Remote Sens. 2021, 13, 991. https://doi.org/10.3390/rs13050991 www.mdpi.com/journal/remotesensing
Clustering of Rainfall Types Using Micro Rain Radar and
Laser Disdrometer Observations in the Tropical Andes
, Rolando Célleri
, Katja Trachte
, Jörg Bendix
and Johanna Orellana-Alvear
Departamento de Recursos Hídricos y Ciencias Ambientales, Universidad de Cuenca, Cuenca EC010207,
Ecuador; email@example.com (G.U.); firstname.lastname@example.org (R.C.)
Facultad de Ingeniería, Universidad de Cuenca, Cuenca EC010207, Ecuador
Institute for Environmental Sciences, Brandenburg University of Technology (BTU), Cottbus-Senftenberg,
D-03046 Cottbus, Germany; email@example.com
Laboratory for Climatology and Remote Sensing, Philipps-University Marburg, D-35032 Marburg,
* Correspondence: firstname.lastname@example.org; Tel.: +593-7-405-1000
Abstract: Lack of rainfall information at high temporal resolution in areas with a complex topogra-
phy as the Tropical Andes is one of the main obstacles to study its rainfall dynamics. Furthermore,
rainfall types (e.g., stratiform, convective) are usually defined by using thresholds of some rainfall
characteristics such as intensity and velocity. However, these thresholds highly depend on the local
climate and the study area. In consequence, these thresholds are a constraining factor for the rainfall
class definitions because they cannot be generalized. Thus, this study aims to analyze rainfall-event
types by using a data-driven clustering approach based on the k-means algorithm that allows ac-
counting for the similarities of rainfall characteristics of each rainfall type. It was carried out using
three years of data retrieved from a vertically pointing Micro Rain Radar (MRR) and a laser dis-
drometer. The results show two main rainfall types (convective and stratiform) in the area which
highly differ in their rainfall features. In addition, a mixed type was found as a subgroup of the
stratiform type. The stratiform type was found more frequently throughout the year. Furthermore,
rainfall events of short duration (less than 70 min) were prevalent in the study area. This study will
contribute to analyze the rainfall formation processes and the vertical profile.
Keywords: rainfall types; k-means; micro rain radar; laser disdrometer; rainfall characteristics;
Precipitation is among the most important components of the hydrologic cycle be-
cause it triggers important processes that determine water distribution and availability
[1–3]. In addition, precipitation is characterized by a high spatiotemporal variability. This
is particularly true in the Tropical Andes, where complex topography is a key factor that
influences rainfall processes . Here, precipitation variability has been studied only at a
certain extent [5–7]. This is because of the lack of high temporal resolution data, which is
one of the main obstacles to understand the rainfall processes and dynamics in this area
. Usually, rainfall characteristics such as rain rate are used to study rainfall variability
. Moreover, microphysical characteristics (e.g., drop size distribution) and the study of
the vertical profile of the rainfall allow to improve the knowledge about microphysical
processes that govern the formation of the hydrometeors and to identify rainfall types.
This rainfall variability can be captured by remote sensing observation with Micro Rain
Radar (MRR) and laser disdrometers. The advantage of these instruments is that they not
only enable to quantify the rainfall but also allow for the analysis of its microphysical
Citation: Urgilés, G.; Célleri, R.;
Trachte, K.; Bendix, J.; Orellana-
Alvear, J. Clustering of Rainfall
Types Using Micro Rain Radar and
Laser Disdrometer Observations in
the Tropical Andes. Remote Sens.
2021, 13, 991. https://doi.org/10.3390/
Academic Editor: Luca Brocca
Received: 28 January 2021
Accepted: 1 March 2021
Published: 5 March 2021
Publisher’s Note: MDPI stays neu-
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Copyright: © 2021 by the authors. Li-
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This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (http://crea-
Remote Sens. 2021, 13, 991 2 of 22
MRRs are instruments that measure the characteristics of the precipitation along its
vertical profile. MRRs retrieve the reflectivity profile, drop size distribution (DSD), rain
rate, velocity, and liquid water content (LWC)  for different atmospheric layers. These
characteristics allow for the analysis of the vertical structure of the rain. They also allow
to differentiate between rain types (convective and stratiform rain) and to identify the
height of the Melting Layer (ML) [2,11–13]. Besides, disdrometers are instruments that
retrieve characteristics as particle spectrum, the rain rate, the quantity, and the type of
rain . These instruments have been used to analyze the rainfall dynamic in mountain
areas [4,12,14–17]. In the Tropical Andes, the diurnal dynamics of the precipitation were
studied by Bendix et al.  using MRR data. The author found that rainfall is mostly of
stratiform type and the afternoon events are influenced by local convection. A study in
Peru and Bolivia using MRR data  showed the dominance of stratiform events during
the night, and suggested that the height of ML is an indicator of climate change. Using
microphysical data (e.g., mean volume diameter Dm) obtained from laser disdrometers,
Orellana-Alvear et al.  analyzed rainfall types at three sites with different height in the
Andes Cordillera in Ecuador. The authors found that convective type (rainfall associated
with higher rain rate and Dm) was more common in the lower elevation sites while light
rain was more frequent in higher sites. Seidel et al.  using MRR data, found that short
events (less than 3 h) were dominant in the Tropical Andes and nocturnal precipitation is
more of the stratiform type.
