추계학적 점 강우모형과 결합된 토양수분 확률밀도함수의 유도 = Derivation of Soil Moisture Probability Density Function Coupled with Stochastic Point Rainfall Model

국문 초록 (Abstract)

강우의 변동성이 토양수분 동역학에 미치는 영향을 분석하기 위한 추계학적 모형이 제안된다. 모형은 강우-토양수분 시스템의 외력으로서 간단힌 추계학적 강우모형과 연계된 추계학적 미분방정식으로부터 cumulant 급수이론을 이용하며 유도되며, 확률밀도함수의 형태로 해를 제공한다는 장점을 갖는다. 이로부터 토양수분에 대한 정상상태 확률밀도함수가 해석적으로 구해질 수 있으며, 결과는 다양한 기후 및 토양, 식생 조건에 따라 분석된다.

다국어 초록 (Multilingual Abstract)

A new stochastic model for the propagation analysis of fluctuations in rainfall to soil moisture dynamics is proposed with major focus on its probabilistic structure. This model is derived by using cumulant expansion theory from a stochastic differential equation with stochastic rainfall forcing which is incorporated by simple stochastic rainfall model, and has the advantage of providing the probabilistic solution in the form of a probability density function. Steady state probability density function for soil moisture is obtained analytically and analyzed for different climate, soil and vegetation conditions.

목차 (Table of Contents)

• Abstract
• 요지
• 1. 서론
• 2. 모형의 유도
• 3. 강우 및 토양수분의 모의발생
• 4. 토양수분 확률밀도함수의 적용
• 5. 결론
• 감사의 글
• 참고문헌

참고문헌 (Reference)

1 "점 강우모형과 강우강도-지속기간-생기빈도 해석" 한국수자원학회 34 : 577-586, 2001

2 "다차원 강우모형의 시간적인 특성연구" 한국수자원학회 33 : 783-791, 2000

3 "nalytical derivation of steady state soil water probability distribution function under rainfall forcing using cumulant expansion theory" 11 : 227-232, 2007

4 "The ecohydrological role of soil texture in a water-limited ecosystem" 37 : 2863-2872, 2001

5 "Stochastic point rainfall modeling for correlated rain cell intensity and duration." 11 : 29-36, 2006

6 "Stochastic differential equations. Phys. Rep." 24 : 171-228, 1976

7 "Stochastic Liouville equations. J. Math. Phys." 4 : 174-183, 1963

8 "Soil water balance and ecosystem response to climate change" 164 : 625-633, 2004

9 "Scale consideration in the modeling of temporal rainfall. Water Resour. Res." 20 : 1611-1619, 1984

10 "Rooting depth water availability and vegetation cover along an aridity gradient in Patagonia" Oecologia 108 : 503-511, 1996

11 "Probabilistic solution to stochastic overland flow equation." 8 : 54-63, 2003

12 "Probabilistic modeling of water balance at a point: The role of climate, soil and vegetation" 455 : 3789-3805, 1999

13 "Plants in water-controlled ecosystems: Active role in hydrologic processes and response to water stress. II: Probabilistic soil moisture dynamics" 24 : 707-723, 2001

14 "Plants in water-controlled ecosystems: Active role in hydrologic processes and response to water stress" 24 : 697-705, 2001

15 "On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers." 179 : 321-351, 1996

16 "Nonlinear hydrologic processes: Conservation equations for determining their means and probability distributions" 8 : 44-53, 2003

17 "Maximum rooting depth of vegetation types at the global scale" Oecologia 108 : 583-595, 1996

18 "Generalized cumulant expansion method. J. Phys. Soc. Japan" 17 : 1100-1120, 1962

19 "Ecohydrology: Darwinian expression of vegetation form and function" Cambridge Univ. Press 2002

20 "Ecohydrology of water-controlled Ecosystems: soil moisture and plant dynamics" Cambridge Univ. Press 2004

21 "Ecohydrology ?a challenging multidisciplinary research perspective" 47 : 811-822, 2002

22 "Assessment of drought vulnerability based on the soil moisture PDF." 21 : 131-141, 2006

23 "Analytical framework for the characterization of the space-time variability of soil moisture. Adv. Water Resour." 17 : 35-45, 1994

24 "Analysis and synthesis. MIT Press." 1983

25 "A global analysis of root distribution for terrestrial biomes." Oecologia 108 : 389-441, 1996

26 "A generalized theory of multiplicative stochastic processes using cumulant techniques. J. Math. Phys." 16 : 289-297, 1975

27 "A cumulant expansion for stochastic linear differential equation II. Physica" 74 : 239-247, 1974

28 "1. Introduction to water balance dynamics. Water Resour. Res." 14 : 705-712, 1978