SPATIAL AND TEMPORAL DISTRIBUTIONS OF MIGRATION IN BIO-RETENTION SYSTEMS

Transcription

1 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp SPATIAL AND TEMPORAL DISTRIBUTIONS OF MIGRATION IN BIO-RETENTION SYSTEMS by Yu-Qi LI a, Kai-Wen WANG a, Ke-Li ZHANG a, Ze-Wei ZHOU a, and Xiao-Hua YANG b a School of Geography, Beijing Noral University, Beijing, China b State Key Laboratory of Water Environent Siulation, School of Environent, Beijing Noral University, Beijing, China Original scientific paper DOI: 0.98/TSCI405557L Urban bio-retention syste is eaningful in reducing rainfall runoff and enhancing infiltration capacity. But the oisture igration in bio-retention systes are not clear under cliate change. The spatial and teporal distribution of oisture under different rainfall events in bio-retention systes are studied in this paper based on experiental data in Beijing. Richards odel is introduced to siulate the spatial and teporal distribution of oisture including pressure head, hydraulic head and water content under different initial and boundary conditions. As a result, we found that fro the depth of the node to the lower boundary, the values of pressure head and hydraulic head increase with depth and decrease with tie, while the values of water content represent opposite trends relative to the distribution of pressure head and hydraulic head in bio-retention systes. Key words: spatial and teporal distribution, bio-retention, Richards odel, oisture igration Introduction Bio-retention syste which generally consists of soil, gravel, and ulch with a variety of plant species, is one of storwater best anageent practices under cliate change [, ]. Bio-retention syste is developed to reduce runoff quantity and iprove water quality in a natural, aesthetically pleasing anner [3]. As an effective easureent, bio-retention syste with different soil texture provides a shallow depression and plant root in order to reduce runoff peak rate and aintain soil infiltration [4, 5]. When rainfall occurs, a bio-retention syste can reduce surface runoff and increase infiltration capacity as surface runoff can be stored in its depression. Bio-retention has a positive influence on the urban sustainable developent. Soe scholars did soe research to stiulate the distribution of pressure head in bio-retention systes [6], but the oisture igration with tie in bio-retention systes is seldo researched. In this paper, Richards odel is introduced to siulate the spatial and teporal distribution of oisture igration including pressure head, hydraulic head and water content under different initial and boundary conditions. The odel is applied in bio-retention systes in Beijing. Richards odel for the oisture in a bio-retention syste The Richards odel is based on the one diensional Richards equation, including three variables of pressure head φ, hydraulic head h, water content θ, and basic soil hydraulic Corresponding author; e-ail: yxh@sohu.co

2 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture 558 THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp paraeters S(θ), K(θ), and M(θ). The odel can be solved by a nuerical odel based on a spatial discretization ethod [7, 8]. Using the Richards odel, the distribution of pressure head, hydraulic head and water content can be stiulated in bio-retention systes. Richards equation The Richards equation is based on the forulation of Darcy s law and the principle of continuity [9]: θ θ ϕ = = K ( ϕ) ( ϕ z) Sr () t ϕ t z z where θ is the voluetric water content [L 3 /L 3 ], z the vertical position [L], t the tie [T], K(θ) the hydraulic conductivity of water [L/T], φ the pressure head [L], and S r the plant transpiration rate [/T]. θ/ φ is the soil oisture capacity function, and is referred to K(θ) below. Soil hydraulic paraeters The soil hydraulic paraeters S(θ), K(θ), and M(θ) are needed to be solved in the Richards equation. Here θ as the voluetric water content is a description of soil porosity. Its axiu value is equal to the porosity of the soil ediu. As an alternative paraeter, the saturation S(θ) can be used between 0 and : θ θr S( θ ) = () θ θ where θ s is the water content in the saturated condition [L 3 /L 3 ], and θ r the residual water content [L 3 /L 3 ]. Then Van Genuchten uses the epirical atheatical for, which frequently appeared in the publications [9]: S( θ) = n ( αϕ (3) + ) where and α are soil specific paraeters, and n = /., n, and α are Van Genuchten paraeters. The hydraulic conductivity of water K(θ) changes with the voluetric water content θ. Van Genuchten has proposed a forula: / / K( ) = K[ S( )] ( S( θ ) K θ θ s r / / ( θ θr) θ θ r ) = ( θs θr) θs θ (4) r Here the paraeter K represents the conductivity of the saturated soil. The following forulation is iproved Richards equation with water content θ: θ ( θs θr) nα( αh) M ( θ ) = = n ϕ + ( + αϕ ) n (5)

