**3. Materials and methods**

The data for this study area is the secondary data of 12 stations with monthly rainfall within the south eastern Nigeria obtained from the Nigeria Meteorological Agency, Lagos, Federal College of Agriculture, Ishiagu, Ebonyi State., Nigeria [23]. The data used is tabulated as shown in **Table 2** below. This table shows the location, annual rainfall amount, latitude, longitude elevation and period of data collection. For some areas however, it is necessary to observe that the data was for period less than 10 years owing to the absence of sufficient data. However, even with missing data as observed from the table below, the information obtained is tested for reliability and consistency before use.

#### **3.1. Measure of reliability**

#### (a) Mean

**2. The study area**

100 Engineering and Mathematical Topics in Rainfall

**2.1. Physical environment**

range of between 27°

electric energy generator site.

undulating Cross River Basin right of the scarpland.

C and 34°

**2.2. Climate and hydrology of study area**

The study site is the South Eastern Zone of Nigeria. This region falls within the latitude 6' N and 8' N and longitude 4′ 30′E and 7′30'E also described as the inland region of the country according to **Figure 1**. Udi escarpment divides the zone into two area viz. South Eastern scarplands under Anambra /Imo River Basin and Eastern borderlands under Cross River Basins and the apex of Udi plateau at 300 m above sea level. The whole region which is densely populated covers an area of about 40,000 sq. km and represent 4% of the country's land mass

The site is of the lowland region of southern Nigeria, which drains to the Atlantic Ocean through the Anambra/Imo River Basin and the Cross River Basin. According to [9], the geology of the area is basically of the stratified sedimentary rock of secondary to tertiary geological era. The unroofing of the anticlines left the Udi escarpment and brought about the

The South Eastern Nigeria is of the wet tropical type climate with mean annual temperature in the

March–April when the overhead Sun passes through Nigeria latitude. The rainfall, however, of the area has an annual average of 1744 mm, which is decreasing inland from the Niger Delta area or the coast of Nigeria .This is quite clear in **Figure 3** below. The Annual rainfall regime of the area is of the double maxima with double peak in July and September and an August break period. The high rainfall between May–September has a lowering effect on temperature of the area.

The climate of Nigeria is classified into Rainy (April – October) and Dry (November – March) seasons, with each of the seasons lasting approximately six months. Annual rainfall ranges from 500 m in the extreme north to 3000 m along the coast. Nigeria is governed by high pressure southwest monsoon wind from the Atlantic in June–July pushing the inter-tropical front to the Sahara (northern) region of the country [1, 9]. At this point the sun is around the tropic of cancer or close to it, hence high temperature (25 ° C south and 40 ° C north) and low pressure. In December–January, on the other hand, the sun is at the tropic of Capricorn causing the wind system to shift to the south. At this time, the Sahara region becomes the high pressure belt forcing dry and cold wind to blow northeasterly to the low pressure area of the south. The wind system usually arrive the country about September and gradually spread throughout the country and last until March when the sun repeats the processes again. This process represents the wet and dry seasons of Nigeria of which the South East is a part. The **Table 1** represents the wind power available in various locations within the country. The area of the

and is classified as class 2 as shown in **Table 1** below. Classification indicates class 1 for the weakest location for siting of wind power generators to class 7 the strongest possible site for

South East with the escarpment has maximum wind power of 122 w/m<sup>2</sup>

C. The temperature of the area as observed by [9] is highest around

, altitude of 167 m

with the physical environment and climate described in the **Figure 2** below.

From the annual mean calculation of each station and the region, a departure from average is determined and plotted to indicate how mean rainfall for each stations differ from the mean. This helps us to determine the variability experienced in the rainfall distribution.

#### (b) Coefficient of variation

The coefficient of variation or relative dispersion is obtained using the formula

$$\mathbf{C}v = \frac{\sigma}{\overline{X}}\tag{1}$$

A coefficient of variation closer to one indicates greater consistency of data set. It is also an indication of the relationship amongst data set within the same area.

