Flood frequency under changing climate in the upper Kafue River
Stoch Environ Res Risk Assess (2013) 27:1883–1898
DOI 10.1007/s00477-013-0724-z
O R I G I N A L P A P E R
Flood frequency under changing climate in the upper Kafue River basin, southern Africa: a large scale hydrological model application
Cosmo Ngongondo • Lu Li • Lebing Gong •
Chong-Yu Xu • Berhanu F. Alemaw
Published online: 19 April 2013
Ó Springer-Verlag Berlin Heidelberg 2013
Abstract The projected impacts of climate change and variability on floods in the southern Africa has not been well studied despite the threat they pose to human life and property. In this study, the potential impacts of climate change on floods in the upper Kafue River basin, a major tributary of the Zambezi River in southern Africa, were investigated. Catchment hydrography was delineated using the Hydro1k at a spatial resolution of 1 km. The daily global hydrological model WASMOD-D model was calibrated and validated during 1971–1986 and 1987–2001 with the simple-split sample test and during 1971–1980 and 1981–1990 with the differential split sample test, against observed discharge at Machiya gauging station.
Predicted discharge for 2021–2050 and 2071–2100 were obtained by forcing the calibrated WASMOD-D with outputs from three GCMs (ECHAM, CMCC3 and IPSL) under the IPCC’s SRES A2 and B1 scenarios. The three
GCMs derived daily discharges were combined by assigning a weight to each of them according to their skills to reproduce the daily discharge. The two calibration and validation tests suggested that model performance based on evaluation criteria including the Nash–Sutcliffe coefficient,
Pearson’s correlation coefficient (r), Percent Bias and R
2 was satisfactory. Flood frequency analysis for the reference period (1960–1990) and two future time slices and climate change scenarios was performed using the peak over threshold analysis. The magnitude of flood peaks was shown to follow generalised Pareto distribution. The simulated floods in the scenario periods showed considerable departures from the reference period. In general, flood events increased during both scenario periods with
2021–2050 showing larger change. The approach in our study has a strong potential for similar assessments in other data scarce regions.
Keywords Climate change Floods WASMOD-D
Peak over threshold Kafue River Southern Africa
C. Ngongondo (
&
) L. Li L. Gong C.-Y. Xu
Department of Geosciences, University of Oslo, P.O. Box 1047,
Blindern, Oslo, Norway e-mail: cosmon@student.matnat.uio.no; cngongondo@cc.ac.mw
C. Ngongondo
Department of Geography and Earth Sciences, University of
Malawi, Chancellor College, P.O. Box 280, Zomba, Malawi
L. Gong
Department Physical Geography and Quaternary Geology,
Bert Bolin Centre for Climate Research, Stockholm University,
Stockholm, Sweden
B. F. Alemaw
Department of Geology, University of Botswana, Pr. Bag
UB00704, Gaborone, Botswana
1 Introduction
Southern Africa’s regional hydrology shows a wide range of natural variability. The region suffers from both extreme droughts and floods (e.g. Reynard et al.
; Mason and
Joubert
). Partly, this variability is due to El Nino
Southern Oscillation (ENSO), the effect of which is pronounced in the Zambezi and Limpopo River basins (Alemaw and Chaoka
on climate change impacts in southern Africa have mainly projected decreases in mean river discharge, an increase in the number of consecutive dry days and more widespread droughts during the 21st century (Strzepek and McCluskey
; Bates et al.
). The region is particularly considered highly vulnerable to climate change due to low level of
123
1884 Stoch Environ Res Risk Assess (2013) 27:1883–1898 infrastructural development (Mason and Joubert
;
Fauchereau et al.
). The rapid increases in developmental demands and a water-stressed population call for a better understanding of the response of regional hydrology to a changing climate (Arnell
; Hughes et al.
).
The impacts of climate change on hydrological extremes, in the form of floods or droughts, have not been sufficiently understood at catchment scale in southern Africa. A
decreasing trend was projected by Andersson et al. ( 2011 ) for
both low and high flows in the Pungwe River basin during
1991–2020 and 2021–2050 under the A2 and B2 climate change scenarios of the InterGovernmental Panel on Climate
Change (IPCC) Special Report on Emission Scenarios
(SRES) by Nakicenovic and Swart (
). On the contrary, in
the Okavango River basin west of the Pungwe, Wolski ( 2009 )
projected increases in both low and high flows, with the projected increase in high flow proportionately stronger than that in low flows during 2046–2065 under the SRES A2 climate change scenario. Both Andersson et al. (
) and
Wolski (
) however did not provide a frequency analysis
of the future floods in these two basins. Mkhandi et al. ( 2000 )
conducted a regional flood frequency analysis in southern
Africa. By clustering southern Africa into 54 homogenous sub-regions, Mkhandi et al. (
) derived regional growth curves with the Pearson type 3 (P3), Lognormal 3-parameter
(LN3), General Pareto (GPA) or General Extreme Value
(GEV) distributions, among which the P3 distribution was
found most acceptable. However, Mkhandi et al. ( 2000 ) did
not conduct frequency analysis for the individual gauging stations.
