# Statistical Analysis of Rainfall Trend for Volta Region in Ghana

Authors: M. Nyatuame; V. Owusu-Gyimah; F. Ampiaw
Journal: International Journal of Atmospheric Sciences
 (2014)

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## Abstract

Climate change is global in nature, but potential changes are not expected to be globally uniform; rather, there may be dramatic regional differences. Considerable effort should be invested to understand climate change at the regional level. The study was conducted to establish the rainfall trends in Volta Region and also to provide the evidence of climate change by analyzing available rainfall record for 30-year period of 1981 to 2011. Records of monthly and yearly rainfall were obtained from the headquarters of Ghana Meteorological Department, Accra, for analysis. The region was grouped into three zones characteristic of the whole country, namely, coastal zone, middle zone, and northern zone, respectively. Graphs were constructed to illustrate the changing trends within the months and years of the zones. Statistical analysis (i.e., LSD, ANOVA) was performed to assess any significant difference among the three zones and within the months and years under study. Significant differences were observed among the three zones. Northern zone recorded the highest precipitation followed by the middle zone and lastly the coastal zone. However the rainfall trends within the aforementioned zones were oscillatory. The highest annual mean rainfall was 202.6 mm and the lowest was 29.9 mm. Linear regression analysis revealed upward and downward trend in the data in some months and years in the mentioned zones but statistically insignificant.


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## Body

## 1. Introduction

Water is one of our most valuable natural resources and vital to all forms of life. Water is also used for transportation, is source of power, and serves many other useful purposes for domestic consumption, agriculture, and industry. The main important source of water in any area is rain. The amount or availability of water for various purposes is very much depending upon the amount of precipitation in that particular area. Excess or extended absence of rainfall will cause flooding and drought, respectively. Adler et al. [1] stated that precipitation information is essential for understanding the hydrologic balance on a global scale and for understanding the complex interactions among the components within the hydrologic cycle.The availability of adequate freshwater of appropriate quality has become a limiting factor for development worldwide [2]. In arid and semiarid regions of the world, water scarcity and low per capita water allocation were always a dominant challenge. The situation has further exacerbated due to increase in population and the associated expansion of urbanization and economic activities, all of which demand more water and thus impose a tremendous pressure on the inadequate water resources.Rainfall is the meteorological phenomenon that has the greatest impact on human activities and the most important environmental factor limiting the development of the semiarid regions [3]. Understanding rainfall variability is essential to optimally manage the scarce water resources that are under continuous stress due to the increasing water demands, increase in population, and the economic development [4].There are many aspects of water resources management including the optimal water allocation, quality assessment and preservation, and prediction of future water demands to strategize water utilization, planning, and decision making. As a preliminary step, these management aspects and others necessitate the characterization of the water sources in the area of interest. One of the established methods to carry out this assessment is through the statistical analysis of the spatial and temporal variability of rainfall. In regions that have heavy agricultural areas and undergo dense activities, water availability and shortage challenges are further exacerbated. In Ghana, many watersheds are under extreme stresses due to the climate changes and drought conditions that influence water availability in a negative manner when considering the increasing need to boost up the agricultural production rate [5].While climate change is global in nature, potential changes are not expected to be globally uniform; rather, there may be dramatic regional differences. Considerable effort should be invested to understand climate change at the regional level. Volta Region is one of the ten regions in Ghana (Figure1), and it is said to be a microcosm of Ghana. That is to say all the six ecological zones in Ghana are represented in Volta Region (Figure 2).Figure 1
Map of Ghana.Figure 2
Map of Volta Region.This situation has compelled the motivation for assessing the magnitude and variability of rainfall for Volta Region. Statistical analysis of rainfall records for long periods is essential to provide information about rainfall variability and to better manage the rain fed agricultural activities such that the impact of climate change as well as changes in land use can be realistically assessed.This paper carries out a statistical analysis of the long-term rainfall data for the Volta Region. The major objective of this work is to statistically analyze the temporal variation in annual and monthly rainfall data of Volta Region. This analysis is essential to provide input data for a management system and to enable the development of optimal water allocation policies and management strategies to bridge the gap between water needs and obtainable water supply under possible drought conditions. On an annual scale, the analysis will help in the evaluation of the total water budget of the water resources in the area. Monthly rainfall analysis can be used in the determination of the crop water requirements. The paper is organized as follows. Description of Volta Region is presented followed by the annual and monthly rainfall statistical analysis. Time series of annual and monthly rainfall data were studied and annual trends were extracted and conclusions are furnished.The Volta Region is located along the southern half of the eastern border of Ghana, which it shares with the Republic of Togo. Greater Accra, Eastern, and Brong Ahafo regions share boundaries with it on the west, on the north by the Northern Region, and on the south by the Gulf of Guinea. The region occupies an area of about 20,570 square kilometres or 8.6 per cent of the total land area of Ghana [6].The region has a length of about 500 kilometres, stretching from the south to the north. It encompasses most of the vegetation zones found in the country, that is, the coastal grassland and mangrove swamps, replete with sandy beaches, the Guinea savannah through moist semideciduous forests in the central highland areas to the undulating Sahel-savannah, and the mountainous wooded savannah in the north [6].As in all other parts of the country, the Volta Region has a tropical climate, characterised by moderate temperatures, 21–32° Celsius (70–90°F), for most of the year. The region has two rainfall regimes in the year; the first is from March to July and the second is from mid-August to October. Rainfall figures, which vary greatly throughout the region, are highest in the central highland areas and in the forest zone; they are lowest in the Sahel-savannah zone in the north of the region. The maximum average annual rainfall figure is 2,103 mm and 1,168 mm, minimum. More than half of the land area of the region falls within the Volta River Basin, with the Volta Lake draining a substantial portion of the region [6]. The region’s mountains form part of the Togo Range, which stretches from parts of the Ashanti and Eastern Regions into the Republic of Togo. The highest mountain in Ghana, Mount Afadjato (Avadzeto), located in the Hohoe District, is part of this range. This mountain, together with several picturesque physical features such as the Wli waterfalls, near Mountain Gemi (Amedzofe), and the monkey sanctuary in Tafi (Hohoe district) are some of the region’s tourist attractions [6].


## 2. Materials and Methods

Monthly rainfall data were obtained from the Ghana Meteorological Department on Volta Region. Volta Region was used in the study because it represents the entire climatic scope of Ghana. The six ecological zones in Ghana are represented in the Volta Region, hence the saying that Volta Region is the microcosm of Ghana. The data obtained cover the period of 1981 to 2011 and the Volta Region was grouped into three zones, namely, coastal, middle, and northern zones, respectively. Statistical analyses were performed to assess any significant difference among the three zones and within the months and years under study on the data and graphs were constructed to illustrate the changing trends within the months and the years for the period. The statistical analysis was used to determine the measure of central tendency (mean, range, etc.) and dispersion (S.D., CV, etc.). For identifying the trend in the rainfall data, the statistical analysis of linear regression was used.Linear regression is one of the simplest methods to calculate the trend of data in time series. The equation of linear regression line is given byY=a+bX, where X is the independent variable and Y is the dependent variable. The slope line is b and a is the intercept (value of Y when X=0). The slope of regression describes the trend whether positive or negative. In this study dependent variable Y is rainfall and independent variable X is year. Linear regression requires the assumption of normal distribution. In this study, the null hypothesis is that the slope of the line is zero or there is no trend in the data. The significance of the slope is shown by the probability value (P value) of it. Microsoft Excel was used to calculate the lines and statistical values of linear regression analysis. The P value from the analysis is the test for the significant level α=0.05.The value ofR-square (R2) or the square of the correlation from the regression analysis was used to show how strong the correlation and relationship between the variables X and Y are. The value is a fraction between 0.0 and 1.0. An R2 value of 1.0 means that the correlation becomes strong and all points lie on a straight line. On the other hand, an R2 value of 0.0 means that there is no correlation and no linear relationship between X and Y.


