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1 

 

 

 

Article 

Seasonal variation of surface energy balance over 

Mubi northeastern Nigeria during 2000-2020 
Abubakar Saidu Umar1*, Adam Usman2 

1Department of Pure and Applied Physics, Adamawa State University, Mubi, Nigeria 
2Department of Physics, Faculty of Physical Science, Modibbo Adama University, Yola, Nigeria 

A R T I C L E   I N F O 
 

Article history: 
Received 01 January 2023  
Received in revised form 
29 January 2023 
Accepted 01 February 2023 
 
Keywords: 
Energy, Temperature, Heat, Surface, Mubi 
 
*Corresponding author 
Email address:  
abuumarsaidu@gmail.com  

 
DOI: 10.55670/fpll.fuen.2.4.1 

A B S T R A C T 
 

Several studies have been undertaken on surface energy balance (SEB) at 
various places in the world, but none have been undertaken for Mubi, 
Northeastern Nigeria. In the effort of consideration, this study aims to evaluate 
the seasonal variation of SEB in Mubi, with emphasis on the observational data 
from 2000 to 2020. Evaluation of seasonal variations was executed using time 
series analysis to find out the impact of precipitation, evapotranspiration, soil, 
and air temperature changes on SEB components. It was found that the SEB 
components variations of sensible heat (H) had a maximum value of 1035.13 
Wm−2 in the dry season, in the month of December, while a minimum value of -
104.13 Wm−2 during the rainy season, in the month of July; latent heat (LH), had 
a peak value of 5243.46 Wm-2 in the dry season in the month of April, while in 
the rainy season, the lower value was found to be 2460.6 Wm-2, in the month of 
August; soil heat (G) had minimum and maximum values of 886.43 Wm-2 in 
March and 275.25 Wm-2 in August respectively; and net radiative (Rn) varies 
roughly between the highest month in March with 2809.35 Wm−2 (rainy season 
months) and lowest month in August with 6879.69 Wm−2 (dry season months). 
It was also found that precipitation, evapotranspiration, soil, and air 
temperature follow the same trend with some SEB results, affirming their 
dependency on each other. Therefore, it is expected that this study will help to 
understand the amount of energy received or emitted in the Mubi region. Along 
with the main work, some recommendations were made by researchers on 
some applications of SEB to the community. 

 
1. Introduction  

It is highly essential to understand the interaction 

between the Earth and the atmosphere, which mainly links to 

the principle of energy conservation, called surface energy 

balance. SEB has been widely used to evaluate and compare 

the strength of the various factors affecting Earth's Surface. 

SEB principle conditions that the amount of energy arriving 

at the Earth's surface must equal the energy leaving the 

Earth's surface over a period of time. Otherwise, the energy is 

imbalanced. Solar radiation is the only significant energy 

source on the Earth that is transformed into various energy 

fluxes after entering into the atmosphere and Earth’s surface 

[1]. Most of these energies come in the form of heat absorbed 

by the Earth's surface. In such processes, the resulting energy 

goes toward heating the Earth's surface by warming up sub-

surfaces, Earth's atmosphere, and water bodies, which are 

later emitted back to the atmosphere. SEB establishes the 

state of the Earth’s environment and responds to changes in 

the various energy transformation processes to account for 

all energy at the surface. Surface energy balance models are 

based on balancing net radiation with ground heat flux, 

sensible heat flux, and latent heat flux assuming that heat 

advection is negligible [2, 3] expressed as: 

𝑅𝑛 = 𝐺 + 𝐻 + 𝐿𝐻                (1) 

where Rn is the net radiation flux (Wm−2), G is the soil heat 

flux (Wm-2), H is the sensible heat flux (Wm-2), and LH is the 

latent heat flux (Wm-2). The equation states that the net 

radiation flux received at the Earth’s surface must either 

warm or cool the air above the Earth's surface (sensible heat 

flux), evaporate water bodies (latent heat flux), or warm or 

cool the soil (soil heat flux). As previously mentioned in 

equation (1), incoming net radiative flux (Rn) equals the 

combination of sensible heat (H), latent heat (LH), and soil 

heat (G) fluxes; the following are details explanations of 

individual’s flux. 

