

































 

 

Mathematical modeling of Climate change and Desertification:  

A case study of Yobe State, Nigeria. 

             Bulama Adamu Bawa �, Abdulaziz Babiker Mohamed Hamed� 

            Department of Mathematics & Statistics, Faculty of Science 

                   Yobe State University, Damaturu, Nigeria 

     Email: adamubulama01@gmail.com,        aziz.hamed12@gmail.com   

Corresponding email: aziz.hamed12@gmail.com  

Abstract: 

The study addressed the effect of climate change and Desertification in Yobe State, 

Nigeria. Desertification as defined by the United Nation Convention to Combat 

Desertification (UNCCD 1994), is the degradation in arid, semi-arid, and dry sub-

humid areas resulting in many factors including human activities and climatic 

variations. Desertification is a silent, invisible crisis that is destabilizing 

communities on a global scale, as victims turn into refugees, internally displaced 

people and forced to migrate from their homes. Hence to restore stability in a 

context where changing weather events are threatening the livelihood of people, 

then everyone must beware and stand to fight desertification, revoke land 

degradation and ease the effect of drought. The researcher implemented some 

mathematical models of climate change on desertification to give a good insight 

into Desert, Desertification and the causes of desertification, that affects our 

communities and provide possible ways of reducing its impact to the barest 

minimal. Furthermore, the research will also help decisions maker to well plan in 

order to protect our Land and Environment. 

 

Key Word: Mathematical Model, Climate Change, Desertification, Drought, 

invisible crisis 

 

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1.1 Introduction 

Climate change and desertification has been an aged long phenomenon that 

has affected the lives and livelihood of many people around the globe both 

positively and otherwise. In the last century, these has been a major area of 

research for many scholars from various areas of disciplines who have provided a 

huge success to the prediction of possible outcomes in the future climate, and have 

provided ways of solving  those problems. This research is going to be narrowed 

on Yobe state Nigeria as our case of study to look into some of the effects of 

desertification and give appropriate solutions (using different climate models) to 

those problems. 

1.2 Background of the study 

Humanity have had a long association with arid and semi-arid regions: the first 

great civilizations in Egypt and Mesopotamia developed at the end of the climatic 

optimum some 3000 years B.C., at a time when the Sahara appears to have been 

vegetated as parts of the Sahel are today. Oguntoyinbo (1981) has traced the 

impact of human activities on climate variability in Africa. He notes that it was not 

until the time of the Roman occupation of North Africa in about 100 BC that we 

began to notice successively drier climates in the Sahara, though this period was 

not as dry as it is today. He argues that the fluctuations in the levels of the Lake 

Chad reveal the nature of climate variation in the Sahara. He therefore concludes 

that if the rise and fall of the Lake Chad can be taken to represent climate 

variability in the arid zone in the period before “instrumental records”, it is 

possible that rainfall in the arid zone has similarly shown dramatic variability 

which has impacted on land use practices periodically. 

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By the time the Egypt pyramids were completed (around 2700 B.C.), the climate of 

the Northeastern and middle east Africa was in a drying phase that resulted in the 

arid landscapes we have known for much of the last 5000 years (El-Baz 1983). The 

federal ministry of environment estimated that Nigeria loses “about 350,000 square 

meters of its land mass to desert condition which is advancing southwards at an 

estimated rate of 0.6 kilometres a year”. This environmental problem has severe 

economic repercussions on the entire nation as it impacts on the socio-economic 

life of rural households (reduction in crop and animal production, death of 

livestock, high prices for food stuffs) and leads to widespread poverty. 

Until around the early 20th century, climate scientists were primarily concerned 

with the study of past climatic states. This was done by observation of the 

environment using mostly geological, geographical and botanical methods. By the 

end of the 1950s, important physical measurement methods were developed. The 

measurement of weak radioactivity of various isotopes was the basis for the dating 

of organic material and enabled the determination of flux rates in different 

environmental systems. 

 Two out of three of the geographical landscape in Africa is classified as drylands, 

of which 319 million hectares has been estimated to be highly vulnerable to 

desertification. These areas are concentrated in Sahelian (used to refer to the semi-

arid) regions bordering the Sahara desert to the south and includes parts of Chad, 

Nigeria, Niger, Burkina Faso, Mali, Senegal, Mauritania and the Gambia (some 

authors include Sudan, Somalia, Ethiopia and Eritrea in the Sahel) region, Horn of 

Africa and Kalahari in the south. Increasing concentration of poverty in the 

drylands of sub-Sahara Africa has been documented, where 41% of the total 

population lives in extreme poverty, which is partly attributed to desertification. 

Drought and desertification are at the core of serious challenges and threats facing 

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sustainable development in Africa, with far reaching adverse impacts on human 

health, food security, economic activity, physical infrastructure, natural resources 

and the environment, with incidence in national and global security. 

4.3 Objective of the study 

The context of desertification and climate change has a wide range of branches, 

where some scholars have questioned whether the phenomenon exists at all. It is 

evident through the reports and proofs that desertification is affecting the lives and 

livelihood of people directly or indirectly. Hence this research is going to discuss 

the nature, causes of desertification in Yobe and also provide a proposal to the state 

government on how to combat its wide spread in the state. 

