Flood frequency under changing climate in the upper Kafue River

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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.

1997

; Mason and

Joubert

1998

). 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

2006 ; Jury and Pathack

1993 ). Previous studies

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

2006

; Bates et al.

2008

). 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

1998

;

Fauchereau et al.

2003

). 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

2004

; Hughes et al.

2006

).

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 (

2000

). 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. (

2011

) and

Wolski (

2009

) 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. (

2000

) 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.

Hirabayashi et al. ( 2008

) 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. (

2011 )

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. (

2011

) and Wang et al. (

2012 )

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.

2006 ; Wilk et al.

2006

;

Sawunyama and Hughes

2008

; Hughes et al.

2010 ; Jung

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.

2008

; 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.

2006

) and establishing long-term data collection programmes (Widen-Nilsson et al.

2007 ). Large

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.

2008 , Cloke

and Hannah

2011 ). As outlined by Widen-Nilsson et al.

( 2007

), 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.

1989 ,

1996

,

1997 , 1998 ), macro-scale hydrological model

(Macro-PDM) (Arnell

1999

,

2003 ), the WaterGap Global

Hydrological Model (WGHM) (Do¨ll et al.

2003

; Kaspar

2004

) and a sub-model of the WGHM (Do¨ll et al.

1999

;

Alcamo et al.

2003 ). Others outlined by Allasia et al.

( 2006

) 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

1995 , 1997

,

2002

,

2004 ; Hughes et al.

2002 ,

2010

; Wilk and Hughes

2002 ) are widely applied for

hydrologic design and water resources assessments. The model was also applied in water resources assessments in the

Kafue River basin by Mwelwa (

2004

). 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

and Moore ( 1991

) 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. (

1997 ) applied the

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

(1999)

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.

2008 ; Zhu and Ringler

2010

; Turton et al.

2004

; Vo¨ro¨smarty and Moore

1991 ; Beck

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.

1989 ). River flow in the

upper Kafue River Basin remains relatively in its natural character (Obrdlik et al.

1989 ).

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)

1996a

; Gong et al.

2009 ) global river

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

1996b

). 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 (

2004 ).

2 Description of the study area

The Kafue River Basin is located in the Zambezi River

Basin in southern Africa (Fig.

1 ) with a total area of

156,995 km

2 and a total length of 1,500 km at its confluence with the Zambezi (Mwelwa

2004

, Obrdlik et al.

1989

). 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

2004

;

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

1998 ; Bartman et al.

2003

; UNEP and

ICRAF

2006

; 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. (

2007 ). WASMOD-M is

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.

2007

). The various equations of the WASMODM-D model are presented in

detail by Widen-Nilsson et al. ( 2007

) and Gong et al. (

2009 ).

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.

2009

):

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.

(

2007

). 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

,

2011 ), as

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.

2010

,

2011 ),

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.

2005

) with bias corrections (Weedon et al.

2010

,

2011 ).

Hydrological models introduces bias when directly forced with GCM output due to the coarse grid of GCM (e.g. Xu

1999

; Piani et al.

2010 ; Taye et al.

2011 ; Wang et al.

2012 ).

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

1999 ).

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

2010 ).

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. (

2011 ),

Li et al. ( 2012

) and Xu ( 2002

) were adopted.

Model performance during calibration was evaluated using regression based and dimensionless statistical measures and graphical measures (Moriasi et al.

2007 ). The

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

1970

), 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.

(

2007

) 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.

2007

). 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

1994

; Westerberg et al.

2011

). The Weibul plotting position formula (Vogel and Fennessey

1994 ) was used for the

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-

icenovic and Swart ( 2000

). 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.

2012

; Gain et al.

2011

) 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.

2011

): 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 (

2009

) and Gain et al. ( 2011

), 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.

2012 ).

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.

2010

).

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.

1997 ). The choice between

the two methods have been widely discussed (e.g. Wang

1991

; Madsen et al.

1997

; Tanaka and Takara

2002 ; Got-

tschalk and Krasovskaia

2002 ; Rosbjerg and Madsen

2004

). 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

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

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

2010

). Threshold exceedancies occurrence (n) in t-years is assumed to be Poisson distributed (Lang et al.

1999

) 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

2001

). 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.

1999 , Engeland et al.

2004 ,

Rustomji et al.

2009 , Petrow and Merz

2009 ). The peaks

were therefore selected following Svensson et al. ( 2005

)

and Lang et al. ( 1999

) 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

1990

). 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

1986

) was applied during the periods

1971–1987 and 1988–2001. The differential split-sample test (Klemes

1986

; Xu

1999

), recommended for hydrological simulations under changing climate, was applied during the wetter period 1971–1980 and drier period

1981–1990. Table

1

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

2

. Figure

2

a shows the observed and simulated daily flows during the period from

1971 to 2001. Mean monthly flows are shown in Fig.

2

b and the daily flow duration curve (FDC) is shown in

Fig.

2 c.

From Tables

1

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.

2

a). This indicates that the model captures the overall seasonal variation, although Fig.

2 b show some

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.

2

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.

1999 , Rosbjerg and Madsen

2004

).

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.

3 a. The mismatch

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.

3

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

1999 ) suggests we can only

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

3

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

3

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.

4 a) suggest

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.

4 a remain largely

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.

4 c)

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

3

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

2006

; Milly et al.

2008 ). Those studies all

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

4

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

5

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

5

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

4

, 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

5

and graphically in Fig.

5

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 (

2009 ).

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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