1.1 Net radiation flux (Rn) 

The net radiation is the amount of heat energy delivered 

to do work at the surface of the earth. Solar radiation (short 

 

 

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AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

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and longwave radiation) are input energies to the surface 

energy balance. These energies, directly or indirectly, are the 

results of nuclear interactions occurring on the solar surface 

and is equal to the total available energy for the occurrence of 

the Earth’s surface and atmospheric processes [4, 5].  

Basically, solar radiation has two acting parts: one is incoming 

(downward Rs↓) radiation on Earth’s surface that depends on 

the atmospheric transitivity, solar constant, solar altitude, 

and incidence angle, and another part are outgoing (upward 

Rs↑) that is reflected back to space due to the combined effect 

of surface, clouds, aerosol, gases, etc [1]. Therefore, surface 

net radiation (Rn) in the one-source surface energy balance 

model is estimated from the sum of the difference between 

the incoming and the reflected outgoing shortwave solar 

radiations (0.15–5 µm) and the difference between the 

downwelling atmospheric and the surface emitted and 

reflected longwave radiations (3–100 µm) [6]: 

𝑅𝑛 = (1 − 𝛼)𝑅𝑔𝑙𝑜𝑏𝑎𝑙 + 𝜀𝑠𝜀𝑎𝜎𝑇𝑎
4 − 𝜀𝑠𝜎𝑇𝑠

4              (2) 

where α is the surface albedo. Surface albedo is a critical 

parameter that controls surface energy balance [7].  Albedo is 

the fraction of incoming radiation attenuated by reflection 

processes in the atmosphere, with values ranging from 0 to 1 

for the lowest and highest reflection, respectively. Most of the 

estimated global solar radiations are often corrected by 

albedo, which contributes greatly to estimating the global 

average amount of incoming solar radiation onto a particular 

place on the Earth's surface. This can affect surface albedo 

and radiation fluxes, leading to a local temperature change 

and, eventually, a vegetation response [8]. This implies that 

the global solar radiation received on the Earth’s surface was 

more than the reflected radiation lost into space [9]. Although 

the global annual mean land albedo varies from 0.18–0.26 

[10,11], climate, biogeochemical, hydrological, and weather 

forecast models require regional surface albedo with an 

absolute accuracy of 0.02–0.05 for snow-free and snow-

covered land [11]. For this study, a typical constant value of 

0.03 is taken based on Bastiaanssen [12], the value also 

corresponds to a value obtained by [7]. Rglobal is the global 

solar radiation in W m–2, εs is the surface emissivity, εa is the 

atmospheric emissivity estimated as a function of vapor 

pressure, and σ is the Stefan–Boltzmann constant. Surface 

emissivity is computed using an empirical equation by 

Tasumi [13], based on soil and vegetative thermal spectral 

emissivities housed in the MODIS UCSB Emissivity Library 

[14]. 

𝜀𝑎 =  0.95 +  0.01 LAI      for LAI  3 ≤ 1                                   (3) 

𝜀𝑎=0.98 when LAI>3, where LAI (m2 m−2) leaf area index; the 

ratio of the total leaf area for the surface one side of leaves per 

unit of ground area. LAI is an indicator of biomass and canopy 

resistance to vapor flux and is computed using an empirical 

equation stemming from Bastiaanssen [14, 15]. 

LAI = −ln[(0.69 − SAVIID/0.59)/0.91                                         (4) 

where, for Landsat images, SAVI 6 is based on the top of 

atmosphere reflectance of bands 3 and 4. Several different 

methods have been proposed to estimate atmospheric 

emissivity, but according to Brutsaert [16], atmospheric 

emissivity is given as: 

𝜀𝑎 = 9.2 × 10−6𝑇𝑎
2               (4) 

1.2 Soil heat flux (G)  

Soil heat flux (G) is the amount of heat transfer in 

vegetation and soil through molecular conduction. It is 

determined by the soil thermal conductivity and heat capacity 

which both depend on properties such as soil texture, i.e. 

