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WATER RESOURCES RESEARCH, VOL. 46, W07526, doi:10.1029/2009WR008423, 2010

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Development and Application of a Multisite Rainfall Stochastic Downscaling Framework for Climate Change Impact Assessment R. Mehrotra1 and Ashish Sharma1 Received 23 July 2009; revised 17 December 2009; accepted 26 February 2010; published 22 July 2010.

[1] The coarse resolution of general circulation models (GCMs) necessitates use of downscaling approaches for transfer of GCM output to finer spatial resolutions for climate change impact assessment studies. This paper presents a stochastic downscaling framework for simulation of multisite daily rainfall occurrences and amounts that strive to maintain persistence attributes that are consistent with the observed record. At site, rainfall occurrences are modeled using a modified Markov model that modifies the transition probabilities of an assumed Markov order 1 rainfall occurrence process using exogenous atmospheric variables and aggregated rainfall attributes designed to provide longer‐term persistence. At site rainfall amounts on wet days are modeled using a nonparametric kernel density simulator conditional on previous time step rainfall and selected atmospheric variables. The spatial dependence across the rainfall occurrence and amounts is maintained through spatially correlated random numbers and atmospheric variables that are common across the stations used. The proposed framework is developed using the current climate (years 1960–2002) reanalysis data and rainfall records at a network of 45 rain gauges near Sydney, Australia, while atmospheric variable simulations of the CSIRO Mk3.0 GCM (corresponding to Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) B1, A1B and A2 emission scenarios) are used for downscaling of rainfall for the current and future (year 2070) climate conditions. Results of the study indicate wetter autumn and summer and drier spring and winter conditions over the region in a warmer climate. The best estimates of annual rainfall project little change in the number of wet days and slight increase (2% in 2070) in the rainfall amount. An increase (about 4%) in daily rainfall intensity (rain per wet day) is estimated in year 2070. Changes in rainfall intensity, wet and dry spells, and rainfall amount in wet spells suggest that the future rainfall regime will have longer dry spells interrupted by heavier rainfall events. Citation: Mehrotra, R., and A. Sharma (2010), Development and Application of a Multisite Rainfall Stochastic Downscaling Framework for Climate Change Impact Assessment, Water Resour. Res., 46, W07526, doi:10.1029/2009WR008423.

1. Introduction [2] General circulation models (GCMs) are widely used to simulate the present and future climates under assumed greenhouse gas emission scenarios, both in space and time [e.g., IPCC, 2007; Bergström et al., 2001; Varis et al. 2004]. One of the key limitations of GCM simulations is the coarse grid resolution at which they are run. As a result, they are incapable of representing local subgrid‐scale features and dynamics that are often required for impact studies, especially at a catchment scale [IPCC, 2007; Charles et al., 2004; Vicuna et al., 2007]. Consequently, techniques have been developed to transfer the GCM output from coarse spatial scales to local or regional scales by means of downscaling. These downscaling techniques can be classified into two categories: “dynamical downscaling” that uses regional climate models (RCMs) to simulate finer‐scale physical processes [e.g., Giorgi et al., 2001; Mearns et al., 2001, 2004; 1 Water Research Center, School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia.

Copyright 2010 by the American Geophysical Union. 0043‐1397/10/2009WR008423

Fowler et al., 2007] and “statistical downscaling” that is based on developing statistical relationships between the regional climate and preidentified large‐scale parameters [e.g., Wilby et al., 2004; Mehrotra and Sharma, 2005; Vrac and Naveau, 2007]. A diverse range of statistical downscaling techniques has been developed over the past few years, with most falling into a category where the responses (precipitation) are related to predictors (coarse scale atmospheric and local scale time‐lagged variables) or into a category where the responses are related to a discrete or continuous state, which is modeled as a function of the atmospheric and local scale predictors [Hewitson and Crane, 1996; Wilby and Wigley, 1997; Hughes et al., 1999; Charles et al., 2004; Bartholy et al., 1995; Stehlík and Bárdossy, 2002; Mehrotra and Sharma, 2005; Vrac and Naveau, 2007]. There are limitations and assumptions involved in both techniques that contribute to the uncertainty of results [see also Yarnal et al., 2001; Fowler et al., 2007]. Yarnal et al. [2001], Charles et al. [2004], IPCC [2007], and Fowler et al. [2007] provide good reviews and discussions of various downscaling techniques. [3] In general, GCMs (and hence the resulting downscaled outputs to some extent) tend to undersimulate year‐to‐year

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MEHROTRA AND SHARMA: A MULTISITE RAINFALL STOCHASTIC DOWNSCALING

(low‐frequency) variability in rainfall and poorly represent extreme events, when compared to the historical climate record [Ines and Hansen, 2006; Knutti, 2008], implying that the probability of sustained droughts or periods of high flows also are likely to be underestimated in future climate projections. This has significant implications in water resource planning and design, with undersimulation of sustained droughts resulting in significantly overestimated reservoir yields, artificially enhancing the reliability associated with our existing water supply infrastructure to sustain future demands [Milly et al., 2008]. Similarly, undersimulated persistence in rainfall also implies reduced variations in catchment conditions prior to design rainfall events, leading to floods that do not exhibit the low‐frequency multidecadal variability often observed in Australian records [Micevski et al., 2006], increasing the uncertainty associated with the specification of a design flood for future infrastructure developments. There is a need to address this limitation in the downscaled rainfall outputs for them to be of use in a water resources context. [4] Commonly used approaches to match the observed variability in the downscaled climate variables include variance inflation, expanded downscaling, and randomization. Variance inflation [Karl et al., 1990] increases the variability by multiplying the downscaled simulations by a suitable factor, however, is of limited use in case of daily rainfall owing to large number of zeros in the rainfall record. Also, the method assumes that all climate variability is related to the large‐scale predictor fields. Another approach is of “randomization” where additional variability is added in the form of white noise [von Storch, 1999]. Kyselý [2002] reports good results in the reproduction of 20 to 50 year return period values of central European surface temperature using this procedure. The “expanded downscaling” approach is developed by Burger [1996] and has been used by Huth [1999], Dehn et al. [2000], and Muller‐Wohlfeil et al. [2000]. A comparison of the three methods notes that each presents different problems [Burger and Chen, 2005]. Variance inflation poorly simulates spatial correlations, while randomization performs well for control climate simulations but is unable to reproduce changes in variability, which may limit the use of the approach for climate change impact studies. Expanded downscaling is sensitive to the choice of statistical process (a variant of canonical correlation analysis) used in its formulation. [5] Recently, there have been many studies assessing the ability of RCMs to reproduce more plausible climate change scenarios for extreme events and climate variability at the regional scale [e.g., Christensen et al., 2007; Fowler et al., 2005; Frei et al., 2006; Schmidli et al., 2007], but we focus on stochastic downscaling in this study. [6] The use of statistical/stochastic downscaling to reproduce short‐ as well as long‐term frequency components in the downscaled rainfall has been attempted in the past by employing combinations of rapidly varying and slowly varying atmospheric circulation variables or by conditioning daily weather generator parameters on indices of atmospheric circulation [Cavazos, 1997; Wang and Connor, 1996; Wilby et al., 2002; Woolhiser et al., 1993]. For example, Cavazos [1997] uses the Pacific North American, El Niño–Southern Oscillation (ENSO) index and 1000–500 hPa thickness indices to model monthly rainfall totals in NE Mexico. Woodhouse [1997] considers six large‐scale climate indices to model

