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Volume capture ratio of annual rainfall (VCRAR) is the key parameter of low-impact development (LID) facilities design, which is significantly affected by the rainfall event division method. However, there is no universal agreement on how to determine an optimal division method to achieve it. A modified minimum inter-event time (MIT) method based on MATLAB software was proposed to find an optimal MIT value. The result showed that the optimal MIT value in Beijing is 200 min based on the daily rainfall data from 1987 to 2016, and the annual average rainfall events were 34.2 with an average rainfall depth of 13.7 mm. Taking bioretention facilities as an example, the errors of design VCRAR under different MIT values were compared based on a Stormwater Management Model (SWMM). The results showed that when design VCRAR was ≤50, 55–60, 60–75, 75–80 and >80%, the optimal MIT value for LID facilities design was 60, 120, 200, 360 and 1,440 min, respectively. Therefore, the optimal MIT should be flexibly selected with the changing of design VCRAR, to ensure that LID facilities meet the design goals.

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  • Combining the MIT with threshold statistical methods based on MATLAB software to obtain an optimal MIT value.

  • Comparing the effect of different MIT values on the design VCRAR based on SWMM.

  • RER, ERD and MERDR were analyzed under different MIT values.

  • The different optimal MIT values of different design VCRARs were obtained in Beijing.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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assessment, bioretention facilities, minimum inter-event time, SWMM, volume capture ratio of annual rainfall
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Rapid urbanization has sharply increased impervious urban surface area, as well as dramatically increased the pollution load of stormwater runoff (You et al. 2019). Low-impact development (LID) can effectively alleviate stormwater runoff pollution (Shrestha et al. 2018), and the volume capture ratio of annual rainfall (VCRAR) is one of its critical design parameters. Design VCRAR is affected by facilities operation conditions, rainfall depth, and rainfall event distribution and statistical analysis which is often based on more than 30 years of continuous rainfall events except for those rainfall depths less than 2 mm. Rainfall event distribution characteristics can be determined when rainfall events are divided by the minimum inter-event time (MIT) method. Meanwhile, rainfall event division methods will greatly affect the rainfall depth of design VCRAR (Yang et al. 2020). MIT often draws from hydrological analysis methods or selected from empirical parameters for rainfall events, but the eigenvalue of which is affected by many factors, such as climate, runoff coefficient and hydrological conditions. The urban drainage manual (manual) (China Architecture Publishing & Media Co. Ltd 2017) proposes that continuous rainfall intensity is not less than 120 min and 0.1 mm/min as the threshold for the division of rainfall events (MIT = 120 min). However, the rainfall event division method described in the construction guideline of sponge city via LID (guideline) (Ministry of Housing and Urban-Rural Development 2014) is that rainfall events between two adjacent 20:00 (MIT = 1,440 min) are the same rainfall event. The manual and guideline, therefore, propose different MIT values, which leads to differences in the design VCRAR.

There are several factors that affect the rainfall events division results via MIT. Dunkerley (2015) analyzed 10 years of rainfall data from Fowler Gorge in Australia and quantitatively characterized rainfall intermittency in rainfall events (Intra-event rainfall intermittency, IERI) and chose eight different MIT values (all < 1,400 min) to divide the rainfall events. Short rainfall duration events accounted for a large portion of the total rainfall events under the lower MIT values. So, the periods without rainfall of intra-rainfall events have an important effect on the rainfall event division results. Balme et al. (2006) analyzed 30 years of rainfall data of the Sahel to generalize rainfall event characteristics. Results showed that half of the total rainfall events' rainfall duration was <4 h with rainfall intensity exceeding 35 mm/h, and 85% of annual rainfall depth was produced by 30–50 major rainfall events annually. Short duration and, high-intensity rainfall will increase the flooding risk. Moreover, a combination of high slope terrain and the above factors will increase the degree of flooding damage. Al-Qallaf et al. (2020) studied the impact of extreme rainfall temporal variability in Kuwait and found that extreme rainfall and flash flood risk increased with a decrease in rainfall events.