fractions of sand, loam, and clay particles, and soil water 

content [17]. It also affects soil physical processes such as soil 

evaporation and aeration, chemical reactions in the soil, and 

biological processes such as seed germination, seedling 

emergence and growth, root development, and microbial 

activity [18]. Soil heat flux (G), which is determined by the 

thermal conductivity of the soil and the temperature gradient 

of the topsoil, can be derived using the method developed by 

Kustas and Daughtry [19] and Bastiaanssen [15], which is a 

function of surface albedo, surface temperature, and 

normalized difference vegetation index (NDVI) written as 

[20]: 

𝐺 = 𝑅𝑛𝑇𝑠(0.0038 + 0.0074𝛼)(1 − 0.98(𝑁𝐷𝑉𝐼)4)              (5) 

where the normalized difference vegetation index, NDVI. 

Vegetation cover is one of the most important biophysical 

factors in determining SEB through NDVI. NDVI is defined as 

a ratio of the difference in reflectivity of the near-infrared and 

red bands to their sum: 

𝑁𝐷𝑉𝐼 =
𝑟𝑁𝐼𝑅−𝑟𝑅𝐸𝐷

𝑟𝑁𝐼𝑅+𝑟𝑅𝐸𝐷
                                                                             (6) 

NDVI is a widely used technique to detect land use land cover 

change, especially changes in vegetation area and its pattern 

[21]. NDVI values range from 1 to -1. Sparse vegetation (e.g. 

shrubs, meadows, and pastures) are expressed by values of 

0.2 – 0.5 [22]. Also, 0.2< NDVI<0.5, assumed to be a mix of 

bare soil and vegetation [23], 0.2-0.3 NDVI value represents 

shrub and grassland, 0.3-0.4 indicates sparse and unhealthy 

forest whereas >0.4 NDVI value represents healthy and dense 

vegetation [21]. High values (from 0.6 to 0.9) correspond to 

areas with dense vegetation, such as forest or agricultural 

vegetation, in the productive phase [24]. In this paper, the 

best features for the Mubi region were described to vary from 

0.1 to 0.5 due to the fractional land cover vegetation 

prevailing almost 80% cropland. The NDVI classification is 

indicated in Table 1. 

Table 1. The NDVI classification [25] 

 

1.3 Sensible heat flux (H) 

The sensible heat flux is the exchange of energy between 

the surface and the atmosphere obtained from the 

Class/Feature NDVI Range  

Water -1 ≤ - 0.014 

Build-up 0.015 - 0.09 

Barren land 0.10-0.20 

Shrub and grassland  0.21-0.30 

Sparse vegetation  0.31-0.40 

Dense vegetation  0.41 - ≤ 1 



AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

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temperature difference between the surface and the 

atmosphere. Calculation of the sensible heat flux of the 

surface is done using an aerodynamic function:  

𝐻 = 𝜌𝑎𝑖𝑟𝐶𝑝
𝑑𝑇

𝑟𝑎ℎ
                                    (7) 

Where, 𝜌𝑎𝑖𝑟 is the air density in kg/m3, Cp is the specific heat 

of air at constant pressure, which is equal to 1000 (J/kgK), 

dT is the indicator of temperature difference in Kelvin 

between two elevations near surfaces of z1 and z2, and 𝑟𝑎ℎ is 

the aerodynamic resistance (m/s) available for the heat 

transfer between z1 and z2, which are considered 0.1 and 2 

meters [4, 26, 27]. Aerodynamic resistance is affected by the 

surface roughness and is determined by vegetation height 

and structure, wind speed, and atmospheric stability [6]. 

Here, aerodynamic resistance is taken to be 2 s/m due to the 

roughness of the study area.  Based on equation (7), the 

higher the temperature difference and the aerodynamic 

resistance, the larger the sensible heat flux. Also, Sensible 

heat flux is zero if the temperature difference or 

aerodynamic resistance is zero. 

