trend and persistence of precipitation under climate change scenarios for kansabati basin, india

HYDROLOGICAL PROCESSESHydrol. Process. 23, 2345–2357 (2009)Published online 22 May 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/hyp.7342

Trend and persistence of precipitation under climate changescenarios for Kansabati basin, India

Ashok K. Mishra,1* Mehmet Ozger1,2 and Vijay P. Singh1

1 Department of Civil, Biological and Agricultural Engineering, Texas A&M University, TX 77843-2117, USA2 Hydraulics Division, Civil Engineering Department, Istanbul Technical University, Istanbul 34469, Turkey

Abstract:

With increasing uncertainties associated with climate change, precipitation characteristics pattern are receiving much attentionthese days. This paper investigated the impact of climate change on precipitation in the Kansabati basin, India. Trend andpersistence of projected precipitation based on annual, wet and dry periods were studied using global climate model (GCM) andscenario uncertainty. A downscaling method based on Bayesian neural network was applied to project precipitation generatedfrom six GCMs using two scenarios (A2 and B2). The precipitation values for any of three time periods (dry, wet and annual)do not show significant increasing or decreasing trends during 2001–2050 time period. There is likely an increasing trendin precipitation for annual and wet periods during 2051–2100 based on A2 scenario and a decreasing trend in dry periodprecipitation based on B2 scenario. Persistence during dry period precipitation among stations varies drastically based onhistorical data with the highest persistence towards north-west part of the basin. Copyright 2009 John Wiley & Sons, Ltd.

KEY WORDS Bayesian neural network; downscaling; trend; persistence; precipitation

Received 7 October 2008; Accepted 24 March 2009

INTRODUCTION

Global warming intensifies the global hydrological cycle(Milly et al. 2002) and it is well established that theearth’s mean surface temperature has been increasing fol-lowing the last glacial maximum 21 000 years ago (Clarket al., 1999), thus increasing global average precipitation,evaporation and runoff. There is abundant evidence fordramatic and rapid climate warming in the past from lake-sediment, paleohydrology and tree-ring records (Fritz,1996). It is likely that the observed global warming hascontributed to a change in rainfall patterns on local orregional scales. To understand climate change impacts,global climate models (GCMs) are generally used tosimulate the present climate and project future climatewith forcing by greenhouse gases (GHGs) and aerosols.GCMs, which describe the atmospheric cycle by mathe-matical equations, are the most adopted tools for studyingthe impact of climate change at regional scales (Prud-homme et al., 2003). GCMs may capture large-scale cir-culation patterns and correctly model smoothly varyingfields, such as surface pressure, but it is unlikely that thesemodels properly reproduce non-smooth fields, such asprecipitation (Hughes and Guttorp, 1994). Additionally,the spatial scale on which a GCM can operate (e.g. 3Ð75°

longitude 3Ð75° latitude) is quite coarse for hydrologicapplications (Prudhomme et al., 2003). Therefore, GCMsimulations of local climate at individual grid points are

* Correspondence to: Ashok K. Mishra, Department of Biological andAgricultural Engineering, Texas A&M University, TX 77843-2117, USA.E-mail: [email protected]

often poor, especially when the area has a complex topog-raphy (Schubert, 1998). However, in most climate changeimpact studies, such as hydrological impacts of climatechange, models are usually required to simulate sub-grid scale phenomena and therefore require input data(such as precipitation and temperature) at similar sub-gridscales. Therefore, to overcome this problem, downscal-ing is necessary to model the hydrologic variables (e.g.precipitation) at a smaller scale at the river basin levelbased on larger-scale GCM outputs.

There are many downscaling techniques, but they canbe identified based on two major approaches, namely,dynamic (in which physical dynamics is incorporatedexplicitly) and empirical (the so-called statistical down-scaling) approaches (Burger and Chen, 2005; Coulibalyand Dibike, 2005). A dynamical downscaling techniqueembeds a higher resolution, limited area climate modelinto GCMs over an area of interest, using the GCMdata as a boundary condition. The dynamic downscalingis achieved by developing and using limited area mod-els or regional climate models (RCMs). RCMs run atfiner horizontal resolutions than the global-scale models,and thus provide a more accurate depiction of impor-tant model components. To date, linear and nonlinearregression, artificial neural networks (ANNs), canoni-cal correlation and principal component analysis havebeen used to derive predictor–predictand relationships(Conway et al., 1996; Dibike and Coulibaly, 2006). Theprocedures include (Wilby et al., 1998): (1) identifying alarge-scale predictor G, which controls the local parame-ter L; (2) finding a statistical relationship between L andG and validating the relationship with independent data;

Copyright 2009 John Wiley & Sons, Ltd.

2346 A. K. MISHRA, M. OZGER AND V. P. SINGH

and (3) if the relationship is confirmed, G can be derivedfrom GCM experiments to estimate L.

