Generation of Daily and Monthly Flows Using the GR4j Method with

ERA5 Grilled Data in the Cañete River Basin to the Putinza

Hydrometric Station

Edgar Manuel Infante Quispe

, Gianfranco Massimo Gutiérrez Buitrón

Abel Carmona Arteaga

and Rubén Kevin Manturano Chipana

Universidad Privada del Norte, Sede Cajamarca, Cajamarca, Peru

Universidad Privada del Norte, Sede Breña, Lima, Peru

Keywords: Cañete Basin, Putinza, GR4j Hydrological Model, Google Earth Engine.

Abstract: The research is carried out in a sub-basin of the Cañete River, delimited from the Putinza hydrometric station,

with the aim of being able to generate the flows at a daily and monthly rate during a period of 39 years (1980

- 2019) and determine the approximate values of maximum flows in the periods that the El Niño phenomenon

existed in the aforementioned basin, the methodology used was the GR4j method. On the one hand, the ERA5

grid data belonging to the European Space Agency Satellite was used, using Google Earth Engine (GEE) from

which precipitation and average temperature information was extracted. Likewise, from the National Water

System (ANA), information was extracted on daily flows from the Putinza hydrometric station between the

period 2014-2017, which was used for the calibration and validation of the model. The analysis of results was

carried out taking into account the Nash coefficient and the coefficient of determination R2 as efficiency

criteria. Finally, the results obtained in the calibration and validation are satisfactory, which indicates that

there is a good performance.

1 INTRODUCTION

In recent years, numerous floods have occurred in

different basins of Peru. Currently, different studies

are being carried out to implement projects that help

reduce the danger that affects the population,

however, in many projects they do not have

satisfactory results because historical records of flow

measurement are required in the affected areas.

One of the affected basins is the Cañete river

basin, in periods of floods it is in danger due to the

recurrent rains where there is the possibility of

exceeding its flood threshold, generating overflows,

flooding of crop fields; unfortunately, it is not

possible to design riparian defenses that are efficient

to minimize the danger in these areas due to the lack

of historical records of flow measurement (Andean

News, 2017).

https://orcid.org/0000-0001-5913-3711

https://orcid.org/0000-0001-8608-2745

https://orcid.org/0000-0003-2895-9582

https://orcid.org/0000-0002-9685-2886

Likewise, the Cañete River basin has suffered the

natural event known as the El Niño phenomenon;

during the last 40 years it was recorded in the periods

1982-1983 (Public Eye, 2017), 1997-1998 (CAF,

2000), 2017-2018 (Government of Peru, 2019),

generating flooding of villages, cultivation areas,

road overflows, collapse of bridges; because the

projects that are designed have little hydrometric and

meteorological information for their design,

obtaining deficient results that directly affect the

population.

Faced with these problems, the present research

work aims to generate historical data of flows at the

daily and monthly level in the Cañete river basin for

a simulation of 39 years (1980 – 2019) and determine

the records of the maximum flows that happened the

El Niño phenomenon in the periods during the last 40

years in the aforementioned basin; These generated

records will serve as a reference for the development

252

Quispe, E., Buitrón, G., Arteaga, A. and Chipana, R.

Generation of Daily and Monthly Flows Using the GR4j Method with ERA5 Grilled Data in the Cañete River Basin to the Putinza Hydrometric Station.

DOI: 10.5220/0011648100003393

In Proceedings of the 15th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2023) - Volume 3, pages 252-259

ISBN: 978-989-758-623-1; ISSN: 2184-433X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

of the design of the riparian defenses, seeking that

they are the most adequate and really comply with the

quality standards and the norms provided, in such a

way that it becomes a good state investment, which

translates into giving a better quality of life to the

population.

For this reason it was proposed to use the

hydrological model GR4j, which in French means

Génie Rural á 4 parameters Journalier, which will be

used for the estimation of flows at the daily level of

the Cañete river basin to the Putinza hydrometric

station, taking the daily flow records (m3 / s)

discharged from the National Water Authority

(ANA); precipitation (mm) and temperature (°C)

data obtained from the Google Earth Engine (GEE)

platform.

1.1 Area of Study

The Cañete River basin is located between parallels

11°58'19'' and 13°18'55'' South Latitude and

meridians 75° 30'26'' and 76°30'46'' West Longitude,

having as hydrographic limits: on the north the Cueca

of the Mantaro River, on the south with the Q°Topara

– Pacific Ocean Interbasin, on the east with the

Mantaro and San Juan River Basin and on the West

with the Omas and Mala and Mala basins. the Pacific

Ocean.

