Agriculture, which used to be the mainstay of the economy of the Niger Delta region of Nigeria, was abandoned because of the discovery of oil in the 1950s. Oil exploration has, however, left a trail of sorrow as a result of environmental pollution. There is now a new awakening in the realization that oil is not a renewable resource an d, hence, effort needs to be diverted to revitalize the agricultural sector. Farmers in this region rely en tirely on rain-fed cropping. Since this area is characterized by distinct dry and wet seasons, cropping activities are scewed towards the wet season, thus resulting in subsistence level of production.

1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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1
MATHEMATICAL RELATIONSHIP BETWEEN SOIL
MOISTURE AND GROUNDWATER LEVEL IN A LOAMY
SAND SOIL IN THE NIGER DELTA REGION OF NIGERIA
Fubara-Manuel, I1
, Otoko, R.G2
1
Department of Agricultural and Environmental Engineering
2
Department of Civil Engineering, Rivers State University of Science and Technology,
Port Harcourt, Nigeria
ABSTRACT
Agriculture, which used to be the mainstay of the economy of the Niger Delta region of
Nigeria, was abandoned because of the discovery of oil in the 1950s. Oil exploration has, however,
left a trail of sorrow as a result of environmental pollution. There is now a new awakening in the
realization that oil is not a renewable resource and, hence, effort needs to be diverted to revitalize the
agricultural sector. Farmers in this region rely entirely on rain-fed cropping. Since this area is
characterized by distinct dry and wet seasons, cropping activities are scewed towards the wet season,
thus resulting in subsistence level of production. Supplemental irrigation has been advocated as a
way forward, but the soil moisture status dictates when to irrigate, and how much irrigation water to
apply. This study therefore investigated the mathematical relationship between soil moisture and
groundwater level in the Niger Delta region of Nigeria. Soil moisture contents and groundwater
levels from shallow wells were measured on a bi-monthly basis in 2013. The data were then
subjected to regression analysis. The result showed a simple linear relationship between soil
moisture and groundwater level. With this regression equation, it is now possible for farmers in this
region to determine the moisture status of the soil just by measuring the level of water in their
shallow wells. This is an invaluable tool in irrigation scheduling.
Keywords: Agriculture, Oil Exploration, Environmental Pollution, Soil Moisture, Groundwater,
Regression Analysis.
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INTRODUCTION
Crop production is largely dependent on soil, availability of soil moisture, and other inputs
that include the materials for cultivation. The soil is the repository of the moisture which the plant
requires to grow. However, it is the rainfall that replenishes the soil. When rain falls, part of it
infiltrates into the soil and can also percolate through the root zone to join the groundwater. This
process, of course, depends partly on the moisture status of the soil which can be depleted by
evaporation, transpiration and other plant processes that require water. In general, therefore, the
variation of soil moisture is the integrated result of many factors such as precipitation, plant
transpiration, soil evaporation, surface runoff, and underground percolation, etc. (Ma et al; 2011).
Plants take up water from the soil through their roots even though the rooting characteristics
vary genetically. Plants may however be limited in their rooting by factors other than genetics. High
water table, shallow soils, and impermeable formation near the ground surface resulting from
compaction by agricultural machines can restrain the extent of plant root formation.
Apart from its importance in agriculture, soil moisture also plays a vital role in climatic
studies. According to Chen and Hu (2004), temporal and spatial variations of soil moisture are
receiving increasing attention in climate studies because soil moisture is an essential element in
processes that drive land surface water and energy fluxes, which affect ecosystem dynamics and
biogeochemical cycles in the land-atmosphere system.
Chen and Hu (2004) also aver that soil moisture variation in shallow ground water areas
behave very differently from those in areas with deep groundwater table. These conditions are
similar to humid tropical climates that have distinct wet and dry seasons. During the wet season, the
moisture content is high, with shallow groundwater table. When rain stops during this period, the
high moisture content is largely attributable to the influence of groundwater. However, in the dry
season, the moisture content is low and the deep groundwater contributes little or nothing to the
moisture content depending, of course, on the depth of soil from the surface. For different soils, the
influence of water table on soil moisture is also different. (Miguez-Macho et al., 2008). Lo and
Famiglietti (2011) also pointed out that several studies have established that soil moisture increases
after adding a groundwater component in land surface models, owing to the additional supply of
subsurface water.
Farmers in the Niger Delta region of Nigeria, which is in the humid tropic, are confronted
with myriads of problems which include lack of genuine government support, soil pollution by oil
companies, fragmented farm land holdings, high illiteracy level , and total dependence on rain-fed
agriculture. The transition from rain-fed to irrigated agriculture has been advocated as one panacea
for evolving from the present subsistence level of crop production (Fubara-Manuel, 2005). However,
one major variable that dictates when to irrigate, and how much water to apply, is the soil moisture
status.
In the less developed countries of the tropics, labour is abundant and cheap. Farmers can
therefore provide hand dug wells or shallow wells (< 10m) in their farms. It is however more
difficult and costly to access soil-testing laboratories that will enable them determine the soil
moisture status. This assertion is supported by Saxton and Rawls (2006). The main objective of this
study, therefore, was to use linear regression analysis to relate soil moisture with groundwater level
with a view to enabling a farmer determine the moisture content of a soil by measuring the water in
his well.
MATERIALS AND METHODS
Theory
When a soil is below field capacity and surplus rainfall collects on the surface, the water
crosses the interface into the ground at an initial rate dependent on the existing soil moisture content.

