## Abstract

In this paper, two approaches to assess the impacts of climate change on streamflows have been used. In the first approach (direct), a statistical downscaling technique was utilized to predict future streamflows based on large-scale data of general circulation models (GCMs). In the second approach (indirect), GCM outputs were downscaled to produce local climate conditions which were then used as inputs to a hydrological simulation model. In this article, some data-mining methods such as model-tree, multivariate adaptive regression splines and group method of data handling were utilized for direct downscaling of streamflows. Projections of HadCM3 model for A2 and B2 SRES scenarios were also used to simulate future climate conditions. These evaluations were done over three sub-basins of Karkheh River basin in southwest Iran. To achieve a comprehensive assessment, a global uncertainty assessment method was used to evaluate the results of the models. The results indicated that despite simplifications included in the direct downscaling, this approach is accurate enough to be used for assessing climate change impacts on streamflows without computational efforts of hydrological modeling. Furthermore, comparing future climate projections, the uncertainty associated with elimination of hydrological modeling is estimated to be high.

## INTRODUCTION

Climate change has had significant impacts on monthly and seasonal variations of streamflows in various basins. Therefore, it is necessary to take the impacts of climate change into account for achieving realistic projections of surface water resources at any location in the future. In the literature, two approaches have been proposed for assessing the effects of climate change on streamflows:

Direct downscaling of the large-scale outputs of GCMs (general circulation models) to estimate streamflows (Landman

*et al.*2001; Cannon & Whitfield 2002; Ghosh & Mujumdar 2008; Tisseuil*et al.*2010; Sachindra*et al.*2013a).Indirect approach in which, at first, a downscaling technique is used to estimate local climate variables (precipitation, temperature, and evaporation) based on GCM simulations. In the second step, the local climate variables are utilized as input data to a hydrological model to estimate streamflows (Menzel & Burger 2002; Chiew

*et al.*2009; Chen*et al.*2012; Fu*et al.*2013; Samadi*et al.*2013).

Streamflows are mainly influenced by precipitation, evaporation, variation in soil water storage and regulating structures such as dams. Since the relationship between rainfall and streamflow is too complex and depends on a wide range of meteorological and environmental factors, mostly unrelated to climate change, the direct approach has been criticized because of over-simplification (Xu 1999). However, previous experiences of using the direct approach have shown that effects of factors unrelated to climate change can be covered indirectly in the process of building the statistical relationship between large-scale predictors (GCM outputs) and streamflows (Landman *et al.* 2001). The simplicity of implementing the direct approach is its main advantage over the indirect approach. Some examples of previous works on direct downscaling are as follows.

Landman *et al.* (2001) utilized NCEP (National Center for Environmental Prediction) reanalysis data to statistically downscale seasonal streamflows classified into the three categories of below-normal, near-normal, and above-normal at the inlets of 12 dams located in South Africa. Although surface characteristics of catchments were not considered in the downscaling process, streamflow categories were successfully estimated. Cannon & Whitfield (2002) drew a comparison between ensemble neural network models and stepwise linear regression for downscaling streamflows of 21 watersheds in Canada using only large-scale atmospheric predictors as model input data. The results proved that the downscaling models were capable of estimating streamflow variations. Ghosh & Mujumdar (2008) proposed a methodology for direct statistical downscaling of streamflows based on sparse Bayesian learning and relevance vector machine and applied it to project streamflows during the monsoon period (June, July, August, September) at Mahanadi River basin in India. Tisseuil *et al.* (2010) carried out comprehensive research for selecting proper spatial and temporal scales to downscale river flows using four statistical models of generalized linear (GLM) and additive models, aggregated boosted trees, and multi-layer perceptron neural networks. Sachindra *et al.* (2013a) employed least square support vector machine regression (LS-SVM-R) and multi-linear regression (MLR) for statistically downscaling monthly GCM outputs directly to monthly streamflows in northwestern Victoria, Australia. It was concluded that LS-SVM-R performed better than MLR. Saghafian *et al.* (2017) used model-tree (MT), group method of data handling (GMDH), and other statistical downscaling models (SDSM and data-mining downscaling models (DMDMs)) to backcast precipitation for two stations in northern Iran both in daily and monthly time resolutions. The proposed method of backcasting is similar to downscaling to predict the previous amount of meteorological variables such as precipitation, evaporation, and temperature (Saghafian *et al.* 2017).

Among studies which have used the indirect approach, Menzel & Burger (2002) applied the expanded downscaling method to regionalize the GCM simulations in order to produce local climate input data which were then utilized as input data of semi-distributed conceptual hydrologic model HBV-D. They studied the impacts of climate change on streamflow characteristics in the Mulde catchment in Germany. Chiew *et al.* (2009) utilized predictions of 23 GCMs to assess the influence of GCM selection on rainfall modeling and streamflow simulation over southeast Australia. In a comprehensive study, Chen *et al.* (2012) assessed the influence of using various GCMs, downscaling techniques, and hydrological models on simulated streamflows in upper Hanjiang basin in China. They used predictions of CGCM3 and HadCM3 models for A2 emission scenario and smooth support vector machine and SDSM as downscaling tools and Xin-anjiang and HBV as hydrological simulation models. Their results showed significant effects of statistical downscaling techniques on the estimated streamflows. Samadi *et al.* (2013) studied the implications of using linear and non-linear downscaling algorithms for temperature and precipitation in streamflow estimation through a hybrid conceptual hydrological model in Karkheh River basin, Iran. The results showed a significant reduction of streamflow with both downscaling projections, particularly in winter. Fu *et al.* (2013) used statistical downscaling to provide daily rainfall series in three spatial scales (site or single point, grid, and catchment scales) for nine catchments located in southeastern Australia by nonhomogeneous hidden Markov model (NHMM). SimHyd, a lumped catchment-scale hydrological model, was then applied to evaluate the hydrological responses.

To the best of our knowledge, this is the first study that makes a comparison between the two direct and indirect approaches in assessing climate change impacts on streamflows and the uncertainties associated with the approaches. In this study, for the direct approach, statistical downscaling was done to formulate a direct relationship between large-scale data from GCMs and local-scale streamflow in daily time resolution. For the indirect approach, GCM outputs were downscaled to produce local climate variables, which were then used as input data to a hydrological model. Finally, the uncertainty of the two approaches was assessed using UNEEC (uncertainty estimation based on local errors and clustering) method and the advantages and limitations of the two approaches compared.

In the next section, the study area and local and large-scale data are presented. In the third section, downscaling models, Guo water balance model and UNEEC method are described. In the fourth section, the results of the case study are reported and discussed, and in the last section, concluding remarks are presented.