Previous studies highlight the importance of differentiating between rainfall types
[3,17–19], principally to analyze the rainfall behavior and find patterns in the rainfall at-
tributes. Furthermore, the definition of rainfall types is useful for improving the quantita-
tive precipitation estimation (e.g., Z-R relation) . Usually, rainfall types (e.g., stratiform
and convective) are defined by using some rainfall characteristics thresholds such as rain
rate [19–21]; DSD [22,23] and; reflectivity . Furthermore, in the case of the reflectivity
profile, it is used to determine the ML presence, which is also used to determine rainfall
types [11,25]. However, these thresholds are site specific  and depend mainly on the
local climate and the study area. This makes rainfall classification closely related to inde-
pendent, arguably subjective decisions rather than the possibility of extracting knowledge
only from the interactions between rainfall characteristics. This can be overcome using
This is a machine learning tool that allows grouping objects with similar characteris-
tics only based on the data. Clustering analysis based on the hierarchical and k-means
algorithm had been successfully used to classify rainfall events in different studies such
as Dilmi et al. , dos Santos et al. , Fang et al. , and Peng and Wang . These
studies were carried out in subtropical regions [26,28,29] and tropical semiarid regions
. However, there is no report of the application of these techniques in tropical high
mountains up to date.
In this context, this study aims to analyze rainfall-event types in the Tropical Andes
by using a clustering approach based on the k-means algorithm that allows accounting
for the similarities of rainfall characteristics (e.g., duration, rain rate, drop size distribu-
tion) of each rainfall type. This will allow for the improvement of the knowledge of rainfall
dynamics and its occurrence in the region.
2. Study Site and Data
2.1. Study Site
The study area Balzay (2°53′S, 79°02′W) is located at 2610 m above sea level (a.s.l), in
the outskirts of the city of Cuenca in the Tropical Andes of southern Ecuador, as shown
in Figure 1. Balzay is located in the inter-Andean depression  and shows a bimodal
rainfall regime with two wet seasons in the months March-April-May and October. The
mean annual precipitation is 969 mm  and the mean temperature is 14 °C . The
precipitation is mainly driven by the displacement of the Intertropical Convergence Zone
Remote Sens. 2021, 13, 991 3 of 22
(ITCZ) [32,33]. The ITCZ is defined as the zone in the vicinity of the equator, where the
trade winds from the north and south converge . The climate in Ecuador shows high
variability in part due to the presence of the Andes Cordillera. In the inter-Andean de-
pression, due to the impact of the ITCZ, the tropical Amazon air masses from the East and
the Pacific coastal regimen from the West are the main factors that control the climatology
of the area .
Figure 1. Study site in the southern Ecuador; the diamond indicates the location of instruments.
The instruments used in this study are the Micro Rain Radar (MRR)  and the laser
disdrometer (Thies Clima LPM—Laser Precipitation Monitor) . A detailed explanation
of the instruments’ operation is provided in the following sections.
2.2.1. Micro Rain Radar
The MRR is a vertically pointing frequency modulated continuous wave (FM-CW)
doppler radar. It operates at 24.1 GHz and 12.5 mm wavelength. The radar transmits a
signal along a vertical orientation in the atmosphere over the antenna [9,36].
The primary advantage of the MRR is its high sensitivity and temporal resolution to
detect small amounts of precipitation (i.e., low rain rates) . The MRR detects droplets
with diameters between 0.25 to 6 mm , and it assumes water drops are spherical. The
MRR retrieves basically the Doppler spectra of the falling droplets and radar reflectivity
where parameters like the mean fall velocity, droplet concentration, rain liquid water con-
tent, and rain rate are derived from. The details of the parameters derivation can be found
in [9,36–38]. The MRR records these parameters for all the vertical profile.
The vertical profile consists of 31 height steps (gates) whose maximum and minimum
height resolution is defined by the user and range between 10 and 1000 m. In our case, the
MRR was operated with a height resolution of 100 m and the data were captured with a
The disdrometer used in this study is a Thies Clima Laser precipitation monitor
(LPM) , which is based on a laser sensor that produces a horizontal light beam. This
sensor has a wavelength of 785 nm and the measuring area is 45.6 cm
. When a precipita-
tion particle falls through the light beam, the receiving signal is attenuated. The particle
diameter is estimated from the reduction in the signal amplitude while its fall velocity is
Remote Sens. 2021, 13, 991 4 of 22
calculated from the duration of the decreased signal. Each drop is assigned to one of 22
size bins and to one of 20 velocity bins. The size bins are between 0.125 and 8 mm and the
velocity bins are between 0 and 10 m s−1. Later, a telegram is sent every minute. This shows
the number of drops that the LPM detected in each class depending on the bin combina-
tion (diameter-velocity). The LPM retrieves the particle spectrum, the rain rate, the quan-
tity, and the type of precipitation. Data were captured with 5-min frequency, as a result
of averaging 1-min observations.
2.3. Data availability and Quality Control
Three years of data, from February 2017 to February 2020 of both instruments were
used in this study. The performance of the disdrometer data has been evaluated in [39,40].
In spite of the good performance of the disdrometer, it shows some issues at high wind
speeds (>15 m s−1) , which, however, were not present in our disdrometer records .
Furthermore, to eliminate uncertainty measurements obtained from misclassification of
particles, margin fallers and splashing effect, we employed the methodology used in Orel-
lana-Alvear et al. . Details regarding the quality control method can be found in Orel-
lana-Alvear et al.  and Friedrich et al. . In the case of the MRR, the data were aver-
aged to 5-min. Several parameters of the MRR such as rain rate (mm h−1), mean fall veloc-
ity (m s−1), liquid water content (g m−3), droplet concentration (m−3 mm−1), and radar re-
flectivity (dBZ) were used for the rainfall classification process.
The validity of the MRR data has been reported by many researchers [11,19,40,42,43].
These studies showed a good agreement between MRR and different types of disdrometer
(OTT Parsivel, Joss-Waldvogel and LPM) through a correlation analysis. Thus, to ensure
the validity of the MRR measurements, we compared the rain rate observed by the MRR
at the lowest height (100m) with the rain rate obtained from the collocated disdrometer at
30-min cumulative interval (Figure 2). This comparison was performed by using the de-
termination coefficient (R2). The coefficient of determination between MRR and LPM rain
rate data was 0.74 (Figure 2). Therefore, we had a good fit in spite of the difference in
height where each sensor is monitoring the rainfall (i.e., the disdrometer is located at
ground level while the MRR first range of monitoring is 0–100 m).