There are many studies on the rationality for determining the MIT value. Zhang et al. (2019) adopted an MIT value ranging from 60 to 1,440 min for rainfall events division and found that rainfall event division, as proposed in the guideline, had a large error when MIT = 1,440 min. Therefore, they recommended that the MIT value for bioretention facilities design should be between 60 and 360 min. MIT values have significant influence on the drain time of bioretention facilities. Li et al. (2019) found that the MIT for a bioretention facility was approximately 0.5 times the facilities drain time, which also affects the water quality of bioretention facilities. Guo (2020) proposed that facilities like bioretention core designs should balance residence and drain times, the longer the drain time, the better the water quality. There also have been several studies on the drain time variation of bioretention facilities under different conditions. Li et al. (2022) found that bioretention drain time under different experimental conditions varied from 10 to 140 min and dry time varied from 6 to 47 h. There are many other methods used to determine MIT value, such as through mathematical statistics, for example, Molina-Sanchis et al. (2016) used regression analysis of runoff time and three rainfall relevant parameters and found that the optimal MIT was 60 min. Other research has focused on the relationship between rainfall events and the MIT value. Dunkerley (2008) summarized the impact of MIT values on rainfall events based on 5 years of rainfall data in an arid area, the results showed that as rainfall events decreased from 550 to 118, the MIT value increased from 15 to 1,440 min. So, the MIT division method is greatly affected by rainfall events and the rainfall capture volume of LID facilities.

Above all, there is still a knowledge gap on the division method of rainfall events for different stormwater management goals, and the MIT between rainfall events has an important impact on the VCRAR. To address these key VCRAR-related challenges, we (i) modified the MIT method with threshold statistical methods based on MATLAB software to obtain an optimal value that the error between the design VCRAR and operational result was minimum with it; (ii) used the Stormwater Management Model (SWMM) to compare the effect of different rainfall event division methods on the VCRAR; and (iii) used bioretention as an example to evaluate the relationship of VCRAR and MIT value and determine the optimal design VCRAR under different MIT value based on SWMM. Therefore, a more comprehensive division method of rainfall events was investigated to minimize errors between the design VCRAR and practical operation effect.

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Rainfall events division via eigenvalue

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MIT effects on rainfall event division

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When record rainfall data are divided by different MIT values, the rainfall events distribution can be significantly different. The rainfall event division trend under different MIT values was shown in Figure 1. When an inappropriate MIT is selected, the same rainfall event (rainfall event 1, Figure 1) could be divided into two separate rainfall events, or different rainfall events could be combined into the same rainfall event (rainfall event 3, Figure 1). If the MIT value is longer, the probability of several adjacent rainfall events being divided into one rainfall event will increase, which will lead to a decrease in the total rainfall events, and ultimately, lead to an increase in design VCRAR rainfall depth (Figure 1). For bioretention facilities, there was little impact on rainfall events when MIT values were >6 h (Zhang et al. 2019). So, it is important to regulate the MIT value to find an optimal eigenvalue for LID facilities design.
Figure 1
Different MIT division conditions (Tsp is the time statistic parameter, min).
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Different MIT division conditions (Tsp is the time statistic parameter, min).

Figure 1
Different MIT division conditions (Tsp is the time statistic parameter, min).
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Different MIT division conditions (Tsp is the time statistic parameter, min).

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Rainfall event eigenvalue division method

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The MIT method is the most frequently used approach for rainfall event division. Previously, the MIT value was selected from empirical parameters which often led to a greater difference with the case original data. Therefore, how to determine the time of intermittent rainfall is very important. The manual method has a lower error than other approaches in the statistical process of rainfall events. So, combining the MIT method with the manual approach, which to determine an optimal MIT value is a sufficient first step. Firstly, the case original data are divided by the MIT, and the rainfall intensity should be <0.1 mm, while the rainfall duration is more than the division rainfall interval. Then, Tsp is gradually increased with the same rainfall interval (e.g., 10 min, Aryal et al. 2007), the total and effective rainfall events with rainfall depth of more than 2 mm under different Tsp are obtained. The eigenvalue is achieved when the total and effective rainfall events attain a statistically steady state and can be selected as the optimal MIT value for the rainfall events division.