3 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp Nuerical odel In this paper, the ixed for of the Richards equation is discretized using a spatial discretization ethod for polar and non-polar parabolic equation in one space variable created by Skeel and Berzins [7]. This ethod considers the syste of quasilinear partial differential equations: C C C C H xtc,,, = x x f xtc,,, + S xtc,,, x t x x (6) x For a x b, where H is a diagonal atrix with non-negative entries and is non- -negative. For parabolic equation like Richards equation, ust be 0,, or, corresponding to slab, cylindrical, or spherical syetry, respectively. The boundary condition is: C pxtc (,, ) + qxtc (,, ) f xtc,,, = 0 at x = a, b (7) x According to eq. (6), the Richards equation is transfored to: / / n ( θs θr) nα( αh) u θ θr θ θr = x K n + ( αϕ ) t x θs θ r θs θ + r / / u θ θr θ θr K x θs θ r θs θ r Here boundary condition is q = 0, ; p = 0, C; and C = constants. We can easily use paraeters of eq. (6) to express Richards eq. (8). n C ( θs θr) nα( αh) H x,, t C, = x n ( ) + + αϕ / / C θ θ r θ θ r f x,, t C, = K x θs θr θs θr (9) / / µ θ θ r θ θ r K x θs θr θs θr C S x,, t C, = 0 x Considering the a spatial esh a = x 0 < x < < x j = b, we can seek difference schee entioned by Skeel and Berzins [7] that is accurate as possible for the spatial case f(x, C, C/ x) = F(x, C) C/ x. For Richards equation we consider it can be expressed as two first-order partial differential equations: (8)

4 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture 560 THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp C C = F( x, C) f x, C, x x ( x v) C C C = x H x, C, f x, C, x x t x Then we asseble the eleent equations into difference equations by eliinating the unknown values of f(x, C, C/ x) at esh points. Finally, the solution is gotten by Shapine and Reichelt ethod [8]. Those are ethods used in calculating partial differential equation in MATLAB, then we use finite eleent ethod to calculate Richards equation. Application Siulation Based on experiental data in bio-retention systes in Beijing, the spatial and teporal distribution of oisture on pressure head, hydraulic head and water content were siulated by above Richards odel. In this case, soil properties α = 0.035, n =.5856, K = c/h, θ r = , θ s = The initial condition is h(z, 0) = 000 c, and the lower boundary condition is 75 c. T = 4 hours. Figures -3 show the stiulation results. (0) Figure. Spatial and teporal distribution of oisture in bio-retention systes when infiltration rate is 0.05 c/h; (a) pressure head, (b) hydraulic head, and (c) water content (for color iage see journal web-site) For fig. (a), when infiltration happens, pressure head is at a stable value of 75 c. Then it begins to rise rapidly and stops at 000 c in about 60 c depth. Fro the depth of the node to the lower boundary, pressure head increases with depth and decreases with tie. For fig. (b), the distribution of hydraulic head is uch ore like to pressure head. For fig. (c). Fro the depth of the node to the lower boundary, water content decreases with depth and increases with tie, which is opposite to the distribution of pressure head and hydraulic head. Figures and 3 represent the distribution of pressure head, hydraulic head, and water content when infiltration rate adds to 0. c/h, 0. c/h. The values of pressure head and hydraulic head decrease faster with tie while the values of water content increase faster

