• Journal of Korean Society on Water Environment
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• v.23 no.5
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• pp.683-688
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• 2007

Water flow into unsaturated soils is most often modeled by Richards equation consisting of the mass conservation law and Darcy's law. Three standard forms of Richards equation are presented as the head (${\Psi}$)-based form, the moisture content (${\theta}$) based form, and the mixed form. Numerical solutions of these partial differential equations with highly nonlinear terms can cause poor results along with significant mass balance errors. The numerical solution based on the mixed form of Richards equation is known that the mass is perfectly conserved without any additional computational efforts. The aim of this study is to develop fully implicit numerical scheme of Richards equation for one-dimensional vertical unsaturated flow in homogeneous soils using the finite difference approximation, and then to perform sensitivity analysis of infiltration to the variations in the unsaturated soil properties and to different soil types.

• Journal of applied mathematics & informatics
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• v.41 no.2
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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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• v.20 no.3
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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.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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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.

• Korean Journal of Environmental Biology
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• v.20 no.4
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• pp.378-385
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• 2002

Growth of Pacific oystey, Crassostrea gigas, in Kamak Bay, Korea was modeled using Von Bertalanffy growth function, seasonal Von Bertalanffy growth function and generalized growth equation of Schnute and Richards' growth model, based on shell length and wet weight frequency data of 9208 oysters. Carrying capacity in the oyster culture ground was also estimated using Schaefer's and Fox's surplus production model. The present results suggest that the generalized growth equation of Schnute and Richards' model is fitter to describe the length growth pattern of C. gigas than Von Bertalanffy growth functions. This results also suggest that the current number of culture facility per unit area in 2000 is similar to the number of facility that produces the maximum production of oyster per unit area.

• The Korean Journal of Ecology
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• v.25 no.1
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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.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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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.

• Journal of The Korean Society of Agricultural Engineers
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• v.52 no.6
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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.

• Journal of Environmental Science International
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• v.31 no.9
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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.

• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.3
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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.