic Conditions.

\textbf{Conflict of Interest Statement}

The authors declare no conflict of interest

\textbf{Abstract:} Extreme precipitation can have profound consequences
for communities, resulting in natural hazards such as rainfall-triggered
landslides that cause casualties and extensive property damage. A key
challenge to understanding and predicting rainfall-triggered landslides
comes from observational uncertainties in the depth and intensity of
precipitation preceding the event. Practitioners and researchers must
select among a wide range of precipitation products, often with little
guidance. Here we evaluate the degree of precipitation uncertainty
across multiple precipitation products for a large set of
landslide-triggering storm events and investigate the impact of these
uncertainties on predicted landslide probability using published
intensity-duration thresholds. The average intensity, peak intensity,
duration, and NOAA-Atlas return periods are compared ahead of 228
reported landslides across the continental US and Canada. Precipitation
data are taken from four products that cover disparate measurement
methods: near real-time and post-processed satellite (IMERG), radar
(MRMS), and gauge-based (NLDAS-2). Landslide-triggering precipitation
was found to vary widely across precipitation products with the depth of
individual storm events diverging by as much as 296 mm with an average
range of 51 mm. Peak intensity measurements, which are typically
influential in triggering landslides, were also highly variable with an
average range of 7.8 mm/hr and as much as 57 mm/hr. The two products
more reliant upon ground-based observations (MRMS and NLDAS-2) performed
better at identifying landslides according to published
intensity-duration storm thresholds, but all products exhibited
hit-ratios of greater than 0.56. A greater proportion of landslides were
predicted when including only manually-verified landslide locations. We
recommend practitioners consider low-latency products like MRMS for
investigating landslides, given their near-real time data availability
and good performance in detecting landslides. Practitioners would be
well-served considering more than one product as a way to confirm
intense storm signals and minimize the influence of noise and false
alarms.

\textbf{Keywords:} precipitation inter-comparison, rainfall-triggered
landslides, natural hazards, extreme precipitation, intensity-duration
thresholds

\section*{Introduction}

{\label{introduction}}

Precipitation measurements and their uncertainties play a key role in
understanding and mitigating rainfall-triggered landslides because they
drive excess runoff and soil saturation that initiate these natural
disasters (Highland \& Bobrowsky, 2008). In spite of the destructive
nature of landslides, which cause tens of thousands of deaths each year
(Froude \& Petley, 2018) these events remain challenging to diagnose, in
part due to uncertainty in antecedent precipitation amounts (Kirschbaum
\& Stanley, 2018). There are many other sources of uncertainty that
contribute to poor landslide diagnosis and prediction, such as unknown
soil properties, vegetation, and anthropogenic modifications to surface
and subsurface soil structure. However, perhaps the largest source of
uncertainty in estimating landslide probability is hydrologic
uncertainty, defined here as uncertainty in the depth and intensity of
liquid precipitation leading up to the event (Chowdhury \& Flentje,
2002). A confounding factor is the wide array of precipitation datasets
ranging from in situ observations, ground-based radar and satellite
retrievals. The goals of this study are to investigate the role of
precipitation uncertainty preceding known historical landslide events,
and to assess the implications for evaluating landslide hazards.

The precipitation products chosen for this inter-comparison represent
three broad categories of primary measurement techniques: precipitation
gauges, ground-based radar, and microwave satellite. Precipitation
gauges operate by periodically measuring the volume of precipitation
collected at a gauge. Their main strength is that they directly measure
the amount of collected water, but nonetheless they can suffer from
issues of persistent bias driven by under-catch from wind (Pollock et
al., 2018) instrument malfunctions (Duchon et al., 2014; Duchon \&
Biddle, 2010), gauges placed too close to other structures (Vose et al.,
2014), and limited spatial representativeness due to sparse sensor
density (Kidd et al., 2017).

In contrast, ground-based radar detects precipitation indirectly using
the backscatter of radar and can measure subtle variations in
precipitation over regions of several hundreds of square kilometers
(Zhang et al., 2015). Since ground-based radar is an indirect
measurement of precipitation, its performance is dependent on skilful
conversion of the radar signal to precipitation volume. Beam blockage
and interference from buildings or even insects in the radar's path are
another limitation (Bousquet \& Smull, 2003; Fornasiero et al., 2004;
Nikahd et al., 2016). Most ground-based radars use multiple bands of
radar and multiple polarities to compute the raindrop shape and size
distributions used in the processing and limit the impact of known
sources of error, which offers an advantage over other indirect
techniques such as some of those incorporated into satellite-based
measurements (Chandrasekar et al., 2008).

Satellite techniques vary in terms of which sensors they use to detect
precipitation, including active and passive microwave, infrared, radar,
or any combination. Depending on the sensor type these satellites can be
deployed in either geostationary or low Earth orbits that cover
particular spatial regions at particular intervals (Huffman et al.,
2020). The key advantage of satellite-based precipitation measurements
over ground-based in situ or radar sensors is that they can deliver
frequent and spatially continuous measurements, although multiple
satellites (Tapiador et al., 2012) with a variety of sensors and orbits
(Ashouri et al., 2015) are required to provide global coverage. For
example, the satellite products used in this analysis incorporate a
fleet of geostationary satellites in addition to a single low Earth
orbit reference satellite (Kidd et al., 2020). Many of the challenges
associated with satellite-based precipitation measurement are related to
sensor calibration and bias-correction relative to ground-based
measurements (Ebert, 2007), as well as the development of algorithms for
merging measurements from diverse sources (Huffman et al., 2007;
Skofronick-Jackson et al., 2017). Estimating drop size distributions is
also a challenge, though it can be addressed through the use of either
ground- or satellite-based radar.

