With COMSOL Multiphysics the users can easily extend models for one type of physics into multiphysics models that solve coupled physics phenomena. The user can access the power of COMSOL Multiphysics as a standalone product  through a flexible Graphical User Interface  or by COMSOL Java API, a Java-based interface. In the COMSOL Java API, models are accessed through the model object, which contains all algorithms and data structures for a COMSOL model. The COMSOL Desktop also uses the model object to represent a model. This means that the model object and the COMSOL Desktop behavior are virtually identical but the model object through COMSOL Java API allows more flexibility and to overcome shortcomings of the COMSOL Desktop in customizing a specific problem of interest. Methods on a model object are used to create, modify, and access the model. The model object provides a large number of methods, including methods for setting up and running sequences of operations to create geometry, meshes, and for solving the model. The top-level methods just return references that support further methods. At a certain level the methods perform actions, such as adding data to the model object, performing computations, or returning data. Thus, there is a potential to use COMSOL Java API in customizing a specific problem of interest such as the hydrological process of a soakaway rain garden. In Section 3.0, the important inner details on modeling a soak-away rain garden using COMSOL Java API is presented. In Section 4.0, the graphical user interface that is used to collect the user specific inputs, which are used inside the code  written using COMSOL Java API, of a soak-away rain garden is presented.Once the inner details were implemented taking into account the codes discussed in Sections 3.1, 3.2, 3.3, and 3.4, using COMSOL JAVA API, a graphical user interface was developed as shown in Figure 4. The interface permits the users to specify the dimensions of the soak-away rain garden, specify the model parameters, input the time series of the stormwater runoff, define the simulation period, define the meshing size, visualize the simulated results, and modify the default options.

As shown in Figure 4, the section for “Garden Dimension” allows the users to input the dimensions of the soak-away rain garden. The width, length, depth of filter media , ponding depth , and depth to ground water table that is defined from bottom of the filter media, are specified in meters. These values and some model generated intermediate values,nft hydroponic which are based on these values, are used as JAVA variables at the appropriate places as discussed in Section 3.1. The section for “Model Parameters” allows the users to input the model parameters of the soak-away rain garden. In this section of the interface, the saturated hydraulic conductivity of the filter media , which describes the ease with which water can move through pore spaces, saturated hydraulic conductivity of the in-situ soil , porosity of the filter media and porosity of the in-situ soil are specified. These parameter values are used by the modeled physics, which is the Richards’ equation, as discussed in Section 3.2. In addition, the user specified saturated hydraulic conductivities for filter media and in-situ soil are used to compute the saturated hydraulic conductivities in X, Y and Z-axis directions if a proportional an-isotropic tensor is specified through the preferences menu. The section for “Runoff Data” allows the users to input the stormwater runoff to the soakaway rain garden. The “Open” dialog box, which becomes visible when the “Open” button is clicked, allows the users to locate the time series data of the stormwater runoff. The time series data is a “tab” delimited text file that has the required data in two columns. The first column represents the time of the observation in seconds at equal intervals and the second column represents the runoff values in m3 /s. Often times, the time series of stormwater runoff  is obtained from a design hyetograph which is the time distribution of rainfall during a storm using a model  that uses the rainfall-runoff algorithm. The time series of stormwater runoff data is used to set the boundary condition as discussed in Section 3.4. The section for “Simulation Period” allows the user to input the start and end time of the simulation. The inputs are specified in seconds. The time step of the simulation is computed based on the user specified time series of stormwater runoff data. As mentioned previously, the stormwater runoff data should be at equal intervals. The section for “Mesh Size” allows the users to split the domains into smaller sub-domains. As shown in Figure 4, the “simulation” button allows the users to perform the simulation. The model performs the simulation based on the user specified inputs that are discussed so far and any additional inputs specified through the preferences menu.

The preferences menu allows the users to change some of the default settings that are used during the simulation. As an example, the preferences menu allows the users to change the proportional tensor of saturated hydraulic conductivities for filter media and in-situ soil. The successful execution of the model allows the users to visualize the simulation result such as hydraulic head, ponding depth: time series of the ponded water during the simulation period, overflow rate: time series of the overflow during the simulation period, vertical ex-filtration: time series of the water soaked away through bottom, horizontal ex-filtration: time series of the water soaked away through sides.The design of soak-away rain gardens involves water quality. Thus, the establishment of a design hyetograph for the design of soak-away rain gardens, specifically, requires data on intensity-duration-frequency  values for relatively frequent storms such as 3-month ARIs that carry up to 90% of the total load on annual basis. As underscored in the literature, to date, there are few methods available for the establishment of design hyetographs using IDF data. In this paper, the alternating block method, which represents an event of a selected return period both for the selected duration of the event and for any period within this selected duration, is used in developing a design hyetograph from an IDF relationship of Singapore. A storm duration of 720 min was considered. Considering an event of 720 min of the 3-month ARIs, a design hyetograph for 3-month ARIs built-up using this method represents a 3-month ARI event both for the 720 min total duration and for any period  within this duration centered on the maximum block. The design hyetograph produced by this method specifies the rainfall depth occurring in n successive time intervals of duration Δt over a total duration of 720 min = nΔt. Duration Δt is often determined by the finest resolution of the hydrological model that is used to generate the design hydrograph, the time distribution of discharge. The hyetograph to represent a 3-month ARI event of 720 min duration is shown in Figure 5 for a duration  of 6 min which is the finest resolution of MUSIC  model which was used to generate the hydrographs for different urbanized  catchment sizes varied from 100 to 250 m2 . The time series of stormwater hydrograph was used to set the boundary condition as discussed in Section 3.4. To understand the variation of horizontal ex-filtration with the in-situ hydraulic conductivity and the surface area of the soak-away rain garden , the simulation was carried out for different values of in-situ hydraulic conductivity and the surface area of the soak-away rain garden . The insitu hydraulic conductivity was varied from 10 mm/hr to 50 mm/hr, typical range in Singapore.

