A Stochastic Analog Downscaling Method 1 Introduction S

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2141 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract HESSD There are a number of statistical techniques that downscale coarse climate information from global circulation models (GCM). However, many of them do not reproduce the 10, 2141–2181, 2013 small-scale spatial variability of precipitation exhibited by the observed meteorological 5 data which can be an important factor for predicting hydrologic response to climatic A stochastic analog forcing. In this study a new downscaling technique (bias-correction and stochastic ana- downscaling method log method, BCSA) was developed to produce stochastic realizations of bias-corrected daily GCM precipitation ﬁelds that preserve the spatial autocorrelation structure of ob- S. Hwang and served daily precipitation sequences. This approach was designed to reproduce ob- W. D. Graham 10 served spatial and temporal variability as well as mean climatology. We used the BCSA method to downscale 4 GCM precipitation predictions from 1961 to 1999 over the state of Florida and compared the skill of the method to the results Title Page

obtained with the commonly used bias-correction and spatial disaggregation (BCSD) Abstract Introduction approach, bias-correction and constructed analog (BCCA) method, and a modiﬁed ver- 15 sion of BCSD which reverses the order of spatial disaggregation and bias-correction Conclusions References (SDBC). Spatial and temporal statistics, transition probabilities, wet/dry spell lengths, Tables Figures spatial correlation indices, and variograms for wet (June through September) and dry (October through May) seasons were calculated for each method. Results showed that (1) BCCA underestimated mean climatology of daily precipita- J I

20 tion while the BCSD, SDBC and BCSA methods accurately reproduced it, (2) the BCSD J I and BCCA methods underestimated temporal variability because of the interpolation and regression schemes used for downscaling and thus, did not reproduce daily pre- Back Close

cipitation standard deviations, transition probabilities or wet/dry spell lengths as well as Full Screen / Esc the SDBC and BCSA methods, and (3) the BCSD, BCCA and SDBC methods under- 25 estimated spatial variability in precipitation resulting in under-prediction of spatial vari- Printer-friendly Version ance and over-prediction of spatial correlation, whereas the new stochastic technique (BCSA) accurately reproduces observed spatial statistics for both the wet and dry sea- Interactive Discussion sons. This study underscores the need to carefully select a downscaling method that

2142 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion reproduces all precipitation characteristics important for the hydrologic system under consideration if local hydrologic impacts of climate variability and change are going to HESSD be accurately predicted. For low-relief, rainfall-dominated watersheds where reproduc- 10, 2141–2181, 2013 ing small-scale spatiotemporal precipitation variability is important, the BCSA method 5 is recommended for use over the BCSD, BCCA, or SDBC methods. A stochastic analog downscaling method 1 Introduction S. Hwang and General circulation models (GCMs) are considered robust tools for simulating future W. D. Graham changes in climate and for developing climate scenarios for quantitative impact as- sessments (Wilks, 1999; Karl and Trenberth, 2003; Fowler et al., 2007). General circu- 10 lation modeling continues to be improved by the incorporation of more aspects of the Title Page complexities of the global system. However, GCM results are generally insuﬃcient to provide accurate prediction of climate variables on the local to regional scale needed Abstract Introduction

to assess hydrologic impacts because of significant uncertainties in the modeling pro- Conclusions References cess (Allen and Ingram, 2002; Didike and Coulibaly, 2005). The coarse resolution of 15 existing GCMs (typically about 200 km by 200 km) precludes the simulation of realistic Tables Figures circulation patterns and accurate representation of the small-scale spatial variability of climate variables (Christensen and Christensen, 2003; Giorgi et al., 2001; Johns et al., J I 2004; Lettenmaier, 1999; Wood et al., 2002). Furthermore, mismatch of the spatial resolution between GCMs and hydrologic models generally precludes the direct use of J I 20 GCM outputs to predict hydrologic impacts. Back Close To overcome this limitation of GCMs, a number of downscaling methods have been developed. It has been shown that fine-scale downscaled results provide better skill Full Screen / Esc for hydrologic modeling (Andreasson´ et al., 2004; Graham et al., 2007; Wood et al., 2004) and agricultural crop modeling (Mearns et al., 1999, 2001) than using the coarse- Printer-friendly Version 25 resolution GCM output directly. Often downscaling techniques use statistical methods Interactive Discussion that employ empirical relations between features simulated by GCMs at large grid scales and surface observations at sub-grid scales (Hay et al., 2002; Wilby and Wigley, 2143 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 1997). The primary advantage of these techniques is that they are computationally in- expensive, and thus can be easily applied to multiple GCM simulations. Additionally HESSD statistical downscaling has been shown to provide climate information at any specific 10, 2141–2181, 2013 resolution of interests so that is the outcome may be directly used for many climate 5 change impact studies (Fowler et al., 2007; Murphy, 1999; Wilby et al., 2004). Although much progress on downscaling precipitation sequences has been made, A stochastic analog current challenges include the need to represent realistic levels of temporal and spa- downscaling method tial variability at multiple scales (e.g. daily, seasonal and inter-annual variability, Timbal et al., 2009) in the generated sequences, the simultaneous downscaling of correlated S. Hwang and W. D. Graham 10 climate variables (i.e. precipitation and temperature, Zhang and Georgakakos, 2012), and the accurate representation of extreme events (Yang et al., 2012; Katz and Zheng, 1999). In particular, accurately representing the spatial variability and patterns of pre- Title Page cipitation can be an important factor for predicting hydrologic response to climatic forcing at the watershed scale, especially in low-relief watersheds affected by convective Abstract Introduction 15 storm systems as in Florida (Hwang et al., 2011; Smith et al., 2004). Statistical downscaling approaches are often applied at a temporally aggregated Conclusions References

scale (e.g. monthly or seasonally) rather than daily or sub-daily time scales because Tables Figures of distortion of GCM daily results (Maurer and Hidalgo, 2008). When applied at a daily time scale, the direct use of GCM results makes them quite susceptible to model biases J I 20 (Ines and Hansen, 2006). Means of addressing the problem include aggregating GCM predictions into seasonal or sub-seasonal means, downscaling to the target grid scale J I or station network, and then using a weather generator (Wilks, 2002; Wood et al., Back Close 2004; Feddersen and Andersen, 2005) or analog methods which re-sample the historic data to disaggregate in time (Salathe et al., 2007; Maurer et al., 2010; Zhang and Full Screen / Esc 25 Georgakakos, 2012). Generally using a weather generator to generate daily climate sequences exhibits no skill at reproducing spatial correlation and is also limited by the Printer-friendly Version assumption that current temporal daily patterns of precipitation will be preserved in the future (Fowler et al., 2007). The use of analogs is constrained by the requirement that Interactive Discussion