1.4 Definition of key terms 

1.4.1 Desertification 

UNCCD (1994) defines desertification as “land degradation in arid, semi-arid and 

dry sub humid areas resulting from various factors, including climatic variations 

and human activities”. 

1.4.2 Climate  

This is a word from ancient Greek “klima”, meaning inclination. Climate is 

commonly defined as the weather averaged or the statistics of weather over a long 

period. The standard averaging period is 30 years, but other period may be used 

depending on the purpose. It is measured by assessing the patterns of variation in 

temperature, humidity, atmospheric pressure, wind, precipitation, atmospheric 

particle count and other meteorological variables in a given region over long 

period of time. 

1.4.3 Land degradation 

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UNCCD (1994) defines land degradation as a “reduction or loss, in arid semi-arid 

and dry sub-humid areas, of the biological or economic productivity and 

complexity of rain-fed cropland, irrigated cropland, or range, pasture, forest and 

woodlands resulting from land uses or from a process or combination of processes, 

including processes arising from human activities and habitation patterns, such as:  

(i) Soil erosion caused by wind or water”;  

(ii) Deterioration of the physical, chemical, and biological or economic 

properties of soil; and  

(iii) Long-term loss of natural vegetation. 

It can also be referred as a loss of adaptive capacity, or a decline in biological and 

economic resilience.[6] 

1.4.4 Drought 

The Wikipedia defines drought as an event of prolonged shortages in the water 

supply, whether atmospheric (below-average precipitation), surface water or 

ground water. Drought is a recurring feature of the climate in most parts of the 

world. However, these regular droughts have become more extreme and more 

unpredictable due to climate change. A drought can last for months or years, or 

may be declared after as few as 15 days.[7] 

1.4.5 Climate model 

A climate model is essentially a representation of the many interactions and 

dynamics within the climate which includes the atmosphere, ocean, land surface, 

and ice to make predictions of possible climate change for the future. Climate 

models are systems of differential equations based on the basic law of physics, 

fluid motion and chemistry. 

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1.4.6 Global warming 

Global warming is the increase in the average temperature of the Earth’s near-

surface air and the oceans. It can also be defined as a gradual increase in the 

overall temperature of the earth’s atmosphere generally attributed to the 

greenhouse effect caused by increased levels of cabondioxide CO2, 

chloroflorocarbons CFCs, and other pollutants. 

1.4.7 Atmosphere 

An Atmosphere (from ancient Greek (atmos), meaning ‘vapour’, and (sphaira), 

meaning ‘ball’ or ‘sphere’). The atmosphere is a layers of gases surrounding a 

planet or other material body that is held in place by the gravity of that body. 

2: The Literature Review: 

The mission of the UN convention to combat desertification is: “To provide a 

global framework to support the development and implementation of national and 

regional policies, programs and measures to prevent, control and reverse 

desertification, land degradation and mitigate the effect of drought through 

scientific and technological excellence, raising public awareness, standard setting, 

advocacy and resource mobilization, thereby contributing to poverty reduction.” 

[6](UNCCD 1996). In this chapter we will look into some literature reviews of 

many other scholars. 

2.1 Reviews 

Aubreville (1949), This French forester was the first to introduce the word 

‘desertification’ in his book “Climats, forets, et Desertification de l’Afrique 

tropical”. He witnessed the degradation and disappearance of tropical forests in 

many humid and sub-humid parts of Africa, and attributed it to a large extent to the 

slash and burn agricultural practices of the local populations. Aubreville had 

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identified climate change as a potential factor, but could not estimate its 

importance for lack of adequate data. It is only later on that the concept became 

commonly associated with arid and semiarid regions. [2] 

Roger (1981), who digitized UNESCO’s map showing the world distribution of 

arid region (UNESCO 1977). This map was constructed on the basis of 

hydrological data using a water balance approach. 

Norman Myers (1984), estimated that some 120000 km2 of agricultural and 

pastoral land were deteriorating beyond fuel economic use per year (Myers 1984, 

p. 46). These numbers should be compared to estimates of deforestation 

worldwide, which range from 100000 to 113 000 km2 per year, with the bulk of 

the destruction occurring in the tropics.[2] 

Warren (1984), said “arid lands are dynamic regions, they have been evolving 

over thousands of years, mostly in response to climatic changes and humanity has 

been able to cope with such evolution and by colonizing new and hitherto 

unaffected areas”.[2] 

Dregne (1986), The intensity of desertification processes can range from slight to 

very severe in terms of the degradation of plant and soil resources.[2] 

Gethner, Robert (1998), A planet’s albedo is the percent of incoming solar 

radiation that is immediately reflected back into space due to coloring of the 

planet. The earth’s albedo, is equal 0.3, so 30% of incoming solar radiation is 

immediately reflected back into space.  