The surface area of the soak-away rain garden  was varied from 6% to 15%. The width and the length of the soak-away rain garden were assumed to be of the same size. The saturated hydraulic conductivity of the filter media was set to 200 mm/hr, the maximum value expected in Singapore. The depth to groundwater table was set to 0.5 m.In catchment hydrology, in practice it is not feasible to measure a desired hydrological variable for every possible hydrological condition mainly due to financial constraints. This limitation, among others, has promoted the application of mathematical models, whose basic principle is the process of solving physical problems by appropriate simplification of reality, in the field of catchment hydrology, specifically in ground and surface water hydrology, to solve many hydrological problems. Hydrological process, such as overflow volume, average vertical ex-filtration rate and horizontal flow coefficient, of a soak-away rain garden, is one of those hydrological problems. Soak-away rain gardens, nft system shallow, landscaped depressions commonly located in parking lots or within small pockets in residential areas, receive stormwater runoff, attenuate surface water and enable it to percolate into the surrounding ground. As catchments become urbanized due to population growth, the impervious surfaces created by buildings and pavements cause rainwater to flow quickly over the landscape. To mitigate the adverse impact of urbanization such as increased flooding and depleted groundwater recharge around the world, several best management practices, in other words, green infrastructures, have been practiced, and soak-away rain garden is one of them. Despite the rapid acceptance of soak-away rain gardens throughout the world by water managers and land-use planners, detailed hydrologic performance information and related hydrologic design guidelines of soak-away rain gardens are not currently available for many regions including Singapore. On the other hand, to have a rapid assessment of soak-away rain gardens on a range of potential hydrologic conditions , detailed hydrologic performance information and related hydrologic design guidelines of soak-away rain gardens from model simulation results need to be rendered into easy to use look-up charts or hydrologic design charts that are specific for local conditions. However, it is not feasible to model for every possible hydrological condition due to resource constraints and the continuous nature of those possible hydrological conditions. Therefore, a need exists to extrapolate and interpolate information from the available model simulation results. In addition, there is also a need to assess the likely hydrological impact of future system response. Therefore, it is the objective of this study to establish regression equations on hydrological processes, specifically on overflow volume, average vertical ex-filtration rate and horizontal flow coefficient, of a soak-away rain garden, based on simulated results of a mathematical model using COMSOL Multiphysics under the possible hydrological conditions.

To solve flow in variably saturated porous media, it is necessary that appropriate boundary conditions are specified. From a mathematical standpoint, the application of boundary conditions ensures that the solutions to the problems are self-consistent. In this study, the following boundary conditions are identified as appropriate. As shown in Figure 2, which represents the frontal view of cut-plane  A-A of Figure 1, the top surface of the rain garden is a rainfall-runoff boundary, a non-steady-state flow condition typical of urban stormwater runoff. The external side boundaries do not allow water to flow in or out of the area of influence, implying that the chosen area is large enough that it does not affect the flow performance around the rain garden. The bottom boundary of the area of influence is specified by a hydraulic head corresponding to an assumed groundwater table level. When water starts to pond, the boundary condition at the top surface of the rain garden becomes a hydraulic boundary. Therefore, there is a need to be able to switch the top surface of the rain garden from flow to hydraulic head. The switching was done using COMSOL Java API, a Java-based interface. The initial condition was set to hydrostatic condition. In other words, above groundwater table, the suction is equal to the distance above groundwater table.To understand the relationship between the dependent variable, overflow volume, and the independent variables, as shown in Figure 4, the graph of overflow volume versus the surface area of the soak-away rain garden  was plotted. The overflow volume is expressed as a % of total runoff volume. For this graph, the saturated hydraulic conductivity of the filter media and the depth to groundwater table were set to 100 mm/hr and 0.5 m, respectively. The graph also shows the variation with the saturated hydraulic conductivities of the in-situ soil. The saturated hydraulic conductivity of the in-situ soil varies from 10 mm/hr to 50 mm/hr.