InGenio Journal

Revista de Ciencias de la Ingeniería de la Universidad Técnica Estatal de Quevedo

https://revistas.uteq.edu.ec/index.php/ingenio

e-ISSN: 2697-3642 CC BY-NC-SA 4.0

Volumen 6 | Número 1 | Pp. 31–43 | Enero 2023 Recibido (Received): 2022/09/27

DOI: https://doi.org/10.18779/ingenio.v6i1.561 Aceptado (Accepted): 2022/11/18

Fourier-based optimization for multivariate spatial-

temporal regression model in chlorophyll-a presence

prediction around Galápagos Islands

(Optimización del modelo de regresión espacio-temporal multivariado

basado en Fourier para la predicción de la presencia de la clorofila-a

alrededor de las Islas Galápagos)

Fernando Chávez-Castrillón

1,2

, Santiago Marchán-Hernánez

, Roberta Ivaldi

, Guido

Sciavicco

Ecuadorian Navy, Dept. of Educ. and Doct., Guayaquil, Ecuador

University of Ferrara, Dept. of Phys. and Earth Sci., Ferrara, Italia

Hydrographic Institute of the Italian Navy, Genova, Italia

University of Ferrara, Dept. of Math. and Comp. Sci., Ferrara, Italia

fchavez@armada.mil.ec, smarchan@armada.mil.ec, roberta_ivaldi@marina.difesa.it,

guido.sciavicco@unife.it

Abstract: Chlorophyll-a (Chl-a) is an indicator of phytoplankton biomass, which can be used

to predict the presence of fish in the ocean. By predicting the Chl-a with sufficient time, this

data can be used to better plan naval operations that combat illegal, unreported and

unregulated fishing by increasing surveillance of the identified areas where the greatest

fishing activity would take place. In this work, a new technique is proposed, based on the

application of the discrete Fourier transform theory to develop multivariate spatial-temporal

regression model, which considers physical and biogeochemical ocean variables to predict

the presence of Chlorophyll-a around Galápagos Islands. This work considers open access

data taken from the Copernicus space program, used in the European Union.

Keywords: Spatial temporal regression, Illegal fishing prevention, Discrete Fourier

transform, biogeochemical ocean variables.

Resumen: La Clorofila-a es un indicador de la biomasa del fitoplancton, que puede ser

utilizado para predecir la presencia de peces en el océano. Al predecir la Chl-a con suficiente

tiempo, se puede utilizar en la planificación de las operaciones navales que combaten la pesca

ilegal, no regulada y no reglamentada, por cuanto se identifica el lugar donde existirá mayor

actividad pesquera, para incrementar su vigilancia. En este trabajo, proponemos una novel

técnica basada en la aplicación de la teoría de la transformada discreta de Fourier, al modelo

de regresión multivariable espacio-temporal desarrollado, que considera las variables físicas

y biogeoquímicas del océano para la predicción de la clorofila-a, alrededor de las Islas

Galápagos. Este trabajo considera datos de acceso libre del programa espacial Copérnico de

la Unión Europea.

Palabras claves: Regresión espacio temporal, Prevención de la pesca ilegal, Transformada

discreta de Fourier, Variables biogeoquímicas del océano.

InGenio Journal, 6(1), 31–43

| 32

1. INTRODUCTION

The increase in the world population and the demand for fish protein are causing pressure on

the oceans [1], depleting their resources, mainly because the most populous countries and some

developed countries fail to meet their fishing quota catches in their seas. They are forced to cross

borders and find shoals offshore or in other countries' territorial waters. In this case, it is a real

challenge to early detect these vessels if their vessel monitoring systems (VMS) are disconnected,

or if the affected country does not have the support of satellite surveillance or the permanent

support of air-maritime exploration aircrafts.

It is essential to mention that illegal, unreported and unregulated fishing (IUU) is a severe

global problem that destroys marine ecosystems and that will also bring about the collapse of the

fishing sector, threaten the diet of the population and cause poverty in the societies depending on

seafood and legal fishing as their way of life [2]. Unfortunately, illegal fishing acts involve from

artisanal fishermen to large fleets with links to criminal organizations, as IUU fishing turns out to

be a good option to maximize gains, with low operating costs, aggravating this situation [3].