Existing precipitation products have been compared and evaluated using a
number of metrics in prior studies, for example annual and monthly
totals (Adler et al., 2001) or the frequency of wet or dry days
(Manzanas et al., 2014). Less attention has been paid to metrics most
directly useful for analysing rainfall-triggered landslides. While some
landslides are triggered by short, intense precipitation events, others
are triggered by saturation of the soil column that can develop over a
longer period of time (Cannon \& Gartner, 2005). In both cases the
triggering event occurs over the course of hours or days rather than
months or years, and for some landslides the critical time period may be
less than an hour.

Published precipitation inter-comparisons typically focus on specific
applications such as evaluating grid-based products over complex
terrain, portraying hydrologic phenomena (Ahmadalipour \& Moradkhani,
2017), climate model downscaling efforts (Gutmann et al., 2014; Wang et
al., 2020), or for merging multiple sensors together (Beck et al.,
2017). A general review of 30 gauge-based, satellite-based, and
reanalysis global precipitation products by Sun et al. (2018) compared
systematic and random errors for daily and annual precipitation,
reporting large disagreements even within the same class of product,
i.e.,~a deviation of 300 mm in annual precipitation over global land
among satellite products. They conclude that the placement and density
of gauges accounts for many of the errors in gauge-based or
gauge-corrected products, further suggesting that cross validation
across multiple datasets is crucial to account for errors. Adler et al.
(2003) similarly analyzed 31 gauge-based, satellite-based, model-based,
and climatological datasets in terms of monthly precipitation, finding
that `quasi-standard' products, e.g.,~those like the Global
Precipitation Measurement (GPM) mission (Hou et al., 2014) that have
undergone substantial testing, perform better. Additionally, they report
that products incorporating both in situ and satellite information
(e.g.,~the Global Precipitation Climatology Project) perform better than
products based on a single data source.

Fewer studies comparing extreme precipitation events (e.g.,~events above
the 90th percentile) exist. Many focus on climate model simulations
(Sunyer et al., 2015; Tryhorn \& DeGaetano, 2011) and trends (Bao et
al., 2017; Janssen et al., 2014) while others evaluate observations and
satellites (AghaKouchak et al., 2011; Lockhoff et al., 2014; Pendergrass
\& Knutti, 2018). AghaKouchak et al. (2011) compared extreme
precipitation across four satellite platforms and found trade-offs
across products in terms of correct identification of precipitation
above a threshold and measurements of the volume of extreme storms.
While they showed that some datasets performed better than others in
certain contexts, they ultimately concluded that no single precipitation
product was ideal for detecting extremes because all of them failed to
detect certain storms in certain regions. Lockhoff et al. (2014) found
that satellite retrieved extreme precipitation values generally matched
station-based precipitation when using fuzzy metrics to evaluate
agreement at larger spatiotemporal scales of \textasciitilde{}330 km and
5 days. Pendergrass \& Knutti (2018) showed that precipitation was less
variable in coarser versus finer-resolution satellite precipitation
datasets, suggesting that coarser precipitation products may be unable
to capture extreme precipitation to the same extent as higher resolution
datasets. Other studies primarily evaluated extreme precipitation
indicators like 90th percentile precipitation, extreme one-day
precipitation and maximum number of consecutive wet days (Amitai et al.,
2012; Manzanas et al., 2014). These measures are meant to capture large
storms that happen on at least an annual basis rather than specific to
storms that trigger natural disasters (Manzanas et al., 2014; Sun et
al., 2018).

This works builds on the handful of studies that have specifically
evaluated multiple precipitation products in the context of landslide
triggering (Rossi et al., 2017; Brunetti et al., 2018; Tajudin et al.,
2020; Chikalamo et al., 2020). For example, Rossi et al. (2017) compared
of satellite and gauge precipitation data preceding landslide events in
Italy, using intensity-duration thresholds as a part of the comparison.
They found that data from Tropical Rainfall Measuring Mission (TRMM)
satellite products (Kummerow et al., 1998) tend to underestimate gauge
data, particularly in mountainous areas where landslides are most likely
to occur. Brunetti et al. (2018) similarly found that satellite
precipitation from four products tended to underestimate rainfall
relative to ground based observations. Both studies ultimately concluded
that the satellite data could still be useful for forecasting landslides
as long as issues of local bias could be accounted for.

The intensity-duration threshold is a type of two-parameter statistical
model used for landslide early warning systems, where rainstorms above
the threshold curve are predicted to cause landslides (Scheevel et al.,
2017). The curves are typically based on a power law
(e.g.,~\(I=aD^{-b}\)) of storm intensity (\(I\)) as a
function of duration (\(D\)) with fitted parameters
\(a\) and \(b\). These power laws are valid in
a particular region or climate and for a range of durations depending on
the training data (Guzzetti et al., 2008). Other statistical rainfall
thresholds have been proposed, but generally rely upon either intensity
or duration or both (Galanti et al., 2018; Leonarduzzi et al., 2017).
Here, we will investigate several power-law intensity-duration
thresholds reviewed by Guzzetti et al. (2008) as a basic way to compare
precipitation measurements from different sources in the context of
landslide hazard estimation. Furthermore, when precipitation is used to
provide warning systems or guide recovery efforts from landslides, the
timeliness, i.e.,~low latency, of the information matters (Kirschbaum et
al., 2012), such that the issue of latency will also be considered in
the investigation of intensity-duration thresholds.