## 3. Results and Discussion

### 3.1. Hypothesis Testing

H0:
there is no significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years.
H1:
there is significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years.Table1 shows an ANOVA to determine whether significant difference existed in the mean annual rainfall among the three climatic zones in the region. The results indicated that the difference in annual rainfall among the zones was highly significant (F=42.55, P=0.000). The hypothesis that there is no significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years is therefore rejected.Table 1
Analysis of variance of mean annual rainfall among coastal, middle, and northern zones of Volta Region in Ghana from 1981 to 2011.
Sum of squares
Df
Mean square
F
P value
Between groups
36877.748
2
18438.874
42.55
.000
Within groups
37699.022
87
433.322
Total
74576.770
89
P
≤
0.001.To determine which of the zones actually differed in terms of mean annual rainfall, the multiple mean comparisons were performed using LSD (the LSD was used because the ANOVA revealed that there were differences in the climatic zones). The results in Table2 indicated that the mean difference in annual rainfall among the zones was highly significant, except that of northern and middle zones. Here the mean difference in annual rainfall observed over the period in the two zones was not statistically significant (mean diff. = 7.673 mm, P=0.157).Table 2
LSD multiple comparisons of mean annual rainfall of the climatic zones in Volta Region from 1981 to 2011.
Zones
(J) zone
Mean difference (I-J)
P value
95% confidence interval
Lower bound
Upper bound
Northern zone
Middle zone
7.673
.157
−3.01
18.3556
Coastal  zone
46.260*
.000
35.57
56.9426
Middle zone
Northern zone
−7.673
.157
−18.35
3.0103
Coastal zone
38.587*
.000
27.90
49.2699
Coastal  zone
Northern zone
−46.260*
.000
−56.94
−35.5767
Middle zone
−38.587*
.000
−49.26
−27.9040
*The mean difference is significant at the 0.05 level.From Figure3 it is evident that the annual rainfall among the zones under consideration could best be described as oscillatory. The trend is not regular but irregular. However comparing the three zones, it can be observed that the middle zone trend is more regular than the rest. Additionally, the northern zone has the highest oscillatory trend of rainfall. The higher precipitation recorded in the northern zone generally could be attributed to the mountainous nature of the area, coupled with thick forests and also the Volta River which supply the bulk of the atmospheric moisture for precipitation. The low rainfall at coastal zone could be attributed to the vegetationless nature of the area. The loss of vegetation in these areas, compared to that of forest and mountainous areas, reduces natural cooling provided by evapotranspiration, the process through which intercepted radiation is utilized by plants, soils, and water bodies to convert water to water vapour [7]. This water vapour rises to the upper atmosphere, condenses, and eventually falls as rain. However, [8, 9] averred that since rainfall in the tropics is extremely variable in both space and time, identifying the precise cause of fluctuations remains problematic.Figure 3
Fluctuation of rainfall for the three zones (1981–2011).From Table3, the year with the highest annual rainfall was 1991, which recorded an amount of 1298.1 mm with a corresponding highest mean value of 108.2 mm. The record indicated the standard deviation correlating the highest annual rainfall was 148.9 mm and the data was skewed right, meaning the rainfall distribution is flat. However, the maximum annual rainfall standard deviation occurred in 1997, with a value of 168.08 mm, meaning the rainfall was highly dispersed or there was inconsistency in the rainfall pattern in 1997, with the corresponding highest range value. This observation again was buttressed by the highest variance and coefficient of variation figures recorded, respectively. According to Dewar and Wallis [10], the variation of CV values indicates the existence of strong variability in the rainfall of the study area. Nonetheless the maximum monthly rainfall occurred in 1997 in June. In addition, the lowest annual rainfall occurred in 1992 with an amount of 359.2 mm and a corresponding annual mean value of 29.9 mm.Table 3
Descriptive statistics of annual rainfall data of coastal zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
Kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
899.4
75.0
43.2
81.4
6634.9
1.1
−0.3
1.1
219.6
218.5
1982
1247.5
104.0
60.6
139.7
19519.8
1.7
2.9
0.0
457.3
457.3
1983
539.7
45.0
11.2
65.7
4324.2
1.4
0.9
0.0
183.2
183.2
1984
726.9
60.6
23.8
76.4
5851.3
1.3
0.5
0.0
210.3
210.3
1985
665.6
55.5
36.0
60.6
3680.5
1.5
2.5
0.0
206.8
206.8
1986
495.8
41.3
32.0
42.4
1798.2
0.7
−0.4
0.0
127.6
127.6
1987
931.0
77.6
27.8
102.1
10438.4
1.7
3.1
0.0
339.9
339.9
1988
798.3
66.5
72.1
51.1
2614.5
−0.1
−1.5
0.0
143.2
143.2
1989
949.9
79.2
43.9
82.7
6847.9
0.5
−1.4
0.0
213.8
213.8
1990
655.9
54.7
46.6
47.2
2236.4
0.5
−1.0
0.0
131.7
131.7
1991
1298.1
108.2
30.8
148.9
22176.2
1.4
0.9
0.0
443.5
443.5
1992
359.2
29.9
10.4
51.1
2614.6
2.5
6.7
0.0
176.5
176.5
1993
759.3
63.3
64.9
44.8
2008.1
0.1
−0.9
0.0
132.3
132.3
1994
700.9
58.4
37.5
66.1
4365.8
1.4
1.4
0.0
207.9
207.9
1995
859.2
71.6
31.5
94.1
8858.3
2.0
4.2
0.0
321.1
321.1
1996
992.1
82.7
36.5
103.9
10793.1
1.1
0.0
0.0
283.8
283.8
1997
1191.2
99.3
29.0
168.1
28252.3
2.7
8.3
0.0
598.3
598.3
1998
484.4
40.4
14.1
58.3
3399.8
1.7
2.4
0.0
183.6
183.6
1999
716.0
59.7
31.9
74.7
5590.8
1.6
1.5
2.8
223.6
220.8
2000
394.3
32.9
21.9
34.8
1213.3
0.7
−0.7
0.0
100.1
100.1
2001
779.2
64.9
23.7
74.7
5587.9
0.7
−1.4
0.0
189.4
189.4
2002
842.6
70.2
45.6
89.8
8065.9
2.1
4.9
0.0
315.3
315.3
2003
1061.9
88.5
30.9
131.8
17377.8
2.1
4.7
3.5
446.4
442.9
2004
698.4
58.2
49.1
53.9
2904.5
0.6
−0.9
0.0
147.3
147.3
2005
790.8
65.9
57.9
61.9
3841.2
0.3
−1.6
0.0
157.3
157.3
2006
746.0
62.2
36.7
67.9
4617.8
0.9
−0.1
0.0
202.4
202.4
2007
897.1
74.8
56.5
71.2
5077.8
1.0
0.7
0.0
232.0
232.0
2008
767.3
63.9
39.6
71.4
5108.2
1.5
1.4
0.0
213.2
213.2
2009
1070.0
89.2
27.7
139.8
19570.4
2.2
5.5
0.2
477.3
477.1
2010
957.4
79.8
78.5
73.6
5416.9
0.6
−0.4
0.0
224.3
224.3
2011
893.5
74.5
57.2
86.7
7522.1
1.4
2.1
0.0
285.7
285.7In Table4, it can be inferred that the maximum annual rainfall of 1747.6 mm and the corresponding mean of 145.6 mm occurred in 1999 for the period under consideration. The minimum annual rainfall occurred in 1992 (808.1 mm) and the maximum annual standard deviation of 124 mm happened in 2004. The high standard deviation value can be easily correlated with the high rainfall range. The rainfall range signifies the difference between the maximum and minimum annual rainfall. The standard deviation and the range indicate the variability of annual rainfall and hence denote how reliable the rainfall is in terms of its persistence as constant and stable replenishing source. To test whether the annual rainfall data follow a normal distribution, the skewness and kurtosis were computed. Skewness is a measure of symmetry or, more precisely, the lack of symmetry. The data set is said to be symmetric if it looks the same to the left and right from the center point. The skewness for a normal distribution is zero, and any symmetric data should have skewness near zero. Negative values for the skewness indicate that data are skewed to the left and positive values for the skewness indicate that data are skewed to the right.Table 4
Descriptive statistics of annual rainfall of middle zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
Kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
1346.7
112.2
95.7
94.9
9013.6
1.4
1.4
0.0
319.8
319.8
1982