The eigenvalue division method combined with the MIT method can be realized in the following steps: setting the rainfall interval as 1 h, then increasing it with the same increment, such as 1, 2, 3, … , n; taking the above rainfall intervals as MIT values; then obtaining total and effective rainfall events under different MIT values. The MIT can be more reasonably determined by analyzing the changing trends of total rainfall events and effective rainfall events. In this study, we used the error analysis of model simulated results and design values to determine the optimal MIT value. To achieve the optimal eigenvalue of the threshold division method, further analysis is performed with an equal increment of 10 min for the rainfall event division during the steady state period. The threshold division method analysis steps are shown in Figure 2 (e.g., Tsp = 120 min), and the explanations of the parameter were shown in Table 1.
Table 1

Parameters explanations of the threshold division method

ParametersMeaning
I The number of original rainfall data in sequence 
Tsp/min The rainfall events ≤120 min and the rainfall depth at any moment in the rainfall event <0.1 mm 
Stsp/min The time of the entire rainfall event 
ParametersMeaning
I The number of original rainfall data in sequence 
Tsp/min The rainfall events ≤120 min and the rainfall depth at any moment in the rainfall event <0.1 mm 
Stsp/min The time of the entire rainfall event 
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Figure 2
Analysis process of threshold division method.
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Analysis process of threshold division method.

Figure 2
Analysis process of threshold division method.
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Analysis process of threshold division method.

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Figure 3
Rainfall characteristics under different MIT values.
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Rainfall characteristics under different MIT values.

Figure 3
Rainfall characteristics under different MIT values.
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Rainfall characteristics under different MIT values.

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Determination the eigenvalue of rainfall events division

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Record rainfall data of Beijing from 1987 to 2016 were selected to analyze the rainfall characteristics under different MIT values. Both effective and average rainfall events decreased gradually with increasing MIT and coincided with a decreasing trend in average rainfall depth, which are shown in Figure 3. There were 734 effective rainfall events when MIT = 1,440 min, and 1,131 when MIT = 360 min. When MIT increased from 60 to 360 min, effective and average rainfall events decreased more quickly, but slowed down after MIT = 360 min. The increasing rate of average rainfall depth is greater from MIT = 60 to 360 min than other MIT change ranges and becomes lower after MIT = 360 min. Moreover, the higher the MIT value, the lower the effective and average rainfall events, the larger the design rainfall depth of each rainfall event.

The impact of MIT on rainfall event division result was shown in the Figure 4. Total and effective rainfall events were all declined with increasing MIT (Figure 4(a)). There are several changing steady state periods on the rainfall event curve (Different color bars in the Figure 4(b)), and which were greatly affected by the MIT value. Dunkerley (2015) proposed that design rainfall depth is closely related to total rainfall events. Statistical results with MIT value varying from 60 to 1,440 min are shown in Figure 4(a). With increasing MIT, rainfall events sharply declined, then reached an inflection point from 120 to 240 min. A similar trend occurred for the curve of effective rainfall events under different MIT values, but with an inflection point from 60 to 360 min. Effective and total rainfall events all decreased with increasing MIT, but effective rainfall events were lower than total rainfall events. These results are consistent with those in the literature review (Dunkerley 2008).
Figure 4
Rainfall events under different MIT values. (a)1–24 h, 1 h rainfall interval; (b) 60–360 min, 10 min rainfall interval; the boxes in the figure means the platform of the steady state).
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Rainfall events under different MIT values. (a)1–24 h, 1 h rainfall interval; (b) 60–360 min, 10 min rainfall interval; the boxes in the figure means the platform of the steady state).

Figure 4
Rainfall events under different MIT values. (a)1–24 h, 1 h rainfall interval; (b) 60–360 min, 10 min rainfall interval; the boxes in the figure means the platform of the steady state).
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Rainfall events under different MIT values. (a)1–24 h, 1 h rainfall interval; (b) 60–360 min, 10 min rainfall interval; the boxes in the figure means the platform of the steady state).

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To determine an optimal MIT value, further analysis was conducted with a 10 min time increment for MIT ranging from 60 to 360 min (Figure 4(b)). Five platforms appeared when MIT was 70–90 min, 130–140 min, 190–210 min, 220–230 min and 290–360 min, respectively, which means that rainfall events were not sensitive to MIT changes during these periods. Moreover, there was a sharp decrease when total rainfall events ranged from 60 to 270 min. The changing trends of rainfall events and MIT are consistent with the findings of Dunkerley (2015). Comparing the range of total and effective rainfall events, 70–90 min, 190–210 min and 130–140 min were selected as the alternative MIT value for the rainfall events division. Moreover, the MIT = 200 min is a boundary in the sharply decreasing position of total and effective rainfall events, after which total rainfall events tend to be a constant. Hence, the MIT threshold for rainfall events division is 200 min.

To obtain the impact of MIT on annual rainfall events. Rainfall event ratio (RER) is defined as the ratio of annual rainfall events to 30-years total rainfall events, and it was used to describe rainfall event inter-annual distribution differences. The RER can be calculated using the following formula:
(1)
where the TRE is the annual total rainfall events from 1987 to 2016, year; i is the sequence of record rainfall data.