) projected increases in floods and droughts in many regions of the world. Exceptions were North America and Western Eurasia where projected flood frequency decreased, and Eastern Australia and
Eastern Eurasia where projected drought frequency decreased. Taye et al. (
2011 ) assessed climate change
impacts on hydrological extremes in Nyando and Lake
Tana catchments, two source regions of the Nile River
Basin. They forced the VHM and NAM hydrological models with 17 GCM outputs under the SRES climate change emission scenarios A1B and B1 from 2046 to 2065.
Increasing peak flows for the Nyando catchment were found whereas there were a lot of uncertainties for the projected extreme flows in Lake Tana catchment (Taye et al.
2011 ). Similar uncertainties in projected flows were
found in the Upper Nile River basin by Booij et al. (
who forced the HBV model with bias corrected outputs from three GCMs with the SRES A2 and B2. Studies on future extremes from other regions include, for example,
Yang et al. ( 2012 ), Liu et al. (
) and Wang et al. (
in the Huaihe, Tarim and Shiyang basins in China and
Cunderlik and Simonovic ( 2005
) in southwestern Ontario river basin, Canada.
123
Among key challenges limiting similar impact studies in southern Africa and other developing countries is paucity of hydrometeorological data at the desired spatial and temporal scales (Shongwe et al.
;
Sawunyama and Hughes
; Hughes et al.
et al.
2012 ). However, there have been significant
improvements in data quality and availability, in various forms, for hydrological model input (Do¨ll et al.
; Samaniego et al.
2011 ). The advantage is that most of the
improved data products can be used to drive large-scale hydrological models in large catchments which in most cases are sparsely gauged. Large scale hydrological models have provided a means of assessing water resources availability for better water resources management, management of international transboundary water conflicts
(Allasia et al.
) and establishing long-term data collection programmes (Widen-Nilsson et al.
scale hydrological modeling further provides the means to understand better the complex nature of the regional hydroclimatology, effects of environmental changes as well as climate change over large domains (Do¨ll et al.
and Hannah
2011 ). As outlined by Widen-Nilsson et al.
), large scale water balance models that have been applied in global water balance assessments include the
Water Balance Model (WBM) (Vo¨ro¨smarty et al.
,
1997 , 1998 ), macro-scale hydrological model
(Macro-PDM) (Arnell
,
Hydrological Model (WGHM) (Do¨ll et al.
; Kaspar
) and a sub-model of the WGHM (Do¨ll et al.
;
Alcamo et al.
2003 ). Others outlined by Allasia et al.
) include VIC family of models, e.g., ISBA-
MODCOU, WATFLOOD, LARSIM and SWIM.
In southern Africa, the semi-distributed Pitman monthly rainfall-runoff model (Pitman
1973 ) and its various modifi-
cations (Hughes
,
,
; Wilk and Hughes
hydrologic design and water resources assessments. The model was also applied in water resources assessments in the
Kafue River basin by Mwelwa (
). Several other authors have also contributed applications of large-scale hydrologi-
cal models in southern Africa. Alemaw and Chaoka ( 2003
) presented application of the Distributed GIS-based Hydrological Model (DGHM) for the southern Africa region with daily surface water abstraction and monthly soil water balance at a spatial grid resolution of 0.5
° 9 0.5
° . Vo¨ro¨smarty
) established substantial anthropogenic influences through impoundments and land use changes as well as climate change influence on the hydrology in the
Zambezi River basin with the monthly WBM at a grid resolution of 0.5
° 9 0.5
° . Reynard et al. (
probability distributed model (PDM) by Moore ( 1985
) over southern Africa and derived a 0.5
° 9 0.5
° gridded runoff for the region. Validation of the model at some catchments
Stoch Environ Res Risk Assess (2013) 27:1883–1898 1885 revealed overestimation of the runoff possibly due to artificial influences. Arnell
applied the Macro-PDM across the region at the same grid resolution.
In this study, future impacts of climate change on floods in the upper Kafue River basin in southern Africa are investigated using the large-scale hydrological model
WASMOD-D. The study was carried out in the following steps: (1) WASMOD-D was calibrated and validated at daily timescale against observed discharge; (2) frequency analysis was performed for both observed and simulated flood peaks; (3) magnitudes of flood peaks under different climate change scenarios was assessed and the corresponding flood frequency analysed. This study is based on previous work by Li et al. (
2012 ), in which the spatial and
temporal trends of simulated runoff over southern Africa were investigated using the WASMOD-D model. The current study is the first in the region that focus on flood frequency for the current climate under different climate change scenarios.
Zambezi, which are all trans-boundary and highly regulated at various points along their courses for water supply and hydropower generation (Heyns et al.
; Turton et al.
; Vo¨ro¨smarty and Moore
and Bernauer
2011 ). Flows of the Kafue are regulated in the
middle and lower reaches by the Itezhi-tezhi and Kafue
Gorge Reservoirs (Obrdlik et al.
upper Kafue River Basin remains relatively in its natural character (Obrdlik et al.
3 Methods and data
3.1 Defining catchment spatial boundaries
The procedures outlined by Gong et al. ( 2009
) were used to register the Machiya discharge station in the Hydro1k ((US
Geological Survey)
; Gong et al.
network, to delineate basin boundaries and to derive basin hydrography. Hydro1k includes raster data sets of digital elevation model (DEM), derived flow directions, flow accumulations, slope, aspect, and a compound topographic
(wetness) index and vector data sets for streamlines and basins at a spatial resolution of 1 km derived from the
GTOPO30 30
00 global elevation dataset (US Geological
Survey
). The upper Kafue River basin has a total registered area of 23,065 km
2 on the Hydro1k flow network, which is slightly larger than the 22,920 km
2 from the official records in Mwelwa (
2 Description of the study area
The Kafue River Basin is located in the Zambezi River
Basin in southern Africa (Fig.