Likewise, for the present study, the Putinza

hydrometric station located at the geographical

coordinates was used: Latitude: 12°40'05.5'',

Longitude: 75°57'35.3" and at an altitude of 1960

m.a.s.l., for the delimitation of the basin from which

we will obtain the average daily flows.

1.2 Previous Studies of the use of the

GR4j Hydrological Model

Research studies related to the GR4j hydrological

model were carried out, in order to make the

application for the estimation of daily flows viable.

In the research: Performance evaluation of

hydrological models GR4J, HBV and SOCONT for

the forecast of average daily flows in the Ramis river

basin, Peru: aims to evaluate the performance of three

hydrological models for the forecast of daily flows in

a basin of the Peruvian highlands; giving as best result

despite using only four parameters the hydrological

model GR4j, the simulation of the flows of avenue

and low water are satisfy (Lujano and others. , 2020).

Also, in the research: Comparison of rain-runoff

hydrological models GR2M and GR4J in obtaining

average flows in the Subacoche river basin: analyzes

the hydrological models GR2M flows at monthly

pace and GR4J for flows at daily step with the aim of

determining the veracity of these rain-runoff models;

providing satisfactory results in calibration and

validation, so it is possible to represent the

hydrological conditions of the Subacoche river basin

(Rodríguez, 2021).

1.3 Cartographic Data

The cartographic information was extracted in

Shapefile format at a scale of 1:100000 from the

National Geographic Institute (IGN). The pages of

the National Charter covering the area of study are:

Table 1: Sheets of the national charter.

Letter No. Numbe

26 -

Lunahuama

26 - l Tupe

25 - l Yauyos

25 -

Huarochiri

24 - l Oro

24 -

Matucama

1.4 Rainfall Data

The rainfall information was extracted using the

ERA5 datasets generated by the Copernicus Climate

Change Service of the European Union through the

Google Earth Engine (GEE) platform using the codes

provided by Mg. Abel C. (Carmona, 2021).

The average precipitation in the period 1/1/2014 –

30/11/2017 was used for the development of the

calibration and in the period 01/12/2015 – 29/10/2017

for the development of the validation.

1.5 Climatological Data

For the development of the calibration in the period

1/1/2014 – 11/30/2017, the average temperature that

was extracted from the Google Earth Engine (GEE)

platform was used using the ERA5 grid data at a daily

rate.

1.6 Hydrometric Data

The hydrometric information was extracted through

the system of the National Water Authority (ANA,

2021), at the Putinza station, the daily flows were

considered for the development of the calibration in

the period 1/1/2014 – 30/11/2015 and for validation

the period 1/12/2015 – 29/10/2017.

Generation of Daily and Monthly Flows Using the GR4j Method with ERA5 Grilled Data in the Cañete River Basin to the Putinza

Hydrometric Station

253

1.7 ArcGIS

It is a complete software that allows you to collect,

organize, manage, analyze, share and distribute

geographic information; as the world's leading

platform for creating and using geographic information

systems (Pucha et al., 2017). For the present work, this

software was used for the delimitation of the sub-basin

of the Cañete River, having as its main point the

Putinza hydrological station.

Figure 1: Sub-basin of the sugarcane basin delimited from

Putinza station.

1.8 Description of Model GR4j

It is a model that simulates the precipitation-runoff

process on a daily time scale using four parameters.

This model has been used as a sequential simulation

of soil moisture and flow data in conceptual

precipitation-runoff models, obtaining very

satisfactory results, which is why it was decided to

use it in the development of this article.

Figure 2: GR4j hydrological model (Perrín et al., 2010).

The GR4j model takes the average daily

precipitation and evapotranspiration within the basin

area as input and the daily flow as the output.

Similarly, it uses the Nash - Sutcliffe coefficient as

the target function in the calibration phase. In the

GR4j model, precipitation and potential

evapotranspiration are expressed as and respectively

(Rincón, 2019).

For our case, the average rainfall values recorded

by remote sensing and provided in a set of ERA5

gridded climates are calculated by spatial

interpolation. It should be noted that all quantities,

whether inputs, outputs or internal variables are

expressed in mm / day, for this reason, the volumes

of water must be divided by the area of the basin when

necessary.