NAP (2000), revealed that about 35% of Nigeria’s landmass is considered arable, 

with 15% being utilized for pastures, 10% for forest reserve, and 10% for 

settlement. The same report also reveals that 30% of the country’s landmass is 

regarded uncultivable. Notably, reports from the Federal Ministry of Environment 

shows that Nigeria is annually losing about 350,000 square meters to 

desertification, which is regarded as the gravest environmental problem affecting 

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10 of the 11 northern states. Yet, rural households, especially inhabitants of 

drylands like those of Gursulu village Yobe state, depend on arable land for their 

livelihoods. 

Parmesan and Yohe (2003), reported that the extent to which traditional forms of 

agriculture including pastoralism degraded the land was and is to some extent 

influenced by the nature of the biophysical environment. Steep slopes are clearly 

more susceptible than gently-sloping land to accelerated erosion; low-lying flood 

plains and flat lands are more likely to be affected by flooding; regions affected by 

strongly seasonal climatic regimes are affected by both floods and droughts; areas 

with highly flammable vegetation are more prone to fire; drylands with sparse 

vegetation cover are more exposed to wind erosion, and so on. However, over 

many centuries, and as a matter of necessity, traditional agriculturalists learned 

how to live ‘with’ nature. It has been mainly since the 18th and 19th centuries that 

exponential rates of population increase in much of the Third World, and 

mechanization and the onset of chemical farming worldwide, have resulted in 

some very serious problems. Global warming at least partly caused by the 

increasing release of ‘greenhouse gases’, with agriculture being a significant 

contributor  is already affecting plants and animals.[9] 

E.U (2010), developed strategies that works both to reduce greenhouse gas 

emissions and prevent damage to the ozone layer, and, to mitigate the unavoidable 

adverse effects of climate change.[8] 

UNCCD (2010), formed an interim secretariat that will fight against desertification 

and to promote actions that will protect dry-lands. The fight is seen as an 

opportunity to make critical changes to secure the long-term ability of dry-lands to 

provide value for humanity's wellbeing. They were charged with: 

i. Raising awareness on the causes of land degradation and its solutions. 

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ii. Mobilizing financial and technical support to fight desertification activities 

worldwide. 

iii. Monitoring and reporting on progress in preparation of the secretary 

general’s report 

IPCC (2018), pointed out that there is limited 30 evidence and medium agreement 

that the extent of deserts will increase in the coming decades. However, the deserts 

are expected to become drier and warmer more rapidly than other terrestrial areas. 

They assessed as “low confidence” that desertification linked to climate change 

will directly or indirectly influence soil health and productivity due to accelerated 

soil erosion in drylands. They also had “low confidence” in the projections of 

future increases in dust storms with higher aridity.[9] 

UNCCD (2021) reported that, Land degradation directly undermines our ability to 

deliver food and nutritional security. By 2050, crop yields are estimated to 

decrease by 10% globally due to land degradation and climate change, with some 

regions suffering up to a 50% reduction. Furthermore, land degradation is 

projected to fuel an estimated 30% increase in world food prices over the next 25 

years. Given the expected growth in global population and food demand by 2050, 

conserving, sustainably managing, and restoring land resources will be essential in 

the transition to sustainable food production, requiring at least a 75% reduction in 

current yield gap.[10] 

Barrack Obama at COP26(2021), said “there has been a success to the agreement 

of nations at the cop25 in France, but yet we are not close to achieving our goal of 

maintaining a steady clean energy globally although the USA has manage to make 

that possible”. He also added that some parts of the world are becoming more 

dangerous to live in, hence more than 100 countries have agreed to address 

deforestation and make use of clean energy by the end of 2030 (every country is 

needed to achieve this goal).[18]  

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Boris Johnson (2021) the prime minister of the united kingdom at the COP26 

(2021), gave an analogy that if the global temperature exceeds its current 1.5℃ to 

2℃, (our food supply will greatly be affected, locusts, bees and other important 

insects that aid pollination will all die), 3℃ (more cases of wildfires, 5x drought, 

36x heat waves etc), 4℃ (major cities like Miami, Shanghai will all disappear 

because of over flooding, hurricanes etc.). Hence the world’s leaders have agreed 

to maintain the net global emissions to 1.5℃ and gradually to a lesser degree[17]. 

 

2.2 Relationship between climate change and desertification 

The European Union analyses the relationship between desertification and climate 

change in the Mediterranean. The central aim of the report is to identify best 

practices in dealing with desertification and to make recommendations as to what 

the Union for the Mediterranean (UfM), the EU and other stake-holders can do to 

respond to the challenges that might  arise due to desertification and climate 

change in the future. 

