https://doi.org/10.37815/rte.v35n2.1028

Original articles

Comparison of methodologies for flow prediction through teleconnection indices. Case study: Paute
river basin

Comparación
de metodologías para la predicción
del caudal mediante
los índices de teleconexión. Caso de estudio: Cuenca del
río Paute

María
Daniela González1
https://orcid.org/0009-0003-3436-0805, Darío Xavier Zhiña1, 2 https:// orcid.org/0000-0001-9556-4025, Alexandra Guanuchi-Quito1, 2 https://orcid.org/0000-0002-5583-8674,

Alex Avilés-Añazco1, 2 https://orcid.org/0000-0001-9278-5738

1Facultad de Ciencias Químicas, Universidad de Cuenca, Cuenca,
Ecuador

[email-masked]

Sent:

2023/06/24

Accepted:

2023/07/07

Published:

2023/10/15

2Grupo de E.valuación de riesgos ambientales en sistemas de producción y
servicios (RISKEN), Universidad de Cuenca,
Cuenca, Ecuador [email-masked], [email-masked], [email-masked]

Esta obra
está
bajo una licencia internacional

Creative Commons Atribución-NoComercial 4.0

Abstract

The Paute river basin (southern Ecuador) suffers hydrological changes due to climate change and human activities. Hydrological changes cause extreme events and affect ecosystems, hydroelectric plants, and quality of life. It highlights the importance of understanding hydrological behavior to make appropriate decisions in extreme
environments. This study seeks to predict discharges in the Paute
river basin through global teleconnection indices. Multiple Linear Regression
(MLR) was obtained using three different methodologies: multicollinearity analysis, Principal Component Analysis
(PCA), and correlation with monthly
delays. It was shown that the principal component analysis scenario obtained
the best predictive fits, specifically by including 41 indices and 20 components. For the scenario
using monthly delays,
the best delay
occurs within a single
month for most seasons. Finally,
with the multicollinearity analysis scenario, better
results were obtained using
41 indices, although
essentially the performance corresponds to the number and

indices of each model. Teleconnection indices are not
sufficient when used as the only input variable for download modeling
and prediction, giving
mostly unsatisfactory results.
However, a clear trend links the behavior of flows and indices, and it
is possible to improve the models based on more climatic variables or with
other predictive methods.

Keywords:
Discharge
prediction. Teleconnection indices. Principal
component analysis. Multiple regression models.
Multicollinearity analysis.

Resumen

La cuenca del río Paute (sur del
Ecuador) sufre cambios hidrológicos por el cambio climático
y las actividades humanas.
Los cambios hidrológicos
causan eventos extremos y afectan a ecosistemas, centrales hidroeléctricas y la calidad de vida. Destaca la importancia de comprender el comportamiento hidrológico para tomar decisiones adecuadas en ambientes extremos. Este estudio busca predecir
las descargas en la cuenca
del río Paute mediante los índices
de teleconexión global. Se obtuvieron modelos de Regresión Lineal Múltiple (MLR)
mediante tres metodologías diferentes: análisis de multicolinealidad, Análisis
de Componentes Principales
(ACP) y correlación con retrasos
mensuales. Se demostró
que el escenario de análisis de componentes principales obtuvo los mejores ajustes
predictivos, específicamente
al incluir 41 índices y 20 componentes. Para el escenario que usa retrasos mensuales, el mejor retraso
ocurre dentro de un solo mes, para la mayoría de las estaciones. Finalmente, en el escenario de análisis de multicolinealidad
se obtuvieron mejores resultados utilizando 41 índices, aunque esencialmente el
rendimiento corresponde a la cantidad y los
índices de cada modelo. Los índices de teleconexión
no son suficientes cuando
se utilizan como la única variable de entrada para el modelado y la predicción de descargas, dando resultados en su mayoría insatisfactorios. Sin embargo, existe una
clara tendencia que vincula
el comportamiento de caudales e índices, y es posible mejorar los modelos en base a más variables
climáticas o con otros métodos predictivos.

Palabras clave: Bases
de datos, predicción
de caudales, Índices
de Teleconexión, Análisis de Componentes Principales, Modelos de Regresión, Análisis de Multicolinealidad.

Introduction

Within studies related to global
teleconnections between ENSO (El Niño South Oscillation) and discharge,
strong and regionally consistent discharge impacts were found in Central and
South America, New Zealand, and Australia, while weaker signals were
observed in parts of Africa and North America
(Kundzewicz,
Szwed, & Pińskwar, 2019). To understand more the localized effects
of teleconnections, a large number
of studies are currently focused
on connecting flooding with climatic variability on a continental scale. Many relevant
studies have been carried
out in Australia, Asia, Europe,
North America, and South America.
These studies utilize indices
such as ENSO,
NAO (North Atlantic
Oscillation), AMO (Atlantic Multidecadal Oscillation), TSA
(Tropical Southern Atlantic),
TNA (Tropical Northern Atlantic), AO (Artic Oscillation), and PDO (Pacific Decadal
Oscillation), among others
(Giddings and Soto,
2006).