1141.2
95.1
90.5
61.5
3788.0
1.1
0.6
30.7
230.1
199.4
1983
1010.2
84.2
90.5
66.9
4482.4
−0.1
−2.1
0.0
163.4
163.4
1984
1337.2
111.4
120.9
92.0
8470.2
0.1
−1.4
0.0
265.7
265.7
1985
1338.4
111.5
125.3
78.7
6202.6
0.4
1.0
2.8
283.6
280.8
1986
1228.1
102.3
108.8
76.5
5855.3
0.0
−1.4
0.0
212.7
212.7
1987
1409.0
117.4
122.0
89.5
8021.7
0.1
−1.1
7.7
254.1
246.4
1988
1382.2
115.2
109.2
65.7
4319.9
0.1
−1.3
21.4
223.1
201.7
1989
1408.5
117.4
130.8
101.9
10382.0
0.8
1.0
0.0
346.4
346.4
1990
1167.7
97.3
109.3
71.7
5143.3
0.4
−0.8
14.6
224.7
210.1
1991
1415.2
117.9
102.4
93.3
8708.8
0.8
0.7
3.1
325.4
322.3
1992
808.1
67.3
66.4
48.7
2380.7
0.3
−0.1
0.0
164.2
164.2
1993
1184.8
98.7
94.8
57.5
3308.8
0.0
−0.2
0.0
204.2
204.2
1994
990.0
82.5
66.0
69.9
4887.3
1.2
1.1
0.0
239.9
239.9
1995
1315.0
109.6
119.6
71.8
5166.8
−0.2
−1.3
0.0
209.8
209.8
1996
1333.8
111.2
86.4
86.7
7526.9
0.9
0.2
5.1
282.9
277.8
1997
1322.7
110.2
95.9
79.4
6314.1
0.3
−1.2
13.7
248.6
234.9
1998
1140.3
95.0
89.8
67.2
4524.6
0.8
0.6
0.3
242.4
242.1
1999
1747.6
145.6
119.5
113.3
12859.2
0.7
−0.1
0.5
374.4
373.9
2000
1220.8
101.7
94.8
70.4
4967.6
0.2
−1.6
10.6
194.8
184.2
2001
1076.4
89.7
84.1
73.0
5338.1
0.1
−1.5
0.0
192.9
192.9
2002
1300.3
108.4
119.4
61.8
3822.2
−0.5
−1.3
6.7
175.3
168.6
2003
1289.4
107.5
79.2
92.4
8550.8
1.2
1.3
10.6
324.9
314.3
2004
1468.5
122.4
102.3
124.0
15380.9
2.0
4.5
3.9
454.2
450.3
2005
1148.7
95.7
68.6
55.8
3121.1
0.5
−1.5
41.2
185.6
144.4
2006
1161.7
96.8
69.7
88.5
7835.3
1.2
0.8
5.0
289.2
284.2
2007
1491.7
124.3
125.4
90.1
8120.3
0.1
−1.1
0.2
262.0
261.8
2008
1551.5
129.3
141.1
78.7
6198.5
−0.3
−1.1
0.0
239.0
239.0
2009
1106.6
92.2
87.4
66.5
4425.1
0.6
−0.2
0.0
224.0
224.0
2010
1324.4
110.4
96.9
78.6
6192.1
0.2
−1.6
6.0
227.0
221.0
2011
1168.8
116.9
133.3
57.3
3286.7
−0.8
0.7
0.0
197.2
197.2Kurtosis is a measure of data peakedness or flatness relative to a normal distribution. That is, data sets with a high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. The standard normal distribution has a kurtosis of zero. Positive kurtosis indicates a peaked distribution and negative kurtosis indicates a flat distribution. Hence the annual rainfall distribution under consideration did not follow normal distribution.As can be observed from Table5 the maximum annual rainfall for the period under review occurred in 1991 (2431.5 mm) with corresponding maximum annual mean and standard deviation of 202.6 mm and 182.8 mm, respectively. The standard deviation is a measure of dispersion. A small value indicates that the data is tightly grouped about the mean. A high value indicates that the data is spread widely on either side of the mean. A high standard deviation also suggests that year-to-year fluctuations are high while a low standard deviation indicates that fluctuations are lower. In other words, rainfall with a high standard deviation is considered more volatile than rainfall with a low figure. The minimum annual rainfall occurred in 2001 with an amount of 915.6 mm for the years under consideration.Table 5
Descriptive statistics of annual rainfall of northern zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
1241.6
103.5
83.7
96.4
9298.6
0.2
−1.8
0.0
239.4
239.4
1982
1071.8
89.3
99.6
68.1
4642.2
0.1
−1.0
0.0
204.8
204.8
1983
1060.7
88.4
60.9
95.2
9068.9
0.8
−0.6
0.0
273.9
273.9
1984
1735.2
144.6
77.1
150.6
22682.2
0.6
−1.3
0.0
384.1
384.1
1985
1336.8
111.4
83.0
112.5
12659.3
0.5
−1.6
0.0
284.0
284.0
1986
1370.1
114.2
108.6
97.8
9571.7
−0.0
−2.0
0.0
229.2
229.2
1987
1351.4
112.6
84.8
126.5
16004.2
1.1
0.8
0.0
398.1
398.1
1988
1064.4
88.7
56.2
88.4
7825.1
0.6
−1.2
0.0
246.2
246.2
1989
1479.5
123.3
23.4
161.7
26155.4
1.1
−0.2
0.0
430.2
430.2
1990
1336.7
111.4
114.4
97.7
9553.3
0.4
−0.8
0.0
296.5
296.5
1991
2431.5
202.6
179.6
182.8
33425.1
0.3
−1.4
0.0
498.1
498.1
1992
970.7
88.2
58.9
88.7
7872.5
0.7
−0.4
0.0
257.4
257.4
1993
1003.2
83.6
44.8
95.1
9052.5
1.5
2.1
0.0
316.3
316.3
1994
1197.9
99.8
116.8
93.7
8780.1
0.0
−1.9
0.0
226.9
226.9
1995
1680.8
140.1
145.6
125.7
15821.9
0.2
−1.4
0.0
350.4
350.4
1996
1539.8
128.3
149.1
119.2
14226.2
−0.1
−2.1
0.0
274.6
274.6
1997
1387.9
115.7
84.8
107.8
11635.4
0.4
−1.5
0.0
277.2
277.2
1998
982.5
89.3
60.3
81.1
6583.3
0.2
−1.7
0.0
205.5
205.5
1999
1580.8
131.7
64.9
142.4
20300.0
0.8
−0.9
0.0
394.4
394.4
2000
1375.6
114.6
85.0
109.4
11972.7
0.5
−1.3
0.0
293.2
293.2
2001
915.6
76.3
38.7
100.1
10016.8
1.3
0.7
0.0
291.8
291.8
2002
1453.8
121.2
155.1
97.7
9550.9
−0.2
−1.8
0.0
240.7
240.7
2003
1423.5
118.6
95.0
110.0
12101.4
0.9
−0.5
0.7
314.0
313.3
2004
1500.6
125.1
109.4
110.2
12157.7
0.6
−0.8
0.0
322.8
322.8
2005
1498.8
124.9
95.7
121.3
14727.5
1.0
0.1
0.0
374.3
374.3
2006
1033.3
86.1
62.7
96.5
9314.4
1.2
0.7
0.4
284.6
284.2
2007
1148.6
95.7
89.1
76.3
5820.8
0.1
−1.6
0.0
208.9
208.9
2008
1853.5
154.5
133.6
151.0
22802.6
0.8
0.2
0.0
479.1
479.1
2009
1617.5
134.8
139.1
109.4
11981.1
0.1
−1.7
0.0
294.7
294.7
2010
1107.2
92.3
86.3
82.0
6729.4
0.6
−0.3
0.0
244.5
244.5It is evident from Table6 that the coefficient of variation for the months of April through July (major season) is less than 0.5 which indicates lower variability from the mean and similar observation is made for the months of September and October (minor season). The low coefficient of variability recorded for the aforementioned months is an indication of highly dependable rainfall. Reference [11] stated that the CV is an indication of the degree of precision to which the treatments are compared and is a good index of the reliability of the experiment. Reference [11] further indicated that the higher the CV value, the lower the reliability of the experiment.Table 6
Statistical summary of monthly rainfall data of middle zone.
Parameter (mm)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean
18.2
52.7
102.3
133.3
154.9
182.1
132.2
94.6
163.2
160.3
47.3
30.4
Median
8.2
43.5
100.2
132.0
147.9
165.1
120.0
84.4
164.2
154.8
42.0
21.6
S.D.
22.2
44.8
59.6
57.2
66.8
78.3
58.2
66.4
79.5
52.9
32.3
32.2
Variance
490.9
2009.3
3553.4
3274.6
4460.5
6127.1
3384.8
4403.6
6332.2
2801.6
1041.9
1039.6
Skewness
1.1
2.0
0.8
−0.1
0.7
0.9
0.5
0.7
1.5
0.9
1.4
0.9
Kurtosis
0.4
4.9
0.5
−0.2
0.2
0.2
0.1
−0.3
4.9
1.5
1.7
−0.2
Min
0.0
5.8
20.3
6.9
35.5
74.4
30.2
9.4
47.5
77.4
5.8
0.0
Max
78.4
212.7
265.7
255.6
325.4
374.4
283.6
254.1
454.2
319.8
133.8
103.4
Range
78.4
206.9
245.4
248.7
289.9
300.0
253.4
244.7
406.7
242.4
128.0
103.4
Sum
564.0
1632.8
3169.9
4132.9
4800.7
5645.0
4097.1
2933.1
5060.3
4968.1
1419.8
911.8
CV
1.2
0.9
0.6
0.4
0.4
0.4
0.4
0.7
0.4
0.3
0.6
1.0The standard deviation is one way of summarizing the spread of a probability distribution; it relates directly to the degree of uncertainty associated with predicting the value of a random variable. High values reflect more uncertainty than low values. Table6 clearly revealed that September in middle climatic zone had the highest standard deviation. The highest amount of average monthly rainfall was recorded in June (182.1 mm) and contributed to 14.3% of annual rainfall, followed by September with 12.8%, and the lowest was in January with 1.4% of annual total followed by December with 2.3%. From the analysis, it was observed that rainfall is usually at its peak between April and July in the major season and between September and October in the minor season.The precipitation changes from month to month are considerable in years. When the standard deviation values are examined, it is observed that the standard deviation values of most months (January, February, July, August, September, and December) are higher than the averages of these months (See Table7). This relation between the standard deviation and the average values indicates that the deviation from the normal distribution cannot be ignored. This fact is especially supported by the coefficients of variation of these months which are over one or close to one. These show that, in coastal zones, the precipitation values are much different from the average. The fact that the CV values are so high is an indication of the rainfall being highly variable and not dependable or reliable or can be attributed to the length of data set being used or the quality of data.Table 7