We should note that desertification is essentially a man-made phenomenon which 

is exacerbated by climate change. This is because an increase in weather extremes 

such as droughts and heavy rains as a result of climate change will lead to further 

land degradation. This in turn aggravates existing problems associated with 

poverty, forced migration, and in some areas conflicts. While desertification is 

already responsible for significant forced migration, more than a billion people 

(one in seven of the current world population) could be forced to leave their homes 

between now and 2050 if climate change worsens. The Middle East and North 

Africa (MENA), in particular, is considered to be the region most at risk if such 

projections prove accurate. The relationship between the two processes does not, 

however, move in only one direction. It is also possible that desertification may in 

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turn affect climate change, due to the effects of land degradation that reduces 

surface moisture. Because less water is available for the sun’s energy to evaporate, 

more energy is left over for warming the ground and, consequently, the lower 

atmosphere. At the same time, wind erosion in dry-lands releases dust and other 

particles into the atmosphere. By absorbing the sun’s rays or reflecting them back 

out into space, they may help to cool the Earth’s surface. However, the energy they 

absorb can heat the lower atmosphere and in this way reduce temperature 

differences between the atmosphere’s vertical layers; this can lead to fewer rain-

showers and thus drier land. Finally, the periodic burning of arid and semi-arid 

grasslands, often associated with unsustainable slash-and-burn agriculture, emits 

greenhouse gases. The unsustainable use of fuel-wood and charcoal, a major cause 

of land degradation, also contributes to greenhouse gas emissions. [9] 

2.3 Causes of desertification 

The two main causes of desertification are ‘Climatic variations’ and ‘Human 

activities’ 

Climatic variations: These include climate change, drought, and moisture loss on 

a global level 

Human activities: These include overgrazing, deforestation and removal of the 

natural vegetation (cover by taking too much fuel wood), agricultural activities in 

the vulnerable ecosystems of arid and semi-arid areas, which are thus strained 

beyond their capacity. These activities are triggered by population growth, the 

impact of the market economy, and poverty. 

Other causes of desertification include: 

i. Lack of adjusting to natural fluctuation 

ii. Rainfall below normal recorded levels 

iii. Low priority often given to environmental protection 

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iv. International economic

v. Ignorance, errors, and natural and man

contribute to land degradation.[9]

Source: Aridity zones and dry

in the world’s dry-lands with particular reference to Afr

2.4 Consequences and risk of desertification

There are several consequences of desertification which can either affects us 

directly or indirectly. Desertification;

i. Reduces the land’s resilience to natural climate variability.

ii. Compromises the soil 

iii. Increases possibilities of famine, malnutrition and starvation in a country.

iv. Indirect pressure on area outside the affected areas such as flooding, reduced 

water quality, sedimentation in rivers and lakes, dust storms and air

pollution. 

economic forces 

Ignorance, errors, and natural and man-made disasters can also 

contribute to land degradation.[9] 

Source: Aridity zones and dry-land populations: an assessment of population levels 

lands with particular reference to Africa.[12] 

2.4 Consequences and risk of desertification 

There are several consequences of desertification which can either affects us 

directly or indirectly. Desertification; 

Reduces the land’s resilience to natural climate variability. 

Compromises the soil potential for food production. 

Increases possibilities of famine, malnutrition and starvation in a country.

Indirect pressure on area outside the affected areas such as flooding, reduced 

water quality, sedimentation in rivers and lakes, dust storms and air

made disasters can also 

 

land populations: an assessment of population levels 

There are several consequences of desertification which can either affects us 

Increases possibilities of famine, malnutrition and starvation in a country. 

Indirect pressure on area outside the affected areas such as flooding, reduced 

water quality, sedimentation in rivers and lakes, dust storms and air 

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v. Leads to socio-economic instability 

The factors mention above have the potential to make worse other challenges 

facing the region. 

2.5 Processes and drivers of desertification due to climate change 

 The process of desertification includes both biological and non-biological 

processes, and is attributable to the physical, chemical and biological properties of 

terrestrial ecosystems. Some of the key drivers of desertification include soil 

erosion; global warming leading to the rise of ��� levels; sea surface temperature 

anomalies which drive rainfall changes; invasive plants which affect ecosystem 

services, wildfire which reduces vegetation cover, increases runoff and soil 

erosion, reduces soil fertility and affects the soil microbial community.  

2.5.1 Anthropogenic drivers of desertification include: cropland expansion, 

unsustainable land management practices such as overgrazing by livestock, urban 

expansion, infrastructure development, and extractive industries. High and growing 

consumption of land-based resources has also been indicated as the ultimate driver 

of land degradation, e.g. through deforestation and cropland expansion, escalated 

by population growth. 

2.5.2 The institutional, policy and socio-economic drivers of desertification: 

include land tenure insecurity, lack of property rights, lack of access to markets, 

and to rural advisory services, lack of technical knowledge and skills, agricultural 

price distortions, agricultural support and subsidies contributing to desertification, 

and lack of economic incentives for sustainable land management. 

2.6 Effect of climate change on desertification 

Desertification is affecting about 45% of the African continent’s land area, out of 

which 55% is at high or very high risk of further degradation. The major 

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mechanism through which climate change and desertification affect food security 

is through their impacts on agricultural productivity. There is robust evidence 

pointing not only to negative impacts of climate change and desertification on crop 

yields, but also on the losses in agricultural productivity and incomes in dry-lands. 

