• 한국물환경학회지
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• 제23권5호
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• pp.683-688
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• 2007

질량보존의 법칙과 Darcy의 법칙으로 표현되는 Richards 방정식은 비포화대의 토양수분흐름을 모의하는데 널리 사용되어 왔다. Richards 방정식은 압력수두의 항으로 표현되는 방정식, 토양수분의 항으로 표현되는 방정식, 그리고 이 둘을 혼합한 형태의 방정식 등, 세가지 형태로 표현할 수 있다. 고차의 비선형 항들을 포함하는 이 편미분방정식들을 수치해석방법으로 풀 때, 질량 비보존을 수반하는 오류의 결과가 초래될 수 있다. 세가지 방정식들 중 혼합형 Richards 방정식이, 다른 추가적인 계산없이 질량을 온전히 보존하는 것으로 알려져 있다. 이 연구의 목적은 동질성 토양에서의 1차원적 연직방향 비포화수 흐름모의를 위해, Richards 방정식의 질량보존적 수치해석법을 완전음해 유한차분법으로 개발하고, 이를 통해 민감도 분석을 실시하여 토양특성인자들과 토양종류에 따른 침투율의 변화를 살펴보는 데 있다.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.295-309
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• 2023

The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2012년도 학술발표회
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• pp.107-107
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• 2012

우리나라의 시설재배는 연중 고품질의 농산물을 요구하는 소비자의 기대와 생산자의 경제적 목적이 부합되어 재배면적이 증가하고 있으며 전체 시설재배면적의 31.3%는 수리시설이 완비된 관개논에 위치한다. 시설재배지에서의 수분관리는 작물의 안정적인 생산과 수자원의 효율적인 사용을 위하여 토양 특성을 고려하여 운영되어야 한다. 따라서 시설재배지 토양 특성을 반영한 작물근군역에서의 물수지와 수분거동 특성에 관한 연구가 선행되어야한다. 불포화토양에서의 수분이동은 토양-작물-대기의 연속계에서 수분의 공급과 증발산, 배수 및 유거에 의한 토양수분 장력의 변화로 이루어지며 토양수분과 토양수분 장력, 수리전도도와의 관계는 토양의 수리적 특성에 따라 상이하다. 실험을 통한 토양수분 거동 분석은 시간적, 비용적 측면에서 비효율적이므로 모형에 의한 분석이 요구된다. 본 연구에서는 불포화토양에서의 수분이동을 모의하기 위하여 Richards 공식을 유한차분법으로 해석하였으며 국내 논 시설재배지 이(異)층토양에 대하여 다양한 관개조건을 적용하여 토양수분 거동 특성을 분석하였다. 관개와 작물의 수분흡수가 지속됨에 따라 근군역을 이탈한 토양수분이 유하되어 밭 토양과 논 토양의 경계에 축적됨을 확인 하였으며 과다관개가 이루어질수록 이러한 현상이 심화되는 것으로 나타났다. 본 연구의 결과는 관개시스템의 설계와 운영에 기초자료로 활용될 수 있다.

• 환경생물
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• 제20권4호
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• pp.378-385
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• 2002

가막만 양식 참굴의 정장양상을 모델화 하기 위해 1997년 3월부터 1998년 5월가지 양식장에서 무작위 채집된 총 9,208개체의 각장 및 습중량을 조사하였으며, 참굴 양식장의 환경용량을 추정하기 위하여 1985년부터 2000년까지의 단위면적 당 생산량과 시설대수를 조사하였다. 참굴의 성장모델 추정에는 Bertalanlffy 성장식, 계절변동을 고려한 Bertalanffy 성장식과 일반화된 Schnute and Richards 성장식이 사용되었고, 환경용량의 추정을 위해서는 Schaefer와 Fox의 잉여 생산량 모델들이 사용되었다. 추정된 길이 성장모델은 Bertalanffy모델을 적용하였을 때 보다 일반화된 Schnute and Richards 성장식을 적용했을 때 적합도가 높았다. 추정된 환경용량은 Schaefer모델에서 $21.1\;7ton\;ha^{-1}$, Fox모델에서는 1$17.7\;ton\;ha^{-1}$, 로 2000년 현재의 단위면적 당 생산량 $26.1\;ton\;ha^{-1}$, 보다 낮았으나 환경용량을 생산하는 시설 대수는 8대$(ha^{-1})$로 2000년 현재의 7.8대$(ha^{-1})$와 유사한 값을 보였다.