2144 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion a suﬃciently long observation record exists so that reasonable analogs can be found (Zorita and Storch, 1999). HESSD Bias-corrected spatial downscaling (BCSD Wood et al., 2002; Maurer, 2007) is 10, 2141–2181, 2013 a widely used technique to downscale GCM results and it has been extensively applied 5 to assess hydrologic impacts of climate change in the US (Christensen et al., 2004; Wood et al., 2004; Salathe et al., 2007; Maurer and Hidalgo, 2008). BCSD generally A stochastic analog preserves relationships between large-scale GCM results and local-scale observed downscaling method mean precipitation trends. Although this method was originally developed for downscaling monthly precipitation and temperature, in principle, daily GCM output can also S. Hwang and W. D. Graham 10 be downscaled directly using this method. However realistic spatial variability of daily precipitation events may not be reproduced by this method because it is designed to preserve only the observed temporal statistics at the time scale chosen for downscaling Title Page and the spatial disaggregation process is essentially a simple interpolation scheme. The constructed analog method (CA; Hidalgo et al., 2008) is a technique developed Abstract Introduction 15 to directly downscale daily GCM products to assess hydrologic implications of climate scenarios. Hidalgo et al. (2008) showed that CA exhibited considerable skill in repro- Conclusions References

ducing observed daily precipitation and temperature statistics but underestimated the Tables Figures mean and standard deviation of daily precipitation over the southeast US. Maurer and Hidalgo (2008) compared CA and BCSD method and demonstrated that CA showed J I 20 better skill than BCSD, particularly in reproducing extreme temperature events. How- ever both methods showed limited skill in reproducing daily precipitation extremes. Sub- J I sequently, Maurer et al. (2010) introduced the bias-correction and constructed analog Back Close (BCCA) method which improved the CA method by removing the biases attributed to GCMs and showed better accuracy in simulating hydrologic extremes. Full Screen / Esc 25 Abatzoglou and Brown (2012) modified the BCSD method by changing the order of the bias-correction and spatial disaggregation procedures. That is, they interpo- Printer-friendly Version lated GCM outputs onto a fine grid first and then the fields were bias-corrected using the CDF mapping approach for each fine scale grid cell (i.e. the target resolution of Interactive Discussion downscaling). This simple modification (hereafter referred to as SDBC) improved the

2145 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion downscaling skill for reproducing local-scale temporal statistics. However the SDBC method does little to improve skill in reproducing spatial variability because the same HESSD approach (interpolation) as used in BCSD is employed for spatial disaggregation. 10, 2141–2181, 2013 The ultimate goal of this study was to improve the existing bias-correction based 5 downscaling methods introduced above by introducing a method that preserves both spatial and temporal statistics of daily precipitation with similar computational cost. This A stochastic analog paper presents a new stochastic generation technique (bias-correction and stochastic downscaling method analog method, hereafter BCSA) to produce downscaled daily GCM precipitation predictions. BCSA is then used to downscale precipitation predictions from 4 retrospective S. Hwang and W. D. Graham 10 GCM simulations over Florida and the skill of the method is comparatively evaluated to the downscaled results obtained using the BCSD, BCCA, and SDBC techniques.

Title Page 2 Data Abstract Introduction

Daily gridded observations at 1/8 degree spatial resolution (about 12 km) were ob- Conclusions References tained over Florida from 1950 to 1999 (Maurer et al., 2002). The climate data (daily 15 and monthly precipitation, maximum, minimum, and average temperature, and wind Tables Figures speed) are archived in netCDF format at http://hydro.engr.scu.edu/files/gridded obs/ daily/ncfiles/. These products are available from 1950 through 1999 over the entire J I US. without missing data. This data was used to bias-correct daily GCM results and to estimate observed spatial correlation structure. J I 20 GCM data from 1961 to 1999 were obtained from the World Climate Research Back Close Programme’s (WCRP’s) Coupled Model Inter-comparison Project phase 3 (CMIP3) multi-model dataset, which are referenced in the Intergovernmental Panel on Climate Full Screen / Esc Change (IPCC) Fourth Assessment Report (AR4, 2007). The GCMs selected for this study are shown in Table 1. The grid resolutions for the GCMs range from 1.4◦ to Printer-friendly Version ◦ 25 2.8 . Figure 1 shows how each model grid configuration covers the study domain over Interactive Discussion Florida.

2146 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3 Statistical downscaling methods HESSD 3.1 Bias-correction and spatial downscaling at daily scale (BCSD daily) method 10, 2141–2181, 2013 The BCSD method is an empirical statistical technique that was developed by Wood et al. (2002). As described above, the method was originally designed to downscale A stochastic analog 5 monthly precipitation and temperature, but daily GCM output can also be directly ap- downscaling method plied using this method. In this study, we employed same methodology but at daily time scale and evaluated the skills in reproducing the spatiotemporal mean and variability S. Hwang and of daily precipitation. The technique will be referred to as the BCSD daily hereafter. W. D. Graham BCSD daily consists of two separate steps for bias-correction and spatial downscaling. 10 In the first step, raw GCM predictions are bias-corrected at the large GCM grid scale using the CDF mapping approach (Panofsky and Brier, 1968, described in detail in Title Page the next paragraph). In the second step anomalies (i.e. the ratio of simulated precip- Abstract Introduction itation field to observed temporal mean precipitation field) of the bias-corrected GCM output are spatially interpolated to the downscaled resolution using an inverse distance Conclusions References 15 weighting technique (Shepard, 1984). Finally these fine-scale anomalies are re-scaled with the mean precipitation field at the fine grid scale resolution. Tables Figures The bias-correction procedure used in the BCSD daily method is similar to that used by Wood et al. (2002); Ines and Hansen (2006); Salathe et al. (2007); and Maurer and J I Hidalgo (2008) and is described as follows: (1) CDFs of observed daily precipitation J I 20 at the coarse GCM scale were created individually for each month using the spatial average of available observed data from Maurer et al. (2002) within each GCM grid. Back Close Thus 12 observed monthly CDFs were created for each GCM grid cell; (2) CDFs of Full Screen / Esc simulated daily precipitation were created for each grid cell for each month; (3) daily grid cell predictions were bias-corrected at the large-scale GCM prediction resolution Printer-friendly Version 25 using CDF mapping that preserves the probability of exceedence of the simulated precipitation over the grid cell, but corrects the precipitation to the value that corresponds Interactive Discussion to the same probability of exceedence from the spatially averaged observation over the 0 GCM grid. Thus bias-corrected rainfall xt,i on day t at grid i was calculated as, 2147 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

