1. Introduction
A paradigm shift in urban stormwater management started in the 1960s to mitigate the impacts of draining stormwater out of cities as fast as possible [
1]. The Sustainable Drainage Systems (SuDS) concept evolved over decades; however, it was connected mainly with water-related problems in cities such as flood protection, surface water quality and ecology protection, restoration of natural local water balance, and stormwater harvesting [
2]. Microclimate improvement as a reaction to climate change impacts was later incorporated as an additional goal of SuDS. The concept of blue-green infrastructure emerged [
3].
Blue-Green Infrastructure (BGI) can be defined as a package of measures supporting ecosystem functions to deliver multiple benefits connected not only with water but also with urban microclimate, biodiversity, urban aesthetics, and social well-being. Its primary goal is to adapt urban areas to climate change [
4]. Key elements of BGI are trees and other vegetation (providing the climate function [
5]) as well as water retention spaces (providing water flow control). To provide the above-mentioned ecosystem functions, the elements are often combined in one BGI structure: an open terrain vegetated depression (bioretention cell) with an underlying trench (referred to as BC-T). Stormwater runoff from the surrounding paved area is conveyed to the terrain depression and infiltrates through a soil filter to the underground trench which also serves as a tree pit. The soil filter serves as the stormwater treatment [
6] to prevent clogging of the underground trench [
7] and protect the quality of underground and/or surface waters [
8].
BC-T has to be optimized for both tree habitat criteria and water management criteria. The tree habitat criteria consist mainly of the sufficient volume of root space provided by the tree pit [
9], type of substrate [
10], and prevention of root system waterlogging [
11]. The stormwater management criteria aim mainly at discharge regulation, stormwater pretreatment [
12], and the duration of the retention space emptying [
13].
To reach an optimal BC-T setup, the above-mentioned criteria must be related to performance criteria and site-specific conditions. Performance criteria consist of:
Site-specific conditions consist mainly of:
groundwater level;
exfiltration rate from the underground trench (i.e., permeability of the native soil);
space availability for BC-T.
The urban environment is specific, especially regarding the available space for BGI both on the surface and underground [
18]. Conflicts of interests with transport, buried infrastructure, and historic preservation are common and lead to constrictions of the BGI design [
19]. Thus, the use of the bioretention cell with the open retention space in close proximity to the tree trunk is often the only possible solution in dense urban environments and/or historical parts of cities. The area of the bioretention cell might be limited to 3-6 m
2 per tree. This means that the open storage area is limited and the retained stormwater volume is reduced. The excess stormwater can be drained directly into the underground trench by a rainfall gully; however, this means that the stormwater is not pretreated by the soil filter in the bioretention cell. The lack of pretreatment increases the risk of groundwater pollution and underground trench clogging [
20]. Therefore, an adequate ratio of drained area (reduced by the runoff coefficient) A
red to bioretention cell area A
BC is a crucial parameter for BC-T performance [
21].
Various authors studied a suitable A
red/A
BC ratio, usually for specific conditions, in selected case studies. The bioretention cell area is considered 2.5% of the impervious drained area when the exfiltration rate from a trench is 34 mm per hour and 8.4% when the exfiltration is limited to 1 mm per hour [
11]. A 100 mm ponding depth in the bioretention cell was considered. It equals the A
red/A
BC ratio between 11 and 36, considering the runoff coefficient of paved surfaces at 0.90. Biofilter performance in Melbourne, Australia was studied in [
22]. The authors considered a ponding depth in the bioretention cell of 200 mm and recommended its area to be at least 2% of the drained area (A
red/A
BC ratio 45 considering the value of the runoff coefficient of paved surfaces of 0.90) to ensure treatment of 90% of the mean annual runoff. Christchurch City, New Zealand [
16] analyzed several scenarios with a goal to capture 80% of stormwater runoff. They found that 350 m
2 of drained area can be connected to a bioretention cell with a ponding area of 8.05 m
2 and a depth of 150 mm (i.e., an A
red/A
BC ratio of 39 considering the runoff coefficient of paved surfaces to be 0.90). Hamburg City, Germany recommends connecting 15-21 m
2 of the drained area to 1 m
2 of bioretention cell area [
23] (i.e., A
red/A
BC ratio 13.5-19 considering the runoff coefficient of paved surfaces of 0.90). The bioretention cell area equaling 2-10% of the drainage area is sufficient for stormwater purification. In cases where it is supplemented by an underlying trench (as in the case of BC–T), a sufficient area is 2-5% according to [
24], resulting in an A
red/A
BC ratio of 18-45 (considering the runoff coefficient of paved surfaces of 0.90). The authors of [
21] declared that the A
red/A
BC ratio for bioretention cells should be between 5 and 15, as a higher value may lead to faster clogging of the soil filter.
