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In regional water resources management and disaster preparedness, the analysis of extreme rainfall events is essential. The need to investigate drought and flood conditions is now heightened within the context of climate change and variability. The Standardised Precipitation Index (SPI) was employed to assess the extreme rainfall event on Tordzie watershed using precipitation data from 1984-2014. The SPI on the time scale of 3, 6, 9 and 12 months were determined using “DrinC” software. The drought was characterised into magnitude, duration, intensity, frequency, commencement and termination at the time scales of SPI-3, SPI-6, SPI-9 and SPI-12. Results indicated that the middle reaches (Kpetoe) of the watershed experienced less severe drought condition compared to the lower reaches (Tordzinu). Mann-Kendall (MK) test and Sen’s slope (SS) revealed general increasing drought trend but insignificant at 95% confidence interval. The SS indicated change in magnitude of 0.016 mm/year, 0.012 mm/year, 0.026 mm/year and 0.016 mm/year respectively at the mentioned time scales at 95% confidence interval at the Tordzinu and that of Kpetoe were 0.006 mm/year, 0.009 mm/year, 0.014 mm/year and 0.003 mm/year. These changes could have implication for agriculture and water resources management and engender food insecurity among smallholder farmers.

Global warming or climate change has been reported by [

A prolonged period of water deficit is referred to as drought, which usually occurs when precipitation receives in an area falls below usual levels for several months. Depending on the components of the hydrological cycle affected by a drought event, the drought can be categorised as meteorological, agricultural or hydrological. The extended period with precipitation below normal levels, which generally appears before other drought types is called meteorological drought. The standardized precipitation index (SPI) proposed by McKee et al. [

The other types of droughts such as agricultural, hydrological and economic ones are connected with meteorological droughts which records below normal rainfall. The deficit of soil moisture supply to the plants usually leads to agricultural droughts and the hydrological droughts are comparatively of long term and normally results in low flows in rivers and depleted reservoir storages.

The concept of drought may differ from place to place since rainfall varies significantly among different regions and localities. As such, for more effective assessment of the drought phenomena, the World Meteorological Organization [

Tordzie watershed is one of the key basins in the Volta Region of Ghana. However, this watershed is one of the least studied in terms of its hydrology in Ghana. Moreover, the temporal drought estimation using standardized precipitation index has not been employed to analyze drought occurrence on the mentioned basin. Additionally, there is no research evidence on drought analysis on the watershed. Thus the investigation of the temporal variability of the extreme climate events is important in order to comprehend better the recent climatic oscillations and their manifestation in local level and to further monitor drought and flood occurrence.

Therefore, the main objective of this study was to assess temporal drought characteristics using standardized precipitation index (SPI) based on rainfall data from 1984 to 2014 for the middle and lower sections of the Tordzie watershed represented by the hydrological stations Kpetoe and Tordzinu respectively.

The study was carried out in selected network stations in the Tordzie watershed in Ghana. The climatic data from the network of meteorological stations covering two (2) different physiographic areas within the Tordzie watershed was collected for analysis. The selection of the physiographic sample area for the study was based on the data availability and the study requirements. Historical rainfall data were collected from the Ghana Meteorological Services Department.

The Tordzie watershed is shown in

Tordzie is a trans-boundary basin. The area in Ghana is 1865 km^{2} which constitutes 83.7% and the remaining area in Togo is 363 km^{2} which is 16.3%. The total area of the basin is 2228 km^{2} [

The data was organised and tabulated in Excel and then imported to DrinC (Drought Indices Calculator), 2015 software to calculate the standardised precipitation index (SPI) at different time scales for all the stations using the data for the period 1984 to 2014 for Kpetoe and Tordzinu portion of the Tordzie watershed. Tigkas et al. [

The rainfall deficit within the Tordzie watershed was computed using the standardised precipitation index. A long term data for a period of 1984 to 2014 was used (31 years). The procedure used by McKee et al. [

The precipitation value is transformed into the SPI for the purpose of transforming: 1) mean of the precipitation value (adjusted to 0); 2) standard deviation of the precipitation (adjusted to 1.0); and 3) skewness of the existing data readjusted to 0).

The standardized precipitation index can be interpreted as mean 0 and standard deviation of 1.0 when the above goals have been achieved.