Figure 2. Correlation between rainfall recorded by the Micro Rain Radar (MRR) and Laser Precipi-
tation Monitor (LPM) data at 30-min accumulation. The solid line denotes the regression line, the
dashed line denotes the bisector line, and R2 is the determination coefficient.
As shown in Figure 2, the MRR tended to slightly underestimate the rainfall amount
compared to disdrometer observations. Nevertheless, the MRR showed some outliers es-
pecially in higher values. Figure 2 also suggests that the MRR tend to overestimate the
Remote Sens. 2021, 13, 991 5 of 22
rainfall above 10 mm 30 min−1. Sarkar et al.  found that the LPM and MRR had a good
fit (R2 = 0.74). The author suggested that over 60 mm h−1, the MRR has a high probability
of underestimating the measures of rain rate. In addition, Rollenbeck et al.  compared
the precipitation measurements between five recording devices. The author found that
the MRR underestimate the precipitation. The MRR had a high sensitivity to detect light
rain, but it had problems detecting higher rain rates [44,45]. These studies agree with our
results and show the good fit between both instruments. Thus, we derived the drop size
distribution (m−3 mm−1) from the disdrometer data. It was calculated from the number of
drops for each size and velocity bins . The details of the drop spectrum calculation can
be found in [4,40,46].
First, we selected rainfall events from the available time series by using three criteria
which are detailed in Section 3.1. Then, for each of them, we determined individual rain-
fall event characteristics (e.g., duration, maximum rain rate, etc.) derived from the MRR
and LPM data. Finally, we applied the k-means algorithm that clusters these events based
on their derived characteristics. A detailed explanation of the last steps is provided in
3.1. Rainfall Events Selection
Representative data of the study period were obtained through the delineation of
rainfall events using three criteria: (i) minimum interevent time, (ii) minimum total rain-
fall accumulation, and (iii) minimum duration. The minimum interevent time is defined
as the minimum lapse of time for a dry period (i.e., no rainfall occurrence or less than a
threshold) between rainfall events, which is necessary to classify two events as independ-
ent. In this study, we used the threshold of rain rate greater than 0.05 mm min−1 for each
time step. This threshold was identified using a sensitivity analysis by testing different
values between 0.01 and 0.1 mm min−1. The value of 0.05 mm min−1 was selected because
it eliminated the long tails and discontinuities that lower rain rate values showed in the
events. The minimum total rainfall accumulation refers to the rainfall total during the
event. The minimum duration is the time where the rainfall was continuous (without
gaps) [47,48]. To identify the proper thresholds for these values we performed a sensitivity
analysis which was carried out by using a variation between a range of values of each
criterion (minimum interevent time, minimum total rainfall accumulation, and minimum
duration) with the purpose of getting a probability distribution. This distribution was
used to find a threshold where the number of events got steady for each criterion and
thus, we got a trade-off between the number of events and their representativeness. The
range of values to find the proper threshold were: (i) 20–60 min for minimum interevent
time; (ii) 2–8 mm for minimum total rainfall accumulation per event and; (iii) 10–30 min
for minimum duration. The methodology of Orellana-Alvear et al.  was used as a start-
ing point to determine such thresholds. Finally, rainfall events that met the criteria were
selected for the current study.
3.2. Rainfall Classification
3.2.1. Derivation of Rainfall Events Characteristics
Rainfall event characteristics are used to describe and synthesize the behavior of a
rainfall event . After the rainfall events were selected, several of their temporal (e.g.,
duration) and hydrometeorological (e.g., rainfall accumulation) characteristics were
picked out for the rainfall classification process. However, there is no universally agreed
set of characteristics to describe a rainfall event . Generally, choosing the rainfall char-
acteristics depends on the instrument, its measured variables, and the objective of the
study. Here, we used the characteristics obtained from the MRR and the LPM; these in-
clude hydrological and microphysical information of the rainfall events (Table A1).
Remote Sens. 2021, 13, 991 6 of 22
Derivation of MRR and Disdrometer Characteristics
We used four hydrological characteristics of rainfall events of the lower height bin of
the MRR, namely rain rate (mm h−1), mean fall velocity (m s−1), liquid water content (g
m−3), and radar reflectivity (dBZ). Moreover, rainfall accumulation and the duration of the
event were calculated.
Regarding microphysical data, the LPM retrieved the drop spectra N(D) (m−3 mm−1)
and drop diameters D (mm). These characteristics are used to represent the Drop Size
Distribution (DSD)  at each time step. Nonetheless, we needed to combine these char-
acteristics to get a representative DSD for each rainfall event. So, we derived the mean
volume diameter (Dm) in mm that represents the proportion between the fourth and third
moment of the DSD, as defined by . It is frequently used to represent the DSD of a
rainfall event [4,26,43,51,52]. Finally, we analyzed the characteristic distribution and ex-
tracted the mean, maximum, minimum, and median value for characterizing the rainfall
properties within each event.
Determination of the Melting Layer
The Melting Layer (ML) is an important characteristic, commonly used to identify
rainfall classes [11,25,53]. The ML determination is based on the identification of a Bright
Band (BB) signature in the vertical profile of the reflectivity. This BB detection consists in
determining the prominent increase of the values in the reflectivity profile at specific
gates, using the maximum slope found in the reflectivity profile [11,54,55]. This band is a
combination of water, air, and ice that highly increase the reflectivity values at certain
gates of the vertical profile. In addition, another factor that influences the increase in re-
flectivity is the density effect, which consists in the water (melted and snow) distribution
in the particles [19,53–55].