1.4 Latent heat flux (LH)  

Latent heat flux is the flux of energy associated with the 

evaporation or transpiration of water from the Earth's 

surface to the atmosphere and vice versa [28], sometimes 

called evapotranspiration (ET). The primary controls on ET 

are energy inputs such as incoming solar radiation and the 

capacity of the air to hold more water vapor both from local 

water vapor (humidity) and from mixing with drier air 

controlled by wind speed [2]. This process cools the Earth’s 

surface and moistens the atmosphere near the surface, which 

is why the estimation of ET is crucial for developing climatic, 

hydrological, bio-geophysical, and ecological models to 

predict the weather and climate or climate change [1]. The 

latent heat flux (LH) can be expressed as: 

𝐿𝐻 = 𝑅𝑛 − 𝐺 − 𝐻                  (8) 

The above said components of Earth’s SEB are responsible for 

the heating or cooling of the land/soil (solar and thermal 

radiation), the heating and cooling of the air (sensible heat 

flux), and the evaporation of water from soil and vegetation 

(latent heat flux) [1]. From equation (1), when the amount of 

energy coming to the surface (Rn) equals the amount of 

energy leaving Earth's surface (G + H + LH), the surface is said 

to be in energy balance (zero), and the temperature remains 

constant. Also, if the sum of the energies in equation (1) is not 

equal to zero, then the resulting energy and temperature are 

said to be an imbalance. Moreover, if the incoming is more 

than the outgoing energy to the surface, then the energy is 

said to be positive imbalance and negative if the outgoing is 

more than the incoming energy. It is a negative imbalance 

because it contributes to global warming, while positive 

contributes to global cooling. Such processes have an 

essential role in regional weather, climate, and hydrosphere 

cycles, as well as in regulating urban heat redistribution [20]. 

Also, the exchange processes occurring at the land surface are 

of paramount importance for the re-distribution of moisture 

and heat in soil and atmosphere [29]. For the past decade, SEB 

has become a standard tool to study the exchange of energy 

between the Earth’s surface and atmosphere. The research of 

SEB is often carried out in different places such as Jakarta and 

Neighboring regions by Ilhamsyah [30], metropolitan cities of 

India during the 2000–2018 winter seasons by Sultana and 

Satyanarayana [28], Greenland ice sheet by Liu [31], Naqu 

region of Qinghai-Tibet Plateau during 2005-2016 by Wang 

and Ma [32], lake Huron by Petchprayoon [33], tilled and non-

tilled bare soils by Akuoko [34], tropical river Basin by Kumar 

et al. [35], semiarid environments by Small and Kurc [36], 

Storglacia¨ren, Sweden by Hock and Holmgren [37], urban 

park and its surroundings by Bäckström [38], two Sahelian 

surfaces by Verhoef et al. [39]. These studies motivated us to 

carry out such research in Mubi, Northeastern Nigeria, to 

benefit from the resources that SEB is disclosing. The 

application of energy balance to a wide mixture of 

agricultural crops and other vegetation is complex enough 

that there are still some areas of considerable empiricism 

and, therefore, the potential for local refinement [14]. At the 

same time, all physical, chemical, and biological processes 

respond to changes in conditions produced by changes in the 

SEB. In recent times of agricultural and settlement expansion, 

increase in human population, over-exploitation of natural 

resources, and intense flux of Earth's surface energy cause a 

serious threat to human beings, agriculture, and settlement. 

This is specifically true in Mubi. Hence, adequate information 

about SEB status is relatively scarce in Nigeria, particularly 

Mubi. Understanding and utilizing metamorphic trends, 

water vapor loss, precipitation, plant growth, drought 

monitoring, revegetating a barren area, irrigation scheduling, 

drainage practices, erosion, desertification, and global 

climate changes, among others, depends on SEB, and has yet 

to be fully exploited in Mubi. In an effort to fill this gap, this 

study aims to evaluate the seasonal variation of SEB in Mubi, 

with emphasis on the observational data from 2000 to 2020. 

Along with the main work, some recommendations were 

made by researchers on some applications of SEB to the 

community. 