x0 F −1 F x HESSD t,i = obs,i ( sim,i ( t,i )) (1) 10, 2141–2181, 2013 where F (x) denote the CDF of daily precipitation x, and its inverse, and subscripts sim and obs indicate GCM simulation and observed daily rainfall, respectively. This bias- correction process removes both bias in the precipitation predictions and the tendency A stochastic analog 5 of the model to under-predict dry days and over-predict the number of low volume downscaling method rainfall days (Hwang et al., 2011). S. Hwang and 3.2 Bias-correction and constructed analog (BCCA) method W. D. Graham

The constructed analog (CA) technique creates a library of observed daily coarse- resolution climate anomaly patterns for the variable to be downscaled, then selects Title Page 10 a set of analogs with patterns that closely match the simulated anomaly pattern that Abstract Introduction must be downscaled. A linear combination of the selected observed daily coarse- resolution climate anomalies patterns is used to estimate a coarse resolution ana- Conclusions References log to the simulated anomaly, and a downscaled anomaly is generated by applying the same linear combination to the corresponding set of high resolution observed Tables Figures 15 climate anomaly patterns. The CA approach retains daily sequencing of weather events from the GCM results and various possible climate variables (e.g. geopoten- J I tial heights, sea level pressure) can be considered as predictors to construct the J I best analog. A significant limitation of the CA approach, as originally developed, is that the biases exhibited by the GCM (resulting from imperfect model parameteriza- Back Close 20 tion of physical processes or inadequate topographic description in the model) are Full Screen / Esc reconstructed in the downscaled fields (Hidalgo et al., 2008; Maurer and Hidalgo, 2008). In order to overcome this drawback, Maurer et al. (2010) suggested a hybrid Printer-friendly Version method, BCCA combining statistical bias-correction (as used in BCSD) prior to applying the constructed analog. However, BCCA may not accurately reproduce the mean Interactive Discussion 25 and variance of precipitation at the downscaled resolution. This is because “anomaly patterns” of the bias-corrected GCM (instead of the bias-corrected GCM, itself) are 2148 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion used to choose analogs and historical records corresponding to the analogs are com- bined using linear regression without further bias-correction at the fine resolution. In HESSD this study, we used previously developed BCCA results available over the entire USA 10, 2141–2181, 2013 from http://gdo-dcp.ucllnl.org/downscaled cmip3 projections/. Four GCMs (i.e. GFDL, 5 CGCM, CNRM-CM3, and MIROC3.2) were used from this data set (Table 1). Note that the BCCA results are not available for BCCR-BCM2.0 and CCSM that we used for A stochastic analog other statistical methods. downscaling method

3.3 Spatial downscaling and bias-correction (SDBC) method S. Hwang and W. D. Graham The SDBC method developed by Abatzoglou and Brown (2012) was the third previously 10 published methodology evaluated in this study. As described above the SDBC method is a modified version of the BCSD method in which the order of bias-correction and Title Page spatial disaggregation is reversed. That is, GCM outputs are interpolated to the fine Abstract Introduction grid scale using inverse distance weighting first and then the interpolated precipitation fields are bias-corrected using the CDF mapping approach described above but at the Conclusions References 15 local grid scale. This modification improves the downscaling skill in reproducing local temporal statistics since bias-correction is conducted at the local grid scale. Tables Figures

3.4 Bias-correction and stochastic analog (BCSA) method J I

A new spatial downscaling technique was developed to generate spatially correlated J I

downscaled precipitation predictions which preserve both the temporal statistical char- Back Close 20 acteristics as well as the small-scale spatial correlation structure of observed precipitation ﬁelds. The technique will be referred to as the BCSA method hereafter. Because Full Screen / Esc the spatiotemporal features (e.g. frequency, spatial patterns, and correlation) of precipitation events may change monthly or seasonally, the BCSA process was performed Printer-friendly Version using temporal and spatial statistics calculated separately for each month. The proce- Interactive Discussion 25 dure for the BCSA method performed for each month is described as follows:

2149 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion i. Gridded precipitation observations were transformed into standard normal variables using the normal score transformation approach (Goovaerts, 1997; Deutsch HESSD and Journel, 1998), i.e.: 10, 2141–2181, 2013 x∗ G−1 F x t,i = ( obs,i ( t,i )) (2) A stochastic analog ∗ 5 where xt,i is the normal score for xt,i (i.e. observed daily precipitation on day t at downscaling method grid i), G−1(·) is the inverse transform function of the standard Gaussian CDF and S. Hwang and Fobs,i (x) denotes the CDF of daily gridded observation for grid i. W. D. Graham ii. Pearson’s correlation coefficients ρ for the normal score transform variables for all pairs of grid cell observations over the study domain were calculated for each 10 month using the following equation: Title Page PN x∗ − x∗ x∗ − x∗ Abstract Introduction 1 t=1 t,i i t,j j ρ = (3) i,j N ∗ ∗ Conclusions References σi σj Tables Figures where N is the number of data points (days) available for each grid cell, x∗ and ∗ i σi denote the temporal mean and standard deviation of normal scores for grid i, J I respectively. The full correlation matrix that consists of all the calculated pair-wise J I 15 correlations was then assembled:   Back Close ρ1,1 ··· ρ1,n . . ρ =  . .. .  (4) Full Screen / Esc  . . .  ρn,1 ··· ρn,n Printer-friendly Version where n is the number of grid cells. Interactive Discussion iii. The symmetric positive-definite correlation matrix ρ was factored using the Cholesky decomposition method (Taussky and Todd, 2006) that decomposes the 2150 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion matrix into the product of a lower triangular matrix and its conjugate transpose, i.e.: HESSD ρ = LL∗ (5) 10, 2141–2181, 2013 where L is a lower triangular matrix with strictly positive diagonal entries, and ∗ 5 L denotes the conjugate transpose of L. A stochastic analog downscaling method iv. Vectors with elements corresponding to each grid cell were randomly generated from independent Gaussian distributions for each day t (r t) then transformed into S. Hwang and ϕ W. D. Graham pair-wise correlated vectors (r t ) by multiplying with the calculated factorization ∗ matrix L . Note that random vector for each day, r t contains n elements corre- 10 sponding to each grid cell. Title Page ϕ ∗ r t = r tL (6) Abstract Introduction ϕ The rt generated by this process honor the observed spatial correlation but have zero mean and unit variance. Conclusions References ϕ Tables Figures v. Spatially correlated normal score variables r t were back-transformed to their ob- 15 served distributions using the CDF of the corresponding gridded observation in the following equation: J I ϕ xˆ F −1 F x J I t,i = obs,i ( norm,i ( t,i )) (7) Back Close xϕ r ϕ i F where t,i is an element of t for grid . norm,i (·) denotes the CDF of generated normal scores for grid i and xˆt,i is the precipitation estimation for day t and grid i. Full Screen / Esc 20 This procedure was repeated for every grid cell to get ensembles of daily precipitation fields that preserve the mean, variance, and spatial correlation structure of Printer-friendly Version the observed field. Interactive Discussion vi. Steps 4 and 5 are repeated to create an ensemble of 3000 replicates of spatially distributed precipitation fields for each month. 2151 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 0 vii. For each bias-corrected daily GCM prediction xt (obtained using the same bias- correction procedure described above for the BCSD method), a realization was HESSD selected from the appropriate monthly ensemble with spatial mean of the gener- 10, 2141–2181, 2013 ated precipitation fields equal to the GCM prediction.

A stochastic analog 5 4 Assessment of downscaling skill downscaling method

The temporal mean, 50th percentile, 90th percentile, and standard deviation of the S. Hwang and precipitation time series for observed and downscaled predictions were calculated for W. D. Graham each grid cell and mapped over the state of Florida to evaluate the spatial distribution of these temporal statistics for both the wet season (June through September) and the 10 dry season (October through May). Daily transitions between wet and dry states were Title Page calculated for both the observed data and predictions using the first-order transition probability (Haan, 1977) and the numbers of events per year with specific wet/dry spell Abstract Introduction durations were estimated over the study area for both the wet and dry seasons to Conclusions References investigate precipitation occurrence patterns. Tables Figures 15 In terms of spatial features, observations and predictions were evaluated using sev- eral indices indicating spatial standard deviation, correlation, and variability (Hubert et al., 1981). The Moran’s I (Moran, 1950; Thomas and Huggett, 1980) index, a com- J I monly used statistical index for identifying spatial dependence, was calculated using the following formula. J I P P Back Close N i j wij xt,i − xt xt,j − xt 20 I = (8) t P P 2 Full Screen / Esc i j wij P i xt,i − xt Printer-friendly Version where xt,i and xt,j refer to the precipitation in station i and j on day t, respectively. xt is the overall spatial mean precipitation on day t. wij is an adjacency weight based on Interactive Discussion inverse distance weighting. The I values are between −1 and 1. Like the correlation coefficient, I is positive if both xt,i and xt,j lie on the same side of the mean (above or 2152 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion below), while it is negative if one is above the mean and the other is below the mean (O’Sullivan and Unwin, 2003). HESSD Geary’s C (Griffith, 2003) was calculated as a measure of spatial covariance of pre- 10, 2141–2181, 2013 cipitation among grid cells, as follows:

P P 2 (N − 1) i j wij xt,i − xt,j A stochastic analog 5 C = (9) t P P 2 downscaling method 2 i j wij P i xt,i − xt S. Hwang and C values range between 0 and 2. The spatial autocorrelation is positive if C is lower W. D. Graham than 1, negative if C is between 1 and 2, and zero if C is equal to 1. In this research average I and C indices were calculated for the wet and dry season over the study period from 1961 to 1999. Moran’s It and Geary’s Ct represent mea- Title Page 10 sures of spatial autocorrelation for each spatial ﬁeld at day t, however the relationship between the geographical distance and correlation are not measured by these statis- Abstract Introduction

tics. We used the variogram, defined as the expected value of the squared difference of Conclusions References the values of the random field separated by distance vector h, to describe the degree of spatial variability exhibited by each spatial random field. The experimental variogram Tables Figures 15 2γ(h) for the observed and simulated precipitation data was calculated using the following formula (Goovaerts, 1997). J I

N(h) J I 1 X 2 2γ(h) = [x(uα) − x(uα + h)] (10) N(h) Back Close α=1 Full Screen / Esc where N(h) denotes the number of pairs of observations separated by distance h, and x(uα) and x(uα + h) are the observed or simulated precipitation at locations uα and Printer-friendly Version 20 uα + h, respectively. Interactive Discussion