A general solution to identify the ML is performing a visual inspection of the reflec-
tivity profile [19,22]. Thus, the BB was identified for each event based on a visual inspec-
tion and the scheme of Fabry and Zawadski . The scheme analyzed the vertical reflec-
tivity profile of each event in order to determine the presence of the BB and to extract
parameters such as the height of the BB. As a result, three possible scenarios related to the
occurrence of the BB were found: (i) the BB is always present during the rainfall event, (ii)
the BB is partially present along the event, and; (iii) the BB is absent. Thus, we used a three
stage ML variable that can be set to 1 (BB always present), 0.5 (BB intermittent), and 0 (no
3.2.2. Clustering Approach: k-means Algorithm
Clustering analysis is a statistical tool used to group objects with similar characteris-
tics. The technique performs an unsupervised classification; thus, it is not based on the
use of a priori labels to determine the clusters [26,56,57]. Therefore, by using a set of objects
(instances from a data set), it finds their natural grouping that maximize the cohesion
within the groups while ensuring higher separation from other clusters . Clustering
algorithms are divided into hierarchical and partitional . In partitional algorithms as
k-means clustering, the definition of the number of clusters and the feature selection are
important conditions in the cluster formation .
The k-means algorithm was used for obtaining the rainfall event classes. This is ac-
complished by identifying different groups of instances (i.e., rainfall events) with similar
features (i.e., the rainfall characteristics such as duration, DSD, etc.) within each group in
a data set . The main idea behind the k-means algorithm is grouping n points of m
dimensions into k clusters, so that for each cluster, the square of the Euclidean distance
between the x points that belongs to n and the centroid of the cluster is minimal (Equation
Remote Sens. 2021, 13, 991 7 of 22
where J is the Euclidean distance, xi is each data point and cj is the centroid of the cluster.
The k-means algorithm is iterative, so the process is repeated until the Euclidean distance
converges to the minimum value. In order to apply the k-means algorithm, it is needed to
fulfill three conditions: determine the features (rainfall event characteristics) to use; stand-
ardize the features and define the number of clusters.
To begin this process, we decided to select a subset of features to diminish redundant
information for the algorithm and for obtaining a parsimonious model. A number of tech-
niques have been developed for feature-selection . We chose each feature by perform-
ing a cross-correlation analysis between all features by means of the Pearson correlation
coefficient. This aimed to highlight the features that contribute redundant information for
the algorithm. With this, we removed these features and we got a parsimonious model
with lower number of features.
In the case of the ML feature, it is worth mentioning that the identification of the ML
and its corresponding feature derivation needed a great effort and was very time consum-
ing because we had to visually check each one of the rainfall events. For these reasons,
this feature was included and excluded from the original list of features with the purpose
of determining its influence over the rainfall clusters formation.
Furthermore, the standardization of features is mandatory for the implementation of
the k-means algorithm. This is because all features should have the same weight for cal-
culating the Euclidean distance. While different methods have been proposed to stand-
ardize the features, Milligan and Cooper  found that standardizing by the range was
the best method of eight standardization methods. So, we decided to use the range method
()() , (2)
where Z is the standardized feature, X is the feature, and Max and Min are the maximum
and minimum value of X, respectively.
Finally, we aimed to select the optimal number of clusters for our data set. Milligan
and Cooper  evaluated thirty procedures to determine the optimal number of clusters
and they found that it highly depends on the data. For this study, we decided to run the
algorithm a priori with two and three clusters because rainfall types are usually classified
in two and three classes (stratiform, convective, and transition or mixed). Furthermore,
we evaluated the quality of the cluster separation, so we decided to use the elbow method.
Here, we needed to identify a sharp elbow between the sum of the squared errors as a
function of the number of clusters . In addition, this value usually indicates the opti-
mal number of clusters. In our case we will include and exclude the ML feature in this
analysis to identify its influence on the cluster’s separation.
4.1. Rainfall Events Selection
We selected 92 rainfall events after finding the thresholds that met the criteria for the
rainfall event separation. The thresholds of the three criteria were: 30 min for minimum
interevent time, 3 mm for minimum total rainfall accumulation per event, and 15 min for
minimum event duration.
Figure 3 illustrates the distribution of the rainfall event duration and occurrence in
each month. The distribution of the rainfall events along the year is in agreement with the
bimodal regime of precipitation in the study area as documented by Campozano et al. 
and Célleri et al. . The higher number of rainfall events occurred in March, May, and
October whereas June, July, August, and September had the lowest number of rainfall
events. However, no rainfall events accomplished the defined criteria (e.g., minimum
interevent time, minimum total rainfall accumulation, and minimum duration) in July,
which is one of the driest months of the year with a mean monthly precipitation of 7mm.
Remote Sens. 2021, 13, 991 8 of 22
Furthermore, the longest events duration was found in April and May, which are the wet-
test months with a mean monthly precipitation of 78 and 98 mm, respectively.
For the selected events, we found that the rainfall event duration was shorter than 3
h (Figure 3). In addition, we found that short rainfall events (i.e., <70 min) were predomi-
nant (around 70%) in the region during the study period. In addition, the mean duration
at every month was less than 70 min.
Figure 3. Violin plots show the frequency distribution of rainfall event duration per month at Balzay. n is the number of
events and the gray point represents the mean value.
4.2. Rainfall Event Features
Determination of the Melting Layer
With the aim of determining the ML feature, we analyzed the vertical reflectivity and
velocity profile and well as their evolution along the rainfall event. Here we used data
with 1 min frequency, as it was necessary to identify the variability of the rainfall charac-
teristics along the event. We had three scenarios linked to the occurrence of the BB: (i)
present, (ii) partially present, and (iii) absent.