In
a local context, the most relevant index
is ENSO due to its effects. In South America, ENSO causes floods and droughts along
the western coast.
However, simulating ENSO in the region faces biases and uncertainties, especially when dealing with long time series. Systematic errors occur in the central
equatorial Pacific, the eastern equatorial Indian Ocean, and regions with
boundary current systems (such as the tropical Pacific and Atlantic) (Cai et al., 2020).

Within the confines
of the study area and its regional
dynamics, some studies
have

been conducted in Ecuador, demonstrating that the Sea Surface Temperature (SST) variability and ENSO phenomena have an impact on discharge
patterns throughout the nation. Similarly, multiple investigations have
established that discharge anomalies can be found nationwide using ENSO and its
modes. (Córdoba Machado et al., 2015). The research holds particular
significance due to its revelation that the three most common natural
catastrophes in Ecuador are floods, droughts, and landslides, with the first two having a significant impact on local living conditions
(Fontaine et al., 2008).

To comprehend the impacts of
teleconnections on climate, it is imperative to situate these events
within a climatological context. Teleconnection indices
are statistically significant correlations of recurrent
atmospheric anomalies that occur in nearby and distant areas, often
concurrently, at the planetary or hemispheric level (Hatzaki
et al., 2007). In line with this methodology, while examining the sequence of
oscillations that constitute climate variability around the mean values, these
anomalies are recognized by detecting deviations. This representation exemplifies the climate's ephemeral condition in response
to modifications and is demarcated by precise temporal and
spatial scales (IDEAM - UNAL, 2018). Additionally,
the teleconnection fluctuations encompass anomalies within their cycles,
generating variability modes. These modes are determined
from sub-calculations or temporal variations in the behavior
of teleconnection indices (Dima and Lohmann, 2004).

Broadly speaking, focusing on Ecuador
and the Andes, ENSO is the primary factor influencing SST and air pressure. El
Niño (warm phase) and La Niña (cold phase) patterns constitute
this phenomenon. Another factor is the PDO, which exhibits warm and cold
interdecadal phases that affect the surface waters of the Pacific Ocean. Recent
investigations have identified that the impact of PDO in South America has increased due to climate
change (Morán et al. 2016). Regarding precipitation, indicators related
to ENSO (such as Niño 3.4 and SOI), can affect rainfall in Ecuador;
also, Niño 3.4 and SST exhibit a significant causal relationship. The only significant impact that NP and WP have on rainfall in South America
is in Brazil. Due to spatial distance, AO and AAO have a minimal influence. Widespread droughts
have been related to TNA and
TSA. However, droughts or excessive rains in Ecuador or the region show no
significant connection to the NAO (Giddings and Soto, 2006).

Due
to its ecological and social relevance, numerous
hydrological studies have focused
on regional factors within the Paute river basin in southern
Ecuador to comprehend patterns in sub-basin
and micro-basin discharge (Celleri et al., 2007; Sotomayor et al., 2018; Ward et al., 2011). However,
considering the recent
understanding of these
teleconnection indices, the use
of these to forecast water
behavior and correlate it with extreme
hydrological events represents a novel exploratory strategy. These indices operate
on a global scale and might exert
a greater influence on
hydrological dynamics than local elements do.

As previously mentioned, the
significance of this study stems from the fact that substantial ecological and
human losses occur in the area, particularly due to floods in the Sierra region induced by rivers within the Paute River basin. For that reason,
the purpose of the
project is to use teleconnection indices and variability modes to forecast the
flow in the Paute river basin. Principal component analysis (PCA), correlation with monthly delay, and MLR with multicollinearity analysis
are all part of the process of forecasting. The levels of prediction for each
methodology will then be evaluated using statistical measures
by contrasting the outcomes
with the original data.

Materials y Methods

Study area

The study was conducted in the Paute river basin in southern Ecuador
(Figure 1). The basin covers approximately 6437 km2, with slopes ranging from
25% to 50% (CELEC EP 2013). The basin covers the Azuay, Cañar, and Morona Santiago provinces and is part
of the Santiago River basin.
Annual rainfall reaches
its maximum average
between 2500-3000 mm in
the eastern region, while in the western region, it ranges between 1200-1500 mm
(Institute of Regime Studies et al., 2017).
The area experiences two distinct periods
of frequent precipitation due to the ITCZ.
The wet season
for the unimodal
regime occurs from June to August, while
for the bimodal regime, it takes place from March to May (Campozano et
al., 2016).

Figure 1

Location of the study site, as well as the location of the different
sub-basins and the
discharge

and precipitation stations

The Paute
basin consists of 18 hydrological sub-basins (Figure 1), which discharge,
through a fall process, feeds the hydroelectric plants with a discharge value
of Mazar (141.10 m3/s), Molino (200 m3/s), Sopladora
(150 m3/s) and Cardenillo (180 m3/s), El Labrado and Chanlud (2.4 m3/s and 4.18 m3/s respectively) (Orbes & Peralta, 2017; Matute Pinos, 2014). The amount
of energy produced
by each of the aforementioned plants is Amaluza (1.075
MW), El Labrado and Chanlud dams feed two plants,
Saymirin and Sucay (14.4 MW
and 24 MW respectively); Mazar (162.6 MW) and Sopladora
(500 MW). It is estimated that in total, it produces 40% of the hydroelectric
production at the country level (Contreras
et al., 2017).