#### **3.2. Frequency analysis**

Frequency factors are used to fit theoretical distributions [6]. As proposed by [24], the general equation for hydrologic analysis is given as:

$$\mathbf{x}\_{\mathbb{T}} = \overline{\mathbf{X}} + \mathbf{K}\sigma \tag{2}$$

Where k is the frequency factor, a function of return period and probability distribution, σ is the standard deviation of hydrologic data and *X*¯ is the mean of hydrologic data. [25, 26] frequency factor is determined and used to determine the magnitude of x and the value of x correspond to return period T, denoted by *xT* as defined in

$$P(X \ge X\_{\gamma}) = \frac{1}{T} \tag{3}$$

(ii) Log-Pearson Type III Distribution

**Table 2.** Showing 12 station with site parameters.

.

**3.3. Principal component analysis**

**3.4. General characteristics of Nigeria wind**

dard deviation *<sup>σ</sup><sup>y</sup>*

by this procedure.

and month) and space (Km<sup>2</sup>

recurrence interval is then estimated from

This is a form of Pearson Type III in which the hydrologic variables are log transformed before analysis using Pearson Type III distribution. The flood magnitude as a variable, for a desired

Geography of Udi Cuesta Contribution to Hydro-Meteorological Pattern of the South Eastern…

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103

log*Q* = *Y*¯ + *K σ<sup>y</sup>* (4)

Where k is a function of return period and skewness and mean *Y*¯ is the mean of log*Q* and stan-

Principal component analysis is used as a reduction procedure for variables that tend to empirical relationship. In this regard, large number of observed variables is reduced to smaller number of principal components which accounts for the variance of the observed variable [2]. The six component variable is reduced to two with linear combinations of data

Manwell, McGowan, & Roger [7] have observed that wind energy varies in both time (second

). Space variations are function of elevation above sea level and

In hydrologic frequency analysis, the probability of occurrence of an event of known return period is evaluated. Several methods of frequency analysis are calculated and compared in this study viz.:

#### (i) Normal Distribution

The Gaussian distribution is used in the study of measurement errors and characteristics of normal distributions. This is the most important probability distribution.

#### (ii) Log-Normal Distribution

In situation where hydrologic variables are right skewed due to influence of natural phenomenon, their frequencies do not follow normal distribution but their logarithm does. This distribution as suggested by the [27] is valuable for the degree of accuracy in estimation.

#### (iii) Extreme Value Type I Distribution

This is also known as the Gumbel distribution for flood frequency analysis. In this case, which is specially used for weather study has largest and smallest values known as extreme values associated with floods and drought respectively. The distribution uses mean, standard deviation and skewness in the analysis of the probability of occurrence of an event.

#### (i) Gamma (Pearson Type III Distribution)

Pearson Type III distribution is a special case of Gamma distribution and it is a frequency analysis method. In this type of distribution, three parameters are used viz. mean, standard deviation and skewness.

Geography of Udi Cuesta Contribution to Hydro-Meteorological Pattern of the South Eastern… http://dx.doi.org/10.5772/intechopen.72867 103


**Table 2.** Showing 12 station with site parameters.

(b) Coefficient of variation

102 Engineering and Mathematical Topics in Rainfall

**3.2. Frequency analysis**

this study viz.:

(i) Normal Distribution

(ii) Log-Normal Distribution

(iii) Extreme Value Type I Distribution

(i) Gamma (Pearson Type III Distribution)

deviation and skewness.

*Cv* = \_\_*<sup>σ</sup>*

equation for hydrologic analysis is given as:

correspond to return period T, denoted by *xT*

*<sup>P</sup>*(*<sup>X</sup>* <sup>≥</sup> *XT*) <sup>=</sup> \_\_1

The coefficient of variation or relative dispersion is obtained using the formula

indication of the relationship amongst data set within the same area.

A coefficient of variation closer to one indicates greater consistency of data set. It is also an

Frequency factors are used to fit theoretical distributions [6]. As proposed by [24], the general

*xT* = *X*¯ + *K* (2)

Where k is the frequency factor, a function of return period and probability distribution, σ is the standard deviation of hydrologic data and *X*¯ is the mean of hydrologic data. [25, 26] frequency factor is determined and used to determine the magnitude of x and the value of x

In hydrologic frequency analysis, the probability of occurrence of an event of known return period is evaluated. Several methods of frequency analysis are calculated and compared in

The Gaussian distribution is used in the study of measurement errors and characteristics of

In situation where hydrologic variables are right skewed due to influence of natural phenomenon, their frequencies do not follow normal distribution but their logarithm does. This distribution as suggested by the [27] is valuable for the degree of accuracy in estimation.