1.9 Mathematical Description of the

GR4j Model

Determination of precipitation and net potential

evapotranspiration:

The main components of the model include: first,

subtracting evapotranspiration E from precipitation P,

determining a net precipitation P

or a net

evapotranspiration capacity E

The net precipitation equation is:

If P≥E then P

=P-E and E

= 0 (1

)

The net precipitation clearance equation is:

If P≥E then P n=0 and E

=E-P (2

)

Production storage: In the case where P

, is not

zero, a part P

of Pn, enters the production tank:

The production storage equation is:

1-





tanh









tanh





(3)

is determined as a function of the level S in the

tank, where x

(mm) is the maximum capacity of the

production tank When En is not zero, an actual

evaporation rate is determined as a function of the

level in the production storage in order to calculate

the amount of water that will evaporate from the tank.

The real evaporation rate equation is:

S 2-





tanh









tanh





(4)

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

254

In this way, the water content in the production

tank is updated as the equation of amount of water

collected:

S = S-E

(5)

It is important to note that S can never exceed x

A quantity P

erc

escapes as production storage

percolation. This value is calculated by the

percolation equation in the production tank:

erc

=S 1- 1+ 





-0.25

(6)

From the above expression it concludes that

percolation does not contribute much to the flow rate

for this reason it is important mainly for the

simulation of minimal events. The percolation value

is always less than S. The new level in the tank is

defined as:

S = S-P

erc

(7)

Linear distribution with unit hydrographs. The

total amount of water P_r which reaches the

distribution functions is given by:

= P

erc

+ (P

-P

) (8)

The value of the P_r is divided into two flow

components: 90% of P_r is distributed by means of a

UH1 unit hydrograph and then by a non-linear

distribution tank. The remaining 10% of P

distributed by means of a UH2 unit hydrograph. With

UH1 and UH2, the lag time between the rain event and

the resulting peak flow can be simulated. The ordinates

of both hydrographs are used in the model to distribute

the effective rainfall over several successive time

intervals. UH1 and UH2 depend on the same parameter

x 4 expressed in days, however, UH1 has a base time

of x 4 days, while UH2 has a base time of 2x

days

The parameter x

can take real values and should be

May 0.5 days. In their discrete form, UH1 and UH2

unit hydrographs have n and m ordered respectively,

where n and m are the smallest integers exceeding x 4

and 2x

respectively. The ordinates of both

hydrographs are derived from the corresponding S-

curves (cumulative proportion of input over time)

denoted by SH1 and SH2 respectively.

2 METHODOLOGY

This section details the procedures used for the

development of this work.

2.1 Calibration of the GR4j Model

The objective of this stage is to identify the values of

the model parameters in order to optimally adjust a

system as close to the real system that the model

represents. The efficiency criteria considered at the

calibration stage are detailed below:

2.1.1 Nash - Sutcliffe Coefficient

Evaluation criterion that determines the efficiency

between a simulated model and another observed by

measuring the variability of observations. It is

expressed as follows:

E=1-

∑



sim,i

-Q



i=1

∑

Q

-Q





i=1

(9)

Where:

Qsim – Simulated flow rates in m3/s

Qi – Observed flow rates in m3/s

𝑄

– Average flow rates observed in m3/s

The following is a table with the reference values

of Nash's criterion:

Table 2: Referential values of the Nash – Sutcliffe Criterion

(Molnar, 2011).

Nash Adjustment

< 0.2 Insufficient

0.2

–

0.4 Satisfactor

0.4 – 0.6 Well

0.6

–

0.8 Ver

> 0.8 Excellent

2.1.2 Criterion Nash - Sutcliffe

It is used when the values of the simulated variable

are very large. It is defined as follows:

E=1-

∑



log(Q

sim,i)

)-log(Q

)



i=1

∑

log(Q

)-log(Q)





i=1

(10)

Where:

Qsim,i – Simulated download in a time I in m3/s

Qi – Discharge observed at a time i in m3/s

𝑄

– Average discharges observed in the period of

time considered in m3/s

2.1.3 Coefficient of Determination (R

)

It is the chart of the correlation coefficient, which

varies from 0 to 1. It is expressed as follows:

Generation of Daily and Monthly Flows Using the GR4j Method with ERA5 Grilled Data in the Cañete River Basin to the Putinza

Hydrometric Station

255

=1-

Cov(Q

)

SdQ

.SdQ



(11)

Where:

Cov(Q0, Qs) – Covariance of observed and

estimated flows.

Sd(Q0) – Standard deviation of observed

values.

Sd(Qs) – Standard deviation of the estimated

heats.

2.2 Validation of the Hydrological

Model

The objective of this stage is to verify the quality of

the calibration settings. For model validation, the

same efficiency criteria are used for results analysis.

Also, in both stages, the verification of the fit is

used to visually compare the duration curve of actual

and estimated flows.