The forecasts for Sub-Saharan Africa suggest that higher temperatures, increase in 

the number of heat-waves, and increasing aridity, will affect the rain fed 

agricultural systems. Without the carbon fertilization effect, climate change will 

reduce the mean yields for 11 major global crops – millet, cowpea, sugar beet, 

sweet potato, wheat, rice, maize, soybean, groundnut, sunflower and rapeseed – by 

15% in Sub-Saharan Africa, 11% in Middle East and North Africa by 2050.  

Desertification has led to reduction in agricultural productivity and incomes; it has 

also contributed to the loss of biodiversity in many dryland regions. It is further 

projected to cause reductions in crop and livestock productivity, modify the 

composition of plant species and reduce biological diversity across drylands. In 

sub-Saharan Africa particularly, crop production may be reduced by 17–22% due 

to climate change by 2050. About 821 million people globally were food insecure 

in 2017, of whom 31% were in Africa. Sub-Saharan Africa, particularly East 

Africa, had the highest share of undernourished populations in the world in 2017, 

with 28.8% and 31.4%, respectively. In North Africa, long-term monitoring (1978–

2014) has shown loss of important perennial plant species due to drought and 

desertification e.g. Stipa tenacissima and Artemisia herba alba 

2.7 Statistic Estimation of desertification 

It is estimated that 46 of the 55 countries in Africa are vulnerable to desertification, 

with some already feeling the effects, the Nile (42% of area), Niger (50%), Senegal 

(51%), Volta (67%), Limpopo (66%) and Lake Chad (26%) (The horn of Africa is 

getting drier). Despite desertification in the Sahel being a major concern since the 

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1970s, wetting and greening conditions have been observed in this region over the 

last three decades. The Sahara is reported to have expanded by 10% over the 20th 

Century based on annual rainfall. However, cropland areas in the Sahel region of 

West Africa have doubled since 1975, with settlement area also increasing by 

about 150%. In Burkina Faso, from 1984 to 2013, bare soils and agricultural lands 

increased by 18.8% and 89.7%, respectively, while woodland, gallery forest, tree 

savannas, shrub savannas and water bodies decreased by 18.8%, 19.4%, 4.8%, 

45.2% and 31.2%, respectively. In Fakara region in Niger, a 5% annual reduction 

in herbaceous yield between 1994 and 2006 was largely explained by changes in 

land use, grazing pressure and soil fertility. Greening has also been observed in 

parts of southern Africa but it is relatively weak compared to other regions of the 

continent.[5] 

3. Mathematical Implementation  

In this section the research is going to be concentrating on the global average 

temperature and the effect of greenhouse gases which can be modeled using the 

energy balance equation (EBE) [Kaper and Engler 2013,14] and a few equations 

on predicting weather and climate. 

3.1 GLOBAL AVERAGE TEMPERATURE MODELS 

�
��

��
= �(1 − �) − ���     Energy balance equation     (3.1) 

�
��

��
= �(1 − �) − ����                                                                                     

(3.2) 

����: � → ����(�) = � + �� − (�� + ���)�                  

(3.3) 

 (where �, �, ��&�� are observational data and � is a cloudiness coefficient)                                                                

����: � → ����(�) = � + �� (where the values of � and � vary with temperature) 

�
��

��
= �(1 − �) − (� + ��) Global surface temperature model  

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3.2 LIOUVILLE EQUATION 

The evolution equation in a climate or weather prediction model are conventionally 

treated as deterministic, they based on spatially-truncated momentum, energy, 

mass and composition conservation equation and can be written as 

� = �[�] 

This conservation equation can also written in the context of Gleeson1996 as  

��

��
=

�

��
(��) = �� 

3.3 SIMPLE FLUVIAL MODELS 

3.3.1 Exner Equation 

 

 

                                                             ℎ                                  � 

                                  �                          

                                                                                                                                       � 

 �                                                                                                                                                                                                        

Fig 3.3.1 

The figure above is a geometry of a river therefore its free surface is at  

� = �(�, �, �), and its bed is at � = �(�, �, �). Hence the depth of the river is 

ℎ = � − � 

it is based on the principle conservation of mass for the substrate, and may be 

written as 

(1 − �)
��

��
+ ∇. � = �� 

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3.3.2 St Venant equation 

The Navier-Stokes equations is also written in this case of two-dimensional flow 

��+�� = 0 

��(����������)� ����������(�������) 

��(����������)� �������√������(�������) 

Where � is the slope. 

3.4 VARIABLE DESCRIPTION AND THEIR UNITS 

 T (K, Kelvins) is the average temperature in the Earth’s photosphere (upper 

atmosphere, where the energy balance occurs in the model) (1kelvin = 1°c); 

 t(years) is time; 

 R = (W-yr/m2K) is the average heat capacity of the Earth/ atmosphere 

system (heat capacity is the amount of heat required to raise the temperature 

of an object or substance 1kelvin (=1°�)); 

 Q =  (W/m2) is the annual global mean incoming solar radiation per square 

meter of the Earth’s surface; 

 � = ORL emissivity factor 

 � ��� � = are empirically determined parameters 

 � = is planetary albedo (dimensionless) 

 � = (w/����) is a constant of proportionality (Stefan-Boltzmann 

constant)[16] 

 ��� = average amount of solar energy reaching one square meter of the 

Earth’s surface per unit time 

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 ���� = average amount of energy emitted by one square meter of the Earth’s 

surface per unit time 

 S(m) = height of the bed relative to some reference height 

 n(dimensionless ) = porosity of the substrate 

 q(�����) = bed transport rate 

 �� = source function corresponding to the exchange of sediment between the 

fluid and the bed. 

