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Evaluating evapotranspiration values in Rwanda using the FAO-56 Evaluating evapotranspiration values in Rwanda using the FAO-56

PM, Turc, and Hargreaves-Samani equations PM, Turc, and Hargreaves-Samani equations

Elizabeth Uwase University of Nebraska-Lincoln

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Uwase, Elizabeth, "Evaluating evapotranspiration values in Rwanda using the FAO-56 PM, Turc, and Hargreaves-Samani equations" (2021). Biological Systems Engineering--Dissertations, Theses, and Student Research. 110. https://digitalcommons.unl.edu/biosysengdiss/110

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Evaluating Evapotranspiration Values in Rwanda Using the FAO-56 PM, Turc, and

Hargreaves-Samani Equations

Elizabeth Uwase, Undergraduate Research Assistant

Department of Biological Systems Engineering

University of Nebraska-Lincoln

April 12, 2021

Working paper prepared as part of a UNL Undergraduate Creative

Activities and Research Experience (UCARE) project

Abstract

Evapotranspiration (ET) is an important component of the hydrologic cycle and involves

exchange of water between the surrounding water bodies, soil, crop surfaces, and the

atmosphere. Crop growth and grain yield are largely affected by the rate of ET, especially in

semi-arid areas where the rate of ET is high and rainfall is not sufficient and reliable to add more

water into the soil for crop use. Solar radiation, relative humidity, air temperature, rainfall, and

wind velocity are some of the meteorological factors that affect ET. Therefore, this research was

aimed at determining ET and its trend across Rwanda using climatic data measured at five sites.

With this research, we accessed meteorological data measured at synaptic stations in the five

provinces of Rwanda (Kigali city/central, Kawangire/Eastern, Ruberengera/Western,

Ruhengeri/Northern and Gikongoro/Southern), and used the data to calculate reference

evapotranspiration (ET) for the recent 9 years (2010-2018).

Equations were used to calculate ET using extra-terrestrial radiations, solar radiations,

evapotranspiration using the FAO-56 guidelines - Turc method (1961) and Hargreaves-Samani

(HS) method (1983). The obtained data from the weather stations were analyzed using the two

methods and graphs were plotted for visualization. The average monthly reference

evapotranspiration for both equations ranges from 3 to 5 mm/day. The Hargreaves-Samani and

Turc graphs for all the five locations showed low values of reference ET (3 to 4 mm/day) for the

year of 2018 compared to the previous years. The Turc method underestimates reference ET

values compared to the HS method. The difference and variation of reference crop ET for both

the equations may be attributed to the different locations since they have variations in climatic

conditions that significantly affects ET in the region. The HS and Turc ET estimates did not

capture the day-to-day variability in ET when compared with the standard FAO Penman-

Monteith method. Hence, the Turc and HS equations may not be implemented for estimating

daily ET but may be more acceptable for estimation of ET on a weekly or monthly basis.

Introduction

Rwanda is a land locked country with no borders to sea or oceans and excessively depends on

natural resources, rainfall, river water and sunlight, to perform different agricultural practices

(Haggag, M. 2016). Most of the farming practices in Rwanda are done using hoes and farmers

depend on the rainfall to supply the necessary water needed for their crop growth. Due to such

practices and the lack of technology and other innovative ways to do agriculture in Rwanda,

farmers face a lot of difficulties during extended hot seasons. For instance, finding enough water

to irrigate their crops is a major problem during such times. It should, however, be recorded that

Rwanda has adequate rivers and lakes that have good recharge capacity. Therefore, with proper

water management strategies, such as creation of dams to store water for use during those

extended hot seasons and short rainfall, agriculture production during the hot seasons would

improve significantly. As mentioned by Haggag and his colleges in their research paper about

the projections of precipitation, air temperature and potential evapotranspiration in Rwanda

under changing climate conditions, climate projections in Rwanda showed warmer and wetter

climate patterns in the 21st century. In addition, they also predicted that future climate changes

will contribute to the increase in average mean temperature and changes in annual and seasonal

rainfall patterns will largely affect the agriculture production, water availability, biodiversity, and

ecosystem services (Haggag, M. 2016). For such reasons, we believe Rwandan farmers need to

find adequate ways to account for crop water requirement and ways to manage water properly in

order to maximize their crop production in all seasons of the year. Therefore, the main aim of

this research paper is to calculate ET and demonstrate the trends in ET over 5 locations with the

five provinces of Rwanda. With the outcomes of this research, we will be able to examine simple

and convenient ways Rwandan farmers and agronomists can use to account for water loss from

the agriculture lands using simple equations and how the results from such calculation would

help them to know how much water they are losing and how much the crops need. As mentioned

by a researcher in Southwestern China, Reference Evapotranspiration (ETo) is a critical factor

used to accurately estimate crop water requirement (Gao, X. 2015). Thus far, with the use of

climatic stations, the farmers and agronomists would also know how much water they are

receiving as rainfall and hence determine how much water is remaining in the ground after

evapotranspiration and how much water they need to irrigate depending on the crops in the

fields. In addition, crop growth and yields are largely affected by the rate of evapotranspiration

