Analysis of spatial and temporal drought variability in a tropical river basin using Palmer Drought Severity Index (PDSI)

Analysis of spatial and temporal drought variability in the upper Tana River basin using Palmer Drought Severity Index (PDSI) was conducted. The drought is critical for formulation of mitigation measures in the river basin. A monthly temporal and 90-m spatial resolution was applied. This was achieved within ArcGIS environment. Climatic data for 1970 to 2010 was used for computation of the PDSI while the missing data sets were filled using Artificial Neural Networks (ANNs). The results of PDSI for dry and wet seasons at meteorological stations indicate that the time series plots for the PDSI values for dry season are generally lower than those for the wet seasons. The PDSI values for meteorological stations located at the lower elevation of the basin are lower than those located at higher elevation. On the other hand, spatially distributed drought severity based on PDSI show that the ranges of maximum and minimum drought severity values in 1970 are -0.868 to -0.804 and -0.675 to -0.610 respectively. These values of drought severity occur respectively in the north-western and south-eastern areas of the basin. PDSI values increased from the range -0.675 to -0.610 in 1970 and from -1.087 to 0.957 in 2010 for the north-eastern areas of the upper basin. The south eastern areas of the basin are more prone to drought risks than north-western parts. Use of the PDSI reflects the spatial heterogeneity and temporal variability of drought across the basin. The drought assessment offer technical approach for comprehensive understanding of drought for effective drought-induced disaster mitigation and its management, with a view to reducing adverse effects on livelihoods.


INTRODUCTION
Drought is a condition on land characterised by scarcity of water that falls below a defined threshold level.The term drought has been defined differently in numerous applications (UNDP, 2012).However, it is a challenge to quantitatively define the term.
Droughts may be expressed in terms of indices that depend on *Corresponding author.E-mail: wambuarm@gmail.com.
Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License precipitation deficit, soil-water deficit, low stream flow, low reservoir levels and low groundwater level.Drought may be defined differently depending on the sector involved.For example, a hydrological-drought occurs whenever river or groundwater levels are relatively low.In addition, water-resources drought occurs when basins experience low stream flow, reduced water reservoir volume and groundwater levels.The water resources drought is influenced by climatic and hydrological parameters within a river basin and drought management practices.The hydrological drought, mainly deals with low stream flows.This drought adversely affects various aspects of human interest such as food security, water supply and hydropower generation (Karamouz et al., 2009;Belayneh and Adamowski, 2013).
It is paramount to analyse and monitor drought due to its adverse effects.For the purpose of understanding drought, the hydro-meteorological variables are encapsulated into drought indices at river basin scales.These drought indices provide critical information on decision making (Quiring and Papakryiakou, 2003).In order to mitigate adverse drought impacts on water resources, ecosystems, economy and peoples livelihoods, it is paramount to undertake drought studies.Key drought studies should describe its characteristics such as temporal trends, spatial distribution of severity frequency and duration.Prior to formulation of drought mitigation mechanism in a river basin, it is essential to first describe its characteristics at the basin scale.Drought affects ecosystem response mechanisms and is thus perceived to influence the future of the global earth carbon balance (Bonal et al., 2016).
In this study, upper Tana River basin was selected because it is a very important resource in Kenya.It is clipped from the larger Tana River basin; the largest river basin in the country that provide huge water resources.The upper Tana River basin has forest land resources located along the eastern slopes of Mount Kenya and Aberdares range which have a critical role in regulating the hydrology of the entire basin (IFAD, 2012).The basin is located within a fragile ecosystem that represents all agro-ecological zones of Kenya where water resource systems, hydro-power generation and food security are negatively impacted by frequent drought occurrences.
A number of drought types have been recognized by previous researchers.According to Zoljoodi and Didevarasl (2013), there are four main categories of droughts; Hydrological, Meteorological, Agricultural and Socio-economic droughts.The first three types are called the operational droughts and can be integrated into a drought management process.Their relation can be used in development of water resources program within a river basin (Karamouz et al., 2003).Propagation of hydrological and agricultural drought starts from meteorological droughts induced by changing phenomena within the hydrological cycle (Figure 1).
The three operational types of droughts are interconnected.For instance, Agricultural drought links meteorological and/or hydrological drought to agricultural impact.Agricultural droughts impact negatively on farming systems whenever they occur.Their impacts are normally two-fold; environmental and economic impacts.The agricultural drought is a type associated with low agricultural production, increased food insecurity, decline in output from agro-processing industries and unemployment incidents in the agricultural sector.From the environmental perspective, agricultural drought is caused by insufficient precipitation, high temperature that causes elevated rates of evapo-transpiration, increased salt concentration in the crop root zones and soils within irrigation systems (Mishra and Singh, 2010).The term environmental drought is sometimes used to address the adverse effects of extremely low flows on ecosystems, and may be analysed in the emerging field of eco-hydrology.
Based on purpose for research, drought indices have previously been developed and applied on drought studies.Some of the most common drought indices include palmer drought severity index (PDSI), standardized precipitation index (SPI), surface water supply index (SWSI), soil moisture deficit index (SMDI), vegetative index (VI) and stream flow drought index (SDI).In the present study, PDSI was used to analyse drought episodes in the uppar Tana River basin.
Several coefficients which are calculated to define local hydrological characteristics influenced by precipitation and temperature are calculated for use in PDSI.These coefficients depend on soil water capacity of the principal layers.The PDSI has been applied on a number of catchments for detecting and planning of drought relief programmes (Loucks and Van Beek, 2005).In the present study, spatial and temporal drought variability in the upper Tana River basin was analysed using Palmer Drought Severity Index (PDSI) to detect the drought prone areas and the severity drought events for the period 1970 to 2010.