The focus of this analysis is to quantify precipitation uncertainty
associated with known historical landslides, and to examine the role of
this uncertainty in modelling landslide hazards. Given the wide-ranging
issues associated with precipitation estimation cited above, this study
presents a multi-product, multi-site analysis focused on
landslide-triggering storms. We address an existing gap in evaluating
extreme precipitation through the lens of rainfall-triggered landslide
hazards, while conducting inter-product analyses into storm
characteristics of potential relevance for the hydrological community.
Additionally, we further the analyses by Rossi et al. (2017) and
Brunetti et al. (2018) by including ground-based radar and by rigorously
analyzing each precipitation estimate preceding specific landslide
events. Greater understanding of the areas of relative agreement and any
divergence across products may provide guidance to practitioners and
researchers choosing among precipitation products for studying
landslides.

\section*{Methods}

{\label{methods}}

We compared precipitation characteristics at known landslide sites
across the features of triggering storms, as well as relative to
intensity-duration thresholds of landslide occurrence.
Rainfall-triggered landslide sites were chosen from the NASA Global
Landslide Catalog (GLC; Kirschbaum et al., 2010) with a subset of
landslide locations verified with ancillary satellite imagery (see
section~2.1). For each landslide location, precipitation was obtained
from four different products (see section~2.2) and the precipitation
time series were split into individual storm events. For each storm, key
characteristics of total depth, duration, intensity, peak intensity, and
return period were calculated (section~2.3). Finally, the storm events
were plotted relative to landslide intensity-duration curves, with
hit-ratios and false-alarm-ratios compared for each model-product
combination (section~2.4).

\subsection*{Study domain and landslide site
selection}

{\label{study-domain-and-landslide-site-selection}}

The NASA Global Landslide Catalog (GLC; Kirschbaum et al., 2010) was
chosen as the source of landslide locations for this study, since it
provides a large sample of landslide locations useful for evaluating
heavy rainfall events. The GLC shares many strengths and weaknesses with
other regional and global databases available (Kirschbaum et al., 2010;
Mirus et al., 2020). Though the GLC covers a broad spatial and temporal
domain, it suffers from problems of precision and completeness. The
catalog is comprised of a collection of second-hand landslide reports
made by organizations like the news media, governmental organizations
like departments of transportation, along with available scientific
reports. This means that landslides that nearby infrastructure and
people are reported more frequently, resulting in a substantial spatial
bias towards populated areas. Landslide location accuracies range from
`exact' locations, to location uncertainties between 1km up to 50 km,
depending on how specific the source article was about the location
(Kirschbaum et al., 2010). Despite these limitations, the GLC was deemed
fit for the purposes of this study, which is not to study landslide
mechanisms and spatial distribution, but rather to compare precipitation
products in the vicinity of hydrologically-triggered landslides where
heavy rainfall events are likely to be present. Overall, the GLC
provided a substantial number of landslide locations (n=228) for this
study that met the following selection criteria:

\begin{itemize}
\tightlist
\item
  Only landslide events reported as rainfall-driven, with a GLC trigger
  category of ``rain,'' ``downpour,'' ``continuous\_rain,'' or
  ``flooding'' were included. Snow-related triggers were not included
  even though these are hydrologically driven, because their
  precipitation is not contemporaneously linked with landslide triggers;
\item
  Landslide events took place in the continental United States (CONUS)
  or Canada below \(60\) N and after May 2015 ensuring data
  availability across each of the selected precipitation products;
\item
  The landslide location accuracy was reported to be 10 km or less. The
  value of 10 km was chosen since it is approximately equal to the
  spatial resolution of two of the precipitation products; and
\item
  The landslide size was reported as ``medium'' or larger so as to
  select for events more likely to have been triggered by substantial
  precipitation.
\end{itemize}

In total, 228 landslides were selected. Of those, the exact locations
for 80 sites were verified by a trained technician searching for a
landslide scarp in visible satellite images of the terrain near the
specified landslide location. The location specified by the GLC was used
for the remaining landslides where 31 were marked in the GLC as
``exact'' locations, 51 as 1 km, 52 as 5 km, and 14 as 10 km accuracy.
Figure~1 shows that many of the sites are located near the Pacific
coast, likely due to the presence of complex topography associated with
landslides, as well as the population reporting bias of the GLC. The
verified landslides are generally distributed evenly relative to the
locations of the full selection of landslides.

{[}Insert Figure 1{]}

\subsection*{Precipitation data
sources}

{\label{precipitation-data-sources}}

The gridded precipitation datasets in this study were chosen to be
reflective of three common measurement methods: gauges, ground-based
radar, and satellite. We were interested in products that are freely
available, have undergone extensive verification, and extend over at
least the CONUS. An important additional criterion was that products be
available at an hourly temporal resolution or finer in order to compute
the characteristics of individual storm events. We further sought to
include products with multiple latencies where available. The above
criteria resulted in the precipitation products and features described
in Table~1 and summarized below.