Commercial exploitation of fish in the Galapagos Islands began in the mid-1900s, with a catch

estimation, from 1950 to 2010, of 797,000 tons, of which 80% represented by the industrial tuna

catch. It is also worrying that shark finning practices have increased since the 1980s and continue

to be carried out even within the Galapagos Marine Reserve, as evidenced by the capture of the

Chinese fishing vessel Fu Yuan Yu Leng 999, carrying about 300 tons [4]. This event, which is

not isolated, highlights the severe problem of IUU fishing around the marine protected areas of

Galapagos Islands. To further emphasize the need to contribute to the protection of the marine

species of the islands, the international community is on alert for news presented during July

2020, which reported that more than 260 ships are currently under international waters on the

outskirts of the Exclusive Economic Zone (EEZ) and warns that the aggressiveness of this vast

fleet is putting at risk the delicate marine ecosystem and the natural balance of species in

Galapagos, [4].

Additionally, illegal, unreported and unregulated fishing is considered a stress factor for the

ocean, due to the over-fishing that occurs, which is influencing in the ecosystem, by changing the

abundance of fish and the performance of other organisms, [5]. This leads to changes in predator-

prey dynamics and competition between species and intra-species. This factor has a negative

impact on marine life, which directly affects sustainable development, being necessary to

formulate policies that allow managing the multiple stress factors that the ocean has nowadays

[4].

Even the "Artisanal Fishing Community of Galapagos" is concerned about the protection of

fishery resources, as many of them agree that the country should take action to try to curb illegal

fishing; however, despite being aware of the impact that large-scale fishing has on the marine

ecosystem, they do not agree with the imposition of fishing quotas or the implementation of strict

regulatory rules to control fishing [6]. For this purpose, Art. 61 of the United Nations Convention

on the Law of the Sea (UNCLOS) establishes that the coastal State has the right to set fish catch

quotas in its exclusive economic zone, as it is its duty, together with the regional fisheries

management organizations, to take measures that seek to maintain or restore fish stocks for the

conservation of the marine ecosystem. [7].

This paper is organized as follows. In Section 2, a short overview of the current literature

concerning the use of the Fourier series theory applied to oceanography and the use of machine

learning applied to the prediction of chlorophyll is provided. In Section 3 is presented the

methodology which includes the procedures, description of the study area and the data used in the

research. Then, in Section 4, the results are explained and discussed. Finally in Section 5, a

conclusion is provided

InGenio Journal, 6(1), 31–43

| 33

2. RELATED WORK

The constant formation process of the islands, coupled with the influence of several ocean

currents, positively affects biodiversity, producing and distributing nutrients, plankton and krill

throughout this geographical area. Among the prevailing currents, there is the cold Humboldt, the

warm El Niño and the Cronwell counter current, [8]. Another aspect to consider is the behavior

of the study area's climate, a region where there are only two types of season, the warm season

from December to May and the cold season, from June to November. [9]

The prediction model for the concentration of Chlorophyll-a developed in [10], had the main

motivation to design a model based on multivariate linear regression, which allows forecasting

the possible areas of illegal fishing, so that the naval forces can plan with enough time the naval

operations that fight the IUU.

In oceanography, spectral analysis of temporal series can be done by making use of the Fourier

Series method, since it can research the interrelation between observed dynamic processes. Any

periodic function following certain requirements, mainly convergence, can be represented as a

series of complex exponential functions, allowing the transformation of a time signal on the

frequency domain, with the objective of analyzing its frequency content in terms of amplitude

and phase, because the Fourier coefficients of the transformed function represent the contribution

of each sine and cosine function at a given frequency [11].

The concept of frequency spectrum was introduced in the field of analysis of oceanographic

temporal series between late 1940s and early 1950s. It was first used in the study of oceanic wind

waves around 1950. During the last five decades, its use has been quickly developed and spread,

despite the fact that it has shown some drawbacks for the analysis of temporal series observed in

nature, as most applications use real values, while the Fourier transform uses complex arithmetic,

transforming a sequence of real data of the time domain in a sequence of complex numbers in the

domain of frequency [11].

