Civil Engineering

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 2, February 2017, pp. 418–422 Article ID: IJCIET_08_02_045
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=2
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
SPATIAL VARIATION OF RAINFALL RUNOFF
EROSIVITY (R) FACTOR FOR RIVER NZOIA BASIN,
WESTERN KENYA
Akali Ngaywa Moses
Department of Disaster Preparedness and Engineering Management,
Masinde Muliro University of Science and Technology, Kenya
ABSTRACT
Rainfall is one of the key drivers of soil erosion with its force expressed in form of rainfall
erosivity (R-Factor). The R-Factor is a function of rainfall amount and the intensity. Given the
inadequacy of quality data, the factor is generally estimated based on rainfall data with low
time-based resolution. The specific objective of this study was to model rainfall runoff erosivity
(R-Factor) for river Nzoia basin. Local rainfall data were collected from 14 rainfall stations
purposively selected from the basin based on sufficiency and quality. GIS techniques were used
to model rainfall runoff erosivity (R) factor for river Nzoia basin. Thematic map for R-factor
was generated. Results revealed that the average R-Factor value ranged between 339.39 and
855.00 MJ mmha−1
year−1
with the highest values experienced in the middle extending to the
lower basin of the study area. Its mean and standard deviation was 574.38 and 130.62
MJmmha−1
year−1
, respectively. This could be attributed to relief kind of rainfall associated
with Mt Elgon, Cherenganyi hills and the Nandi escarpment.GIS techniques were successfully
used to generate rainfall runoff erosivity (R-Factor) for river Nzoia basin. There is significant
spatial variation in the rainfall erosivity (R-Factor) in River Nzoia basin. If this factor is
considered in isolation, then the middle extending to the lower basin of the study area will be
affected more in terms of the soil erosion due to high rainfall erosivity values. Therefore,
further quantitative studies need to be undertaken to evaluate the principal factors influencing
spatio-temporal variations in the R-factor for river Nzoia basin.
Key words: Spatial variation; Rainfall; R-factor; GIS techniques; Thematic map.
Cite this Article: Akali Ngaywa Moses, Spatial Variation of Rainfall Runoff Erosivity (R)
Factor for River Nzoia Basin, Western Kenya. International Journal of Civil Engineering and
Technology, 8(2), 2017, pp. 418–422.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=2
1. INTRODUCTION
The erosive power of precipitation is accounted for by the rainfall erosivity factor (R-factor).As
argued by Mbugua (2009), the factor gives the combined effect of the duration, magnitude and
intensity of each rainfall event. It quantifies the interrelated erosive forces of rainfall and runoff. It’s
an annual factor that represents all the erosive rains throughout the year and it’s based on the rainfall
energy and intensity values. According to Kassam, et al. (1992), Rainfall-Runoff erosivity (R-Factor)

2. Akali Ngaywa Moses
http://www.iaeme.com/IJCIET/index.asp 419 editor@iaeme.com
is an aggregate measure of the amounts and intensities of individual rain storms over the year. Rainfall
and runoff play an important role in the process of soil erosion, which is usually expressed as the R-
factor.
As contended by Renard, et al. (1997), this factor is used to quantify the ability of rainfall to cause
soil loss under different conditions. Mbugua (2009) notes that, the rainfall-runoff erosivity factor (R)
for any given period is calculated from an annual summation of rainfall data using rainfall energy (E)
and the maximum 30-minute intensity (I30) as defined in Equation 1. Relative fall velocity of a single
droplet and the overall rainfall intensity determines the erosive properties of rain droplets
(Hrissanthou, et al., 2003).
  .
1
1 1
30  









n
i
m
j
jj IE
n
R
(1)
Where;
n -Total number of years
m -Total number of rainfall storms in ith
year
I30 -Maximum 30-min intensity (mm hr−1
)
Ej - Total kinetic energy (MJ ha−1
) of jth
storm of ith
year, see Equation 2.
k
p
i
kj deE *
1

 (2)
Where;
P -Total number of divisions of jth
storm of ith
year
dk -Rainfall depth of kth
division of the storm (mm)
ek -Kinetic energy (MJ ha−1
mm−1
) of kth
division of the storm
Renard, et al. (1991) define kinetic energy as shown in Equation 3.
 ki
k ee 005.0
72.0129.0 