156,995 km
2 and a total length of 1,500 km at its confluence with the Zambezi (Mwelwa
, Obrdlik et al.
). The Kafue River Basin is located mostly in the
Republic of Zambia, although the basin’s headwaters are close to the border of Zambia and Congo to the north of the
Ndola town. The whole of the Zambezi River basin spreads in eight countries namely Angola, Botswana, Malawi,
Mozambique, Namibia, Tanzania, Zambia and Zimbabwe
(Fig.
1 ). For this study, the upper Kafue River basin, i.e.,
the upstream area of the Machiya Ferry discharge station was used for flood frequency analysis.
The Kafue River basin experiences predominantly tropical climate with strongly seasonal rainfall pattern as most of southern Africa. Over 80 % of the annual total rainfall occurs during the Austral summer months from November to April when the Inter-Tropical Convergence Zone (ITCZ) and the
Congo Air Boundary (CAB), semi-permanent subtropical high pressure systems located to the southwest Indian and southeast Atlantic Oceans respectively, are active in the region. Spatially, there is however a marked gradual north to south decreases in rainfall within the basin (Mwelwa
;
Beck and Bernauer
2011 ). The whole of region is however
characterized by high inter-annual rainfall variability, especially in the drier regions, as evidenced by the droughts of 1992, 1995 and 1998 and floods of 2000 and 2001 (Unganai and Kogan
; UNEP and
ICRAF
; Layberry et al.
2006 ). Major river basins in the
region include the Limpopo, Orange, Okavango and
3.2 Description of the WASMOD-D
This study applied the WASMOD-D large scale hydrologi-
cal model by Gong et al. ( 2009
), with the -D standing for daily timescale. The WASMOD-D is a daily version of the monthly WASMOD-M global water balance hydrological model by Widen-Nilsson et al. (
based on the original monthly Water and Snow Balance
Modeling system by Xu ( 2002 ), with the -M standing for
macro-scale (Widen-Nilsson et al.
). The various equations of the WASMODM-D model are presented in
detail by Widen-Nilsson et al. ( 2007
) and Gong et al. (
The two model versions differ in their runoff equations with the WASMOD-D having, in place of the linear functions in
WASMOD-M, the following non-linear exponential functions that simulate fast and slow runoff (Gong et al.
):
SP ¼ 1 e c
1
LM
F ¼ P n
SP
S ¼ LM ð 1 exp c
2
LM Þ
ð
ð
ð
1
2
3
Þ
Þ
Þ where SP is the percentage of each cell area that is saturated, LM is the land moisture (water available in each cell
123
1886 Stoch Environ Res Risk Assess (2013) 27:1883–1898
Fig. 1 Map of the Zambezi basin ( coloured ) showing the Kafue River Basin ( left ) and Map of Africa showing Zambia for actual evapotranspiration and runoff), F is the fast runoff, S is the slow runoff or base flow, P n rainfall and c
1 and c
2 is the net are model parameters. The model in its original form has 3–6 parameters, with snow-free catchments like those used in this study requiring only three of these parameters namely: the evaporation parameter a
4
( ), the fast-runoff parameter c
1 slow-runoff parameter c
2
(mm
1
).
(mm
1
), and the
The WASMODM-D model uses gridded data sets of daily precipitation, temperature and potential evapotranspiration to calculate the runoff from each grid cell. Daily potential evapotranspiration, calculated from daily air temperature ( ° C) and relative humidity (RH%) derived from the dew temperature, was used to compute actual evapotranspiration as follows:
E ¼ min E p
AW
ð 1 a
4
Ep Þ ; AW ð 4 Þ where AW is the water available (mm day
1
) for actual evapotranspiration and E p
(mm day
1
) is the potential evapotranspiration calculated as in Widen-Nilsson et al.
(
). Daily runoff in each cell was computed as the sum of fast and slow flows whose non-linear exponential for-
mulations are presented in Gong et al. ( 2009
,
opposed to their linear formulations in the monthly
WASMOD-M by Widen-Nilsson et al. ( 2007
). The runoff generated from each cell is routed through the catchment using the aggregated network-response-function (NRF)
routing algorithm by Gong et al. ( 2009 ).
3.2.1 Input dataset, calibration and validation of WASMOD-D model
Daily precipitation, mean and dew point temperature data for the upper Kafue River basin were extracted from the
WATCH Forcing Data (WFD, Weedon et al.
,
a gridded global climate dataset developed by the EU
Water and Global Change (WATCH) project. The WFD was derived from the ERA-40 reanalysis (Uppala et al.
) with bias corrections (Weedon et al.
,
Hydrological models introduces bias when directly forced with GCM output due to the coarse grid of GCM (e.g. Xu
; Piani et al.
Therefore, GCM output has to be bias corrected and/or downscaled before being used as input for hydrological models (Piani et al.
2010 ). Downscaling of GCM output
can either be statistical or dynamic (Xu
The daily dataset includes 2-m air temperature, dew point temperature and wind speed, 10-m pressure and specific humidity, downward longwave and shortwave radiation, rainfall and snowfall rates. Hydrological time series were extracted from 1958 to 2001 at a spatial resolution of 0.5
° 9 0.5
° that covers the registered basin area in Hydro1k, which served as input for the WASMOD-D.