The discrete Fourier transform (DFT), is the discrete version of the Fourier transform (FT).

This technique allows doing the spectral analysis of signals and can be used in various areas like

science and engineering. A data series can be considered as a linear combination of frequency

components, where the time domain can be represented as the sum of the frequency components,

and so all waveforms can be reconstructed with an infinite number of sinusoids of various

frequencies. In practice, only a finite number of sinusoids is used to reconstruct the wave [12].

In Fourier decomposition, any N points of signal can be decomposed into N+2 signals, half

of them in sine waves and the others in cosine waves where the lowest frequency corresponds to

the DC signal. It is possible to create any waveform from superimposed sinusoids. Fourier

decomposition provides a direct analysis of the waveform composition, including information

about the frequency, phase and amplitude of its components [13]. The variables related with the

ocean constantly oscillate their values and can be considered as signals that can be decomposed

into its components, in order to analyze their behavior depending on the seasonality where they

are found.

It is often difficult to analyze biological signals due to their non-linear and non-stationary

characteristics. To solve this problem, time-frequency decomposition methods are used to analyze

the very slight changes that exist between these signals and that may be related with an external

phenomenon. If a signal is uniformly sampled and its characteristics change slowly with time, it

can be considered that the seasonality is maintained during this time interval, and then the Fourier

transform can be applied to this part of the signal. [14].

InGenio Journal, 6(1), 31–43

| 34

3. METHODOLOGY

3.1 Methods and procedures

A prediction model with enough anticipation can help to plan better and quicker maritime

surveillance routes, in order to ensure an early vessel detection. The presence of Chlorophyll-a in

combination with relevant physical, chemical, and biological variables at a certain geographical

point can be thought as a multivariate spatial-temporal series, in which the Chlorophyll-a ([Chl-

a]) plays the role of dependent variable, which is interesting to predict because it is used as an

indicator of phytoplankton biomass [15]. Likewise, multivariate spatial-temporal regression can

be used to estimate not only the functional model, but also the temporal component for each

predictor. Multivariate spatial-temporal regression is simply a multivariate regression in which

the spatial-temporal component is explicitly taken into account via suitable data transformations.

In its simplest form, it consists of adding suitable lagged data to the original ones so that the

temporal history of an element plays a role in the regression. In [10] it is proven that lagged data

improves the Chlorophyll-a prediction, but some limitations could be appreciated, as the data used

for testing consists of one month and there is no bathymetric study that allows to specify the study

area. The use of data from 01-December-2020 to 30-November-2021 makes it possible to take

into account the seasonality, which also influences the Chlorophyll-a behavior. In addition, a

bathymetric study around the Galápagos Islands was included in order to select the study area.

Also, we consider open access data taken from the Copernicus space program to predict

Chlorophyll-a presence surrounding Galapagos Islands. The main objective is to optimize the

prediction of chlorophyll levels, that is conducted by using the multivariate spatial-temporal

regression technique, for which the discrete Fourier transform is applied in order to first determine

the behavior of the physical, chemical and biological variables (independent variables), in relation

to the dependent variable (Chl-a), to subsequently optimize the model by restructuring the dataset,

taking into account the lag (delay) between the variables and the Chl-a.

In order to compare the variables, a normalization of the data series is performed, to

subsequently apply a decomposition of the data series applying the one-dimensional discrete

Fourier transform. Next, the data series is recomposed again by applying the inverse discrete

Fourier transform in n-point using the first 15 main frequencies. In this way, the noise that can

occur in the data series is eliminated, and the measurement of the lag between variables is

possible. Once the lag is determined, the dataset is finally reconstructed, considering the lag

between different variables. Although the method is used to determine the variables which are

ahead and behind in relation to the chlorophyll, in the prediction model, only those variables

which are ahead of chlorophyll are taken into account, as their variation affects the Chl-a level.