3 RESULTS

3.1 Calibration

The analysis period is 699 days from 01/01/2014 to

11/30/2015, with a trial period of 10 days. Likewise,

it should be noted that this period of analysis was used

due to the lack of data offered by the ANA in said

hydrometric station.

Table 3 shows that the efficiency criteria are

within the evaluation range. According to Table 2, the

fit is excellent when the Nash coefficient is greater

than 0.8. In this case, the value of Nash is 86.5 %.

Therefore, the adjustment made is interpreted to be

excellent.

Table 3: Efficiency criteria (%) in the calibration stage.

Efficiency criteria (%)

Nash(Q) 86.5

Nash

(

)

78.8

Nash

(

))

45.2

Balance sheet 96.3

3.2 Validation

For this stage, the analysis period is 699 days from

01/12/2015 to 10/29/2017 with a trial period of 10

days. Likewise, it should be noted that this period of

analysis was used due to the lack of data offered by

the ANA in said hydrometric station.Table 6 shows

that the Nash coefficient = 84.4% is higher than the

coefficient obtained in the calibration. Therefore, the

adjustment made is interpreted to be excellent.

Table 4: Parameters of the GR4j model in the calibration

stage.

Name of the basin Cañete

Area of the basin

(

km2

)

3139.60

Initial values

Initial fill rate S0/x1 0.30

Initial fill rate R0/3 0.70

Parameters Unit Transf.

X1 m

5.68

X2 m

-4.88

X3 m

6.45

X4 days -13.62

Table 5: Averages of the hydrometric data used in the

calibration stage.

Average observed rainfall (mm/day) 4.409

Average observed ETP (mm/day) 1.234

Observed mean flow rates

(

mm/da

1.113

Average of the roots of the observed

flows

0.974

Avera

e lo

arithm of observed flows -0.161

Figure 3: Comparison of measured flow rates (ANA) with

the flows generated with the GR4j model using ERA5 grid

data for the period 01/01/2014 to 30/11/2015.

Figure 4: R2 correlation between daily flows (m3/s)

generated with the GR4j method and daily flows (m3/s)

recorded for the Cañete basin to Putinza station.

100

120

140

160

180

200

31/01/2014

31/03/2014

31/05/2014

31/07/2014

30/09/2014

30/11/2014

31/01/2015

31/03/2015

31/05/2015

31/07/2015

30/09/2015

30/11/2015

Flow rates (m3/s)

Days

Measured

flows

Flows

generated

y = 0.0072x

+ 0.1966x + 13.254

R² = 0.9096

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Original average flows (m3/s)

Average daily flows with GR4j generated m3/s

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

256

Table 6: Efficiency criteria (%) in the validation stage.

Efficienc

criteria

(

)

Nash

(

)

84.4

Nash

(

)

82.5

Nash(ln(Q)) 74.9

Balance sheet 105.9

Table 7: Parameters of the GR4j model in the validation

stage.

Name of the basin Cañete

Area of the basin (km2) 3139.60

Initial values

Initial fill rate S0/x1 0.30

Initial fill rate R0/3 0.70

Parameters Unit Transf.

X1 m

6.74

X2 m

-4.05

X3 m

5.78

X4 da

s -13.62

Table 8: Averages of hydrometric data used in the

validation stage.

Avera

e observed rainfall

(

mm/da

4.642

Avera

e observed ETP

(

mm/da

1.228

Observed mean flow rates

(

mm/da

1.255

Average of the roots of the observed flows 0.989

Average logarithm of observed flows -0.189

Figure 5: Comparison of measured flows (ANA) and those

generated with the GR4j model using ERA5 grid data for

the period 01/12/2015 to 29/10/2017.

4 ANALYSIS OF RESULTS

In the calibration and validation sections, NASH

efficiency criteria are shown 86.5% and 84.4%

respectively; Figure 4 shows that R2 = 0.9096 is

greater than 0 and close to 1, Figure 6 shows that R2

= 0.8973; therefore, it can be deduced that the GR4j

method is effective for the study of the Cañete River

basin.

Figure 6: R2 correlation between daily flows (m3/s)

generated with the GR4j method and daily flows (m3/s)

recorded for the Cañete basin to Putinza station.

Figure 7: Daily flow rates generated with the GR4j method,

in the period 1980 - 2019.

Figure 8: Monthly flow rates generated with the GR4j

method, in the period 1980 - 2019.

Figure 9: R2 correlation between daily flows (m3/s)

generated with the GR4j method for the period 1980-2019

years and daily flows (m3/s) recorded for the Cañete basin

to Putinza station.