## STUDY AREA AND DATA

### Study area

Karkheh River basin has an area of over 51,481 km^{2} lying within 46°-06′ to 49°-10′ eastern longitudes and 30°-58′ to 35°-00′ northern latitudes. Even though Karkheh basin is one of the important watersheds in Iran, due to its high wheat yield and hydropower production potential, few studies have focused on quantification of climate change impacts on its agricultural or hydropower generation potentials (Jamali *et al.* 2012, 2013; Ashraf Vaghefi *et al.* 2014, 2015). In this study, as shown in Figure 1, Karkheh basin was divided into seven sub-basins for hydrologic modeling purposes. Three sub-basins, namely, Ghoorbaghestan, Polechehr, and Poledokhtar, located in Khouzestan, Lorestan, and Kermanshah provinces of Iran were selected as the case studies of this research. These basins are abbreviated as Ghoor., Polech., and Poled. in this paper. The areas of these relatively large sub-basins are 5,370, 10,924, and 9,547 square kilometers.

### Local-scale data

Available data for the three gauging stations located at the outlets of the three sub-basins have been recorded since February 1972. The rainfall observations in 19 rain gauge stations and temperature and evaporation records in six climatological stations scattered over the three sub-basins have been recorded since 1980. These datasets were extracted from the Iranian hydrological data bank provided by the Iran Ministry of Energy. Statistical information about the hydro-climatology of these basins is presented in Table 1.

Basin . | Area (km^{2})
. | Rainfall (mm/km^{2}). | Pan evaporation (mm/km^{2}). | Runoff (mm/km^{2}). | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Max . | Min . | Average . | Max . | Min . | Average . | Max . | Min . | Average . | ||

Ghoor. | 5,370 | 259.4 | 0 | 35.9 | 516.5 | 1.25 | 179.5 | 145.2 | 0.14 | 10.4 |

Polech. | 10,924 | 173.1 | 0 | 35.6 | 571.3 | 0.33 | 180.6 | 70.5 | 0.06 | 7.8 |

Poled. | 9,547 | 193.9 | 0 | 38.5 | 515.1 | 16.4 | 199.6 | 299.8 | 2.74 | 52.44 |

Basin . | Area (km^{2})
. | Rainfall (mm/km^{2}). | Pan evaporation (mm/km^{2}). | Runoff (mm/km^{2}). | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Max . | Min . | Average . | Max . | Min . | Average . | Max . | Min . | Average . | ||

Ghoor. | 5,370 | 259.4 | 0 | 35.9 | 516.5 | 1.25 | 179.5 | 145.2 | 0.14 | 10.4 |

Polech. | 10,924 | 173.1 | 0 | 35.6 | 571.3 | 0.33 | 180.6 | 70.5 | 0.06 | 7.8 |

Poled. | 9,547 | 193.9 | 0 | 38.5 | 515.1 | 16.4 | 199.6 | 299.8 | 2.74 | 52.44 |

### Large-scale data

The daily NCEP reanalysis data were used as the observed large-scale climate data (predictor) to calibrate and validate the direct downscaling model during the period of 1961–2000. There are 26 different atmospheric variables for each grid box in this database (Table 2). Daily outputs of HadCM3 for A2 and B2 emission scenarios were used to project future climate conditions over the study area. Spatial resolution (dimensions of grid box) of HadCM3 outputs is 3.75° (longitude) × 2.5° (latitude), while it is 2.5° (longitude) × 2.5° (latitude) for NCEP data, therefore large-scale predictors of NCEP have been re-estimated on HadCM3 computational grid points. HadCM3 outputs published by the Canadian Climate Impacts Scenarios (CCIS) website have been used in this study (www.cics.uvic.ca/scenarios/sdsm/select.cgi). Figure 2 shows the grid points covering over and around the study area which were utilized in this study. In addition, 1- to 3-day lagged series of the predictors have also been used in the daily downscaling process.

No. . | Variable . | Code . | No. . | Variable . | Code . |
---|---|---|---|---|---|

1 | Mean sea level pressure | Mslp | 14 | 850 hpa airflow strength | p8_f |

2 | Surface airflow strength | p_f | 15 | 850 hpa zonal velocity | p8_u |

3 | Surface zonal velocity | p_u | 16 | 850 hpa meridional velocity | p8_v |

4 | Surface meridional velocity | p_v | 17 | 850 hpa vorticity | p8_z |

5 | Surface vorticity | p_z | 18 | 850 hpa wind direction | p8th |

6 | Surface wind direction | p_th | 19 | 850 hpa divergence | p8zh |

7 | Surface divergence | p_zh | 20 | 500 hpa geopotential height | p500 |

8 | 500 hpa airflow strength | p5_f | 21 | 850 hpa geopotential height | p850 |

9 | 500 hpa zonal velocity | p5_u | 22 | Relative humidity at 500 hpa | r500 |

10 | 500 hpa meridional velocity | p5_v | 23 | Relative humidity at 850 hpa | r850 |

11 | 500 hpa vorticity | p5_z | 24 | Near surface relative humidity | Rhum |

12 | 500 hpa wind direction | p5th | 25 | Near surface specific humidity | Shum |

13 | 500 hpa divergence | p5zh | 26 | Mean temperature at 2 m | Temp |

No. . | Variable . | Code . | No. . | Variable . | Code . |
---|---|---|---|---|---|

1 | Mean sea level pressure | Mslp | 14 | 850 hpa airflow strength | p8_f |

2 | Surface airflow strength | p_f | 15 | 850 hpa zonal velocity | p8_u |

3 | Surface zonal velocity | p_u | 16 | 850 hpa meridional velocity | p8_v |

4 | Surface meridional velocity | p_v | 17 | 850 hpa vorticity | p8_z |

5 | Surface vorticity | p_z | 18 | 850 hpa wind direction | p8th |

6 | Surface wind direction | p_th | 19 | 850 hpa divergence | p8zh |

7 | Surface divergence | p_zh | 20 | 500 hpa geopotential height | p500 |

8 | 500 hpa airflow strength | p5_f | 21 | 850 hpa geopotential height | p850 |

9 | 500 hpa zonal velocity | p5_u | 22 | Relative humidity at 500 hpa | r500 |

10 | 500 hpa meridional velocity | p5_v | 23 | Relative humidity at 850 hpa | r850 |

11 | 500 hpa vorticity | p5_z | 24 | Near surface relative humidity | Rhum |

12 | 500 hpa wind direction | p5th | 25 | Near surface specific humidity | Shum |

13 | 500 hpa divergence | p5zh | 26 | Mean temperature at 2 m | Temp |

## METHODOLOGY

In this section, selected methodologies for statistical downscaling, hydrological modeling, and uncertainty assessment are briefly introduced. DMDM, developed by Tavakol-Davani *et al.* (2012), was utilized for direct downscaling of daily streamflows and precipitation. A regression model based on GMDH developed initially by Ivakheneko (1971) was also utilized for temperature and evaporation downscaling in monthly time scale. Both models work based on SDSM general platform. Due to the time resolution of recorded evaporation and temperature, the monthly water balance model developed by Guo *et al.* (2005) that accounts for soil moisture, groundwater storage, and snowpack, the hydrological model was used to simulate streamflows in the indirect approach.