(ET), which is an important component of the hydrologic cycle and involves the exchange of

water between the surrounding water bodies, soil, crop surfaces, and the atmosphere. With this

research, we used solar radiation, relative humidity, air temperature, rainfall, and wind velocity,

which are some of the meteorological factors that affect ET, to calculate reference crop

evapotranspiration for five locations, Kigali city/central, Kawangire/Eastern,

Ruberengera/Western, Ruhengeri/Northern and Gikongoro/Southern, in Rwanda for a period of 9

years (2010 -2018). We used the FAO-56 guidelines - Turc method (1961), Hargreaves-Samani

(HS) method (1983) and the FAO Penman-Monteith equation to calculate reference

evapotranspiration for the five locations. The results were analyzed and graphs were plotted for

visualization.

Unfortunately, due to limited climatic data availability across the country of Rwanda, many of

the regions we used did not meet the requirement of the FAO-56 Penman Monteith (PM) method

for calculating the ETo. Even though, the country has various meteorological stations located in

multiple locations of the five provinces in Rwanda. A few of those stations are able to measure

solar radiation which is a key climatic component used in calculating ETo with the FA0-56 PM

method. According to some of the researches on calculating ETo using FAO-56 PM method in

the developing and undeveloped regions, researchers have raised concerns about unavailability

of some of the climatic valuables such as solar radiation (Heydari, M. 2014). Due to the

unavailability of enough weather data to calculate ETo using the FAO-56 Penman Monteith

method, for this research we used the Penman Monteith to calculate ETo for one of the regions

which had solar radiation data, Kigali AERO, and results from this calculation was compared to

the results from other simple equations used, Turc and Hargreaves-Samani, to understand the

difference in the ETo trends.

Consequently, the Turc method (Turc 1961) is one of the simplest and most accurate empirical

equations used to estimate reference evapotranspiration (ETo) under humid conditions (Jensen et

al. 1990). In addition, the Turc method requires minimum weather parameters such average,

maximum and minimum daily values of temperature and extraterrestrial radiation (Ra). During a

research on windspeed on accuracy of the Turc method in a humid climate, the researcher found

out that reliability of the Turc method depends on the wind speed, where the method

overpredicted FAO-56 PM ETo estimates at windless locations and generally underpredicted

ETo at windy locations (Trajković, S. 2007). Also, the Hargreaves-Samani equation is one of the

simple equations that was used in this research on calculating evapotranspiration values in five

provinces in Rwanda. The Hargreaves-Samani method uses few weather parameters similar to

the Turc method and the equation used to calculate ETo involves simple terms which makes it

manageable and easy to use. According to a research done by Razzaghi and Sepaskhah (2010),

Hargreaves-Samani method was reported to be the appropriate method to use in semiarid

environments. In addition, during a research done on proper methods and its calibration for

estimating reference crop evapotranspiration using limited data in southwestern China, the

various calculation methods, FAO-56 PM, Hargreaves-Samani, Priestley-Taylor, Irmak-Allen,

McCloud, Turc, and Valiantzas, used yielded inconsistent results when applied to different

regions. Which makes it a necessity to calibrate the equations for a specific region before using

them for calculations (GAO, X. 2015). This has proven to show more accurate and consistent

results for ETo calculations specific to any region.

The objective of this research study is to evaluate the accuracy and efficiency of the three ETo

calculation methods, FAO-56 PM, Turc, and Hargreaves-Samani, within the five provinces of

Rwanda and to select the best simple, accurate, and efficient method to use while calculating

ETo with limited weather parameters for both farmers and agriculturists in Rwanda.

Material and Methods

Study area and data collection

For this research, we used five study areas with one area from every province in Rwanda. One of

the study areas is Kigali Aero which is the central of Rwanda in Kigali City, it has a latitude and

longitude of -1.95º S and 30.11º E with an elevation of 1490 m. Kigali Aero has an average

rainfall, windspeed, solar radiation, minimum, and maximum temperature of 3.05 inches, 5.03

mph, 195 RAD, 16 ºC and 27 ºC. Kawangire is one next study area that is located in the Eastern

province of Rwanda. Kawangire has an average rainfall, windspeed, minimum, and maximum

temperature of 2.9 inches, 5.3 mph, 15.6 ºC and 26 ºC. Also, Rubengera which is the western

province of Rwanda is among our study areas. This study area has an average rainfall,

windspeed, minimum, and maximum temperature of 6 inches, 5.08 mph, 17.8 ºC and 26 ºC. In

addition, Ruhengeri which is the Northern province of Rwanda is among our study areas with an

average rainfall, windspeed, minimum, and maximum temperature of 5.9 inches, 4.63 mph, 14.4

ºC and 24 ºC. Lastly, Gikongoro in the Southern province of Rwanda is our study area with an

average rainfall, windspeed, minimum, and maximum temperature of 3.4 inches, 5.4 mph, 14 ºC

and 26.7 ºC.