Figures 4–6 show the three scenarios (i–iii) about the BB identification. The event
shown in Figure 4a,b shows a constant enhancement in the reflectivity and in the velocity
profile around 2000 m above ground level (a.g.l), which evidence a BB. In the reflectivity
profile, there is a clear increase of the reflectivity value around this height. In addition, a
closer inspection of the velocity profile showed an extreme variation in the values around
the 2000 m a.g.l. and in consequence supports the presence of the ML. In this case, the ML
variable was set to 1.
In contrast, Figure 5a,b shows that the BB was not always present during the entire
rainfall event as seen in the reflectivity and velocity profiles. Thus, the ML related feature
was set to 0.5. The clear BB appeared from 15:00 h until the end of the event around 2000
m a.g.l. In the reflectivity and velocity profiles, we could see an increase of their values
around this height from 15:00 h until the 15:35 h which is the end of the event. However,
there is no previous signature of BB.
Finally, Figure 6a,b illustrates the absence of the BB along the entire event in the re-
flectivity and velocity profiles. There are no strong variations in the reflectivity and veloc-
ity profiles as in the previous scenarios. This means that the ML was not evident in the
rainfall event. Here, we set the ML related feature to 0.
Furthermore, in Figures 4c, 5c, and 6c, we differentiated between the rain rate range
and the evolution of the event in the three scenarios of the BB.
Remote Sens. 2021, 13, 991 9 of 22
Figure 4. Event with a clear bright band on 21 March 2019: (a) reflectivity profile (dBZ), (b) vertical
fall velocity (m s−1), (c) rain rate at range of 100 m a.g.l (mm h−1).
Figure 5. Event with intermittent bright band on 26 December 2017: (a) reflectivity profile (dBZ),
(b) vertical fall velocity (m s−1), (c) rain rate at range of 100 m a.g.l (mm h−1). White color in (a),
represents missing data.
Remote Sens. 2021, 13, 991 10 of 22
Figure 6. Event without bright band on 29 January 2019: (a) reflectivity profile (dBZ), (b) vertical
fall velocity (m s−1), (c) rain rate at range of 100 m a.g.l (mm h−1). White color in (a), represents
In Figure 4c, we found that the rain rate ranged between 0 and 16 mm h−1. In Figure
5c, the range was between 0 and 35 mm h−1. In addition, the rain rate reveals two peaks
before 15:00 h. Figure 6c shows that the rain rate ranged between 0 and 80 mm h−1 and
also has two peaks.
4.3. Clustering Using k-means
4.3.1. Features Selection
We analyzed the cross-correlation between the 23 features determined in Table A1.
Results of the cross-correlation analysis are provided in Figure A1. From the cross-corre-
lation analysis, we found that features as reflectivity and liquid water content are related
especially with rain rate. Therefore, rain rate could explain these features in the algorithm.
Furthermore, the median value distribution of all the features are linked in their majority
with the mean value distribution of the same or other feature. Therefore, the features with
a Pearson correlation coefficient higher than 0.8 are found to provide repetitive infor-
mation in the clusters, so we kept only one feature and removed the related one(s). Thus,
we determined that 12 features were the most important and these capture all the varia-
bility during the event (see Table 1). In the case of Mean Rain Rate (RRmean), it had a
Pearson correlation coefficient of 0.8 with the Maximum Rain Rate (RRmax) feature. How-
ever, we kept this feature because it is commonly considered to determine thresholds for
rainfall types. The list of the selected features is provided in Table 1.
Table 1. Features selected for the cluster analysis.
Number Variable Name Unit Symbol
1 Maximum Rain Rate mm h−1 RRmax
2 Minimum Rain Rate mm h−1 RRmin
3 Mean Rain Rate mm h−1 RRmean
Remote Sens. 2021, 13, 991 11 of 22
4 Rainfall Accumulation mm Raccum
5 Maximum Velocity m s−1 Vmax
6 Minimum Velocity m s−1 Vmin
7 Mean Velocity m s−1 Vmean
8 Event Duration minutes Dur
9 Melting Layer - ML
10 Maximum Mean Volume Diameter mm Dmmax
11 Minimum Mean Volume Diameter mm Dmmin
12 Mean Liquid Mean Volume Diameter mm Dmmean
4.3.2. Features Standardization
As stated previously, standardization is mandatory for applying the k-means clus-
tering algorithm. This ensures that all features are equally weighted in the process. This
method compensates the differences among the range of all the features. For example, the
RRmax values range between 5 and 100 mm h−1 whereas the Dm values range between
0.30 and 5 mm.
Figure 7 shows the 12 features in a standardized mode. In the case of the rain rate
related features (RRmax, RRmin and RRmean), we had a few events with high values,
especially in RRmax. In this feature, around 80% of the events showed values below 0.5.
Figure 7. Standardized features using the range method.
With respect to rainfall accumulation (Raccum), we had the same pattern as RRmax,
but here around 70% of the events showed values below 0.25. In the case of Duration
(Dur), short duration events (less than 0.5) were predominant. For the three velocity fea-
tures, high values were dominant in all of the events. Finally, Dm max and Dm mean
showed a similar distribution in their values.
4.3.3. Clustering with k = 2 and k = 3
The 12 standardized features and the a priori selected number of clusters (k = 2 and
k = 3) were used to apply the k-means algorithm. In addition, by applying the elbow
method, we found that k = 3 was the optimal k when we include the ML feature. However,
when we exclude the ML feature, we find that k = 2 was the optimal k (see the Figure A2).
So, these results agreed with our number of clusters selected a priori. To facilitate the
graphical visualization of the clusters, we elaborated Figure 8 by using the two principal
components from the principal component analysis (PCA); details regarding the method-
ology of PCA can be found in Abdi and Williams  and Wold et al. .
