IJCRR

IJCRR - 6(18), September, 2014

Pages: 01-06

Date of Publication: 21-Sep-2014

ANALYSIS OF DROUGHT EFFECT ON ANNUAL STREAM FLOWS OF RIVER MALEWA IN THE LAKE NAIVASHA BASIN, KENYA

Author: Marshal M. Kyambia, Benedict M. Mutua

Category:

Abstract:The main parameters of drought phenomenon are the longest duration and largest severity for a desired return period. These parameters form the basis for designing water storage structures to cope with drought effects. In this study, these drought parameters were estimated using the probability based theory. The sample estimates of the mean, coefficient of variation, skewness, correlation and information on the probability distribution of flow sequence, were used as the basic input parameters. The truncation level was considered at mean level of the annual flow sequences of River Malewa in Lake Naivasha basin. In this basin, 100, 50, 10, 5 and 2-year droughts may persist continuously for 6, 4, 3, 2 and 1 years respectively. From the probabilistic approach for a normal probability distribution function, high values of coefficient of variation resulted in high values of the actual severity. The results show that there is drought severity in Lake Naivasha basin especially in parts experiencing high inter-annual variability in annual flow regimes.

Keywords: Drought, Severity, Return Period, Probability Theory, Truncation Level

Full Text:

INTRODUCTION
In the design, planning and management of water resources, it is necessary to estimate the hydrological drought characteristics under certain return periods. This provides a scientific base for estimating engineering design and water resources utilisation. Changing drought characteristics have affected the function and operation of existing water resources management practices (Below et al., 2007). Adverse effects of hydrological droughts have aggravated the impacts of other stresses, such as population growth, changing economic activities, land-use change and urbanisation (Mogaka et al., 2006; Jahangir et al., 2013). The current water management practices need to be made dynamic so as to cope with the changes in hydrological characteristics which have direct impact on water resources (Wilhite and Easterling, 1997; Svoboda et al., 2002; Abad et al., 2013). Hence, the characteristics of hydrological drought events need to be studied so as to apply the appropriate adaptation and mitigation measures (Mishra et al., 2009). The effects of drought in many activities depend on the severity, duration and geographical extent of precipitation deficiency, and on whether precipitation is used directly to maintain soil moisture or whether water supplies are drawn from the stream flows (Below et al., 2007). Different types of drought have been described, for instance by the World Meteorological Organisation (Subrahmanyan, 1967; Hayes et al., 2011), by Wilhite and Glantz (1985) and also by Zoljoodi and Didevarasl (2013). Of importance among the different types of droughts is the hydrological drought, defined in terms of reduction of stream flows, reduction in lake or reservoir storage, and lowering of ground water levels below a predefined threshold level. Such a threshold level has been termed as the truncation level in hydrological droughts (El-Jabi et al., 2013). This truncation level reflects the demand level for water hence the reason for the examination of this type of drought as presented in the paper. The choice of truncation level is largely governed by the purpose of investigation (Meigh et al., 2002; Sung et al., 2013). Studies have considered it as long term mean flow (Sharma, 1997), while others took it as a percentile level of the flow duration curve ranging from Q50 (flows exceeding 50% of the time) to Q95 (Hisdal and Tallaksen, 2003).

A flow duration curve could be constructed based on annual, monthly or daily flow sequences. For example, when the interest is in the design and planning of a water storage system, on a permanent or long-term basis, for ameliorating drought, then a truncation level corresponding to the mean level of flow could result in a conservative design to produce a desirable drought mitigation scenario. In contrast, in regional drought frequency analysis, a value of truncation level such as Q70 or Q80 would portray more tangible drought impacts over the region (Panu and Sharma, 2002). However, in shortterm contingency planning for drought amelioration, when drought impacts are tangible, drought investigation could even be carried out at a truncation level of Q90, to allow mobilisation of resources on a cost- effective basis. There are two principal methods for predicting the duration and severity of droughts associated with return period. In the time series simulation approach, the simulated stream flow is truncated at the desired level. The drought episodes (runs of deficits) are analysed empirically using the theory of runs or through counting technique (Chung and Salas, 2000). For instance, Horn (1989) successfully used this approach to describe the behaviour of droughts in Idaho, USA. In the probability theory-based approach, the properties of a drought, including the length (duration) and depth (severity) are derived from basic axioms of probability. This approach enables estimates of length of the longest run and associated greatest severity for a desired return period (Sharma, 1997). This approach requires information on the underlying probability distribution of the stream flow series. This method was adopted in this study because it can be computed using the drought probability (q) and return period (T). The main objective of this study was to determine the critical parameters of hydrological drought using the probability based theory.