This is also known as the Gumbel distribution for flood frequency analysis. In this case, which is specially used for weather study has largest and smallest values known as extreme values associated with floods and drought respectively. The distribution uses mean, standard devia-

Pearson Type III distribution is a special case of Gamma distribution and it is a frequency analysis method. In this type of distribution, three parameters are used viz. mean, standard

normal distributions. This is the most important probability distribution.

tion and skewness in the analysis of the probability of occurrence of an event.

as defined in

*<sup>X</sup>*¯ (1)

*<sup>T</sup>* (3)

#### (ii) Log-Pearson Type III Distribution

This is a form of Pearson Type III in which the hydrologic variables are log transformed before analysis using Pearson Type III distribution. The flood magnitude as a variable, for a desired recurrence interval is then estimated from

$$
\log Q = \overline{Y} + K\sigma\_y \tag{4}
$$

Where k is a function of return period and skewness and mean *Y*¯ is the mean of log*Q* and standard deviation *<sup>σ</sup><sup>y</sup>* .

#### **3.3. Principal component analysis**

Principal component analysis is used as a reduction procedure for variables that tend to empirical relationship. In this regard, large number of observed variables is reduced to smaller number of principal components which accounts for the variance of the observed variable [2]. The six component variable is reduced to two with linear combinations of data by this procedure.

#### **3.4. General characteristics of Nigeria wind**

Manwell, McGowan, & Roger [7] have observed that wind energy varies in both time (second and month) and space (Km<sup>2</sup> ). Space variations are function of elevation above sea level and global and local geographical conditions. In Nigeria, regions of high altitude are observed to have higher wind speed, with Jos having the highest average wind speed in the country. For the 24 stations in Nigeria where records of wind speed are kept, measurement is made with cup anemometers at 10 m height. The nature of the wind in Nigeria is observed to follow the seasons, viz.: Rainy and Dry seasons. To determine the characteristics of Nigeria wind, the country is divided into four zones namely: Far-North, Middle Belt, Inland and Coastal areas. The monthly and annual characteristics of the wind speed for each zone are determined using the following parameters.

Long-term average wind speed,

$$
\overline{V} = \frac{1}{N} \sum\_{i=1}^{N} V i \tag{5}
$$

(ii) Annual

*3.5.2. Location variation*

*3.5.3. Estimation of available wind power resources*

Where *ρ* is the air density (assumed 1.225 Kg/m<sup>3</sup>

**4.1. Spatial and temporal distribution of rainfall**

\_\_*P*¯

density for various stations.

or within the escarpment.

under observation not neglected.

**4. Results and discussions**

Available wind power density is calculated according to [20, 30] as:

*<sup>A</sup>* <sup>=</sup> \_\_1 <sup>2</sup> *<sup>ρ</sup>* \_\_1 *<sup>N</sup>* ∑ *i*=1 *N*

and v is the wind speed. The computed wind power density is compared with the wind classification according to [13]. **Table 1** above shows the result of classification of wind power

The **Figure 3** above, it shows the rainfall concentration and distribution that exist in the South Eastern zone of Nigeria. From the coefficient of variation obtained, it is evident that the rainfall data of the area shows greater consistency with an average of 22% in these zones. Also in **Figure 4** below, the influence of Udi Plateau is also seen in the dispersion of the rain from the mean. On the location axis, it is seen that from Nkwelle–Akwette, there is a positive value in the rainfall difference which shows the escarpment in contact with the wind bearing rain while the other side of the escarpment is noticed by the negative result obtained from Nsukka–Awka. This has significantly resulted to a variance in rainfall pattern in areas around

Furthermore, it is clearly seen that Awka has the highest negative dispersion and this is attributed to its closeness to the plateau top with the effect of the distance of each of the stations

Generally, South Eastern Nigeria rainfall follow the same pattern as other parts of Southern Nigeria with bi-modal rainfall between May–October, that is, wet season and Nov-April dry

season. The rainfall indicates a double peak in July and September.

*Vi*<sup>3</sup> (10)

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105

), N the number of data, i the sample number

Significant variations exist within seasons (Wet and Dry) and monthly averaged wind speeds. The zonal average wind speed are calculated and plotted to show the seasonal variation.

Geography of Udi Cuesta Contribution to Hydro-Meteorological Pattern of the South Eastern…

Local topographical and ground cover variations affect wind speed. Hiester & Pennell [29] have shown that difference of mean between two cities close to each other can be significant. Within each zone, a plot of the monthly and annual trend of wind against average wind speed is made. The plots are made for Coastal, Inland, Middle Belt and Far-Northern zones.