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winter rain days and maximum temperatures at multiple stations in the United States. Wilby et al. [2002] compare three downscaling models using daily precipitation data of United Kingdom for sites located in the regions of strongest North Atlantic forcing. The parameters of first model are implicitly conditioned by three regional airflow indices; while the parameters of the second model are explicitly conditioned by either the North Atlantic Oscillation (NAO) index or sea surface temperature (SST) anomalies and daily vorticity; and finally, the parameters of the last model are unconditional. They conclude that the conditional models display greater skill for monthly rainfall statistics relative to unconditional model, and explicit conditioning offers additional advantages for the chosen sites and seasons of greatest forcing. Similarly, Katz and Parlange [1993, 1996] use two discrete states of monthly mean sea level pressure to condition the January daily precipitation parameters and report that the conditional model reproduces the variance of total monthly precipitation. Kiely et al. [1998] condition the occurrence and intensity parameters of a daily precipitation model on the multistate indices of mean monthly sea level pressure and geostrophic wind directions at Valentia, Ireland, and find improved estimates of the site’s standard deviation of monthly precipitation in relation to the unconditional model. Wilby [1998] reports encouraging results in downscaled monthly precipitation diagnostics for two sites in the United Kingdom by using the NAO index and SST anomalies to continuously condition the parameters of a stochastic rainfall model. However, the improvements are limited to specific seasons and locations according to the choice of low‐frequency predictor(s). [7] The performance of downscaling methods varies across seasons, locations, GCMs, and depends strongly on biases inherited from the driving GCM and the presence and strength of regional scale features such as orography, proximity to sea, and land use and vegetation. In general, statistical downscaling methods are more appropriate where point values of extremes are needed for impact studies. Consideration of these analyses suggests that, at least for present‐day climates, dynamical downscaling methods provide little advantage over statistical techniques [Fowler et al., 2007]. [8] This paper presents a stochastic downscaling framework for simulation of multisite daily rainfall occurrences and amounts, which is capable of maintaining persistence attributes that are consistent with the observed record. The framework operates in two stages: (1) the downscaling of rainfall occurrences (whether rain or no rain) and (2) downscaling of rainfall amounts on days simulated as wet in the first stage. The rainfall occurrence downscaling model is a variation of the stochastic generation‐modified Markov model (MMM) [Mehrotra and Sharma, 2007b], facilitating the use of exogenous atmospheric predictors and local low‐ frequency variability indicators so as to simulate properly the sustained extreme events and year‐to‐year variations in the downscaled rainfall occurrence field. At site rainfall amounts on wet days are simulated using a kernel density estimation‐ based approach (hereafter referred to as KDE) that also allows proper representation of temporal dependence attributes. Spatial dependence in rainfall occurrence and amounts fields is maintained by making use of random innovations that are spatially correlated yet serially independent in nature [Wilks, 1998]. The smooth transition from one season to another as well as estimation of transition probabilities, conditional

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densities, spatial correlations, skewness, and other variables for each day is achieved by using the concept of a moving window [Harrold et al., 2003; Mehrotra and Sharma, 2005]. [9] The rainfall occurrence downscaling model MMM proposed here departs from the commonly used weather generators in a sense that transition probabilities or the parameters of the model are updated at each time step on the basis of the past rainfall behavior and the current time step values of the atmospheric variables. Thus, providing a more logical and refined way of incorporating the low‐frequency variability and the influence of atmospheric variables in the downscaled results. Rather than using mixture of discrete stochastic processes [Katz and Parlange, 1993, 1996] or continuous regression relationship [Wilby, 1998; Wilby et al., 2002], the proposed approach explicitly considers the combined effect of atmospheric variables influencing the climate and of the longer‐term wetness state characterizing the low‐ frequency variability. We expect that owing to the parameter updating procedure at each time step, it should adapt better to the changes that are expected to occur in the future. It also deviates from the logic of weather state‐based models like nonhomogeneous hidden Markov model, NHMM [Hughes and Guttorp, 1994] and nonparametric nonhomogeneous hidden Markov model, NNHMM [Mehrotra and Sharma, 2005] and weather state downscaling model of Vrac and Naveau [2007] as rainfall occurrences are considered directly conditional upon the atmospheric variables, thereby, evading the use of discrete or continuous weather states. Additionally, the model provides a better representation of the observed low‐frequency variability and spell extremes by incorporating the behavior of the climate over the recent past periods. [10] The downscaling framework comprising of the MMM rainfall occurrence simulator and the KDE rainfall amount simulator, is referred hereafter as MMM‐KDE. This framework is initially calibrated using reanalysis atmospheric data and observed daily rainfall (1960–2002) at 45 rain gauges located around Sydney, Australia, and subsequently validated using current climate GCM data. The model performance is evaluated on the basis of reproduction of a few important rainfall attributes representing at site temporal and across site spatial dependencies. We also demonstrate the improvements offered by including the aggregated wetness state predictor in the rainfall occurrence downscaling model. Finally, the model is applied to downscale daily rainfall for year 2070 and changes in rainfall behavior evaluated.

PðRt ¼ 1jRt1 ¼ i; Xt Þ ¼

¼

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by presenting the summary and conclusions drawn from the results, in section 5.

2. Methodology [12] In the discussions that follow, all multivariable vectors or matrices are expressed as bold and single variables or parameters using nonbold characters or symbols. We denote rainfall occurrence at a location k and time t as Rt(k) and at the pth time step before the current as Rt–p(k). Also, a ns‐site rainfall occurrence vector at time t is denoted as Rt and a vector of predictor variables (consisting of atmospheric and/or other relevant indicators) as Zt. Unless explicitly specified, hereafter, the term rainfall represents rainfall amount. The following subsections describe the rainfall occurrence and amount models and the procedure that was used to incorporate the spatial dependence in the downscaled occurrence and amount series. 2.1. Downscaling of Rainfall Occurrence Using MMM [13] The general structure of the rainfall occurrence downscaling model (MMM) is presented in the study of Mehrotra and Sharma [2007b] in a stochastic generation context and is described here in the context of downscaling. In general, the rainfall downscaling problem could be expressed as the conditional simulation of Rt(k)∣Zt(k), where Zt(k) represents a vector of conditioning variables at a location k and at time t, that consists of atmospheric predictor variables, lagged rainfall to assign daily or short‐term persistence, and derived rainfall indicators selected to impact specific characteristics of interests. If Zt(k) comprises of Rt − 1(k) alone, then MMM reduces to a simple Markov order 1 model, whereas addition of variables representing longer time scale persistence also, would reduce it to the stochastic rainfall generator presented in the study of Mehrotra and Sharma [2007b]. [14] In the following discussions, we present the parameterization of Rt(k)∣Zt(k) as a modulation of the Markov order 1 (or higher) transition probability representation by the impact of nondiscrete exogenous predictors. For brevity, site notations are dropped in the subsequent discussions. The parameters (or transition probabilities) of the Markov order 1 rainfall occurrence process are represented as P(Rt∣Rt − 1). Inclusion of nondiscrete predictors Xt in the conditioning vector Zt modifies the transition probabilities to P(Rt∣Rt − 1, Xt), which can be expressed as

PðRt ¼ 1; Rt1 ¼ i; Xt Þ f ðXt jRt ¼ 1; Rt1 ¼ iÞ PðRt ¼ 1; Rt1 ¼ iÞ ¼ PðRt1 ¼ i; Xt Þ f ðXt jRt1 ¼ iÞ PðRt1 ¼ iÞ