Before explaining details of the two approaches, it should be noted that, for the case study of this research, daily streamflow and precipitation records were available, but evaporation and temperature records have been accessible only in monthly time resolution. Therefore, different downscaling models were used for climatic variables in monthly and daily time resolutions.

As mentioned earlier, two direct and indirect approaches for assessing climate change impacts on streamflows have been compared in this study. Figure 3 shows how these two approaches were utilized and compared. In the indirect modeling approach, the following steps were taken:

The observed time series of daily precipitation and time series of NCEP predictors were used to calibrate DMDM downscaling model. The calibrated model was then used for estimating downscaled daily precipitation time series. The daily downscaled precipitation was then transformed to monthly time series.

The observed time series of monthly evaporation and temperature and time series of NCEP predictors were used to calibrate GMDH downscaling model. The calibrated model was then used for estimating downscaled monthly evaporation and temperature time series.

Monthly observed time series of streamflows, precipitation, temperature, and evaporation were used to calibrate the Guo monthly water balance model. The calibrated model was then used to estimate monthly streamflows (final output of indirect approach) based on monthly downscaled precipitation, evaporation, and temperature.

In the direct modeling approach, the observed time series of daily streamflows and time series of NCEP predictors were used to calibrate the DMDM downscaling model. The calibrated model was then used for estimating downscaled daily streamflow time series. The daily downscaled streamflows were then transformed to monthly time series.

Since daily records of streamflows are available for the study area, the direct downscaling of streamflows was done at daily time scale and then converted to monthly time scale to be compared with the results obtained from the indirect approach.

Among the climate variables taken into account in this study (precipitation, temperature, and evaporation), precipitation variations have the highest impact on the streamflow fluctuations. Therefore, by daily downscaling of precipitation in the indirect approach, it was attempted to make a fair comparison with direct downscaling approach in which streamflows were also downscaled in daily resolution. Although unavailability of evaporation and temperature in daily time scale was the main reason behind monthly downscaling of these variables, less fluctuations of temperature and evaporation compared with precipitation and streamflow and the cyclic behavior of variations of these two variables (evaporation and temperature), make their monthly downscaling justifiable. Another reason for not downscaling the precipitation in monthly time scale in this study is that SDSM and other downscaling tools developed based on it, such as DMDM, consider precipitation a conditional variable for which amounts depend on wet-day occurrence. Well-documented and tested statistical downscaling tools such as SDSM have not yet been developed for monthly precipitation downscaling.

### Statistical downscaling model

Spatial resolution of GCM outputs is not sufficiently fine to assess local impacts of climate change and therefore it must be transformed to a finer resolution to be instrumental in local analyses. For this purpose, downscaling techniques were developed to resolve the scale discrepancy and extract regional-scale data from GCM outputs. There are two main approaches in the literature to downscale large-scale data: dynamical and statistical approaches. Dynamical techniques or regional climate models, physically model smaller-scale dynamical processes (Mearns *et al.* 2003).

Statistical approaches, which are mainly based on statistical relationships between large-scale predictors (GCM outputs) and observed local climate variables, are generally divided into three categories: (1) regression-based models, (2) weather pattern models, and (3) stochastic weather generators. Due to computational simplicity, statistical methods have been used more frequently than the dynamical ones. Various techniques have been utilized to develop different models for statistical downscaling, such as linear regression (Wilby *et al.* 2002; Hessami *et al.* 2008), polynomial regression (Hewiston 1994), artificial neural networks (Pasini 2009; Tomassetti *et al.* 2009; Mendes & Marengo 2010; Fistikoglu & Okkan 2011); *k*-nearest neighbors (Yates *et al.* 2003; Gangopadhyay *et al.* 2005; Raje & Mujumdar 2011; Nasseri *et al.* 2013a), and support vector machines (Tripathi *et al.* 2006; Chen *et al.* 2010; Nasseri *et al.* 2013a; Sachindra *et al.* 2013b; Sarhadi *et al.* 2016).

In this study, DMDM developed by Tavakol-Davani *et al.* (2012) was employed to statistically downscale the daily streamflows and precipitation. DMDM uses the statistical platform of SDSM (Wilby *et al.* 2002). MLR, ridge regression, multivariate adaptive regression splines (MARS), and MT constitute the mathematical core of DMDM. DMDM uses linear basis functions in MARS and linear regression rules in MT to stay consistent with the linear structure of SDSM.

General process of downscaling using DMDM is shown in Figure 4. It should be mentioned here that DMDM does not impose any restriction on the method of predictor selection and it is possible to use different approaches for this purpose (for further details, such as bias correction and variance inflation, readers are referred to Tavakol-Davani *et al.* 2012).

Saghafian *et al.* (2017) used GMDH to use the downscaling concept to backcast and reconstruct the precipitation times series recorded in the two climatological stations, Urmia and Tabriz, in the northwest of Iran, by means of large-scale atmospheric predictors. In this article, a regression model based on GMDH was used to downscale monthly temperature and evaporation. Since daily records of these two variables were not available, monthly mean temperature and total monthly evaporation have been downscaled. Temperature and evaporation are two smooth type data and downscaling of them is much less complicated than precipitation and streamflow. Statistical monthly downscaling using GMDH is like daily downscaling considering two alterations. The first difference is time resolution. Both predictands (NCEP, past and feature scenarios of GCM variables) and predictors (observed records such as temperature and evaporation) are monthly based information. In daily downscaling, 12 models must be calibrated for each month; but in the implemented monthly downscaling procedure, one calibrated model with monthly information is used for all months of a year.

GMDH was first introduced in the 1970s by Ivakhninkho at the Institute of Technology of Ukraine (Ivakheneko 1971; Ivakheneko & Ivakheneko 1995). This method can be classified as polynomial-based artificial neural networks (Kim *et al*. 2009). GMDH has various applications both in pattern recognition and regression. Different applications of the method have been taken into account in the realm of hydrology and water resources management (Chang & Hwang 1999; Abdel-Aal 2005; Samsudin *et al.* 2011; Najafzadeh & Zahiri 2015; Tsai & Yen 2016). The proposed methodology for utilizing GMDH for statistical downscaling is based on SDSM (differs in time resolution), and bias correction and variance inflation are also included in the model structure. In addition to the time resolution, another big difference between SDSM and the proposed application of GMDH for monthly downscaling is in the number of utilized mathematical kernels. In the proposed method, one GMDH kernel is used for monthly downscaling while SDSM utilizes 12 linear kernels for various months. In a backcasting procedure proposed by Saghafian *et al.* (2017), two important sections of downscaling models, ensemble modeling and statistical modifications (bias correction and variance inflation), were not used. The GMDH toolbox developed by Jekabsons (2010) in MATLAB was utilized in this study.