2153 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 5 Results and discussion HESSD 5.1 Evaluation of temporal variability 10, 2141–2181, 2013 Gridded annual total precipitation observations, spatially averaged over the state of Florida, ranged from 1048 mm to 1657 mm with a mean of 1343 mm over the study A stochastic analog 5 period from 1961 to 1999. The standard deviation of the spatially averaged annual to- downscaling method tal observation time series was 152 mm. Figure 2 shows the spatially averaged annual total precipitation time series and mean monthly precipitation of gridded observation S. Hwang and (Gobs) over the study period. Table 2 compares the mean and standard deviation of W. D. Graham observed and predicted spatially averaged annual precipitation. The BCCA method 10 underestimated the observed mean annual precipitation over the study period by 8 % (CGCM3) to 11 % (CNRM-CM3) while the rest of methods reproduced the mean an- Title Page nual precipitation, with errors less than ±20 mm (< 2 % of observed mean annual pre- Abstract Introduction cipitation). The temporal standard deviation was slightly underestimated by the BCSD results (114 mm to 147 mm over the GCMs) and BCCA (128 mm to 147 mm), and over- Conclusions References 15 estimated by SDBC results (153 mm to 247 mm). The SDBC method overestimates the temporal standard deviation of spatially averaged annual total precipitation because the Tables Figures large-scale daily GCM precipitation predictions are spatially disaggregated by interpolation and then bias-correction at the downscaled grid resolution. Thus each fine-scale J I grid cell preserves the precipitation percentile event predicted by the large-scale GCM, J I 20 exaggerating the spatial extent of high and low percentile events. Note that predicted annual time series from GCMs are not expected to reproduce the actual annual time Back Close series for the study period since they do not use actual observed initial conditions or Full Screen / Esc boundary conditions in the simulations. Figures 3 and 4 compare the spatial distribution of mean precipitation for the wet Printer-friendly Version 25 (June to September) and dry seasons (October through May) over the study period and show that mean climatology was accurately reproduced over the state of Florida Interactive Discussion by the BCSD daily, SDBC, and BCSA methods. These results are expected since the CDF mapping bias-correction technique employed in these methods is designed to fit 2154 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion the predictions to historic mean climatology. Meanwhile, the BCCA results accurately reproduced the spatial pattern of observed mean precipitation for both seasons, but HESSD slightly overestimated mean precipitation in the southern part of the state in the wet 10, 2141–2181, 2013 season and underestimated over the entire state in the dry season. 5 The spatial distribution of the temporal standard deviation of precipitation however, showed significant differences among the downscaling methods. Figures 5 and 6 com- A stochastic analog pare the spatial distribution of the temporal standard deviation of the daily precipitation downscaling method time series over the state of Florida for the wet and dry seasons over the study period, respectively. While the SDBC and BCSA results accurately reproduced the standard S. Hwang and W. D. Graham 10 deviation for both the wet and dry seasons, the BCSD daily results significantly underestimated the standard deviation for both seasons. The BCCA results improved over the BCSD daily results but still under-predicted the daily precipitation standard devi- Title Page ation because the linear regression scheme used to construct the analogs in BCCA attenuates extreme events and thus decreases temporal variance. Abstract Introduction 15 Figures 7 and 8 show the spatial distributions of 90th percentile (5 mm ∼ 20 mm) and 50th percentile (< 3 mm) daily precipitation for the wet season, respectively. The re- Conclusions References

sults show that the BCSD daily and BCCA method underestimated the observed 90th Tables Figures percentile daily precipitation amount and overestimated the 50th percentile of daily precipitation because of their tendency to overestimate the occurrence of small rainfall J I 20 events. Note that BCCA exhibits better skill than BCSD daily in reproducing 50th percentile of daily precipitation amount but still overestimates compared to observations. J I On the other hand the SDBC and BCSA method accurately reproduce both the 90th Back Close percentile and 50th percentile daily precipitation. The inaccuracies in the temporal variability produced by the BCSD daily method are Full Screen / Esc 25 caused by the interpolation scheme that is used to disaggregate the bias corrected GCM predictions which produces smooth downscaled results. Note that the temporal Printer-friendly Version standard deviation at downscaled locations corresponding to the center point of the GCM grid produces slightly higher temporal variability (Figs. 5 and 6) because the in- Interactive Discussion terpolation procedure produces less smoothing at these locations. This weakness of

2155 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion the BCSD daily method is improved by exchanging the order of the bias-correction and interpolation procedures (i.e. SDBC) as shown in Figs. 5 through 8. When the in- HESSD terpolated GCM results are bias-corrected using fine scale gridded observations at the 10, 2141–2181, 2013 last step of the downscaling process, the final results reproduce the full observed CDF 5 and thus both the observed temporal mean and temporal standard deviation. Although SDBC has been recently introduced for downscaling daily GCM products (Abatzoglou A stochastic analog and Brown, 2012), explicit insight into these distinctions between the BCSD daily and downscaling method SDBC downscaling frameworks was not provided by the previous studies. In addition to reproducing temporal statistics of daily rainfall, day to day precipita- S. Hwang and W. D. Graham 10 tion patterns are also important for most hydrologic applications. The differences in precipitation occurrence between local and coarse grid scale precipitation series are quite large because precipitation at the coarse grid scale is non-zero when precipita- Title Page tion occurs at any location within the grid cell. Due to this spatial averaging process, the probability of precipitation occurrence for area-averaged time series is necessar- Abstract Introduction 15 ily larger than the corresponding probabilities at any point within the coarse grid cell. Daily transitions between wet and dry states estimated for the observed gridded data Conclusions References

and the downscaled GCM predictions obtained using the BCSD daily, BCCA, SDBC, Tables Figures and BCSA methods are shown in Figs. 9 and 10. The BCSD daily results produced more low rainfall events and thus wet to wet transition probabilities (P {11}) were over- J I 20 estimated and dry to wet probabilities (P {01}) were underestimated for this method. P {11} and P {01} for the BCCA results are closer to the observed transition probabil- J I ities than the BCSD daily results but are not as accurate as the SDBC and BCSA re- Back Close sults. It should be noted that the difference of transition probabilities among the GCMs were not significant for any of the downscaling methods. Full Screen / Esc 25 The frequency and duration of consecutive wet and dry days reflect dynamic proper- ties of precipitation that have important implications for producing extreme hydrologic Printer-friendly Version behavior (i.e. flood and drought events). For evaluation purposes a wet spell was defined as the length of a period of consecutive wet days (P > 0.1 mm) that were pre- Interactive Discussion ceded and followed by a dry day, and a dry spell was defined as the length of a period

2156 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion of consecutive dry days (P ≤ 0.1 mm) that were preceded and followed by a wet day. The average number of specific wet and dry spell events over the study period for HESSD gridded observation and predictions are compared in Fig. 11. The results indicate that 10, 2141–2181, 2013 BCSD daily and BCCA results have fewer events for 5 to 15 wet and dry spell lengths 5 during the wet season. This is because both methods produced too many wet days (> 0.1 mm) and thus fewer total number of events. In contrast, the SDBC and BCSA A stochastic analog methods reproduced wet and dry spell lengths much more accurately for all GCMs. downscaling method Note that the difference in the results obtained by different downscaling techniques is larger than the difference obtained from different GCMs using the same downscaling S. Hwang and W. D. Graham 10 technique.

