Case study of optimizing Low Impact Development Strategy in School: Allocation by the Drainage Distance

Under the concept of urban stormwater management, integrated efficiency of runoff and pollutant control via low impact development facilities came into focus, whereas a few specific descriptions are provided to quantify the strategy of these facilities, including the selection patterns of the locations and sizes and the connection of LID facilities and the drainage system, which is of important for the evolvement of LID strategy. Based on the weighted multi-object goal, the optimizing LID strategy reduces of runoff, pollutant, peak flow, and flooding time under required precipitation conditions, respectively. This paper concluded LID strategy under local requirements and tougher conditions in the aspect of the size and drainage distance of each facility, a new quantified index of locations of specific types of facilities. Then interpret the adjustment pattern based on the feature of rainfalls by correlation analysis. Correlation results show that the drainage distance of green roofs and the storage tank correlated to stormwater management indicators while the retention facilities did not, and the correlation respectively weakened and stronger when storm intensity increased, helping designers to establish better LID planning for schools.


Introduction
The rapid expansion of impermeable surfaces in Chinese cities has prompted the adoption of a stormwater management approach focused on mitigating urban flooding and non-point source pollution caused by increased runoff."Sponge city" construction has been promoted, encompassing a range of low impact development (LID) techniques aimed at maintain the status of the original hydrological effect before urbanization.In practice, the goal is to integrately reduce the total runoff, pollutants, ponding area, and the peak flow in drainage.Optimizing the installation and management of LID facilities and their combination is of great necessity but not sufficient.Researchers have developed several hydrological models, e.g., stormwater management model (SWMM), to assist in previewing the outcome of the LID planning in research area when the variations of hydrological and hydraulic characteristics can be mastered.Using SWMM-based analysis and the scenario analysis, the LID strategy in site-scale for multi-objective optimization has encouraged and developed [1,2,3] , and they revealed the runoff can be well controlled by proper strategy, which means the patterns to choosing locations, sizes, and combination of LID facilities, but most of planning studies focus on providing general parameters such as the ratio of impervious area and storage volume.Some researches indicated the location of LID facility, particularly its position relative to the drainage connections with different type of facilities, will impact on the runoff control efficiency due to the chain effect [4,5] , whereas the representative of these features has not been well concluded.
Under the multi-target of maximizing the integrated efficiency of runoff control, flooding reduction, and pollutant removal, this study aims to optimize the design strategy of LID facilities arrangement in the manner of exploring the relationship between the location and the drainage distance of each type of LID facility in school project.Three normally used green infrastructures (GI) and grey infrastructure were investigated separately when features of precipitation were investigated as influence variations for they determine the threshold of runoff formation.

SWMM-based model of school
A SWMM-based model was adopted in an intensive layout school as the model sample in a 3.5 hm 2 area in Shenzhen, China.Shenzhen has a high frequent rainfall with annual average volume of 1924.7 mm and 142 rain days.The school is newly-build who has a primary goal is to reduce runoff at least 72%.The model was constructed with 44 km of links, 45 nodes, 1 outlets, and 53 sub-catchments.Some influential features are summarized as: 1) a large ratio of impervious area such as athletics tracks, formatting a high inflow to connecting point; 2) outer-ring green space next to the main road, being beneficial to introduce the runoff on the road; 3) inner garden with poor infiltration capacity.And school-project has as a centralized detached architect surrounded by the beltway and few greenery coverage.As aforementioned, the GI-predominant strategy and grey infrastructure-predominant strategy were applied to the school.

LID facilities
Three types of GI and the storage tank are available: 1) Green roof (GR) with 150 mm loam covered by dense plants; 2) Concave-down greenbelt (CG) with 300 mm loam, which is 50 mm lower than the adjacent road and covered by smallish grass; 3) Rain garden (RG) with 600 mm loam and 300 mm drainage layer linked with a gutter inlet, which is 300 mm lower than the adjacent road.LID strategy of School SX is designed as green-grey strategies where the sizes of LID facilities have the access to make most of greenbelts, but for school SG, only green roof and storage tank is available because of the poor infiltration condition.