Empirical downscaling methods have enjoyed a rapiddevelopment over the last few years with many dif-ferent statistical methods employed: multiple regression(Karl et al. 1990), canonical correlation, neural net-works or stochastic simulation (Cannon and Whitfield,2002; Coulibaly and Dibike, 2005; Dibike and Coulibaly,2006), empirical orthogonal functions (Goodess and Palu-tikof, 1998), cluster analysis (Fowler et al., 2005) orfuzzy rules (Bardossy et al., 2005), singular value decom-position (Huth, 1999; von Storch and Zwiers, 1999) andsupport vector machine (Anandhi et al., 2008; Ghoshand Mujumdar, 2008). For recent advances in down-scaling techniques for hydrological modelling, one canrefer to Fowler et al. (2007). Several studies conductedin the last decade to understand the impact of climatechange on different sectors, for example, precipitation(Tatli et al., 2004; Anandhi et al., 2008; Dibike et al.,2008), streamflow (Miller et al., 2004; Yaning et al.,2006; Ghosh and Mujumdar, 2008), drought (Mishra andSingh, 2009), groundwater (Allen and Scibek, 2006) andland-use change (IPCC, 2001). Several investigators havedemonstrated either downscaling of precipitation and itstrend or persistence (Burn and Hesch, 2007). It will, how-ever, be interesting to understand the changes in trend andpersistence structure of projected precipitation.

The objective of this study was to investigate theimpact of climate change on Kansabati basin, India,which is a drought-prone catchment (Mishra et al., 2007).A downscaling method based on the Bayesian neuralnetwork (BNN) was applied to project precipitationfrom six GCMs using two (A2 and B2) scenarios. TheMann–Kendall test and Hurst exponent were used forstudying trend and persistence, respectively.

STUDY AREA

The physical area considered in this study is a portion ofthe Kansabati basin upstream of the Kansabati dam, in theextreme western part of the West Bengal state in easternIndia. The basin has an area of 4265 km2. The elevationranges from 110 to 600 m above mean sea level (m.s.l).The average elevation of the region is ¾200 m. The basinexperiences very hot summer with temperature in theregion exceeding 45 °C in May and June. Generally, dryperiods are accompanied by high temperatures, whichlead to higher evaporation affecting natural vegetationand agriculture of the region along with larger waterresource sectors. Mainly three rivers (Kansai, Kumariand Tongo) contribute flow in the Kansabati catchment.Kansabati dam was constructed at the confluence of threerivers in Purulia District of West Bengal. The water of theKansabati dam is primarily used for irrigation. Lands aremostly mono-cropped having limited surface irrigationfacilities. The water demand due to extensive cultivationhas led to over-exploitation of groundwater, which hasconsequently led to the degradation of water resources,

especially during summer months. Irrigated crops are notwidespread, because there is not always enough wateravailable.

DATA

For this study, five rain gauge stations were consid-ered, as shown in Figure 1, and statistical properties oftheir precipitation (1965–2001) along with their geo-graphic location are shown in Table I. The mean annualprecipitation varied from 1152Ð57 to 1345Ð7 mm dur-ing 1965–2001. The standard deviation for Phulberiastation is high because of high fluctuations of annualprecipitation from a minimum of 674 mm to a maxi-mum of 2081 mm. Since the basin is frequently affectedby meteorological droughts (Mishra and Singh, 2009),it is necessary to investigate the trend and persistenceof precipitation in the basin. Three types of precipitationscenarios were considered: (1) annual time series consist-ing of sum of monthly precipitation of individual years,(2) wet-month time series consisting of sum of precipi-tation of June, July, August and September of individualyears and (3) dry-month time series consisting of sumof precipitation of all months except the wet months ofindividual years.

METHODOLOGY FOR ANALYSIS

Scenarios to be analysed

GHG emissions are the product of very complexdynamic systems, determined by driving forces, such asdemographic development, socio-economic developmentand technological change. Their future evolution is highlyuncertain (IPCC, 2001). Scenarios are alternative imagesof how the future might unfold and are an appropriate toolwith which to analyse how driving forces may influencefuture emission outcomes and to assess the associateduncertainties (IPCC, 2001). This study uses two scenarios(A2 and B2).

Figure 1. Location of precipitation stations used in the study

Copyright 2009 John Wiley & Sons, Ltd. Hydrol. Process. 23, 2345–2357 (2009)DOI: 10.1002/hyp

PRECIPITATION UNDER CLIMATE CHANGE SCENARIOS 2347

Table I. Rain gauge stations in the Kansabati basin

Rain gaugestations

Elevation(m) (a.m.s.l)

Geographiccoordinates

Statistical properties of annual rainfall series (1965–2001)

Latitude Longitude Mean (mm) Max (mm) Min (mm) Standard deviation Skewness Kurtosis

Simulia 220Ð97 23° 100 86° 220 1300Ð68 1840 828 260Ð32 0Ð174 �0Ð605Rangagora 222Ð92 23° 40 86° 240 1152Ð57 1729 743 219Ð1 0Ð782 0Ð656Tusuma 158Ð6 23° 080 86° 430 1268Ð3 1683 746 239Ð31 �0Ð221 �0Ð547Kharidwar 135Ð96 23° 000 86° 380 1216Ð97 1814 827 248Ð2 0Ð637 �0Ð306Phulberia 144Ð32 22° 550 86° 370 1345Ð7 2081 674 322Ð73 0Ð329 �0Ð006

A2 Scenario. The A2 storyline and scenario familydescribe a very heterogeneous world. The underlyingtheme is self-reliance and preservation of local identities.Fertility patterns across regions converge very slowly,which result in continuously increasing population. Eco-nomic development is primarily regionally oriented andper capita economic growth and technological change aremore fragmented and slower than that in other storylines.

B2 Scenario. The B2 storyline and scenario familydescribe a world in which the emphasis is on localsolutions to economic, social and environmental sustain-ability. It is a world with continuously increasing globalpopulation, at a rate lower than A2, intermediate lev-els of economic development and less rapid and morediverse technological change than that in the B1 and A1storylines. While the scenario is also oriented towardsenvironmental protection and social equity, it focuses onlocal and regional levels.

