This paper investigates the effect of increasing levels of atmospheric carbon dioxide (CO2) on rainwater. The design of this research includes the collection and analysis of recorded partial pressures of carbon dioxide (pCO2) at six air-space control stations in Nigeria. The already established equations for the chemistry of water constitute the theoretical framework of this investigation. These equations resolve into a mathematical model which connects the pCO2 and the activity index of hydrogen ions (pH) in rainwater. A cubic polynomial, which represents the predictive framework of this study, fits the average pCO2, while the model generates the corresponding pH. The obtained results show that the increasing levels of CO2 contribute to climate change and the proportionate decrease of pH in rainwater. An extrapolated result reveals that the acidity of rainwater will increase from 5.3% in 2000 to 93.7% by 2050.

INTRODUCTION

It is well documented that the atmospheric levels of carbon dioxide have been increasing over the past 50 years. This has contributed immensely to climate change in the 21st century. Thus, many aspects of the human and the natural world have been adversely affected (IPPC 2007). Deforestation and high demand for energy have become a global issue. Moreover, most causes of global warming and the rise in carbon dioxide level are the result of increased and uncontrolled human activities at different stages of energy generation, transportation and industry. Porter & Brown (2009) stated that the take-off stage of development and industrialization progress can lead to increased environmental damage due to greater use of natural resources, more emission of carbon dioxide, the operation of less efficient and relatively dirty technologies and disregard for the environmental consequences of growth. The effects of carbon emissions have been devastating, affecting both the environment and human beings in the environment (Stern 2009). While media and public attention have focused on the effects of higher concentrations of CO2 on global climate, rising CO2 concentrations are likely to have profound direct effects on the growth, physiology and chemistry of plants (Ziska 2008). Yes, human well-being is under threat as a result of increasing climate change on agriculture. This problem will compound the current challenges of food supply, which will lead to more people being undernourished (FAO 2014). In Nigeria, rainwater, which is the main source of human and agricultural life, would have been adversely affected by this increasing rise of carbon dioxide in the atmosphere.

This paper, therefore, investigates numerically the rate of this increase and how this trend of carbon dioxide affects the pH of rainwater in Nigeria. A literature review appears below, followed by a section presenting methods of data collection and analysis. The implications of the obtained results follow and then finally the concluding section.

LITERATURE REVIEW

The pursuit of economic growth and sustainable energy has produced pollution (CO2) that contributes nothing to human happiness (Galeotti et al. 2009). In 1971, Jay Forrester of MIT developed an economic model which predicted that in the future population level, food production and industrial production will collapse during the 21st century if air pollution (CO2) is not controlled. Thus, the future natural resources will be exhausted and if, in addition, industrial activities continue, it will give rise to catastrophic results (Seldon & Song 2004). In a related study, Porter & Brown (2009) found that carbon emissions have a negative impact on economic growth. Indeed, increased carbon dioxide emissions have negative effects on growth (Baltimoore & Tudok 2010).

Climate change in the 21st century will impact many aspects of the human and natural world (IPCC 2007). The rising atmospheric CO2 is the driving force behind the greater temperatures and water stress, which threaten to reduce future crop yields (Hoffman et al. 1986; Stinner et al. 1988; AGWT 2003). It also has the potential to directly affect crop physiology (Andrew 2009). This problem will compound the current challenges to food supply, which led to approximately 825 million people being undernourished in 2006 (Leslie 2000). Andrew added that this rising concentration of CO2 in the atmosphere is driving the global warming and climate change that will negatively impact crop yields in many parts of the world this century. Many research findings indicated that carbon dioxide is the primary determinant of the pH of rainwater (Ozcan 2000; Turekan & Sermin 2005). The measure of the activity of hydrogen ions in water, thus its alkalinity or acidity, is called pH. For dilute aqueous solutions, its value is 
formula
1
where is the molar concentration of hydrogen ions (Wong 1979). Carbon dioxide does dissolve in water, however the system is somewhat complex (Reid et al. 1987). The CO2 dissolves according to: 
formula
According to Reid, an equilibrium is established between the dissolved CO2 and H2CO3, carbonic acid: 
formula
 