To further estimate the impact of MIT on rainfall duration characteristics, we propose the effective rainfall duration (ERD), which can be defined by the total rainfall duration minus the accumulation time without rainfall in a year.

In order to analyze the impact of MIT on ERD distribution, an effective rainfall duration rate (MERDR) was proposed, which refers to the ratio of the accumulation of ERD less than the MIT value to the total ERD in 30 years' rainfall data. The MERDR can be calculated using the following formula:
(2)
where ERD is the effective rainfall duration, min; ERDM is the ERD less than the selected MIT, the MIT with 60, 120, 200, 360 and 1,440 min were selected; i is the year's order.

The effect of rainfall event division methods on VCRAR

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Runoff capture volume of bioretention
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Bioretention design runoff capture volume was calculated using the following formula:
(3)
where V is the rainfall capture volume of the bioretention facility, m3; is the ratio of bioretention area to a catchment area that usually takes 5–10%, which is 5%; P is the design rainfall depth, mm; F is the bioretention area, as the bioretention facility surface area is 0.25 m2, which means the F to be taken as 5 m2; is the runoff coefficient, reference to empirical values of urban comprehensive runoff coefficient, which is 0.65:
(4)
where VCRAR is the volume capture ratio of annual rainfall which is the ratio of controlled rainfall volume to total rainfall volume, %; n is the total number of years; R is the study region or projection annual average rainfall depth, which is the sum of daily rainfall depth which greater than 2 mm divided by n, mm; S is the daily rainfall depth of 30 years, mm; is the sum of daily rainfall depth which less than or equal to P, mm; is the sum of the sum of rainfall depth, which means the total number of rainfall events whose rainfall depth greater than P times P, mm.

The larger the design VCRAR, the larger the rainfall capture volume, and the higher the costs for construction. Xi et al. (2017) found that when VCRAR lies between 70 and 90%, its design rainfall depth is changing more markedly, which means that the cost–benefit ratio is higher. Thus, a broader VCRAR variation range (from 50 to 95%) was adopted, to determine the optimal design VCRAR. Then, Formula (3) was used to calculate rainfall capture volume with different MIT values and VCRAR (Table 2). These rainfall capture volumes were used as the storage capacity basis for calculating reservoir thickness.

Table 2

Simulated rainfall capture volume under different MIT values (m3)

MIT/minVCRAR/%
50556065707580859095
60 0.052 0.065 0.078 0.091 0.111 0.130 0.163 0.202 0.273 0.377 
120 0.059 0.072 0.085 0.104 0.124 0.143 0.182 0.221 0.286 0.403 
200 0.065 0.078 0.091 0.111 0.130 0.156 0.189 0.234 0.299 0.410 
360 0.072 0.085 0.098 0.117 0.143 0.169 0.202 0.247 0.312 0.449 
1,440 0.091 0.111 0.130 0.150 0.176 0.208 0.254 0.299 0.377 0.527 
MIT/minVCRAR/%
50556065707580859095
60 0.052 0.065 0.078 0.091 0.111 0.130 0.163 0.202 0.273 0.377 
120 0.059 0.072 0.085 0.104 0.124 0.143 0.182 0.221 0.286 0.403 
200 0.065 0.078 0.091 0.111 0.130 0.156 0.189 0.234 0.299 0.410 
360 0.072 0.085 0.098 0.117 0.143 0.169 0.202 0.247 0.312 0.449 
1,440 0.091 0.111 0.130 0.150 0.176 0.208 0.254 0.299 0.377 0.527 
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Bioretention model calibration and validation
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Taking bioretention facilities as an example, design VCRAR comparisons were processed under different MIT values. Bioretention models based on SWMM were built with different VCRAR, calibrated via eight typical rainfall events with rainfall duration of 60, 120, 180, 300 and 600 min, rainfall depth from 57.7 to 118.7 mm and other rainfall information as shown in Figure 5, then validated by one rainfall event. The SWMM model takes the Horton infiltration to simulate the bioretention facility infiltration process and the calibration results are shown in Figure 5. The relative errors of the simulated results and the measured data were between 1.63 and 16.55%. When rainfall depth is higher (e.g., rainfall depth is 100 mm), the relative error (RE) is negative, indicating that the model simulation results are larger.
Figure 5
Bioretention model calibration results.
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Bioretention model calibration results.