Statistical summary of monthly rainfall data of coastal zone.
Parameters
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean (mm)
3.3
23.2
61.0
107.3
150.4
206.2
64.9
19.8
56.0
78.7
29.9
11.2
Median (mm)
0.0
11.2
49.0
86.7
145.7
174.2
44.2
10.8
33.9
65.2
22.0
2.5
S.D. (mm)
6.1
30.8
45.8
67.8
60.4
138.5
87.6
31.7
71.0
63.2
29.0
18.3
Variance (mm)
36.8
950.2
2098.5
4606.9
3645.8
19185.3
7675.3
1005.1
5050.3
3997.5
841.2
336.0
Skewness
2.2
1.4
0.7
1.2
0.0
1.2
3.0
3.2
2.5
0.6
0.8
2.6
Kurtosis
4.8
0.9
−0.0
1.9
−0.5
1.1
11.4
12.9
7.7
−0.8
−0.1
6.9
Min (mm)
0.0
0.0
0.0
18.3
34.5
47.0
1.2
0.0
0.0
0.5
0.0
0.0
Max (mm)
22.6
96.3
181.1
324.7
269.6
598.3
443.5
160.6
339.9
210.9
107.6
77.7
Range (mm)
22.6
96.3
181.1
306.4
235.1
551.3
442.3
160.6
339.9
210.4
107.6
77.7
Sum (mm)
102.0
719.5
1890.7
3325.0
4663.9
6391.7
2012.5
612.4
1735.9
2440.0
928.3
347.0
CV
1.8
1.3
0.7
0.6
0.4
0.6
1.3
1.6
1.2
0.8
0.9
1.6The lower the coefficient of variation of rainfall amount in any month, the lower the variability and the greater the dependability. Coefficient of variation values less than 0.5 shows lower variability from the mean. Table8 reveals that from June to September the rainfall variability is low and therefore highly dependable. Considering the coefficient of variation, September shows the minimum variation from year to year, compared to the rest of the months. However, since the coefficients of variation of each of the four months (June–September) are less than 0.5, the changes of precipitation from year to year in these months are low. September is the month with the highest mean monthly rainfall of 252.3 mm followed by August with 227.6 mm. Incidentally the above mentioned months traditionally fall within the minor season which usually records lower rainfall. This change in the rainfall season could be attributed to the so-called climate change. The month with the lowest rainfall is December (7.6 mm) followed by January (7.7 mm).Table 8
Statistical summary of monthly rainfall data of northern zone.
Parameter
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean (mm)
7.7
11.1
38.2
93.9
128.8
217.2
210.9
227.6
252.3
142.5
22.2
7.6
Median (mm)
0.0
0.3
35.2
82.3
125.4
213.5
201.9
243.6
235.2
119.8
6.3
0.7
S.D. (mm)
16.0
19.6
31.6
61.3
80.0
83.4
94.0
80.3
70.3
93.9
31.1
16.0
Variance (mm)
255.1
383.7
1000.6
3756.6
6394.8
6952.4
8831.9
6445.9
4947.0
8812.8
964.4
255.3
Skewness
2.1
1.8
0.7
0.9
1.2
0.5
1.7
−0.3
0.9
1.3
1.6
2.8
Kurtosis
3.8
1.8
0.1
0.4
3.1
0.2
3.6
−0.5
0.0
2.4
2.1
7.4
Min (mm)
0.0
0.0
0.0
7.3
6.0
93.6
91.7
73.0
146.8
9.2
0.0
0.0
Max (mm)
60.0
65.7
117.3
245.6
398.6
430.2
498.1
373.5
400.6
440.7
112.0
66.1
Range (mm)
60.0
65.7
117.3
238.3
392.6
336.6
406.4
300.5
253.8
431.5
112.0
66.1
Sum (mm)
231.6
323.3
1107.5
2817.5
3864.7
6516.0
6326.4
6827.3
7567.5
4274.7
665.9
228.9
CV
2.1
1.7
0.8
0.6
0.6
0.3
0.4
0.3
0.2
0.6
1.3
2.1The results of the linear regression trend analysis are presented in Tables9, 10, and 11, respectively, covering northern, middle, and coastal zones, respectively, of the Volta Region. In these trend tests, trend of rainfall for 30 years from January to December has been computed for each month independently.Table 9
Regression statistic results for annual and monthly rainfall for northern zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y = 0.35X  − 681.8
0.04
0.32
No
Feb
Y = 0.30X  − 592.4
0.02
0.47
No
Mar
Y = 0.19X  − 355.3
0.00
0.80
No
April
Y = 1.19X  − 2285.5
0.03
0.38
No
May
Y =  −2.06X + 4231.2
0.05
0.22
No
June
Y =  −1.73 + 3672.1
0.03
0.30
No
July
Y = 0.91X  − 1596.4
0.01
0.69
No
Aug
Y = 0.68X  − 1126.2
0.01
0.75
No
Sept
Y =  −0.57X + 1392.3
0.01
0.65
No
Oct
Y = 1.73X  − 3318.1
0.03
0.41
No
Nov
Y = 1.05X  − 2064.5
0.09
0.12
No
Dec
Y = 0.47X  − 927.3
0.07
0.17
No
Annual
Y = 2.51X  − 3651.9
0.00
0.80
NoTable 10
Regression statistic results for annual and monthly rainfall for central zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y = 0.31X  − 609.8
0.02
0.50
No
Feb
Y = 0.34X  − 629.0
0.00
0.73
No
Mar
Y =  −0.99X + 2095.1
0.02
0.39
No
April
Y = 1.49X  − 2856.9
0.06
0.22
No
May
Y =  −1.53X + 3212.6
0.04
0.24
No
June
Y = 2.33X  − 4486.8
0.07
0.15
No
July
Y =  −0.97X + 2080.8
0.02
0.38
No
Aug
Y =  −0.47X + 1041.2
0.00
0.70
No
Sept
Y = 2.74X  − 5315.2
0.09
0.09
No
Oct
Y =  −0.72X + 1594.7
0.02
0.46
No
Nov
Y =  −0.27X + 599.3
0.01
0.67
No
Dec
Y = 0.22X  − 412.0
0.00
0.77
No
Annual
Y = 2.02X  − 2760.5
0.01
0.71
NoTable 11
Regression statistic results for annual and monthly rainfall for coastal zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y
=
0.80
X
-
154.7
0.01
0.53
No
Feb
Y
=
0.90
X
-
1774.88
0.07
0.15
No
Mar
Y
=
-
1.16
X
+
2384.64
0.05
0.20
No
April
Y
=
-
0.35
X
+
811.97
0.00
0.77
No
May
Y
=
-
0.87
X
+
1881.74
0.02
0.45
No
June
Y
=
3.38
X
-
6540.3
0.05
0.24
No
July
Y
=
-
1.65
X
+
3357.27
0.03
0.35
No
Aug
Y
=
0.32
X
-
617.20
0.01
0.64
No
Sept
Y
=
-
0.04
X
+
132.05
0.00
0.96
No
Oct
Y
=
1.66
X
-
3234.97
0.06
0.21
No
Nov
Y
=
-
0.26
X
+
545.28
0.01
0.65
No
Dec
Y
=
0.18
X
-
353.72
0.01
0.64
No
Annual
Y
=
2.19
X
-
3562.80
0.01
0.70
NoThe linear trend lines of the monthly rainfall indicated a downward trend in May, June, and September and an upward trend for other months and annual rainfall data for the northern zone. Since the probability value (P value) from the regression analysis for the slopes of the monthly and annual trend lines was greater than the significant level α=0.05, the null hypothesis (Ho: there is no trend in the data, fail to reject. That means there is no statistically significant trend in the annual and monthly rainfall data for northern zone. Additionally, the R-square statistic also indicated a very weak relationship between the variables, rainfall, and year.Table10 revealed downward trends in the rainfall for the months of March, May, July, October, and November and the rest of the months recorded upward trend in the rainfall data for the middle zone. However, the trends are not statistically significant. This argument is buttressed by the P values of the linear regression analysis being greater than α=0.05.Annual rainfall for coastal zone showed upward trend; however, there is a decreasing trend in the months of March, April, May, July, September, and November and the rest of the months of the year revealed an increasing trend. Again, these trends are insignificant statistically as indicated by theP values.Figure4 clearly reveals that for the period under consideration for middle zone the highest mean monthly rainfall was recorded in June and the lowest in January. It is also evident from the graph that the highest average minor season rainfall occurred in September.Figure 4
Average monthly rainfall for the three zones from 1981 to 2010.For the northern zone the highest average monthly rainfall for the period under review as indicated in Figure4 was recorded in September which is a minor season for the northern climatic zone. The result clearly indicated that the peak mean monthly rainfall in the minor season was more than the major season which suggested a discrepancy. However, this could be attributed to climate change effects.The graph for coastal zone revealed that December and January were the driest months. The highest rainfall occurred in June for the major season while the highest corresponding minor season rainfall was recorded in October.