Study area
The study area; upper Tana River basin is located within latitudes 00° 05 ' and 01° 30' south and longitudes 36° 20' and 37° 60' east.The study area covers 17,420 km 2 and is illustrated in Figure 2).
Upper Tana River basin is a portion of the Kenya's largest rivers system called Tana River basin (Jacobs et al., 2004;WRMA, 2010).There are very important vast land and forests on eastern slopes of Mount Kenya and Aberdares range within the study area.The river basin greatly regulates the hydrological processes (IFAD, 2012) and as subsequently influence the hydro-electric generation.This basin is plays a key role in hydro-electric generation, water supply and agricultural production in Kenya.

Climatic data acquisition
The data, precipitation, potential, soil moisture content and In the upper Tana River basin, data from twenty four meteorological stations were obtained from the Ministry of Water and Irrigation.The stations provided meteorological; precipitation, temperature, evaporation data.The data were then subjected to exploratory data processing.It was found out that only eight stations had reliable and sufficient data.Where the available data contained less than 20% data gaps, then these data were selected for computation of the PDSI.The eight stations used in the study (Table 1) were also objectively located within the low (LE), lower middle (LME), middle (ME) and high (HE) elevations.The stations are located at different agro-ecological zones of the basin.

Consistency test of the climatic data
A double-mass curve was fitted for the collected hydrometeorological data to test for consistency.The homogeinity of climatic data time series data was conducted to detect for any possible errors resulting from the data measurements.In addition, homogeneity was used to check for the fluctuations due to climate changes.The cumulative total climatic variable, precipitation were computed for each station and then plotted against the cumulative total of an adjacent station (Figure 3).Any sudden change in the gradient of the double-mass curve was considered to indicate inconsistency in the data.Although there were some changes at some points on the curves for some stations, it was considered insignificant for the present study.In this study, the ANN structure for each station was obtained by considering different input neurons for different time delays; t, t-1, t-2,…, t-n, in the input layer.The number of input variables was equal to the input neurons.The initial number of hidden neurons of the ANN model architecture was determined using the procedure adapted from Belayneh and Adamowski (2012) where the hidden layer neurons were initially set at 2n+1 where n is the input neurons.The Hidden Neurons (HN) were then increased and decreased through trial and error technique for data sets at each hydrometric station.This resulted to an output that was taken as the estimated variable.
The output layer comprises neurons in all the networks that are equal to the following month's variable value (It+1).In this study, the  Initially three different training algorithms were applied to train the structures.These were the back-propagation (BP), Levernberg-Marquardt (LM) and Conjugate Gradient (CG) algorithms.From preliminary results, it showed that a three-layer feed forward neural network with different input and hidden neurons was superior in performance, and that the best results were also obtained using the LM training algorithm.Thus the best ANN structure of three-layer feed forward network based on LM training algorithm was adopted for filling in of missing data in this study.The data was first normalized at each station before exporting it into the graphical user interface (GUI) of the MATLAB.This was done by applying the function given in Equation ( 1) which was adapted from Morid et al. (2007).
Where, Xn = normalized value Xmin = the selected minimum value for standardization Xmax = the selected maximum value for standardization Xo = original value xmin = minimum value present in the original data set xmax = maximum value present in the original data set.