Hydrometeorological and climatic data

Data from discharge stations of the Ecuadorian Institute for Meteorology and Hydrology (INAMHI)
were collected for 20 years (1995-2015) on a monthly scale. Only stations with
at least 40% data availability were considered, resulting in a total
of nine stations
(Table 1). Data filling was performed using the ten nearest discharge and precipitation stations for each selected
station. The average monthly discharge amount was used to complete the
missing data.

Table 1

Discharge and precipitation stations used for the study

STATION NAME

X

Y

ID

% MISSING VALUES

PAUTE AJ DUDAS

78.62

2.68

H900

53

GUALACEO AJ PAUTE

78.76

2.86

H0931

60

TOMEBAMBA EN MONAY

78.96

2.88

INA895

38

PAUTE EN PAUTE (DJ GUALACEO)

78.74

2.75

H894

35

SURUCUCHO AJ LLULLUCCHAS

79.12

2.83

INA897

18

MATADERO EN SAYAUSI

79.66

2.87

INA896

14

COLLAY AJ PAUTE

78.64

2.73

H929

50

DUDAS EN PINDILIG

78.68

2.62

H902_R

40

MAZAR JP PAUTE

78.64

2.57

H0892

59

In
addition, data for time series
of teleconnection indices
and modes of variability were obtained from the database of the National Oceanic and Atmospheric Administration [41 indices
(NOAA - https://psl.noaa.gov/data/climateindices/list/)].

Flow modeling using
atmospheric and oceanic climatic indices

Teleconnection indicators, climate
variability modes, and MLR were used in the flow modeling process. A variety
of criteria, including PCA, correlation with monthly delays, and multicollinearity analysis, were used to generate MLRs. For calibration and validation, the study
used 80% of the data. Data were utilized
for calibration directly from January 1995 to September
2011, and for validation directly from September 2011 to December 2015.

Flow modeling using Principal
Component Analysis (PCA)

PCA
was used on teleconnection indices
and climate variability modes to minimize
the number of variables. MLR analyzed factors
accounting for 70% and 90% of the variance (Rea and Rea 2016). R software's "prcomp" function was employed for this. PCA is
essential for reducing dimensionality in data analysis
while maintaining data variety and representativeness
(Shabri and Shuhaida, 2014).

Modeling using Atmospheric and Oceanic Climate
Indices and Monthly
Delays

Three forecast scenarios were
constructed to take into account the delay processes between atmospheric circulation and precipitation/flow effects. In these circumstances, the indices
were delayed by the flow values by one, two, and three months. The top
five teleconnection indicators for each discharge station with the highest
Pearson correlation coefficients were chosen for MLR creation.

Modeling using multicollinearity analysis

A multicollinearity
study was carried out to reduce the number of variables to address the problem
of many variables. Multicollinearity, which indicates linear dependence across
predictors and interferes with each predictor's effects on the dependent variable, was discovered using the Variance
Inflation Factor (VIF) (Vega Vilca and Guzman, 2011). The appropriate VIF value
was five, and variables that exceeded this limit were eliminated. For MLR
building, the Leap Sequence criterion, combining forward and backward
selections, was utilized (Hastie et

al., 2021). RStudio
software with the MASS package
and the "leapseq" function
were utilized for this
process.

Goodness of fit of the resulting
models

To determine the accuracy of the
predictions made, a series of metrics were processed in the R software
V4.0.2, using the “hydroGOF” package. The metrics used in this study were KGE
(Knoben, Freer and Woods, 2019), NSE (Krause,
Boyle and Bäse, 2005), RMSE (Meyer, 2010), and R2. The model with the highest
value in their
metrics was considered the best model.

Results and Discussion Modeling using Principal
Component Analysis (PCA)

Of the 41 teleconnection indices, 10
and 20 main components were obtained, which explain 70% and 90% of the
variance, respectively. It is considered that a 70% explanation of variance
is a significant percentage for the study; however, the components that explained 90% of the explanation of variance were used to obtain a better prediction of flows (Rea and Rea, 2016).

The components obtained in the PCA analysis were used to perform a multiple
regression model. The results obtained with the PCA analysis were plotted in time series and
dispersion diagrams; the results can be seen in Figures 2 - 5.

Figures 2-5 illustrate that the results
align with observed
values, but predictions deviate from the actual values. Underestimation occurs at low values, while overestimation occurs at high values. Although the model
performs better for lower values, it fails to accurately reflect extreme
events. This limitation arises from using
only MLR and station values
without considering environmental behavior or hydrological processes.