• The Korean Journal of Ecology
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• 제25권1호
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• pp.29-31
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• 2002

The purpose of this study is to estimate height growth patterns and site index cuties (base index age 50 years) for Japanese red cedar trees(Cryptomeria japonica D. Don) grown in southern regions of Korea. The Chapman-Richards growth function was selected for stand height prediction using on the results of stem analysis data sets. Anamorphic base age invariant site index cuties were presented based on this height prediction equation. The resulting site index prediction equation can provide an indication of the productivity of the site quality based on Japanese red cedar trees plantation ages planted in southern regions of Korea.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2003년도 총회 및 춘계학술발표회
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• pp.163-167
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• 2003

Based on the transient finite difference solution of Richards' equation, an infiltration model is developed to analyze temporal variation of precipitation recharge in the region of monsoon climates. Simulation results obtained by using time series data of 20-year daily precipitation and pan evaporation indicate that a linear relationship between the annual precipitation and the annual recharge holds for the soils under the monsoon climates with varying degrees of the correlation coefficient depending on the soil types. A sensitivity analysis reveals that the water table depth has little effects on the recharge for the sandy soil, whereas, for the loamy and silty soils, rise of the water table at shallow depths causes increase of evaporation by approximately 100㎜/yr and a corresponding decrease in recharge. A series of simulations for two-layered soils illustrate that the amount of recharge is dominantly determined by the soil properties of the upper layer, although the temporal variation of recharge is affected by both layers.

• 한국농공학회논문집
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• 제52권6호
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• pp.19-26
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• 2010

Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

• 한국환경과학회지
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• 제31권9호
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• pp.793-801
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• 2022

This study was carried out to provide basic data for logical forest management by developing a site index curve reflecting the current growth characteristics of Cryptomeria japonica stands in Korea. The height growth model was developed using the Chapman-Richards, Schumacher, Gompertz, and Weibull algebraic difference equations, which are widely used in growth estimation, for data collected from 119 plots through the 7th National Forest Inventory and stand survey. The Chapman-Richards equation, with the highest model fit, was selected as the best equation for the height growth model, and a site index curve was developed using the guide curve method. To compare the developed site index curve with that on the yield table, paired T-tests with a significance level of 5% were performed. The results indicated that there were no significant differences between the site index curve values at all ages, and the p-value was smaller after the reference age than before. Therefore, the site index curve developed through this study reflects the characteristics of the changing growth environment of C. japonica stands and can be used in accordance with the site index curve on the current yield table. Thus, this information can be considered valuable as basic data for reasonable forest management.

• 한국농공학회논문집
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• 제54권3호
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• pp.19-28
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• 2012

Greenhouse cultivation has been increasing for high quality and four season crop production in South Korea. For the cultivation in a greenhouse, maintaining adequate soil moisture at each crop growth stage is quite important for yield stability and quality while the behavior of moisture movement in the soil has complexity and adequate moisture conditions for crops are vary. Drip irrigation systems have been disseminated in the greenhouse cultivation due to advantages including irrigation convenience and efficiency without savvy consideration of the soil moisture redistribution. This study aims to evaluate soil moisture movement of drip irrigation according to the soil moisture uniformity assessment. Richards equation and finite difference scheme were adapted to simulate soil moisture behavior in soil. Soil container experiment was conducted and the model was validated using the data from the experiment. Two discharge rate (1 ${\ell}/hr$ and 2 ${\ell}/hr$) and three spaces between the emitters (10 cm, 20 cm, and 30 cm) were used for irrigation system evaluation. Christiansen uniformity coefficient was also calculated to assess soil moisture redistribution uniformity. The results would propose design guidelines for drip irrigation system installation in the greenhouse cultivation.