Simulated discharge was then calibrated against daily observed discharge data of the upper Kafue River at
Machiya Station for the period 1971–2001 (GRDC
The first year (1971) was used as a warm-up period. The procedures for selecting the ‘‘optimal’’ parameter set
123
Stoch Environ Res Risk Assess (2013) 27:1883–1898 1887 during model calibration as outlined in Gong et al. (
) were adopted.
Model performance during calibration was evaluated using regression based and dimensionless statistical measures and graphical measures (Moriasi et al.
study by Moriasi et al. (
2007 ) explored a wide range of
model accuracy evaluation criteria and recommended the use of the Nash–Sutcliffe (NS) coefficient (Nash and
Sutcliffe
), percent bias error (PBIAS) and ratio of the root mean square error to the standard deviation of measured data (RSR). These measures are expressed as follows:
NS ¼ 1
PBIAS ¼ 1
X
ð Q
Obs h X
ð Q
Q
Sim
Obs
Þ
.X
Q
Obs
Q
Sim
Q
Sim
Þ 100
.X
Q
Obs i
ð
ð
5
6
Þ
Þ
RSR ¼
¼
RMSE q Obs
ð Q
Obs
Q
Sim
Þ
2 q
ð Q
Obs
Q
Obs
Þ
2
ð 7 Þ where Q
Obs are the observed flows with mean Q
Obs and
Q
Sim are the simulated flows with mean Q
Sim
. Moriasi et al.
(
) recommended that model performance is acceptable if NS [ 0.5, RSR B 0.70, and PBIAS ± 25 %. These suggested accepted levels of performance indicators are generally for normal water resource assessments. Since this study is aimed at predicting and analysing future extreme flows which can be highly uncertain, higher acceptable levels of model performance indicators were adopted to reduce the uncertainty with the NS [ 0.80, RSR B 0.5 and
PBIAS ± 10 %. Other selected model performance indicators used in the study include the Pearson’s correlations coefficient between the observed and simulated flows
( r [ 0.8), coefficient of determination ( R
2
[ 0.85) and the index of agreement (d) represented as the ratio between mean square error and the potential error (Moriasi et al.
). The simulated and observed flows were also qualitatively assessed by comparing their plots of th daily hydrographs and flow duration curves (FDC), a plot the percentage of time that a given daily flow rate is equalled or exceeded over a historic period (Vogel and Fennessey
; Westerberg et al.
). The Weibul plotting position formula (Vogel and Fennessey
FDC plots in this study.
3.3 Climate change scenarios
Daily climate outputs from three Global Climate Models
(GCMs): (ECHAM from Max Plank Institute, Germany;
CNCM3 from Meteo-France, France; and IPSL from
Institute Pierre-Simon Laplace, Paris) served as input data for the WASMOD-D model. Each GCM provided daily precipitation, mean and dew temperature at a spatial resolution of 0.5
° for the reference period (1961–1990) and future climate change scenarios A2 and B1 under the IPCC
Special Report on Emission Scenarios (SRES) by Nak-
). The A2 scenario storyline is based on continuous global population growth reaching 15 billion in 2100 coupled with regionally oriented economic developed. This would result in approximate doubling of
CO
2 and a global temperature increase of between 2.0 and
5.4
° C. The B1 scenario story line is more environmentally friendly oriented characterized by rapid economic growth, global population rising to 9 billion by 2050, reduction in material intensity and introduction of efficient and environmentally friendly technologies with emphasis on global solutions to economic, social and environmental stability.
Global temperature under the B1 scenario is expected to increase by between 1.1 and 2.9
° C (Nakicenovic and
Swart
2000 ; IPCC 2007). The WASMOD-D model was run
using these input data and the simulated discharge during
1961–1990 served as reference for the projected discharge in two future time slices: 2020–2050 and 2071–2100.
3.4 Weighted average of GCM-derived discharge
This study used the discharge-weighted ensemble technique (Sperna Weiland et al.
; Gain et al.
) to combine simulated discharge from the various GCM forcing data. The discharge weighted ensemble technique calculates a weighted average of discharge time series derived from each GCM. The weight is calculated based on the skill of each GCM-derived discharge in reproducing observed mean monthly discharge (Gain et al.
): w i
¼ exp
!,
1 y i
2
12 j ¼ 1 r 2 z ij i ¼ 1 exp
1
12 j ¼ 1 y i r 2 z ij
2
!
ð 8 Þ where w i is the GCM specific weighting factor, j is the month (1 = January, 12 = December), r 2 is the standard error of discharge observation, y i observed discharge, z ij is the monthly mean is the monthly mean simulated discharge for the i th GCM in the j th month and n is the number of GCMS (n = 3). Following Di Baldassarre and
Montanari (
), the standard error of discharge observations was assumed to average 25 % of the observed mean value for each month. The daily weighted mean discharge ( l ) and variance r
2 are then calculated from the simulated discharge ( z i
).
l z
¼ i ¼ 1 w i z i
ð 9 Þ
123
1888 Stoch Environ Res Risk Assess (2013) 27:1883–1898 r 2 ¼ i ¼ 1 w i z i l z
2
ð 10 Þ
The technique has been found by other studies to have more reliable results as compared to non-weighted ensemble mean technique (Sperna Weiland et al.