PðRt ¼ 1; Rt1 ¼ iÞ f ðXt jRt ¼ 1; Rt1 ¼ iÞ PðRt1 ¼ iÞ ½ f ðXt jRt ¼ 1; Rt1 ¼ iÞPðRt ¼ 1jRt1 ¼ iÞ þ ½ f ðXt jRt ¼ 0; Rt1 ¼ iÞPðRt ¼ 0jRt1 ¼ iÞ

[11] The paper is organized as follows. The methodology and the models used are discussed and described in section 2. Details on the application of models considered, data, and study region used are presented in section 3. This is followed by a description of the downscaled results obtained for current and future climates, in section 4. We conclude the paper

ð1Þ

The first term in (1) defines the transition probabilities P(Rt∣Rt − 1) of a first‐order Markov model (representing order 1 dependence), while the second term signifies the effect of inclusion of predictor set Xt in the conditioning vector Zt. If Xt consists of derived measures (typically linear combinations) of atmospheric variables and/or summation of number

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of wet days in prespecified aggregation time periods (as explained later), one could approximate the associated conditional probability density f(Xt∣Rt = 1, Rt − 1 = i) using a multivariate normal distribution. Consequently, the conditional probability density f(Xt∣Rt = 1) as specified in (1) can be expressed as a mixture of two multivariate normals. This leads to the following simplification:

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and optimal if the underlying probability density is Gaussian. However, when modeling variables exhibiting significant skewness, assuming a Gaussian distribution and assuming the variance associated with each kernel (or each observation) to be the same, may not be appropriate. In such situations, varying the bandwidth depending on the associated observation helps characterizing the probability more meaning-

1 T 1 1 1=2 exp Xt 1;i V1;i Xt 1;i 2 det V1;i PðRt jRt1 ; Xt Þ ¼ p1i "

# "

#; 1 T 1 T 1 1 1 1 V V exp X exp X p p0i Þ þ X X t 1;i t 1;i 1i t 0;i t 0;i 1=2 1=2 1;i 0;i 2 2 det V1;i det V0;i

ð2Þ

where the m1,i represent the mean vector E(X∣Rt = 1, Rt − 1 = i) and V1,i is the corresponding variance‐covariance matrix, and similarly, m0,i and V0,i represent the mean vector and the variance‐covariance matrix of X when (Rt − 1 = i) and (Rt = 0), respectively. The parameters p1i represent the baseline transition probabilities of the first‐order Markov model defined by P(Rt = 1∣Rt − 1 = i.) with p0i equaling (1 − p1i). The det() represents the determinant operation and T represents the transpose operator. While the assumption of a multivariate normal distribution simplifies the specification of the conditional probabilities in (2), this assumption may be inappropriate for variables that are known to have skewed or other non‐Gaussian traits. In such situations, use of some appropriate transformation to convert the data back to normal may be useful. However, it may be noted that most common data transformation technique are developed for univariate cases only while data set X as described here is multivariate, and therefore, univariate normal transformation may not necessarily translate into multivariate normal. Alternatively, the conditional multivariate probabilities f(Xt∣Rt = 1, Rt − 1 = i) and f(Xt∣Rt = 0, Rt − 1 = i) of (1) may be estimated using a nonparametric kernel density estimation procedure as described next. [15] For a d‐dimensional multivariate Gaussian kernel, the conditional multivariate density f(Xt∣Rt, Rt − 1) at a time step t can be written as: f ðXt jRt ¼ j; Rt1 ¼ iÞ ¼

N 1X 1 d=2 d N k¼1 ð2Þ detðSÞ1=2 ðXt Xk ÞS1 ðXt Xk Þ ; exp 22

ð3Þ

where Xk is kth multivariate data point of X under the condition that (Rt = j (0 or 1), Rt − 1 = i) and N is number of such data points. f(Xt∣Rt, Rt − 1) is the estimated conditional multivariate probability density expressed as a weighted sum of N Gaussian density functions each with a mean Xk and covariance l2S, where, S is a sample covariance of data set X when (Rt = j (0 or 1), Rt − 1 = i), and l is a smoothing parameter, known as the bandwidth of the kernel density estimate. [16] A simplistic choice of bandwidth, the Gaussian reference bandwidth [Scott, 1992] is considered as appropriate

fully, especially in regions where there may be many observations (requiring a smaller bandwidth) or where there may be few (requiring a larger bandwidth). The local Gamma bandwidth lXk for the kth data point of the individual variables in X series is written as [Mehrotra and Sharma, 2007a]: 0

11=ðdþ4Þ

B C 1 B C Xk ¼ B 2 C @ pffiffiffi A 2 ð 1 Þ ð 1 Þ ð 2 Þ þ 2 f ðX k Þ 2 2 Xk Xk N ð1=ðdþ4ÞÞ ;

ð4Þ

where f(Xk) is the Gamma density at Xk, g and h, respectively, are the scale and shape parameters of the Gamma distribution for the variable being modeled (resulting in different local bandwidths associated with individual variables in X), N is again the number of observations in X when (Rt = j (0 or 1), Rt − 1 = i), d is the number of predictor variables, and lXk being equivalent to l of equation (3). Further details on the derivation of equation (4) are given by Mehrotra and Sharma [2007a] while derivation of equation (3) and further discussions related to the kernel density procedure are given by Sharma and O’Neill [2002] and Mehrotra and Sharma [2007a, 2007b]. [17] In the present application, we consider the nondiscrete conditioning vector X (for rainfall occurrence downscaling) as consisting of variables representing selected atmospheric variables and long‐term persistence indicators formulated as aggregate wet days preceding the current time step. Parameters of MMM are estimated on a daily basis using either (2) or (3) depending on the joint distribution of predictor variables in X. In order to save computer time, the switching from parametric to nonparametric multivariate density estimation (which requires significantly greater computational efforts than the parametric case) at each time step is decided on the basis of average skewness of the data set X. If the average skewness is less than 0.3 then the parametric approximation is used; otherwise, the nonparametric procedure is used to estimate the conditional multivariate density. 2.2. Formation of Aggregated Wetness State [18] A vector of aggregated rainfall Xrt representing the wetness over the recent past can be expressed as [following

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on the previous day as a conditioning variable provides a Markov order 1 dependence to the downscaled series. Further details on the general structure of the KDE model are available in Mehrotra and Sharma [2007a, 2007b].

Figure 1. Reanalysis and CSIRO GCM data grids and study region. Harrold et al., 2003; Sharma and O’Neill, 2002; Mehrotra and Sharma, 2007a, 2007b]:

Xrt 2 Xrj1 ;t ; Xrj2 ;t ; . . . ::; Xrjm ;t ;

Xrji ;t ¼

ji 1X

ji

Rtl ;

ð5Þ

2.4. Modeling Spatial Dependences in Rainfall Occurrence and Amounts [20] As discussed in the above sections, stochastic downscaling of rainfall occurrences or amounts for a given location proceeds through simulation from the associated conditional probability (or transition probability) distribution independently. The method used to incorporate spatial dependence in such simulations over many point locations involves using uniform random variates that are independent in time but exhibit a strong dependence across the multiple point locations considered. Denote ut as a vector of uniform [0,1] variates of length ns at time step t, with ns being the number of stations. The vector ut (≡ ut (1), ut (2),……ut (ns)) is defined such that for locations k and l, corr[ut(k), ut + 1(k)] = 0 (or, random numbers are independent across time) but corr[ut(k), ut(l)] ≠ 0 (or, random numbers are correlated across space). As a result, there is spatial dependence between individual elements of the vector ut, this dependence being introduced to induce observed spatial dependence in the response variables they are used to simulate. More details on this approach are given by Wilks [1998] and Mehrotra et al. [2006].