Mean = x ¯ = ∑ x N (1)

Standard deviation, S = ∑ ( x − x ¯ ) 2 N (2)

log mean ( x ) = x ¯ l n = ln ( x ¯ ) (3)

U = x ¯ l n − ∑ ln ( x ) N (4)

This is called U parameter, where; x is rainfall amount (mm), x ¯ is the mean rainfall (mm) and N is the number of observations.

β = 1 + 1 + 4 U 3 4 U (5)

This is referred to as shape parameter

α = x ¯ β (6)

This is called scale parameter.

The gamma distribution is expressed in terms of its probability density function as:

g ( x ) = 1 α β Γ ( β ) x β − 1 e − x α (7)

where; α is the scale parameters, β is the shape parameter and x is the rainfall amount (mm), Γ ( β ) is the value of the gamma function and x ¯ is the mean rainfall (mm).

The gamma function Γ ( β ) , a standard mathematical equation is stated as follows:

Γ ( β ) = ∫ 0 ∞ y β − 1 e y d y = 1 y β − 1 e − y (8)

where, y is the value computed from Equation (7) that is y is equal to g(x).

The numerical method was used in evaluating the gamma function in Equation (8), by incorporating in the tabulated values that depended on the value taken by shape parameter β . A maximum probability was used in estimating the optimal values of α and β using Equations (5) and (6).

Equation (7) which is referred to as probability density function g(x) is integrated with respect to x to obtain an expression for cumulative probability G(x). This function is applicable to a certain amount of rainfall for a particular month of specific duration of time.

G ( x ) = ∫ 0 x x β − 1 e − x α d x (9)

Equation (9) was used to compute values of cumulative probability for non-zero rainfall. The gamma function is applicable for rainfall values x > 0 for the rainfall time series of the watershed under study. For non-zero values, cumulative probability of both zero and non-zero are computed. This probability is denoted by a function H(x) defined as:

H ( x ) = q + ( 1 + q ) F ( x ; α , β ) (10)

where; H(x) is the cumulative probability and q is the probability of zero rainfall. q = m/n; where m was taken as the number of zero rainfall entries in the time series rainfall data and n is number of observations.

After the above computations were carried out using the mentioned equations, the cumulative probability was transformed into a standard normal distribution. This was done in such a manner that the mean and variance of the SPI values were zero and one respectively.

Z = S P I = − ( t − c 0 + c 1 t + c 2 t 2 1 + d 1 t + d 2 t 2 + d 3 t 3 ) for 0 < H ( x ) ≤ 0.5 (11)

Z = S P I = + ( t − c 0 + c 1 t + c 2 t 2 1 + d 1 t + d 2 t 2 + d 3 t 3 ) for 0.5 < H ( x ) ≤ 1 (12)

where; t in the Equations (11) and (12) respectively were determined by:

t = ln ( 1 H ( x ) 2 ) for 0 < H ( x ) ≤ 0.5 (13)

t = ln ( 1 1.0 − H ( x ) 2 ) for 0.5 < H ( x ) ≤ 1.0 (14)

where; c 0 = 2.515517 , c 1 = 0.802853 , c 2 = 0.010328 , d 1 = 1.432788 , d 2 = 0.189269 , d 3 = 0.001308

The criteria established by [

Considering the time series of n data points and T_{i} and_{ }T_{j} are two sub-sets of data where

i = 1 , 2 , 3 , ⋯ , n − 1 and j = i + 1 , i + 2 , i + 3 , ⋯ , n .

Each data point T_{i} was used as a reference point and compared with all the T_{j} data points such that:

sign ( T ) = { 1 for T j > T i 0 for T j = T i − 1 for T j < T i (15)

The Kendal test’s S-statistic was compared as:

S = ∑ i = 1 n − 1 ∑ j = i + 1 n sign ( T j − T i ) (16)

The variance for the S-statistic is defined as:

δ 2 = n ( n − 1 ) ( 2 n + 5 ) − ∑ i = 1 n − 1 t j ( i ) ( i − 1 ) ( 2 i + 5 ) 18 (17)