The GCM ensemble-weighted and WFD simulated discharges were compared with the observed discharge during their common period from 1972 to 2000 on a FDC.
For the future climate change scenarios, the daily ensemble-weighted discharge for the A2 and B1 scenarios were combined by simple arithmetic average.
The direction of temporal trends of the daily weighted flows was quantified using the Mann-Kendal (MK) statistic and the slopes of the trends were determined by linear regression (Yang et al.
).
3.5 Flood frequency analysis
Two commonly used flood frequency analyses methods are, Annual Maxima Series (AMS) and the peak over threshold (POT; also called Partial Duration series, PDS).
The POT method analyses peak flows above some predefined threshold u (Madsen et al.
the two methods have been widely discussed (e.g. Wang
; Madsen et al.
; Tanaka and Takara
tschalk and Krasovskaia
). It is generally agreed that POT gives more robust results provided certain pre-conditions such as the independence of selected peaks, selection of appropriate
threshold level, are met. Lang et al. ( 1999
) however recommended that both approaches should be tested and the results compared. In this study, both approaches were therefore tested using the observed and calibrated flows for the period 1971–2001. The one-day Annual maxima Series
(AMS1) were analysed by fitting the Generalized Extreme
Value (GEV) distribution which has a cumulative distribution function of the form:
ð x Þ ¼
( exp n
1 þ exp exp n x l r x l r
1 = n if if n n
6¼
¼
0
0
ð 11 Þ where n is a shape parameter, r is the scale parameter, l is a location parameter and 1 þ n x l r
[ 0 is the support.
Quantile estimates with return period T and exceedance probability p can then be estimated from: x p
¼ ^ ½ 1 ð log 1 p Þ Þ
1
; with p ¼
T
ð 12 Þ
POT analysis was used to model excesses above a selected threshold u . Such series normally follow the generalised Pareto distribution (GPA), which has the following cumulative distribution function:
G n ; b
8
>
1
¼
>
: 1 exp x
1 þ n b x b
1 n if if n n
6¼
¼
0
0
ð 13 Þ where x are the excesses above the threshold u , b is a scale parameter and n is a shape parameter. When n C 0 x C 0 and b [ 0 and if n \ 0 ; then 0 x n b
(Ghosh and
Resnick
). Threshold exceedancies occurrence (n) in t-years is assumed to be Poisson distributed (Lang et al.
) with probability distribution expressed as: p n ð t Þ ¼ n g ¼ exp k t k t n !
n n ¼ 1 ; 2 ; 3 . . .
; where k ¼ n t
ð 14 Þ
Threshold selection is a key problem for POT analysis and is in many cases subjective. Three approaches were applied to select an optimum threshold u . The first two were the graphical mean excess plot (MEP) and the shape parameter plot (SP). The mean excess plot is constructed from the average threshold exceedances E ð X u X [ u Þ against the u governed by:
ð u X [ u Þ ¼ b n u
1 þ n
ð 15 Þ
The threshold is selected for the lowest value of u which has an approximately linear relationship with the mean excess E X u Þ (Coles
). The SP plot was used to qualitatively determine where the distribution parameters are approximately constant above a particular threshold.
The following expression was used to estimate quantiles with return period T and exceedance probability p : x p
¼
8
<
: u u þ b ln k T p
; n b
1 -
1 k T p for all n ¼ 0
; for all n 6¼ 0
ð 16 Þ
The third is the inter flood period ( h ), i.e. the period between the time of the falling limb of the previous flood crossing the threshold and the time when the rising limb of the next flood crosses the selected threshold (Petrow and
Merz
2009 ), has to ensure the serial independence of the
flood peaks (Lang et al.
Rustomji et al.
were therefore selected following Svensson et al. ( 2005
)
) using the range:
5 days h 5 days þ log A ð 17 Þ
123
Stoch Environ Res Risk Assess (2013) 27:1883–1898 1889 where A is the catchment area in square miles (miles
2
). In
the study by Svensson et al. ( 2005 ),
h = 5 days if
A \ 45,000 km
2
. Independence of the POT series’ was only accepted when the lag 1 and 2 autocorrelation coefficients were not statistically significant.
L-moments of the observed and simulated peak flows by both AMS1 and POT methods were used to estimate parameters of the GEV and GPA distributions respectively, based on the regional frequency (RFA) analysis approach
(Hosking and Wallis
1997 ). L-moments are expectations of
certain linear combinations of order statistics (Hosking
). The upper Kafue catchment area was in this considered as one homogeneous region with a single discharge station with the AMS1 and POT series. The quantiles, confidence intervals and RMSE values were determined and the series yielding the most minimum RMSE vales were preferable. Goodness of fit of the POT and AMS1 to the extreme distributions was also tested graphically (e.g.
P–P and Q–Q plots). Flood magnitudes with return period periods T = 5, 10, 20, 50, 100-years for the current and the
GCM weighted future scenarios were then estimated.