 ∇= (
�

��
,

�

��
) two-dimensional 

 CONSTANT VALUES OF SOME VARIABLES 

 Values for the parameters are: 

 R= 2.912 w-yr/m2K [Ichii et al. 2003]; 

 Q= 342 W/m2 

 �= 0.30 

 � = 0.6 

 � = 5.67 x 10-8 W/m2K4 

SUMMARY 

As this stage, we have seen different climate models which include; the energy 

balance equation, simple fluvial model, liouville equation etc. All the models 

provided in 3.1 are similar to each other but all of them are important depending on 

the initial variables available and will help us calculate the global average 

temperature. 

4.0 INTRODUCTION 

We have discovered from our chapters points the review of different scholars and 

organization on the diverse effects of desertification and climate change our 

environment and the world at large. We have also discussed some mathematical 

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model that will enable us to clearly see its impact and behaviors. The data that will 

be used in this chapter was collected from Nigerian Meteorological Agency 

(NIMET), National Population Commission (NPC) and researches done by 

different scholars and will be used to display graphs and to solve a few problems. 

4.1 DATA COLLECTION 

Table 4.1 Population in the sampled villages.[16] 

Development 

area 

Population 

in 

clustered 

villages 

Male Female Total 

Household 

Sampled 

household 

Percentage 

Balle 11,635 63 58 2327 116 4.98 

Bulanguwa 11,034 54 56 2297 110 4.78 

Dagona 10,277 56 51 2055 102 4.96 

Dapchi 10,034 45 30 1406 80 5.68 

Degeltura 7,882 44 39 1576 78 4.94 

Dumburi 10,022 55 50 2004 100 4.99 

Futchimiran 4,209 21 26 841 52 6.18 

Gumsa 5,147 25 30 1029 61 5.92 

Gwio kura 16,377 86 82 3275 163 4.97 

Gorgoram 9,046 45 50 1809 100 5.52 

Kanama 6,889 34 37 1377 69 5.01 

Karasuwa 5,049 25 30 1009 60 5.94 

Kaska 13,747 68 70 2749 137 4.98 

Machina 18,081 65 70 2616 130 4.96 

Muguram 10,905 58 54 2181 119 5.46 

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Yunusari 8,822 44 49 1764 95 5.39 

Yusufari 11,089 56 61 2218 111 5.00 

Wachakal 8,140 46 41 1628 96 5.90 

Total 170,385 895 884 34077 1779 5.22 

Source: National Population Commission (2001) 

Table 4.2 Migration per 1000 population in 2002[16] 

Development 

area 

In-Migration Out-Migration 

Balle 12 150 

Bulanguwa 54 56 

Dagona 13 59 

Dapchi 30 40 

Degeltura 10 6 

Dumburi 40 60 

Futchimiran 9 38 

Gumsa 8 36 

Gwio kura 81 82 

Gorgoram 6 37 

Kanama 25 44 

Karasuwa 3 123 

Kaska 76 61 

Machina 11 140 

Muguram 53 56 

Yunusari 36 52 

Yusufari 43 67 

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Wachakal 48 52 

Total 558 1154 

1.1 Chart for Migration per 1000 population 

 

Table 4.3 Showing Social Impacts of Desertification (SID) 

Sl. No.  Questions  4  3  2  1  Mean  STD  

SID1  Desertification leads 
to destruction and 
relocation of houses  

73 (25.5)  169 (59,1) 37 (12.9) 7 (2.4)  3.68  .692  

SID2  Sometimes whole 
settlements relocate 
as a result of 
desertification  

95 (33.2)  126 (44.1) 56 (19.6) 9 (3.1)  3.07  .807  

SID3  Conflicts among 
people do occur as a 
result of 
desertification  

188 (65.7) 90 (31.5)  8 (2.8)  0 (0)  3.63  .539  

         

 SID4  Desertification 
affects soil fertility  

175 (61.2)  111 (38.8)  0 (0)  0 (0)  3.61  .488  

SID5  Farming and 
grazing activities 
are also affected by 
desertification  

136 (47.6)  141 (49.3)  9 (3.1)  0 (0)  3.44  .558  

0

20

40

60

80

100

120

140

160

ar
ea

B
al

le
B

u
la

n
gu

w
a

D
ag

o
n

a
D

ap
ch

i
D

eg
el

tu
ra

D
u

m
b

u
ri

Fu
tc

h
im

ir
an

G
u

m
sa

G
w

io
 k

u
ra

G
o

rg
o

ra
m

K
an

am
a

K
ar

as
u

w
a

K
as

ka
M

ac
h

in
a

M
u

gu
ra

m
Yu

n
u

sa
ri

Yu
su

fa
ri

W
ac

h
ak

al

In-Migration

Out-Migration

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SID6  Desertification leads 
to drying up of 
sources of water  