Figure 2

Observed and modeled flow time series
using MLR and ACP (calibration stage). a) Paute AJ Dudas, b) Gualaceo,
c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 3

Observed and modeled flow time series
using MLR and ACP (validation stage). a) Paute AJ Dudas, b) Gualaceo,
c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 4

Dispersion plots of observed and modeled discharge
using MLR and ACP (calibration stage).

a) Paute
AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 5

Dispersion plots of observed and modeled discharge
using MLR and ACP (validation stage).

a) Paute
AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

During the validation phase,
synchronization is seen in severe events that are within the station ranges of
each participant. The precision is still less than at the calibration stage,
though. The minimum p-values on the dispersion plots in both stages demonstrate
statistical significance and a distinct correlation between the indices
and the stations
from the Paute basin. It's crucial to remember
that these outcomes
are dependent on the data utilized and independent
of the robustness of the model.

Among all the stations, Paute AJ Dudas
and Dudas (Figures 2a-2h, 3a-3h, 4a-4h, and 5a-5h) exhibit the best-fit models
with correlations of 0.41 and 0.48, respectively, during the calibration stage. However, during the validation stage, none of the stations achieved satisfactory
results, with the highest correlation observed in Dudas
at 0.36 and Mazar at 0.26. This indicates
that the models heavily rely on the initial conditions of the study and do not
effectively incorporate other environmental or hydrological data.

Paute DJ Gualaceo and Surucucho demonstrate the lowest correlation results during the calibration stage, with values of 0.23 and 0.26 (Figures 2d-2e, 3d-3e, 4d-4e, and 5d-5e). Overall,
the calibration results exhibit low correlations, sometimes as low as
0.01, indicating a lack of robustness in the models using this methodology.

Table 2

Metrics results at calibration and validation stage

STATIONS

CALIBRATION STAGE

VALIDATION STAGE

RMSE

NSE

R2

KGE

RMSE

NSE

R2

KGE

PAUTE AJ DUDAS

24.35

0.41

0.41

0.49

30.25

-1.02

0.03

0.02

GUALACEO

13.27

0.34

0.34

0.41

12.93

-1.55

0.01

-0.06

TOMEBAMBA

10.74

0.27

0.27

0.33

9.5

-0.98

0.07

0.06

PAUTE DJ GUALACEO

26.05

0.23

0.23

0.27

32.07

-1.26

0.01

-0.29

SURUCUCHO

0.68

0.26

0.26

0.31

0.89

-0.05

0.08

0.08

MATADERO

3.56

0.28

0.28

0.34

3.67

0.05

0.11

0.2

COLLAY

1.6

0.29

0.29

0.34

1.52

-5.44

0.03

-0.33

DUDAS

1.19

0.48

0.48

0.57

2.5

-0.68

0.36

0.21

MAZAR

2.57

0.29

0.29

0.35

3.12

0.12

0.26

0.16

There aren’t satisfactory results
in these models;
in Table 2 we can observe that Dudas,
Collay, and Mazar
were the stations
with less RMSE even when only Dudas
had a good model fit, which means this could be related to the low original discharge
values and their predictions
and not properly with the model functioning. According to Moriasi et al. (2007),
the NSE does not show satisfactory results (from 0.6 or higher), classification describes a performance as very good,
good, satisfactory, and unsatisfactory with values higher to 0.75, between 0.65
– 0.75, between 0.5 –
0.65 and lower to 0.5 respectively. Dudas and Paute AJ Dudas also domain this metric in the calibration stage. KGE gets better performance values than NSE, without changing
the results of stations.

In the validation stage, Dudas still
has one of the best performances, but Mazar and Matadero
also appear here. These metrics do not have any special tendency. A study
made in New Gales, Australia, using
the indices ENSO, MEI, IOD, Niño 3.4, PDO, and TPI to predict the study zone discharges, got NSE values between
0.15 – 0.55, which means that indices by themselves are not enough
to predict discharge
(Esha, Imteaz y Nazari, 2019).
A study realized in western Canada mentions
that PDO (used
in our study), even when related to ENSO, also has
great uncertainty regarding the nature and origin of the index
variability itself; which
results in a waste of
potential use in forecasting studies, especially because the statistic shows
that it is highly related to water resources (Whitfield et al., 2010).

In comparison to other approaches,
PCA had the lowest RSME, indicating
that other indices may be more closely associated than the ENSO index or its
variability modes (unique indices have the potential to affect only this methodology). Additionally, there may be several variables utilized for the study; however, the VIF approach challenges this idea because, in some instances,
the indices used for the models soar to 13. Metrics show that incorporating 90%
of variance in all models rather than just 70% results in an improvement.