All the input and output values for ANN were normalized to range between Xmin of equal to 0.1 and Xmax of less than 1.According to Morid et al. (2007), the values of the Xmin 0.1 and Xmax of 0.9 perform best for drought indices such as SPI and EDI.Thus these values were adapted for this study.After normalization, the various drought forecasting ranges were determined.
For each of the ANN model run on the graphical user interface (GUI) of the MATLAB performance was evaluated based on the correlation coefficient R and Mean Square Error (MSE) criteria and the best model.The best ANN models were then adopted for filling any missing data for respective hydro-meteorological stations.The steps that were followed in filling the missing data are summarized in Figure 4.

Computation of drought using PDSI
The Palmer Drought Severity Index (PDSI) was developed based on a criterion for determining the beginning and end of drought or wet period spell (Palmer, 1965;Wang, 2010).It is a simple monthly water balance model which requires rainfall, temperature and catchment soil moisture content as input parameters.This tool applies a concept of supply and demand over a two-layer model.In this concept, the difference between the quantity of precipitation needed to maintain a natural water balance level and the actual precipitation is determined.The index does not consider stream flow, reservoir water balance, and other hydro-meteorological variables that influence the drought (Karl and Knight, 1985;Yan et al., 2013a;b).The index has been modified and applied by a number of researchers.For instance Wondie and Terefe (2016) used a self-calibrated PDSI to assess drought in Ethiopia for the period 1901 to 2014).The Palmer Drought Severity Index (PDSI) was computed using precipitation, temperature and the local Available Water Content (AWC) of the soil as the input variables.The available water capacity (AWC) and Total Available Water (TAW) were estimated based on the dominant soil characteristics for the each elevation band of the upper Tana River basin.For the gauge stations within the four partitions of elevation bands, the AWC values adapted for PDSI computation were 172, 98, 74 and 82 mm which were based on values given in Table 2, for defined dominant soil types.Table 3 shows some of the physical and chemical properties of the dominant soils.

Normalization of data
The PDSI was determined by getting the difference between actual precipitation and water deficiency or surplus in any given month i.This was achieved by applying the relation: Where, di = difference between actual precipitation and pi and the climatically appropriate for existing conditions (mm) Pi = actual precipitation (mm) i P ˆ= an indicator of water deficiency or surplus in month i.

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The water deficiency or surplus was estimated from the relation: Where, i P ˆ= an indicator of water deficiency or surplus in month i (mm).PEi = potential evapo-transpiration of month i (mm).PRi = potential recharge that gives the quantity of water required to bring the soil to its water holding capacity (mm).PROi = the potential runoff (which is defined as the difference between the precipitation and potential recharge (mm).PLi = potential loss or the amount of soil moisture that could be lost from soil by evapo-transpiration during a zero precipitation period (mm).
The α, β, γ and δ are climatic coefficients which provide mean value averaged within the base period.These coefficients were computed from the following relations: Where, ET = mean actual evapo-transpiration (mm).PE = mean potential evapo-transpiration (mm).R = mean actual recharge (mm).PR = mean potential recharge (mm).RO = mean actual runoff (mm).PRO = mean potential runoff (mm).L = mean water loss due to evapo-transpiration when precipitation is zero (mm).