2. Method and materials 

2.1 Study area  

Mubi, Northeastern Nigeria, is within the foothills zone 

of Mandara Mountains terrains (characterized by hill 

landforms and flat plain land), at Longitude 13.125 and 

Latitude of 10.333 with an average altitude of about 650 m 

above sea level. Due to its topography and climate, which is 

dominated by crops, Mubi serves as one of the major 

agricultural regions in Nigeria and is one of the most 

important economic activities in the region, with about 65% 

of the total working population being engaged directly. The 

seasonal variations of Mubi were dry (in the months of 

November, December, January, February, March, and April) 

and rainy (in the months of May, June, July, August, 

September, and October) season. The estimated average 

temperature and precipitation in Mubi are respectively 

28.83°C and 1,154.75 mm over the last 20 years. The highest 

and lowest temperatures, respectively, occur in April and 

August, while precipitation almost occurs in the rainy season. 

2.2 Types and sources of data 

Several parameters were acquired for this study. Some of 

them are literature based, while others were obtained from 

Meteoblue, as shown in Table 2. Mean daily global solar 

radiation, soil temperature (at 0-10cm depths), and air 



AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

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temperature (at 10m height) historical weather simulation 

data used in this research, with a spatial resolution between 

4 and 30 km for the Mubi location, were obtained from 

Meteoblue product for the period of 20 years (2000-2020). 

Although soil temperature may increase, decrease, or vary 

monotonically with depth, depending on the season and the 

time of the day [40, 41]. For this study, daily soil temperature 

data taken at the soil surface (0-10 cm) was adopted from the 

available data. These parameters are assumed to be 

homogeneous throughout the Mubi station and offer an 

opportunity to evaluate SEB and help understand the 

variability over time.  

Table 2. Data used for the analysis 

Type of 
parameters  

Values Source of 
data  

Global solar 
radiation (Rglobal) 

Varies over time 
(Wm-2) 

Meteoblue  

Soil temperature 
(Ts) 

Varies over time 
(°C) 

Meteoblue  

Air temperature 
(Ta) 

Varies over time 
(°C) 

Meteoblue  

Albedo (𝛼) 0.03 Dintwe, [7] 
Soil emissivity (𝜀𝑠) 0.85 Estimated by 

study  

Air emissivity (𝜀𝑎) Varies over time  
(unit less) 

Evaluated  

Air density (𝜌𝑎𝑖𝑟) 1.225 kg m-3 Constant  

Specific heat 
capacity of air (𝐶𝑝) 

1000 J/kgK Constant  

Aerodynamic 
resistance (rah) 

2 s/m Tang et al. 
[6]  

NDVI 0.3 Bid [21] 
Stefan–Boltzmann 
constant (σ) 

5.67 × 10-8W m-2K4 Constant  

Evapotranspiration Varies over time 
(mm) 

Meteoblue  

Precipitation  Varies over time 
(mm) 

Meteoblue  

 

2.3 Method of data analysis and presentation 

As shown in Table 2, the data acquired from literature 

and Meteoblue weather station for Mubi are all known 

constants, dependents, and independent variables that are 

accordingly derived, evaluated, or directly computed into 

equations 1 to 8 of SEB fluxes. The data obtained went 

through pre-processes by averaging daily data to monthly and 

annual time intervals before calculations were taken. These 

methods of calculating SEB components are purely empirical 

and were carried out basically to establish time series to 

capture the trends associated with changes. To present the 

result obtained from calculations, we selected dry and rainy 

seasons for typical weather conditions to analyze the 

variation of each component under SEB for the analysis, and 

to test whether the variability is in line with the evaluation. 

Application of time series analysis for annual and seasonal 

evidence of 2000 to 2020 periodicity was carryout using 

Mathematica software for the presentation of results. 

3. Result and discussions  

It is very important to note that the monthly potential 

combination of net radiative heat (Rn), sensible heat (H), 

latent heat (LH), and ground heat (G) fluxes equated monthly 

SEB. Therefore, the results of each of these parameters are 

discussed for better understanding. 