Figure 6

Factorial Components of ACP using 41 indices
and 20 Components

In
Figure 6, we can observe
the loading factor
of ACP, which
is the influence of every index on the 20 components.
According to the study, the best models (90%) are indirectly related to ENSO indices
and not to the study
area, as can be identified in a comparison between the indices and their influence
on each component used in the modeling
(AT SST EOF, PWR, and SWMRR (South West Monsoon Region Rainfall) with positive values,
NAO (Jones), NP, PNA,
SR, and TP SST EOF (Tropical Pacific
SST Empirical Orthogonal Function) (negatives).
The highest correlations occur with SWMRR (0.39) and AT SST EOF (0.21). This correlation
could occur because the rainfall
season of SWMRR in Mexico and Arizona
happens from June to
September, matching the wet season of the Paute River Basin of the unimodal regimen
from June to August (Campozano
et al., 2016 & Crimmins, 2014). And AT SST EOF correlation is related to the
location of this anomaly in Ecuador (Fan and Schneider, 2012).

The PNA and other ENSO patterns used in research on the Canadian
Columbia River basin showed that depending on the station (certain months),
ENSO variability modes could be more or less influent,
even causing an anomaly in the river discharges (Gobena,
Weber y Fleming, 2013). As the results of our models are not accurate,
this can be considered an explanation, having indexes that are more related to anomalies in the ACP study, being necessary
to realize a correlation study
considering each station’s anomaly values on the data time series.

In a study made in Iran, 25
variability modes of teleconnection indices were used to explain the variability of precipitation using ACP methodology (AMO, AMM, BEST, Niño 3.4, El Niño 4, NTA, SOI, and TNA).
Results show eight
principal components that explain 80% of
the variance (Choubin et al., 2016).
In Colombia, a study that analyzes the climatic variability of the Cauca River using the ACP in Index (CCC,
an index of the own river; ONI; PDO; EMI, El Niño Midoki;
SST; SOI; and MEI) has as results that two components that explain 80% of the
variance, an only one explaining 70%. The eigenvalues (proportional to loading
factors) showed that this first component with 70% of variance was more associated with ENSO and the
two components with 80% of variance were more related to the index of the study
zone CCC (Sedano, 2017). In our study,
the models work similarly, most of the indices directly
correlate with ENSO and SST. It is also visible in the studies
of Choubin et al. (2016)
and Sedano (2017) that the percentage of input data needed to explain 70% of the variance is from 25 – 30%, and
for upper percentages, it is from 35 – 50% of them. The influence of
every index involved decreases with the number of components, focusing on their
correlation.

Modeling using Atmospheric and Oceanic Climate
Indices and Monthly
Delays

To determine the variables of each
prediction model for the discharge stations, the Pearson correlation was carried out for the different
stations and the teleconnection indices,

making delays of one to three months, considering the
absolute value of the correlations. The
first five indices with the highest values were used. The best results were obtained by performing
a one-month delay between the values of the stations and the
teleconnection rates. The results of
the correlation using a delay month can be seen in Figure 7.

Figure 7

Graphic representation of the existing
correlation between discharge
stations and teleconnection
indices

The
absolute values of correlation are usually in a range from 0.35 to 0.61. The highest correlation is the Dudas station
with a CIP index of 0.61, and the
lowest belongs to the same station with an NTA index with 0.11. Once the correlation values between the discharge stations
and the different teleconnection indices were obtained, the following
was to identify the five indices with the highest absolute correlation values,
which are presented in Table 3.

Table 3

Absolute Correlation values
of the indices used for the multiple
regression models of each

discharge station

STATION

INDICES AND CORRELATION VALUES

PAUTE AJ DUDAS

SF

NP

CAR

GB

WHWP

0.35

0.29

0.21

0.19

0.18

GUALACEO

NP

CIP

GB

AMM

PWR

0.28

0.26

0.23

0.20

0.19

TOMEBAMBA

AMM

WHWP

Niño 4

PWR

TNI

0.23

0.22

0.22

0.22

0.21

PAUTE DJ GUALACEO

NP

CAR

PWR

GB

AMM

0.23

0.22

0.21

0.20

0.19

SURUCUCHO

AMM

NP

Niño 4

PWR

NTA

0.31

0.30

0.23

0.23

0.23

MATADERO

PWR

WHWP

Niño 4

AMM

TNA

0.29

0.28

0.28

0.26

0.24

COLLAY

CAR

AMOU

TNI

SR

AT SST EOF

0.26

0.22

0.18

0.18

0.17

DUDAS

CIP

NP

AMM

NBRA

WHWP

0.61

0.44

0.25

0.24

0.23

MAZAR

AMM

NP

AMOS

SF

NTA

0.30

0.28

0.28

0.28

0.23

The MLRs were generated with the
indices from Table 2. The results are presented in Figures 8-11 with a
one-month delay; the behavior of the modeled time series adjusts to the trend of the series of each station,
especially at mean values and low values. However, it presents
the same problem
as the series predicted with the PCA method. All values are indifferent to the
model results.