89 (31.1)  176 (61.5) 11 (3.8)  10 (3.5)  3.20  .671  

SID7  As a result of 
desertification loss 
of biodiversity is 
experienced  

68 (23.8)  105 (36.7)  98 (34.3)  15 (5.2)  2.79  .865  

SID8  Desertification 
induced problems 
lead to overall 
reduced quality of 
life among people  

144 (50.3)  138 (48.3)  4 (1.4)  0 (0)  3.49  .528  

SID9  Desertification leads 
to migration of 
people from the area  

86 (30.07)  146 (51.04)  39 (13.64)  15 (5.24)  3.02  .778  

        

SID10  Increase in soil 
erosion is noticed in 
recent years  

99 (34.61)  177 (61.89)  10 (3.50)  0 (0)  3.45  .535  

Overall  

Average  

 

 

 

117(40.95)  

 

133(46.70)  

 

29(10.18)  

 

6(2.18)  

 

3.33  

 

.661 

 

 

The table above shows the responses of the people living in some few villages 

within our case study with respect to social impacts of desertification in their 

communities. The table shows that 88.46% agreed that these impacts of 

desertification are far reaching and the situation is very bad. These impacts 

manifest in form of destruction, migration from the whole settlement, diminishing 

grazing fields, drying up of water sources, erosion, and reduced quality of life 

among the local people[15]. 

Table 4.4 Average monthly rainfall and temperature anomalies 

Month Rainfall 
(mm)  

Minimum 
Temp. 
(°�) 

Maximum 
Temp. 
(°�) 

January 19.06 21.92 32.40 

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February 45.75 22.49 33.08 

March 141.43 21.38 32.48 

April 154.9 21.26 28.90 

May 209.81 23.14 31.15 

June 222.39 21.78 25.71 

July 460.22 22.54 29.00 

August 361.7 20.84 29.16 

September 361.44 18.32 28.32 

October 293.98 22.62 30.34 

November 142.71 22..97 31.27 

December 22.94 22.23 31.13 

Average 203.03 21.79 30.25 

                            

 

It was observed that there was an increase in the of daily amount of rainfall and the 

extension of rainy season which is usually 8 months (March-October) to 10 

months(February-November) this was evident even in some states of the northern 

part of the country (Potiskum L.G.A, Yobe State) for the last few years 

0

50

100

150

200

250

300

350

400

450

500

Rainfall (mm) 

Minimum Temp. ( )

Maximum Temp. ( )

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(2017,2018). The dry season had been observed shorter and hotter as the years 

progress. These phenomena are in conformity with the consequences of global 

warming resulting from increased anthopogenic activities. (Tamunoberetonaria et. 

al. 2013). 

Table 4. Anti-desertification plants used in Yobe State, Nigeria[16] 

Scientific Name Vernacula Name Hausa Name 

Amaranthus spp. Amaranth Dangme 

Annona cherimola Cherimoya  

Annona muricata Guanabana, soursop, graviola  

Asimina triloba Asimina  

Cleome gynandra African, cabbage, cat’s whiskers Yar unguwa 

Dacryodes edulis Safou or butter fruit  

Ipomoea batatas Sweet potato Dankalin hausa 

Irvingia gabonensis Dika tree Goron biri(Goron 

ruwa) 

Moringa oleifera Moringa Zogale 

Oxytenanthera Drought-resistant Goradi 

Abyssinica Bamboo Gwangwala 

Prosopis cineraria Prosopis Akiye 

Simmondsia chinensis Jojoba  

Solanum scabrum African nightshade  

Strychnos spinosa Monkey orange Girigita 

4.2 PROBLEM 

The models developed in the previous chapter (3.4) will be used to solve few 

examples as seen below 

1.  �
��

��
= �(1 − �) − ��� 

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Data 

� = 2.912 W-yr/m2K[Ichii et al 2003],   � = 342W/m2[Kaper and Engler 2013],   

� = 0.30[Kaper and Engler 2013],  � = 5.67X10-8,  � = 30.71 

 �∗ = �
�(���)

�
�1/4  Equilibrium temperature 

�∗ = �
���(���.��)

�.������� �1/4 

= �
���(�.��)

�.��������1/4 

= �
���.�

�.��������1/4 

= (4.22222)1/4 

= 1.4335℃  

Hence the equilibrium temperature is increasing at a very slow pace but yet its 

impact to the surrounding can be clearly noticed with time. 

4.3 Discussion 

It is clearly evident that climate change is affecting the rate of desertification all 

over the globe.  

Boris Johnson the prime minister of the united kingdom at the COP26 (2021), gave 

an analogy that if the global temperate exceeds 1.5℃ to 2℃, (our food supply will 

greatly be affected, locusts, bees and other important insects that aid pollination 

will all die), 3℃ (more cases of wildfires, 5x drought, 36x heat waves etc), 4℃ 

(major cities like Miami, Shanghai will all disappear because of over flooding, 

hurricanes etc.). Hence the world’s leaders have agreed to maintain the net global 

emissions to 1.5℃ and gradually to a lesser degree[17]. 