With the reconstructed dataset, the multivariate spatial-temporal regression is applied, predicting

the chlorophyll, trying to improve the correlation between the calculated value and the real value

of Chl-a. Finally, up to 10-days lag of each variable are considered, and the dataset is restructured

again to create a new regression model, trying to further improve the correlation between the

calculated value and the real value of Chl-a. The analysis is conducted in the 2090 geographical

points that compose the dataset, and in the period of one year. Half of the dataset is used to train

the model and the other half, to test the model.

3.1.1 Optimization Model Conceptualization

DFT and IDF. A periodic time domain sequence 󰇛󰇜, with period N, can be expressed as

summation of a set of  harmonically related complex sinusoids with coefficients 󰇛󰇜 as



󰇛



󰇜







󰇛



󰇜











   





(1)

InGenio Journal, 6(1), 31–43

| 35

Applying Euler's formula, we can express this equation in terms of sines and cosines:



󰇛



󰇜















󰇣

󰇡





󰇢󰇡





󰇢

󰇤

Discrete Fourier transforms (DFT) are extremely useful because they indicate the periodicities

in the data of a signal, as well as the contribution of each of its periodic components, and can be

used on samples containing certain numbers of points. In our case, the analyzed data consist on

daily samples of physical, chemical and biological values, represented as a data series, to which

we can apply DFT, determining its components.

After applying DFT, it has been chosen to reconstruct the data series using exclusively its first

15 components of the data series, this way it is possible to remove noise and understand the

behavior of Chlorophyll in relation with other variables. For this effect, the Inverse Discrete

Fourier Transform (IDFT) is used, serving as pass band filter, where the first few components are

selected to reconstruct the signal in N-dimensional complex vectors.



󰇛



󰇜







 

󰇛



󰇜











   





The result obtained after applying the DFT and then the IDFT can be observed in the

Figure 1.

Figure 1. Chl real vs Chl Fourier (nFFT=15).

As it can be observed in Figure 3, the CHL, reconstructed with 15 components, shows the

tendency of the variables observed in the analysis. A previous analysis helped to identify that 15

components adequately reconstruct the signal. This transformation must be performed for every

variable and for every one of the 2091 geographical points in the dataset, per day.

Afterwards, a comparison between the different variables is performed, relative to the CHL,

in order to determine the phase lag between these waves. Due to the fact that the analyzed waves

use different units and magnitudes, it is first necessary to normalize the datasets.

The phase angles are calculated from a one cycle discrete Fourier transform (DFT), based on

phase to phase between data series Chl-a and each variables in all 2091 points. For this

calculation, specialized Python libraries of signal processing have been used. This process is used

to increase the correlation in the dataset used to design the multivariate spatial-temporal

regression model. It is estimated that if the waves are in phase, the Chlorophyll prediction must

(2)

(3)

* Comparison of real Chl-a data series vs Chl-a reconstructed with 15 components

InGenio Journal, 6(1), 31–43

| 36

improve, being this the hypothesis of our study. In Figure 2, you can see an example of the gap

between the behavior of the O2 and Chl-a data series at a specific point in the dataset.

Figure 2. Example of the gap between the O2 and Chl-a data series at specific point.

3.2 Study area

The Galápagos Islands located 965 km westward of mainland Ecuador in the eastern Pacific

Ocean, have had a continuous evolving process since Cretaceous, for more than 20 million years

ago (m.a.), and are the result of the ongoing interaction between the Galapagos hotspot located

on the Isabela Island and the Cocos Nazca Plates (CN) [16]. This interaction has allowed the

formation of the islands’ platform composed of 13 large islands, 9 small islands, and 107 islets,

as well as the Carnegie and Coco's submarine volcanic ridges, [17].

The hot spot of the islands’ platform is under Isabel Island, considered the most active of the

archipelago [16], having 190 km from this point to the CN ridge. The expansion of this ridge

ranges from 90° to 98° West, and the strong influence of the hot spot on the western side has

caused the formation of underwater ridges in a depth range of -3500 to -1000 m. It is noteworthy

that the evolving process of the Galapagos Islands and submarine ridges is permanent, since the

Cocos Plate moves 8 cm/year NE, while the Nazca plate moves 5.8 cm/year E [18]. In the figure

3, it can see the submarines ridges of Galápagos.