formula
 
formula
It has also been reported that greenhouse gases certainly affect the pH of rainwater (Menz & Seip 2000; Senanayake et al. 2005; Wang et al. 2006). This is true, since, at the global background level of atmospheric CO2, pure water should have a standard pH value from the calculation of H+ after absorption of the CO2. However, CO2 partial pressure changes certainly influence pH of rainwater. Andrew also stated that it is important to have reliable estimates of how this CO2 trend affects the pH of rainwater and ultimately crop yields in order to take the necessary action to minimize the negative consequences. The negative consequences include depletion of the ecosystem (Walton et al. 1982; Greller & Locke 1990; Hendershot et al. 1993; Zhang et al. 2004). It has been reported that in poor countries like Africa, any reduction in crop productivity resulting from this rise in CO2 will impoverish the continent (Rosegrant et al. 2006). A direct response to this life-threatening phenomenon is the objective of this paper.

METHODS

The design of this research includes the collection of measured partial pressures of carbon dioxide at the air-space control stations located at the six geopolitical zones in Nigeria. These zones include Enugu, Lagos, Port Harcourt, Makurdi, Kano and Yola. The unit of measurement is parts per million (ppm). Tables 13 contain the data, while Figures 16 show their pictorial views and the resulting information. A high precision software, MATLAB, drives the numeric analysis of data and the plot of these figures. A data processor (SPSS version 17) handled the correlation analysis of these data. In order to predict the future level of CO2, the method of least squares aids the derivation of a cubic interpolating polynomial for these data given that the correlation analysis is significant. Subsequently, the rate of increase becomes the derivative of the cubic polynomial with respect to time. The best research approach is to review the already established equations that govern the chemistry of water: 
formula
2
 
formula
3
 
formula
4
 
formula
5
 
formula
6
 
formula
7
Table 1

Obtained partial pressures of carbon dioxide in ppm

Year Month Enugu Port Harcourt Lagos Makurdi Kano Yola 
2000 366.3 365.7 365.7 360.5 368.5 368.3 
2000 368.5 366.2 364.5 360.2 368.2 368.2 
2000 371.6 366.9 366.1 368.6 368.5 370.6 
2000 372.8 365.8 365.8 370.4 379.4 371.8 
2000 372.5 367.9 366.9 369.4 369.4 371.5 
2000 371.7 366.7 367.1 368.6 369.6 371.9 
2000 369.9 367.2 367.6 368.6 368.9 371.7 
2000 368.8 367.7 366.9 368 369 370.5 
2000 371.9 368.9 368.2 368.7 368.9 371.3 
2000 10 369.9 369.2 367.6 369 369.2 370.8 
2000 11 372.3 370.3 366.9 370.2 369.7 371.7 
2000 12 371.8 369.5 367.8 370.5 369.5 371.5 
2013 395.4 390.4 390.4 390.5 392.1 391.8 
2013 396.8 391.8 391.5 391.7 392.5 392 
2013 397.3 391.3 391.7 391.5 392.7 391.8 
2013 398.5 392 392.1 392.1 392.8 392.5 
2013 399.7 391.7 391.8 391 392.5 392.4 
2013 398.5 392.5 392.6 392.7 392.5 392.6 
2013 397.2 391.2 391.3 391.5 391.9 392.1 
2013 395.5 392.5 392.4 392.4 392.2 391.8 
2013 393.5 391.8 391 391.7 391.9 392.6 
2013 10 393.6 392.5 392.1 392.4 392 392.5 
2013 11 395.1 392.4 392.9 392.2 392.1 393.1 
2013 12 396.8 392.7 392.5 392.5 392.9 393.8 
Year Month Enugu Port Harcourt Lagos Makurdi Kano Yola 
2000 366.3 365.7 365.7 360.5 368.5 368.3 
2000 368.5 366.2 364.5 360.2 368.2 368.2 
2000 371.6 366.9 366.1 368.6 368.5 370.6 
2000 372.8 365.8 365.8 370.4 379.4 371.8 
2000 372.5 367.9 366.9 369.4 369.4 371.5 
2000 371.7 366.7 367.1 368.6 369.6 371.9 
2000 369.9 367.2 367.6 368.6 368.9 371.7 
2000 368.8 367.7 366.9 368 369 370.5 
2000 371.9 368.9 368.2 368.7 368.9 371.3 
2000 10 369.9 369.2 367.6 369 369.2 370.8 
2000 11 372.3 370.3 366.9 370.2 369.7 371.7 
2000 12 371.8 369.5 367.8 370.5 369.5 371.5 
2013 395.4 390.4 390.4 390.5 392.1 391.8 
2013 396.8 391.8 391.5 391.7 392.5 392 
2013 397.3 391.3 391.7 391.5 392.7 391.8 
2013 398.5 392 392.1 392.1 392.8 392.5 
2013 399.7 391.7 391.8 391 392.5 392.4 
2013 398.5 392.5 392.6 392.7 392.5 392.6 
2013 397.2 391.2 391.3 391.5 391.9 392.1 
2013 395.5 392.5 392.4 392.4 392.2 391.8 
2013 393.5 391.8 391 391.7 391.9 392.6 
2013 10 393.6 392.5 392.1 392.4 392 392.5 
2013 11 395.1 392.4 392.9 392.2 392.1 393.1 
2013 12 396.8 392.7 392.5 392.5 392.9 393.8 