4 Results and discussions
4.1 Model calibration and validation
The WASMOD-D was calibrated and validated using observed discharge from 1971 to 2001. The split-sample test (Klemes
) was applied during the periods
1971–1987 and 1988–2001. The differential split-sample test (Klemes
; Xu
), recommended for hydrological simulations under changing climate, was applied during the wetter period 1971–1980 and drier period
1981–1990. Table
summarizes some of the statistics of the daily observed and simulated discharge for the simple split-sample test, whereas results for the differential splitsample test are shown in Table
. Figure
a shows the observed and simulated daily flows during the period from
1971 to 2001. Mean monthly flows are shown in Fig.
b and the daily flow duration curve (FDC) is shown in
Fig.
From Tables
and
2 , it is seen from the evaluation
indicators that the model performance was comparable and acceptable during all calibration and validation periods. In all calibration and validation cases, the NS [ 0.82,
PBIAS \ ± 10, RSR \ 0.43, R
2
[ 0.82, d [ 0.95, and r [ 0.91. The annual flow regime in southern Africa, characterized by rising flows from November to April followed by recession between May and October, is well reproduced during the entire calibration and validation period (Fig.
a). This indicates that the model captures the overall seasonal variation, although Fig.
slight overestimation towards the end of the rainy season
(March and April) and underestimation of most of the flow recession months in the dry season. Similar graphical analysis for the differential split-sample test (figures not shown) also revealed that the WASDMOD-D model is capable of reproducing flows when calibrated during the wetter and validated in the drier period and vice versa.
The GCM weightings for the daily simulated flows were
0.44 (CNCM3), 0.25 (ECHAM) and 0.31 (IPSL). The FDC for the WFD-driven calibrated flow and weighted average of GCM-driven simulated flows during 1972–2000
(Fig.
c) shows that the model, with either WFD-driven or
GCM-driven, can reasonably reproduce frequencies of both high and low flows, although. It can however be observed that the intermediate flows on the FDC were slightly overestimated whereas the low flows were being slightly underestimated.
4.2 Comparison of AMS1 or POT peak flows
To select an appropriate approach for modeling the hydrological extremes, results from AMS1 and POT analysis were compared in terms of the sensitivity of the estimated quantiles. Based on the MEP and SPP, thresholds u
01
= 540 m
3 s
1 for observed POT series
(mean = 608 m
3 s
1
) and u
02
= 490 m ulated POT series (mean = 532 m
3 s
3
1 s
1 for the sim-
) were selected.
Both the thresholds corresponds to a total of 62 extreme flow events giving intensity k = 2.07 year
1
, which is just above the recommended minimum threshold of 1.65 (Lang et al.
).
For the AMS1 series, the means were respectively
405 m
3 s
1 and 417 m
3 s
1 for the simulated and observed discharge for the 31 extreme events. These are somewhat lower than those of the POT series. The growth curve for different exceedence probabilities of the GPA distribution fitted observed and simulated POT series and GEV distribution fitted observed and simulated AMS1 by the
L-moments method is shown in Fig.
between the AMS1 series is evident in the upper tails of the growth curve where the most severe and rare events occur.
The POT series in Fig.
3 a however show a much better fit
both in the upper and lower tails.
Sensitivity analysis of the AMS1 and POT estimated extremes during the calibration and validation period for the simple split sample test (Fig.
b) show that the AMS1 had less accurate RMSE values as shown by the higher
RMSE values especially in the frequently occurring floods
T B 50 years. RMSE results are presented up to 100 years since the length of the observed data is only 30 years. The
5T rule (Robinson and Reed
estimate floods with return period of up to 150 years with
123
1890 Stoch Environ Res Risk Assess (2013) 27:1883–1898
Table 1 Model performance by simple split-sample test in the upper Kafue River basin during 1971–1986 and 1987–2001
Calibration
Period Mean discharge
(m
3 s
1
)
Obs Sim
NS PBIAS RSR Days R
2 r
Validation
Period Mean discharge
(m
3 s
1
)
Obs Sim
NS PBIAS RSR Days R
2
1971–1986 156.4
1987–2001 102.04
158
110.6
0.83
1.0
0.82
2.8
0.38
0.96
0.86
0.93
1987–2001 102.04
106.40
0.43
0.95
0.82
0.90
1971–1986 156.4
154.8
0.82
6.9
0.83
2.2
r
0.43
0.95
0.82
0.91
0.41
0.95
0.83
0.91
Table 2 Model performance by differential split-sample during test wet (1971–1980) and dry years (1981–1990) for the upper Kafue River basin
Calibration Validation
Period NS PBIAS RSR Days R
2 r Period NS PBIAS RSR Days R
2 r Mean discharge
(m
3 s
1
)
Obs Sim
Mean discharge
(m
3 s
1
)
Obs Sim
1971–1980 170.8
1981–1990 127.5
165.5
114.8
0.84
3.1
0.81
8.2
0.40
0.95
0.84
0.92
1981–1990 127.5
0.43
0.95
0.83
0.91
1971–1980 170.8
120.3
168.2
0.82
3.9
0.84
1.6
0.42
0.95
0.82
0.91
0.40
0.96
0.84
0.92
confidence. From the sensitivity results, future floods for
GCM based scenarios were analysed using POT analysis.