Daily meteorological data for our study areas recorded from 2010 to 2018 were derived from

Rwanda meteorology agency in Kigali such as, average maximum and minimum temperature,

mean daily rainfall, and wind speed. In addition, solar radiation recorded from 2013 to 2018

were also recorded from synaptic stations in Kigali Aero.

Figure 1. The four provinces of Rwanda and Kigali city locations highlighted on the map.

Northern Western Eastern Southern Kigali City

Figure 2. Mean rainfall amount (mm) in the four provinces of Rwanda and Kigali City.

Reference evapotranspiration calculation equations

The FAO-56 PM equation was used as the standard equation for measuring reference crop

evapotranspiration from observed climatic variables. Also, other alternative for estimating daily

ETo with minimum weather data were used, including Hargreaves-Samani and the Turc

equations. The estimated reference crop evapotranspiration from the alternative equations used

were compared with data from the FAO-56 PM for Kigali Aero and based on the data from every

study area. The corresponding meteorological input variables for all the three equations are listed

in Table 1.

Table 1. Reference crop evapotranspiration input data.

Method used Input data

Standard FAO-56 PM T, Tmax, Tmin, and RH, U2, n

Alternative Hargreaves-Samani T, Tmax, Tmin

Alternative Turc T, RH, n

FAO-56 PM Equation

ETo = 0.408∆(𝑅𝑛 −𝐺)+𝑦

900

𝑇+273 𝑈2(𝑒𝑠− 𝑒𝑎)

∆ + 𝑦(1 +0.34𝑈2) (1)

Hargreaves-Samani Equation

ETo = 0.0023(𝑇 + 17.8)(𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛)0.5 𝑅𝑎 (2)

Turc Equation

ETo = 0.0133 (𝑇𝑚𝑒𝑎𝑛

𝑇𝑚𝑒𝑎𝑛 +15) (𝑅𝑠 + 50) (3)

From above equations, T, Tmin, and Tmax represents the mean, minimum, and maximum

temperatures (ºC). Whereby U2 is the mean daily wind speed at a 2 m height (m s-1), that was

converted from the wind speed which was measured at a 10 m height; n is the sunshine hour; es

is the saturation vapor pressure (KPa) and ea is the actual vapor pressure (KPa). In addition, Δ is

the slope of the vapor pressure curve (KPa ºC-1); Ra is the extra-terrestrial radiation (MJ m-2 d-1);

Rs is the solar radiation (MJ m-2 d-1); Rn is the net radiation at the crop surface (MJ m-2 d-1); G is

the soil heat flux density (MJ m-2 d-1) and lastly 𝛾 is the psychometric constant (KPa ºC-1) (Gao

et la. 2015).

Results and Discussions

Below are graphs showing the performance of the three different reference evapotranspiration

estimation methods in various years.

Graph 1. Reference crop evapotranspiration for Kigali Graph 2. Reference crop evapotranspiration for Kigali AERO in Kigali City with the Turc-eqn. AERO in Kigali City with the Hargreaves- Samani-eqn.

0

1

2

3

4

5

2005 2010 2015 2020

Ref

eren

ce E

T (

mm

/da

y)

Years (2010-2018)

Monthly average Turc ET for Kigali AERO

0123456

2005 2010 2015 2020

Mo

nth

ly R

efer

ence

ET

(mm

/day

)

Years (2010-2018)

Monthly average HS-ETO for Kigali AERO

Graph 3. Reference crop evapotranspiration for Graph 4. Reference crop evapotranspiration for

Gikongoro in the south province with Gikongoro in the south province with the Turc-eqn.

the Hargreaves-Samani-eqn.

Graph 5. Reference crop evapotranspiration for Graph 6. Reference crop evapotranspiration for

Rubengera in the Western province with Rubengera in the Western province with the Turc-eqn.

the Hargreaves-Samani-eqn.

Graph 7. Reference crop evapotranspiration for Graph 8. Reference crop evapotranspiration for

Ruhengeri in the northern province with the HS-eqn. Ruhengeri in the northern province with the Turc-eqn.