Based on the cited studies, it can be concluded that the recommended Ared/ABC ratio varies substantially from 5 to 45. The reason for this may be different locations of the studies, climatic data, different setups of bioretention cells, ambient soil characteristics, and performance criteria used for analysis. The methods used (where declared) are based on experimental studies and do not provide general methodical guidance that can be used in engineering and landscaping practice.
Generally, the quantification of an adequate A
red/A
BC ratio is based on the calculation of the hydrological balance. A common practice is to calculate the hydrological balance using IDF (Intensity-Duration-Frequency) rainfall curves (i.e., uniform rainfalls) [
25]. However, it is suitable for stand-alone BGI structures only [
21]. For BGI structures connected in series (as in the case of BC-T, where the bioretention cell is connected in series with an underground trench), a more detailed description of the performance dynamics is necessary.
Data needed for the calculation of the hydrological balance of a BC-T consist of BC-T structural data (e.g., dimensions, used materials, and their characteristics), drainage area data (e.g., initial losses, runoff coefficient), geological data (e.g., exfiltration rate from underground trench), rainfall data (historical rainfall series), and tree water uptake data. Some of these data are easy to obtain (e.g., rainfall data is provided by national hydrometeorological institutes, or the exfiltration rate can be measured on-site before the BC-T construction) or are subject to the design process (e.g., dimensions of the B-CT or the drainage area size). However, there are data that are not readily available for an arbitrary location and/or are the subject of scientific research. Examples of these data are the tree water uptake (consisting of transpiration and tree water storage; [
26]) and the available water holding capacity of the soil filter and structural substrates (stone-soil media used for the growth of tree roots) used in the underground trench [
27].
The tree water uptake data are site-specific (e.g., climatic conditions, site conditions, degree of shading by adjacent buildings) and differ by tree species; the size of the tree must also be considered. The tree water uptake can be calculated theoretically, but the calculation is based on many data and parameters (such as radiation, air temperature, air humidity, wind, soil water content and the ability of the soil to conduct water to the roots, waterlogging, soil water salinity, water stress, growing season length, tree characteristics – type of tree, size of tree, diameter of crown, canopy structure, internal water storage, etc. [28-30]) that are difficult to obtain and quantify. This leads to a high level of uncertainty in the quantification of tree water uptake.
Water holding capacity in structural substrates was analyzed in several studies, both in the laboratory and in situ. The available water holding capacity in compacted stone-soil media was estimated by [
31] as 7-11% by volume, which is comparable to loamy sand.
Adding biochar to structural substrates can increase the available water holding capacity by 25% in coarse-textured soils [
32], by 50% (2-5% of biochar added to soil, [
33]), or even by 100% (9% of biochar added to soil, [
34]). However, the mentioned studies were not carried out with structural substrates and therefore the increase in the available water holding capacity by adding biochar under such conditions remains rather uncertain.
The effect of using or neglecting tree water uptake and available water holding capacity data in the calculation of the hydrological balance is unknown.
The goal of this presented paper is (i) to study the sensitivity of the tree water uptake rate and water holding capacity in the hydrological balance calculation used for the BC-T design (permissible Ared/ABC ratio) and (ii) to recommend a possible simplification of the hydrological balance used for the BC-T design in engineering and landscaping practice.
3. Results
3.1. Calculation with reference values
At first, A
drained is optimized for different exfiltration rates from the underground trench and reference values of parameters that are subject to the sensitivity analysis. Results are summarized in
Table 11.
