### 1. Introduction

### 2. Materials and Methods

### 2.1. The Nonstationary Markov Chain Models

*p01*and

*p11*) are used to describe rainfall occurrence.

*p01*indicates the probability of a wet day following a dry day, and

*p11*is the probability of a wet day following a wet day. Similarly, the amount of rainfall on wet days is described by probability density functions (e.g., gamma distribution and exponential distribution). In this study, the gamma distribution having two parameters (scale (

*α*) and shape (

*κ*) parameter) was used for this purpose. To link the set of four parameters (

*p01, p11*,

*α*, and

*κ*) of the regular Markov chain model to the climate change pattern, a regression framework is used. The stochastic parameters (

*p01, p11*,

*α*, and

*κ*) are calculated for every month or season using an observed daily rainfall series in every year. Given the constructed relationship between seasonal rainfall and stochastic parameters, stochastic parameters are generated with the help of the RCM precipitation, and then daily rainfall sequences are finally simulated by using the generated stochastic parameters for future projection. A flow-chart for the nonstationary Markov chain model is displayed in Fig. 2.

### 2.2. Hydrological Model

### 2.3. Nonparametric Rainfall Elasticity

##### (2)

$${\in}_{p}=median(\frac{{Q}_{t}-\overline{Q}}{{P}_{t}-\overline{P}}\frac{\overline{P}}{\overline{Q}})$$*P̄*and

*Q̄*are the mean annual rainfall and streamflow, respectively.

*Q*

*and*

_{t}*P*

*are annual streamflow and rainfall for*

_{t}*t*year.

### 3. Results and Discussion

### 3.2. The Impact of Climate Change on Annual Rainfall

### 3.3. The Impact of Climate Change on Annual Streamflow

### 3.4. Estimation of Rainfall Elasticity

### 3.5. Effects of Climate Change on Rainfall Elasticity on Each Basin

#### 3.5.1. Grading using nonparametic kernel density functions

_{i}are actual observation values distributed independently and evenly, K (formula) is the kernel function, and h is the positive bandwidth value. In this paper, a simple rule of thumb was used to estimate the bandwidth.

#### 3.5.2. Comparison between current elasticity and future one

### 4. Conclusions

As a result of analyzing the effects of climate change on the variation of annual precipitation, it was simulated as follows: the variation of rainfall in comparison to the present (1973 to 2006) were analyzed. It was simulated that rainfall increased by 7.66% from 2007 to 2030 (2015) compared to the present, 6.11% from 2031 to 2060 (2045), and 7.18% from 2061 to 2090 (2075) on the basin of Han River. In addition, annual mean rainfall tended to increase. However, it was analyzed that the range of rainfall variation increased compared to the present and that 1,000 mm or less of annual rainfall occurred. The analysis results were as follows: on Nakdong River, annual rainfall would increase by 21.14% in 2015, 22.62% in 2045, and 26.20% in 2075. On Geum River, annual rainfall increased by 11.94% in 2015, 4.10% in 2045, and 12.62% in 2075. On Seomjin River, annual rainfall would increase by 10.51% in 2015, 14.86% in 2045, and 25.57% in 2075. On Yeongsan River, annual rainfall would increase by 9.82% in 2015, would decrease by 6.16% in 2045, and would increase by 3.80% in 2075. On Yeongsan River, annual rainfall would decrease in 2045 only.

The results of analyzing the effects of climate change on annual streamflow are as follows: on the basin of Han River, flow rate would increase by 26.23% in 2015 compared to the present (1973–2006), by 10.30% in 2045, and by 8.53% in 2075. On the basin of Nakdong River, flow rate would increase by 5.85% in 2015, 4.66% in 2045, and 11.40% in 2075. On the basin of Geum River, flow rate would increase by 3.56% in 2015, and would decrease by 17.90% in 2045 and 5.63% in 2075. On the basin of Seomjin River, flow rate would increase by 8.96% in 2015, 10.48% in 2045, and 34.02% in 2075. On the basin of Yeongsan River, flow rate would increase by 16.98% in 2015, and would decrease by 26.35% in 2045 and 3.90% in 2075.

As a result of analyzing rainfall elasticity on five river basins, the result showed the range of 0.68 to 2.03. As precipitation or evapotranspiration got higher, the value of both elasticity and streamflow increased, and that of elasticity decreased. In addition, it turned out that area, a geomorphic variable, did not significantly affect elasticity.

It was confirmed that rainfall elasticity increased on all river basins other than Han River. This demonstrates that the sensitivity of water cycle factors may increase due to climate change and that the balance of the water resource structure may change.