5.2 Evaluation of spatial variability Title Page Figure 12 compares the relationship between the spatial standard deviation and mean Abstract Introduction of daily precipitation events for Gobs and predictions downscaled using the four methods. The results indicate that the observed relationship between spatial variability and Conclusions References 15 event size was reproduced fairly well by the all methods, but that the BCSA method reproduced the relationship more accurately than the other methods. The spatial vari- Tables Figures ability of daily Gobs and downscaled GCMs were quantified also by calculating the average Moran’s I and Geary’s C for each month (Fig. 13). In general the BCSD daily J I and SDBC results produced precipitation fields with overestimated spatial correlation J I 20 (high Moran I, i.e. ∼ 0.4 and 0.3, respectively, compared to ∼ 0.2 for observations) and underestimated spatial variance (low Geary’s C, i.e. ∼ 0.4 ∼ 0.5 compared to 0.6 ∼ 0.8 Back Close for observations). The BCCA results showed better skills than the BCSD daily and Full Screen / Esc SDBC results for both the Moran’s I and Geary’s C indices, but was not as accurate as the BCSA method. Note that the spatial variance of precipitation (Geary’s C index) Printer-friendly Version 25 was found to show strong seasonality, i.e. higher in the wet season and lower in the dry season. No significant seasonality in spatial correlation (Moran’s I) was found. Interactive Discussion Figure 14 compares wet season and dry season variograms calculated for each downscaled result to the variograms of the gridded observations. These figures indicate 2157 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion that the BCSD method significantly underestimated the observed variogram at all sepa- ration distances for both wet (June through September) and dry (October through May) HESSD seasons. The BCCA and SDBC variogram improved over the BCSD results, but still 10, 2141–2181, 2013 underestimated the observed variogram. As designed, the BCSA results reproduced 5 the pattern and magnitude of observed variograms accurately for both seasons. A stochastic analog 5.3 Discussion downscaling method

Overall, the existing interpolation-based statistical downscaling methods (i.e. S. Hwang and BCSD daily, SDBC) and historical analog method (i.e. BCCA) showed limited skills in W. D. Graham reproducing temporal and spatial variability of daily precipitation. The skill of the BCSA 10 method improved over these methods. The BCSA method can be applied to downscale coarse resolution climate data into any temporal (e.g. monthly, sub-daily) and spatial Title Page scale (e.g. gridded or irregularly distributed points) wherever observations are avail- Abstract Introduction able to estimate the cumulative distribution functions and spatial correlation structure of precipitation. Additionally, because it generates an ensemble of possible local-scale Conclusions References 15 precipitation patterns the uncertainty due to the downscaling process could be exam- ined using a collection of equally probably downscaled climate ﬁelds. The procedure Tables Figures can also be applied to temperature and other surface-weather variables. One drawback of using the BCSA technique is that spatial disaggregation of coarse J I scale precipitation prediction is conducted independently on a daily basis, not taking J I 20 into account day to day, week to week or seasonal temporal relationships at the local scale. Thus the temporal trends and persistence of downscaled precipitation results Back Close depend on the large scale bias-corrected GCMs’ skill to reproduce the temporal cor- Full Screen / Esc relation of precipitation patterns. Nonetheless we found that the observed transition probabilities and wet and dry spell lengths were reasonably reproduced by the BCSA Printer-friendly Version 25 method. These results indicate that the GCMs have acceptable skill in representing plausible temporal precipitation patterns. Interactive Discussion

2158 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 6 Summary and conclusions HESSD This study developed a new technique (i.e. bias-correction and stochastic analog method, BCSA) to downscale bias-corrected daily GCM precipitation predictions to 10, 2141–2181, 2013 accurately reproduce observed temporal and spatial statistics. Four GCM results 5 were used to examine the skill of the new downscaling technique for reproducing A stochastic analog local temporal mean, standard deviation, 90th (5 ∼ 20 mm) and 50th (< 3 mm) per- downscaling method centile daily precipitation, wet to wet and wet to dry transition probabilities and the length of wet and dry spell compared to the gridded observations, compared to the S. Hwang and BCSD daily, BCCA, and SDBC downscaling techniques. Downscaled GCM results us- W. D. Graham 10 ing BCSD daily, SDBC, and BCSA accurately reproduced the temporal mean of the daily precipitation as well as the annual cycle of monthly mean precipitation while the BCCA results showed underestimation of the mean daily precipitation. The temporal Title Page

standard deviation and the magnitude of 90th percentile daily precipitation were under- Abstract Introduction estimated by the BCSD daily method especially for the wet season. Furthermore the 15 BCSD daily overestimated low precipitation frequency and wet to wet transition prob- Conclusions References abilities and underestimated dry to wet transition probabilities. These inaccuracies of Tables Figures the BCSD daily results in reproducing temporal variability of daily precipitation at the ﬁne-grid scale were improved by the BCCA and SDBC method. However the BCCA method underestimated and the SDBC method overestimated the temporal standard J I

20 deviation of spatially averaged precipitation. The BCSA reproduced the observed tem- J I poral standard deviation, magnitudes of both high (90th percentile) and low (50th percentile) rainfall amounts and wet to wet transition probabilities more accurately than the Back Close

BCSD daily and the BCCA method. Full Screen / Esc More signiﬁcantly, the interpolation-based downscaling methods (both BCSD daily 25 and SDBC) were unable to reproduce the observed spatial variability of daily precip- Printer-friendly Version itation, which may have important implications for predicting hydrologic behavior in low-relief rain-dominated watersheds (Hwang et al., 2011). The BCCA method was Interactive Discussion also unable to accurately reproduce the spatial variability of daily precipitation. The

2159 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion BCSA technique was designed to generate daily precipitation ﬁelds that accurately reproduce observed spatial correlation of daily rainfall. Analysis of spatial standard HESSD deviation, Moran’s I, Geary’s C, and variograms quantitatively showed that BCSA is 10, 2141–2181, 2013 superior in reproducing the spatial variance and correlation of observed daily precipi- 5 tation compared to the other methods. This study underscores the need to carefully select a downscaling method that repro- A stochastic analog duces all precipitation characteristics important for the hydrologic system under con- downscaling method sideration if local hydrologic impacts of climate variability and change are going to be accurately predicted. For low-relief, rainfall-dominated watersheds where reproducing S. Hwang and W. D. Graham 10 small-scale spatiotemporal precipitation variability is important, it is anticipated that the BCSA method will produce superior results over the BCSD, BBCA, or SDBC methods. The next phase of this work will examine the relative abilities of these statistical meth- Title Page ods to reproduce historic hydrologic behavior in low-relief rain-dominated watersheds in Florida using an integrated hydrologic model using retrospective GCM simulations. Abstract Introduction 15 Ultimately the most promising technique will be used to downscale both retrospective GCM predictions and future GCM climate projections, and to use these results with an Conclusions References

integrated hydrologic model, to assess potential climate change impacts on regional Tables Figures hydrology.