0

1

2

3

4

5

2005 2010 2015 2020Mo

nth

ly R

efer

ence

ET

(mm

/da

y)

Years (2010-2018)

Monthly average HS-ETO for

Gikongoro

0

1

2

3

4

5

2005 2010 2015 2020

Mo

nth

ly R

efer

ence

Et

(mm

/da

y)

Years (2010-2018)

Monthly average Turc ET for

Gikongoro

0

1

2

3

4

5

6

2005 2010 2015 2020Mo

nth

ly R

efer

ence

ET

(MM

/DA

Y)

Years (2010-2018)

Monthly average HS-ETO

for Rubengera

0

1

2

3

4

5

2005 2010 2015 2020Mo

nth

ly R

efer

ence

ET

(mm

/da

y)

Years (2010-2018)

Monthly average Turc ET

for Rubengera

0

2

4

6

2005 2010 2015 2020

Mo

nth

ly R

efer

ence

ET

(mm

/day

)

Years (2010-2018)

Monthly average HS-ETO

for Ruhengeri

0

1

2

3

4

5

2005 2010 2015 2020

Mo

nth

ly R

efer

ence

ET

(mm

/day

)

Years (2010-2018)

Monthly average Turc ET for

Ruhengeri

Graph 9. Reference crop evapotranspiration for Graph 10. Reference crop evapotranspiration for

Kawangire in the Eastern province with the HS-eqn. Kawangire in the Eastern province with the Turc-eqn.

Graph 11. Comapring the performance of the three equations in Kigali AERO.

0

1

2

3

4

5

6

2005 2010 2015 2020

Mo

nth

ly R

efer

ence

ET

(mm

/da

y)

Years (2010-2018)

Monthly average HS-ETO

for Kawangire

0

1

2

3

4

5

2005 2010 2015 2020Mo

nth

ly R

efer

ence

ET

(mm

/da

y)

Years (2010-2018)

Monthly average Turc ET

for Kawangire

Graph 12. Comparing ETo results for Kigali AERO for the Penman Monteith and the Turc Equations.

Graph 13. Comparing ETo results for Kigali AERO for the Penman Monteith and the Hargreaves-Samani

Equations.

Monthly reference ETo estimates for each one of the three reference ETo estimation methods of

the five provinces are presented in graphs 1 through 10.

The results from the graphs were analyzed and the average monthly reference crop

evapotranspiration for the five locations was analyzed by comparing the efficiency of the three

equations used.

According to the results from the graphs, the average monthly reference evapotranspiration for

the turc and hagreveas-Samani equations ranges from 3 to 5 mm/day whereas ET for the penman

monteith equation ranges from 0.9 to 12 mm/day. It is noted from the Penman Monteith graph

for Kigali Aero that ET was low in the year of 2013 with the maximum ET at 7.8 mm/day and

was highest in the year of 2014 with a maximum of 15 mm/day.

In addition, by comparing the three equations from Graph 11. It shows that ET PM was high for

all the nine years compared to the ET results for the other two equations. According to Graphs

11 & 12. The Turc equation underestimated reference crop evapotranspiration for all the nine

years in Kigali AERO.

The HS graphs for all the five locations shows a low value of reference ET (3 to 4 mm/day) for

the year of 2018 compared to the previous years. Also, the turc method showed concistency in

results for the nine years. According to one of the researches done in China about estimating

reference crop evapotranspiration using simple equations, the turc method has shown to perform

well under humid conditions (Gao et la. 2015).

Conclusions

The standard FAO Penman-Monteith equation is usually used while estimating ETo, however

the equation is very complex and requires more climatic data that sometimes is not available in

many developing countries. Thus far, more simple equations such as Hargreaves-Samani and the

Turc equations that use limited data are used to account for reference evapotranspiration (Aydin,

2019). The two ETo equations were evaluated against the FAO Penman-Monteith while using

the required weather parameters for the five provinces of Rwanda. All the three equations were

evaluated by using a comparison of their estimates of monthly average reference ETo for 9 years

(2010 -2018) (Daniel, 2013).

Compared to FAO Penman-Monteith as the standard method, both the Turc and the HS

equations failed to adequately predict day-to-day variation in ET. Therefore, the Turc and the HS

equations should not be used if accurate daily ET is required, although they may be more

acceptable for estimating ET on a weekly or monthly basis.

More science and technology need to be involved to account for better agriculture management

decisions in the future. In addition, more recent and accurate climatic weather data need to be

used while calculating reference crop evapotranspiration to get more efficient and effective

results.

ACKNOWLEDGEMENTS

The Climatic data collected using weather stations across the country were optained from

Rwanda Meteorology Agency for the five provinces in Rwanda and was used as input for the

three reference evapotranspiration methods to obtain monthly ETo estimates. This research

project was financed by UCARE (Undegraduate Creative Activities and Research

Experience) at the University of Lincon – Nebraska. The author extends great appreciation to

the kind support and services provided by Dr. Derek Heeren – Research advisor, Dr. Lameck

Odhiambo – Research advisor, Sandeep Bhatti – Research assistant, and Ankit Chandra –

Research assistant.

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