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As the rainfall supply continues, the rate of infiltration decreases as the soil becomes wetter and less
able to take up water (Shaw, 1983). Thus, the capacity of any soil to absorb rain water, falling
continuously at an excessive rater, goes on decreasing with time until infiltration is reached at the
minimum time, since infiltration is a function of time (Surech, 2006)
Groundwater occurrence is chiefly the result of infiltration from the soil and from streams
and lakes, all of which receive their supply of water from precipitation. However, Kumar (1995)
posits that of all the factors controlling groundwater recharge, the antecedent soil moisture regime
probably is the most important. Soil moisture and groundwater variations can therefore be effectively
analyzed by water balance. The water balance equation is generally derived from the conservation of
mass principle which can be stated as
Inflow – outflow = ∆S (1)
Where
Inflow, outflow = total flow into and out of the area during the time interval being
considered
∆S = change in soil moisture within the area during the time being
considered.
de Ridder and Boonstra (1994) derived three water balance equations, one each for the unsaturated
zone, land surface, and saturated zone (groundwater), and then integrated these equations to arrive at
an overall water balance for the area, given as
P - Eo - E + 1000
ொೞ೔ ష ೂೞ೚
஺
+ 1000
ொ೒೔ ష ೂ೒೚
஺
=
∆ௐ೔
∆௧
+
∆ௐೞ
∆௧
+ ߤ
∆௛
∆௧
(2)
Where
P = Precipitation for the time interval, ∆t
Eo = evaporation from the land surface
E = rate of evaporation from the unsaturated zone
Qsi = Lateral inflow of surface water into the water balance area
Qso = Lateral outflow of surface water from the water balance area
A = Water balance area
Qgi = Total rate of groundwater inflow into the shallow unconfined aquifer.
Qgo = Total rate of groundwater outflow from the shallow unconfined aquifer
∆Wu = Change in soil water storage in the unsaturated zone during the
computation interval of an equivalent layer of water.
∆Ws = Change in surface water storage
µ = Specific yield or effective porosity, as a fraction of the volume of soil
∆h = Rise or fall of the water table during the computation interval.
Rennolls et al. (1980) formulated a first-order autoregressive model to describe the response
of water level in a borehole to a series of rainfall events. The mathematical model is of the form:
‫ݕ‬௧
∗
= λ ‫ݕ‬௧ିଵ ା ∝ ௫೟
∗
(3)

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and ‫ݕ‬௧ = ‫ݕ‬௧
∗
+ ݁௧ (4)
where
‫ݕ‬௧
∗
= actual water-table level
λ = a constant (drainage factor)
∝ = a factor depending on drainage pore space (constant)
xt = rainfall
yt = measured water-table level in the borehole.
(subscript t indicates on day “t”)
et = the difference between the actual water-table level and measured level in the
borehole.
Viswanathan (1983) observed that two implied assumptions in the model by Rennolls et al.
(1980) were too restrictive. The assumptions were that (i) λ and ∝, which represent the state of the
aquifer (including soil conditions) are constant, and (2) there is no time lag between the rainfall and
water-table level. The model was therefore modified by assuming that (1) the aquifer parameters are
time dependant, and (2) the water-table level rise on day “t” is a function of rainfall on days t, t-1, t-
2, …… etc Viswanathan’s model is of the form:
ℎ௧
∗
= λt ht-1 + ∝o, t Rt + ∝1,t Rt-1 + ∝2,t Rt-2 + ∝8,t Rt-8 + βt (5)
and ht = ℎ௧
∗
+ ߳t (6)
where
ℎ௧
∗
= estimated water level in the borehole above certain datum level (m)
ht = measured water level in the borehole (m)
Rt = rainfall (m)
߳t = error between estimated and actual water-table levels (m)
Subscript t indicates day “t”, while t-1, t-2……………… indicate days t-1, t-2, etc.
λt, ∝o,t, ∝1,t…………∝8,t, βt are model parameters considered as time-dependent variables.
߳t is assumed to have the following properties
(i) ‫ܧ‬ [߳௧ ] = 0
(ii) ‫ܧ‬ ൣ߳௧,୫ . ߳௧,୬ ൧ = ߪଶ
. ߜ୫,୬
Where
ߜ୫,୬ = 1 (m = n)
ߜ୫,୬ = 0 (m ≠n)
(iii) ߳௧ is dependent of ht-1, Rt,
Rt-1,……………Rt-8 (7)
Where E [ ] is the expected value
From the data obtained, the model was able to assert that most of the recharge due to rainfall
usually takes places within the first two days of the event. After two days, there is very little