Figure 5
Bioretention model calibration results.
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Bioretention model calibration results.

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Nash coefficients (NSE) and coefficients of determination (R2) were used for analyzing bioretention model accuracy, and calculated using the following formulas:
(5)
(6)
where qobs,t is the experimental overflow volume, l; qsim,t is the simulation overflow volume, l; qave,t is the average experimental overflow volume, l; qave,s is the average simulation overflow volume, l.

The Nash–Sutcliffe efficiency coefficient (NSE) was 0.79 which demonstrates a favorable simulation effect, and the coefficient of determination (R2) was 0.84. The bioretention model was validated using a rainfall event with a rainfall depth of 75.54 mm and a rainfall duration of 60 min. The experimental total runoff volume was 169.6 l, while the simulated total runoff volume was 166.9 l, and the RE was 1.62%. So, the bioretention model accuracy is high enough to simulate VCRAR under different MIT values.

Bioretention model schematic diagram and parameters

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Bioretention cell with 500 mm × 500 mm × 1,000 mm (L × B × H) was designed, so as to achieve the key parameters to build and calibrated the bioretention model, the land type of which is an urban road. The design VCRAR goal of the bioretention cell is 70%. Specifically, the planting soil layer is composed of loam and sand mixed in a volume ratio 1:1 (H = 400 mm); the fill layer is sand and soil mixed in a volume ratio 1:1, (H = 400 mm); the drainage layer is filled with gravel (H = 100 mm); and the diameter of the perforated pipe is Ф = 20 mm. The bioretention in SWMM schematic diagram is shown in Figure 6.
Figure 6
Bioretention in SWMM schematic diagram.
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Bioretention in SWMM schematic diagram.

Figure 6
Bioretention in SWMM schematic diagram.
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Bioretention in SWMM schematic diagram.

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Structural layer parameters in the bioretention model are shown in Table 3, including vegetation volume, porosity, field capacity, conductivity and seepage rate as determined from the guideline (Ministry of Housing and Urban-Rural Development 2014) and SWMM User's Manual (Rossman 2015). Data on some model parameters were fine-tuned from previous research, including vegetation volume (Ekmekcioğlu et al. 2021), porosity (Ekmekcioğlu et al. 2021), field capacity (Hamouz & Muthanna 2019), conductivity (Hamouz & Muthanna 2019) and seepage rate (Yin et al. 2021).

Table 3

Parameters adopted in the bioretention model

LayerParametersValueParameter source
Surface Berm height/mm 200 Device 
Vegetation volume/% 0.18 Ekmekcioğlu et al. (2021)  
Soil Thickness/mm 400 Device 
Porosity/% 0.6 Ekmekcioğlu et al. (2021)  
Field capacity/% 0.2 Hamouz & Muthanna (2019)  
Conductivity/(mm/h) 30.0 Hamouz & Muthanna (2019)  
Storage Thickness/mm 200 Device 
Seepage rate/(mm/h) 1.0 Yin et al. (2021)  
LayerParametersValueParameter source
Surface Berm height/mm 200 Device 
Vegetation volume/% 0.18 Ekmekcioğlu et al. (2021)  
Soil Thickness/mm 400 Device 
Porosity/% 0.6 Ekmekcioğlu et al. (2021)  
Field capacity/% 0.2 Hamouz & Muthanna (2019)  
Conductivity/(mm/h) 30.0 Hamouz & Muthanna (2019)  
Storage Thickness/mm 200 Device 
Seepage rate/(mm/h) 1.0 Yin et al. (2021)  
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Changing characteristics of rainfall events under different MIT values

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Rainfall events division results under different MIT values

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RER inter-annual distribution differences under different MIT values were shown in Figure 7. The RER distribution with 30 years were changed from 0.92 to 7.86%, 1.09 to 6.81%, 1.28 to 6.70%, 1.63 to 6.12% and 2.26 to 4.52% when MIT was 60, 120, 200, 360 and 1,440 min, respectively. When MIT = 200 min, the RER difference between the maximum and minimum is about 7%. When the MIT = 1,440 min, RER is almost evenly distributed. Furthermore, the RE of RER was decreased with increasing MIT. When the MIT was 60, 120, 200, 360 and 1,440 min, the average RE of RER was 0.53, 0.48, 0.42, 0.35 and 0.18%, respectively, which indicates that the inter-annual distribution difference declined with MIT increased. So, the larger the MIT value, the lower the difference in the RER distribution.
Figure 7
RER with different MITs (1987–2016).
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RER with different MITs (1987–2016).