{[}Insert Table 1{]}

\subsubsection*{North American Land Data Assimilation System version 2
(NLDAS-2) meteorological
dataset}

{\label{north-american-land-data-assimilation-system-version-2-nldas-2-meteorological-dataset}}

The NLDAS-2 meteorological dataset (Xia et al., 2012) is a combination
of daily gauge-based National Center for Environmental Prediction (NCEP)
Climate Prediction Center (CPC) precipitation with orographic
corrections and hourly NCEP Doppler radar-based precipitation. The
gauge-based estimates are disaggregated to hourly using the radar-based
estimates, resulting in a near real-time hourly gridded product
at\(0.125\) (\textasciitilde{}\(12\) km) resolution
across North America going back to 1979 with a latency of approximately
four days. Though it has coarser horizontal resolution relative to the
other precipitation products used here, NLDAS-2 meteorological is a
widely used gauge-based product that has been extensively validated over
a recent period overlapping with this study (Livneh et al., 2015; Long
et al., 2014; Xia et al., 2016).

\subsubsection*{Multi-Radar Multi-Sensor (MRMS) Quantitative
Precipitation
Estimate}

{\label{multi-radar-multi-sensor-mrms-quantitative-precipitation-estimate}}

MRMS precipitation estimates are primarily based on a centralized radar
mosaic with 2-minute resolution over the US and Canada. This study uses
an hourly version that also integrates data from numerical weather
prediction, satellites, gauges, lightning sensors, and precipitation
models (Zhang et al., 2015). While both NLDAS-2 and MRMS estimates
contain common information from gauges and radar, the NLDAS-2 product is
primarily a gauge-based estimate while MRMS focuses on radar inputs.
MRMS is the precipitation product with the shortest period of record
among the products selected for this study, and so there are relatively
few years of data for validation. However, it has by far the highest
resolution at \(0.01\) (\textasciitilde{}1.1 km) and
represents the state of the art in terms of leveraging computing
resources to take advantage of a multitude of overlapping radar and
other types of sensors.

\subsubsection*{Integrated Multi-satellitE Retrievals for GPM
(IMERG)}

{\label{integrated-multi-satellite-retrievals-for-gpm-imerg}}

GPM IMERG precipitation estimates are a combination of multiple
satellite measurements, including the GPM Core Observatory Microwave
Imager which is considered the standard for the other included
satellites. In addition to active and passive microwave sensors, IMERG
estimates include Infrared sensors, satellite-based radar, and
precipitation gauge adjustments. The gauges are used for monthly bias
correction (Huffman et al., 2020). There are three IMERG products,
Early, Late, and Final, of which we use the Early
(\textasciitilde{}4-hour latency) and the Final
(\textasciitilde{}3.5-month latency) in this study. The IMERG-Early
product is available much more promptly than the IMERG-Final, but as a
result some of the satellite retrievals are not incorporated because
they have not yet arrived, and it cannot take advantage of some
processing steps or monthly gauge correction (O et al., 2017).
IMERG-Final is recommended for research applications as being the most
accurate but would not be useful for predicting landslides in a timely
fashion (Huffman et al., 2020). Since IMERG products use the GPM active
and passive microwave data as a standard with little-to-no information
from gauges, they are fundamentally different from many other
precipitation products available.

\subsection*{Precipitation inter-comparison and computation of storm
characteristics}

{\label{precipitation-inter-comparison-and-computation-of-storm-characteristics}}

For each of the precipitation products, data were extracted for the
precipitation grid enclosing the landslide location for the period
between May 2015 (the earliest date MRMS data are available) and May
2020 (the latest release of IMERG-Final data at the time of this
analysis). Following (Dinku et al., 2008), a minimum threshold of 1
mm/hr was applied to the precipitation data to reduce noise. The data
were then split into storm events, where a minimum inter-event time
(MIT) criterion of 24 hours as described in Dunkerley (2008) was
considered to mark the end of one storm and the beginning of the next.

For each storm, the characteristics of total depth, duration, intensity,
and peak intensity were computed and compared. The peak intensity for a
storm was the intensity of the single maximum precipitation measurement
of the storm. Depth and frequency were chosen since they reflect the
most common metrics used in extreme hydrologic events (England et al.,
2019). Intensity and duration were included because they are parameters
commonly used to study rainfall-triggered landslides (Kirschbaum et al.,
2012). Previous studies have suggested that for certain landslides high
peak intensity can contribute significantly to triggering a landslide
independent of the overall storm depth, duration or intensity (Corominas
et al., 2002; Yu et al., 2006). This idea is supported for example by
observations that landslides are commonly initialized within hours of
the peak intensity (Premchitt et al., 1986). The precipitation rank and
z-score among the four products for each landslide event were also
computed for the day of the landslide as well as for the full May
2015-May 2020 precipitation record. Rank was chosen as in indicator of
the relative magnitude of each product relative to the others, and the
z-score as an indicator of the variability of each product relative to
the others.