Figure 3. Galápagos’ Rides

Ω

* Gap between Chl-a vs O2 data series

InGenio Journal, 6(1), 31–43

| 37

Based on Galapagos' ocean geomorphology, it was necessary to divide the study area into 12

sub-areas related to different depths existing in that area to increase the model's performance (See

Figure 4). For this purpose, we have performed a statistical analysis of both the bathymetry of the

area and the variation of chlorophyll, to select the area that will be the basis of this study. It should

be mentioned that, according to the study carried out by Renteria et al [19], national and

international fishing effort is mainly concentrated in the west of the Galápagos Islands, included

inside the Marine Reserve and outside the Insular Exclusive Economic Zone [19].

Figure 4. Study area division

Finally, the A6 area was selected because it is located to the west of Galápagos Islands and

includes the insular exclusive economic zone (IEEZ), as well as after analyzing the behavior of

the bathymetry in that area, variance, and standard deviation of this variable, is low compared

with the results obtained in other subareas (see Table No. 1). The basic statistical values of the

variable of interest in this study (Chlorophyll-a) were also analyzed and area A6 has a wide range,

which will help to generalize the prediction model, its variance and standard deviation are also

relatively low, (See Table No. 2). It should be mentioned that in area A6, constant overfishing

activities have been identified.

Table 1. Basic statistical values of bathymetry during year, 2021.

AREA

Max.

Min.

Mean

Range

Var.

Std.

Dev.

-2875

-4222

-3482

1347

52130

228

0.17

-2703

-4214

-3626

1511

31488

177

0.12

-2703

-4221

-3677

1518

71010

266

0.18

-2191

-4152

-3513

1961

123058

351

0.18

-2154

-4048

-3353

1894

35509

188

0.10

-2349

-3737

-3273

1388

36317

191

0.14

703

-3712

-2601

4415

944219

972

0.22

-52

-3452

-2322

3400

450137

671

0.20

-2151

-4679

-3365

2528

48572

220

0.09

A10

-2333

-3953

-3322

1620

108416

329

0.20

A11

-844

-4018

-2995

3174

278410

528

0.17

A12

-2151

-4679

-3365

2528

48572

220

0.09

InGenio Journal, 6(1), 31–43

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Table 2. Basic statistical values of chlorophyll-a during year, 2021.

AREA

Max.

mg/m

Min.

mg/m

Mean

mg/m

Range

mg/m

Var.

Std.

Dev.

2.127

0.135

0.385

1.992

0.070

0.264

0.13

2.146

0.140

0.409

2.006

0.130

0.361

0.18

1.940

0.142

0.387

1.798

0.052

0.228

0.13

1.899

0.165

0.487

1.735

0.061

0.246

0.14

1.572

0.165

0.426

1.406

0.026

0.162

0.12

2.175

0.169

0.486

2.006

0.052

0.228

0.11

1.645

0.111

0.513

1.534

0.038

0.194

0.13

1.976

0.152

0.663

1.825

0.090

0.300

0.16

1.589

0.135

0.271

1.454

0.018

0.134

0.09

A10

2.146

0.140

0.409

2.006

0.130

0.361

0.18

A11

2.146

0.142

0.391

2.004

0.061

0.246

0.12

A12

1.899

0.165

0.487

1.735

0.061

0.246

0.14

The subarea A6 is located between 2° N and 2° S and between 95° W and 100° W. These

waters have high potential fisheries resources, so it attracts the world's fishing vessels, especially

from Asia.

3.3 Data

Our dataset come from the data base of European Space Program, called Copernicus that

provides measurements of several physical, chemical, and biological oceanic variables. The

values of physical variables come from data base “Global Analysis Forecast-PHY- 001-024-TDS

[20], and values of biochemical variables come from data base “Global Analysis Forecast-BIO-

001-028-TDS [21].

Table 3. Description of the physical and the biogeochemical variables.