Standard Deviation,

Standard Deviation, 
$$\sigma = \sqrt{\frac{1}{N-1} \sum\_{i=1}^{N} \left( Vi - \overline{V} \right)^{2}} \tag{6}$$

Coefficient of variation,

$$\mathbf{C}v = \frac{\sigma}{\mathcal{V}}\tag{7}$$

Shape factor,

$$k = \left(\frac{\sigma}{\overline{V}}\right)^{-1.098} \tag{8}$$

and Scale factor,

$$c = \frac{\vec{V}}{\Gamma\left(1 + \frac{1}{\vec{k}}\right)}\tag{9}$$

#### **3.5. Analysis of wind speed**

#### *3.5.1. Time variation*

A looked at Nigeria wind speed time variation in terms of Inter-annual and annual relationship.

#### (i) Inter-annual

This shows the difference in wind speed overtime scale of more than one year [13]. They have effect in the estimation of long-term wind for turbine production. Fourteen years record used for this work is adequate for long-term planning. Aspliden, Elliot, and Wendell [28] have suggested that one year mean wind speed have accuracy of 10% and is within 90% confidence level.

#### (ii) Annual

global and local geographical conditions. In Nigeria, regions of high altitude are observed to have higher wind speed, with Jos having the highest average wind speed in the country. For the 24 stations in Nigeria where records of wind speed are kept, measurement is made with cup anemometers at 10 m height. The nature of the wind in Nigeria is observed to follow the seasons, viz.: Rainy and Dry seasons. To determine the characteristics of Nigeria wind, the country is divided into four zones namely: Far-North, Middle Belt, Inland and Coastal areas. The monthly and annual characteristics of the wind speed for each zone are determined using

> *<sup>N</sup>* ∑ *i*=1 *N*

\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_ <sup>1</sup>

(*Vi* − *V*¯) 2

*<sup>N</sup>* <sup>−</sup> <sup>1</sup> ∑ *i*=1 *N*

> \_\_*σ <sup>V</sup>*¯) −1.086

*<sup>Γ</sup>*(<sup>1</sup> <sup>+</sup> \_\_1 *k*)

A looked at Nigeria wind speed time variation in terms of Inter-annual and annual relationship.

This shows the difference in wind speed overtime scale of more than one year [13]. They have effect in the estimation of long-term wind for turbine production. Fourteen years record used for this work is adequate for long-term planning. Aspliden, Elliot, and Wendell [28] have suggested that one year mean wind speed have accuracy of 10% and is within 90%

*Vi* (5)

*<sup>V</sup>*¯ (7)

(6)

(8)

(9)

the following parameters.

Standard Deviation,

Coefficient of variation,

Shape factor,

and Scale factor,

*3.5.1. Time variation*

(i) Inter-annual

confidence level.

**3.5. Analysis of wind speed**

Long-term average wind speed,

104 Engineering and Mathematical Topics in Rainfall

*V*¯ = \_\_1

*Cv* = \_\_*<sup>σ</sup>*

*k* = (

*<sup>c</sup>* <sup>=</sup> \_\_\_\_\_\_ *<sup>V</sup>*¯

*<sup>σ</sup>* <sup>=</sup> <sup>√</sup>

Significant variations exist within seasons (Wet and Dry) and monthly averaged wind speeds. The zonal average wind speed are calculated and plotted to show the seasonal variation.

#### *3.5.2. Location variation*

Local topographical and ground cover variations affect wind speed. Hiester & Pennell [29] have shown that difference of mean between two cities close to each other can be significant. Within each zone, a plot of the monthly and annual trend of wind against average wind speed is made. The plots are made for Coastal, Inland, Middle Belt and Far-Northern zones.

#### *3.5.3. Estimation of available wind power resources*

Available wind power density is calculated according to [20, 30] as:

$$\frac{\overline{P}}{A} = \frac{1}{2}\rho \frac{1}{N} \sum\_{i=1}^{N} V \overline{i}^{3} \tag{10}$$

Where *ρ* is the air density (assumed 1.225 Kg/m<sup>3</sup> ), N the number of data, i the sample number and v is the wind speed. The computed wind power density is compared with the wind classification according to [13]. **Table 1** above shows the result of classification of wind power density for various stations.