Source: Air-space control stations: Enugu, Port Harcourt, Lagos, Makurdi, Kano and Yola.

Table 2

Correlation of data within the observed stations

Station Enugu Port Harcourt Lagos Makurdi Kano Yola 
Enugu: Pearson correlation 0.988** 0.995** 0.911** 0.889** 0.992** 
Sig. (2-tailed) – 0.000 0.000 0.000 0.000 0.000 
Port Harcourt: Pearson correlation 0.988** 0.988** 0.953** 0.941** 0.996** 
Sig. (2-tailed) 0.000 – 0.000 0.000 0.000 0.000 
Lagos: Pearson correlation 0.995** 0.988** 0.928** 0.894** 0.991** 
Sig. (2-tailed) 0.000 0.000 – 0.000 0.000 0.000 
Makurdi: Pearson correlation 0.911** 0.953** 0.928** 0.977** 0.948** 
Sig. (2-tailed) 0.000 0.000 0.000 – 0.000 0.000 
Kano: Pearson correlation 0.889** 0.941** 0.894** 0.977** 0.932** 
Sig. (2-tailed) 0.000 0.000 0.000 0.000 – 0.000 
Yola: Pearson correlation 0.992** 0.996** 0.991** 0.948** 0.932** 
Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 – 
Station Enugu Port Harcourt Lagos Makurdi Kano Yola 
Enugu: Pearson correlation 0.988** 0.995** 0.911** 0.889** 0.992** 
Sig. (2-tailed) – 0.000 0.000 0.000 0.000 0.000 
Port Harcourt: Pearson correlation 0.988** 0.988** 0.953** 0.941** 0.996** 
Sig. (2-tailed) 0.000 – 0.000 0.000 0.000 0.000 
Lagos: Pearson correlation 0.995** 0.988** 0.928** 0.894** 0.991** 
Sig. (2-tailed) 0.000 0.000 – 0.000 0.000 0.000 
Makurdi: Pearson correlation 0.911** 0.953** 0.928** 0.977** 0.948** 
Sig. (2-tailed) 0.000 0.000 0.000 – 0.000 0.000 
Kano: Pearson correlation 0.889** 0.941** 0.894** 0.977** 0.932** 
Sig. (2-tailed) 0.000 0.000 0.000 0.000 – 0.000 
Yola: Pearson correlation 0.992** 0.996** 0.991** 0.948** 0.932** 
Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 – 

**Correlation is significant at the 0.01 level (2-tailed).

Table 3

Average partial pressures of carbon dioxide from 2000 to 2013

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 
Average pCO2 (ppm) 368.92 371.49 374.19 377.96 379.76 381.43 382.90 383.98 385.13 386.29 387.76 389.68 391.15 392.81 
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 
Average pCO2 (ppm) 368.92 371.49 374.19 377.96 379.76 381.43 382.90 383.98 385.13 386.29 387.76 389.68 391.15 392.81 
Figure 1

The average partial pressure of carbon dioxide per month.