3.1 Variations of air and soil temperatures on the SEB 

Soil temperature is a measure of soil internal energy or 

heat content and changes in the heat gained or lost by the soil 

[42]. Soil temperature is one of the most important factors 

that affect soil heat storage, soil heat flux, soil water flux, seed 

emergence, nutrient transformation, transport, uptake, and 

plant growth [43] plays a major role in ensuring crop 

productivity, sustainability and control of biological and 

biochemical processes which invariably affects soil organic 

matter formation, fertilizer efficiency, seed germination, plant 

development, the ability of the plant to survive during the dry 

season, nutrient uptake and decomposition, and disease and 

insect occurrence [44-48]. Furthermore, increased soil 

temperatures will have a direct impact on water demand and 

crop yield [49], shift spring temperature threshold, indicating 

potentially longer vegetative period and earlier yield and 

subsequent secondary crop yield [50], and major changes in 

the morphology of the plant was evident [51]. Plants stop 

growing when the soil temperature becomes too cool, and 

some stop growing when the soil temperature is too hot. The 

optimum range of soil temperature for plant growth is 

between 20 and 30°C, and the rate of plant growth declines 

drastically when the temperature is less than 20°C (sub-

optimal) and above 35°C (supra-optimal) [48]. Based on this, 

it is observed that the soil temperature values of Mubi were 

considerably stable, as expected for crops (Figure 1). Being 

able to determine temperature differences in Mubi is 

important in the discussion of SEB.  

 

Figure 1. Time series of monthly variations of air and soil 

temperature for Mubi during 2000-2020 

As shown (Figure 1), the air and soil temperature trend 

is almost the same, but the difference has obvious seasonal 



AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

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changes. Both air and soil temperature in November has a 

higher trend, which gradually decreases before reaching a 

peak in April. The soil temperature from October to April is 

higher than the air temperature (dry season), and the air 

temperature is higher than the soil temperature from May to 

September (rainy season). The trend values of temperature 

difference during dry and rainy seasons period of the year 

revealed interesting spatial variability patterns. As a result, 

groundwater loss is greater as drier and warmer conditions 

in Mubi increase evaporative losses in the rainy season. The 

losses were less prominent in the dry season (that is from 

October to April than in the months in the dry season. The 

differences indicate why temperature highlights the 

importance of SEB. In both cases, the month of April had the 

highest temperatures (33.34 °C), whereas the lowest was in 

the month of August (24.63°C). Results also demonstrated 

that during the dry (November to May), both soil and air 

temperatures were warmer than the rainy (May to October) 

seasons temperatures. The air temperature showed an 

opposite trend, with soil temperature being warmer than the 

air temperature in the dry season. Monthly, from January to 

April, the temperature increases higher and decreases from 

April to August, which then increases to the month of 

November, then decreases to January. January to December of 

each year indicates the temperature path reversal, creating 

seasonal and annual variations. In this situation, dry-season 

soils had a significantly higher temperature than rainy-season 

soils temperature. Accordingly, continual air and soil 

temperature variations depend on response to changes in 

Earth and atmospheric conditions of solar radiation, an 

increase of soil moisture content, air temperature, wind 

speed, rainfall, and others weather conditions. This 

phenomenon was due to the effects of weather conditions, 

which allow solar radiation to warm the Earth's surface. 

Therefore, the lower temperature of the surface of the Earth 

generally gains cold at a higher rate of rainfall than the Earth's 

surface in the dry season.  

3.2 Variations of precipitation and evapotranspiration 

on the SEB 

As shown in Figure 2, Mubi experiences average 

precipitation and evapotranspiration of 1,154.75 and 479.33 

mm annually. The highest and the lowest monthly 

precipitation value of 276.31 mm is found in the month of 

August and 0 mm in the months of December, January, and 

February, respectively. At the same time, the highest and the 

lowest monthly evapotranspiration value of 85.89 mm are 

found in the month of September and 9.63 mm in the month 

of January, respectively. During the dry season, both 

precipitation and evapotranspiration in Mubi experience 

fewer magnitude variations than the associated rainy season 

values. A similar trend of precipitation and 

evapotranspiration variations was observed during this 

period of 20 years (Figure 2). These similarities are 

attributable to the changes in various climatic variables such 

as air and soil temperature, heat from solar radiation, rainfall 

infiltrated into the soil, crop residue covering the soil surface, 

snow cover, freezing, and thawing. Another reason could be 

the presence of a cloud, which may allow only a small part of 

solar radiation to reach the ground surface due to its ability to 

reflect a good part of the solar radiation [40, 41]. In the rainy 

season, this is not because of the input precipitation but due 

to the influence of the harmattan wind, which significantly 

reduces the amount of potential evapotranspiration [52].  