To facilitate comparison of storm characteristics within a single
over-arching framework, the return period of the landslide-triggering
storms was computed using the NOAA precipitation atlas frequency
estimations (US Department of Commerce, 2013). The NOAA atlas provides
return periods for discrete precipitation durations, namely 1, 2, 3, 6,
12, 24, 48, 72, 96, and 168 hours. In order to define a consistent
return period for each storm, we used the maximum precipitation value
for each applicable NOAA atlas duration rather than attempting to expand
the storm duration to one of the NOAA atlas durations which might have
artificially lowered the return periods. For example, for the 3-hour
duration, cumulative 3-hour precipitation totals were calculated for
each time step of the storm, and the maximum value chosen. The return
period for this maximum value was then retrieved from NOAA atlas. We
then selected the maximum return period from among the 10 possible
durations noted above for each landslide. For example, if the maximum
3-hour interval during the MIT-defined storm had a 25-year return period
while the maximum 48-hour interval during the storm only had a 2-year
return period, the return period of the 3-hour return period would be
used in preference over the 48-hour return period or any other duration
where the maximum return period was less than 25 years. This procedure
ensured that we used the maximum applicable return period available from
the NOAA atlas that occurred during each landslide-triggering storm.
Values less than a 2-year return period are not included in the NOAA
atlas, such that return period values were only assigned for a subset of
landslide-triggering storms that exceeded that threshold. Return period
data were also unavailable for Canadian sites.

\subsection*{Performance of intensity-duration thresholds using different
precipitation
products}

{\label{performance-of-intensity-duration-thresholds-using-different-precipitation-products}}

Intensity-Duration thresholds are a category of simple models of
landslide occurrence whereby a threshold is defined as a power law of
the storm duration

\begin{equation}
I=aD^{-b}\quad\quad(1)\nonumber \\
 \end{equation}

where \emph{I} is intensity, \emph{D} is duration, and \emph{a}
and\emph{b} are fitted parameters to a particular dataset. Intensities
above the threshold are used to predict the occurrence of a landslide
(Segoni et al., 2014). A range of thresholds have been calculated under
different climates and over multiple scales, including globally (Caine,
1980; Kirschbaum et al., 2012; Scheevel et al., 2017). Three thresholds
for this study (Caine, 1980; Cannon \& Gartner, 2005; Guzzetti et al.,
2007) were obtained from a review by Guzzetti et al. (2008) as a way to
test the sensitivity of our results to a chosen threshold. Thresholds
were only applied to applicable subsets of the data based on climate or
other conditions. For example, since the Guzzetti et al. (2007) was
defined for ``mild, marine west coast climates,'' only data west of
longitude 115W was included in that portion. The Cannon \& Gartner
(2005) is intended for burned areas, and since the fire history of the
locations in this study are unknown it is included only as a comparison
point to the other thresholds. For each threshold-product combination,
we computed a hit ratio (correctly predicted landslides over the total
number of landslides) and a false alarm ratio (incorrectly predicted
landslides over the total number of non-landslides)

\section*{Results}

{\label{results}}

The four precipitation products examined in this study exhibit a great
deal of variability in the time period leading up to the landslide
event. As an example of the magnitudes and qualitative characteristics
of that variability, figure~2 shows the cumulative precipitation in the
30-days before a landslide at five sites. The selected sites showcase
multiple ways in which precipitation can differ among the products. For
example, while the precipitation in panel (a) matches fairly closely for
all products, while in panel (b) precipitation still appears to be
correlated but also demonstrates a factor of two spread of precipitation
values. In panel (c) the IMERG products diverges substantially from the
ground-based products early on in cumulative volume, but the
landslide-triggering storm is recorded as nearly twice as large by the
satellite-based products, demonstrating that the differences in
precipitation measurement can partially cancel out in the right
situation. In panel (d) the IMERG-Early product reports nearly doubled
precipitation values throughout while all three of the remaining
products are very similar. Among the events where IMERG-Final recorded a
much lower than average value, it was common for the high average to be
driven by the IMERG-Early measurements almost exclusively, as shown here
in panel (d). Panel (e) shows a likely landslide location error since
none of the products register any precipitation close to the time of the
event. Such events are not included in most of the analysis of
landslide-triggering storms because no such storm could be identified.
We note that the differences in precipitation depths accumulated over
these 30-day periods are of the same order of magnitude as
the\emph{annual} error in depth reported for products of the same
category by Sun et al. (2018). This may be because variability among
products of different categories, e.g.,~satellite vs.~radar, whereas the
figure from Sun et al. (2018) includes only satellite products.
Alternatively, when aggregating over a whole year some of the
variability among products cancels out, whereas landslide-triggering
storms have a greater potential for error by virtue of being relatively
brief events.

{[}Insert Figure 2{]}

The variability among products is also evident in the distribution of
daily precipitation rank among products and z-score within products. The
relative magnitude of the different precipitation products on the day of
the landslide is shown in Figure~3 in terms of the rank among the four
products for each day, and z-score among all non-zero data for a
particular product. Both day-of-landslide precipitation and all other
non-zero days in the study period are shown for comparison. The ranks of
each product do not reveal substantial biases across the entire
precipitation record, with the exception of MRMS which has a larger
proportion of above median ranks than the other products. On the day of
the landslide only, the IMERG products have lower ranks overall,
suggested that the satellite-based measurements are less consistent at
detecting extreme precipitation. This idea is reinforced by the z-scores
of the precipitation among measurements from the product and landslide
site. Though the median z-score is similar for all products across the
entire record, it is lower for both IMERG products on the day of the
landslide. Conversely, some outliers in the IMERG-Early have the highest
z-scores among day-of-landslide precipitation even the median and third
quartile values are higher, suggesting that the further processing of
the IMERG-Final product reduces unusually high precipitation
measurements while also increasing low values. For all products, each
quartile of the day-of-landslide precipitation is larger than that of
the non-landslide-triggering precipitation, though none of the maximum
precipitation z-scores appears to have occurred on the day of the
landslide.