Figure 1

The average partial pressure of carbon dioxide per month.

Figure 2

The average pCO2 from 2000 to 2013.

Figure 2

The average pCO2 from 2000 to 2013.

Figure 3

The average pH of rainwater per year.

Figure 3

The average pH of rainwater per year.

Figure 4

The average pH of rainwater and partial pressures of carbon dioxide.

Figure 4

The average pH of rainwater and partial pressures of carbon dioxide.

Figure 5

Data and interpolated points from 2000 to 2013.

Figure 5

Data and interpolated points from 2000 to 2013.

Figure 6

Rate of increase of carbon dioxide in the atmosphere.

Figure 6

Rate of increase of carbon dioxide in the atmosphere.

Here, is Henry's constant. , and are equilibrium coefficients. The five unknowns are total inorganic carbon, = bicarbonate, = carbonate, = hydrogen ion and = hydroxyl ion. Using , this paper seeks a mathematical model that connects the partial pressures of atmospheric carbon dioxide (pCO2) and the pH of rainwater from Equations (2)–(6). From Equations (2)–(4), Equations (8)–(10) follow: 
formula
8
 
formula
9
 
formula
10
Substituting Equations (8)–(10) into Equation (6) gives: 
formula
11
It follows that: 
formula
12
Thus, the mathematical model becomes a real valued cubic function of two variables: 
formula
13
Given a value, the pH of rainwater is the solution of . Many numerical methods could be used to solve this problem. This paper used the MATLAB computing environment to solve . A function written in MATLAB (‘findRealRoot’; in Appendix, available with the online version of this paper) solves . The following section gives the details of the aforementioned.

RESULTS AND DISCUSSION

The varying patterns of are shown in Table 1.

Figure 1 shows the pictorial view of this observation in Enugu State.

Other stations have similar patterns. On the whole, Figure 2 presents the information contained in Table 1 clearly.

These trends show that there is a steady rise in the volume of atmospheric carbon dioxide across the observed stations in Nigeria. Using these values, the trends of the computed pH of rainwater are shown in Figure 3.

The values in Table 1 suggest that the six stations have the same trend of data. Figure 4 shows that the trends of average data in the regions (Nigeria) coincided with each other.

In addition, Pearson's correlation analysis shows that the correlation among the data is significant at the 0.01 level. A p-value of 0.000 < 0.01 has been reported, among the stations, in Table 2.

Hence, the correlation analysis has shown that the means of the observed data at the six stations are very close to each other. This observation suggests that all the data, from the entire regions and indeed Nigeria, could be represented by their average values. Hence, the average pCO2 values for the six stations are as follows.

In order to assess the appropriate rate of pCO2 increase with respect to time, a cubic polynomial was selected to fit these data. Thus, the following cubic polynomial follows from the method of least squares technique at a time  
formula
14
It is obvious that this polynomial is a good estimate of the data distribution. The approximation error is negligible. This polynomial is the predictor function for this analysis. Figure 5 shows how this polynomial approximates the data points from 2000 to 2013 in Nigeria.
The data distribution has been closely represented. Therefore, the rate of pCO2 increase , with respect to time, becomes the following quadratic polynomial. 
formula
15
A global minimum of occurs at where . Above 2008, the rate of pCO2 emission continues to increase exponentially. Figure 6 explains this phenomenon clearly.