PL = mean potential water loss (mm).
The values of monthly PRi, PROi and PLi were derived from the generated results of soil water content for every month i using the technique given by Yan et al. (2013a;b).These variables were calculated from the following relations: The di was then converted into indices of moisture anomaly zi which was calculated using the equation: Table 3. Physical-chemical properties of the dominant soils (Muchena and Gachene, 1988).

Soil type
Particle Where, kc = climatic characteristic that was estimated using the relation: The PDSI function was used in this study is of the form: Where, PDSI = The PDSI for the i th month Xi-1 = previous months PDSI Zi = Palmer Moisture Anomaly Index (PMAI) The value of PDSI for the initial month of was taken as equal to The Zi (PMAI) is expressed as: was used.The k2 which is a function of average water demand and supply (Barua, 2010;Yan et al., 2013a;b;Zoljoodi and Didevarasl, 2013) was estimated using the relation: Where, D = mean of the absolute values of d The conceptual parameters C3 and C4 were equated to 1.2459 and 3.3684 respectively adapted from Yan et al. (2013a;b).The computed PDSI values were used to classify drought conditions based on the threshold levels given in Table 4 which was adapted from Palmer (1965) and Castano (2012).The drought severity was computed for 1970 and 2010 based on the severity equation.The area for each severity class was captured using the ArCGIS and summarized in Table 5.

Evaluation of spatial distribution of drought severity
The sum of drought severity (DId) values below zero during each year for the study period was calculated.The probability P of drought occurrence was determined by dividing the number of months that had DI values less than zero by 12 months of the year.The drought severity was then computed at each station using the relation:  Where, S = annual drought severity for a defined year DId =The sum of drought severity values below zero during a particular year P = probability of drought occurrence for the defined year N=period in months in the year (=12 months in this case).
The resulting data was then used to estimate spatial distribution of drought severity using the Krigging estimator in the ArcGIS 10.1.In this study, sixteen hydrometric stations within the upper Tana River basin were used for hydrological evaluation.These stations have unique geographical location and their spatial extent was created through the application GIS.The GIS tool was used to compute and present the spatial distribution, variation and trends of droughts for PDSI.(PDSI=-0.400)droughts are detected annually.

Temporal
The rest of the months have positive PDSI values indicating wetness of different magnitudes in the river basin (Figure 9).
The area under extreme and severe droughts are 3758.01(21.57%) and 1784.90 (10.25%) respectively for the year 1970 while the values for 2010 are 4540.36(26.06%) and 2537.55 (14.57%) respectively as given in Table 6.

Spatially distributed drought severity based on PDSI
The results of spatially distributed drought severity based on PDSI show that the ranges of maximum and minimum drought severity values in 1970 are -0.868 to -0.804 and -0.675 to -0.610, respectively.

DISCUSSION
The spatial and temporal drought was found to significantly change for the period 1970 to 2010.The temporal variability of drought from 1970 to 2010 is described by negative values that indicate droughts of different severity and duration while the positive ones correspond to wet conditions.The findings indicate that extreme drought occurred twice in the four decades.It is observed that for dry seasonal PDSI, the values in the months of January to March (J-M) are constantly higher than the ones for July to September (J-S).By comparing the time series PDSI values for dry and wet seasons for the meteorological stations, it can be seen that the time series plots for the PDSI values for dry season are generally lower than those for the wet seasons.The PDSI time series values for meteorological stations located at the lower elevation of the upper Tana River basin were lower than those for the stations which located at higher elevation.Thus, the PDSI results indicate that the areas within the lower elevations are more prone to drought risks than those in higher elevations.From the results of spatially distributed drought magnitude, there is a general increase in area under the extreme and severe drought as given by PDSI from 1970 to 2010.The distribution of extreme and severe drought categories dominate in the south-eastern parts of the upper Tana River basin while extreme wet and moderate wet conditions dominate the north-western areas.Thus, south-eastern parts of the basin have the highest risk of experiencing high drought magnitudes (Figure 10).However, the north-western areas have the lowest drought risks.Comparing the findings with similar research by Yan et al. (2013a;b) in Luanhe River basin, showed that the lowest PDSI values (PDSI< -4.00) are persistently observed in the north-western areas of Luanhe basin.On the other hand, the south-eastern areas of the upper Tana River basin exhibit similar lowest values of PDSI (PDSI< -4.00).The drought severity gave maximum and minimum drought severity values occurring respectively in the north-western and south-eastern areas of the basin.The maximum and minimum severity values increased from -1.478 to -1.348 and from -1.087 to -0.957 in 2010 as presented in the results.There was an increase in drought severity over the years of record (Figure 11).The trend in spatial PDSI severity values over time compared closely with the spatial patterns trend explained as by Zoljoodi and Didevarasasl (2013).For instance, these authors showed that the PDSI severity values increased from -1. 28 (1951-2005) to -7.68 (1999-2002) in Iran.In comparison with the present study, the results show that the PDSI increased from the range -0.675 to -0.610 in 1970 and from -1.087 to 0.957 in 2010 for the north-eastern areas of the upper Tana River basin.Thus, the findings can be used in decision making especially in prioritized drought mitigation measures within the river basin.