Figure 8

Observed and modeled
flow time series
using MLR and one-month delay (calibration stage).

a) Paute
AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 9

Observed and modeled
flow time series
using MLR and one-month delay (validation stage).

a) Paute
AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

In 2018, an investigation into the
evolution of the sediments of several lakes in the El Cajas National Park
determined that, with a one-month delay for the ENSO index, the results of the
correlation with the precipitations close to the local stations were solid,
proving that there is a strong positive link between intense rains and
therefore an increase in flow between La Niña, Niño 3.4 (which explains
the variability of the Ecuadorian Andes), El Niño 4 (a more intense relationship), El Niño
1+2 (which explains the variability of the coastal plains), and a more neutral
link with El Niño (Schneider et al., 2018).

The delay of one month in our study
proves that there is a delay in the effects of the teleconnection rates on the climatic conditions of the Paute river basin. And that the variability
of the indices fits with the level
of correlation found
considering the spatial
configuration of the studies. In a study carried out in
Brazil on the relationship between the alluvial plains and the connection with
the signals (variability modes) of ENSO teleconnection (El Niño,
Niño 3.4, SOI), it was determined that for the Amazon basin,
there is a delay of two months.
This occurs from January
to March and causes lower
rainfall, causing a decrease in flow (Schöngart et al.,
2004). However, an investigation carried out in Peru on the relationship between monthly rainfall
and SST identified that in
the areas of the equatorial Pacific, ENSO has a delay of one month in the wet
season and zero in the dry season (Bazo, Lorenzo and Porfirio Da Rocha, 2013).
When comparing our results with the literature, it confirms our results because
the indices with the
highest correlation for this scenario
are AMM, NP, PWR and, WHWP, which
are strongly influenced by
ENSO variability modes.

Figure 10

Dispersion
plots of observed and modeled discharge using MLR and one-month delay
(calibration stage). a) Paute AJ Dudas,
b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo,

e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 11

Dispersion
plots of observed and modeled discharge using MLR and one-month delay
(validation stage). a) Paute AJ Dudas,
b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo,

e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

The PWR index is conditioned by El
Niño (Carreric, 2020); on the other hand, the
WHWP index is also directly
affected by El Niño in the summer through the TNA temperature increase that occurs during
the El Niño winter in the Pacific (Wang y Enfield, 2001). NP is
dominated by the interannual variations of the El Niño and La
Niña events (Espino Sánchez, 2014); AMM, for its part, produces
anomalies in the SST north of Ecuador,
but it occurs during the boreal spring (March)
with greater intensity. In a case study of the rivers of Quebec in Canada
was discovered that between ENSO, NAO, and PDO there is a large delay between the effect of the patterns and the answer on the discharge. It is also mentioned that the modes of variability associated with teleconnection
patterns can change the periodicity and the stationary effects. This can
explain the non-optimal fit models in this methodology (McGregor, 2017).

For
the modeling, an acceptable R2 value is obtained in Dudas with 0.53 (Figure
10h), which confirms the ability of the models
to capture the averages. The second-best performance occurs at the Gualaceo station with a coefficient of 0.31 (Figure 10b)
and Matadero with 0.28 (Figure 10f). In this case, two of the stations
varied in the indices used, which represented a great improvement
for both cases. The models with the lowest
performance are Paute DJ Gualaceo
and Tomebamba, both with a value of 0.16 (Figure 10c
– 10d).

When analyzing the coefficient of
determination (Table 4), it can be seen that Dudas station is acceptable according to the bibliography. Since values less than 0.5 indicate in a

hydrological model that there is a large error variance
integrated into the model and that it cannot be explained by it, in other
words, using only the values of the indices in a multiple regression model does
not give good results for the flows of the Paute
river basin. There are local and regional variables that could be integrated
into the model, improving its predictive capacity (Moriasi
et al., 2007).

Table 4

ACP metrics results
at calibration and validation stage

STATIONS

CALIBRATION STAGE

VALIDATION STAGE

RMSE

NSE

R2

KGE

RMSE

NSE

R2

KGE

PAUTE AJ DUDAS

27.69

0.24

0.24

0.28

26.79

-0.65

0.18

0.11

GUALACEO

13.62

0.31

0.31

0.37

13.92

-1.95

0.15

-0.27

TOMEBAMBA

11.54

0.16

0.16

0.16

8.49

-0.6

0.07

0.01

PAUTE DJ GUALACEO

27.29

0.16

0.16

0.15

32.68

-1.37

0.01

-0.41

SURURCUCHO

0.71

0.21

0.21

0.24

0.84

0.08

0.14

0.09

MATADERO

3.57

0.28

0.28

0.34

3.44

0.16

0.18

0.25

COLLAY

1.69

0.21

0.21

0.23

1.46

-4.96

0

0

DUDAS

1.15

0.53

0.53

0.61

1.96

-0.06

0.43

0.37

MAZAR

2.66

0.24

0.24

0.28

2.98

0.2

0.31

0.13

In
this modeling, we get the best fit of the model. NSE reaches a satisfactory result
in the calibration stage with
Dudas, and KGE gets a good fit model (0.61). Paute AJ Dudas´s results are reduced
compared with other
methodologies; this can occur when analyzing where
stations are located and how the delay effects
affect every station.
Tomebamba and Gualaceo have the
lowest results, reaching
0.15 and 0.16 on NSE and KGE, respectively. RMSE is only related to the discharge of each station and not
the results of the modeling.