It is obvious that with the decreasing exfiltration rate, the maximum size of the drained area, Adrained, is rapidly decreasing. Therefore, the tree water need, TWUpotential, is covered to a smaller extent as well. For exfiltration rates lower than 18 mm.h-1, it might be helpful to speed up the emptying of the underground trench by incorporating an underdrain with regulated outflow (e.g., by an orifice). In cases where the regulated outflow of 0.5 l.s-1 is applied for exfiltration rates of 1.8 mm.h-1, the drained area can be increased from 14 to 112 m2, and as a result TWUcover increases from 16 to 68%.
3.2. Sensitivity of water holding capacity in soil filter
Results of the sensitivity analysis of the water holding capacity in the soil filter WHC
soil_filter are shown in
Figure 3.
Changing the value of the WHCsoil_filter has a negligible effect on Adrained, which can be connected to the BC-T, as the soil filter deals only with a small amount of stormwater in comparison to the underground trench. A small effect can be seen in scenarios with lower exfiltration rates, in which even the small amount of water released from the soil filter into the underground trench can affect the duration of the trench emptying. However, the change is in the range of 1 m2 of connectable drained area.
TWUcover varies more. With the decreasing water holding capacity of the soil filter, even small rainfall events have a chance to percolate to the trench and contribute to its available water holding capacity and tree water uptake. The difference is more significant for very low exfiltration rates, as the amount of stormwater potentially held in the soil filter plays a more significant role in the overall water balance.
3.3. Sensitivity of available water holding capacity of underground trench
Results of the sensitivity analysis of the available water holding capacity in the underground trench AWHC
trench are shown in
Figure 4.
Changing the AWHCtrench has a significant effect on Adrained, which can be connected to the BC-T. For higher exfiltration rates (and the trench with the underdrain), the amount of water held in the structural substrate of the trench decreases the available retention volume for stormwater inflow. It is especially important during heavy rainfall events that have the potential to surcharge the underground trench more often. Therefore, when AWHCtrench is neglected, the connectable drained area Adrained increases by 7-15% compared to the reference value of AWHCtrench (note: in the 180 mm.h-1 exfiltration scenario, Adrained for both the neglected and the 5% AWHCtrench is the same as percentage of water treated by the soil filter determines the result of calculation). Accordingly, with the increasing AWHCtrench value, the maximum drained area Adrained decreases by 12-22%.
The opposite situation occurs in cases of very low exfiltration rates when the duration of the trench emptying plays a major role. A lower value of AWHCtrench means that more water exfiltrates and Adrained must be significantly decreased (by 30% compared to the reference values); when AWHCtrench is higher, a larger area may be connected (increase by up to 35%).
TWUcover is increasing with the increase of AWHCtrench in all studied exfiltration scenarios. Omitting AWHCtrench from the hydrological balance means that the tree can take up water only during the rainfall runoff and shortly after it (until the trench is emptied, i.e., within 48 h). Therefore, TWUcover is very low (2-7%). Even the small value of AWHCtrench (5%) increases TWUcover by tenths of a percent. Coverage progress with further increases in AWHCtrench is still significant (15-30%).
3.4. Sensitivity of potential tree water uptake
Results of the sensitivity analysis of tree water uptake claim TWU
potential are in
Figure 5.
Adrained is slightly increasing with an increase in TWUpotential as the tree water uptake helps to empty the underground trench faster. It is not so important in cases of very good exfiltration rates (the volume of water taken up by the tree is of little significance in the overall water balance of BC-T); however, in cases of very low exfiltration conditions, Adrained doubles (from 8 m2 in the case of TWUpotential to a neglected 15 m2 in the case of ´high´ TWUpotential).
TWUcover decreases because Adrained does not increase substantially with the TWUpotential increase.
3.5. Summary of the sensitivity analysis
The most noticeable change in Adrained was caused by a change in AWHCtrench; however, the change in Adrained is generally within 10% in the case of good exfiltration conditions. Therefore, it is possible to state that the uncertainty in the value of the AWHCtrench (as well as the other two parameters) does not affect the results of the BC-T optimization significantly. Cases of very low exfiltration rates are a different situation, where values of AWHCtrench and TWUpotential can lead to more than a 20% change in Adrained. However, at such exfiltration rates it should be preferred to equip the underground trench with an underdrain to increase TWUcover.