Index value | Classification | Probability | Occurrence |
---|---|---|---|

SPI ≥ 2.00 | Extremely wet | 0.977 - 1.000 | 2.3% |

1.50 ≤ SPI < 2.00 | Very wet | 0.933 - 0.977 | 4.4% |

1.00 ≤ SPI < 1.50 | Moderate wet | 0.841 - 0.933 | 9.2% |

−1.00 ≤ SPI < 1.00 | Near normal | 0.159 - 0.841 | 68.2% |

−1.50 ≤ SPI < −1.00 | Moderately drought | 0.067 - 0.159 | 9.2% |

−2.00 ≤ SPI < −1.50 | Severe drought | 0.023 - 0.067 | 4.4% |

SPI < −2.00 | Extremely drought | 0.000 - 0.023 | 2.3% |

Source: Adopted from [

In which t, denote the number of ties to extent i. The test statistic Z_{s} was calculated as:

Z s = { s − 1 δ for s > 0 0 for s = 0 s + 1 δ for s < 0 (18)

Z s is used as a measure of significance of trend. If Z s is greater than Z α / 2 , where α represent the chosen significance level (5%, with Z_{0.025}), then the null hypothesis is invalid, meaning the trend is significant. The null hypothesis in Mann-Kendal test is that the data are independent and randomly ordered. The Mann-Kendal test does not require the assumption of normality and only indicates the direction but not the magnitude of significant trends. Equation (15) implies that if T_{i} is greater than T_{j} the value of T will be 1, and the second condition shows that if T_{i} is less than T_{j} the value of T will be −1, while the last condition implies that if T i = T j , then the value will be 0. Mann-Kendall analysis is started from the bottom and is computed towards the top values because the reference point is being compared with all the T_{j} values above.

The Sen’s slope method was used to estimate the rate of change:

Δ = median ( X j − X i j − i ) , i < j (19)

where X_{j} and X_{i} are the data values in times j and i respectively. The Δ sign represents the direction of change and its value indicates the steepness of change. According to Yue et al. [

The results of SPI at different time scales and the drought/flood characteristics at the mentioned network stations on Tordzie watershed are presented. The analysis revealed five (5) characteristics of historical temporal drought/flood condition of the mentioned watershed. The features of the dry/wet condition of the historical climate are: duration, frequency, intensity, severity and magnitude of the drought/flood at different time scales of SPI-3, SPI-6. SPI-9 and SPI-12 corresponding to 3, 6, 9 and 12 months respectively. Furthermore, the commencement and termination of the extreme climate events (drought and flood) are indicated in

The analysis also revealed that SPI-3 (short time scale) depicts frequency fluctuation below or above the zero line too frequently and the duration of the wet and dry period is very short compared to other time scales (longer time scales). The analysis of SPI-3 presented in

The implication of the above results is that the watershed experienced extreme drought for three (3) months in the aforementioned years. The consequence is its negative impact on agricultural production in the watershed since SPI-3 drought is associated with soil moisture. This implied there was not enough soil

moisture for plant production as a result of less than normal rainfall for the stated period (October-December) in the particular year. The soil moisture predominantly comes from rainfall which recharges the soil moisture deficit. The findings suggest crop losses could have occurred during the period which is normally the minor production season. The deduction is consistent with Williams et al. [

Additionally, the analysis showed that SPI-6 of extreme drought event happened in the year 2000 with a drought magnitude of −2.14 at the Kpetoe part of the watershed, however, there was no extreme drought event at the downstream side (Tordzinu), of the watershed. Nevertheless, there was a wet event at both sides of the watershed, which occurred in the years 1999 with a magnitude of

2.22 and 2014 with a magnitude of 2.59 at Kpetoe and Tordzinu respectively. The implication for the SPI-6 drought is low basin flows that can be associated with it. The SPI-6 drought is typically a hydrological drought since it represents surface water availability conditions. This implies that years with negative SPI-6 values had low river flows (October-March). The drought years could be connected with low rainfall years and may be attributed to climate change and variability. The global warming could be responsible for this recurrent drought phenomenon. This assertion is agreed upon by IPCC [

Also, 9 months’ time scale (SPI-9) rainfall analysis revealed that the extreme drought event occurred in the year 1993 with drought magnitude of 2.69 at Kpetoe and none occurring at Tordzinu. Finally, 12 months (SPI-12) drought analysis of the rainfall revealed that extreme droughts occurred in 1993 with a drought magnitude of −2.93 and −2.31 respectively at Kpetoe and Tordzinu. The longer time scales, SPI-9 and SPI-12 particularly relate to stream flows, reservoir levels and long term storage including ground water storage availability, thus resulting in low flow regimes in the basin. Besides,