In the calibration stage, Dudas is
still the best station with 0.37 on KGE, while Collay
gets the worst results with -4.96 on NSE and zero on KGE. This means that the average
monthly values are a better predictor than our model (Krause et al.,
2005). The variance range is very wide, and these results prove that the models have no statistical robustness even when the p-value
maintains infinity in all cases (both stages).

Modeling using multicollinearity analysis

The third case used for flow modeling was a preliminary analysis of multicollinearity, as explained in
the previous section on materials and methods.
When using the VIF criterion
for the reduction of the variables, a total of 22 variables
were obtained (reduction of almost half of
the original variables); the resulting
variables were PNA, WP, EA/WR, NAO, TSA, PDO, NP, AO,
AAO, PWR, CAR, AMOS, QBO, SR, SF, GB, EP/NP, NAO (Jones),
NOI, CIP, NBRA,

SWMRR and AT SST EOF. None of the modes of variability or signals directly related to ENSO (MEI V2, Niño 1+2, Niño 3, Niño 3.4, Niño 4, SOI, ONI) are reflected in the results.
Indirectly, we find NP, which indicates its high influence on the rest
of the indices and its intimately connected and similar behavior. This also
happens with the indices AMO UNSMOOTHED, AMM,
and AMO SMOOTHED, since only one is kept after VIF analysis.
With the resulting

variables, the next step was the construction of the MLR using the stepwise criterion. The best model for
each of the discharge stations is presented in Table 5.

Table 5

MLR used for prediction with Multicollinearity Analysis

DISCHARGE

N° VARIABLES

INDICES

PAUTE AJ DUDAS

5

AMOS + AT SST EOF + NP + PDO +
SOLAR

GUALACEO

2

NP + PDO

TOMEBAMBA

5

EA/WR + NP
+ PWR + CIP + NBRA

PAUTE DJ GUALACEO

4

AMOS + CAR + NP
+ PDO

SURUCUCHO

2

NP + PWR

MATADERO

1

PWR

COLLAY

2

CAR + SR

DUDAS

1

CIP

MAZAR

5

AMOS + NP + SOLAR+TSA+NBRA

Figures 12-15 show the results of the
predictions made under the VIF analysis for multicollinearity. The trends are maintained in all seasons, and visually, the results are acceptable
(Dudas achieves the best modeling).

Figure 12

Observed
and modeled flow time series using MLR and Multicollinearity Analysis
(calibration stage). a) Paute AJ Dudas,
b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo,

e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Figure 13

Observed and modeled flow time series
using MLR and Multicollinearity Analysis
(validation stage). a) Paute AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Table 6

Metrics results at the calibration and the validation stage

STATIONS

CALIBRATION STAGE

VALIDATION STAGE

RMSE

NSE

R2

KGE

RMSE

NSE

R2

KGE

PAUTE AJ DUDAS

26.2

0.32

0.32

0.38

39.73

-7.51

0.02

-0.36

GUALACEO

15.01

0.16

0.16

0.14

16.05

-5.86

0.02

-0.09

TOMEBAMBA

11.46

0.17

0.17

0.18

8.76

-2.69

0.03

-0.01

PAUTE DJ GUALACEO

26.45

0.21

0.21

0.24

35

-7.26

0.02

-0.24

SURURCUCHO

0.72

0.18

0.18

0.19

0.89

-8.96

0.03

-1.25

MATADERO

4.03

0.08

0.08

-0.02

3.66

-6.92

0.07

-1.02

COLLAY

1.69

0.21

0.21

0.23

1.70

-2.83

0.01

-0.15

DUDAS

1.29

0.40

0.40

0.48

1.98

-2.77

0.45

-0.10

MAZAR

2.9

0.10

0.10

0.03

3.39

-15.73

0.02

-2.13

Using VIF to select the indices as
variables in every model gave us different results for every station, and these results are not related to the
functioning of indices but only to methodology. In the calibration stage, Dudas obtained the closest to a good result on correlation,
NSE, and KGE, with 0.40 and 0.48, respectively. Paute AJ Dudas gets another close result to
satisfactory with 0.38 in KGE. The worst
fits occur on Matadero and Gualaceo, reaching
even negative values on KGE (0.14 to -0.02). In this model, it is very
clear that the results are not improved by using more variables. As a result, Dudas only uses one index to obtain better results
in comparison with Mazar, which uses 5 (the maximum number of variables
in each station) and gets poor results. The
noise in this methodology does not influence it drastically since all RMSEs
tend to maintain low values, which means the results are a show of the
functioning itself. Dudas has one variable,
Paute AJ Dudas 5, Matadero, and Gualaceo 1 and 2, proving

that only one index is enough to capture the variability of the
discharges if it is related to the environment of the station.