{[}Insert Figure 3{]}

Variability among the precipitation products is also revealed in a
comparison of day-of-landslide precipitation with mean values among each
of the products. Figure~4 shows the characteristics of the
landslide-triggering storms plotted against the ensemble mean of all the
products for all the landslide sites and separately for the verified
locations. There is reasonable agreement among products on the depth and
duration of storms, with the exception of outliers below 10mm of total
depth---corresponding with a fairly modest storm depth. Among the
verified locations, there are fewer low-depth or duration values that
are either outliers or near to the mean, suggesting that low
measurements may reflect limitations in the GLC location accuracy for
sites with only approximate locations.

The two satellite products have a pattern of distinctive readings
relative to ground-based products in that they contain both the highest
and lowest values of several storm characteristics. The IMERG products
generally report higher peak hourly intensities for the storms with the
highest mean peak intensity, which is likely at least partially due to
the shorter 30-minute time step. The higher peak intensities are also
reflected to some degree in longer return periods, which are based on
hourly durations or longer for comparison with the NOAA Atlas. An
examination of the relationship between return period and peak intensity
showed a clear relationship, with the return period data reflecting a
subset of the highest intensity storms due to the 2-year return period
cut-off. The relationship between peak intensity and return period is
not surprising given that the return period values were calculated by
searching for the most intense period of each NOAA atlas duration.
However, IMERG-Final has lower return periods over all when all
landslide locations are included despite reporting high peak
intensities. This anomaly disappears in an examination of verified
locations alone. An examination of the 30-day precipitation record prior
to the landslide for sites where the IMERG-Final return period was much
lower than the average revealed that in most of those cases the higher
mean was driven primarily by anomalously high IMERG-Early values not
reflected in any of the other datasets. MRMS and NLDAS-2 have lower
return periods that the IMERG products even among the verified locations
only, suggesting that these products may not consistently detect the
highest return period precipitation events.

{[}Insert Figure 4{]}

The precipitation products are examined in the context of landslide
triggering thresholds in Figure~5, with the performance summarized in
Table~2. Interestingly, the choice of intensity-duration threshold does
not appear to make a large difference in performance because the
threshold curves are more similar than the variation in the
precipitation data across sites and among products. The MRMS or NLDAS-2
products tend to perform better than either IMERG product, with hit
ratios between 0.84-0.88 and 0.65-0.76 rather than 0.59-0.61 and
0.59-0.73 among the verified landslide locations, respectively. All
products perform comparably or better when using only the verified
landslide locations relative to the approximate locations

Figure~5 shows a concentration of long-duration, low-intensity storms
that are in the vicinity of 24-hour duration for all products. These
storms may be an artifact of the MIT storm identification algorithm.
Since the landslides did not have times specified, the entire day of the
landslide was always included unless there was no rain until the end of
the day, and this may have extended some storms past when the landslide
occurred. This would have the effect of computing lower total intensity
values for storms that lasted only through the time of the landslide but
persisted only at a much lower intensity thereafter. Many of the storms
that did trigger landslides but were not correctly identified by the
intensity-duration threshold fall into this group of approximately
24-hour low-intensity storms. Adjustments to storm delineation through a
different algorithm or a higher minimum threshold may increase
performance, especially for the IMERG products which showed the most
low-intensity landslide triggering storms.

{[}Insert Figure 5{]}

{[}Insert Table 2{]}

\section*{Discussion}

{\label{discussion}}

Among the precipitation products chosen for this study, the two IMERG
products identify both higher peak intensities and longer return periods
relative to the other products. Interestingly, they also detect more
anomalously low precipitation values. Low-intensity precipitation in all
products was associated with long duration storm events (see figure~5)),
which may occur because of ``drizzle,'' i.e.,~low-intensity
precipitation slightly above the 1 mm threshold that extended the
MIT-computed duration of the storm and thereby reduced its overall
intensity. As a result, the IMERG products were particularly vulnerable
to the identification of long-duration low-intensity storms as a result
of the MIT method used in this study to separate storms. Those
long-duration low-intensity storms had the effect of lowering the hit
ratio. Because the IMERG products were able to identify higher intensity
precipitation than the other products, it is possible that they would in
fact perform better for identifying landslides if the low-intensity
storm problem were mitigated.

All precipitation products performed reasonably well at identifying
landslides using the published intensity-duration thresholds
particularly considering that these thresholds were developed on
training data from different datasets spanning large regions. However,
they did not perform as well at excluding false alarms, most likely
because of factors beyond intensity and duration that can influence
landslide occurrence such as topography, soil type, recent wildfire or
disturbance or land development. Some of the high-intensity
precipitation that did not trigger any recorded landslides could be more
reflective of adjacent areas that are not as susceptible to landslides.
Conversely a landslide at a highly susceptible location, such as an area
with high slopes that had recently been burned by wildfire could be
triggered by less intense rain, potentially resulting as a miss on an
intensity-duration curve. Even the 1.1 km resolution of the MRMS data
could contain substantial variation in landslide susceptibility within
an individual grid cell. The poorest performing products were the IMERG
products because despite their detecting more high-intensity events they
also detected many low-intensity long-duration events, causing the
intensity-duration threshold to miss landslides.