The total monthly drought characteristics in terms of magnitude, duration and severity for the period of 1984-2014 is display in

Months | Kpetoe | Tordzinu | ||||
---|---|---|---|---|---|---|

Magnitude | Duration (months) | Severity | Magnitude | Duration (months) | Severity | |

January | 6.91 | 15 | 0.46 | 4.22 | 17 | 0.25 |

February | 10.86 | 14 | 0.78 | 9.65 | 14 | 0.69 |

March | 12.49 | 14 | 0.89 | 11.81 | 15 | 0.79 |

April | 10.65 | 14 | 0.76 | 11.46 | 16 | 0.72 |

May | 11.80 | 14 | 0.84 | 11.99 | 17 | 0.71 |

June | 13.02 | 17 | 0.77 | 13.75 | 15 | 0.92 |

July | 12.68 | 16 | 0.79 | 13.00 | 14 | 0.93 |

August | 12.69 | 15 | 0.85 | 12.17 | 16 | 0.76 |

September | 11.27 | 12 | 0.94 | 12.78 | 15 | 0.85 |

October | 12.42 | 12 | 1.04 | 13.01 | 16 | 0.81 |

November | 12.27 | 16 | 0.77 | 11.94 | 15 | 0.80 |

December | 11.42 | 15 | 0.76 | 10.18 | 17 | 0.60 |

drought duration could be attributed to the differences in the ecological zones between the two areas.

An SPI of a short time step (SPI-3) reveals high volatility of change between dry and wet periods. When the time scale is increased the drought and flood periods indicated a lower volatility of change and longer duration. The drought and flood periods are clearly seen in SPI longer than 6 months. In

It is also revealed that drought intensity is inversely proportional to its duration, meaning as drought frequency increases its corresponding duration decreases. Primarily, the global warming is responsible for the changes in the hydrological cycle, for instance the changes in the frequency and intensity of precipitation, temperature, evapotranspiration, soil moisture level and the underground water capacity [

more frequent since 1950 in some regions, including southern Europe and western Africa. It is worthy to note also that at Tordzinu area of the watershed, there was no extreme wet condition recorded at the time scale of SPI-3 and SPI-12 for the period under study.

A drought event occurs whenever SPI values are continually negative and ends when the values become positive. Drought has a duration defined by its commencement and termination. The positive sum of the SPI values for all the months within a drought event is termed as drought magnitude. The intensity of drought event is defined as the ratio of event magnitude to its duration.

The historical drought characteristics like drought duration, magnitude and intensity are provided in the

Simelton et al. [

One purpose of the current study is to derive new information on the duration/number of drought events on the Tordzie watershed and to characterise its historical temporal pattern. For each SPI time scale, the number of droughts with a given duration was estimated. The results for duration 3, 6, 9 and 12 months are shown in

Tordzinu | Kpetoe | |||||||
---|---|---|---|---|---|---|---|---|

Year | Months | Duration (months) | Magnitude | Intensity | months | Duration (months) | Magnitude | Intensity |

1984 | 1-2-4-5-6-8-11 | 7 | 4.20 | 0.60 | 1-2-4-9-12 | 5 | 6.83 | 1.37 |

1985 | 12 | 1 | 0.99 | 0.99 | 2-4-5-6-9-10-12 | 7 | 4.80 | 0.69 |

1986 | 1-5-7-8-9-10-11-12 | 8 | 4.58 | 0.57 | 1-4-6-8-9-12 | 6 | 5.42 | 0.90 |

1987 | 1-5-6-7-9-10 | 6 | 4.83 | 0.81 | 2-4-6-7-10-11-12 | 7 | 3.63 | 0.52 |

1988 | 1-3-4-5-6-7-12 | 7 | 5.16 | 0.74 | 8-10 | 2 | 2.39 | 1.20 |

1989 | 1-2-3-4-5-12 | 6 | 1.99 | 0.33 | 1-2-4-9-10-11-12 | 7 | 3.68 | 0.53 |

1990 | 3-5-8-9-10 | 5 | 5.30 | 1.06 | 2-3-5-6-7-8-11 | 7 | 4.52 | 0.65 |

1991 | 3-4-6-8-9-10-11-12 | 8 | 7.05 | 0.88 | 3-6-8-12 | 4 | 1.58 | 0.40 |

1992 | 1-2-4-6-7-8-10-11 | 8 | 8.72 | 1.09 | 1-2-3-4-5-6-7-8-9-10 | 10 | 10.96 | 1.10 |