## 3.1. Hypothesis Testing

H0:
there is no significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years.
H1:
there is significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years.Table1 shows an ANOVA to determine whether significant difference existed in the mean annual rainfall among the three climatic zones in the region. The results indicated that the difference in annual rainfall among the zones was highly significant (F=42.55, P=0.000). The hypothesis that there is no significant difference in the mean annual rainfall among the climatic zones in the Volta Region over the period of thirty years is therefore rejected.Table 1
Analysis of variance of mean annual rainfall among coastal, middle, and northern zones of Volta Region in Ghana from 1981 to 2011.
Sum of squares
Df
Mean square
F
P value
Between groups
36877.748
2
18438.874
42.55
.000
Within groups
37699.022
87
433.322
Total
74576.770
89
P
≤
0.001.To determine which of the zones actually differed in terms of mean annual rainfall, the multiple mean comparisons were performed using LSD (the LSD was used because the ANOVA revealed that there were differences in the climatic zones). The results in Table2 indicated that the mean difference in annual rainfall among the zones was highly significant, except that of northern and middle zones. Here the mean difference in annual rainfall observed over the period in the two zones was not statistically significant (mean diff. = 7.673 mm, P=0.157).Table 2
LSD multiple comparisons of mean annual rainfall of the climatic zones in Volta Region from 1981 to 2011.
Zones
(J) zone
Mean difference (I-J)
P value
95% confidence interval
Lower bound
Upper bound
Northern zone
Middle zone
7.673
.157
−3.01
18.3556
Coastal  zone
46.260*
.000
35.57
56.9426
Middle zone
Northern zone
−7.673
.157
−18.35
3.0103
Coastal zone
38.587*
.000
27.90
49.2699
Coastal  zone
Northern zone
−46.260*
.000
−56.94
−35.5767
Middle zone
−38.587*
.000
−49.26
−27.9040
*The mean difference is significant at the 0.05 level.From Figure3 it is evident that the annual rainfall among the zones under consideration could best be described as oscillatory. The trend is not regular but irregular. However comparing the three zones, it can be observed that the middle zone trend is more regular than the rest. Additionally, the northern zone has the highest oscillatory trend of rainfall. The higher precipitation recorded in the northern zone generally could be attributed to the mountainous nature of the area, coupled with thick forests and also the Volta River which supply the bulk of the atmospheric moisture for precipitation. The low rainfall at coastal zone could be attributed to the vegetationless nature of the area. The loss of vegetation in these areas, compared to that of forest and mountainous areas, reduces natural cooling provided by evapotranspiration, the process through which intercepted radiation is utilized by plants, soils, and water bodies to convert water to water vapour [7]. This water vapour rises to the upper atmosphere, condenses, and eventually falls as rain. However, [8, 9] averred that since rainfall in the tropics is extremely variable in both space and time, identifying the precise cause of fluctuations remains problematic.Figure 3
Fluctuation of rainfall for the three zones (1981–2011).From Table3, the year with the highest annual rainfall was 1991, which recorded an amount of 1298.1 mm with a corresponding highest mean value of 108.2 mm. The record indicated the standard deviation correlating the highest annual rainfall was 148.9 mm and the data was skewed right, meaning the rainfall distribution is flat. However, the maximum annual rainfall standard deviation occurred in 1997, with a value of 168.08 mm, meaning the rainfall was highly dispersed or there was inconsistency in the rainfall pattern in 1997, with the corresponding highest range value. This observation again was buttressed by the highest variance and coefficient of variation figures recorded, respectively. According to Dewar and Wallis [10], the variation of CV values indicates the existence of strong variability in the rainfall of the study area. Nonetheless the maximum monthly rainfall occurred in 1997 in June. In addition, the lowest annual rainfall occurred in 1992 with an amount of 359.2 mm and a corresponding annual mean value of 29.9 mm.Table 3
Descriptive statistics of annual rainfall data of coastal zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
Kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
899.4
75.0
43.2
81.4
6634.9
1.1
−0.3
1.1
219.6
218.5
1982
1247.5
104.0
60.6
139.7
19519.8
1.7
2.9
0.0
457.3
457.3
1983
539.7
45.0
11.2
65.7
4324.2
1.4
0.9
0.0
183.2
183.2
1984
726.9
60.6
23.8
76.4
5851.3
1.3
0.5
0.0
210.3
210.3
1985
665.6
55.5
36.0
60.6
3680.5
1.5
2.5
0.0
206.8
206.8
1986
495.8
41.3
32.0
42.4
1798.2
0.7
−0.4
0.0
127.6
127.6
1987
931.0
77.6
27.8
102.1
10438.4
1.7
3.1
0.0
339.9
339.9
1988
798.3
66.5
72.1
51.1
2614.5
−0.1
−1.5
0.0
143.2
143.2
1989
949.9
79.2
43.9
82.7
6847.9
0.5
−1.4
0.0
213.8
213.8
1990
655.9
54.7
46.6
47.2
2236.4
0.5
−1.0
0.0
131.7
131.7
1991
1298.1
108.2
30.8
148.9
22176.2
1.4
0.9
0.0
443.5
443.5
1992
359.2
29.9
10.4
51.1
2614.6
2.5
6.7
0.0
176.5
176.5
1993
759.3
63.3
64.9
44.8
2008.1
0.1
−0.9
0.0
132.3
132.3
1994
700.9
58.4
37.5
66.1
4365.8
1.4
1.4
0.0
207.9
207.9
1995
859.2
71.6
31.5
94.1
8858.3
2.0
4.2
0.0
321.1
321.1
1996
992.1
82.7
36.5
103.9
10793.1
1.1
0.0
0.0
283.8
283.8
1997
1191.2
99.3
29.0
168.1
28252.3
2.7
8.3
0.0
598.3
598.3
1998
484.4
40.4
14.1
58.3
3399.8
1.7
2.4
0.0
183.6
183.6
1999
716.0
59.7
31.9
74.7
5590.8
1.6
1.5
2.8
223.6
220.8
2000
394.3
32.9
21.9
34.8
1213.3
0.7
−0.7
0.0
100.1
100.1
2001
779.2
64.9
23.7
74.7
5587.9
0.7
−1.4
0.0
189.4
189.4
2002
842.6
70.2
45.6
89.8
8065.9
2.1
4.9
0.0
315.3
315.3
2003
1061.9
88.5
30.9
131.8
17377.8
2.1
4.7
3.5
446.4
442.9
2004
698.4
58.2
49.1
53.9
2904.5
0.6
−0.9
0.0
147.3
147.3
2005
790.8
65.9
57.9
61.9
3841.2
0.3
−1.6
0.0
157.3
157.3
2006
746.0
62.2
36.7
67.9
4617.8
0.9
−0.1
0.0
202.4
202.4
2007
897.1
74.8
56.5
71.2
5077.8
1.0
0.7
0.0
232.0
232.0
2008
767.3
63.9
39.6
71.4
5108.2
1.5
1.4
0.0
213.2
213.2
2009
1070.0
89.2
27.7
139.8
19570.4
2.2
5.5
0.2
477.3
477.1
2010
957.4
79.8
78.5