Precipitation conditions
In this study, simulative single-peak rainfall events and several measured precipitations were investigated, wherein the former was designed using the Chicago Approach by the recurrence period of 1a, 3a, 5a, 10a, and 20a [6] .Four actual recorded rainfall events in Shenzhen are also investigated to reveal the influences of precipitation sequence, of which the total precipitation are 31.8mm, 203 mm, 76.5 mm, and 145 mm (Fig. 1), refer to the storm strength of the local require, a torrential rain, and the daily precipitation recurrence period of 1a and 2a, respectively.

Drainage distance index
In this study, the drainage distance (D) denotes the distance between the LID facility and the outfall of its drainage area.In order to more precisely describe the arrangement of LID facilities and identifying optimal locations when implementing a strategy involving multiple facilities, the drainage distance index (R d ) of one LID strategy was defined as the sum of all LID facilities using their corresponding area ratio to local subcatchment (A) as weight, as shown in Equation.1.

Indicators of LID planning strategy
Based on the requirements of "Sponge City technical guideline" and local regulations, four quantitative indicators are used to evaluate the capability of stormwater management of the LID strategies: Firstly, the strategy contains no LID facility was conducted by SWMM to obtained the values of total runoff flow, the peak flow of the link to the outfall, the pollutant accumulation, and the total flooding time of all nodes as the baseline values.Then the reduction rate of runoff (R rf ), the peak flow(R pf ), pollutant (averaging when more than one pollutant was set, R p ) , and the flooding (R f ) were respectively calculated as the stormwater management indicators between corresponding values of the testing LID strategy and the baseline.Comparing the multiple goals of sponge city construction and the demand hierarchy, the weights of indicators was built.Indicators are divided to water quantity indicators and water quality indicators, the former includes R rf , R pf , R f , and the latter includes R p as the average removal efficiency of three pollutants as chemical oxygen demand (COD), suspended solid (SS) and NH 4 -N.Considering the critical concern of inundation issue under the background of locating at a pluvial city, the total weight of water quantity indicators was set as 0.700 and the weight of water quality was set as 0.300 refer to previous researches [7] , among them, the weight of R rf was set as as 0.35 while the weight of the other two indicator was set as 0.175 since the R rf is the predominate comprehensive index of the sponge city design discipline in Shenzhen.

Simulation and data analysis
The input file was produced including basic information (e.g., climate condition, geographic information, infiltration factors, land use features) and control variables (e.g., rainfall information, LID location and size).Evaluation indexes were calculated and recorded using R package "swmmr" and SWMM (US EPA, version 5.2).Under each precipitation condition, over 1000 layouts of LID facilities were simulated to optimized for the best layout for the integrated indicators through particle swarm optimization (PSO) then further to obtained the corresponding outcomes of the drainage distance and evaluation indexes.The simulation outcomes were applied for Spearman correlation analysis and significance testing (p presents the significance level) after Shapiro-Wilk normality test, using R (version 4.1.3)program.

Optimized allocation of LID strategy
To find the best strategy for LID facilities on the integrated goal of weighted indicators, PSO optimization was obtained under five actual recorded rainfall conditions, as shown in Table 1, Pareto optimizing strategies of all the rainfall conditions are listed.In all these optimized strategies, R rf , R pf , R p , and R f respectively achieved over 89%, 86%, 86%, and 97%, which is above the local requirements.As a matter of fact, the total size of GI decreased with the rainfall intensity increase while the storage tank is always located downstream near the outfall.Comparing the size of different GI types, the total size of GR sharply decreased by 22.18% but RG had a 2-fold increase, suggesting the volume retention of the runoff became the main issue above heavy rain.Compared to other reports, it is remarkable that the precipitation of all the rainfall events in this study is quite high due to the climatic feature in Shenzhen [8] .Meanwhile, the small-scale and negative features (e.g.impervious ground) of school projects should be considered when determining the suitable size of LID facility, thus, the size of LID facilities would be larger than previously reported [9] .Figure 2 visually shows the variation in the allocation of optimized LID facilities.It reveals the optimized location of LID facilities shifted to the direction where the drainage distance is long with the total precipitation increases, but no clear difference in the catchment distance.For example, RG allocation significantly shifted from downstream to the middle area along with the size increase while the upstream GR area narrowed.Precisely, the quantile of the R d of RG increased from [40,50] to [90,100] while the R d of RG decreased from [90,100] to [60,70] then increased to [90,100] via the total precipitation increased, but the R d of GR sharply decreased from [70,80] to [10,20].Furthermore, Fig. 2 indicates that the dispersion of LID facilities also increased, resulting in the collection of more runoff and an improvement in the disposal ratio of pollutants.The movement of retention GI confirms the pattern that the runoff occupied the main issue via the rainfall intensity increase.In brief summary, a LID strategy with large GR at upstream, over 20% of RG combined with a storage tank at downstream of drainage system would met the local requirements.For daily rainfall events, 1a would be the threshold when the strategy contains smaller GRs, decentralized retention GIs with a rearward storage tank is more efficient.