Conclusion
Spatial distribution of drought indicates that south-eastern parts of the basin are the most susceptible to droughts while the north-western areas are least prone to the droughts.From the results of spatially distributed drought magnitude, it can be seen that there is a general increase in area under the extreme and severe drought as given by PDSI from 1970 to 2010.The application of the PDSI reflects the spatial heterogeneity and temporal variability of drought across the upper Tana River basin.The drought assessment from this study offer technical approach for comprehensive understanding of drought for effective drought-induced disaster mitigation and its management, with a view to reducing adverse effects on livelihoods in the river basin.The findings show that the lowest PDSI values (PDSI< -4.00) are persistently observed in the north-western areas of upper Tana River basin.On the other hand, the south-eastern areas of the upper Tana River basin exhibit similar lowest values of PDSI (PDSI< -4.00).By comparing the time series results of PDSI for dry and wet seasons indicate that the temporal drought detected by PDSI values for dry season are generally lower than those for the wet seasons.The results of the study can be incorporated in drought early warning system and reduce adverse impacts of drought on water resources, ecosystems and peoples livelihoods.

Figure 2 .
Figure 2. The location of the upper Tana River basin in Kenya.

Figure 3 .
Figure 3. Double mass curve based on precipitation upper Tana River basin.

Figure 4 .
Figure 4. Flow chart of the steps used in filling the missing data using ANN.
, k2 = weighting factor d = water deficiency (mm) c2 = conceptual parameter D = absolute value of d In this study, a C2 value of 438.91 adapted from Yan et al. (2013a; b)

Figure 5 .
Figure 5.Time series of PDSI for dry seasons of at MIAD meteorological station.
Figures 5 and 6 illustrate the frequencies and duration of

Figure 6 .
Figure 6.Time series of PDSI for wet seasons at MIAD meteorological station.

Figure 7 .
Figure 7. Time series of PDSI for dry seasons at Naro-Moru meteorological station.
The available data was on daily time step but had to be re-organized into monthly average time scales for all the variables to match with the data requirements of the present research.The daily stream and monthly flow data was obtained from the Ministry of Environment and Natural Resources, and Water Resources and Management Authority (WRMA).

No. Station name Station ID Coordinates Elevation (m) Longitude (Degrees) Latitude (Degrees)
respectively.The data for each station was partitioned into training and validation data sets comprising 70% and 30% respectively of the total continuously recorded data.

Table 2 .
Dominant soils for the upper Tana River basin.
ElevationDominant soil type MC at saturation % MC at field capacity % MC at wilting point % AWC (%) TAW (mm) HE, ME, LME, LE means highest elevation, middle elevation, lower middle elevation and lowest elevation respectively.Source: Hunink et al. (2009).Feed Forward Neural Network (FFNN) and Recursive Neural Network (RNN) were applied and tested in the model training.

Table 4 .
Classification of drought based on PDSI.

Table 5 .
Drought Category-Area-Distribution (CAD) as detected using PDSI for October in 1970 and 2010.