73.6
5416.9
0.6
−0.4
0.0
224.3
224.3
2011
893.5
74.5
57.2
86.7
7522.1
1.4
2.1
0.0
285.7
285.7In Table4, it can be inferred that the maximum annual rainfall of 1747.6 mm and the corresponding mean of 145.6 mm occurred in 1999 for the period under consideration. The minimum annual rainfall occurred in 1992 (808.1 mm) and the maximum annual standard deviation of 124 mm happened in 2004. The high standard deviation value can be easily correlated with the high rainfall range. The rainfall range signifies the difference between the maximum and minimum annual rainfall. The standard deviation and the range indicate the variability of annual rainfall and hence denote how reliable the rainfall is in terms of its persistence as constant and stable replenishing source. To test whether the annual rainfall data follow a normal distribution, the skewness and kurtosis were computed. Skewness is a measure of symmetry or, more precisely, the lack of symmetry. The data set is said to be symmetric if it looks the same to the left and right from the center point. The skewness for a normal distribution is zero, and any symmetric data should have skewness near zero. Negative values for the skewness indicate that data are skewed to the left and positive values for the skewness indicate that data are skewed to the right.Table 4
Descriptive statistics of annual rainfall of middle zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
Kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
1346.7
112.2
95.7
94.9
9013.6
1.4
1.4
0.0
319.8
319.8
1982
1141.2
95.1
90.5
61.5
3788.0
1.1
0.6
30.7
230.1
199.4
1983
1010.2
84.2
90.5
66.9
4482.4
−0.1
−2.1
0.0
163.4
163.4
1984
1337.2
111.4
120.9
92.0
8470.2
0.1
−1.4
0.0
265.7
265.7
1985
1338.4
111.5
125.3
78.7
6202.6
0.4
1.0
2.8
283.6
280.8
1986
1228.1
102.3
108.8
76.5
5855.3
0.0
−1.4
0.0
212.7
212.7
1987
1409.0
117.4
122.0
89.5
8021.7
0.1
−1.1
7.7
254.1
246.4
1988
1382.2
115.2
109.2
65.7
4319.9
0.1
−1.3
21.4
223.1
201.7
1989
1408.5
117.4
130.8
101.9
10382.0
0.8
1.0
0.0
346.4
346.4
1990
1167.7
97.3
109.3
71.7
5143.3
0.4
−0.8
14.6
224.7
210.1
1991
1415.2
117.9
102.4
93.3
8708.8
0.8
0.7
3.1
325.4
322.3
1992
808.1
67.3
66.4
48.7
2380.7
0.3
−0.1
0.0
164.2
164.2
1993
1184.8
98.7
94.8
57.5
3308.8
0.0
−0.2
0.0
204.2
204.2
1994
990.0
82.5
66.0
69.9
4887.3
1.2
1.1
0.0
239.9
239.9
1995
1315.0
109.6
119.6
71.8
5166.8
−0.2
−1.3
0.0
209.8
209.8
1996
1333.8
111.2
86.4
86.7
7526.9
0.9
0.2
5.1
282.9
277.8
1997
1322.7
110.2
95.9
79.4
6314.1
0.3
−1.2
13.7
248.6
234.9
1998
1140.3
95.0
89.8
67.2
4524.6
0.8
0.6
0.3
242.4
242.1
1999
1747.6
145.6
119.5
113.3
12859.2
0.7
−0.1
0.5
374.4
373.9
2000
1220.8
101.7
94.8
70.4
4967.6
0.2
−1.6
10.6
194.8
184.2
2001
1076.4
89.7
84.1
73.0
5338.1
0.1
−1.5
0.0
192.9
192.9
2002
1300.3
108.4
119.4
61.8
3822.2
−0.5
−1.3
6.7
175.3
168.6
2003
1289.4
107.5
79.2
92.4
8550.8
1.2
1.3
10.6
324.9
314.3
2004
1468.5
122.4
102.3
124.0
15380.9
2.0
4.5
3.9
454.2
450.3
2005
1148.7
95.7
68.6
55.8
3121.1
0.5
−1.5
41.2
185.6
144.4
2006
1161.7
96.8
69.7
88.5
7835.3
1.2
0.8
5.0
289.2
284.2
2007
1491.7
124.3
125.4
90.1
8120.3
0.1
−1.1
0.2
262.0
261.8
2008
1551.5
129.3
141.1
78.7
6198.5
−0.3
−1.1
0.0
239.0
239.0
2009
1106.6
92.2
87.4
66.5
4425.1
0.6
−0.2
0.0
224.0
224.0
2010
1324.4
110.4
96.9
78.6
6192.1
0.2
−1.6
6.0
227.0
221.0
2011
1168.8
116.9
133.3
57.3
3286.7
−0.8
0.7
0.0
197.2
197.2Kurtosis is a measure of data peakedness or flatness relative to a normal distribution. That is, data sets with a high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. The standard normal distribution has a kurtosis of zero. Positive kurtosis indicates a peaked distribution and negative kurtosis indicates a flat distribution. Hence the annual rainfall distribution under consideration did not follow normal distribution.As can be observed from Table5 the maximum annual rainfall for the period under review occurred in 1991 (2431.5 mm) with corresponding maximum annual mean and standard deviation of 202.6 mm and 182.8 mm, respectively. The standard deviation is a measure of dispersion. A small value indicates that the data is tightly grouped about the mean. A high value indicates that the data is spread widely on either side of the mean. A high standard deviation also suggests that year-to-year fluctuations are high while a low standard deviation indicates that fluctuations are lower. In other words, rainfall with a high standard deviation is considered more volatile than rainfall with a low figure. The minimum annual rainfall occurred in 2001 with an amount of 915.6 mm for the years under consideration.Table 5
Descriptive statistics of annual rainfall of northern zone.
Year
Parameters
Annual (mm)
Mean (mm)
Median (mm)
S.D. (mm)
Variance (mm)
Skewness
kurtosis
Min (mm)
Max (mm)
Range (mm)
1981
1241.6
103.5
83.7
96.4
9298.6
0.2
−1.8
0.0
239.4
239.4
1982
1071.8
89.3
99.6
68.1
4642.2
0.1
−1.0
0.0
204.8
204.8
1983
1060.7
88.4
60.9
95.2
9068.9
0.8
−0.6
0.0
273.9
273.9
1984
1735.2
144.6
77.1
150.6
22682.2
0.6
−1.3
0.0
384.1
384.1
1985
1336.8
111.4
83.0
112.5
12659.3
0.5
−1.6
0.0
284.0
284.0
1986
1370.1
114.2
108.6
97.8
9571.7
−0.0
−2.0
0.0
229.2
229.2
1987
1351.4
112.6
84.8
126.5
16004.2
1.1
0.8
0.0
398.1
398.1
1988
1064.4
88.7
56.2
88.4
7825.1
0.6
−1.2
0.0
246.2
246.2
1989
1479.5
123.3
23.4
161.7
26155.4
1.1
−0.2
0.0
430.2
430.2
1990
1336.7
111.4
114.4
97.7
9553.3
0.4
−0.8
0.0
296.5
296.5
1991
2431.5
202.6
179.6
182.8
33425.1
0.3
−1.4
0.0
498.1
498.1
1992
970.7
88.2
58.9
88.7
7872.5
0.7
−0.4
0.0
257.4
257.4
1993
1003.2
83.6
44.8
95.1
9052.5
1.5
2.1
0.0
316.3
316.3
1994
1197.9
99.8
116.8
93.7
8780.1
0.0
−1.9
0.0
226.9
226.9
1995
1680.8
140.1
145.6
125.7
15821.9
0.2
−1.4
0.0
350.4
350.4
1996
1539.8
128.3
149.1
119.2
14226.2
−0.1
−2.1
0.0
274.6
274.6
1997
1387.9
115.7
84.8
107.8
11635.4
0.4
−1.5
0.0
277.2
277.2
1998
982.5
89.3
60.3
81.1
6583.3
0.2
−1.7
0.0
205.5
205.5
1999
1580.8
131.7
64.9
142.4
20300.0
0.8
−0.9
0.0
394.4
394.4
2000
1375.6
114.6
85.0
109.4
11972.7
0.5
−1.3
0.0
293.2
293.2
2001
915.6
76.3
38.7
100.1
10016.8
1.3
0.7
0.0
291.8
291.8
2002
1453.8
121.2
155.1
97.7
9550.9
−0.2
−1.8
0.0
240.7
240.7
2003
1423.5
118.6
95.0
110.0
12101.4
0.9
−0.5
0.7
314.0
313.3
2004
1500.6
125.1
109.4
110.2
12157.7
0.6
−0.8
0.0
322.8
322.8
2005
1498.8
124.9