(3)
Where,
- Intensity of rainfall of kth
division of the storm (mm hr−1
)
2. MATERIALS AND METHODS
2.1. Study Area
The study was carried out in river Nzoia basin. The basin is Lake Victoria’s largest inlet basin in
Kenya. It lies between latitudes 10
30’ N and 00
05’ S and longitudes 340
and350
45’ E. The river
originates from the slopes of Mount Elgon, Nandi Hills, Cheranganyi Hills and Kakamega forest. It
drains into Lake Victoria at an altitude of 1100 m above sea level (Nyadawa,et al., 2010). River Nzoia
measures about 334 km long with a basin area of about 12, 709 Km2
, and a mean annual discharge of
1.740 X 109
m3
(Githui, et al., 2010). In the view of WMO (2004), the mean annual rainfall varies from
a maximum of 1100 to 2700 mm and a minimum of 600 to 1100 mm. The basin is characterized by
clayey (68%), very clayey (7%), loamy (18%) and sandy (7%) types of soils.
ki

3. Spatial Variation of Rainfall Runoff Erosivity (R) Factor for River Nzoia Basin, Western Kenya
http://www.iaeme.com/IJCIET/index.asp 420 editor@iaeme.com
2.2. Methods
2.2.1. Rainfall Data
Rainfall data was obtained from Kenya Meteorological Department (KMD). A total of 14 spatially
distributed rainfall gauging stations were considered for the study. Two methods: Thiessen polygon
and Inverse Distance Weighting Method (IDWM) (Equation 4) were used to fill in the missing data for
gauging stations with less than 10% gaps. In the latter, rainfall gauging stations with missing data were
used to fill in the gaps.






 n
i
k
mi
n
i
k
mii
m
d
d
1
1


(4)
Where,
n - Number of gauges with recorded daily rainfall values on the estimation day
θi - Recorded observation at station i
dmi - Distance from gauge i to gauge m and
k - Denoted friction distance whose value ranges from 1.0 to 6.0 (Vieux, 2001)
This was guided by the principle of shared similarities of the stations to each other owed to spatial
immediacy. Figure 1 shows rain gauging stations and Thiessen polygons that were used to fill in
missing rainfall data values.
Figure 1 Sampled rainfall stations and Thiessen polygons
2.2.2. Rainfall-Runoff Erosivity (R-Factor) Estimation
For the computation of R-factor, data from 14 rainfall gauging stations within river Nzoia basin was
used and Equation 1 (Kassam, et al., 1992) was then applied to determine precipitation change

4. Akali Ngaywa Moses
http://www.iaeme.com/IJCIET/index.asp 421 editor@iaeme.com
according to elevation. Monthly rainfall data were converted to raster format and summed to give the
annual rainfall sum for each year. The annual averages and the monthly rainfall averages were then
used as the inputs to Equation 1 by use of the raster calculator tool in Arc GIS 10.1.
3. RESULTS AND DISCUSSION
3.1. Rainfall Runoff Erosivity (R) Factor
The average annual R factor value varied from 339.39 to 855.00 MJ mmha−1
year−1.
Its mean and
standard deviation 574.38 and 130.62 MJmmha−1
year−1
, respectively, see Figure 2.
Figure 2 River Nzoia basin R-Factor statistics
More rainfall erosivity was observed in the middle basin extending towards the lower part of the
basin. The upper basin covering areas such as Mount Elgon, Cherenganyi hills and Nandi escarpments
which coincide with higher elevation of the study area, experience low rainfall erosivity. The
decreasing R factor has a strong relationship with the increasing trend of elevation. Figure 3 shows the
spatial distribution of R-factor map for the study area.
Figure 3 River Nzoia basin runoff erosivity (R) factor

5. Spatial Variation of Rainfall Runoff Erosivity (R) Factor for River Nzoia Basin, Western Kenya
http://www.iaeme.com/IJCIET/index.asp 422 editor@iaeme.com
If this factor is considered in isolation, then the middle extending to the lower basin of the study
area will be affected more in terms of the soil erosion hazard due to high rainfall erosivity values.
4. CONCLUSION
GIS techniques were successfully used to generate rainfall runoff erosivity (R-Factor) for river Nzoia
basin. There is significant spatial variation in the rainfall erosivity (R-Factor) in River Nzoia basin.
Areas covering the middle towards the lower river Nzoia basin experience maximum erosivity, while
the upper basin areas spanning Mt. Elgon, Cherenganyi and Nandi Escarpment had the minimum
erosivity values. If this factor is considered in isolation, then the middle extending to the lower basin
of the study area will be affected more in terms of the soil erosion due to high rainfall erosivity values.
5. RECOMMENDATION
Further quantitative studies need to be undertaken to evaluate the principal factors influencing spatio-
temporal variations in the R-factor for river Nzoia basin.
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