• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.20-20
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• 2018

다년동안 지속되는 가뭄현상이 빈번하게 발생하고 있지만, 우리나라에서는 지금까지 장기 가뭄보다 단기 가뭄에 초점을 맞춰 연구가 진행되어 왔다. 다년 가뭄을 반영하지 않고 댐의 저수용량을 평가할 경우, 저수용량이 과소평가될 수 있기 때문에 다년간의 가뭄을 반영한 시계열 모형을 통해 다양한 시나리오를 생성하고 분석해야 한다. 본 연구에서는 2015년부터 2017년까지 장기 가뭄이 발생한 보령댐의 1998년-2017년까지의 관측 월평균 유입량 자료를 바탕으로 Autoregressive Moving Average(ARMA)시계열 모형과 Hurst Coefficient를 추가하여 장기지속성을 반영하도록 개발된 시계열 모형인 Autoregressive Fractionally Integreated Moving Average(ARFIMA)를 사용하여 보령댐 500년 기간의 유입량 자료를 생성하였다. Hurst Coefficient는 Hurst가 제안한 Rescaled Range(R/S)방법 외에도 경험식, 이론식을 모두 사용하여 산정하였다. 생성된 자료가 관측 자료의 장기지속성을 잘 반영하는지에 대한 검증을 위해 관측자료의 누적유입량으로부터 선형 이동평균방법을 사용하여 가뭄기준을 산정하고, 생성한 유입량 자료가 장기가뭄을 반영하고 있는지 판단하였다. 그 결과 가뭄의 장기지속성을 잘 반영하는 시계열 모형을 선정하였으며, 향후 연구를 통해 미래 기후변화 시나리오를 반영한 장기가뭄 분석을 수행할 예정이다.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.7
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• pp.37-45
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• 2005

In this study, R/S analysis which was proposed by Mandelbrot & Wallis (1969) was applied to evaluate the presence of the fractal property in the cone tip resistance of in-situ CPT data. Hurst exponents (H) were evaluated in the range of 0.660$\sim$0.990 and the average was 0.875. It was confirmed that a cone tip resistance data had the characteristic of fractals and it was expected that cone tip resistance data sets are well approximated by a fBm process with an Hurst exponent near 0.875. It was also observed that the boundary between layers were obviously identified as a result of R/S analysis and it will be usage in practices.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.27-27
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• 2023

To analyze the evolution of water resources in Qiandao Lake Basin under the condition of climate change, a WEP-L distributed hydrological model was established to simulate the water cycle process in the basin during 1960-2020. The Mann-Kendall non-parametric test method and Hurst index method were used to analyze the inter-annual variation and annual distribution characteristics of the total water resources in the basin. The multi-scale temporal and spatial distribution and evolution trend of water resources in Qiandao Lake Basin were evaluated. The results show that: (1) The WEP-L model has good simulation results in the Qiandao Lake basin, and the Nash coefficient rate is above 0.83 in the periodic period and above 0.85 in the verification period. (2) The water yield coefficient of the whole basin ranges from 0.436 to 0.630. The annual average total water resource is 12.25 billion m³, equivalent to 1176.4mm of water depth. The annual distribution process shows a unimodal structure, and the water depth of each sub-basin ranges from 742 mm to 1266 mm, and the spatial distribution is higher in the west and lower in the east. (3) The annual water resources series in the basin showed an insignificant upward trend, and the Hurst index was 0.86, indicating a continuous upward trend. From the perspective of monthly water resources, January and February increased significantly, the other months were not significant changes.