5 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp when infiltration rate increases. In general, the infiltration processes of three soil hydraulic paraeters in figs. and 3 are uch ore like to fig.. Figure. Spatial and teporal distribution of oisture in bio-retention systes when infiltration rate is 0. c/h; (a) pressure head, (b) hydraulic head, and (c) water content (for color iage see journal web-site) Figure 3. Spatial and teporal distribution of oisture in bio-retention systes when infiltration rate is 0. c/h; (a) pressure head, (b) hydraulic head, and (c) water content (for color iage see journal web-site) Discussion The Richards odel provides a good way to stably stiulate the distribution of the pressure head, hydraulic head and water content in sall scale like bio-retention systes. At the sae tie, by coposing the Richards equation and nuerical odel, the change of pressure head, hydraulic head, and water content in bio-retention systes with tie under different rainfall events could be stiulated directly. So the Richards odel entioned in this paper can be applied to stiulate the igration of the water in bio-retention systes. It is obvious that different soil has different oisture igration process, which causes different surface runoff and different groundwater recharge. Future research should stiulate oisture igration under different bio-retention systes with different soil texture. As bio-retention systes with depression storage can help reduce rainfall runoff and increase in-

6 Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture 56 THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp filtration capacity, city designers and planners can create storwater anageent landscapes using various kinds of bio-retention systes. Conclusions The Richards odel is used to analyze the spatial and teporal distribution of oisture in bio-retention systes based on experiental data in Beijing. The ain conclusions can be drawn as follows. The Richards odel provides a good way to stably stiulate the distribution of the pressure head, hydraulic head, and water content based on experiental data in bio-retention systes in Beijing. Fro the depth of the node to the lower boundary, the values of pressure head, hydraulic head increase with depth and decrease with tie based on the Richards odel. The values of water content decrease with depth and increase with tie, which are opposite to the distribution of pressure head and hydraulic head. The study results of the spatial and teporal distribution of oisture in bio-retention systes will provide guidance for urban water resources allocation and anageent. Acknowledgents This work was supported by the Project of National Natural Foundation of China (No , , ), the Funds for Creative Research Groups of China (No. 5003), the National Basic Research Progra of China (No. 00CB9504), and the Specialized Research Fund for the Doc Progra of Higher Education (No ). References [] Yang, X. H., et al., Coprehensive Assessent for Reoving Multiple Pollutants by Plants in Bioretention Systes, Chinese Science Bulletin, 59 (04), 3, pp [] Mei, Y., et al., A New Assessent Model for Pollutant Reoval Using Mulch in Bioretention Processes, Fresenius Environental Bulletin, (03), 5a, pp [3] Mei, Y., et al., Phosphorus Isotheral Adsorption Characteristics of Mulch of Bioretention, Theral Science, 6 (0), 5, pp [4] Mei, Y., et al., Therodynaic and Kinetics Studies of the Adsorption of Phosphorus by Bioretention Media, Theral Science, 6 (0), 5, pp [5] He, J., et al., The Inversion of Soil Moisture by the Theral Infrared Data in Liaoning, China, Theral Science, 7 (03), 5, pp [6] Alejandro, R., Richards Equation Model of a Rain Garden, Journal of Hydrologic Engineering, 9 (004), 3, pp. 9-5 [7] Skeel, R. D., Berzins, M., A Method for the Spatial Discretization of Parabolic Equations in One Space Variable, SIAM Journal on Scientific and Statistical Coputing, (990),, pp. -3 [8] Shapine, L. F., Reichelt, M. W., The Matlab Ode Suite, SIAM Journal on Scientific Coputing, 8 (997),, pp. - [9] Celia, M. A., et al., A General Massconservative Nuerical Solution for the Unsaturated Flow Equation, Water Resources Research, 7 (990), 7, pp Paper subitted: March 5, 03 Paper revised: April 9, 04 Paper accepted: July, 04