4.3 Climate change impacts on peak flows
4.3.1 Changes in daily flows
Table
shows statistics of GCM-derived daily weighted discharge during the reference period (1961–1990) and the projected changes in the future periods from 2021 to 2050 and 2071 to 2100. The table shows that, relative to the reference period (1960–1990), mean daily GCM-weighted discharge increase from 2021 to 2050 by 16 % on average, with the A2 scenarios projecting a slightly higher increase than the B1 scenario. Table
also show that the negative trend for the daily flows during the reference period, where the all GCM average trend was 0.78 m
3 s
1 year
1
, continues during 2021–2050 but with less intensity, as the trend magnitude decreases in both the A2 and B1 scenarios
(scenarios average = 0.63 m
3 s
1
). A transition from negative to positive trends from 2050 is suggested. After
2071, the flows show less changes from the reference period as compared to the 2021–2050 period, but are still above the reference period on average by 40.3 % with a scenarios mean trend of 0.24 m
3 s
1 year
1
. The A2 and
B1 scenarios during 2071–2100 however suggest opposite trends.
The simulated seasonal variation during the reference period and the two scenario periods (Fig.
considerable increases between January and May but with no change in terms of the timing of the peak. Projected monthly means for the A2 and B1 scenarios are similar during 2021–2050. However, the B1 scenario during
2071–2100 suggests more change than the A2, although
123 both are above the reference period but below the
2021–2050 period. On the other hand, dry season flows between July and October in Fig.
unchanged in terms of magnitudes. However, the ratios of the monthly mean flows during the reference and projected flows (Fig.
4 b) show considerable changes in the dry sea-
son months as well especially in September and October.
The comparison of the daily FDC during 1960–1990 with the two future scenario periods (FDC in Fig.
shows that the high flows (with low exceedence probability) increased in both 2021–2050 and 2071–2100, with the former period showing higher increases than the later. It can also be observed from Table
that the daily flows both in the reference and future scenarios are marked by high coefficients of variation (CVs). There was an overall increase in the CVs, from 1.21 between 1960 and 1990 to
1.25 (representing ?
3.3 %) during 2020–2050 and to 1.26
(representing ?
4.1 %) during 2071–2100. Our results do not entirely agree with previous findings within in general and other parts of southern Africa (e.g. Strzepek and
McCluskey
; Milly et al.
projected general decreases in future mean flows in the region as compared to various reference periods during the last century. The differences can be attributed to different base and projection periods, the scenarios used as well as grid based assessments in contrast to the catchment approach used in this study.
4.3.2 Projected peak flows during 2021–2050 and 2071–2100
Peak flows from the POT analysis show different change patterns for the two climate-change scenarios A2 and B1, as well as for the two 30 year time periods. Table
Stoch Environ Res Risk Assess (2013) 27:1883–1898
Fig. 2 a Observed and simulated daily flows for the upper Kafue River at Machiya during calibration (1971–1986) and validation (1987–2001) for the simple split sample test.
b Observed and simulated monthly mean discharge for the upper Kafue River at Machiya during calibration and validation period.
c FDC for observed, WFD simulated and
GCM weighted discharge for the upper Kafue River at
Machiya (1972–2000)
1891
123
1892
Fig. 3 a Growth curve for observed and simulated AMS1 and POT series in the upper
Kafue River Basin at Machiya
(1972–2001).
b RMSE for
AMS1 and POT of flows with return period T = 2, 3, 4, 5, 10,
50 and 60 years for the upper
Kafue River basin at Machiya
(1972–2001)
Stoch Environ Res Risk Assess (2013) 27:1883–1898
Table 3 Comparison of GCM weighted simulated daily mean discharge during reference (1960–1990), 2021 (2021–2050) and 2071
(2071–2100) under scenarios A2 and B1
Scenario Mean (m
3 s
1
) Stdev (m
3 s
1
) CV Skew Kurt MK Slope (m
3 s
1
/year) Change (%)
Reference
A2-2021
B1-2021
Mean-2021
A2-2071
B1-2071
Mean-2071
73.24
117.20
114.70
115.95
96.35
109.08
102.71
88.62
150.95
149.80
144.90
129.12
140.24
129.88
1.21
1.29
1.31
1.25
1.34
1.29
1.26
0.95
1.31
1.32
1.05
1.53
1.20
1.11
2.56
4.14
4.01
2.79
5.39
3.45
3.05
6.10
5.01
1.42
3.38
1.84
1.14
0.28
0.78
0.99
0.26
0.63
0.21
0.69
0.24
?
?
?
60.0
56.6
58.3
?
31.6
?
48.9
?
40.3
summarizes the characteristics of the projected peak flows for 2020–2050 and 2171–2100. Table
shows the quantiles of the projected flows. Qualitative assessments of the
P–P plot (comparing the empirical probability with the distribution probability) and Q–Q plot (compares empirical quantiles with distribution quantiles (figures not shown)
123
Stoch Environ Res Risk Assess (2013) 27:1883–1898
Fig. 4 a Projected changes in the monthly flow regime as compared to the reference period for the upper Kafue
River Basin.
b Ratios of projected to the reference monthly mean discharge for the upper Kafue River basin.
c FDC for the reference (1961–1990) and projected scenarios
(2021–2050, 2071–2100) mean discharge for the upper Kafue
River Basin
1893
123
1894 Stoch Environ Res Risk Assess (2013) 27:1883–1898 suggest acceptable fit of the peak flows to the GPA distribution. Figure
presents the projected weighted quantiles of A2 and B1 scenarios T = 5, 10, 20, 50, 100 years and the mean for the two scenarios.