### Hydrological model

Since evaporation and temperature were only available in monthly time resolution in the study area, to assess the hydrological response of the sub-basins to climate change impacts as a part of the indirect approach, a monthly water balance model was used. Continuity and conservation laws of water (including soil water storage, precipitation, deep penetration, evaporation, and streamflow) are the conceptual foundations of all monthly water balance models. Considering their hydrological modules, they are different in their used meteorological variables (e.g., evaporation and temperature) and also the implemented relationships between the hydrological variables (i.e., precipitation, temperature, etc.) (Xu & Singh 1998). It is worthwhile to mention that monthly time scale of the hydrological model is a suitable time resolution for the purpose of climate change impact assessment (Guo 2002; Wang *et al.* 2011).

Due to the relatively accurate results obtained from the monthly water balance model proposed by Guo *et al.* (2005) in recent studies in some basins scattered over Iran (Nasseri *et al.* 2013b, 2014a, 2014b), it has been employed in this research. General structure of the Guo model is shown in Figure 5. This model is based on various storage tanks such as ground water, snow pack, and soil moisture (one soil layer). It also takes into account snow melt, groundwater discharge, surface runoff, and evapotranspiration in water balance modeling. Pseudo code of this model and descriptions for its parameters are presented in Appendix A (available with the online version of this paper) (Nasseri *et al.* 2014b).

### Uncertainty assessment model

Uncertainties associated with water resources modeling practices stem mainly from four important sources and relate our understanding and measurement capabilities regarding real-world systems. These four sources include uncertainty in input data (e.g., precipitation and temperature), in output data (e.g., output data such as streamflow), in model parameters, and finally, in model structure. For the decision-making processes, especially in water resources management, it is more important to know the total model uncertainty accounting for all sources of uncertainty than the uncertainty resulting from individual sources (Solomatine & Shrestha 2009).

Solomatine & Shrestha (2009) presented an innovative method to estimate the uncertainty of the model that takes into account all sources of errors. The approach is referred to as UNEEC. The method uses data-mining techniques to estimate the uncertainty of a model by analyzing the model residuals (errors) estimated as the difference between the model estimations and the observed data. UNEEC assumes that the historical residuals are the best available quantitative indicators of the discrepancy between the model and the real-world system or process.

The idea of UNEEC is to learn the pattern and relationship between the distribution of the residuals and the input and/or state variables and to use this information to predict the distribution of the residuals when it predicts the output variable (e.g., runoff). This method consists of three main parts: (1) clustering/partitioning of the selected input variables to estimate model residual (difference between observation and results of the calibrated model); (2) estimation of the residual probability distribution for each cluster; and (3) building the uncertainty model which estimates upper and lower bounds of probable residual (see Figure 6). Clustering of data is the main step of the UNEEC method. Its goal is to partition the data into several clusters that can be interpreted. When data in each cluster belong to a certain ‘class’, local error models can be built in a more robust and accurate way (than that of global model which is fitted on the whole data). Before clustering, the most relevant variables should be selected from the input data or state variables and additional lagged vectors of them based on correlation and/or average mutual information analysis.

Typically, the hydrologic models are nonlinear and contain many parameters. This hinders the analytical estimation of the probable distribution function (pdf) of residuals. Thus, the empirical pdf of the residuals for each cluster is independently estimated by analyzing historical model residuals estimated for the calibration dataset. Then, the uncertainty estimation model (which is intended to predict the pdf of the residuals for the unseen input vectors) is trained employing machine learning techniques (here for instance based on learning method) to relate the selected relevant variables to the pdf of the residuals. Finally, the prediction interval (PI) is estimated for the requested level (e.g., for 90% PI, 5% and 95% quantiles are extracted from the pdf) and model performance is assessed.

### Statistical evaluation

^{2}) were used to evaluate monthly downscaling efficiency, and for evaluating water balance models normal mean square error (NMSE), mean square error (MSE), and Nash–Sutcliffe (NS) were used. These indicators are calculated as follows:

*n*, *Obs*_{t}, , and *Q _{m}*, are number of observations, observation at time

*t*, mean of observation over the time, and model result, respectively. var ( ) and cov (,) represent variance and covariance of data, respectively.

*ARIL*),

*P*, and normalized uncertainty efficiency (

_{level}*NUE*) were used in this study. To achieve PI equal to 100 × (1 −

*α*)%, , the percentile values must be calculated via empirical distribution. To assess different PIs, these indicators,

*ARIL*and

*P*, are calculated as follows:

_{level}*n*, *UpLi _{t}*,

*LoLi*,

_{t}*Obs*

_{t}, and

*NQ*, are number of observations, upper and lower bounds of the PI in time

_{in}*t*, observation in time

*t*, and number of observations within the PI, respectively.

*ARIL*describes the width of uncertainty bounds versus the observed values.

*P*describes the bracketed observations with upper and lower bounds of a specific confidence interval.

_{level}For an ideal PI, *ARIL* and *P _{level}* will be close to 0 and 100, respectively. In other words, a lower value of

*ARIL*shows that PI is narrower than a higher value of

*ARIL*, and a higher value of

*P*represents how many data are located within the PI. Based on the meaning of these two statistical indicators, modeled uncertainty with lower

_{level}*ARIL*and higher

*P*values are preferred.

_{level}*P*in probabilistic uncertainty assessment has a conceptual upper limit (equal to its PI).

_{level}*ARIL*and

*P*indices during selection of the most suitable model, the

_{level}*NUE*proposed by Nasseri

*et al.*(2013b, 2014a, 2014b) was utilized in this study.

*NUE*is estimated as follows: Higher

*NUE*means higher ratio of the grouped observation points with upper and lower bounds to the covered area between these bounds. It should be noted that very low

*ARIL*values do not necessarily result in high

*NUE*s since low

*ARIL*is usually followed by low

*P*values. Thus, among the PIs being studied, the one with higher

_{level}*NUE*has the best performance. For further information, readers are referred to Solomatine & Shrestha (2009) and Nasseri

*et al.*(2013b, 2014a, 2014b).

## RESULTS

### Downscaling results

According to the inherent linearity of the used mathematical kernels in DMDM, stepwise regression was implemented to select the suitable predictors for daily downscaling of streamflow and precipitation. Selected predictors are reported in Tables 3 and 4. It can be seen that meridional and zonal velocity and vorticity at different elevations and air temperature are the main variables selected for streamflow downscaling. However, in the case of precipitation, relative humidity and airflow strength at different elevations for occurrence and near surface specific humidity for amount are the most selected variables. It should be noted that selected predictors for direct downscaling are mostly from the 3-day lagged series, while for precipitation they are mostly from 1- or 0-day lagged series.