GCM models used

The GCM data used in the study are extracted from theIPCC data distribution center (http://www.mad.zmaw.de/IPCC DDC/html/ddc gcmdata.html) website. A brief dis-cussion of different GCM models, which include CCSR/NIES AGCM C CCSR OGCM, CGCM2, CSIROmk2,HADCM3, GFDL (R30) and ECHM4OPY, are discussedin the following section.

CCSR/NIES AGCM C CCSR OGCM. The model usedhere is a coupled ocean-atmosphere model that consistsof the CCSR/NIES atmospheric GCM, the CCSR oceanGCM, a thermodynamic sea-ice model and a river routingmodel (Abe-Ouchi et al., 1996). The spatial resolution isT21 spectral truncation (roughly 5Ð6° latitude/longitude)and 20 vertical levels for the atmospheric part, androughly 2Ð8° horizontal grid and 17 vertical levels forthe oceanic part. The vertical distribution of the sulphateaerosol is assumed to be constant in the lowest 2 km ofthe atmosphere.

CGCM2.The second version of the Canadian Centre for Cli-

mate Modelling and Analysis (CCCma), coupled globalclimate model (CGCM2), is based on the earlier CGCM1,but with some improvements aimed at addressing short-comings identified in the first version. The atmospheric

component of the model is a spectral model with triangu-lar truncation at wave number 32 (yielding a surface gridresolution of roughly 3Ð7° ð 3Ð7°) and 10 vertical levels.The ocean component is based on the GFDL MOM1Ð1code and has a resolution of ¾1Ð8° ð 1Ð8° and 29 verticallevels.

CSIROmk2. This version of the CSIRO model includesthe Gent–McWilliams mixing scheme in the ocean andshows greatly reduced climate drift relative to earlierversions (e.g. Dix and Hunt, 1998). The drift in globalmean surface temperature in the new control run is about�0Ð02 °C/century. The model atmosphere has nine levelsin the vertical and horizontal resolution of spectral R21(¾5Ð6 by 3Ð2 degrees). The ocean model has the samehorizontal resolution with 21 levels.

HADCM3. HADCM3 is a coupled atmosphere-oceanGCM developed at the Hadley Centre and described byGordon et al. (1999). It has a stable control climatologyand does not use flux adjustment. The atmosphericcomponent of the model has 19 levels with a horizontalresolution of 2Ð5° of latitude by 3Ð75° of longitude, whichproduces a global grid of 96 ð 73 grid cells. The oceaniccomponent of the model has 20 levels with a horizontalresolution of 1Ð25° ð 1Ð25°.

GFDL (R30). The coupled model consists of generalcirculation models of the atmosphere and ocean, withrelatively simple formulations of land surface and sea-iceprocesses. The model shares many formulations with pre-vious versions of GFDL coupled climate models with theexception of higher spatial resolution in both the atmo-spheric and oceanic components. The effects of clouds,water vapour, carbon dioxide and ozone are included inthe calculation of solar and terrestrial radiation. Ozoneis specified as a function of latitude, height and seasonbased on observations. The mixing ratio of carbon diox-ide is assumed to be uniform throughout the atmosphere.Carbon dioxide levels in the model are used to representthe well-mixed greenhouse gases CO2, CH4, N2O andhalocarbons. Thus, these greenhouse gases can be thoughtof as being represented by an ‘effective CO2’ level inthis model. The details of this model can be referred toDelworth et al. (2002) and Dixon et al. (2003).



ECHM4OPY. ECHAM4 is the current generation alongthe lines of ECHAM models. A summary of devel-opments regarding model physics in ECHAM4 and adescription of the simulated climate obtained with theuncoupled ECHAM4 model is given in Roeckner et al.(1996). The GHG only forced experiment (referred to asGGa1) uses historical GHG forcing from 1860 to 1990followed by a 1% annual increase in radiative forcingfrom 1990 to 2099. The GHG and sulphate aerosol forcedexperiment (referred to as GSa1) uses the GGa1 forcing,plus the negative forcing due to sulphate aerosols.

Downscaling experiments

This section discusses the methods, which were usedfor downscaling experiments. Entropy was used forselecting predictors and BNN for downscaling and dis-tribution mapping approach for bias correction.

Selection of predictors. The selection of predictors isone of the most important steps in the downscaling exper-iment, for example, variables most suitable for describ-ing the large-scale climatic conditions that are relevantto the period. There may be substantial differences inlocal values derived from different large-scale variables(Huth, 2004). Some common guidelines for selection ofpredictors (Wilby et al., 1999; Benestad 2004) include:(1) predictors that are skilfully predicted by GCMs, (2)readily available from archives of GCM outputs and (3)large-scale parameters with a strong relationship with thepredictand that reflect a well-understood physical con-nection. In the present study, five stations with 37 yearsof monthly rainfall data representing the current climate(1965–2001) were used for downscaling experiments.Monthly climate data corresponding to the future climatechange scenarios were extracted from six GCM modelsat grid points closest to the rain gauge stations. To mea-sure the dependencies between predictor and predictands,transinformation coefficients based on entropy were used,which is briefly discussed here.

Entropy, as defined in information theory, is a mea-sure of uncertainty of a particular outcome in a ran-dom process and provides an objective criterion inselecting a mathematical model (Shannon, 1948; Singh,1997). Uncertainty of two variables, X and Y, canbe described by joint entropy H�X, Y�. The joint andmarginal entropies are related as:

H�X, Y� D H�X� C H�Y� � T�X, Y� �1�

where T�X, Y� is the information transferred from X toY, which is known as transinformation. Transinformationis a reduction of the original uncertainty and it can beviewed as information about a predicted variable trans-ferred by the knowledge of a predictor. In other words,mutual information or transinformation is a measure ofthe information contained in one process about anotherprocess, which was used in the present study for selectingpredictors for downscaling experiments.