Variable

Description

Unit

Biogeochemical variables

Chl

Total chlorophyll-a

mg/m

Dissolved iron

mmol/m

NO3

Nitrate

mmol/m

Dissolved oxygen

mmol/m

PO4

Phosphate

mmol/m

Dissolved silicate

mmol/m

SPCO2

Surface CO2

Nppv

Net primary production

mmol/m

Phyc

Phytoplankton concentration in carbon

mmol/m

Physical variables

Sea water -40m temperature

ºC

Salinity

1/e

Zos

Sea surface height

Mlots

Mixed layer depth

Northward sea current water vel.

m/s

Eastward sea current water velocity

m/s

InGenio Journal, 6(1), 31–43

| 39

The variables considered in this study are described in Table 3, while our data set was

structured with daily mean values of these variables. The training dataset is the values recorded

from December-2020 to May-2021 (Atraining) and the test dataset considers the values from Jun-

2021 to November-2021 (Atest), with a spatial granularity of 0.1 grade in every direction, for

2091 geographically distinct points per day, in total 7´259.952 measurements. Our data contained

no missing values. The correlation one-to-one of 16 physical and biogeochemical variables can

be found in Table. 4.

Table 4. Correlation matrix for our variable recorded during Dic-2020 to Nov-2021.

Chl

CO2

Mlots

Zos

Chl

0.68

-0.81

0.75

-0.66

-0.69

0.02

0.67

Chl

Nppv

0.79

-0.62

0.81

-0.55

-0.61

0.11

0.63

CO2

phyc

0.87

0.75

-0.88

0.78

0.89

-0.06

-0.71

0.91

0.84

0.78

-0.76

-0.81

0.08

0.69

0.88

0.83

0.78

0.97

0.76

0.01

-0.56

Mlots

NO3

0.88

0.75

0.71

0.94

0.92

-0.03

-0.63

Zos

PO4

0.85

0.76

0.78

0.89

0.95

0.90

0.05

-0.77

-0.71

-0.55

-0.89

-0.85

-0.92

-0.75

-0.80

-0.73

-0.72

-0.83

-0.92

-0.83

-0.93

0.74

Chl

Nppv

Phyc

NO3

PO4

4. RESULTS AND DISCUSSION

4.1. Chlorophyll-a prediction (30 days) without optimization model

Figure 5. Correlation of Chlorophyll-a prediction without optimization.

First, the chlorophyll-a prediction is conducted using the multivariate spatial-temporal

regression method, in order to determine the efficacy of this method without applying any kind

of optimization. Two datasets are configured; the first one will be used for model training and the

0,2

0,4

0,6

0,8

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Correlation

Days

Correlation

Forecast without Optimization

* Correlation of chlorophyll vs. physical (White color) and biogeochemical (Grey color) variables.

InGenio Journal, 6(1), 31–43

| 40

second one will be used for its evaluation. Each dataset contains data of 180 days, evaluated from

each of the 2091 geographical positions and the 16 analyzed variables. The correlation between

the real value and the predicted value is evaluated, and this will be our reference value to evaluate

the method optimization. In the Figure 5, the results from the preliminary evaluation can be

observed. The prediction without optimization of the chlorophyll substance decreases from 0.85

to 0.39, this prediction is made during the following 30 days, on each day considered in the

training dataset.

4.2 Chlorophyll-a prediction (30 days) applying optimization model

Once the phase lag is determined for each of the variables, the dataset is once again

restructured, taking into consideration the variables that are ahead of phase with respect to Chl-a,

given that these are the ones that influence its variation. For the variables that are delayed with

respect to Chl-a, their last known value is kept. It must also be mentioned that it has been tested

taking into account only the delayed variables, but the performance of the model did not improve.

After the dataset restructuration, the prediction model is executed and the result can be

observed in Figure 6.

Figure 6. Correlation of Chlorophyll-a prediction with optimization.

As it can be observed on this graph, when taking into account the phase lag of the variables

with respect to Chl-a, the Chlorophyll prediction is improved on average 6% up to the 18

day,

after which the optimization model turns out to not be very efficient.

4.3 Chlorophyll-a prediction (30 days) applying optimization model and lags.

The multivariate spatial-temporal regression mode is performed, including 10-days lag

transformation to the data set Atraining, determining that the model becomes even more

optimized, obtaining an improvement of up to 10% in the Chl-a prediction on days 10 and 11;

nonetheless, the effectiveness does not improve after the 18th day, remaining at 52%. From this

day, this optimization model is not suitable. In the Figure 7, the final model optimization is

presented, considering the number of phase delays with better performance for each prediction

day.