Figures 2 and 3 indicate that the increasing levels of carbon dioxide have introduced a great climatic change and global warming within a short period of time. The fertility of the soil and rainwater would have been adversely affected. Figure 3 confirms this assertion. It shows that the pH of rainwater continues to decrease across the observed regions over the years. It implies that the hydrogen ion concentration in rainwater has been increasing too. The rate of increase of average data shows that 1.15 is the incremental value from 2007 to 2008. The interpolated value is very close to the actual rate. Thus, gives a meaningful prediction. Yes, this quadratic polynomial predicts that will become 69.24 in 2050, if this climate change is not controlled. In particular, pCO2 increased from 360.2 ppm to 399.7 ppm, that is, a increase. This increase caused a decrease in pH of rainwater from 5.60 to 5.58. All the pCO2 values exceeded the generally accepted value of 350 ppm. Thus, this observation implies that rainwater and invariably soil water are increasingly acidic. This is true since the computed values of pH (highest and lowest), and , implies that concentration has increased too. That is, increase. Thus, a rise in atmospheric carbon dioxide levels has produced an additional acidity in rainwater. Similarly, using 368.92 ppm in 2000, the model and the polynomial predict that the average acid content of rainwater will grow to a dangerous level of 93.7% (: 1,385.57 ppm) by 2050, if the emission of carbon dioxide into the atmosphere is not controlled. This prediction is accurate since the extrapolated value, 398.09 ppm, agrees with the observed data, 397.9 ppm, in 2015. It follows that this development will spell doom for Nigerians whose major source of human and agricultural life is water. It will further compound the current challenges to food supply and many people will be undernourished by 2050. In fact, the ecosystem will be depleted and the evil effects of global warming will be on the high side. A spiral effect of this climate change would have touched the economic growth in Nigeria. It has reduced the level of aggregate output in the economy through the hazardous effects and global warming.

CONCLUSIONS

The results have shown that the increase in atmospheric carbon dioxide has increased the acidic content of rainwater and soil fertility in Nigeria. Recent debates on greenhouse gas trends focus on whether these changes are contributing to global warming and poor fertility of the soil. Figure 4 shows that these have produced smaller values of pH. The results show that hydrogen ion concentration in rainwater has increased by over the years. Moreover, the results predict that the average acid content of rainwater will grow to a high level of 93.7% by 2050, if the emission of carbon dioxide into the atmosphere is not controlled. This assertion is correct since the extrapolated value, 398.09 ppm, agrees with the observed data, 397.9 ppm, in 2015. The obtained results also show that something as large as our atmosphere has changed so much over a relatively short period of time. This trend would have affected Nigeria's gross domestic product negatively. Finally, this research illustrates how simple models, numerical methods and MATLAB can be employed to analyse and interpret climate change.

The published findings of this research will help our agricultural planners, engineers and scientists gain increased understanding of how much the continuous rise in atmospheric carbon dioxide levels has affected the hydrogen ion concentration in rainwater, the ecosystem, the soil fertility index and global warming. Thus, the findings will, therefore, help scientists who will design ways of improving and refining drinking water sources in Nigeria. This is important since about 80% of our body make-up is water. It will also provide the Food and Agricultural Organization (FAO) and other researchers with some vital information on why global warming must be controlled. The findings will provide a new ground for further research on global warming and control of carbon dioxide emission. This paper will necessitate the use of modern biotechnology for providing high yielding crop species that could adapt to the prevailing soil conditions. All these will further promote better living conditions and human health for all. In essence, this study provides valuable information for all who have the powers to check human-made sources of CO2, such as continuous gas flaring and industrial wastes.

ACKNOWLEDGEMENTS

The authors hereby acknowledge, with thanks, the financial support provided by Tertiary Education Trust Fund (TETFund) for transportation and feeding. The field supervision and encouragement by Senate Research Grant Committee, Federal University, Ndufu-Alike, Nigeria, at every moment of this work is also acknowledged. Finally, the authors acknowledge with gratitude everyone who has contributed to the success of this research (FUNAI/TETFund/2013/BI/004).