Downscaling method. The available data set wasdivided into a training set consisting of 70% of the dataand a testing set consisting of the remaining 30% of thedata. BNN was used for downscaling precipitation basedon selected large-scale atmospheric predictors, which arediscussed below.

Bayesian neural network: In this section, we restrictour attention to the evidence framework for Bayesianlearning as introduced by MacKay (1992a, b). Otherimplementations of Bayesian learning have been pre-sented by Neal (1996). Let p�w� be the prior probabilitydistribution over the weight vector ‘w’. The posteriorprobability density can be calculated by Bayes’ Theormas:

p�wjD� D p�Djw�p�w�

p�D��2�

where p�Djw� is the dataset likelihood function, andthe denominator, p�D�, is a normalization factor thatguarantees the integration of the right-hand side ofequation (2) to one over the weight space. The latter isoften referred to as the evidence and equation (2) can bewritten as:

Posterior D likelihood ð prior

evidence�3�

Obtaining good predictive models is dependent on theuse of the right prior distributions. The remainder of thissection summarizes the Bayesian approach as stated byMacKay (2003).

The prior: The Bayesian approach considers a proba-bility density function (pdf) over the weight space. Thispdf represents degrees of belief represented by differ-ent values of the weight vector. The pdf is set initiallyas some prior distribution and converted into a posteriordistribution, once the data have been observed throughthe use of Bayes’ Theorem. In this study, the Gaussiandistribution was used as a prior distribution as also usedby several others (e.g. MacKay, 2003). The prior distribu-tion, p�w�, which is not related to data, can be expressedin terms of weight decay regularizer, (EW), of the con-ventional learning method. Mathematically, the Gaussiandistribution is represented by

p�w� D 1

zw�˛�exp��˛EW� �4�

where ˛ is the hyperparameter that controls the noise ofparameters and the expression for EW can be suggestedin order to favour small values of network weights

EW D 1

2

∑i

wi2 �5�

with i running over all elements of the weight vector‘w’. This method for improving generalization constrainsthe size of the network weights ‘w’ and is referred to as



regularization. Zw�˛� is the normalization factor, whichis mathematically represented as

Zw�˛� D∫

exp��˛EW�dw D(

2�

˛

)W2

�6�

The likelihood function: Considering the training dataas independent, the likelihood p�Djw� can be expressedas (Tito et al., 1999):

p�Djw� D∏N

iD1p�t�i�jx�i�, w� �7�

More generally the equation of p�Djw� can be expressedas:

p�Djw� D 1

ZD�ˇ�exp��ˇED� �8�

where ED is the error function. Again, the choice ofa Gaussian likelihood function leads to a probabilisticinterpretation of the error function ED and it is denotedas

ED D 1

2

∑N

iD1fy�x�i�; w� � t�i�g2 �9�

and the normalization factor ZD�ˇ� as

ZD�ˇ� D(

2�

ˇ

)N2

�10�

The posterior distribution: Upon deriving the expres-sions for the prior and the likelihood function, and basedon equation (2), the posterior distribution of weights canbe obtained in the form

p�Djw� D 1

zSexp��ˇED � ˛EW� D 1

zSexp��S�w��

�11�where

S�w� D ˇED C ˛EW

D ˇ

2

∑N

iD1fy�x�i�; w� � t�i�g2 C ˛

2

∑iwi

2 �12�

and the normalization factor ZS is expressed as

ZS�˛, ˇ� D∫

exp��ˇED � ˛EW�dw �13�

The procedure used here follows the work done by Khanand Coulibaly (2006).

Bias correction. Many GCMs either overestimate orunderestimate rainfall, while some of the models areunable to reproduce the seasonal cycle. The correctionscheme brings the distributions close to the observedpattern. This study used a distribution mapping approachto correct the bias in monthly precipitation. The methodsfor mapping one distribution onto another are wellestablished in probabilistic modelling and they were usedto correct the bias of both monthly and daily GCMprecipitation data (Wood et al., 2002; Ines and Hansen,2006). The quantile mapping method uses the empiricalprobability distributions for observed and simulated flows

to remove biases. Let FGCM denote the cumulativedistribution function (cdf) of GCM-simulated monthlyrainfall and Fobs denote the cdf of monthly observedrainfall. The corrected monthly rainfall is

QxGCM D F�1GCM�Fobs�Qx�� 14�

where QxGCM denotes the bias corrected monthly rainfalland Qx denotes the observed monthly rainfall.