Figure 2. Time series of monthly variations of precipitation 

and evapotranspiration for Mubi during 2000-2020 

The evapotranspiration (ET) increases with 

precipitation and contributes to the highest water loss or gain 

in SEB. The differences between them are wide in the rainy 

season, where ET is relatively small and thus contributes to a 

larger fraction in lowering Rn and LH (Figure 3). Higher values 

of ET occurred during the corresponding months of higher 

precipitation in Mubi. Here, ET is a collective term that 

includes evaporation from vegetation or any other moisture-

containing living surface (transpiration) and evaporation 

from the water bodies and soil and is used to describe the loss 

of water from the Earth’s surface to the atmosphere by the 

combined processes of evaporation and transpiration [53]. A 

thorough understanding of the factors controlling the energy 

balance of cropped soil enables making accurate estimates or 

predictions of evapotranspiration and irrigation water 

requirements [54]. While contributing to the surface energy 

balance, ET quantifies the water requirement for efficient 

water management [55-57], especially in sub-humid and 

humid climates [54]. According to the energy budget concept, 

when the surface is wet or heavily vegetated, net energy is 

mainly consumed by the evaporation and evapotranspiration 

of water in soil and vegetation [20]. In essence, if there is 

adequate water in the soil, the incoming solar radiation will 

be used for convective activities [52]. Moreover, an increase 

in soil moisture gives rise to increased evaporation from the 

soil surface, and a substantial part of net radiation goes into 

evaporation, which also gives rise to the observed low 

temperature [41], and increasing evapotranspiration can 

decrease the surface temperature of tree canopy [57, 58]. 

Atmospheric temperature is projected to increase with 

climate change, and it provides more energy to cause more 

evaporation [57]. Salman et al. [59] used simple water-

balance equations and identified that when the temperature 

increases, it contributes to an increment in 

evapotranspiration, which leads to a large increase in crop 

water demand and a decrease in climatic water availability. 

With this, it is affirmed that evapotranspiration and 

precipitation are both important for balancing the effects of 

SEB in Mubi. Here, seasonal variation of precipitation and 

evapotranspiration often represents the amount of water 



AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

6 

 

consumed from agriculture. Thereby significantly helping 

farmers in Mubi by projecting water management in farms. 

 

Figure: 3. Time series of monthly variations of sensible heat 

(H), latent heat (LH), soil heat (G), and net radiative fluxes 

during 2000-2020 

3.3 Surface Energy Balance  

Results for each SEB component of equations (2 to 8) are 

explained in this section. It is noted that each component of 

net radiative heat (Rn), sensible heat (H), latent heat (LH), and 

ground heat (G) fluxes are discussed separately as follows:  

3.3.1 Net Radiative Flux 

Net Radiation flux (Rn) is the component of SEB 

defined by equation 2. As shown in Figure 3, Rn over the entire 

20 years appeared to be a very wide trend, varying roughly 

between the highest month in March with 2809.35 Wm−2 

(rainy season months) and the lowest month in August with 

6879.69 Wm−2 (dry season months). Here, Rn controlled most 

of the variations in SEB due to the large values of incoming 

global solar radiation energy onto the Earth's surface. As the 

short wave radiation balance is lower due to high albedo 

(equation. 1), air and soil temperatures tend to be low. Its 

trend follows the same pattern with temperature variations 

(Figure 1). Implying that higher Rn defines higher 

temperature at the same time. Principally, the differences of 

Rn play major role in SEB than others components. Explaining 

that Rn is higher than any other energy in SEB. As shown, both 

the Rn and LH in dry and rainy seasons have the same diurnal 

variation trend as that of air and soil temperatures (Figure1). 

This revealed to us that they depend on each other. 