In
the validation stage,
Tomebamba is the “best” fit model with -2.69; the rest have also
negative values on NSE, in KGE. These results are similar, except
in the case of Dudas with a

0.45 correlation, proving
that is the station with the best results throughout the study. RMSE in
both
cases still obeys the initial values of the data to show results more than the model prediction,
which is why the stations with the highest values, Paute
AJ Dudas and Paute DJ Gualaceo,
have high RSME, but their
performance is very different, with Paute AJ Dudas
the second-best station to
fit the models.

Figure 14

Dispersion
plots of observed and modeled discharge using MLR and Multicollinearity
Analysis (calibration stage).
a) Paute AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

A
study made in Indonesia that used SOI, Niño 3.4, and IOD indices to analyze the Java
discharge regimen identified that the results on LRM with KGE metrics were best
when the model included more variables (Nugroho, Tamagawa and Harada, 2022).
This also happened in our study
using this specific
methodology, where we used a different number
of variables for every station. In addition, from a
general perspective, when using 20 components as variables on ACP also
happened.

When
we analyze Figure 14f, we can see the worst result: Matadero used only PWR to
get the predictions, and we can see no relation between the behavior
of the original series and

the predicted one. P- value maintains low in every station which
means they are statistically representative. RSME is dominated by the same
behavior as in the two other methodologies.

Figure 15

Dispersion
plots of observed and modeled discharge using MLR and Multicollinearity
Analysis (validation stage).
a) Paute AJ Dudas, b) Gualaceo, c) Tomebamba, d) Paute DJ Gualaceo, e) Surucucho, f) Matadero, g) Collay, h) Dudas, i) Mazar

Even
when the best models tend to have more variables, the variables change for every station; this is proven
because stations with the same indices can have bad or good indices and are independent of each other. Also, there are stations that, using the
same number of indices, can have better results than other stations. The results are directly linked with how
the values of the time series couple with the indices data in an individual
way. And the value of the data
itself does not influence the results.

There are no similar
indices used in all scenarios, but the ones that are present in the two methodologies (VIF and using monthly
delays) are: NP, PWR, CAR, and CIP; also, this one has the most influence on loading factors
in ACP (NP and PWR). The two better-fitting stations are Dudas and Paute AJ Dudas since this one does not have
extreme events as frequently as the other stations,
allowing LRM to work better.
This methodology is good for approximation
but it is limited to mathematical procedure because the only input data is the
time series and not any environmental variable that can help to understand the
hydrological behaviors (not environmental context or another variable). The
stations with the worst results are Mazar, Gualaceo, and Matadero. Also, the validation range time could be amplified
to improve the

models by catching more variability, especially in the
extreme events that are not so frequent. In
the Amazon Basin,
research determined that ENSO domains
the conditions of the discharges but does not fully understand
the behavior of each variability mode and its effects. This is caused by the
temporal SST anomalies, their magnitude, and their position in the equatorial
Pacific Ocean. The study also points out that some statistical tests,
such as Kendall,
could not be suitable for certain regions. With a large-basin memory, it leads to autocorrelation and misleading
significance (Towner et al., 2020).
This is not only observed
in our study but also evidenced in each of the methodologies used.

Conclusions

The best models can follow the
original data tendency but cannot predict whether
the values are too low or too high. The best scenarios were obtained when using PCA as a general
view, but the best values in metrics were obtained when using a 1-month delay.
The models except Dudas and Paute AJ Dudas
mostly didn’t reach a satisfactory result in all metrics (NSE, KGE, R2). This means
that indices are not enough
as discharge predictors. RSME is not a good metric in our study since its values
were associated with the data and not with the model’s performance in all
cases. It shows a very light tendency on PCA, lowering their values. The
validation stage determines that the models
do not have robustness, and this is directly related
to the initial conditions of our models
not applying to different contexts. We have several
indices associated with ENSO that do not represent any relevance in the
study (AO, BEST, ENSO, GIAM, MEI V2, NAO, Niño 3, Niño 3.4, ONI, SOI, TPI, and IPO). It is important to recognize if this index has a direct
or indirect effect
on the zone and which
of his variability modes better represents it. Finally, it is important
to highlight that being a first approximation to the use of all teleconnection indices to measure their predictive capacity in the Paute river basin, the results are very interpretable. It is essential to mention that the teleconnection indices (signals and modes
of variability), in addition to providing global
information, maintain a well-studied atmospheric and oceanic circulation. This makes it possible not only to observe climate
variability on a large
spatial and temporal scale but also to analyze variables
dependent on these phenomena without having to resort to breaking them
down for a single study.

Acknowledgments

The authors would like to thank the
INAMHI for the information provided. This work was founded for Corporación
Ecuatoriana para el
Desarrollo de la Investigación y la Academia
(CEDIA) within the research project “Análisis
Nexus agua-alimentos-energía- servicios ecosistémicos ante cambios del clima, uso
del suelo y población. Un enfoque novedoso para el desarrollo sostenible local a escala de una cuenca
hidrográfica” and Vicerrectorado de Investigaciones
de la Universidad de Cuenca (VIUC).

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