3. Application of Downscaling Model [21] This section presents the details on the data and the study area and the selection of model parameters for downscaling framework.

l¼1

where m is the number of such predictors and Xrji,t describes how wet it has been over the preceding ji days with Rt − 1 representing rainfall occurrence. This aggregated wetness state, by formulation, assumes values between 0 and 1 that are increasingly continuous as the aggregation period ji increases. Please note that the aggregated wetness state is calculated separately for each station. 2.3. Downscaling of Rainfall Amounts [19] A nonzero rainfall amount (with a rainy day defined using a threshold of 0.3 mm/d following Harrold et al. [2003] and Mehrotra et al. [2004]) must be simulated for each day at each location that the MMM occurrence downscaling model simulates as wet. Additionally, the downscaled rainfall amount series (for the current climate) should represent accurately the spatial and temporal dependence present in the observed rainfall record. The downscaling of rainfall amount is based on the kernel density procedure similar to what has been described in section 2.1. The amounts model downscales the rainfall at individual stations conditional on the selected atmospheric variables as well as the previous days’ rainfall. As rainfall amounts are downscaled independently at each location, observed spatial dependence across the stations is not directly reproduced. This is introduced by making use of spatially correlated random numbers as described in section 2.4. In addition to this, a local wetness fraction (as defined later in section 3.2) is used to enforce smooth spatial continuity across the realizations. The use of rainfall amounts

3.1. Data sets, Study Area, and Variables 3.1.1. Study Area [22] The study region is located around Sydney, eastern Australia spanning between 149°E–152°E longitude and 32°S–36°S latitude (Figure 1). The physiogeographical conditions near Sydney cause large climatic gradients even over short distances, e.g., from lowland areas to mountain regions and from the coast to the inland. Most significant rainfall events in winter in this region involve air masses that have been brought over from the east coast low‐pressure systems. Orographic uplift of these air masses when they strike coastal ranges or the great dividing range often produces very heavy rain. Several of the most severe floods experienced east of the great dividing range have resulted from east coast low‐pressure systems. In summer, tropical depressions moving southward from Queensland into New South Wales bring warm, cloudy, and drizzly weather to coastal regions of eastern Australia. These conditions can result in heavy rainfall if some means of lifting is available. 3.1.2. Rainfall [23] For this study, a 43‐year continuous record (from 1960 to 2002) of daily rainfall at 45 stations around Sydney (Figure 1) is used. The study area therefore has both the preconditions to develop stochastic downscaling models and the need to apply them, adding value to the coarse climate scenarios provided by global climate models. 3.1.3. Large Scale Observed Atmospheric Variables [24] The required observed atmospheric variables for 25 grid points over the study area are extracted from the

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National Center for Environmental Prediction (NCEP) reanalysis data provided by the NOAA‐Cooperative Institute for Research in Environmental Sciences, Climate Diagnostics Center, Boulder, Colo, from their Web site at http://www.cdc. noaa.gov/. These variables are available on 2.5° latitude × 2.5° longitude grids on a daily basis for the same period as the rainfall record (Figure 1). As an observed rainfall value represents the total rainfall over a 24 hour period ending at 0900 hours (local time, LT) in the morning, the available atmospheric measurements on the preceding day are considered as representative of current day’s rainfall. These data are regridded from the 25 NCEP grids (2.5° latitude × 2.5° longitude) to the 9 CSIRO climate model grids (3.73° latitude × 3.75° longitude) prior to the predictor identification and model fitting exercises as the output from the CSIRO global climate model forms the basis when statistical downscaling is applied to produce local climate scenarios for current (1960–2002) and future conditions (2061–2080) (Figure 1). For defining a grid‐averaged value and North–South and East–West gradients, all 9 grid point values are used to smoothen out the bias and spatial shifts, if any, at an individual grid point values. 3.1.4. Large‐Scale GCM Variables [25] Runs of Commonwealth Scientific and Industrial Research Organization (CSIRO), Australia Mark3 GCM [Gordon et al. 2002] for the three emission scenarios SRES B1, A1B, and A2 [IPCC 2007] are considered in the present study. The required information about atmospheric variables for current and future climates, as an output of Mark3 GCM, is provided by the Atmospheric Research Division of the CSIRO. The atmospheric component of the CSIRO Mark3 coupled model has a horizontal resolution of T63 (approximately 1.875° longitude × 1.875° latitude) and 18 vertical levels. A detailed description of the physical representations in the CSIRO Mark3 is given by Gordon et al. [2002]. [26] GCM data sets of atmospheric variables for the baseline (covering a 43 year period between 1960 and 2002 and representing the current climate) and the future climate by 2070 (2061–2080) periods are considered in the analysis. For mean sea level pressure, single daily observations at 0000 hours GMT while for the remaining variables twice‐ daily observations at 0000 hours and 1200 hours GMT are available. These variables are extracted from a single continuous (transient) run (corresponding to each of the three SRES emission scenarios) for the grid nodes over the study region. Again, as an observed rainfall value represents the total rainfall over a 24 hour period ending at 0900 hours (local time, LT) in the morning, similar to the reanalysis data, the available atmospheric measurements on the preceding day are considered as representative of current day’s rainfall. For mean sea level pressure, observation at 0000 hours GMT while for other variables average of 0000 hours and 1200 hours GMT values on the preceding day is adopted. [27] The climate change studies commonly focus on the years 2030, 2050, 2070, or even 2100 for assessing the impacts of climate change in the future. It is argued that the climate projections too far into the future may not be realistic, at least with the models available at the present time partly because population projections and related developments have generally been made (which are somewhat reliable) only until year 2050 (year 2025, in most cases), which also forms an important basis for future emission scenarios; and the IPCC [2007] considers mostly year 2030 (perhaps a

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possible “change point”) in their assessment of climate change impacts for Australia (and also New Zealand), especially for water resources and agriculture. However, on other hand, it is believed that the most GCMs show large uncertainties in the projected regional climate changes for 2030 mostly due to differences between the results of the climate models rather than the different emission scenarios [Hennessy et al., 2008]. In the present study, results reported later are derived for year 2070 only under the assumption that the results for 2070 are much more strongly affected by emissions rather than model uncertainties. 3.1.5. Adjustment of GCM Data [28] A preliminary comparison of current climate GCM and corresponding reanalysis atmospheric fields (1960– 2002) on the basis of calendar day means (average across all years), standard deviations, and distribution plots suggest subtle differences in these characteristics. This necessitates some scaling to be carried out on the GCM data in order to remove the regional bias in the data. We adjust the GCM data for the baseline (1960–2002) and future climate period (2061–2080) by adopting a two‐stage adjustment procedure. In the first stage, the GCM series (current and future climates) is corrected for bias in the mean by subtracting the mean of the baseline period GCM data and adding the mean of the baseline period reanalysis data. In the second stage, the mean‐ corrected GCM series (for current and future climates) is rescaled to correct for bias in standard deviation without affecting the mean. This is achieved by first subtracting the mean (of the mean‐corrected series) and then rescaling the resulting data series by the ratio of the standard deviations of the reanalysis data and baseline period GCM data, with the final step being the readdition of the mean (of the mean‐ corrected series) thereafter. This ensures that any biases in the GCM atmospheric fields are removed before their use for downscaling while the mean shift from current to future climate is maintained. Means and standard deviations for the standardization procedure are estimated on a daily basis by considering a moving window of 31 days centered on the current day. The daily time scale is found to provide a better agreement of various spatial and temporal attributes of observed and downscaled rainfall in comparison to monthly or seasonal scale. The standardization procedure helps removing the mean bias from the raw data and reducing the differences in the first two moments of the reanalysis and the altered GCM series. 3.1.6. Identification of Significant Predictors [29] There is little consensus on the most appropriate choice of predictor variables. Atmospheric circulation strongly influences the local climate. Nevertheless, the ability of circulation indices alone to account for long‐term or decadal variability for temperature and also for precipitation, varies with time [Hanssen‐Bauer and Forland, 2000; Benestad, 2001]. Additional predictors therefore have to be included not only to project a possible future climate change but also to describe climate development in the past. When the downscaled response is precipitation, inclusion of a predictor variable representing atmospheric moisture is found to provide better results [Yarnal et al., 2001, Charles et al. 1999]. Trenberth et al. [2003] argue that the main changes in rainfall to be experienced in future will be due to better availability of moisture in the atmosphere, leading to higher rainfall rates and greater intervals between rain events. Harpham and Wilby [2005] found specific humidity, whereas