Measures of trend and persistence. Hurst exponent:The Hurst exponent is used as an indicator of thepersistence of a time series. It is defined as the relativetendency of a time series to either regress to a longerterm mean value or ‘cluster’ in a particular direction.The values of the Hurst exponent range between 0 and1. A Hurst exponent value (H), close to 0Ð5, indicates arandom walk (i.e. a Brownian time series). In a randomwalk, there is no correlation between any element anda future element and there is a 50% probability thatfuture values will go either up or down, any series ofthis type are hard to predict. A Hurst exponent valuebetween 0 and 0Ð5 exists for a time series with ‘anti-persistent behaviour’. This means that an increase willtend to be followed by a decrease (or a decrease will befollowed by an increase). This behaviour is sometimescalled ‘mean reversion’, which means future values willhave a tendency to return to a longer term mean value.The strength of this mean reversion increases as Happroaches 0. A Hurst exponent value between 0Ð5 and 1indicates ‘persistent behaviour’, that is, the time series istrending. For details of the Hurst exponent, one can referto SakalauskienPe (2003). To compute the Hurst exponent,the following steps are outlined:

1. The time series must be divided into d contiguous sub-series of length n, where d ð n D N, the total length ofthe time series. For each of these sub-series m, wherem D 1, . . . , d:Determine the mean, Em, of each sub-series.Determine the standard deviation, Sm, of each sub-

series.Subtract the mean from each data pointXim D Zim � Em for i D 1, . . . , n.

2. Calculate a cumulative time series by consecutively

summing the data pointsYim Di∑

jD1Xjm

3. Using the new cumulative series find the range by sub-tracting the minimum value from the maximum value:Rm D maxfY1,m, . . . Yn,mg � minfY1,m, . . . Yn,mg

4. Rescale the range by dividing it by the standarddeviation.

5. Calculate the mean of the rescaled range for all sub-series of length n:

�R/S�n D 1

d

d∑mD1

�Rm/Sm� �15�

6. The length of n must be increased to the next highervalue, where d ð n D N, and d is an integer value.



Steps 1–4 are then repeated, these steps should berepeated until n D N/2.

7. Finally, the value of H is obtained using an ordinaryleast square regression with log(n) as the independentvariable and n log(R/S) as the dependant variable, theslope of the resulting equation is the estimate of theHurst exponent.

Mann–Kendall test: The Mann–Kendall non-parametric test was first proposed by Mann (1945) andthen Kendall (1975) derived the test statistic distribution.This test has been widely used to test randomness againsttrend. It is robust to the influence of extremes and per-forms well with skewed variables due to its rank-basedprocedure. On the other hand, it has an ability to copewith missing values. The test statistic that has a zeromean and a finite variance is calculated as

S Dn�1∑kD1

n∑jDkC1

sgn�Xj � Xk� �16�

where

sgn�x� D{ 1 if x > 0

0 if x D 0�1 if x < 0

�17�

Var�S� D[

n�n � 1��2n C 5� �∑

t

t�t � 1��2t C 5�/

18

]

�18�

where Xj and Xk are the sequential data values, n is thelength of the data record and t is the extent of any giventime. The standard normal variate z is computed as

z D

S � 1√Var�S�

if S > 0

0 if S D 0S C 1√Var�S�

if S < 0�19�

The null hypothesis, H0, should be accepted if jzj � ˛0/2at the ˛0 level of significance in a two-sided test for trend.A positive value of S indicates an upward trend and anegative value a downward trend.

RESULTS AND DISCUSSION

The methodology was applied to the Kansabati basin,India. This section discusses downscaled precipitationresults obtained from BNN followed by trend and per-sistence of downscaled precipitation based on annual,dry and wet periods for historical, 2001–2050 and2051–2100 durations.

Downscaling of precipitation

The predictors that share maximum information aswell as signify a well-understood physical connectionwith predictands are chosen as potential predictors fordownscaling experiments. The transinformation betweenprecipitation stations and different large-scale predictorvariables are tested for all scenarios considered in thestudy. It is observed that the transinformation coefficientsbetween predictors do not change significantly amongstation precipitation values, shown in Figure 2 (for ‘B2’ scenario of CGCM2 model). The results show thatalmost the same set of large scale predictors is neededfor all precipitation stations under a particular scenario forthe present study basin. The predictor variables identifiedfor each scenarios used for downscaling experiment are(Mishra and Singh, 2009): Precipitation (PREC), meansea level pressure (MSLP), and specific humidity (SPFH200) and for GFDL R30 model precipitation and MSLPare used as predictors. After getting the predictors thescattered plot between MSLP, SPFH 200 with respectto precipitation at Simulia station using B2 scenario ofCGCM2 model plotted (Figure 3). It is observed thatincrease in MSLP decreases monthly precipitation. Themonthly precipitation at Simulia station increases with

DSWF

HGT500

HGTVARMSLP

PRECSMC

SPFH

TempvarTmax

TMIN TMP TS

UGRD200

UVAR200

VGRD200

VVAR200Wind --

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tra

nsi

nfo

rmat

ion

Co

effi

cien

t

Predictors

Simulia Rangagora TusumaHaridwar

Figure 2. Transinformation coefficient between predictors and precipitation at different stations for B2 scenario of CGCM2 model (abbreviations ofpredictors to be referred in appendix)



(a) (b)

Figure 3. Scattered plot between (a) monthly precipitation and MSLP and (b) monthly precipitation and SPFH for Simulia station under B2 scenarioof CGCM2 model

increases in SPFH. The selection of predictors looksreasonable for downscaling experiment.

For downscaling of precipitation with BNN, fiveneurons were found to be optimal in the hidden layerto obtain the best network. Unlike the standard ANNmodel, the initialization of parameters in BNN wasdone using a distribution of parameters. The initialvalues of the weights and biases were obtained froma Gaussian prior distribution of zero mean and inversevariance (also known as regularization coefficient orprior hyperparameter). The Gaussian prior was chosenfor the network weights because a network with largeweights would usually give rise to a mapping with alarge curvature (Nabney, 2004). Moreover, the Gaussianprior also provides computational simplicity. For priorhyperparameter ˛, a single initial value was chosen forboth hidden and output layer weights. In defining theobjective function in the Bayesian framework, an errormodel for the data likelihood function is required. It isassumed that the target data is generated from a smoothfunction with additive zero-mean Gaussian noise. Thus,for the noise model, a Gaussian distribution with zeromean and constant inverse variance was used as definedin Khan and Coulibaly (2006). After defining prior andlikelihood functions, the objective function was set asposterior distribution of weights.