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Correlation

Days

Correlation

Forecast with Optimization

Optimized Without Optimization

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Figure 7. Correlation of Chlorophyll-a prediction with optimization including lags.

5. CONCLUSION

In this work, a model that optimizes the prediction of the concentration of Chlorophyll around

the Galapagos Islands has been designed, making use of the discrete Fourier transform theory,

that allows, on one hand, to understand the relationship between the physical and biogeochemical

variables of the ocean in relation to the Chl-a, as well as, on the other hand, to restructure the

dataset, considering the displacement of the variables that are ahead of the Chlorophyll, in order

to optimize the prediction using the multivariate spatial-temporal regression model. This

prediction makes it possible to identify the areas which will be more productive in the ocean, so

that the naval forces can intensify maritime surveillance at these points, in order to combat illegal,

unreported and unregulated fishing. The best correlation is given in a time gap of 3 days (>0,7),

while it remains above 0,5 up to 18 days. It is necessary to mention that the Ecuadorian Navy

takes 0.6 days (14 hours) to deploy a Coast Guard from San Cristobal Island to the furthest point

in Galapagos (200 Mn), and if it is necessary to send a Coast Guard from Manta (Mainland

Ecuador) to the furthest point (930 Mn), it takes 3 days of navigation.

REFERENCES

[1] United Nations Educational, Scientific and Cultural Organization. The Ocean Decade at

COP26 of the United Nations Framework Convention on Climate Change [Online]. 2021.

Available: https://www.oceandecade.org/wp-content/uploads//2021/11/356287-

The%20Ocean%20Decade%20at%20COP26.

[2] D. Agnew, J. Pearce, G. Pramod, T. Peatman, R. Watson, et al. Estimating the Worldwide

Extent of Illegal Fishing [Online]. 2009. PLoS ONE 4(2): e4570. Available:

https://doi.org/10.1371/journal.pone.0004570

[3] K. Metuzals, R. Baird, T. Pitcher, U. Sumaila, P. Ganapathiraju. “One fish, two fish, IUU,

and no fish: unreported fishing worldwide” [Online]. 2009. Handbook of marine fisheries

conservation and management. Oxford University Press, New York, 2010, pp. 165-18.

Available:

https://www.researchgate.net/publication/262602332_One_fish_two_fish_IUU_and_no_fis

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Correlation

Days

Correlation

Forecast with Optimization

Optimized with Lags

Without Optimization

InGenio Journal, 6(1), 31–43

| 42

h_unreported_fishing_worldwide_In_Handbook_of_marine_fisheries_conservation_and_m

anagement_Oxford_University_Press_Oxford_United_Kingdom_pp_165-181

[4] A. Valery. The Charles Darwin Foundation’s Position in Relation to Illegal Fishing in

Galapagos Islands [Online]. 2017. Available:

https://www.theguardian.com/environment/2020/jul/27/chinese-fishing-vessels-galapagos-

islands.

[5] P. Boyd et al. Multiple Ocean Stressors: A Scientific Summary for Policy Makers. [Online].

2022. (eds). Paris. IOC-UNESCO. 20 pp. (IOC Information Series, 1404) doi:10.25607/OBP-

1724. Available: https://unesdoc.unesco.org/ark:/48223/pf0000380891

[6] X. Castro. Analysis of the Current Socio Economic Situation of the ‘Galapagos Artisanal

Fishing Community [Online]. 2005. Ecuador: Parque Nacional Galápagos/JICA (Japanese

International Cooperation Agency). Available:

https://www.jica.go.jp/project/ecuador/3185011E0/materials/pdf/analysis.pdf

[7] J. Harrison and E. Morgera. Article 61 Conservation of the living resources. Washington

Post [Online]. 2012. Available:

https://strathprints.strath.ac.uk/63127/1/Harrison_Morgera_2017_United_Nations_conventi

on_on_the_law_of_the_sea_commentary_to_articles_61_65.pdf.