TWUcover results are mainly affected by the parameters AWHCtrench and TWUpotential. Within their usual range of values, the effect on TWUcover is 10–40% for all exfiltration scenarios studied. If TWUcover is required for decision-making, these parameters should be quantified as accurately as possible. WHCsoil_filter has only a small effect on TWUcover (1-3%), especially in good exfiltration conditions. In the case of very low exfiltration rates, it might be up to 20%; however, the same conclusion as in the case of Adrained applies (i.e., the necessity to equip the underground trench with an underdrain).
3.6. Neglecting the parameters
A situation of neglecting all three studied parameters in the hydrological balance was also studied. To get an idea of to what extent it affects the result of optimization, the maximum drained area A
drained is calculated with WHC
soil_filter, AWHC
trench and TWU
potential neglected. The results, including their comparison with the above-presented results, are in
Table 5.
The standard design procedure overestimates Adrained by 6-13% under good exfiltration conditions and in the scenario with the underdrain. The overestimation would be more significant with an increase in the AWHCtrench reference value (22% in the case where the AWHCtrench reference value is set to 20%). The other two parameters are not of such importance. In the case of a very low exfiltration rate, the Adrained is significantly underestimated by 50%; the underestimation would be more significant with an increase in the AWHCtrench reference value (63% when the AWHCtrench reference value is set to 20%) and less significant in the case of a decrease in TWUpotential (36% when the TWUpotential reference value is set to ´low´).
Figure 1.
Scheme of a BC-T used for the hydrological balance calculation.
Figure 1.
Scheme of a BC-T used for the hydrological balance calculation.
Figure 2.
Schematization of AWHCtrench calcuation in hydrological balance (hret is depth of retained water in time t, hret,max is a maximum depth of retained water).
Figure 2.
Schematization of AWHCtrench calcuation in hydrological balance (hret is depth of retained water in time t, hret,max is a maximum depth of retained water).
Figure 3.
Effect of water holding capacity of the soil filter WHCsoil_filter on: (a) Adrained; (b) TWUcover.
Figure 3.
Effect of water holding capacity of the soil filter WHCsoil_filter on: (a) Adrained; (b) TWUcover.
Figure 4.
Effect of available water holding capacity of underground trench AWHCtrench on: (a) Adrained; (b) TWUcover.
Figure 4.
Effect of available water holding capacity of underground trench AWHCtrench on: (a) Adrained; (b) TWUcover.
Figure 5.
Effect of potential tree water uptake TWUpotential on: (a) Adrained; (b) TWUcover
Figure 5.
Effect of potential tree water uptake TWUpotential on: (a) Adrained; (b) TWUcover
Table 1.
Overview of groups of data used in sensitivity analysis procedure.
Table 1.
Overview of groups of data used in sensitivity analysis procedure.
Data groups |
Data used |
Given characteristics and inputs |
BC-T physical setup Tree physical characteristics Soil filter infiltration rate Initial and interception losses, runoff coefficient of drained area Historical rainfall series |
Variable local conditions |
Exfiltration rates from underground trench to ambient soil Use/non-use of underdrain for emptying of underground trench |
Performance criteria |
Frequency of underground trench surcharge Minimum amount of stormwater treated by soil filter Duration of underground trench emptying |
Target variable 1
|
Size of area drained to BC-T (Adrained) that can be connected to BC-T, can be also expressed as Ared/ABC ratio |
Subject to sensitivity analysis |
Water holding capacity of soil filter (WHCsoil_filter) Water holding capacity of underground trench substrate (WHCtrench, can be substituted by available water holding capacity AWHCtrench) Potential tree water uptake (TWUpotential) |
Table 2.
Open storage characteristics.
Table 2.
Open storage characteristics.
Characteristic |
Value / Comment |
Area |
3 m2
|
Ponding area |
2.8 m2 (a tree with a 0.5 m trunk diameter is considered) |
Depth |
0.10 m |
Storage volume |
0.28 m3
|
Overflow |
In case open storage is surcharged the excess water is diverted directly to the underground trench |
Table 3.
Soil filter characteristics.
Table 3.
Soil filter characteristics.
Characteristic |
Value / Comment |
Area |
2.8 m2
|
Thickness |
0.25 m |
Material |
Soil with ca. 10% of clay and 3% of moisture-containing matter (humus, biochar) |
Infiltration rate |
180 mm.h-1 (recommended by [21]) |
Water holding capacity |
Subject to the sensitivity analysis |
Table 4.
