[논문]확률론적 저장대모형을 이용한 하천에서의 물질혼합거동 해석

김병욱; 서일원; 권시윤; 정성현; 윤세훈

doi:10.3741/jkwra.2021.54.5.335

확률론적 저장대모형을 이용한 하천에서의 물질혼합거동 해석
Analysis of solute transport in rivers using a stochastic storage model 원문보기

Journal of Korea Water Resources Association = 한국수자원학회논문집, v.54 no.5, 2021년, pp.335 - 345

김병욱 (서울대학교 건설환경공학부) , 서일원 (서울대학교 건설환경공학부) , 권시윤 (서울대학교 건설환경공학부) , 정성현 (서울대학교 건설환경공학부) , 윤세훈 (서울대학교 건설환경공학부)

초록
AI-Helper

하천에서의 용존물질의 혼합거동을 신속하게 예측하기 해석하기 위하여 1차원 추적모형이 개발되어 왔다. 그 중 저장대모형(Transient Storage Model, TSM)은 자연하천의 복잡하고 불규칙한 수리·지형적인 특성을 단순하게 반영할 수 있다는 장점때문에 가장 많이 사용되는 1차원 추적모형이다. 하지만 TSM의 정확도는 본류대 및 저장대의 면적, 물질교환계수 등 모형의 매개변수에 의존하며 이들은 직접적으로 측정될 수 없다는 단점이 있다. 또한 TSM은 농도곡선의 꼬리에 나타나는 저장대특성의 형태를 지수함수형태로 반영하는데 이는 실제 추적자실험을 통해 관측되는 꼬리는 형태와 다르다는 평가가 제기되고 있다. 이에 따라 본 연구에서는 1차원 확률론적 저장대모형에 대한 수치모형을 개발하여 자연하천에 적용하고 그 결과를 TSM의 모의결과와 비교하였다. 상기의 모형을 검증하기 위하여 낙동강의 1차 지류 중 하나인 감천의 4.85 km의 구간에서 추적자 실험을 실시하였다. 본 추적자 실험을 통해 측정한 농도곡선과 본 연구에서 제시된 확률론적 저장대모형의 모의 곡선의 꼬리부 멱함수 기울기를 비교해본 결과, 오차율은 평균 0.24으로 나타났는데, 이는 1차원 이송-분산 모형과 TSM로부터의 오차율인 14.03과 1.87에 비해 보다 정확한 값이다. 본 연구 결과, 감천에서의 저장대 특성을 나타내는 하상의 체류시간분포는 지수함수분포보다는 멱함수 분포에 가까운 것으로 밝혀졌다.

Abstract ▼ AI-Helper

The one-dimensional solute transport models have been developed for recent decades to predict behavior and fate of solutes in rivers. Transient storage model (TSM) is the most popular model because of its simple conceptualization to consider the complexity of natural rivers. However, the TSM is highly dependent on its parameters which cannot be directly measured. In addition, the TSM interprets the late-time behavior of concentration curves in the shape of an exponential function, which has been evaluated as not suitable for actual solute behavior in natural rivers. In this study, we suggested a stochastic approach to the solute transport analysis. We delineated the model development and model application to a natural river, and compared the results of the proposed model to those of the TSM. To validate the proposed model, a tracer test was carried out in the 4.85 km reach of Gam Creek, one of the first-order tributaries of Nakdong River, South Korea. As a result of comparing the power-law slope of the tail of breakthrough curves, the simulation results from the stochastic storage model yielded the average error rate of 0.24, which is more accurate than the 14.03 and 1.87 from advection-dispersion model and TSM, respectively. This study demonstrated the appropriateness of the power-law residence time distribution to the hyporheic zone of the Gam Creek.

주제어

표/그림 (8)

그림 Fig. 1. Schematic diagram of the stochastic trapping mechanism in a river
그림 Fig. 2. Modelling framework for the stochastic storage model
그림 Fig. 3. Distribution of φ_r according to varying parameter T_h (a) semi-log plot (b) log-log plot
그림 Fig. 4. (a) Site map of the test bed in Gam Creek, South Korea (b) Tracer behavior affected by storage effect in shallow area (c) Streambed shape of Gam Creek where dunes are formed
표 Table 1. Surveyed average hydraulic data in each sub-reach
표 Table 2. Estimated parameters required by each model
그림 Fig. 5. BTCs measured from tracer test and simulated from each one-dimensional solute transport model (a) measured BTC at S1 applied as boundary condition (b) BTC comparison at S2 (c) BTC comparison at S3 (d) BTC comparison at S4
표 Table 3. Comparison of the power-law slope of the tail of BTCs at each section

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