[8] M. Guarderas. Temporal and spatial patterns influence reef fish community structure along

an upwelling gradient in the Galápagos Marine Reserve (Bachelor's thesis, Quito) [Online].

2019. Available: http://repositorio.usfq.edu.ec/handle/23000/8482.

[9] SENPLADES. Planificación y Ordenamiento del Espacio Marino Costero Ecuatoriano

[Online]. 2017. Guayaquil. Subsecretaría de Planificación Nacional - Dirección de Asuntos

Marino Costeros DAMC. Available: https://www.planificacion.gob.ec/wp-

content/uploads/downloads/2018/07/Plan-de-Ordenamiento-del-Espacio-Marino-

Costero.pdf

[10] F. Chávez, M. Coltorti, R. Ivaldi, E. Sánchez. G. Sciavicco. Temporal Aspects of

Chlorophyll-a Presence Prediction Around Galapagos Islands [Online]. 2020. 6th

International Conference on Technologies and Innovation. CITI 2020. Available:

https://link.springer.com/chapter/10.1007/978-3-030-62015-8_8

[11] G. Rodriguez. Hartley transform: Basic theory and applications in oceanographic time series

analysis [Online]. 2002. Coastal Environment: Environmental Problems in Coastal Regions

IV, pp. 191-200. 8. Available: http://hdl.handle.net/10553/51982

[12] D. Sundararajan. The discrete Fourier transform: theory, algorithms and applications. World

Scientific, 2001.

[13] S. Smith. Digital signal processing: a practical guide for engineers and scientists. Elsevier

2013.

[14] Y. Wang and K. Veluvolu. Time-Frequency Analysis of Non-Stationary Biological Signals

with Sparse Linear Regression Based Fourier Linear Combiner. Sensors 2017, 17, 1386.

Available: https://doi.org/10.3390/s17061386.

[15] O. Barocio-Leon, R. Millan-Nunez, E. Santamaria-del-Angel, E and A. Gonzalez-Silvera.

Productividad primaria del fitoplancton en la zona eufótica del Sistema de la Corriente de

California estimada mediante imágenes del CZCS. Cienc. mar [Online]. 2007. Vol.33, n.1,

pp.59-72. Available: http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0185-

38802007000100006&lng=es&nrm=iso>. ISSN 0185-3880.

[16] J. Collot, V. Sallares, N. Pazmino. Geología y Geofísica marina y terrestre del Ecuador:

desde la costa continental hasta las Islas Galápagos [Online]. 2009. Guayaquil (ECU);

InGenio Journal, 6(1), 31–43

| 43

Marseille (FRA); Guayaquil: CNDM; IRD; INOCAR, 269 p. ISBN 978-9978-92-737-3.

Available: https://horizon.documentation.ird.fr/exl-doc/pleins_textes/divers12-

04/010051349.pdf

[17] R. Dunn, V. Lekić, R. Detrick, and D. Toomey. Three‐dimensional seismic structure of the

Mid‐Atlantic Ridge (35 N): Evidence for focused melt supply and lower crustal dike injection

[Online]. 2005. Journal of Geophysical Research: Solid Earth, 110(B9). Available:

https://doi.org/10.1029/2004JB003473.

[18] R. Trenkamp, J. Kellogg, J. Freymueller, H. Mora. Wide plate margin deformation, southern

Central America and northwestern South America, CASA GPS observations [Online]. 2002.

Journal of South American Earth Sciences, 15(2), 157-171. Available:

https://doi.org/10.1016/S0895-9811(02)00018-4.

[19] W. Rentería, O. Valarezo, G. García. “Análisis del Esfuerzo Pesquero en el Territorio

Marítimo Ecuatoriano,” Revista de Ciencias de Seguridad y Defensa, 4(6), 2019.

[20] COPERNICUS, Product User Manual for Global Physical Analysis and Coupled System

Forecasting Product. Marine Environment Monitoring Service [Online]. 2022. Available:

https://doi.org/10.48670/moi-00016

[21] COPERNICUS, Product User Manual for Global Biogeochemical Analysis and Forecasting

Product. Marine Environment Monitoring Service [Online]. 2019. Available:

https://doi.org/10.48670/moi-00015

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