Figure 7
RER with different MITs (1987–2016).
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RER with different MITs (1987–2016).

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To further estimate rainfall duration characteristics under different MIT values, ERD was investigated. ERD under different MIT values shown in Figure 8, shows that it can be found that the MIT value has a great effect on ERD and rainfall events. For example, when MIT was 60 min, most ERD was less than 1,000 min, a similar result to when MIT = 120 and 200 min. However, under higher MIT values (e.g., MIT = 1,440 min), more than 100 rainfall events' ERD exceeded 1,000 min. So, the rainfall events were decreased with longer MIT values, but their ERD was increased.
Figure 8
ERD under different MIT values.
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ERD under different MIT values.

Figure 8
ERD under different MIT values.
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ERD under different MIT values.

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The MERDR was calculated by the Formula (5) under different ERD. MERDRSi-Sj, refer to the MERDR when ERD changes from Si to Sj, under different MIT values is shown in Figure 9. When MIT = 1,440 min and ERD lies in the range of 1–60, 61–120,121–200, 201–360 and 361–1,440 min, all MERDRSi-Sj was about 20%. MERDR increases with increasing MIT. When MIT = 60, 120, 200, 360 and 1,440 min, MERDR was 39.69, 67.21, 74.79, 89.19 and 99.45%, respectively. When MIT ranged from 60 to 1,440 min, the ratio of ERD less than 200 min decreased from 80.01 to 60.49%, and most of the rainfall duration was <200 min. So, the larger the MIT value, the larger the MERDR is.
Figure 9
MERDR under different MIT values.
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MERDR under different MIT values.

Figure 9
MERDR under different MIT values.
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MERDR under different MIT values.

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Comparing the VCRAR under different MIT values

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LID facilities’ performance can be accessed via computer models, and continuous rainfall-runoff simulations were adopted in the study area based on water balance principles (Guo et al. 2014). VCRAR and its corresponding design rainfall depth under different MIT values were shown in Figure 10. Rainfall depth gradually increases with increasing MIT in differently design VCRAR, which is consistent with the literature review (Yang et al. 2020). Design rainfall depth difference between MIT = 200 min and MIT = 1,440 min is 7 mm when the design VCRAR is 70%, and increased to 10 mm when the design VCRAR increased to 80%. Record rainfall data divided by the longer MIT values result in a bigger design rainfall depth of the same rainfall event when IERI is higher. When evaluating the design VCRAR, design rainfall depth increases with increasing MIT. For example, when MIT = 200 min and the design VCRAR ranges from 50 to 75%, the design rainfall depth increases from 10 to 24 mm, and for design VCRAR ranging from 80 to 95%, the design rainfall depth increases from 29 to 63 mm. The design rainfall depth is 17 and 20 mm, respectively, when MIT = 60 and 200 min with the same design VCRAR of 70%. When the design VCRAR is 50% and MIT increases from 60 to 360 min, the design rainfall depth difference is 3 mm, and increases to 11 mm when the design VCRAR reaches 95%. So, the larger the MIT value, the larger the design rainfall depth of the design VCRAR was.
Figure 10
Rainfall depth and VCRAR under different MIT values.
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Rainfall depth and VCRAR under different MIT values.

Figure 10
Rainfall depth and VCRAR under different MIT values.
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Rainfall depth and VCRAR under different MIT values.

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VCRAR simulation results via bioretention under different MIT values

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Comparison of bioretention VCRAR based on SWMM

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Rainfall capture volume was simulated by bioretention model in SWMM when VCRAR ranged from 50 to 95% (Figure 11). Simulated rainfall capture volume was closest to that of the design value when the MIT = 200 min and design VCRAR was changing from 60 to 75%. At the same time, simulated VCRAR were 64.99 and 69.10% when MIT = 60 and 200 min, respectively, with the same design VCRAR of 70%, indicating that simulated VCRAR increases with increasing MIT values. Simulated VCRAR under different MIT values were investigated, and results showed that when design VCRAR is 55% and MIT = 60 min, the simulation error is the lowest among the different MIT values. The Minimum error also occurred when design VCRAR was <50, 55–60, 60–75, 75–80 and >80%, and corresponding MIT was 60,120, 200, 360 and 1,440 min, respectively. Simulated VCRAR was <50.25, 55.9–59.4, 59.4–69.10, 73.99–79.25 and >83.90%, respectively. The simulated VCRAR is proximate to the design VCRAR.
Figure 11
Simulated VCRAR under different MIT values.
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Simulated VCRAR under different MIT values.