Meanwhile, during the dry season, a large amount of Rn 

reaches the Earth's surface from the atmosphere leading to 

the temperature differences between the Earth and the 

atmosphere. Therefore, the high amount of Rn found in the 

Mubi region during the dry season and low in the rainy season 

may have a great impact on balancing energy between the 

Earth's surface and atmosphere.  

3.3.2 Soil heat flux (G) 

As shown in Figure 3, the minimum and maximum 

values G are respectively 886.43 Wm-2 in the months of March 

and 275.25 Wm-2 in August. At the same time, Rn, LH, and G 

follow the same trend but at different values. The reason for 

this phenomenon is that solar radiation inhibits heat 

exchange between the atmosphere and the underlying Earth's 

surface, which strongly impacts evapotranspiration and 

precipitation (Figure 2). Comparatively, the contribution of 

the G to SEB is lower than that of Rn and LH throughout these 

20 years.   

3.3.3 Sensible heat flux (H) 

As shown in Figure 3, during the dry season, in the 

month of December, H had maximum value of 1035.13 Wm−2, 

while the minimum value during the rainy season, in the 

month of July is -104.13 Wm−2. H values are the highest 

positive values during the months of October, November, 

December, January, February, March, April, and August 

mostly occur in the rainy season. While negative values were 

observed in the rainy season in the months of May, June, July, 

and September. It is positive because the incoming energy is 

absorbed by the soil and negative when emitted to the 

atmosphere. Sensible heat flux is caused by an interaction 

between the Earth's surface and the atmosphere, whose 

values are mainly determined in terms of thermal differences 

and wind speed.  

3.3.4 Latent heat flux (LH) 

As shown in Figure 3, in the dry season, the peak value 

of LH is 5243.46 Wm-2, observed in the month of April, while 

in the rainy season, a lower value was found to be 2460.6 Wm-

2, in the month of August. The LH is usually characterized by 

the soil water contents on the Earth's surface. As shown 

(Figure 3), LH is in the opposite trend with precipitation and 

evapotranspiration (Figure 2). Therefore, the lower the value 

of LH, the higher the water contents on Earth's surface 

(precipitation). LH has a great impact on determining and 

detecting seasonal variation in Mubi. 

3.4 Surfaces energy imbalance  

Surface energy imbalance is the method of evaluating 

whether the energy that is coming onto the Earth's surface is 

the same as that is going out to the atmosphere. It is obtained 

by subtracting all outgoing energy fluxes from all incoming 

energy fluxes. That is Rn - LH+G+H. Surface energy imbalance 

requires that the G+H+LH be equivalent to Rn. When both 

sides are the same (subtracted to be zero), the interaction 

between the Earth's surface and the atmosphere is balanced, 

called SEB. As shown in Figure 4, the energy exchange 

between the atmosphere and the Earth's surface is minimal. 

The result shows close agreement with SEB of +/- 2×10-12 to 

4×10-12. Therefore, the result is in agreement with SEB 

(equation 1). 

Figure 4. Time series of annual surface energy imbalance for 

Mubi during 2000-2020 



AS. Umar and A. Usman/Future Energy                                                                               November 2023| Volume 02 | Issue 04| Pages 01-09 

7 

 

4. Conclusion  

It was concluded that the results based on the SEB 

components are in agreement with its stated equations, 

thereby revealing the amount of incoming and outgoing 

energy in the Mubi Earth surface in inferences to long-term 

trends. It was also found that the seasonal variation results 

obtained is highly influenced by local precipitation, 

evapotranspiration, soil and air temperature, which might be 

affected by incoming solar radiation, rainfall, or other related-

meteorological conditions such as albedo, soil moisture, wind 

speed, soil temperature. The information provided in this 

study would help in planning, decision-making, and assessing 

the changes in SEB, which can comprehensively explore the 

recent seasonal changes and weather conditions over Mubi.  

Acknowledgments 

The authors are extremely grateful to the meteoblue AG, 

Basel, Switzerland, for providing us with the necessary data 

to carry out the present work. 

Ethical issue 

The authors are aware of and comply with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
Data sharing does not apply to this article as no datasets were 

generated or analyzed during the current study.  

Conflict of interest 

The authors declare no potential conflict of interest. 

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