95.7
121.3
14727.5
1.0
0.1
0.0
374.3
374.3
2006
1033.3
86.1
62.7
96.5
9314.4
1.2
0.7
0.4
284.6
284.2
2007
1148.6
95.7
89.1
76.3
5820.8
0.1
−1.6
0.0
208.9
208.9
2008
1853.5
154.5
133.6
151.0
22802.6
0.8
0.2
0.0
479.1
479.1
2009
1617.5
134.8
139.1
109.4
11981.1
0.1
−1.7
0.0
294.7
294.7
2010
1107.2
92.3
86.3
82.0
6729.4
0.6
−0.3
0.0
244.5
244.5It is evident from Table6 that the coefficient of variation for the months of April through July (major season) is less than 0.5 which indicates lower variability from the mean and similar observation is made for the months of September and October (minor season). The low coefficient of variability recorded for the aforementioned months is an indication of highly dependable rainfall. Reference [11] stated that the CV is an indication of the degree of precision to which the treatments are compared and is a good index of the reliability of the experiment. Reference [11] further indicated that the higher the CV value, the lower the reliability of the experiment.Table 6
Statistical summary of monthly rainfall data of middle zone.
Parameter (mm)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean
18.2
52.7
102.3
133.3
154.9
182.1
132.2
94.6
163.2
160.3
47.3
30.4
Median
8.2
43.5
100.2
132.0
147.9
165.1
120.0
84.4
164.2
154.8
42.0
21.6
S.D.
22.2
44.8
59.6
57.2
66.8
78.3
58.2
66.4
79.5
52.9
32.3
32.2
Variance
490.9
2009.3
3553.4
3274.6
4460.5
6127.1
3384.8
4403.6
6332.2
2801.6
1041.9
1039.6
Skewness
1.1
2.0
0.8
−0.1
0.7
0.9
0.5
0.7
1.5
0.9
1.4
0.9
Kurtosis
0.4
4.9
0.5
−0.2
0.2
0.2
0.1
−0.3
4.9
1.5
1.7
−0.2
Min
0.0
5.8
20.3
6.9
35.5
74.4
30.2
9.4
47.5
77.4
5.8
0.0
Max
78.4
212.7
265.7
255.6
325.4
374.4
283.6
254.1
454.2
319.8
133.8
103.4
Range
78.4
206.9
245.4
248.7
289.9
300.0
253.4
244.7
406.7
242.4
128.0
103.4
Sum
564.0
1632.8
3169.9
4132.9
4800.7
5645.0
4097.1
2933.1
5060.3
4968.1
1419.8
911.8
CV
1.2
0.9
0.6
0.4
0.4
0.4
0.4
0.7
0.4
0.3
0.6
1.0The standard deviation is one way of summarizing the spread of a probability distribution; it relates directly to the degree of uncertainty associated with predicting the value of a random variable. High values reflect more uncertainty than low values. Table6 clearly revealed that September in middle climatic zone had the highest standard deviation. The highest amount of average monthly rainfall was recorded in June (182.1 mm) and contributed to 14.3% of annual rainfall, followed by September with 12.8%, and the lowest was in January with 1.4% of annual total followed by December with 2.3%. From the analysis, it was observed that rainfall is usually at its peak between April and July in the major season and between September and October in the minor season.The precipitation changes from month to month are considerable in years. When the standard deviation values are examined, it is observed that the standard deviation values of most months (January, February, July, August, September, and December) are higher than the averages of these months (See Table7). This relation between the standard deviation and the average values indicates that the deviation from the normal distribution cannot be ignored. This fact is especially supported by the coefficients of variation of these months which are over one or close to one. These show that, in coastal zones, the precipitation values are much different from the average. The fact that the CV values are so high is an indication of the rainfall being highly variable and not dependable or reliable or can be attributed to the length of data set being used or the quality of data.Table 7
Statistical summary of monthly rainfall data of coastal zone.
Parameters
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean (mm)
3.3
23.2
61.0
107.3
150.4
206.2
64.9
19.8
56.0
78.7
29.9
11.2
Median (mm)
0.0
11.2
49.0
86.7
145.7
174.2
44.2
10.8
33.9
65.2
22.0
2.5
S.D. (mm)
6.1
30.8
45.8
67.8
60.4
138.5
87.6
31.7
71.0
63.2
29.0
18.3
Variance (mm)
36.8
950.2
2098.5
4606.9
3645.8
19185.3
7675.3
1005.1
5050.3
3997.5
841.2
336.0
Skewness
2.2
1.4
0.7
1.2
0.0
1.2
3.0
3.2
2.5
0.6
0.8
2.6
Kurtosis
4.8
0.9
−0.0
1.9
−0.5
1.1
11.4
12.9
7.7
−0.8
−0.1
6.9
Min (mm)
0.0
0.0
0.0
18.3
34.5
47.0
1.2
0.0
0.0
0.5
0.0
0.0
Max (mm)
22.6
96.3
181.1
324.7
269.6
598.3
443.5
160.6
339.9
210.9
107.6
77.7
Range (mm)
22.6
96.3
181.1
306.4
235.1
551.3
442.3
160.6
339.9
210.4
107.6
77.7
Sum (mm)
102.0
719.5
1890.7
3325.0
4663.9
6391.7
2012.5
612.4
1735.9
2440.0
928.3
347.0
CV
1.8
1.3
0.7
0.6
0.4
0.6
1.3
1.6
1.2
0.8
0.9
1.6The lower the coefficient of variation of rainfall amount in any month, the lower the variability and the greater the dependability. Coefficient of variation values less than 0.5 shows lower variability from the mean. Table8 reveals that from June to September the rainfall variability is low and therefore highly dependable. Considering the coefficient of variation, September shows the minimum variation from year to year, compared to the rest of the months. However, since the coefficients of variation of each of the four months (June–September) are less than 0.5, the changes of precipitation from year to year in these months are low. September is the month with the highest mean monthly rainfall of 252.3 mm followed by August with 227.6 mm. Incidentally the above mentioned months traditionally fall within the minor season which usually records lower rainfall. This change in the rainfall season could be attributed to the so-called climate change. The month with the lowest rainfall is December (7.6 mm) followed by January (7.7 mm).Table 8
Statistical summary of monthly rainfall data of northern zone.
Parameter
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean (mm)
7.7
11.1
38.2
93.9
128.8
217.2
210.9
227.6
252.3
142.5
22.2
7.6
Median (mm)
0.0
0.3
35.2
82.3
125.4
213.5
201.9
243.6
235.2
119.8
6.3
0.7
S.D. (mm)
16.0
19.6
31.6
61.3
80.0
83.4
94.0
80.3
70.3
93.9
31.1
16.0
Variance (mm)
255.1
383.7
1000.6
3756.6
6394.8
6952.4
8831.9
6445.9
4947.0
8812.8
964.4
255.3
Skewness
2.1
1.8
0.7
0.9
1.2
0.5
1.7
−0.3
0.9
1.3
1.6
2.8
Kurtosis
3.8
1.8
0.1
0.4
3.1
0.2
3.6
−0.5
0.0
2.4
2.1
7.4
Min (mm)
0.0
0.0
0.0
7.3
6.0
93.6
91.7
73.0
146.8
9.2
0.0
0.0
Max (mm)
60.0
65.7
117.3
245.6
398.6
430.2
498.1
373.5
400.6
440.7
112.0
66.1
Range (mm)
60.0
65.7
117.3
238.3