Both Rossi et al. (2017) and Brunetti et al. (2018) also found satellite
products did not perform as well as gauge data relative to
intensity-duration thresholds, as a result of underestimating
precipitation. However, those studies found that adjusting the threshold
accounted for precipitation bias, suggesting that the intensities were
lower in a more or less uniform pattern across different durations. By
contrast, in this study we found that the low-intensity values were more
often clustered around a relatively small duration band, which would be
more challenging to bias-correct. Though the intensity-duration
thresholds still show promise for diagnosing landslides using
satellite-based data, the adjustments to improve performance may prove
more complex for the IMERG products across the broader spatial domain of
the continental US and Canada.

MRMS and NLDAS-2 are relatively low latency products. In the case of
IMERG-Early the short latency seemed to come at a cost of an
exaggeration of the weaknesses and strengths of IMERG in identifying
landslides. In particular, IMERG-Early had the greatest prevalence of
low storm intensities, and so it ultimately performed the worst at
landslide identification. Without changes to the precipitation
processing, the low latency does indeed appear to be a liability in this
case.

Precipitation measurements at verified landslide sites tended to be of
higher magnitude than those at other sites with approximate locations
for all products. The intensity-duration thresholds subsequently
performed better at verified locations across all precipitation
products. Though this difference remains unexplained, one possibility is
that some of the approximate landslide locations were too far away from
the true landslide location for the precipitation measurements to be
representative. Alternatively, there may have been other factors such as
vegetation cover that made it more difficult to locate landslides on
satellite imagery and also lowered the precipitation threshold that
would trigger a landslide. Since work on this study began, a compilation
of U.S. landslides has been released by the USGS (Mirus et al., 2020)
which would also be a suitable source of landslide locations with
perhaps greater location precision that could help resolve this question
in future work along the same lines.

\section*{Conclusion}

{\label{conclusion}}

The precipitation products chosen for this study represent diverse
measurement techniques that often recorded large differences in
precipitation leading up to the landslide events evaluated here. As a
result, each precipitation product differed in overall performance in
predicting landslides using intensity-duration thresholds. Overall, the
choice of intensity-duration threshold was not as consequential as the
choice of precipitation product in identifying landslides. Performance
from products that rely on ground-based sensors showed a more consistent
landslide signal despite generally recording lower peak intensities and
return periods.

Though it was hypothesized that peak intensity would be an important
factor in identifying landslides, the results suggest instead that
removal of noise on the low end, i.e.,~drizzle, may be more important. A
particular challenge was the presence of low-intensity, long-duration
storms preceding landslide events, most prevalent in the IMERG products.
A more expansive evaluation of processing techniques for separating
storms may potentially mitigate these issue, although each technique
will produce artifacts in the comparisons. Another potential avenue for
addressing this problem is to combine multiple dataset, since the
low-intensity long-duration storms did not appear in all datasets to the
same degree.

Another limitation to the study landslide-triggering storms is the
general lack of both exact landslide locations and specific time of day
of the landslide events. The location limitation was reflected in better
performance for verified landslide locations as compared to approximate
locations, which implies that some of the approximate locations were
incorrect to such an extent that the precipitation measurements were
misaligned. This problem could be addressed by more extensive manual
searches such as the one used in this study that identified the 80
verified landslide locations, or perhaps in the future by machine
learning methods. Since work on this study began, a compilation of U.S.
landslides has been released by the USGS (Mirus et al., 2020) which
would also be a suitable source of landslide locations with perhaps
greater location precision that could be used in future work along the
same lines.

Using the methods tested in this study, those practitioners attempting
to use intensity-duration thresholds as operation landslide models would
do well to select a product like MRMS that has extremely low latency and
performs well at identifying landslides. None of the products were
particularly good at filtering out false alarms of landslides.
Therefore, an additional recommendation would be for practitioners to
consider more than one precipitation product, i.e.,~multiple
precipitation estimates simultaneously, as a way to confirm stronger
precipitation signals and to minimize the influence of noise.

\section*{Data Availability}

{\label{data-availability}}

These data were derived from the following resources available in the
public domain: The NASA Global Landslide Catalog was downloaded from
NASA's Open Data Portal
(https://data.nasa.gov/Earth-Science/Global-Landslide-Catalog/h9d8-neg4);
Both IMERG products were retrieved from the Global Precipitation
Measurement data portal (https://gpm.nasa.gov/data/directory); NLDAS-2
data is available on NASA's EarthData site
(https://disc.gsfc.nasa.gov/datasets/NLDAS\_FORA0125\_H\_002/summary?keywords=NLDAS/);
and MRMS data was retrieved from a public archive at Iowa State
University (https://mtarchive.geol.iastate.edu/). The verified locations
of GLC landslides used in this study are available from the
corresponding author upon reasonable request.