Remote Sens. 2021, 13, 991 12 of 22
Figure 8. The classified rainfall events based on cluster analysis: (a) two classes (with Melting Layer—ML feature), (b) two
classes (without ML feature), (c) three classes (with ML feature), (d) three classes (without ML feature). Cl1, Cl2, Cl3 are
the number of events per each class.
Figure 8 shows the results of the clustering approach by using k = 2 and k = 3. For
each k we present the subsequent results of including or excluding the ML feature in the
clusters formation. For simplicity we would refer as Class x (e.g., Class 1, Class 2) to every
group resulting of the clustering process. Figure 8a,b with k = 2, present the Class 1 and
Class 2. By excluding the ML feature, only two events shifted from Class 1 to Class 2. Also,
this could be observed in the variation of the number of events in each Class (Cl).
Figure 8c,d with k = 3, present the Class 1, Class 2 and Class 3. By using k = 3, we
found that 11 events shifted the class they belong initially. In addition, this could be ob-
served in the variation of the number of events in each Cl.
Furthermore, when we increased the number of groups (i.e., k = 2 to k = 3) inde-
pendently of the ML feature, it can be seen in Figure 8a–c and Figure 8b–d that Class 3 is
formed principally by a splitting of Class 2. Besides, applying three classes (k = 3), we
found a higher variability in the formation of the clusters.
Features Distribution Analysis per Each Class
Furthermore, we analyzed the distributions of the features obtained per each class in
order to identify the thresholds of the features value for rainfall classification. Figure 9
shows the distribution of all the features using k = 2 and k = 3 and the influence of the
presence or absence of the ML feature in the clusters formation.
Remote Sens. 2021, 13, 991 13 of 22
Figure 9. Boxplots of variables: (a) two classes, (b) three classes.
Remote Sens. 2021, 13, 991 14 of 22
In the clusters with k = 2 (Figure 9a), we found that the highest values of all features
but the duration occurred in Class 1. Thus, in this class we had events with higher rain
rate, velocity, Dm, and rainfall accumulation. However, the same events had the shortest
duration in comparison with Class 2. On the other hand, Class 2 had events with lower
values in all features, but these were also the events with the longest duration. Moreover,
we observed that the ML feature has no effect in the clusters’ formation. This can be seen
in the similarity of the feature distributions for both scenarios.
Similarly, we obtained comparable results in the clusters with k = 3 (Figure 9b). Class
1 showed events with higher values in the rain rate, velocity, rainfall accumulation, and
Dm but shorter values in the event duration. However, in Class 2 and Class 3, it was dif-
ficult to define a tendency because there was not an evident pattern in all the features. For
instance, in comparison with Class 2, Class 3 showed higher value in RRmax but shorter
values in RRmin. However, Class 2 showed the highest value in the duration event fea-
Furthermore, in the clusters with k = 3, we observed a more notorious range differ-
ence regarding the values of the features when using the ML feature in comparison with
their counterparts when using k = 2.
Distribution of Rainfall Classes along the Year
In order to analyze the rainfall events frequency, we calculated the events percentage
by month from every cluster as seen in Figure 10.
Figure 10a,b present the events percentage when we included or not the ML feature
with k = 2. In concordance with the Figure 8a,b, the 2 events that shifted of Class, belonged
to January and May. For this reason, we found a slight variation in these months in the
Figure 10a,b. In addition, these two events did have a BB and their rain rate showed a
range between 0 and 60 mm h
in 1min frequency.
Figure 10. Monthly event percentage for two classes: (a) with ML feature, (b) without ML feature. Events for three classes:
(c) with ML feature, (d) without ML feature.
Remote Sens. 2021, 13, 991 15 of 22
Furthermore, we found that Class 1 was dominant (more than 50%) only in March
and November. As a result, we had a predominance of the Class 2 along the year.
Figure 10c,d shows the events percentage by including or excluding the ML feature
with k = 3. In Figure 10c,d, we found a different percentage of events in January, March,
April, October, November, and December especially in the Class 2 and Class 3.
Our study shows that we have a prevalence of short rainfall duration in the study
area. These results about short rainfall duration support evidence from previous observa-
tions [4,14]. Orellana-Alvear et al.  analyzed the rainfall events duration using the LPM
disdrometer and found that the mean event duration is around 3 h. In the same way,
Seidel et al.  confirmed that the short duration events are dominant in this study area
by using MRR data. Furthermore, the short duration of the events evidenced the necessity
of high temporal resolution to capture their variability. However, the instruments’ time
resolution (e.g., rain gauge) limit capturing the variability in these events [14,68]. Padrón
et al.  already discussed the influence of different instrument time resolution (rain
gauge and disdrometer laser) in rainfall data after finding that the rain gauge underesti-
mates rainfall catch. In our case, with the MRR and LPM data, we could analyze the tem-
poral variability (i.e., 1 min frequency) with respect to rain rate, velocity, reflectivity, liq-
uid water content, rainfall accumulation, and mean volume diameter.
With respect to the rainfall characteristics, it is interesting to note that the events with
a clear BB were related to the low rainfall rain rate range at the ground level. In addition,
events with intermittent BB had an intermediate rainfall rain rate range between the other
two scenarios of BB. This suggested that these events are mixed case of the other scenarios
of BB. In the same way, events with no BB were related to the high rainfall rain rate range
at the ground level. This finding was also reported by Das et al. , Seidel et al. , and
Das and Maitra . The authors related these scenarios of the BB to stratiform, transition,
or mixed and convective classes. Furthermore, Seidel et al.  pointed out that the BB
typically lies between 1700 and 2400 m a.g.l; this is in concordance with our results.