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Table 1. Identified Seasonal Large‐Scale Atmospheric Variables Used in Rainfall Occurrence and Amount Downscaling Seasons

Rainfall Occurrences

Autumn

Dew point temperature depression at 700 hPa North–south gradient of geopotential height at 850 hPa Vertical velocity at 850 hPa Vertical velocity at 500 hPa Dew point temperature depression at 700 hPa North–south gradient of geopotential height at 850 hPa Vertical velocity at 850 hPa Vertical velocity at 500 hPa Dew point temperature depression at 700 hPa North–south gradient of geopotential height at 850 hPa Dew point temperature depression at 850 hPa 500–1000 hPa thickness of vertical velocity Dew point temperature depression at 700 hPa North–south gradient of geopotential height at 850 hPa Dew point temperature depression at 850 hPa Vertical velocity at 850 hPa

Winter

Spring

Summer

Rainfall Amounts

Martin et al. [1997] and Easterling [1999] found relative humidity as a good indicator of precipitation. Buishand et al. [2004] suggested using relative humidity for precipitation occurrence and specific humidity for precipitation amounts as representatives of atmospheric moisture. Charles et al. [1999] suggest using difference of air and dew point temperatures as a predictor for rainfall occurrences because it is an indicator of relative moisture rather than absolute moisture. Similarly, Evans et al. [2004] advocate using difference of equivalent potential temperatures at different pressure levels as one of the predictor to capture the instability of the atmosphere. It may, however, be noted that GCMs provide less accurate simulations of moisture than of sea level pressure and geopotential heights [Yarnal et al. 2001; Cavazos and Hewitson, 2005]. [30] On the basis of above discussions and the results of earlier downscaling studies, we picked a large set of atmospheric predictors comprising of atmospheric circulation and moisture variables at various levels and their horizontal and vertical gradients as the potential predictors. The predictor identification exercise is carried out at daily time step for each season (MAM, JJA, SON, DJF). To simplify the procedure, area‐averaged wetness fraction (average of rainfall occurrences (0, 1) at all stations on a given day) for rainfall occurrence and area‐averaged rainfall for rainfall amount processes is considered as a solo predictand in the predictor identification exercise adopted here. As some of these predictors might be highly correlated among themselves, an initial screening is carried out to exclude the highly correlated predictors (having correlation higher than 0.90). This leads to only a handful of potential atmospheric predictors. Finally, a nonparametric stepwise predictor identification analysis based on partial mutual information [Sharma, 2000] is carried out to identify sets of significant atmospheric predictors for each season and for the occurrence and amounts models. To account for the short‐term persistence in the rainfall occurrence/amount downscaling process, the previous day area‐averaged wetness fraction/rainfall is included as a preidentified predictor in the conditioning vector for each season before carrying out the predictor identification exercise. For rainfall occurrence process, one additional preidentified

Dew point temperature depression at North–south gradient of geopotential height at 850 hPa Vertical velocity at 500 hPa Vertical velocity at 850 hPa Dew point temperature depression at North–south gradient of geopotential height at 850 hPa Geopotential height at 850 hPa Vertical velocity at 850 hPa Dew point temperature depression at Dew point temperature depression at

700 hPa

700 hPa

700 hPa 850 hPa

Vertical velocity at 500 hPa Vertical velocity at 850 hPa Dew point temperature depression at 700 hPa Dew point temperature depression at 850 hPa Vertical velocity at 500 hPa Vertical velocity at 850 hPa

predictor, namely, the previous 365 days’ area‐averaged wetness state is also included. This predictor is identified based on a sensitivity analysis and is found to improve significantly the representation of low‐frequency variability in the simulated rainfall [Mehrotra and Sharma, 2007b]. Table 1 provides the list of atmospheric predictors identified as significant for occurrence and amount processes and for all seasons. 3.2. Selection of Model Parameters [31] For rainfall occurrence downscaling model (MMM), we consider individual at site Markov order 1 models conditional on preidentified atmospheric variables (common across all stations) and the previous 365 days’ wetness state (for each site). To improve the representation of area averaged wetness fraction, the previous day’s area‐averaged local wetness fraction (ascertained using an inverse distance squared weighting) is also included as a conditioning variable. Thus, the short‐term persistence in the downscaled rainfall is maintained through an order 1 Markovian structure and the localized previous day’s wetness fraction, while the longer‐time scale persistence is introduced through the previous 365 days’ wetness state, apart from the effect of the atmospheric predictors used. As the distribution of the local area averaged previous day’s wetness fraction is found to be highly skewed rather than attempting a transformation, the two conditional probabilities of equation (1) for this variable, are estimated empirically, and an assumption made that this variable is independent of the remaining predictors. The relationship between the correlations of the series of normally distributed random numbers and corresponding simulated rainfall occurrence and amounts at a station pair is ascertained on a daily basis based on the observations that fall within a moving window of length 31 days centered on the current day. [32] For rainfall amounts, it is observed that as the procedure incorporating spatial dependence considers the correlations of rainfall amounts for each station pair with both stations being wet, the distribution of downscaled rainfall amounts on occasions when only one station (of a station pair) is wet, does not correspond well with observations. This

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Table 2. Observed and Downscaled (5th, Median (50th), and 95th Percentile Estimates) Seasonal and Annual Wet Days and Rainfall Amount Using Reanalysis and GCM Data for the Current Climate Wet Days

Rainfall Amount (mm)

Simulated Percentile Estimates Season

Observed

Using reanalysis data Autumn 28 Winter 26 Spring 29 Summer 30 Annual 112 Using current climate GCM data Autumn 28 Winter 26 Spring 29 Summer 30 Annual 112

Simulated Percentile Estimates

5th

Median

95th

Observed

5th

Median

95th

28 26 29 30 113

27 26 29 29 111

26 25 28 28 109

266 210 230 280 984

291 230 264 302 1047

273 212 246 285 1020

256 196 235 269 989

29 26 29 31 114

28 25 28 30 111

27 25 27 29 109

266 210 230 280 984

253 209 246 298 981

238 195 235 284 951

223 182 222 270 918

situation occurs when a wet station lies close to the boundary of a wet region. Neighboring dry stations tend to influence the rainfall amount at the wet station being lesser than the value otherwise obtained had both stations were wet. We address the influence of neighboring stations on the downscaled rainfall amount at a station by incorporating an additional variable in the predictor set, representing the ratio of the number of wet stations to the total number of stations in the neighborhood (again applying a weighting factor proportional to the inverse interstation distance). The conditioning vector considered for downscaling of rainfall amount at a station thus includes preidentified atmospheric variables for each season, previous day rainfall, and a variable defining the local wetness fraction.