Figure 11
Simulated VCRAR under different MIT values.
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Simulated VCRAR under different MIT values.

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VCRAR error analysis

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Simulated and design VCRAR error analysis under different MIT values was conducted via RE, standard error (SE) (Jang et al. 2007) and standard deviation (SD) (Jensen 1984) (Figure 12). When MIT ranged from 60 to 120 min, SE and SD decreased from 0.831 to 0.428% and from 2.63 to 1.35%, respectively. Meanwhile, SE and SD increased from 0.767 to 2.34% and from 2.43 to 7.55% when MIT values ranged from 200 to 1,440 min, respectively. Simulated VCRAR had a large SD when MIT = 1,440 min (e.g., SD = 7.5%). When MIT ranged from 120 to 360 min, SD and the SE were lower, ranging from 0.428 to 1.094%, and from 1.354 to 3.461%, respectively. So, when MIT = 200 min, the SD and SE were lower than that of other MIT values.
Figure 12
Simulation VCRAR error analysis under different MIT values.
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Simulation VCRAR error analysis under different MIT values.

Figure 12
Simulation VCRAR error analysis under different MIT values.
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Simulation VCRAR error analysis under different MIT values.

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RE was lower than other MIT values under different design VCRAR when MIT = 200 and 120 min, and range from −3.36 to 4.46% and from −4.10 to 1.71%, respectively (Figure 13). RE was greater compared with other MIT values when MIT = 1,440 min, and which ranged from 0.21 to 10.81% when design VCRAR increased from 50 to 95%. RE ranged from −6.09 to 0.25% when MIT = 60 min, and from −2.78 to 5.90% when MIT = 360 min, and which indicates that simulated VCRAR fluctuates greatly. Hence, simulated VCRAR's RE increased with increasing design VCRAR. So, RE is lowest when MIT = 200 min. Moreover, the negative RE decreased and the positive RE increased with increasing MIT (Figure 13), which indicates that more simulated VCRAR is larger than the design VCRAR with the MIT increasing. So, the larger the MIT value adopted for rainfall event division, the larger the rainfall volume captured by the corresponding design VCRAR.
Figure 13
Simulated VCRAR RE for different MIT values.
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Simulated VCRAR RE for different MIT values.

Figure 13
Simulated VCRAR RE for different MIT values.
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Simulated VCRAR RE for different MIT values.

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According to the error analysis between simulated and design VCRAR under different MIT values, MIT = 60–360 min had a lower error, then the design VCRAR was 75–80%. Moreover, RE was larger when MIT = 120 min than MIT = 200 min, which means there is a significant difference between simulated and design VCRAR. Meanwhile, MIT = 200 min had lower RE when design VCRAR was between 60 and 75%. The Sponge city academic planning of Beijing (planning) (The People Government of Beijing Municipality 2017) proposed that the design VCRAR should not be less than 70% in the whole city. Based on the RE, SE and SD error analysis results, and from conducting a comprehensive analysis of the construction requirements in the planning, MIT = 200 min can be selected as an optimal rainfall event division threshold in Beijing.

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  • (1)

    To determine optimal design VCRAR for LID facilities design, a modified rainfall event division method was proposed from combined MIT and threshold methods which can more accurately determine the optimal MIT according to different design VCRAR. The optimal MIT value for the Beijing rainfall events division is 200 min.

  • (2)

    MIT value has an important effect on the effective rainfall events, RER, ERD and MERDR. The larger the MIT value, the fewer the rainfall events and the larger the MERDR. An appropriate MIT must be selected to minimize the error between the design VCRAR and operation effect, and lower bioretention facilities construction costs.

  • (3)

    Simulated VCRAR increased with increasing MIT. Furthermore, the larger the MIT adopted for rainfall events division, the larger the rainfall volume captured than the corresponding design VCRAR. So, it is important to select the proper MIT value according to its design VCRAR value to improve the efficiency of LID facilities.

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We gratefully acknowledge the support of National Natural Science Foundation of China, grant number 52070013 and the National Key R & D Program of the Science and Technology of China (research on flooding management techniques in urban renewal scenarios; No.2021YFC3001402-02).

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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