MATERIALS AND METHODS
Study area
The Lake Naivasha basin which is approximately 3376 km2 , is located in the Kenyan Rift Valley and it is approximately 70 km from the Kenyan capital city, Nairobi. The maximum altitude is about 3990m above mean sea level (a.m.s.l) on the eastern side of the Aberdare ranges to a minimum altitude of about 1900m (a.m.s.l). There are two rainy seasons experienced in this basin with the long and short rains occurring in March to May and October to November respectively. The Lake Naivasha basin receives an average annual rainfall of 610 mm, with the wettest slopes of the Aberdare ranges receiving as much as 1525 mm per annum. The lake is fed by two main perennial rivers namely; the Malewa and Gilgil. The River Malewa (Figure 1) with a catchment area of 1600km2 is the major river feeding the lake, contributing about 90% of the total discharge into the lake (Lukman, 2003). Due to the difference in altitude, diverse climatic conditions exist within the Lake Naivasha basin.

Data Acquisition
To analyse hydrological droughts in the River Malewa, the daily flow data at the gauging station 2GB1 were acquired from Water Resources Management (WRMA) Naivasha regional office. The 2GB1gauging station was chosen since it had uninterrupted streamflow data records for over 50 years (from 1959-2008). Prior to trend analysis, the hydrological records were tested for homogeneity and normality. Homogeneity of time series records is confirmed when observed variations result entirely from fluctuations in weather and climate. Testing for homogeneity was done to find out if or not there were any errors that could have resulted from gauge station and environmental changes (Wijngaard et al., 2003). The non-parametric Pettit’s test (Mann, 1945; Mann and Whitney, 1947; Petti, 1979; Libiseller and Grimvall, 2002) was used to check for the homogeneity of the time series records.

Evaluation of Extreme Drought Severity based on Drought Duration and Intensity
The length of a drought spell and its associated sever ity for a given return period were calculated using the probability based analytical relationships. The theorem of extremes of random variables using q and r provided a basis for derivation E(LT ) and E(ST ) relationships. Any uninterrupted sequence of deficits below the mean flow was regarded as drought length equal to the number of deficits in the sequence. This was carried out at gauging station 9036002 on River Malewa which is the main river draining the basin and feeding Lake Naivasha. Critical Drought Duration, E(LT ) and Severity E(ST ) In order to identify the underlying probability of the annual stream flow and their dependence structure, natural flow sequences were used in the analysis. The values of µ, γ, ρ, σ and cv were computed using the standard procedure as documented in Chow et al. (1988). For a time series xi truncated at a level x0 , the truncation level m0 is equal to ( x0 m) σ − , Further, if x is normally distributed, so would be u. Thus, for a normally distributed sequence, u will be written as a standard normal deviate (z) and the probability:

For instance, the value of q at a truncation level equivalent to the mean level for a normal probability distribution of flow sequence is 0.5, which can be integrated from the above standard normal probability function from -∞ to 0 . For a flow sequence with a coefficient of variation of cv and the truncation level at Tl of the mean flow, the value of u0 = z0 = . In this study, the value of q was obtained by using standard probability tables. The probabilistic relationship for and was obtained by applying the theorem of extremes of random variables as applied by Sharma (2000) and Biamah et al. (2005) as expressed in equations (2) and (3). (2) (3) Where, j stands for the length of the drought duration and takes on values 1, 2, 3,…, up to infinity. In this study, the value of j was considered at a maximum of 25, as probabilities beyond j >25 are extremely small and can be regarded negligible. Equation (3) thus was expressed as: (4) The value of r, representing an extended continuance of drought years, was related to q, as shown by Sen (1977): (5) Where, v is a dummy variable for integration. The integral in equation (5) was evaluated using excel spreadsheet and values of r for a given q and z0 were computed. For an independent or random stream flow series r = q and a value of drought intensity I was estimated using a formula by Sharma (2000): (6) The value of I in equation (6) turned out to be negative (since drought epochs are below the truncation level and hence negative in terms of sign); therefore absolute values were used in the calculation of the severity defined as: (7) It is noted that, when the analysis is implemented in the standard domain, and are all dimensionless and without units. Thus, the actual drought severity was computed using the relationship which results to:

RESULTS AND DISCUSSION
Evaluation of Extreme Drought Severity based on Duration and Intensity The probabilistic approach was used to estimate the duration and severity of a T-year drought on historical data of annual flows. The truncation was at the mean level of the gauging station 2GB1 in Lake Naivasha basin. For the probabilistic approach, the assumption that annual flow sequences are normal and independent was a reasonable choice for analysis, since ρ and γ happen to be insignificantly small. This is because, this assumptions yields marginally conservative values of severity which is a desirable feature for design aspects of water resources systems for ameliorating drought conditions. The value of zo is 0.0 for the truncation level equal to the mean flow, and the corresponding value of q is 0.5 as given in Table 1. For a flow sequence, the value of r = q = 0.5 indicates that flows are random and, consequently, the drought episodes are also random. By using the values of zo , q, r and T = (2, 5, 10, 50 and 100 years) in equations (2) to (7), the values of LT, I and ST were calculated and their results are presented in Table 2. The Table also presents results of the values of DT for different return periods that were calculated using equation (8).

From the results given in Table 2, it can be observed that on average, the 100-year drought in Lake Naivasha basin is expected to last for 6 years in a row and with a corresponding severity of 4.78. Similarly, the 2, 5, 10 and 50-year droughts are expected to last for 1, 2, 3 and 4 years respectively with the drought lengths rounded off to a whole year. All these computations were done using the MS Excel spreadsheet and the summary of the computations for a 10-year drought is presented in Table 3.

For any desired design return period, the important elements of a drought phenomenon considered are the longest duration and the largest severity (Sharma, 1998). These elements form the basis for designing water storage structures to cope with droughts for adaptation planning to climate variability. It is evident from the probabilistic approach for a normal probability distribution that high values of cv result in high values of DT. Based on this, drought severity is expected to be greater in the basin parts experiencing high inter-annual variability in annual flow regimes. Such occurrences will be common in the semi-arid regions of the Lake Naivasha basin which routinely experience variable precipitation patterns. The values of drought duration for normal independent flows were predicted using two independent variables, T and q. The results show that critical droughts will persist for the same number of years in the entire Lake Naivasha basin. Likewise, standardized severity is also expected to be the same in the entire basin. However, each river will undergo a different level of actual severity DT (m3 ), because of different values of mean flows and associated coefficient of variation. These results have a significant implications pertaining to future water resources planning in the Lake Naivasha basin, especially against the backdrop of a higher likelihood of multi-year droughts due to climate variability. This risk must be considered in planning, design, operation and selection of water resources development scenarios in the Lake Naivasha basin. In particular, when attention is being focused on developing the lower parts of the basin, planners have to appreciate the fact that this region is very prone to droughts, unlike the abundantly water-rich upper parts of the basin near the Aberdare forest.

CONCLUSIONS
The overall objective of the study was to analyze hydrological drought characteristics with a view to providing information for planning local coping mechanisms to water resources management. The critical drought parameters, namely the longest drought duration and the greatest severity were predicted using the probability based approach. The analysis revealed that the annual stream flow sequences can be construed as samples from the normal independent flow sequences. The probabilistic analysis of drought revealed that, in the prevailing hydrological regimes, 100-year, 50-year, and 10-year droughts will persist for 6, 4 and 3 years respectively. The longest drought duration and severity have uniform values for the entire study area in view of the normal and random probability structure of annual flows. However, actual severity will display variability in proportion to the coefficient of variation or standard deviation. These results can be applied in the design of water storage systems to combat the persistent extreme hydrological drought. This study was important because it has enhanced the understanding of hydrological drought characteristics, which can be used to enhance water sources management within Lake Naivasha basin.

ACKNOWLEDGEMENT
The authors would like to appreciate the support that they received from the Water Resources Management Authority (WRMA) Naivasha, during the field work and data collection. In addition, the authors do appreciate the support from the Faculty of Engineering and Technology, Egerton University. In addition, the authors acknowledge the immense help received from the scholars whose articles are cited and included in references of this paper. The authors are also grateful to authors / editors / publishers of all those articles, journals and books from where the literature for this article has been reviewed and discussed.

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