Evidently, the socio-economic impacts of desertification in all the study locations 

with the exception of Gumshi were found to be high. Thus, with the unprecedented 

increase in the rate of deforestation activities such as logging coupled with the non-

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chalet attitudes of the local communities towards controlling desertification and its 

impacts, continuous deforestation acts by the local people, lukewarm attitudes of 

the Government, increasing over dependence of the local communities on fire 

wood as the dominant source of domestic energy as well as the growing 

dependence of considerable number of the local communities on fire wood selling 

as a source of income, desertification can continue taking toll in these areas and its 

impacts both socially and economically can escalate. The change in the climate and 

weather system is also responsible for the unstable yield of most farm product[15]. 

5.1 CONCLUSION 

Based on the research so far, we have discovered a framework for developing a 

better understanding of the nexus between the environmental changes, population 

response and environmental policy and management. Solutions to desertification 

must be aimed to increase the amount of food production in the area in 

concomitance with farm practices that must encourage environmental stabilization. 

It is also clear that the general public have little knowledge about how their day to 

day use of unchecked car exhaust, bush burnings, etc is dangerous to them and to 

the world at large. [15]  

5.2 RECOMMENDATION 
Here are a few recommendations to the Government, Non-Governmental 

Organizations (N.G.O), affected communities and every individual to address 

some of the findings in this research respectively: 

A. The government must be all round committed to fight desertification and 

gain the participation of the local population combat desertification in their 

local communities. The key area to be given priority is massive tree planting 

exercise, construction of earth dams, etc this calls for more fund allocation 

to both State and Federal Forestry Departments in Nigeria. The aim should 

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be a long term sustainable participatory environmental resources 

management programme.[16] 

B. Non-governmental organizations in partnership with the local stakeholders 

should create a forum for massive reforestation programme, leading to 

improved environmental management capacity. There is the need for the 

tapping of underground water for domestic and irrigational purposes. 

Fadama areas should be protected with trees to avoid drying up of the 

catchment areas.[16] 

C. All affected communities most take the responsibility of ensuring that all 

government policies concerning desertification are backed up and obeyed by 

every resident in that community. They are also responsible for the 

maintenance of amenities provided by the government, N.G.O’s and 

stakeholders to combat desertification. 

D. As we have seen in this research how indirectly desertification can affect 

people who are far away from the affect communities by causing shortage of 

food supply, flooding, poverty etc. hence everyone must take the 

responsibility to ensure we combat climate change by reducing the use of 

excess carbon exhaust and desertification to the barest minimal. 

 

 

 

 

 

  

 

 

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REFERENCES 

[1] Gbahabo, Percy, (2011) “Desertification and rural livelihoods the case of 

Gursulu village” Yobe State, Nigeria. 

[2] M.M Verstraete and S.A Schwartz Vegetato vol 91. (1991) “Desertification and 

global change” 

[3] Oguntoyinbo. J (1981), “climate variability and food crop production in west 

Africa” Geojournal vol. 5.2 

[4] El-Baz, F. (1983), “A geological perspective of the desertt”, S. wells and D. 

haragan “Origin and evolution of deserts”, university of new mexico press, 

Albuquerque. 

[5] Agnes, (march 2020), “Desertification and climate change in Africa, policy 

brief No. 1”. 

[6] M.S Reed, L.C Stringer (march 2015), “climate change and desertification: 

anticipating,, assessing and adapting to future changes in drylands”. 

[7] en.wikipedia.oeg/wiki/drought 

[8] http://ec.europa.eu/dgs/clima/mission/index.en.html 

[9] European union, (2011), “The relationship between desertification and climate 

change in the Mediterranean.” 

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[10] Coriacher, Arthur vol1 “Land degradation and desertification: history, nature, 

cause, consequences and solutions.” 

[11] UNCCD (2021), “land degradation neutrality for sustainable agriculture and 

food security.” 

[12] UNDP/UNSO (1997), “Aridity zones and dryland populations: an assessment 

of population level’s in the world drylands with particular reference to Africa.” 

[13] T.N Palmer (1999), “Predicting uncertainty in forecast of weather and 

climate” 

[14] James Walsh, (2015) “climate modeling in differential equation” Oberlinn 

college. 

[15] J.A Opara, M.Babagana and A.Adamu, (2017) “Environmental health, 

desertification and sustainable development in north-eastern Nigeria: A socio-

economi impact assessment” 

[16]  Amadi et al. (2011), “Human coping strategies to desertification in Yobe 

state Nigeria”, animal research international. 

[17] https://www.youtube.com/watch?v=oofxDQQKE7M 

[18] https://www.youtube.com/watch?v=69EMd4csZRY 

 

 

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https://www.youtube.com/watch?v=oofxDQQKE7M
https://www.youtube.com/watch?v=69EMd4csZRY