Acknowledgements. We acknowledge the modeling groups, the Program for Climate Model Di- J I 20 agnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modelling (WGCM) for their roles in making available the WCRP CMIP3 multi-model dataset. Support J I of this dataset is provided by the Oﬃce of Science, US Department of Energy. We also ac- Back Close knowledge “bias corrected and downscaled WCRP CMIP3 climate projections” for providing the BCCA results. Full Screen / Esc

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S. Hwang and Table 1. GCMs considered in this study. W. D. Graham Modeling Group, Country WCRP CMIP3a I.D. Primary Reference Bjerknes Centre for Climate Research, Norway BCCR-BCM2.0 Furevik et al. (2003) US Dept. of Commerce/NOAA/Geophysical Fluid GFDL-CM2.0b Delworth et al. (2006) Title Page Dynamics Laboratory, USA Canadian Centre for Climate Modeling & CGCM3.1b Flato and Boer (2001) Abstract Introduction Analysis, Canada National Center for Atmospheric Research, USA CCSM3 Collins et al. (2006) Conclusions References Meteo-France/Centre National de Recherches CNRM-CM3b Salas-Melia et al. (2005) Meteorologiques, France Tables Figures Center for Climate System Research (The University of MIROC3.2b K-1 model developers (2004) Tokyo), National Institute for Environmental Studies, and Frontier Research Center for Global Change, Japan J I a World Climate Research Programme’s Coupled Model Inter-comparison Project phase 3. The GCMs presented bold in the table indicate the models downscaled in this study. J I b Indicate the models additionally selected for BCCA results for the purpose of comparative evaluation. Back Close

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A stochastic analog downscaling method

S. Hwang and Table 2. The mean and standard deviation of spatially averaged annual total precipitation over W. D. Graham the state of Florida for the downscaled GCM results using 4 diﬀerent statistical downscaling methods. Title Page The spatially averaged The standard deviation of the spatially mean annual total precipitation averaged annual total precipitation Abstract Introduction Gobs: 1343 mm Gobs: 152 mm Units: mm BCSD BCSD Period: 1961 ∼ 1999 daily BCCA SDBC BCSA daily BCCA SDBC BCSA Conclusions References

BCCR-BCM2.0 1359 – 1356 1356 147 – 233 178 Tables Figures GFDL-CM2.0 1359 1227 1357 1357 165 147 247 187 CGCM3.1 1362 1239 1361 1360 132 128 223 167 CCSM3 1363 – 1361 1359 114 – 153 125 J I CNRM-CM3 – 1190 – – – 133 – – MIROC3.2 – 1236 – – – 134 – – J I

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Title Page Latitude Abstract Introduction 27 Conclusions References BCCR, 2.8ox 2.8o 26 GFDL, 2.0ox2.5o Tables Figures CGCM3, 2.8ox2.8o CCSM, 1.4ox1.4o J I 25 CNRM-CM3, 2.8ox2.8o (only for BCCR) J I MIROC3.2, 2.8ox2.8o (only for BCCR) 24 Back Close -88 -87 -86 -85 -84 -83 -82 -81 -80 Longitude Full Screen / Esc 1 Fig.2 1.FigThe. 1. study The domain study and domain the center and locationthe center of grids location for the of GCMs grids used for inthe the GCMs study. Noteused in the study.Printer-friendly Note that Version the grid that the grid resolutions and conﬁgurations for BCCR, CGCM3, CNRM-CM3, and MIROC3.2 are3 identical. resolutions and configurations for BCCR, CGCM3, CNRM-CM3, and MIROC3.2Interactive are Discussion identical. 4 2168

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(a) Gobs (1343, 152) (b) Gobs S. Hwang and

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Nov Mar 1 May 2 Fig. 2. Comparison of (a) spatially averaged annual total precipitation time series and (b) the Tables Figures Fig. 2. Comparison of (a) spatially averaged annual total precipitation time series and (b) the 3 mean monthly precipitation over the study period for gridded observations (Gobs). mean monthly precipitation over the study period for gridded observations (Gobs). The bright 4 The bright and dark gray zones represent total data range and 5th to 95th percentile of and dark gray zones represent total data range and 5th to 95th percentile of Gobs at the 12 km J I 5 Gobs at the 12 km grid scale indicating the spatial variability of observed annual total grid scale indicating the spatial variability of observed annual total precipitation and the mean 6 precipitation and the mean monthly precipitation over Florida. Mean and standard monthly precipitation over Florida. Mean and standard deviation of annual preciptiation predic- J I 7 deviation of annual preciptiation predictions are represented in the panel. Units in tions8 are representedmm in the panel. Units in mm. Back Close

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Back Close 1 2 Fig. 3. Spatial distribution of the mean of Gridded observation (Gobs.), BCSD_daily, BCCA, Full Screen / Esc Fig.3 3. Spatial distributionSDBC, and BCSA of the daily mean precipitation of Gridded for wet observation season (June through (Gobs.), September), BCSD daily,units BCCA, SDBC,4 and BCSAin dailymm precipitation for wet season (June through September), units in mm. Printer-friendly Version

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Back Close 1 Full Screen / Esc Fig.24. SpatialFig. 4. Spatial distribution distribution of of the the mean mean of of Gridded Gridded observation observation (Gobs.), (Gobs.), BCSD_da BCSDily, BCCA,daily, BCCA, SDBC,3 and BCSASDBC, daily and precipitation BCSA daily butprecipitation for dry but season for dry (October season (October through through May). May) Printer-friendly Version 4 Interactive Discussion

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1 Back Close Fig.2 5. SpatialFig. 5. Spatial distribution distribution of of the the temporal temporal standard standard deviation deviation of Gobs., of precipitation Gobs., precipitation predictions downscaled predic- Full Screen / Esc tions3 downscaledusing using BCSD BCSD_dailydaily,, BCCA, BCCA, SDBC, SDBC,and BCSA and for BCSAwet season for (June wet through season September), (June through units in September),4 unitsmm in mm. Printer-friendly Version 5 Interactive Discussion