From Table
, it can be seen that the averages of the projected peak flows increased during 2021–2050 followed by a decrease from 2071 to 2100. There is also, however, a gradual increase in the intensity ( k ) by 18.32 % from an average of 2.57 per year to 3.63 events during 2071–2100.
It is seen from Table
and graphically in Fig.
that the extremes during 1960–1990 ranged from about
780.7 m
3 s
1 for the 5-year event to a maximum of about
1,467 m
3 s
1 for the 100-year event. The 2021–2050 period sees the largest increase in the flood events occurrence especially for the A2 scenario. For example, the magnitude of the 100 year event during 1960–1990 is projected to change to the 20 year event according to the A2 scenario, with a more intense 100-year event. The B1 scenario projects more modest extreme flows during 2021–2050
Table 5 Extreme flows and their return periods during 1961–1990
(reference), 2020–2050 and 2071–2100
Scenario Return period (T-years)
5 10 20 50 100
Reference
A2-2021
B1-2021
Mean-2021
A2-2071
B1-2071
Mean-2071
780.7
1020.8
853.6
937.2
975.5
878.7
927.1
903.3
1204.4
944.3
1074.3
1104.5
1004.0
1054.2
1043.5
1421.7
1034.1
1227.9
1237.9
1139.5
1188.7
1265.0
1789.7
1156.6
1473.1
1428.2
1341.2
1384.7
1466.6
2156.4
1254.4
1705.4
1586.9
1515.1
1551.0
with those events below 20 years being less than those for the reference period. The mean for the A2 and B1 scenarios during 2021–2050 projected a 5 year flood magnitude of
937.2 m
3
1705.4 m
3 s
1 s
1 and a 100 year flood of magnitude
, representing an increase over the
Table 4 Summary statistics of simulated POT extremes summary during 1960–1990, 2020–2050 and 2070–2100
Period Threshold
(m
3 s
1
)
Exceedances # Events # Min
(m
3 s
1
)
Median
(m
3 s
1
)
Mean
(m
3 s
1
)
Reference
A2-2021
B1-2021
Mean-2021
A2-2071
B1-2071
Mean-2071
411.8
430.2
420.3
425.2
437.1
403.7
420.4
486
590
700
645
678
661
669
77
92
110
101
109
107
108
412.6
430.6
421.1
425.9
438.0
405.1
421.6
482.6
541.3
498.3
519.8
545.7
484.1
514.9
500.7
584.0
538.8
561.4
584.5
522.9
553.7
Max
(m
3 s
1
)
751.5
1106.8
1039.7
1073.3
1141.1
887.7
1014.4
Fig. 5 Future extremes flows in the under the A2 and B1 scenarios during 2020–2050 and
2170–2100 k
(year
1
)
2.57
3.07
3.68
3.37
3.66
3.59
3.63
123
Stoch Environ Res Risk Assess (2013) 27:1883–1898 1895
1960–1990 extremes by 20.1 and 16.3 % respectively. The projected increases in the extremes during 2021–2050 agree in general with the Okavango River basin projections by Wolski (
The projected flood extremes during 2071–2100 suggest an increase in magnitudes over the reference period, but with lower magnitudes as compared to the 2021–2050 extremes.
The difference between the A2 and B1 scenarios during
2071–2100 is not as large as that during 2021–2050. The mean magnitude of the 5 year event for the A2 and B1 scenarios during 2071–2100 is still comparable to that during
2021–2050, with a slight decrease of 1.1 % and representing a total overall of increase of about 18.7 % over the
5 year event for the reference period event. The 100 year extreme event during 2071–2100 however suggests an overall increase of 5.8 % over the reference period event.
5 Conclusion
In this study, the large scale hydrological model WAS-
MOD-D was applied at daily timescale driven by the WFD in the upper Kafue River basin. Three GCMs outputs under the A2 and B1 SRES scenarios were further used as input to the model to simulate future daily flows during
2021–2050 and 2071–2100. The WMO reference period from 1960 to 1990 was used for comparison of any changes. Daily flow series were derived from the GCM output simulated flows using the discharge weighted ensemble approach. The performance of the WASMOD-D model during calibration and validation was acceptable under stationary and non-stationary conditions. The period during
2021–2050 showed more increased in daily mean discharge from the reference period especially under the A2 scenarios. POT events fitted to the GPA distribution suggest that extreme high flows will increase in magnitude during
2021–2050 and 2071–2100 as compared to the reference period. These changes were however scenario dependent, with the largest changes occurring during 2021–2050 under the A2 scenario. The annual intensity of the extreme events increases from 2021 to 2100. This study demonstrates an approach that can be applied in data scarce regions to understand the behavior of simulated future floods.
Acknowledgments This study was supported by the project
Capacity Building in Water Sciences for the Better Management of
Water Resources in (NUFUPRO-2007) funded by the Norwegian
Programme for Development, Research and Education (NUFU) and the Environment and Development Programme (FRIMUF) of the
Research Council of Norway, project 190159/V10 (SoCoCA). The second author was also supported by The Research Council of Norway (RCN) with project number 171783 (FRIMUF), and by the
Programme of Introducing Talents of Discipline to Universities—the
111 Project of Hohai University. We gratefully thank the E.U funded
Watch Project for availing to us the WFD and the GCM future scenarios data as well as their technical support with data retrieval.
The GRDC is gratefully acknowledged for kindly providing the discharge data for the Kafue River at Machiya station.
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