4. Model Results [33] In all the results that follow, the statistics reported are ascertained by generating 100 realizations of the downscaled rainfall from the model. The individual statistics from these realizations are ranked, and 5th, 50th, and 95th percentile values are extracted. The best estimate refers to the 50th percentile value (median) while 5th and 95th percentile values are used to form the confidence bands around the median estimate. As all emission scenarios exhibit similar performances for the baseline period, results of only one emission scenario are presented for the current climate and these are mentioned hereafter as “GCM current climate.” The performance of the downscaling framework, MMM‐KDE, is evaluated on a daily, seasonal, and annual basis for its ability to simulate various observed spatial and temporal characteristics of rainfall including those of importance in water resource management. This assessment is performed for the baseline period (1960–2002) during both calibration (using reanalysis) and evaluation (using GCM current climate data) stages. In the subsequent discussions, reanalysis or GCM rainfall implies the downscaled rainfall using either reanalysis or GCM derived atmospheric variables. In addition to statistics, such as means and standard deviations over defined periods (daily, seasonal, and annual), the comparison also assesses various low‐frequency and extreme rainfall attributes such as year‐to‐year rainfall dependence attributes, number of instances when daily rainfall is greater than a prespecified threshold, extended periods of wet and dry

spells, and associated rainfall in the wet spells. Quite a few of our results are presented in the form of contour plots exhibiting the spatial distribution of rainfall attributes over the study region. This is followed by the application of downscaling framework to simulate rainfall for year 2070 using the B1, A1B, and A2 emission scenario runs and results compared with those for the GCM current climate and conclusions drawn. 4.1. Model Calibration and Evaluation Over the Baseline Period 4.1.1. Number of Wet Days and Rainfall Totals [34] For reservoir operation and flood management applications, it is important that the downscaling model accurately reproduces number of wet days and rainfall amounts in the downscaled simulations. One of the strengths of the MMM‐ KDE downscaling approach presented here is that the rainfall occurrence and amounts series are simulated individually at each station. That is, the model used for each station works in isolation, and therefore, it allows the desired properties of the individual station rainfall to be included in the downscaling algorithm without introducing additional complexities. Table 2 compares the observed and downscaled (5th, median, and 95th percentile estimates) seasonal and annual wet days and rainfall totals over the study region. The model adequately reproduces these rainfall occurrences and amounts attributes over the study area for all seasons and year during calibration (using reanalysis data) and evaluation (using GCM current climate data) stages. The model also captures the observed high and low rainfall regions, for example, more wet days over the inland region in comparison to coastal during winter, more rainfall in the northern part of the region in comparison to the southern on an annual basis, and more rainfall in northern coastal region during summer (results not included). 4.1.2. Distribution of Area‐Averaged Annual Wet Days and Rainfall Totals [35] For efficient design and management of water resource projects, not only the accurate reproduction of the average number of wet days and rainfall amount but their distribution at seasonal or annual time scales over the catchment is also desired. The year‐to‐year persistence or low‐frequency variability forms an important rainfall characteristic when it is used to assess the likelihood of sustained

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Figure 2. Distribution plots of observed and model simulated area−averaged annual wet days and rainfall amount (in mm) for the baseline period using reanalysis and GCM current climate data sets. droughts or flood regimes. Figure 2 presents the year‐to‐year distribution of area‐averaged wet days and rainfall amounts obtained using the reanalysis and GCM data sets. The yearly area‐averaged time series is formed by averaging across the stations individual station values of annual wet days and annual rainfall. Ranking of this area‐averaged series provides an indication of the over‐the‐year distribution of annual rainfall or wet days over the study region. On this figure, percentiles of the model‐simulated values are shown as continuous lines while the observed values are superimposed as circles. The downscaling model successfully reproduces the distribution of observed area‐averaged annual rainfall occurrences and amounts in the downscaled sequences, using both the reanalysis as well as GCM data. The good fit of the simulated statistic indicates that the downscaling model is capable of reproducing the observed occurrences of dry and wet years successfully over the study region. The model performs equally well at a majority of individual stations (results not included). 4.1.3. Extreme Rainfall Characteristics [36] Sustained periods of wet and dry spells form the basis of reservoir design and operation and agricultural studies. Similarly, proper estimation and distribution of the observed extreme daily rainfall peaks in the modeled simulations is of significance in catchment studies dealing with flood estimation and reservoir operation. The specification of a design flood also forms an important input for a wide range of infrastructure development applications, including design of roads, bridges, and so on all being inferred from an estimated design flood value with specified probability of exceedance. In the plots and discussions that follow, a wet spell is defined

as a continuous sequence of days when daily rainfall is greater than or equal to 0.3 mm, and likewise, a dry spell represents a sequence of days with daily rainfall being less than 0.3 mm. Rainfall amount in a wet spell represents the total amount of rainfall received during that spell. The top row of Figure 3 compares the average annual frequency of occurrence of wet spells of durations 5–7 days and greater than 7 days at individual stations using observed, reanalysis data and GCM data simulated rainfall. The second row presents the plots of average rainfall totals (in mm) in these wet spells (amount per wet spell), and the third row shows the average number of dry spells of 9–18 days and more than 18 days in a year. The bottom row shows the plots of average number of days in a year when daily rainfall is greater than 35 mm. The dots refer to the values for individual stations. As can be seen from these plots, the model adequately reproduces these extreme rainfall attributes at individual station using both reanalysis and GCM data sets simulated rainfall albeit some underestimation of number of wet spells and days with extreme rainfall at many stations for GCM data simulated rainfall. 4.2. Model Results for Year 2070 [37] A warmer atmosphere increases the moisture holding capacity of the atmosphere and influences the wind circulation patterns and hence the rain patterns. Localized changes in rainfall can be quite sensitive to small differences in wind circulation and other processes. In the following discussions, a likely range of change, as well as a best estimate, of future rainfall statistic over the study region is included. For many impact applications, the percentage change in rainfall is of

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Figure 3. Observed and models simulated (a) number of wet spells of 5–7 and >7 days in a year, (b) average total rainfall (in mm) in these wet spells, (c) number of dry spells of 9–18 and >18 days in a year, and (d) number of days with daily rainfall >35 mm in a year.