. | Station . | Predictor . | Lag . |
---|---|---|---|

1 | Ghoor. | Rhum | 3 |

2 | temp | 3 | |

3 | Shum | 3 | |

4 | p5_f | 3 | |

5 | p5_u | 3 | |

6 | temp | 3 | |

7 | p8zh | 2 | |

1 | Polech. | p_v | 0 |

2 | p_v | 3 | |

3 | Rhum | 3 | |

4 | p8_z | 0 | |

5 | p8_z | 3 | |

6 | Rhum | 1 | |

7 | p_v | 0 | |

8 | p_v | 3 | |

9 | p_z | 0 | |

10 | p_z | 3 | |

1 | Poled. | p_u | 0 |

2 | p5_v | 1 | |

3 | p8_u | 2 | |

4 | p500 | 3 | |

5 | p850 | 3 | |

6 | p_v | 1 | |

7 | temp | 3 | |

8 | temp | 3 | |

9 | p_u | 1 | |

10 | p_u | 1 |

. | Station . | Predictor . | Lag . |
---|---|---|---|

1 | Ghoor. | Rhum | 3 |

2 | temp | 3 | |

3 | Shum | 3 | |

4 | p5_f | 3 | |

5 | p5_u | 3 | |

6 | temp | 3 | |

7 | p8zh | 2 | |

1 | Polech. | p_v | 0 |

2 | p_v | 3 | |

3 | Rhum | 3 | |

4 | p8_z | 0 | |

5 | p8_z | 3 | |

6 | Rhum | 1 | |

7 | p_v | 0 | |

8 | p_v | 3 | |

9 | p_z | 0 | |

10 | p_z | 3 | |

1 | Poled. | p_u | 0 |

2 | p5_v | 1 | |

3 | p8_u | 2 | |

4 | p500 | 3 | |

5 | p850 | 3 | |

6 | p_v | 1 | |

7 | temp | 3 | |

8 | temp | 3 | |

9 | p_u | 1 | |

10 | p_u | 1 |

Station . | Occurrence . | Predictor . | Lag . | Amount . | Predictor . | Lag . |
---|---|---|---|---|---|---|

Polech. | 1 | p_f | 0 | 1 | p_z | 2 |

2 | r500 | 0 | 2 | mslp | 1 | |

3 | r850 | 0 | 3 | p_f | 3 | |

4 | r500 | 1 | 4 | r500 | 0 | |

5 | r850 | 0 | 5 | shum | 0 | |

6 | Rhum | 1 | 6 | p8_u | 0 | |

7 | p8_u | 0 | 7 | p8_v | 1 | |

8 | p8_z | 0 | ||||

9 | p5zh | 0 | ||||

10 | p8_f | 1 | ||||

11 | p_f | 1 | ||||

12 | p_zh | 1 | ||||

Ghoor. | 1 | p8_f | 0 | 1 | p8_z | 0 |

2 | r500 | 0 | 2 | shum | 0 | |

3 | r850 | 0 | 3 | p_u | 0 | |

4 | p8_v | 1 | 4 | p8_v | 1 | |

5 | p_v | 2 | 5 | p850 | 3 | |

6 | r850 | 0 | ||||

7 | Shum | 0 | ||||

8 | p5_v | 1 | ||||

9 | p8_f | 1 | ||||

10 | p_f | 0 | ||||

11 | p8_f | 0 | ||||

12 | p_v | 1 | ||||

13 | p8_v | 0 | ||||

Poled. | 1 | p5zh | 0 | 1 | r500 | 0 |

2 | Shum | 0 | 2 | shum | 3 | |

3 | p5_v | 1 | 3 | rhum | 0 | |

4 | Rhum | 0 | 4 | p8_v | 1 | |

5 | r500 | 0 | 5 | p_u | 0 | |

6 | r850 | 0 | 6 | shum | 2 | |

7 | Rhum | 3 | 7 | p8zh | 0 | |

8 | p5_z | 0 | ||||

9 | p_f | 0 | ||||

10 | p8_f | 0 | ||||

11 | p8th | 0 | ||||

12 | p_v | 0 | ||||

13 | p8zh | 0 |

Station . | Occurrence . | Predictor . | Lag . | Amount . | Predictor . | Lag . |
---|---|---|---|---|---|---|

Polech. | 1 | p_f | 0 | 1 | p_z | 2 |

2 | r500 | 0 | 2 | mslp | 1 | |

3 | r850 | 0 | 3 | p_f | 3 | |

4 | r500 | 1 | 4 | r500 | 0 | |

5 | r850 | 0 | 5 | shum | 0 | |

6 | Rhum | 1 | 6 | p8_u | 0 | |

7 | p8_u | 0 | 7 | p8_v | 1 | |

8 | p8_z | 0 | ||||

9 | p5zh | 0 | ||||

10 | p8_f | 1 | ||||

11 | p_f | 1 | ||||

12 | p_zh | 1 | ||||

Ghoor. | 1 | p8_f | 0 | 1 | p8_z | 0 |

2 | r500 | 0 | 2 | shum | 0 | |

3 | r850 | 0 | 3 | p_u | 0 | |

4 | p8_v | 1 | 4 | p8_v | 1 | |

5 | p_v | 2 | 5 | p850 | 3 | |

6 | r850 | 0 | ||||

7 | Shum | 0 | ||||

8 | p5_v | 1 | ||||

9 | p8_f | 1 | ||||

10 | p_f | 0 | ||||

11 | p8_f | 0 | ||||

12 | p_v | 1 | ||||

13 | p8_v | 0 | ||||

Poled. | 1 | p5zh | 0 | 1 | r500 | 0 |

2 | Shum | 0 | 2 | shum | 3 | |

3 | p5_v | 1 | 3 | rhum | 0 | |

4 | Rhum | 0 | 4 | p8_v | 1 | |

5 | r500 | 0 | 5 | p_u | 0 | |

6 | r850 | 0 | 6 | shum | 2 | |

7 | Rhum | 3 | 7 | p8zh | 0 | |

8 | p5_z | 0 | ||||

9 | p_f | 0 | ||||

10 | p8_f | 0 | ||||

11 | p8th | 0 | ||||

12 | p_v | 0 | ||||

13 | p8zh | 0 |

As previously stated, daily records of temperature and evaporation were not available for the study area and so monthly mean amounts were downscaled. GMDH and AMI were chosen as regression and feature selection methods for monthly downscaling of evaporation and temperature at six climatological stations.