The network training was done by a trial and errorapproach as described above, and the network weightswere optimized using the scaled conjugate gradient opti-mization technique to find the most probable weights(wMP) by maximizing the posterior distribution of weightsp�wjD� or it can be said by minimizing the error func-tion S(w). The hyperparameters, denoted by ˛ and ˇ, werealso optimized during training using the evidence proce-dure (Bishop, 1995) in which hyperparameters were setto a value that maximized the evidence of the modelp�Dj˛, ˇ�. Once the network was trained, simulationswere carried out, in which the posterior distribution wasapproximated by a Gaussian distribution. For furtherdetails on the BNN numerical implementation and train-ing algorithm, the reader is referred to Nabney (2004)and for the application to downscaling precipitation toMishra and Singh (2009).

Table II. Statistical properties of BNN model for 1990–2000period

Station Observed BNN simulatedname

Mean(mm)

SD(mm)

Mean(mm)

SD(mm)

NMSE

Simulia Wet 1142Ð1 192Ð16 1012Ð7 147Ð92 0Ð89Dry 285Ð91 110Ð43 223Ð01 22Ð35 0Ð79

Rangagora Wet 1040Ð4 264Ð48 912Ð38 107Ð77 0Ð80Dry 216Ð36 105Ð69 206Ð12 25Ð86 0Ð81

Tusuma Wet 1120Ð5 215Ð77 1025Ð8 118Ð30 0Ð80Dry 265Ð80 93Ð49 211Ð12 25Ð12 0Ð81

Kharidwar Wet 1123Ð8 250Ð42 912Ð16 69Ð18 0Ð96Dry 241Ð18 108Ð44 221Ð32 31Ð13 0Ð83

Phulberia Wet 1205Ð5 251Ð67 1013Ð1 46Ð16 0Ð86Dry 277Ð73 110Ð27 256Ð12 32Ð12 0Ð79

After downscaling precipitation using BNN, the biascorrection was applied to the downscaled precipitationusing a gamma distribution for monthly precipitation dataand the baseline period. A few large deviations occurredin the dry season, when the gamma distribution assump-tion became less appropriate and the number of pointsused to fit it became small for some models/months(Mishra and Singh, 2009). The performance of BNN wasbetter that ANN for Kansabati basin for downscaling pre-cipitation (Mishra and Singh, 2009). To develop the BNNmodel, precipitation during 1965–1990 was taken as thetraining set and precipitation of 1991–2000 was consid-ered as the testing set. Statistical properties of the BNN-simulated precipitation during 1990–2000 are shown inTable II. The projected downscaled precipitation for theperiod 2001–2100 based on multiple GCM models forboth A2 and B2 scenarios for Rangagora station is shownin Figure 4 as an example. It is observed that differentGCMs have different projected values, which is due tothe differences in grid resolution, initial conditions anduncertainty in scenarios. In order to overcome this prob-lem, the ensemble mean based on six GCMs was usedfor the analysis of precipitation in 21st century.

The wet and dry period precipitation values are plot-ted based on historical and projected scenarios for all



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Table III. Mann–Kendall statistics for historical precipitation (1965–2000)

Stations Annual scale Wet period (JJAS) Dry period

MK-stat p-value MK-stat p-value MK-stat p-value

Simulia 1Ð604762 0Ð108546 0Ð809482 0Ð418238 2Ð575 0Ð010Rangagora 0Ð979899 0Ð327136 0Ð355036 0Ð722563 0Ð981 0Ð327Tusuma 2Ð570459 0Ð010156 2Ð102024 0Ð035551 2Ð179 0Ð029Kharidwar 2Ð172819 0Ð029794 1Ð789561 0Ð073525 0Ð477 0Ð633Phulberia 1Ð604762 0Ð108546 1Ð68997 0Ð091034 0Ð218 0Ð827

JJAS, June, July, August and September.

stations as shown in Figure 5 and their mean valuesare compared in Figure 6. It was observed that precip-itation during the historical period for dry precipitationwas more in three stations in comparison with the pro-jected precipitation. When 2001–2050 and 2051–2100periods were compared, it was observed that dry pre-cipitation during 2051–2100 was more in comparison tothe 2001–2050 in all stations. The dry precipitation wasfound to be maximum at Phulberia station and minimumat Rangagora station for both historical and projected pre-cipitation. When wet precipitation values were compared,precipitation during 2051–2100 would be higher than2001–2050 and historical records. During 2001–2050,the wet period precipitation would be lower than thosethat occurred historically. The wet precipitation followeda distinct pattern for all time scales among all stations.After studying the variation of both wet and dry periodsamong stations based on historical as well as projectedscenarios, it will be interesting to study their trend andpersistence that are discussed in the following section.