REFERENCES

REFERENCES
AGWT (American Ground Water Trust)
2003
Acid rain and groundwater pH
.
Originally published in The American Well Owner, 2003, Number 3
.
Andrew
D. B. L.
2009
Rising atmospheric carbon dioxide concentration and future of C4 crops for food and fuel
.
Proceedings of the Royal Society B: Biological Sciences
276
,
2333
2343
.
Baltimoore
C.
Tudok
R.
2010
Relationships between energy and GNP
.
Journal of Energy and Development
3
,
401
403
.
Food and Agriculture Organization (FAO) of the United Nations
2014
News update on food security.
Galeotti
M.
Manera
M.
Lanza
A.
2009
On the robustness of robustness checks of the environmental Kuznets curve
.
Environmental and Resource Economics
42
,
551
574
.
Greller
M.
Locke
C.
1990
Changes in vegetation composition and soil acidity between 1922 and 1985 at a site on North shore of Long Island
.
Journal of New York Bulletin of the Torrey Botanical Club
117
(
1
),
450
458
.
Hendershot
W. H.
Lalande
H.
Duquette
M.
1993
Soil reaction and exchangeable acidity
. In:
Soil Sampling and Methods of Analysis
(
Carter
M.
, ed.).
Lewis Publishers
,
Boca Raton, FL
,
USA
.
Hoffman
J.
Pichard
L.
Mass
L.
1986
Irrigation water quality options for corn on saline organic solids
.
Journal of Irrigation Science
7
(
1
),
265
275
.
IPCC
2007
Climate Change 2007: The Physical Science Basis
.
Cambridge University Press
,
New York
,
USA
.
Leslie
J.
2000
Running dry. What happens when the world no longer has enough freshwater?
Harper's Magazine
,
July issue, 200–201, reference section
.
Menz
C.
Seip
M.
2000
Acid rain in Europe and the United States: an update
.
Journal of Environmental Science and Policy
7
,
253
265
.
Ozcan
H.
2000
Monitoring and evaluation of the spatial temporal changes of PH, SPCOND, DO, ORP and TDS in the waters of Troia (Turkey) by GIS
.
Journal of Gottinger Geographische Abhandlungen
133
,
175
183
.
Porter
A.
Brown
H. J.
2009
Energy consumption, economic growth and prices; a reassessment using panel VECM for developed and developing countries
.
Energy Policy
35
,
2481
2490
.
Reid
R. C.
John
M. P.
Brice
E. P.
1987
The Properties of Gases & Liquids
,
4th edn
.
McGraw-Hill
,
New York
,
USA
.
Rosegrant
M. W.
Ringler
C.
Benson
T.
Diao
X.
Orden
D.
2006
Agriculture and Achieving the Millennium Development Goals
.
The World Bank
,
Washington, DC
,
USA
.
Seldon
T.
Song
D.
2004
Environmental quality and development: Is there a Kuznet curve for air pollution emissions
.
Journal of Environmental Economics and Management
8
,
147
162
.
Senanayake
N.
Perera
M. T.
Weragoda
M.
2005
Acid rains and rains causing acidity of soils in Sri Lanka
.
Proceedings (AQM)
62
(
4
),
20
29
.
Turekan
O.
Sermin
O.
2005
Elemental composition of rainwater in Mersin an urban site in the North Eastern Mediterranean
.
Proceeding (AQM)
62
(
4
),
20
29
.
Walton
E.
Camptom
M.
Allan
D.
Daniels
D.
1982
The effect of acid stress on survivorship and reproduction of Daphnia pulex
.
Canadian Journal of Zoology
60
(
1
),
573
579
.
Wong
S. C.
1979
Elevated atmospheric partial pressure of CO2 and plant growth
.
Journal of Environmental Science
44
,
68
74
.
Zhang
P.
Wang
J.
Zhao
M.
Dou
W.
Chen
Y.
2004
Effects of simulated acid rain on the physiology of carmine spider mite
.
Journal of Applied Entomology
128
,
342
347
.

Supplementary data