1993 | 1-2-3-5-10-11 | 6 | 3.64 | 0.61 | 1-2-3-5-6-7 | 6 | 3.09 | 0.52 |

1994 | 2-4-6-7-9-12 | 6 | 5.42 | 0.90 | 3-4-6-7-8-9-11-12 | 8 | 7.35 | 0.92 |

1995 | 1-2-4-5-8-9-10-12 | 8 | 5.52 | 0.69 | 1-2-6-10-11 | 5 | 2.57 | 0.51 |

1996 | 1-9-10-11-12 | 5 | 5.60 | 1.12 | 1-5-9-11 | 4 | 4.01 | 1.00 |

1997 | 1-2-4-8-11 | 5 | 3.80 | 0.76 | 3-7-11-12 | 4 | 1.53 | 0.38 |

1998 | 1-3-4-5-6-7-10 | 7 | 5.20 | 0.74 | 1-3-6-7-9 | 5 | 5.20 | 1.04 |

1999 | 5-8-9-10-11-12 | 6 | 3.19 | 0.53 | 5-12 | 2 | 1.76 | 0.88 |

2000 | 1-2-3-4-7-9-12 | 7 | 3.27 | 0.47 | 2-3-6-10-11 | 5 | 5.64 | 1.13 |

2001 | 1-3-7-8-10 | 5 | 2.65 | 0.53 | 1-2-4-6-7-10-11-12 | 8 | 7.89 | 0.99 |

2002 | 3-8-9-12 | 4 | 3.27 | 0.82 | 2-4-5-9-11-12 | 6 | 2.38 | 0.40 |

2003 | 2-3-4-5-6-7-8 | 7 | 7.44 | 1.06 | 3-5-7-8 | 4 | 6.36 | 1.59 |

2004 | 4-6-7-10 | 4 | 2.93 | 0.73 | 1-2-3-4-6-8-10 | 7 | 2.96 | 0.42 |

2005 | 1-2-4-5-8-9-11-12 | 8 | 3.25 | 0.41 | 5-6-7-8-9 | 5 | 4.22 | 0.84 |

2006 | 1-2-4-6-7-8-11-12 | 8 | 5.67 | 0.71 | 4-7-8-9-11-12 | 6 | 7.07 | 1.18 |

2007 | 1-2-3-5-9-10-11 | 7 | 4.42 | 0.63 | 1-5-8-12 | 4 | 1.71 | 0.43 |

2008 | 2-3-10-11-12 | 5 | 2.29 | 0.46 | 1-4-5-9-11 | 5 | 2.09 | 0.42 |

2009 | 3-5-7-9-10 | 5 | 4.94 | 0.99 | 1-4-5-7-9-11 | 6 | 5.36 | 0.89 |

2010 | 4-5-6-7-12 | 5 | 4.86 | 0.97 | 3-5-7-8-11-12 | 6 | 3.49 | 0.58 |

2011 | 1-3-6-8-9-12 | 6 | 3.30 | 0.55 | 1-3-5-6-11-12 | 6 | 4.38 | 0.73 |

2012 | 5-6-7-8-9-11 | 6 | 3.77 | 0.63 | 1-3-7-8-10 | 5 | 3.48 | 0.70 |

2013 | 2-3-6-8-9-12 | 6 | 4.66 | 0.78 | 2-4-6-7-8-10-11 | 7 | 6.70 | 0.96 |

2014 | 4-5-6-10-11 | 5 | 2.83 | 0.57 | 2-3-6-7-8-10 | 6 | 5.45 | 0.91 |

NB: 1, 2, ・・・, 12 denote the months from January, February-December.

slightly higher number of hydrological droughts (SPI-6 and SPI-12) were recorded. Possible explanation could be that the upper reaches of the watershed experienced drought the previous wet season or the lag in phase between the occurrence of agricultural and meteorological droughts respectively. The implication of drought at the middle reaches of the watershed which received higher

rainfall and maintains river flow during the dry season may be dry condition of river flow in the lower reaches of the basin. It is observed that SPI-3 and SPI-12 results were similar, revealing uniformity in distribution of events among the stations. As have been reported earlier, as the SPI time scale increased the number of drought events decreased, because the drought at longer time scales tend to be longer. Thus, the number of droughts at longer duration increased with longer SPI time scales. The total number of droughts for the period under study in case of SPI-12 was 175 and 187 months for Kpetoe and Tordzinu respectively.