5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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variation in the water-table level due to rainfall although there is a slight drop on the third, fourth and
fifth day, presumably due to the escape of entrapped air beneath the water-table level.
Description of the Study Area
The study was carried out at the Research Farm of the Rivers State University of Science and
Technology, Port Harcourt, in the Niger Delta Region of Nigeria. Port Harcourt is characterized by a
humid tropical climate with a mean annual rainfall of about 2100mm, and temperature that varies
between 24 and 300
C. The soil type is ultisol (USDA Classification) and its texture is loamy sand.
The experiment was conducted in a field, 50m x 50m that had been kept fallow for about six
months. It was divided into grids, 5m x 5m with two shallow wells dug 25m apart at the centre of
each 25m x 25m area. The upper part of each well was cemented, and 0.3m above ground level to
prevent entry of surface runoff.
Data Collection
The moisture content of the soil was determined by the gravimetric method. Soil samples
from each grid square was collected at random at a depth of 0.5m in air-tight polythene bags and
taken to the laboratory for analysis. In order to avoid depletion of the soil to an intolerable level,
samples were collected on a bi-monthly basis. This was done every second and last week of each
month, between January and December, 2013. Groundwater level measurements were made with
water tapes, while rainfall data were obtained from the Nigerian Meteorological station.
RESULTS AND DISCUSSION
Figure 1 presents the rainfall trend in the last ten years from 2004 to 2013.
Fig.1: Annual rainfall trend (2004-2013)

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The figure indicates that rainfall increased from 2004 to 2007, but drastically decreased in
2008. There was another increase in 2009 but this was followed by a continuous decline from 2010
to 2011. Although the rainfall increased again in 2012, there was a further decrease in 2013. This
trend does not however conform with the findings of Mbajiorgu (2013). According to this scientist,
the effects of global warming phenomenon on the terrestrial water balance include (i) higher rainfall
intensities i.e heavier rainfalls, and (ii) higher frequency of great floods with increasing trends in
runoff in humid areas. It is therefore obvious that these effects are yet to fully manifest in our study
area.
Mbajiorgu (2013) further posits that climate change is expected to impact water resources in
Nigeria and Africa through a decrease in both quality and quantity, threatening rain-fed agriculture.
This is particularly evident in the Niger Delta region of Nigeria, where farmers rely entirely on rain-
fed cropping. Hitherto, farmers used to commence planting in late February or early March.
However, in recent times, farmers have been compelled to shift the planting period to April or May
because of insufficient soil moisture in February and March. Figure 2 corroborates this assertion.
The figure shows that the minimum rainfall in 2013 occurred
Fig. 2: Monthly Average Rainfall, 2013
between August and March, although there was heavy rainfall in October. The most critical periods
were December and February, usually the driest period. Cline (2008) observes that beyond a certain
range of temperatures, warming tends to reduce yields because crops speed through their

7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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7
development, producing less grain in the process. Furthermore, high temperatures also interfere with
the ability of plants to get and use the water. On the whole, Figure 2 suggests that without irrigation,
no effective crop growth could have taken place between November and March under rain-fed
condition, taking into consideration the high surface runoff usually associated with rainfall in this
region. Fubara-Manuel (2005) also observed that in July 2003 and 2004, supplemental irrigation was
needed by maize for effective growth, even though July always witnessed one of the heaviest
rainfall.
Superimposed on Figure 3, the regression curve, is the regression equation which shows that
the mathematical relationship between soil moisture and groundwater level is of the form:
Y = - 4.5289 X + 22.672 (7)
Where
Y = soil moisture content (%)
X = groundwater level from the surface.
Fig. 3: Groundwater vs Soil moisture

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The general trend is that soil moisture content is inversely proportional to groundwater level
measured from the ground surface. The coefficient of retardance R2
is 0.8567. This indicates that
about 86% of the variation in soil moisture is explained or accounted for by variation in groundwater
level. This high value of R2
is desirable for forecasting purposes because the higher the value of R2
,
the smaller the value of the standard error of estimate.
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