Trend analysis of downscaled precipitation

For trend analysis in the present study, the Mann–Kendall non-parametric test was performed for annual,wet and dry periods for two scenarios (A2 and B2) basedon ensemble mean of six GCMs downscale precipitation.A value of 0Ð05 was chosen as the local significance level

for a two-sided test. Based on this significance level,values larger than 1Ð96 or lower than �1Ð96, respec-tively, indicate a significant positive or negative trend.The Mann–Kendall test was carried out for three timeintervals, i.e. 1965–2000 (historical data), 2001–2050and 2051–2100 in order to compare the trend associatedwith historical rainfall with that of likely future precipita-tion in the basin. The results of Mann–Kendall test basedon the historical data for annual, wet and dry are shown inTable III. It was observed that the Tusuma station has sig-nificant increasing trend for annual, wet and dry periodswith MK-stat value more than 1Ð96. Kharidwar stationhas an increasing annual rainfall trend where as Simuliahas got a increasing trend in dry period rainfall.

The results of the Mann–Kendall test based on theA2 and B2 scenarios for annual, wet and dry periods forperiod 2001–2050 are shown in Tables IV and V. It isobserved that during 2001–2050 there is no significanteither positive or negative during this period for all fivestations during annual, wet and dry periods. Based on2051–2100 for A2 scenario (Figure 6; Table VI), thereis significant increasing trend for all five stations duringannual and wet period and negative trend in dry periodbut these are not significant negative trend. Whereasbased on B2 scenario (Figure 7; Table VII), no significanttrend was observed during annual and wet periods. In thecase of B2 scenario, the rainfall during dry periods shows



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Figure 5. Historical and projected precipitation for two scenarios based on annual, wet and dry periods

significant negative trends for all stations except Simuliastation.

The stations were compared among each other in termsof significant positive and negative trend with respectto time periods and different scenarios (Table VIII).It is observed that the rainfall at Simulia station hasa positive trend during historical dry period and forA2 scenario during 2051–2100 based on annual andwet period. Rangagora station showed increasing trendsduring 2051–2100 for A2 scenario in terms of annualand wet period, but there was a decrease in dry periodprecipitation for B2 scenario. This showed that the trend

in rainfall pattern for Rangagora station only wouldchanges during later half of the 21st century. A positivetrend pattern for Tusuma station was observed historicallyfor annual, wet and dry periods. There was no significanttrend observed during 2001–2050 but positive trendwas again observed for annual and wet period during2051–2100 for A2 scenario. A negative trend for dryperiod rainfall was observed during 2051–2100 basedon B2 scenario for Tusuma station. Increasing trend wasobserved for Kharidwar station for historical period usingannual period. Kharidwar also showed an increasing trend



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Figure 6. Mean of wet and dry period precipitations for different stationsand different scenarios

during 2051–2100 period based on annual precipitationand wet period precipitation based on A2 scenario.There was no significant trend observed for Phulberiastation either historically or during 2001–2050. When2051–2100 duration was considered significant trendswere observed for Phulberia indicating positive trendsduring annual and wet periods (A2 scenario) and anegative trend during dry periods (B2 scenario).

Persistence study of downscaled precipitation

The Hurst exponent (H) of annual, wet and dryprecipitation time series based on the ensemble meanof six GCMs downscale precipitation for two timeintervals (2001–2050 and 2051–2100) were comparedwith historical time interval (1965–2000). The value ofH was greater than 0Ð5, indicating that precipitation waspersistent for the time series under study. Values of theHurst exponent that lie between 0Ð5 and 1 are essentially

Table IV. Mann–Kendall statistics for A2 scenario based on2001–2050

Stations Annual scale Wet period(JJAS)

Dry period

MK-stat

p-value

MK-stat p-value

MK-stat p-value

Simulia 0Ð527 0Ð598 0Ð995 0Ð320 �0Ð995 0Ð320Rangagora 0Ð594 0Ð553 1Ð347 0Ð178 �0Ð912 0Ð362Tusuma 0Ð443 0Ð658 1Ð230 0Ð219 �0Ð862 0Ð389Kharidwar 0Ð510 0Ð610 0Ð828 0Ð408 �1Ð012 0Ð311Phulberia 0Ð393 0Ð694 1Ð096 0Ð273 �0Ð912 0Ð362


Table V. Mann–Kendall statistics for B2 scenario based on2001–2050

Stations Annual scale Wet period(JJAS)

Dry period

MK-stat

p-value

MK-stat p-value

MK-stat p-value

Simulia �0.494 0Ð622 �0Ð176 0Ð861 �0.142 0Ð887Rangagora �0.125 0Ð900 0Ð427 0Ð670 �1.598 0Ð110Tusuma �0.125 0Ð900 0Ð602 0Ð547 �1.782 0Ð075Kharidwar �0.276 0Ð783 0Ð460 0Ð645 �1.681 0Ð093Phulberia �0.125 0Ð900 0Ð527 0Ð598 �1.648 0Ð099


Table VI. Mann–Kendall statistics for A2 scenario based on2051–2100


MK-stat

p-value

MK-stat

p-value

MK-stat p-value

Simulia 3Ð862 0Ð00011 3Ð534 0Ð00041 1Ð362 0Ð173Rangagora 3Ð586 0Ð00034 3Ð327 0Ð00088 1Ð362 0Ð173Tusuma 3Ð689 0Ð00022 3Ð534 0Ð00041 1Ð379 0Ð168Kharidwar 3Ð793 0Ð00015 3Ð638 0Ð00028 1Ð431 0Ð152Phulberia 3Ð465 0Ð00053 3Ð086 0Ð00203 1Ð638 0Ð101


Table VII. Mann–Kendall statistics for B2 scenario based on2051–2100


MK-stat

p-value

MK-stat p-value

MK-stat p-value

Simulia 0Ð414 0Ð679 1Ð000 0Ð317 �1.655 0Ð098Rangagora 0Ð776 0Ð438 0Ð862 0Ð389 �2.069 0Ð039Tusuma 0Ð931 0Ð352 1Ð034 0Ð301 �2.034 0Ð042Kharidwar 0Ð965 0Ð334 1Ð103 0Ð270 �1.983 0Ð047Phulberia 0Ð724 0Ð469 1Ð000 0Ð317 �2.120 0Ð034


black noise processes, these processes are seen in natureand are in long-run cyclical records.