The analysis of the temporal drought trend and change at different time scales (SPI-3, SPI-6, SPI-9 and SPI-12) employing Mann-Kendal (MK) test and Sen’s Slope (SS) to determine the magnitude of the change in drought from year to year indicated some changes though insignificant (p ≥ 0.05), have already occurred in the watershed. The negative and positive values estimated by SS indicate dry and wet periods respectively. The MK test revealed that there was increasing trend in the drought at the time scale of SPI-3, SPI-6, SPI-9 and SPI-12 (

events had been increasing since the 1970s till now. In that study, the investigators employed the standardised precipitation index for the analysis. Again in a related study by Owusu et al. [

The seasonal temporal drought analysis of the lower reaches (Tordzinu) of the said watershed revealed changes in magnitude of drought in the months of April, May June, September and October as 0.012 mm/year, 0.003 mm/year, −0.007 mm/year, −0.015 mm/year and 0.016 mm/year respectively indicated by the SS estimator. For the same months above the corresponding temporal drought changes as indicated by SS estimator in the middle reaches (Kpetoe) of the watershed were 0.009 mm/year, −0.004 mm/year, 0.028 mm/year, 0.024 mm/year and 0.020 mm/year respectively. Additionally, the change in drought magnitude as estimated by SS is 0.027 mm/year at confidence interval of 95 %. The differences between the SPI and the corresponding trend in the two stations could be due to the variation in temperature. Evidence from the study of Vicente-Serrano et al. [

The SPI is robust tool for temporal historical drought/flood analysis. The analysis revealed that the watershed is prone to both drought and flood hazards. The changes in drought magnitude have been indicated by SS and the trend by MK at different time scales. Generally, there was a slight upward trend in the drought characteristics, further indicating possible climate change and variability in drought/flood in tandem with the rainfall variability. The study further employed SPI to identify the frequencies of occurrence of dry and wet conditions in the middle and lower reaches of Tordzie watershed for the period under study at different temporal time scales. The tendency towards dryness is higher in magnitude and severity at the lower reaches than the middle reaches of the watershed. The probable explanation could be the difference in the ecological zones and therefore the geomorphology. The middle reaches are located at the middle belt and forest savannah transitional zone with some hilly areas making precipitation more concentrated and the generation of runoff more intense and fast. On the other hand, the lower reaches are found within the coastal savannah with relatively flat terrain, marshes, swamps, strand and low grassland vegetation. It is also clear regarding the identification of dry/wet period, that it is better detected over longer temporal time scales of 6 months and above. It is concluded that, the increasing rainfall variability and rising temperature attributable to anthropogenic activities may not be the only cause for ascendancy in drought/flood events intensity and frequency over the watershed. It is recommended that a further study be conducted to ascertain the roles played by land use/land cover changes. It is further suggested that spatial analysis of drought be conducted in the future to know the spatial extent of drought phenomena on the Tordzie watershed as data become available with expansion of network stations.

We acknowledge with thanks the authors whose works have been reviewed and duly cited. Special thanks to the Ghana Meteorological Agency (GMA) for providing us with the climate data. The authors would like to thank the editors and the anonymous reviewers for the relevant comments and suggestions, which significantly improved the quality of the manuscript.

This paper is part of the corresponding author’s PhD thesis who conducted this research as a part of his PhD thesis and wrote the initial version of the manuscript and the second author is advisor/supervisor. The first author designed the research. The second author advised on the content and analysis. The second author helped in improving the manuscript, proofread and helped in the discussion of the results.

The authors declare no conflict of interest.

Nyatuame, M. and Agodzo, S. (2017) Analysis of Extreme Rainfall Events (Drought and Flood) over Tordzie Watershed in the Volta Region of Ghana. Journal of Geoscience and Environment Protection, 5, 275-295. https://doi.org/10.4236/gep.2017.59019