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\section*{Tables}

{\label{tables}}

\textbf{Table 1} \textbf{\textbar{}} The four precipitation products
included in the comparison, representing gauge-, radar-, and
satellite-based measurements.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Precipitation product\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Description\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Spatial Resolution\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Temporal resolution\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
Typical Latency\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Integrated Multi-satellitE Retrievals for Global precipitation
measurement early run (IMERG-Early; Hou et al., 2014)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Global network of satellites unified by measurements from a single
reference radar/radiometer satellite.\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\[0.1\] (\textasciitilde{}10 km)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
30 minutes\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
4 hours\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Integrated Multi-satellitE Retrievals for Global precipitation
measurement (IMERG-Final; Hou et al., 2014)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
In addition to the satellite data included in IMERG-Early, IMERG-Final
includes late-arriving microwave overpasses, monthly gauge-based
adjustments, and an algorithm that interpolates forward as well as
backward in time.\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\[0.1\] (\textasciitilde{}10 km)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
30 minutes\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
3.5 months\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Multi-Radar Multi-Sensor (MRMS; Zhang et al., 2015)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Integrates data from radars, satellites, precipitation gages, and other
sensors to provide near real-time decision support.\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\[0.01\] (\textasciitilde{}1.1 km)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
1 hour\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textless{} 5 minutes\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
North American Land Data Assimilation System version 2 (NLDAS-2)
meteorological (Xia et al., 2012)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Disaggregation of Climate Prediction Center daily precipitation using
bias-corrected radar\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\[0.125\] (\textasciitilde{} 12 km)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
1 hour\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
4 days\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2 \textbar{}} Hit ratio and false alarm ratio for each
product and the Guzzetti et al. (2008), Clarizia et al. (1996), and
Cannon et al. (2008) intensity-duration thresholds.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
Product & Include sites & \textbf{Hit ratio} & \textbf{Hit ratio} &
\textbf{Hit ratio} & \textbf{False alarm ratio} & \textbf{False alarm
ratio} & \textbf{False alarm ratio}\tabularnewline
\midrule
\endhead
Intensity-duration threshold: & & Guzzetti et al. (2008) & Clarizia et
al. (1996) & Cannon et al. (2008) & Guzzetti et al. (2008) & Clarizia et
al. (1996) & Cannon et al. (2008)\tabularnewline
IMERG-Early & All (n=146) & 0.56 & 0.54 & 0.47 & 0.17 & 0.16 &
0.11\tabularnewline
& Verified (n=59) & 0.61 & 0.59 & 0.54 & 0.19 & 0.18 &
0.12\tabularnewline
IMERG-Final & All (n=145) & 0.61 & 0.61 & 0.53 & 0.20 & 0.20 &
0.13\tabularnewline
& Verified (n=56) & 0.73 & 0.75 & 0.59 & 0.23 & 0.23 &
0.16\tabularnewline
NLDAS-2 & All (n=131) & 0.73 & 0.74 & 0.68 & 0.22 & 0.24 &
0.19\tabularnewline
& Verified (n=55) & 0.76 & 0.76 & 0.65 & 0.22 & 0.24 &
0.19\tabularnewline
MRMS & All (n=134) & 0.82 & 0.83 & 0.78 & 0.24 & 0.26 &
0.21\tabularnewline
& Verified (n=56) & 0.88 & 0.86 & 0.84 & 0.26 & 0.28 &
0.22\tabularnewline
\bottomrule
\end{longtable}





\section*{Figure legends}

{\label{figure-legends}}

\textbf{Figure 1 \textbar{} Map of all landslide sites considered in
this analysis:} 228 landslide sites colored by whether the location was
approximate (n=148) or verified using aerial satellite imagery to
identify a visible scarp (n=80); Source of landslide locations was the
GLC (Kirschbaum et al., 2010), source of the DEM data used for the base
map (\emph{North America Elevation 1-Kilometer Resolution} , 2007).
Elevations above 3000 m are indicated as the highest value on the color
scale.

\textbf{Figure 2 \textbar{} Exposition into the types of precipitation
differences leading up to landslide events:} Cumulative precipitation
measurements at select landslide sites for the 30 days before the event.
The precipitation is variable across the different products, and the
selected sites each demonstrate diverse types of variability. Panel (a)
shows similar measurements among all products throughout the 30 days. In
panel (b), all products are well correlated, but the accumulated depths
greatly differ. In panel (c) both IMERG products reports less
precipitation until the landslide-triggering storm when they reverse and
report more precipitation. In panel (d) IMERG-Early reports much more
precipitation than the other products. Finally, in panel (e) no
landslide-triggering precipitation was detected by any product,
suggesting a location error in the landslide record.

\textbf{Figure 3 \textbar{} Relative magnitude of precipitation products
on the day of the landslide} : Rank among all products for each day, and
z-score of daily precipitation as measured by each product for each of
228 events. Panels (a) and (c) show the entire precipitation record
while panels (b) and (d) show only the day-of-landslide precipitation
for comparison. Z-score are plotted on a pseudo-log scale, a combination
of a linear scale near zero and a log scale for higher values.

\textbf{Figure 4 \textbar{} Storm characteristics vs.~the ensemble
mean:} Depth, duration, intensity, peak intensity, and return period for
each of the landslide-triggering storms as measured by four
precipitation products. Least-squares regression lines with
\(95\%\)confidence intervals are also shown. Panels (a)-(e)
show all 228 sites while the bottom panel only shows the 80 verified
locations.

\textbf{Figure 5 \textbar{} Comparison of landslide-triggering
precipitation relative to intensity-duration thresholds:} Each storm in
the precipitation record and established global or climactic
intensity-duration thresholds. Landslide-triggering storms are shaded
with darker blue. The panels (a)-(d) contains precipitation data for all
sites while in panels (e)-(h) only verified sites are included. Points
above each threshold are predicted by the threshold to be landslides,
and so a larger proportion of landslides above the threshold indicates
better performance.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/figure-1-site-map/figure-1-site-map}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/figure-2-cumulative-precip/figure-2-cumulative-precip}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/figure-3-summary/figure-3-summary}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/figure-4-scatter/figure-4-scatter}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/figure-5-idt/figure-5-idt}

\end{center}
\end{figure}

\selectlanguage{english}
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