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Figure 7. Hurst exponent based on annual, wet and dry periods for historical and projected series

Table VIII. Stations showing significant positive and negative trends for different time periods

Time period Precipitation station Historical observation 2001–2050 2051–2100

A2 scenario B2 scenario A2 scenario B2 scenario

Annual Simulia — — — " —Rangagora — — — " —Tusuma " — — " —Kharidwar " — — " —Phulberia — — — " —

Wet Simulia — — — " —Rangagora — — — " —Tusuma " — — " —Kharidwar — — — " —Phulberia — — — " —

Dry Simulia " — — — —Rangagora — — — — #Tusuma " — — — #Kharidwar — — — — —Phulberia — — — — #

Values larger than 1Ð96 or lower than �1Ð96 indicate, respectively, a significant positive or negative trend



The persistence of historical annual precipitationwas compared with projected annual precipitation for2001–2050 based on A2 and B2 scenarios (Figure 7a).It is noted that persistence in historical annual precip-itation found for all stations are higher than projectedannual precipitation for both A2 and B2 scenarios dur-ing 2001–2050. Significant persistence was not observedfor A2 scenario during 2001–2050 for all stations. Dur-ing 2051–2100, the persistence for annual precipitationbased on A2 scenario is higher than that of historicalseries and B2 scenario (Figure 7b), and all the annualprecipitation series have significant persistence (H > 0Ð5)during second half of the 21st century.

When the persistence of wet period precipitation werecompared between historical and projected scenarios for2001–2050 (Figure 7c), it is observed that persistenceof historical precipitation is higher than other two (A2and B2) scenarios. The persistence for both A2 andB2 scenarios does not differ much during 2001–2050.Whereas during 2051–2100, all stations have very highpersistent based on A2 scenario in comparison with B2scenario (Figure 7d). The persistence does not vary muchamong the stations with in the scenarios.

Interesting results were observed when persistence ofhistorical dry period precipitation was compared withprojected scenarios. The persistence of historical dryperiod precipitation has high fluctuations from one stationto another. Only Simulia and Tusuma stations showsignificant persistence (H > 0Ð5) in comparison withother stations for dry period precipitation (Figure 7e).Kharidwar station that has high persistence for annualand wet period precipitation does not show significantpersistence for dry period precipitation. Both A2 andB2 scenarios show similar persistence for dry periodprecipitation during 2001–2050, whereas B2 scenarioshows higher persistence in comparison with A2 scenarioduring 2051–2100 (Figure 7f).

CONCLUSIONS

For future water resources management, the effectivenessof GCM outputs plays an important role for understand-ing the behaviour of precipitation in the basin. This paperdescribes trend and persistence of annual, wet and dryperiod precipitation values based on Six GCMs with twoscenarios (A2 and B2). The following conclusions aredrawn from this study:

1. Comparing the historical and projected precipitationfor dry, wet and annual precipitation in terms oftheir annual mean, it is observed that the amountof dry period precipitation that occurs historicallyis higher for most of the stations in comparison tothe 2001–2050 and 2051–2100 time periods. During2051–2100, the annual mean of wet precipitation isexpected to be higher than that of the 1965–2000 and2001–2050 time periods.

2. Historically, there is an increasing trend of precipita-tion observed for Tusuma station for all annual, wet

and dry period precipitation values. Simulia stationhas an increasing dry period precipitation, whereasKharidwar has got an increasing trend for annual pre-cipitation.

3. The precipitation for all three time periods (dry, wetand annual) does not show any significant increasingor decreasing trend during the 2001–2050 time period.There is likely an increasing trend of precipitationfor annual and wet periods during 2051–2100 basedon A2 scenario and a decreasing trend of dry periodprecipitation based on B2 scenario.

4. The persistence of historical precipitations variesamong the stations and is higher in comparison toboth projected scenarios. Persistence during dry periodprecipitation among stations varies drastically basedon historical data with the highest persistence towardsnorth-west part of the basin. The persistence of annualand wet period precipitations based on A2 scenarioseems to be higher than historical period and B2 sce-nario during the 2051–2100 time period

ACKNOWLEDGMENTS

The authors gratefully acknowledge the editor and fouranonymous reviewers who provided constructive reviewsand thoughtful comments on the paper.

APPENDIX: LIST OF ABBREVIATIONS USED FORPREDICTORS

DSWF Total incident solar radiation (w/m2)HGT 500 500 hPa heightHGTVAR hPa height varianceMSLP Mean sea level pressure (hPa)PREC Total precipitation (mm/day)SMC Soil moisture content (mm)SPFH Specific humidity (kg/kg)TempVar Screen temperature variance (k2)Tmax Maximum temperature (°C)Tmin Minimum temperature (°C)TMP Mean temperature (°C)TS Surface skin temperature/SST (k)UGRD 200 200 hPa u-wind (m/g)UVAR 200 200 hPa u-wind variance (m/g)VGRD 200 200 hPa v-wind (m/g)VVAR 200 200 hPa v-wind variance (m/g)Wind Mean scalar wind speed (m/s)

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