It is worth mentioning that 70% of the observed records (1961–1989) were used for calibration and the rest (1990–2000) utilized for validation. RRMSE and R^{2} are reported in Tables 5 and 6 for validation and calibration datasets. Comparison between the reported values for these two indicators for the validation and calibration datasets shows that no overfitting occurred.

Basin . | Station code . | Calibration . | Validation . | ||
---|---|---|---|---|---|

RRMSE . | R^{2}
. | RRMSE . | R^{2}
. | ||

Ghoor. | 129 | 0.47 | 0.78 | 0.37 | 0.86 |

133 | 0.75 | 0.43 | 0.33 | 0.89 | |

393 | 0.33 | 0.89 | 0.34 | 0.88 | |

642 | 0.33 | 0.89 | 0.44 | 0.81 | |

Polech. | 127 | 0.35 | 0.88 | 0.39 | 0.85 |

Poled. | 175 | 0.33 | 0.89 | 0.42 | 0.82 |

Basin . | Station code . | Calibration . | Validation . | ||
---|---|---|---|---|---|

RRMSE . | R^{2}
. | RRMSE . | R^{2}
. | ||

Ghoor. | 129 | 0.47 | 0.78 | 0.37 | 0.86 |

133 | 0.75 | 0.43 | 0.33 | 0.89 | |

393 | 0.33 | 0.89 | 0.34 | 0.88 | |

642 | 0.33 | 0.89 | 0.44 | 0.81 | |

Polech. | 127 | 0.35 | 0.88 | 0.39 | 0.85 |

Poled. | 175 | 0.33 | 0.89 | 0.42 | 0.82 |

Basin . | Station code . | Calibration . | Validation . | ||
---|---|---|---|---|---|

RRMSE . | R^{2}
. | RRMSE . | R^{2}
. | ||

Ghoor. | 129 | 0.61 | 0.63 | 0.55 | 0.7 |

133 | 0.43 | 0.81 | 0.38 | 0.86 | |

393 | 0.58 | 0.66 | 0.37 | 0.86 | |

642 | 0.35 | 0.88 | 0.36 | 0.87 | |

Polech. | 127 | 0.45 | 0.8 | 0.49 | 0.76 |

Poled. | 175 | 0.52 | 0.73 | 0.43 | 0.81 |

Basin . | Station code . | Calibration . | Validation . | ||
---|---|---|---|---|---|

RRMSE . | R^{2}
. | RRMSE . | R^{2}
. | ||

Ghoor. | 129 | 0.61 | 0.63 | 0.55 | 0.7 |

133 | 0.43 | 0.81 | 0.38 | 0.86 | |

393 | 0.58 | 0.66 | 0.37 | 0.86 | |

642 | 0.35 | 0.88 | 0.36 | 0.87 | |

Polech. | 127 | 0.45 | 0.8 | 0.49 | 0.76 |

Poled. | 175 | 0.52 | 0.73 | 0.43 | 0.81 |

In Appendix B (available with the online version of this paper), statistical properties of downscaling models calibrated for daily precipitation of the climatological stations are presented. MT and MARS are the most selected for amount and occurrence modeling. As can be seen in Appendix B, the highest errors were observed in the standard deviation values of the downscaled daily precipitation. Overall, the results show that the downscaling models were appropriately calibrated and their performances during validation period were suitable as well.

### Water balance modeling

Thiessen polygon method was used to estimate areal average precipitation, temperature, and evaporation over the sub-basins (the input variables of the water balance model). For all of the basins, 70% of the total length of available datasets (1971–2002) was used for calibration and the remaining part (2003–2011) for validation. A genetic algorithm optimization model was used to calibrate the parameters of the water balance model. For all three sub-basins, NS efficiency index was considered as fitness function. The optimized parameters and NS efficiency index are reported in Table 7. The reported scale factors of precipitation (*sf*) were used based on the suggestion of de Vos *et al.* (2010) to find a more accurate estimation of precipitation over the basins.

Basin . | Parameters . | Calibration . | Validation . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

. | . | . | . | . | . | . | . | . | NS . | NS . | |

Ghoor. | 1.25 | −1.8 | 16.1 | 0.03 | 1.97 | 0.1 | 0.81 | 36.81 | 0.69 | 0.76 | 0.65 |

Polech. | 0.82 | −3.0 | 20.0 | 0.12 | 3.0 | 0.19 | 0.81 | 40.0 | 0.39 | 0.82 | 0.71 |

Poled. | 1.5 | 12.29 | 20 | 3.0 | 2.3 | 0.62 | 3.0 | 40.0 | 0.30 | 0.68 | 0.63 |

Basin . | Parameters . | Calibration . | Validation . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

. | . | . | . | . | . | . | . | . | NS . | NS . | |

Ghoor. | 1.25 | −1.8 | 16.1 | 0.03 | 1.97 | 0.1 | 0.81 | 36.81 | 0.69 | 0.76 | 0.65 |

Polech. | 0.82 | −3.0 | 20.0 | 0.12 | 3.0 | 0.19 | 0.81 | 40.0 | 0.39 | 0.82 | 0.71 |

Poled. | 1.5 | 12.29 | 20 | 3.0 | 2.3 | 0.62 | 3.0 | 40.0 | 0.30 | 0.68 | 0.63 |

As can be seen, the performance of hydrological model is better in Ghoor. and Polech. sub-basins. Similarity between the model performances in the calibration and validation periods shows that the model was properly trained for the three sub-basins and no over-training occurred.

### Comparison between direct and indirect approaches

In this section, results of the two direct and indirect approaches are discussed. Statistical indictors of the streamflows estimated using the two approaches including monthly mean, standard deviation, and skewness are depicted in Figures 7–9.

In Ghoor. station, the direct approach shows superiority in estimation of monthly mean values specifically in the last five months of the year in the validation period. Overestimation of the indirect approach during these months is noticeable. In this station, monthly standard deviations were underestimated in almost all months during both calibration and validation periods by the direct approach, and the indirect approach shows superiority especially in the validation period. Better estimations of monthly skewness values were obtained by the direct downscaling approach in Ghoor. station. Significant underestimation of high flows by the direct downscaling approach is noticeable in Figure 7(d) in the validation period.

Figure 8 clearly shows that in Polech. station, monthly mean values were overestimated by the indirect approach in both validation and calibration periods. Similar to the results reported for Ghoor. station, monthly standard deviation values were underestimated by the direct approach, and superiority of the indirect approach is noticeable especially in the validation period. The direct approach showed slightly better performance in estimation of monthly skewness values both in the calibration and validation periods. Overestimation of mid-flows by the indirect approach can also be seen in Figure 8(d) in the validation period. Both approaches show similar performances in estimating low and high flows in the validation period.