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Figure 4. Seasonal and annual wet day anomalies expressed as a percentage difference of model simulated and current climate wet days for year 2070 and for selected seasons and scenarios. more interest than the absolute amounts, so the analysis will focus on percentage changes relative to the current climate. All the anomaly plots are drawn using the median best estimate of rainfall statistics (ranking a particular rainfall statistic derived from 100 realizations and picking up middle value of the ranked series) for future climates and finding the percent change in relation to the current climate. For majority of statistics analyzed, climate projections show wide variations across the scenarios and seasons. All emission scenarios are assigned equal weightage in the overall results presented in the subsequent sections. 4.2.1. Projected Rainfall Changes for 2070 [38] Tables 3 and 4 provide the details on the estimated changes in the number of wet days and rainfall amount on seasonal and annual basis in year 2070. These tables also includes the 5th and 95th percentile ranges on the best (median) estimate of the percent changes in year 2070 from the current climate drawn from the simulated 100 realizations. Distribution of annual and seasonal rainfall occurrence and amount anomalies (in %) over the study area are shown in Figures 4 and 5 for selected seasons and scenarios. For other seasons and scenarios, changes broadly follow similar spatial varia-

tions. The results show wide variations in the projected wet days and rainfall amount over the study area from season to season and from one scenario to another. On the whole, results project wetter autumn and summer and drier spring and winter conditions over the region in year 2070. Also, wetter conditions along the coastal areas and drier conditions for far inland region are projected (bottom rows, Figures 4 and 5). By 2070, under the B1 scenario, the range of annual wet days change is −1.3% to +4.4% with the best estimate of 1.5% increase while for annual rainfall the change is from +5% to +15.9% with the best estimate of 9.4% increase (Tables 3 and 4). Both A1B and A2 scenarios project slight decreases in annual number of wet days and rainfall amount. For A1B the decrease is 5.4% (range −8.4% to −2.5%) for wet days and 3.4% (range from −7.7% to +0.8%) for rainfall amount while the corresponding figures for A2 are 2.6% (range −5.7% to −2.6%) and 0.5% (range −5.7% to +4.8%), respectively. Collectively, by 2070 the estimated range of annual wet days change is −8% to +4% with 2% decrease and of annual rainfall as −8% to +16% with 2% increase. [39] In a recent study, Suppiah et al. [2007] derived the climate change projections for Australia using the results

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Figure 5. Seasonal and annual rainfall anomalies expressed as a percentage difference of model simulated and current climate rainfall for year 2070 and for selected seasons and scenarios. from 15 best climate models simulations performed for the IPCC Fourth Assessment Report. In the study, changes in rainfall are reported for high (3.77°C by 2070), mid (2.47°C by 2070), and low (1.17°C by 2070) global warming scenarios, with the midscenario being close to the A2 emission scenario. The results of the study point out increases of about 10%–20% in summer and 0%–5% in autumn rainfall and

decreases of about 10% to 20% in winter and 0% to 5% in spring for midscenario. Our median estimates (Table 4, scenario A2) of 11% increase in summer, 2% increase in autumn, 9% decrease in winter, and 6% decrease in spring follow these projections fairly closely. [40] It is interesting to note that the significant increases in the rainfall amount (25% in autumn and 16% in summer

Table 3. Percent Changes in Seasonal and Annual Number of Wet Days and Rainfall Amounts in 2070 Scenario B1

A1B

Season

Current Climate Number of Wet Days

Median Estimate of Number of Wet Days

Percent Change in Median, 5th, and 95th Percentile Values

Autumn Winter Spring Summer Annual

28 25 28 30 111

32 23 28 32 113

+13 (+18 to +9) −11 (−6 to −15) −2 (+3 to −6) +6 (+11 to +2) +2 (+4 to −1)

A2




30 23 26 28 106

+7 (+12 to +2) −10 (−6 to −14 −8 (−4 to −13) −7 (−3 to −12) −5 (−3 to −8)

29 23 26 31 109

a

Percent changes in number of wet days in 2070.

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Percent Change in Median, 5th, and 95th Percentile Values +3 −9 −7 +3 −3

(+7 to −2) (−4 to −13) (−2 to −11) (+7 to −1) (0 to −6)

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Table 4. Percent Changes in Rainfall Amount in Year 2070 Scenario B1

Season

Current Climate Rainfall Amount (mm)

Median Estimate of Rainfall (mm)


Autumn Winter Spring Summer Annual

238 195 235 284 951

297 177 249 329 1040

+25 (+41 to +12) −9 (+3 to −20) +6 (+17 to −4) +16 (+25 to +8) +9 (+16 to +5)

A1B

A2





266 190 207 265 919

+12 (+21 to +3) −3 (+11 to −12) −12 (−4 to −19) −7 (+1 to −14) −3 (+1 to −8)

242 178 221 314 946

+2 (+10 to −6) −9 (+4 to −19) −6 (+4 to −15) +11 (+22 to 0) −1 (+5 to −6)

seasons, Table 4) are found for B1 scenario. This is contrary to general expectations as B1 is a low emission scenario. The preliminary investigations suggest that the values for vertical velocity at 500 and 850 hPa differ significantly (30% to 50%) for B1 and A2 scenarios for summer in 2070. However, the reasons for these differences require further research, which is beyond the scope of this study. We intend to investigate this issue in our future studies. 4.2.2. Daily Rainfall Intensity, Wet and Dry Spells, and Extreme Rainfall [41] Along with the changes in number of wet days and average rainfall, the statistics of daily rainfall may also change, e.g., rainfall intensity (rainfall amount per wet day), spells of wet and dry days and the intensity of extreme rainfall. Changes to extreme events would have the potential to increase erosion and flood frequency, with implications for agriculture, forestry, river flow, water quality, insurance risk, and the design standards of bridges, roads, dams, storm water, and other infrastructure. [42] Results of projected changes in per wet day rainfall amount and maximum daily rainfall in 2070 are analyzed at seasonal and annual levels with annual results being presented in Figure 6 for B1 and A2 scenarios. In general, north– east part of the study area is expected to get a slight increase (5%) in per wet day rainfall while west and south–west parts experience a slight decrease (5%) in per wet day rainfall amount. An increase (about 4%) in daily rainfall intensity (rain per wet day) is estimated with B1 projecting a maximum increase of 7.7% (top row). Number of days with extreme rainfall (greater than 35 mm/d) are likely to increase annually (bottom row) and in all seasons (with maximum increase of about 45% in summer for B1 scenario, results not included). More specifically, this increase (at annual level) is more pronounced in the north–east part of the study area varying from 25% to 35% while west and south–west part of the region projects a decrease from 0% to15%. Increased occurrences of short spells of days with intense rain of greater than 35 mm in the future are estimated. [43] Figure 7 provides the changes in the longer‐duration wet (≥7 days) and dry (≥18 days) spells at annual level over the study region for B1 and A2 scenarios. Increased instances of wet spells of 7 days or more are projected more specifically along the coastal areas (Figure 7) with B1 scenario projecting more than 35% increase. Far inland region projects a decrease of about 10% to more than 35% in the frequency of occurrence of longer wet spells in a year. Changes in these spells are also evaluated on seasonal basis with increase instances in autumn and summer and decreases in winter and spring in the

frequency of such events (results not included). The rainfall amount in wet spells of 7 days or more is likely to increase in all seasons with about 6% (−7% to +24%) increase annually. Similarly, wet spells of 3–4 days show decrease of 5.2% (−14% to +4% range) annually with increase in autumn and decrease in other seasons. Rainfall amount in these spells is likely to increase in autumn and summer and decrease in winter. Increased frequency of occurrences of longer dry spells (of 18 days or more in a year) is also estimated in the future (Figure 7, bottom row). These results project a mild decrease in the north–west part of the region for B1 scenario and about 5% to 10% decreases along the coast for A1B scenario annually. The increased frequency of longer wet spells with lesser increase in wet spell rainfall and decreased frequency of wet spells of 3–4 days with increased wet spell rainfall suggest that the future rainfall regime will have fewer shorter rainfall events with increased intense rainfall. 4.3. Influence of Low‐Frequency Variability Variable on the Results [44] The downscaling approach proposed here provides a time‐dependent parameter updating procedure and is formulated to reproduce the most part of the observed low‐ frequency variability in the downscaled simulations. To emphasize this point further, we focus on a few rainfall characteristics indicative of the low‐frequency behavior of rainfall. These include standard deviation of the aggregated wet days at monthly, seasonal, and annual levels and frequency of sustained wet and dry spells. We rerun the downscaling model by dropping the 365 days’ wetness state variable and evaluate these rainfall attributes in the revised downscaled simulations and compare them with the observed and original downscaled results. Table 5 compares these results in terms of mean squared error (MSE) measure. MSE of these rainfall attributes is calculated, by computing the median statistic from the 100 realizations, calculating squared difference of observed and median statistic at each station and averaging across the stations. The MSE for future climate is calculated only to convey the message that the proposed model provides a realistic representation of low‐frequency variability (also referred to as long‐term persistence) in the rainfall, leading to simulations that are consistent with observations, making them viable for water planning and design for a future climate. These results indicate that the use of 365 days’ wetness state variable not only improves the standard deviation of wet days at seasonal and annual time scale but also improves the representation of frequency of dry

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Figure 6. Annual “rainfall per wet day” (top row) and number of days in a year with daily rainfall greater than 35 mm (bottom row); anomalies expressed as a percentage difference of models simulated and current climate values for year 2070 and for B1 and A2 scenarios. spells in the downscaled sequences specifically when using GCM data set.