100

150

200

250

300

350

31/12/2015

29/02/2016

30/04/2016

30/06/2016

31/08/2016

31/10/2016

31/12/2016

28/02/2017

30/04/2017

30/06/2017

31/08/2017

Flow rates (m3/s)

Days

Measured

flows

Flows

generated

y = 0.0056x

+ 0.1815x + 11.598

R² = 0.8973

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0.00 50.00 100.00 150.00 200.00 250.00

Original average flows (m3/s)

Average daily flows with GR4j generated m3/s

100

150

200

250

300

350

01/01/1980

01/01/1981

01/01/1982

01/01/1983

01/01/1984

01/01/1985

01/01/1986

01/01/1987

01/01/1988

01/01/1989

01/01/1990

01/01/1991

01/01/1992

01/01/1993

01/01/1994

01/01/1995

01/01/1996

01/01/1997

01/01/1998

01/01/1999

01/01/2000

01/01/2001

01/01/2002

01/01/2003

01/01/2004

01/01/2005

01/01/2006

01/01/2007

01/01/2008

01/01/2009

01/01/2010

01/01/2011

01/01/2012

01/01/2013

01/01/2014

01/01/2015

01/01/2016

01/01/2017

01/01/2018

01/01/2019

Flow rates (m3/s)

Days

Measured

flows

Flows

generated

0.00

50.00

100.00

150.00

200.00

250.00

Ene-1980

Set-1982

May-1985

Ene-1988

Set-1990

May-1993

Ene-1996

Set-1998

May-2001

Ene-2004

Set-2006

May-2009

Ene-2012

Set-2014

May-2017

Flow rates (m3/s)

Days

Measured flows

Flows

generated

y = 0.0068x

- 0.1385x + 15.888

R² = 0.8805

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0.00 50.00 100.00 150.00 200.00 250.00

Original average flows (m3/s)

Average daily flows with GR4j generated (m3/s)

Generation of Daily and Monthly Flows Using the GR4j Method with ERA5 Grilled Data in the Cañete River Basin to the Putinza

Hydrometric Station

257

For the simulation of the 39-year period, the

values x1,x2,x3,x4 of the validation were used; of

these results a revalidation was carried out to improve

the data by accommodating in a quadratic equation of

second degree, obtaining Figure 7 the record of flows

at the daily level, in Figure 8 the registration of flows

at the monthly level, in Figure 9 the correlation R2 =

0.8805 is shown; then, it follows that the GR4j

method was properly adjusted, since the correlation is

very close to 1; There is also little variability between

measured and recorded flows.

Figure 7 shows the maximum flows generated

with the GR4j method during the periods that the El

Niño phenomenon occurred in the last 40 years, these

being in the periods: i) 1982-1983, a maximum flow

of 132.50 m3/s on the date 02/10/1982, ii) 1997-1998,

a maximum flow of 276.51 m3/s was recorded on the

date 02/8/1998 and iii) 2017-2018, a maximum flow

of 305.71 m3/s was recorded on 03/15/2017; from

which it can be deduced that in the Cañete River basin

the El Niño phenomenon had the greatest impact in

the period 2017-2018 and the least impact in the

period 1982-1983.

5 CONCLUSIONS

It can be concluded that the GR4j model was properly

applied for the estimation of daily and monthly flows

in the Cañete River basin to the Putinza hydrometric

station resulting in a satisfactory representation of the

series of daily flows. Also, allowing to reconstruct

past historical records using the grid data of

precipitation and temperature ERA5 for the period

1980 – 2019.

The GR4j method can serve as a basis for other

studies in other basins to generate extensive flow

records over time, since it uses four main variables.

The flows generated by this method can be used

in the planning of various hydraulic and civil projects,

such as irrigation works for agricultural land,

construction of bridges, taking into account the

Putinza hydrometric station.

The area surrounding the sub basin of Cañete

towards the Putinza station, has been roughed 3 times

in the last 40 years by the El Niño phenomenon, this

phenomenon has caused structural havoc to the

population, this because there is no hydrological

study that can serve as a basis for a correct design of

riparian defense, That is why it is expected that the

present work will serve as a reference for the

compilation of necessary information to be able to

plan projects that meet the needs of the population.

The values of the Nash efficiency criterion for

calibration and validation are 86.5% and 84.4%

respectively. Both values are within an excellent

range demonstrating that the model was adjusted

properly.

Bilan's criteria values for calibration and

validation are 96.3% and 105.9% respectively,

showing optimal model performance.

The graph for monthly flows will also allow us to

estimate the monthly prorated distribution over an

extended period of the year, which will give us a

better idea of the monthly profile distribution.

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