392.6
336.6
406.4
300.5
253.8
431.5
112.0
66.1
Sum (mm)
231.6
323.3
1107.5
2817.5
3864.7
6516.0
6326.4
6827.3
7567.5
4274.7
665.9
228.9
CV
2.1
1.7
0.8
0.6
0.6
0.3
0.4
0.3
0.2
0.6
1.3
2.1The results of the linear regression trend analysis are presented in Tables9, 10, and 11, respectively, covering northern, middle, and coastal zones, respectively, of the Volta Region. In these trend tests, trend of rainfall for 30 years from January to December has been computed for each month independently.Table 9
Regression statistic results for annual and monthly rainfall for northern zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y = 0.35X  − 681.8
0.04
0.32
No
Feb
Y = 0.30X  − 592.4
0.02
0.47
No
Mar
Y = 0.19X  − 355.3
0.00
0.80
No
April
Y = 1.19X  − 2285.5
0.03
0.38
No
May
Y =  −2.06X + 4231.2
0.05
0.22
No
June
Y =  −1.73 + 3672.1
0.03
0.30
No
July
Y = 0.91X  − 1596.4
0.01
0.69
No
Aug
Y = 0.68X  − 1126.2
0.01
0.75
No
Sept
Y =  −0.57X + 1392.3
0.01
0.65
No
Oct
Y = 1.73X  − 3318.1
0.03
0.41
No
Nov
Y = 1.05X  − 2064.5
0.09
0.12
No
Dec
Y = 0.47X  − 927.3
0.07
0.17
No
Annual
Y = 2.51X  − 3651.9
0.00
0.80
NoTable 10
Regression statistic results for annual and monthly rainfall for central zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y = 0.31X  − 609.8
0.02
0.50
No
Feb
Y = 0.34X  − 629.0
0.00
0.73
No
Mar
Y =  −0.99X + 2095.1
0.02
0.39
No
April
Y = 1.49X  − 2856.9
0.06
0.22
No
May
Y =  −1.53X + 3212.6
0.04
0.24
No
June
Y = 2.33X  − 4486.8
0.07
0.15
No
July
Y =  −0.97X + 2080.8
0.02
0.38
No
Aug
Y =  −0.47X + 1041.2
0.00
0.70
No
Sept
Y = 2.74X  − 5315.2
0.09
0.09
No
Oct
Y =  −0.72X + 1594.7
0.02
0.46
No
Nov
Y =  −0.27X + 599.3
0.01
0.67
No
Dec
Y = 0.22X  − 412.0
0.00
0.77
No
Annual
Y = 2.02X  − 2760.5
0.01
0.71
NoTable 11
Regression statistic results for annual and monthly rainfall for coastal zone.
Month
Regression equation
R-square
P value
Statistically significant
Jan
Y
=
0.80
X
-
154.7
0.01
0.53
No
Feb
Y
=
0.90
X
-
1774.88
0.07
0.15
No
Mar
Y
=
-
1.16
X
+
2384.64
0.05
0.20
No
April
Y
=
-
0.35
X
+
811.97
0.00
0.77
No
May
Y
=
-
0.87
X
+
1881.74
0.02
0.45
No
June
Y
=
3.38
X
-
6540.3
0.05
0.24
No
July
Y
=
-
1.65
X
+
3357.27
0.03
0.35
No
Aug
Y
=
0.32
X
-
617.20
0.01
0.64
No
Sept
Y
=
-
0.04
X
+
132.05
0.00
0.96
No
Oct
Y
=
1.66
X
-
3234.97
0.06
0.21
No
Nov
Y
=
-
0.26
X
+
545.28
0.01
0.65
No
Dec
Y
=
0.18
X
-
353.72
0.01
0.64
No
Annual
Y
=
2.19
X
-
3562.80
0.01
0.70
NoThe linear trend lines of the monthly rainfall indicated a downward trend in May, June, and September and an upward trend for other months and annual rainfall data for the northern zone. Since the probability value (P value) from the regression analysis for the slopes of the monthly and annual trend lines was greater than the significant level α=0.05, the null hypothesis (Ho: there is no trend in the data, fail to reject. That means there is no statistically significant trend in the annual and monthly rainfall data for northern zone. Additionally, the R-square statistic also indicated a very weak relationship between the variables, rainfall, and year.Table10 revealed downward trends in the rainfall for the months of March, May, July, October, and November and the rest of the months recorded upward trend in the rainfall data for the middle zone. However, the trends are not statistically significant. This argument is buttressed by the P values of the linear regression analysis being greater than α=0.05.Annual rainfall for coastal zone showed upward trend; however, there is a decreasing trend in the months of March, April, May, July, September, and November and the rest of the months of the year revealed an increasing trend. Again, these trends are insignificant statistically as indicated by theP values.Figure4 clearly reveals that for the period under consideration for middle zone the highest mean monthly rainfall was recorded in June and the lowest in January. It is also evident from the graph that the highest average minor season rainfall occurred in September.Figure 4
Average monthly rainfall for the three zones from 1981 to 2010.For the northern zone the highest average monthly rainfall for the period under review as indicated in Figure4 was recorded in September which is a minor season for the northern climatic zone. The result clearly indicated that the peak mean monthly rainfall in the minor season was more than the major season which suggested a discrepancy. However, this could be attributed to climate change effects.The graph for coastal zone revealed that December and January were the driest months. The highest rainfall occurred in June for the major season while the highest corresponding minor season rainfall was recorded in October.


## 4. Conclusion

The rainfall characteristics especially variability and trend are necessary for the proper design of hydro related schemes such as clean water supply, reservoir, and storm water channels in rapidly growing regions like Volta Region. From the results of the linear regression analysis, there is statistically insignificant increasing trend in annual mean rainfall data among the zones under study. The mean monthly rainfall data from the linear regression analysis revealed upward trend in some months and downward trend in others. However, the results indicated statistically insignificant trend in the monthly rainfall and very weak correlation between rainfall and period. It is evident from the results that there is no significant detectable effect of climate change on both the annual and monthly trend in Volta Region.Comparatively coastal zone recorded the lowest maximum and minimum annual rainfall of 1298.1 mm and 359.2 mm, respectively, followed by the middle zone with 1747.6 mm and 808.1 mm. The northern zone recorded the highest maximum annual rainfall of 2431.5 mm and the minimum of 915.6 mm in the years 1991 and 2001, respectively.Further studies are required to be carried out to establish other rainfall characteristics such as extreme rainfall, rain days, and other climate change parameters for this region to verify whether the significant trend has occurred and also to establish a correlation between temperature and extreme rainfall.



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*Source: 203245-2014-10-19.xml*