Furthermore, as can be seen in Figures 4–6, rainfall starts forming at higher height
gates (around 2000 m a.g.l), which is the height where we found the BB. Later, this rainfall
comes to the ground gate with a lag time. This is named the boundary effect . Moreo-
ver, Seidel et al.  identified that it could be a problem in its rainfall classification. So,
to evaluate their rainfall classification method, the author employed other approaches that
used different features (e.g., Dm).
Regarding the clustering method, previous studies [58,62,64] have noted the im-
portance of defining the number of clusters and the features selected before applying the
algorithm. In our case, we defined the number of clusters considering the typical rainfall
classes (convective, stratiform, and mixed).
In the case of the features selected, we reduced from 23 to 12 features. Dilmi et al. 
reduced the number of features from 23 to 5 using a genetic algorithm and self-organizing
maps. Despite using different features than in this study, the rain rate, duration, and rain-
fall accumulation features belonged to the features selected. So, it suggests that these fea-
tures are important in the rainfall classification. In relation to data standardization, our
results are in agreement with [26,59,63], who found that data standardization is required
to get the same weighting of the features before clustering.
Further by using the clustering method we conducted a classification of rainfall
types. With respect to the number of clusters, one interesting finding is to note that the
Class 3 and Class 2 (with k = 3) are principally part of the Class 2 (with k = 2) (Figure 8).
So, the Class 3 could be considered like a subclass of the Class 2. These results are in agree-
ment with Dilmi et al.  findings, which showed five subclasses of the two mainly rain-
fall types (convective and stratiform). Furthermore, our results suggest that with k = 2, we
obtain remarkable features differences between the Class 1 and Class 2 (Figure 9a). These
Remote Sens. 2021, 13, 991 16 of 22
findings suggest that when we have another class (i.e., Class 3), it will be a result of split-
ting one of the main classes (k = 2). Besides, we analyzed the influence of including or
excluding the ML feature in the cluster formation. In the case of k = 2, the results suggest
that the ML feature did not affect the cluster formation. However, in k = 3, we had a shift
of 11 events where more than 50% of these events change from Class 3 to Class 2 or vice
versa. A possible explanation for this might be that the Class 3 and Class 2 (k = 3) are a
subclass of the Class 2 (k = 2). So, the ML feature influenced in the cluster formation when
we used three classes (k = 3).
Therefore, the features selected and determination of number of clusters play an im-
portant role in the cluster formation. For these reasons, these conditions should be defined
carefully. In addition, we have to notice that k-means is an unsupervised method, so we
did not evaluate the information a priori  to get these rainfall classifications.
For the purpose of determining the threshold values of the features for the rainfall
classification, we assessed the features distribution. Rainfall is usually classified in strati-
form, mixed, and convective rain. Stratiform rain is defined like a homogenous rain, with
low rain rate, high duration, and low velocity . Convective rain consists of variable
rain types, with high rain rate, low duration, and high velocity . Mixed rain is consid-
ered as a transition between convective and stratiform rain . Several authors have
identified rain rate and Dm thresholds for rainfall classification (Table 2).
Table 2. Summary of rainfall features thresholds of Tropical Zones.
Feature (Units) Author Location Rainfall
Rain Rate (mm h−1) Tokay, (1999) Marine
Das and Maitra,
This study Tropical
Class 1 (k = 2) 14.86 ± 0.20
Class 2 (k = 2) 6.55 ± 0.08
Class 1 (k = 3) 15.08 ± 0.32
Class 2 (k = 3) 5.43 ± 1.06
Class 3 (k = 3) 7.27 ± 0.14
Dm (mm) Seidel, (2019) Tropical
This study Tropical
Class 1 (k = 2) 1.55 ± 0.01
Class 2 (k = 2) 1.09 ± 0.01
Class 1 (k = 3) 1.57 ± 0.02
Class 2 (k = 3) 1.1 ± 0.05
Class 3 (k = 3) 1.1 ± 0.01
Table 2 shows that Das and Maitra  and Tokay et al.  agreed that the convec-
tive rain type showed the highest values in comparison with the stratiform rain type. In
the case of the mixed rain type, Caracciolo et al.  suggested that the values of rain rate
between 2 and 10 mm h−1 are complex to interpret because this range can show a mixed
of convective and stratiform rainfall. In addition, Bendix et al.  found that mixed rain
type had values of rain rate around 2.4 mm h−1. Besides rain rate, Dm has also been related
to rainfall type. Bringi et al.  found that events with larger Dm are considered convec-
tive. Seidel et al.  confirmed that convective events present values of Dm higher than
Remote Sens. 2021, 13, 991 17 of 22
stratiform events (Table 2). In this context, in our study, Class 1 events represent a con-
vective rain type, Class 2 events are associated with stratiform rain type, and Class 3
events exhibit characteristics of a mixed rain type.
The analysis of the distribution of the rainfall classes along the year show that the
stratiform type (Class 2) with k = 2 is not affected by the ML feature. Furthermore, the
convective type (Class 1) for k = 3 showed a maximum value in March which may be
related to the first ITCZ passage and a slightly higher value in October and November as
a result of the secondary ITCZ. Nonetheless, in k = 3 the stratiform type (Class 2) and
mixed type (Class 3) showed that the ML influenced the clusters formation. In addition,
our results support the finding of Seidel et al.  that during most of the year the strati-
form and mixed rain types are dominant.
The results obtained in this study are representative of the rainfall types in the high
Tropical Andes, above 2400 m a.s.l. Since the land-sea contrast and related sea breezes
have a great influence on the precipitation regime in the coastal lowlands, a different cat-
egorization of rainfall types may be found.
This is the first study that analyzed rainfall-event types in the Tropical Andes of Ec-
uador by using a data-driven clustering approach (k-means algorithm). The algorithm
was efficient to identify rainfall types based on the similarities of rainfall attributes only.