Figure 9 shows the results obtained for Poled. station. It can be inferred that the direct approach provided better estimations of monthly mean values in the calibration period while the indirect approach performed better in the last four months of the year in the validation period. Overall, the performance of the two approaches in the validation period was similar. In this station, the direct approach significantly underestimated standard deviation values similar to the results obtained for the other two stations. While in the calibration period, the direct approach provided better estimations of monthly skewness values; in the validation period, neither of the two methods showed superiority over the other. Significant underestimation of high flows by both indirect and direct approaches in the validation period can be seen in Figure 9(d).

Overall, in all of the three gauging stations located at the outlets of the basins, both methods present acceptable compatibility between observed and computed monthly mean values. The direct approach provided better estimations of monthly mean values (except for Poled. station, in which both direct and indirect approaches performed the same). The direct approach underestimated monthly standard deviation values in all the three stations. The direct approach also showed superiority in the estimation of monthly skewness values. Furthermore, in two stations, Ghoor. and Poled., high flows were underestimated by the direct approach.

Table 8 shows the statistical comparison between the results of the direct and indirect approaches at the outlets of the three basins during the observation period (years before 2000). This table shows overall superiority of the direct approach.

Basin . | Direct approach . | Indirect approach . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Calibration . | Validation . | Calibration . | Validation . | |||||||||

MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | |

Ghoor. | 25.68 | 0.10 | 0.92 | 95.29 | 0.53 | 0.47 | 27.2 | 0.29 | 0.76 | 88.02 | 0.53 | 0.62 |

Polech. | 20.82 | 0.14 | 0.95 | 98.37 | 0.55 | 0.59 | 68.5 | 0.24 | 0.71 | 109.3 | 0.80 | 0.59 |

Poled. | 33 | 0.11 | 0.90 | 210 | 0.54 | 0.44 | 184.1 | 0.33 | 0.66 | 143.8 | 1.00 | 0.53 |

Basin . | Direct approach . | Indirect approach . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Calibration . | Validation . | Calibration . | Validation . | |||||||||

MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | MSE . | NMSE . | NS . | |

Ghoor. | 25.68 | 0.10 | 0.92 | 95.29 | 0.53 | 0.47 | 27.2 | 0.29 | 0.76 | 88.02 | 0.53 | 0.62 |

Polech. | 20.82 | 0.14 | 0.95 | 98.37 | 0.55 | 0.59 | 68.5 | 0.24 | 0.71 | 109.3 | 0.80 | 0.59 |

Poled. | 33 | 0.11 | 0.90 | 210 | 0.54 | 0.44 | 184.1 | 0.33 | 0.66 | 143.8 | 1.00 | 0.53 |

Projected future streamflows based on the two SRES scenarios, A2 and B2, for the three basins are shown in Table 9 in decennial time resolution. Based on the results presented in this table, the direct and the indirect approaches provided significantly different results. According to this table, the indirect approach predicted higher values for streamflows, sometimes even twice as great as streamflows estimated by the direct approach (for the same basin and climate change scenario). Higher variability for both climate change scenarios was also obtained, which was expected considering the results shown in Figures 7–9. Overestimation of monthly mean streamflows by the indirect approach and underestimation of monthly standard deviation values by the direct approach justifies the differences between the predictions made for the climate change scenarios. This means that variations of simulated future streamflows around the mean values of the indirect method are greater than in the direct approach. The *q-q* plots of the observed and computed streamflows (especially for the validation period) depicted underestimation of high flow values estimated by direct approach versus observations. The differences between the projections of the two methods were considerable in Polech. and Poled. basins. As can be seen in Table 9, future streamflows predicted by the direct method were significantly lower than those estimated by indirect approach for both climate change scenarios, so the uncertainty resulting from the elimination of hydrological modeling (implementing direct method) is considerable versus indirect method. For both scenarios, the direct approach projected a decrease in streamflows for Polech. and Poled. stations and no considerable change in Ghoor. station, which seems more consistent with other studies done on the Karkheh River basin. The indirect approach projected relatively higher streamflows than the baseline period.

. | Polech. . | Ghoor. . | Poled. . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Direct . | Indirect . | Direct . | Indirect . | Direct . | Indirect . | |||||||

A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | |

Observed annual mean = 8.06 . | Observed annual mean = 10.86 . | Observed annual mean = 51.25 . | ||||||||||

2001–10 | 6.33 | 6.24 | 9.74 | 9.95 | 10.63 | 10.46 | 11.86 | 12.54 | 44.79 | 44.59 | 52.56 | 53.53 |

2011–20 | 6.53 | 6.33 | 11.78 | 10.22 | 11.03 | 10.79 | 14.87 | 12.63 | 45.58 | 44.68 | 64.99 | 53.57 |

2021–30 | 6.01 | 5.95 | 9.85 | 10.39 | 10.28 | 10.07 | 12.85 | 13.62 | 42.99 | 42.98 | 50.93 | 55.12 |

2031–40 | 6.34 | 6.00 | 11.55 | 11.74 | 10.53 | 10.30 | 15.44 | 15.31 | 44.37 | 42.65 | 61.10 | 61.80 |

2041–50 | 6.36 | 6.13 | 11.95 | 10.64 | 10.74 | 10.75 | 16.97 | 14.34 | 43.01 | 44.16 | 66.07 | 59.87 |

. | Polech. . | Ghoor. . | Poled. . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Direct . | Indirect . | Direct . | Indirect . | Direct . | Indirect . | |||||||

A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | |

Observed annual mean = 8.06 . | Observed annual mean = 10.86 . | Observed annual mean = 51.25 . | ||||||||||

2001–10 | 6.33 | 6.24 | 9.74 | 9.95 | 10.63 | 10.46 | 11.86 | 12.54 | 44.79 | 44.59 | 52.56 | 53.53 |

2011–20 | 6.53 | 6.33 | 11.78 | 10.22 | 11.03 | 10.79 | 14.87 | 12.63 | 45.58 | 44.68 | 64.99 | 53.57 |

2021–30 | 6.01 | 5.95 | 9.85 | 10.39 | 10.28 | 10.07 | 12.85 | 13.62 | 42.99 | 42.98 | 50.93 | 55.12 |

2031–40 | 6.34 | 6.00 | 11.55 | 11.74 | 10.53 | 10.30 | 15.44 | 15.31 | 44.37 | 42.65 | 61.10 | 61.80 |

2041–50 | 6.36 | 6.13 | 11.95 | 10.64 | 10.74 | 10.75 | 16.97 | 14.34 | 43.01 | 44.16 | 66.07 | 59.87 |

### Uncertainty analysis results

In order to assess the uncertainty associated with streamflows obtained from direct and indirect approaches, time series of streamflows based on HadCM3 predictions for A2 and B2 scenarios were estimated. Figure 10 shows the procedure used for this purpose.