Correlation analysis
Under simulated rainfall events, the correlation analysis between the Rd of each LID facility type and the indicators are applied to summarise a pattern for their arrangement.Fig. 3 illustrates that GR is the only GI type that always has a significant positive correlation (coefficient of 0.36-0.58)withR f while the drainage distance while RG and CG show irrelevant to stormwater management indicators, suggesting a foreseeable capability of GR on reducing or delaying the formation of runoff in the research area, although such influence is limited due to the minor retention volume of GR.The two retention GI, RG and CG, also have positive correlations with water quantity and quality control indicators under 1a rainfall, but turn to be negative and then absence of correlation when the rainfall strength increases.As for actual recording rainfalls, GR also has a significant positive correlation with R p , R rf , R pf , and R f under conditions of rainfall 1 and 3 (coefficient ~0.3), which are approach conditions to the designing, but all types of GI absent correlation when the precipitation intensity increase (rainfall 2 and 4).
In the meantime, the correlation between the R d of the storage tank and all four indicators became evident whatever the strength of the rainfall and the coefficients increased with the recurrence period or the total precipitation.When the recurrence period of 20a, the coefficients are 0.95, 0.97, 0.95, and -0.82, respectively for R p , R rf , R p , and R f .Similar variation was found under the conditions of actual recorded rainfalls.

Figure 3.
Pearson coefficient between the drainage distance index and stormwater management indicators under actual recorded rainfall conditions.Based on the correlation analysis, GR is more favorable to be set at the area near the start of the drain system while the allocation of RG and CG is more complicated.The difference between them is due to the different mechanisms of runoff reduction on them as GR has large potential site selection with lower unit control capacity but RG and CG do quite the contrary, this raises the threshold of the capacity of GR on stormwater management to take maximum of it by additive effect, in accordance of a former research [10] .Another possible reason for the absence of correlation is the potential location of RG and CG in this school project is relatively small and separated from the main impervious area, avoiding their collection of most runoff.The strong correlation between the R d of the storage tank and indicators is consistent with the general understanding that maximum utilization of reserving abundant cushion volume for intense rainstorms at the drainage downstream.However, the strong negative correlation to R f indicated the waterlogging risk would increase along with the increasing elapsed nodes with the storage tank being located too far from the corresponding catchment area.

Conclusion
This study investigated the optimized LID strategy of allocation and size of different types of GIs using SWMM and PSO in a school project in Shenzhen.According to local requirements, the optimized LID strategy contains large GRs located upstream, smaller RGs, and storage tanks located downstream.However, the strategy of narrowed GRs and decentralized retention GIs with a rearward storage tank is more efficient for heavier rainfalls.In this case, the daily rainfall of 1a was to be the threshold among them.The above conclusion agreed with correlation analysis that found the drainage distance positively correlated to the stormwater management indicators, but the correlation is absent on RG and CG.This result indicated that there is no simplified strategy to arrange LID facility locations when the rainfall has changeable features and provides a holistic guideline for the selection of optimal LID strategy for designers.

Acknowledgments
Authors wishing to acknowledge assistance from colleagues of China Construction Science & Technology Group Co., Ltd by technical designing support of the paper.

Figure 1 .
Figure 1.Hyetograph of the recorded rainfall events.

Table 1 .
Area ratio or of GIs and drainage distance of ST in optimized strategies (unit: % or m).