So, this method allowed disregarding subjective classification criteria of a human investi-
gator. Furthermore, this methodology could be used to study rainfall classes in other areas
because it is only based in data knowledge extraction. The investigation used common
rainfall characteristics such as rain rate but also included microphysical data (e.g., DSD).
Finally, it evaluated the influence of the Melting Layer (ML) as a feature in the clusters’
formation. From the study, the main conclusions are as follows:
• Rainfall types were identified by applying a clustering method and thus ensured an
objective separation of rainfall events because the classification is based exclusively
on the data (i.e., rainfall characteristics). The use of microphysical characteristics,
which are not commonly used due to instrument limitations, allowed for the provi-
sion of additional insights about each rainfall type.
• Three rainfall classes were identified in the study area: convective, stratiform, and
mixed. The rainfall classes show that the clustering method (k-means) works well to
distinguish the different rainfall patterns and identify the rainfall types. The first two
main classes, i.e., convective and stratiform, were obtained by first using the method
with two classes (k = 2). Here, the two groups showed a clear difference in the fea-
tures, especially in the mean values of rain rate, velocity, and Dm. In addition, the
convective type (class 1) showed rainfall events with shorter duration and higher rain
rate than the stratiform type (class 2). The inclusion/exclusion of the Melting Layer
feature did not influence the clustering results. Thus, it proves that the other rainfall
features are able to properly describe the differences between these two main groups.
When using three classes (k = 3), the mixed type (class 3) resulted as a subgroup of
one of the main groups (k = 2). So, the convective type remained almost invariable
regarding its rainfall characteristics. With respect to the stratiform type and mixed
type, their rainfall features are most similar between them. It suggests that the mixed
type has a dominant stratiform behavior.
• Rainfall events with shorter duration of less than 70 min are more frequent in the
study area. Furthermore, there is a prevalence of convective rainfall events in March
and November, while rainfall events of the stratiform and mixed type are common
during all the year.
The findings of this research provide insights about the rainfall dynamics in this trop-
ical mountain setting and show that data with high temporal resolution is necessary to
analyze the temporal variability in this area. Furthermore, these rainfall types identified
Remote Sens. 2021, 13, 991 18 of 22
here will be of interest to analyze the vertical profile of rainfall and identify the rainfall
formation process. Applications that can benefit from rainfall classification include (i) Nu-
merical Weather Prediction (NWP) verification regarding convective rainfall at high alti-
tudes, (ii) the improvement of quantitative precipitation estimation from scanning
weather radar, (iii) the parameterization of cloud microphysical processes in numerical
models, and (iv) the analysis of rain-fed soil erosion.
This study allowed for the analysis of the rainfall-event types and their occurrence in
the study area. Further analyses on the intraevent rainfall variability is suggested for fu-
Author Contributions: Conceptualization, G.U., J.O.-A., R.C.; methodology, G.U., J.O.-A., R.C.; soft-
ware, G.U.; formal analysis, G.U., J.O.-A., R.C., J.B., K.T.; data curation, G.U., J.O.-A., K.T.; writing—
original draft preparation, G.U.; writing—review and editing, J.O.-A., R.C., K.T., J.B.; visualization,
G.U.; supervision, J.O.-A., R.C.; project administration, R.C.; funding acquisition, R.C. All authors
have read and agreed to the published version of the manuscript.
Funding: This research was funded by the project “High-resolution radar analysis of precipitation
extremes in Ecuador and North Peru and implications of the ENSO-dynamics”. It was funded by
the German Research Foundation (Deutsche Forschungsgemeinschaft- DFG; DFG GZ.: RO3815/2-1)
and the Research Office of the University of Cuenca (DIUC). We want to thank these institutions for
their generous funding. The APC was financed by the Marburg University´s Open Access Publish-
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data are not publicly available due to university policies because
current research is being developed.
Acknowledgments: Thi s manu scrip t is an out com e of the Ma estría en Hidrología mención en Ecohi-
drología offered by Universidad de Cuenca. We are grateful to the technical staff that contributed
to the hydrometeorological monitoring. Furthermore, we would like to thank the three anonymous
reviewers whose comments helped to improve the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Table A1. The 23 Rainfall events features determined for each event.
Number Feature Name Unit Symbol Instrument
1 Maximum Rain Rate mm h−1 RRmax MRR
2 Minimum Rain Rate mm h−1 RRmin MRR
3 Mean Rain Rate mm h−1 RRmean MRR
4 Median Rain Rate mm h−1 RRmedian MRR
5 Rainfall Accumulation mm Raccum MRR
6 Maximum Velocity m s−1 Vmax MRR
7 Minimum Velocity m s−1 Vmin MRR
8 Mean Velocity m s−1 Vmean MRR
9 Median Velocity m s−1 Vmedian MRR
10 Event Duration minutes Dur MRR
11 Maximum Reflectivity dBZ Rmax MRR
12 Minimum Reflectivity dBZ Rmin MRR
13 Mean Reflectivity dBZ Rmean MRR
14 Median Reflectivity dBZ Rmedian MRR
15 Melting Layer - ML MRR
16 Maximum Liquid Water Content g m−3 LWCmax MRR
17 Minimum Liquid Water Content g m−3 LWCmin MRR
Remote Sens. 2021, 13, 991 19 of 22
18 Mean Liquid Water Content g m
19 Median Liquid Water Content g m
20 Maximum Mean Volume Diameter mm Dmmax LPM
21 Minimum Mean Volume Diameter mm Dmmin LPM
22 Mean Liquid Mean Volume Diameter mm Dmmean LPM
23 Median Mean Volume Diameter mm Dmmedian LPM
Figure A1. Cross-correlation matrix between rainfall characteristics. The highlight characteristics are the features selection
for the algorithm.
Figure A2. Sum of square errors in function of the number of clusters: (a) including ML, (b) excluding ML.
Remote Sens. 2021, 13, 991 20 of 22
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