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Fig.26. SpatialFig. 6. Spatial distribution distribution of of the the temporal temporal standard standard deviation deviation of Gobs., of precipitation Gobs., precipitation predictions predic- Full Screen / Esc tions3 downscaleddownscaled using BCSD usingdaily, BCSD BCCA,_daily, BCCA, SDBC, SDBC, and BCSAand BCSA for for dry dry season season (October (October through May).4 through May) Printer-friendly Version

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1 Back Close Fig.2 7. SpatialFig. 7. Spatial distribution distribution of the of the 90th 90th percentile percentile daily daily precipitation precipitation of Gobs, of Gobs, BCSD BCSD_daily, BCCA,daily, BCCA,SDBC, Full Screen / Esc SDBC,3 and BCSAand GCMs BCSA forGCMs each for each grid grid cell cell for for wet wet season season (June (June through through September), September), units in mm units in mm. 4 Printer-friendly Version

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1 Back Close 2 Fig. 8. Spatial distribution of the 50th percentile daily precipitation of Gobs, BCSD_daily, BCCA, SDBC, Fig.3 8. Spatial distributionand BCSA ofGCMs the for 50th each percentile grid cell for daily wet season precipitation (June through of Gobs, September), BCSD unitsdaily, in mm BCCA, Full Screen / Esc SDBC, and BCSA GCMs for each grid cell for wet season (June through September), units in mm. Printer-friendly Version

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0 0 0 0 5 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Full Screen / Esc 6 Fig. 9. First-order dry to wet transition probability (P_{01}) comparisons of observation (first row), Fig. 9. First-order7 dryBCSD to wet_daily transition results (second row), probability BCCA results ( P(third{01 row),}) SDBC comparisons (forth row), and BCSA of observation (ﬁrst 8 results (fifth row) for each month and 4 GCM products over all grids in the study area. Box plot Printer-friendly Version row), BCSD daily9 resultspresents (second minimum, row), 10th percentile, BCCA median, results 90th percentile, (third and row), maximum SDBC over the (forthgrids. row), and BCSA results (ﬁfth10 row) for each month and 4 GCM products over all grids in the study area. Box plot presents minimum, 10th percentile, median, 90th percentile, and maximum over the grids. Interactive Discussion 1

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0.2 0.2 0.2 0.2 Back Close BCSA_BCCR BCSA_CCSM3 BCSA_CGCM BCSA_GFDL 0 0 0 0 5 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Full Screen / Esc 6 Fig. 10. First-order wet to wet transition probability (P_{11}) comparisons of observation (first row), Fig. 10. First-order7 wetBCSD to wet_daily results transition (second row), probability BCCA results( (thirdP { 11row),} )SDBC comparisons (forth row), and BCSA of observation (ﬁrst 8 results (fifth row) for each month and 4 GCM products over all grids in the study area. Box plot Printer-friendly Version row), BCSD daily9 resultspresents (second minimum, row), 10th percentile, BCCA median, results 90th percentile, (third and row), maximum SDBC over the (forth grids. row), and BCSA results (ﬁfth row) for each month and 4 GCM products over all grids in the study area. Box plot presents minimum, 10th percentile, median, 90th percentile, and maximum over the grids. Interactive Discussion 1

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BCCA BCCA BCCA BCCA BCCA BCCA > 5 days > 10 days > 15 days > 5 days > 10 days > 15 days J I 2 Dry spell lenth_ Wet season Dry spell lenth_ Dry season 3 Back Close Fig. 11. Number of the events for given (a) wet (≥ 0.1 mm) and (b) dry (< 0.1 mm) spell lengths 4 Fig. 11. Number of the events for given (a) wet ( 0.1mm) and (b) dry (<0.1mm) spell lengths (5, 10, and 15 Full Screen / Esc (5, 10,5 and 15 days)days) forfor the the Gobs. Gobs. and andstatistically statistically downscaled downscaled GCM results using GCM BCSD results_daily using, BCCA, BCSD SDBC, daily, BCCA,6 SDBC, andand BCSA BCSA for for wet wet(left column) (left column) and dry season and dry(right season column). (rightDotted line column). indicates Dotted the line in- dicates7 the observedobserved exceedence exceedence probability. probability. Note that, Note exceptionally that, exceptionally for BCCA results, for the BCCA markers results,indicate the Printer-friendly Version markers8 indicatethe the GCMs, GCMs, BCCR BCCR and CCSM3 and present CCSM3 the CNRM present-CM3 the and CNRM-CM3MICRO3.2 results, and respective MICRO3.2ly. results, respectively. Interactive Discussion 9

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0.1 Full Screen / Esc 0.1 1 10 100 1 Spatially averaged precipitation (mm) Printer-friendly Version Interactive Discussion 2Fig. 12. Comparison of the relationship between spatial standard deviations of daily precipita- 3tion andFig the. spatially 12. Comparison averaged daily precipitation. of the relationship between spatial standard deviations of daily precipitation and the 4 spatially averaged2179 daily precipitation. 5

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0.4 Geary's index Geary's C Moran's I index I Moran's 0.2 Conclusions References Gobs BCSD_daily 0.2 BCCA SDBC Tables Figures BCSA 0 0 1 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec J I Fig.2 13. FigComparison. 13. Comparison of observedof observed and simulated simulated mean mean daily spatial daily correlation spatial correlationindices (a) I and indices spatial (a) I and J I spatial3 variance indicesvariance indices(b) C (b)for C eachfor each month. month. Back Close

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40 40 variogram (mm2) variogram variogram (mm2) variogram 20 20 Full Screen / Esc 0 0 0 100 200 300 400 500 0 100 200 300 400 500 4 distance (km) distance (km) 5 Fig. 14. Variogram comparison of (a) BCSD_daily, (b) BCCA, (c) SDBC, and (d) BCSA daily precipitation Printer-friendly Version Fig. 14. Variogram6 comparisonpredictions for wet of (left(a) column,BCSD June throughdaily, September)(b) BCCA, and dry(c) seasonSDBC, (right column, and October(d) BCSA daily 7 through May). precipitation predictions for wet (left column, June through September) and dry season (right Interactive Discussion column, October8 through May).

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