• Journal of Korea Multimedia Society
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• v.24 no.12
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• pp.1614-1623
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• 2021

In this paper, the purpose is evaluation of the effect of using fractal feature in machine learning based pancreatic tumor classification. We used the data that Pancreas CT series 469 case including 1995 slice of benign and 1772 slice of malignant. Feature selection is implemented from 109 feature to 7 feature by Lasso regularization. In Fractal feature, fractal dimension is obtained by box-counting method, and hurst coefficient is calculated range data of pixel value in ROI. As a result, there were significant differences in both benign and malignancies tumor. Additionally, we compared the classification performance between model without fractal feature and model with fractal feature by using support vector machine. The train model with fractal feature showed statistically significant performance in comparison with train model without fractal feature.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.479-489
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• 2019

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian sheet with Hurst parameters H, H' > 1/2, and a drift coefficient satisfying the linear growth condition. The result is obtained using a suitable Girsanov theorem for the fractional Brownian sheet.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.09a
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• pp.140-143
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• 2003

Air permeabilities in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona, exhibit a self-affine behavior, thus renders a field random fractal. Based up fractal scaling, the observed scale effect has been interpreted [Hyun et al., 2002]. Recently, Frantziskonis and Hansen [2000] presented that fractal scaling can be represented based on wavelets. This study deals with the way of using wavelets for fractal scaling. A numerical study is presented to examine the applicability of wavelet-based approach to determining upscaled air permeability values on various data supports at the site. To characterize the scaling property of self-affine fields generated based upon wavelets, Hurst coefficient, H. was inferred by applying the average wavelet coefficient (AWC) method. The result yielded H = 0.24, which is very close to the result of geostatistical analysis using a power variogram (H = 0.22). The study concludes that wavelet-based scaling is a useful way of determining parameter values on different data supports, which is an essential task for modeling of subsurface flow and mass transport in a numeric grid with different resolutions (grid size).

• Magazine of the Korean Society of Agricultural Engineers
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• v.23 no.4
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• pp.46-52
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• 1981

The aim at this study has the stochastic hydrological analysis for the annual mean discharge and monthly discharge which were observed at Lobith of River Rhine in the Netherlands from 1901 to 1972. After this study was analysed by computer IBM 370 and Hewlett Parkard 9800, the results were as follows; 1.When 72 data was divided into two groups of subsample data as 36 data, they do not have their properties to be non-homogeneous and inconsistent due to F-test and t-test. 2.The credit limits of the serial correlation coefficient was fluctuated $\pm$0. 231 which was shown in Fig. 3. at significant level 99% by Anderson's test. 3.The correlogram at short term was shown to be no short-term persistence as Fig. 3. 4.Since the correlogram at long term has displayed that Hurst's coefficient was 0.6144 between 0.6 and 0.7, it was to be no long-term persistence. 5.The stochastic model with annual discharge of this River Rhine was shown with $\chi$t=2195+483. 8 $\varepsilon$t as $\chi$t=$\mu$+oet and $\varepsilon$t=$_1$ø$\varepsilon$t-$_1$+ζt where t=1,2,3,..., ζt is an independent series with mean zero and variance (1-ø2), $\varepsilon$t is the dependent series, and 4' is the parameter of the model. 6.The serial correlation coefficient of monthly discharge was explained as $\chi$$_1$ = 0.34 . sin(6-$\pi$t+$\pi$) as Fig.4. and the River Rhine has no large fluctuation and smoothly changed during that time.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.69-69
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• 2021

From the unprecedented 2011 spring flood, the residens reside by Lake Champlain and Richelieu River encountered enormous damages. The International Joint Committee (IJC) released the Lake Champlain-Richelieu River (LCRR) Plan of Study (PoS). One of the major tasks for the PoS is to investigate the possible scenarios that might happen in the LCRR basin based on the stochastic simulation of the Net Basin Supplies that calculates the amount of flow into the lake and the river. Therefore, the current study proposed a novel apporach that simulate the annual NBS teleconnecting the climate index. The proposed model employed the bivariate empirical decomposition to contamporaneously model the long-term evolution of nonstationary oscillation embeded in the annual NBS and the climate signal (here, Artic Oscillation: AO). In order to represent the variational behavior of NBS correlation structure along with the temporal revolution of the climate index, a new nonstationary parameterization concept is proposed. The results indicate that the proposed model is superior performance in preserving long and short temporal correlation. It can even preserve the hurst coefficient better than any other tested models.