In this study, for the predicted streamflow time series obtained from the two direct and indirect approaches, three PIs of 60%, 80%, and 90% were calculated. According to Table 10, the direct approach always performs better based on *NUE* indicator for the three sub-basins. Based on *ARIL*, as was expected, 90% PIs are wider all the time in comparison to 60% and 80% intervals because they contain more observations within. For example, in Figure 11, upper and lower uncertainty bounds versus observations for Polech. (PI equal to 80%, indirect approach, the lowest *NUE*) and Poled. (PI equal to 60%, direct approach, the highest *NUE*) are depicted.

Basin . | Direct approach . | Indirect approach . | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PI 60% . | PI 80% . | PI 90% . | PI 60% . | PI 80% . | PI 90% . | |||||||||||||

ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | |

Ghoor. | 0.98 | 61.35 | 62.6 | 1.63 | 82.21 | 50.4 | 2.46 | 91.20 | 37.09 | 2.34 | 61.64 | 26.3 | 3.64 | 83.37 | 22.9 | 5.42 | 92.24 | 17.01 |

Polech. | 0.99 | 63.19 | 63.8 | 2.19 | 82.21 | 37.5 | 3.65 | 93.25 | 25.58 | 3.20 | 60.73 | 18.9 | 5.06 | 81.96 | 16.2 | 7.36 | 92.69 | 12.59 |

Poled. | 0.47 | 61.15 | 130.1 | 0.89 | 82.41 | 92.6 | 1.41 | 91.21 | 64.75 | 1.10 | 65.57 | 59.6 | 1.74 | 87.59 | 50.3 | 2.61 | 94.15 | 36.08 |

Basin . | Direct approach . | Indirect approach . | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PI 60% . | PI 80% . | PI 90% . | PI 60% . | PI 80% . | PI 90% . | |||||||||||||

ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | ARIL
. | P
. _{level} | NUE (%)
. | |

Ghoor. | 0.98 | 61.35 | 62.6 | 1.63 | 82.21 | 50.4 | 2.46 | 91.20 | 37.09 | 2.34 | 61.64 | 26.3 | 3.64 | 83.37 | 22.9 | 5.42 | 92.24 | 17.01 |

Polech. | 0.99 | 63.19 | 63.8 | 2.19 | 82.21 | 37.5 | 3.65 | 93.25 | 25.58 | 3.20 | 60.73 | 18.9 | 5.06 | 81.96 | 16.2 | 7.36 | 92.69 | 12.59 |

Poled. | 0.47 | 61.15 | 130.1 | 0.89 | 82.41 | 92.6 | 1.41 | 91.21 | 64.75 | 1.10 | 65.57 | 59.6 | 1.74 | 87.59 | 50.3 | 2.61 | 94.15 | 36.08 |

Both direct and indirect approaches had the most accurate estimations in the case of Poled. basin. This may be because of the higher values of observed streamflows which lead to smaller *ARIL*s and therefore higher *NUE*s.

The differences between *NUE* values in the direct and indirect methods of Poled. basin are related to the large difference in their *ARIL* values. The results of the indirect method represent a wider bracketed area in all uncertainty levels and basins; one reason for this might be the application of additional mathematical operators in the hydrological model in the indirect method. In Table 11, for PI levels and all the basins (90, 80, and 60%), average interval lengths are presented. This indicator behaves as convex and concave for the indirect and direct methods, respectively, with increasing the month index. Also, their average interval lengths increased with increasing their PI levels. In all cases, the bracketed areas with PI equal to 80% were the smallest. As an example, in Figure 12, uncertainty bounds of different PIs and A2 climate change scenario under indirect and direct approaches for Poled. sub-basin are presented.

PI (%) . | Polech. . | Ghoor. . | Poled. . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Direct . | Indirect . | Direct . | Indirect . | Direct . | Indirect . | |||||||

A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | |

60 | 1.9 | 1.9 | 4.4 | 4.4 | 2.9 | 2.9 | 5.9 | 5.8 | 4.4 | 4.4 | 25.4 | 25 |

80 | 0.8 | 0.8 | 2.1 | 2.2 | 1.2 | 1.2 | 2.9 | 2.8 | 1.9 | 1.9 | 11.1 | 10.9 |

90 | 9.2 | 9.1 | 16.1 | 15.7 | 12.6 | 12.6 | 20.9 | 20.6 | 26.3 | 26.3 | 111.3 | 108.1 |

PI (%) . | Polech. . | Ghoor. . | Poled. . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Direct . | Indirect . | Direct . | Indirect . | Direct . | Indirect . | |||||||

A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | A2 . | B2 . | |

60 | 1.9 | 1.9 | 4.4 | 4.4 | 2.9 | 2.9 | 5.9 | 5.8 | 4.4 | 4.4 | 25.4 | 25 |

80 | 0.8 | 0.8 | 2.1 | 2.2 | 1.2 | 1.2 | 2.9 | 2.8 | 1.9 | 1.9 | 11.1 | 10.9 |

90 | 9.2 | 9.1 | 16.1 | 15.7 | 12.6 | 12.6 | 20.9 | 20.6 | 26.3 | 26.3 | 111.3 | 108.1 |

The pattern of modeled uncertainties is another difference between the results of direct and indirect approaches. For example, the pattern of monthly average interval lengths is depicted for Ghoor. sub-basin in Figure 13. Simulated uncertainty for the direct method was very smooth with wider uncertainty bounds in low flow months. This pattern changed in wet months (month 9 to 11). The uncertainty bounds for the indirect method had more fluctuations. Higher uncertainties were estimated for high flow months. Generally, the uncertainties associated with the indirect method were higher than the direct method. The same patterns of simulated uncertainty bounds were also observed for Ghoor. and Polech. sub-basins.

## CONCLUSIONS

This study draws a comparison between the direct and indirect approaches assessing climate change impacts on streamflows. Direct downscaling is easier than the indirect approach because it omits an important and challenging step of hydrological modeling. Differences between the results obtained from the two approaches showed significant uncertainty associated with elimination of hydrological modeling in evaluating climate change impacts.

The results presented in the article have shown that direct downscaling can be a suitable method for estimation of average monthly streamflows. Weaknesses in prediction of streamflow variability in future climate change scenarios can limit the application of direct downscaling in flood frequency prediction under climate change conditions. In the case of uncertainty simulation, the resulted uncertainty bounds of the two methods showed different patterns. The indirect method represents more realistic uncertainty bounds than the direct method. In addition, the *ARIL* indicator in the indirect method is greater than the direct method due to more mathematical operators (downscaling + hydrological modeling).

Testing the performance of direct and indirect downscaling approaches in different climatic conditions, assessing the sensitivity of these approaches to the selected GCMs, incorporating hydrological modeling in the structure of downscaling models, and employing different mathematical kernels in order to upgrade the performance of direct approach can be important topics for future studies.