5. Summary and Conclusions [45] This paper has demonstrated the calibration, evaluation, and application of a stochastic downscaling framework for multisite rainfall simulation using current and future climate atmospheric information. The approach downscales rainfall occurrences at multiple stations using a parametric modified Markov model (MMM) while rainfall amounts for the stations specified as wet on a given day by the occurrence model, are downscaled using conditional kernel density estimation procedure (KDE) with spatially dependent forcing of uniform random numbers. The novelty of the downscaling approach proposed here lies in its capability of providing a time‐dependent parameter updating procedure and reproducing the observed low‐frequency variability in the downscaled simulations. The approach modifies the day‐to‐day transition probability of rainfall occurrences incorporating the changes in the values of atmospheric variables and low‐

frequency variability indicator. Similarly, rainfall amounts on the wet days are simulated conditional on the atmospheric variables using a nonparametric approach. Thus, the method is capable of taking into account the variability of the climate under the assumption that the parent distribution of atmospheric variables remains the same in current as well as in future conditions. Additionally, the approach allows rainfall simulations at individual locations independently and therefore the restriction of spatial (in)dependence is not strictly imposed. The only assumption involved is that given a storm, its spatial distribution across locations remains the same in current and future climates. [46] The selection of appropriate downscaling predictors to represent the low‐frequency components of precipitation at point locations is not a straightforward task. The capability of GCMs to represent continental‐scale processes governing low‐frequency variations in rainfall (such as El Niño– Southern Oscillation, Indian Pacific Oscillation, or similar climatic anomalies), and the significance of future projections of such mechanisms remain indecisive [e.g., Trenberth and Hoar, 1997, Wilby et al., 2002]. Acknowledging these

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Figure 7. Number of wet spells of 7 or more days in a year (top row) and number of dry spells of 18 or more days in a year (bottom row); anomalies expressed as a percentage difference of models simulated and current climate values for year 2070 and for B1 and A2 scenarios. reservations, it might be practical to develop downscaling models that avoid explicit use of GCM predictors to represent low‐frequency climate variability as has been attempted in this paper.

[47] The downscaling approach simulates the rainfall series in a way that ensures an appropriate representation of rain in both space and time. This makes the downscaled sequences especially useful for a range of catchment management

Table 5. Mean Squared Error for Selected Area‐Averaged Rainfall Attributes in the Downscaled Simulations Obtained Using Reanalysis and GCM Data Sets Only and Also Including the 365 Days’ Wetness State Variablea Mean Square Error (MSE) Rainfall Attribute Standard deviation of annual wet days Standard deviation of monthly wet days Standard deviation of seasonal wet days

Number Number Number Number

of of of of

Autumn Winter Spring Summer dry spells of 9–18 days in a year dry spells of >18 days in a year wet spells of 5–7 days in a year wet spells of >7 days in a year

Observed Statistic

RE

RE + L

GCM

GCM + L

A2 2070

A2 2070 + L

20.49 3.41 8.38 7.91 7.66 8.09 5.3 1.2 3.7 0.9

16.35 0.00 0.82 1.79 0.39 0.97 5.28 1.23 3.65 0.87

0.09 0.01 0.03 0.31 0.04 0.20 0.13 0.00 0.03 0.00

66.23 0.14 3.97 2.94 3.37 2.31 0.03 0.00 0.02 0.00

20.03 0.00 1.44 0.49 0.64 0.65 0.00 0.10 0.31 0.07

33.51 0.01 3.98 0.03 1.50 5.42 0.02 0.01 0.11 0.01

12.38 0.03 4.20 0.28 0.20 3.54 0.10 0.00 0.12 0.00

a

R, reanalysis; L, 365 days’ wetness state variable.

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applications. Additionally, attributes such as the distribution of wet and dry spells, number of wet days, and rainfall amounts at individual stations have a significant impact in crop simulation studies and drought management applications. Such spatiotemporal rainfall attributes assume even more importance when the downscaling procedure is applied for investigating possible changes that might be experienced by hydrological, agricultural, and ecological systems in future climates. The substantial topographic and spatiotemporal rainfall variations of the study region provide a challenging setting to evaluate the downscaling model. [48] The model calibration and evaluation results for the baseline period (1960–2002) indicate that the downscaling model proposed here simulates fairly accurately not only the standard rainfall attributes such as the average number of wet days and rainfall amounts but also maximum daily rainfall amount, extended periods of wet and dry spells, and the longer time scale variations. The scheme of updating of transition probabilities of the at site rainfall occurrence model and the logic of providing separate treatments for rainfall occurrence and amounts at individual locations, provides considerable improvements in the representation of characteristics of interest in hydrologic studies for current and future climates and therefore offers a convenient tool for use in climate change impact assessment studies. [49] The utility of the proposed downscaling framework is subsequently demonstrated by estimating the plausible changes in rainfall in year 2070. Downscaled results for 2070 show variations across the seasons and emission scenarios. In general, wetter autumn and summer and drier winter and spring with coastal region getting wetter and inland region becoming drier are estimated. Increased instances of longer dry and wet spells with lighter rain are expected to occur in the future. [50] The present study makes use of three emission scenarios runs simulated using a single GCM (CSIRO Mk3.0) only. While this not the main focus of the paper, this represents a limitation of the work presented here. Use of additional GCMs with multiple ensemble members are likely to contribute to a more appropriate reflection of the uncertainty associated with the rainfall projections for the future. It should, however, be noted, that while there are significant inconsistencies across GCMs in their simulation of variables such as rainfall or flow for a future climate, these inconsistencies are generally lower for the atmospheric predictors the downscaling application has utilized. For instance, in a study across Australia, Johnson and Sharma [2009] report a variable convergence score having a range of 0 to 100 (with 100 representing uniformity in GCM simulations for a future climate for the variable), which associates high skills for monthly simulations of the predictors that have been used in the downscaling model (averaged skills for the grid cell locations used in the downscaling model for surface pressure, geopotential heights (700 hPa) and dew point temperature depression (700 hPa) being 97, 89, and 53, respectively, in contrast to precipitation, which has a skill of 14. Skill scores for vertical velocity are not available. Consequently, we argue that if downscaling models are formulated using predictors that are deemed to be more skillful across GCMs in their simulations for a future climate, the consequences of using fewer GCMs in a downscaling assessment are likely to be lower.

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[51] Acknowledgments. The work described in this paper is partially funded by the Australian Research Council, Sydney Catchment Authority and Department of Environment, Climate Change and Water, New South Wales, Australia. We are also thankful to three anonymous referees for their constructive comments.

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