Underground trench characteristics.
Table 4.
Underground trench characteristics.
Characteristic |
Value / Comment |
Area |
8.4 m2 (width 1.2 m × length 7 m) |
Depth |
1.3 m (effective storage depth from the trench bottom to the level of the safety spill is considered 1.0 m) |
Material |
Structural stone-soil substrate |
Porosity |
30% |
Storage volume |
2.52 m3
|
Exfiltration rate |
Scenarios: 180 mm.h-1, 18 mm.h-1 and 1.8 mm.h-1 without underdrain and 1.8 mm.h-1 with underdrain (regulated outflow at the bottom of the trench with maximum of 0.5 l.s-1) |
Ground water level |
3 m below trench bottom |
Water holding capacity |
Subject to the sensitivity analysis |
Table 5.
Tree characteristics.
Table 5.
Tree characteristics.
Characteristic |
Value / Comment |
Trunk diameter at ground |
0.5 m |
Crown diameter |
7 m |
Tree type |
Broad leaved, mature |
Interception of rainfall |
1.1 mm in tree crown area (according to [35]) |
Tree water uptake |
Subject to the sensitivity analysis |
Table 6.
Performance criteria and their requested values.
Table 6.
Performance criteria and their requested values.
Criterion |
Value / Comment |
The maximum permissible frequency of underground trench surcharge |
1 per 5 years |
The minimum amount of water infiltrating to the soil filter ensure the restoration of the natural water regime and proper pretreatment of stormwater |
85% |
The maximum duration for emptying the underground trench when it is full (prevention of tree roots waterlogging) |
48 h |
Table 7.
Historical rainfall series characteristics.
Table 7.
Historical rainfall series characteristics.
Characteristic |
Value / Comment |
Location |
Prague, Czech Republic |
Length of the record |
10 years (from 2006 to 2015) |
Time resolution |
1 hour |
Average rainfall depth |
532 mm.y-1
|
Table 8.
Drained area characteristics.
Table 8.
Drained area characteristics.
Characteristic |
Value / Comment |
Area |
Target variable |
Initial losses |
0.5 mm (according to [36]) |
Runoff coefficient |
0.90 (typical for urban paved surfaces in city centers) |
Table 9.
Potential tree water uptake TWUpotential data used in the hydrological balance.
Table 9.
Potential tree water uptake TWUpotential data used in the hydrological balance.
Month |
Average air temperature in ⁰C |
TWUpotential in l.d-1
|
Average |
Low |
High |
January |
0.9 |
1.3 |
0.7 |
1.7 |
February |
1.6 |
2.6 |
1.3 |
3.3 |
March |
5.8 |
19.6 |
9.8 |
25.5 |
April |
11.7 |
50.5 |
25.3 |
65.7 |
May |
15.3 |
98.6 |
49.3 |
128.2 |
June |
19.0 |
138.2 |
69.1 |
179.6 |
July |
21.6 |
147.1 |
73.5 |
191.2 |
August |
20.2 |
118.6 |
59.3 |
154.2 |
September |
15.5 |
57.6 |
28.8 |
74.9 |
October |
10.1 |
21.3 |
10.6 |
27.7 |
November |
6.3 |
2.1 |
1.1 |
2.7 |
December |
2.3 |
1.2 |
0.6 |
1.6 |
Table 10.
Parameters that are subject to sensitivity analysis and their studied values.
Table 10.
Parameters that are subject to sensitivity analysis and their studied values.
Parameter |
Reference value |
Tested range |
Increments |
Neglected |
WHCsoil_filter
|
10% |
5 – 20% |
5% |
parameters neglected in hydrological balance |
AWHCtrench
|
10% |
5 – 20% |
5% |
TWUpotential
|
Average |
Low to High |
-50%; +30% |
Table 11.
Summary of results for different exfiltration rate scenarios with reference values of parameters that are subject to the sensitivity analysis (both WHC
soil_filter and AWHC
trench are set to 10%, average TWU
potential is used); determining performance criterion shows which of the three performance criteria used (
Table 6) is critical for the optimization (i.e., two other criteria are fulfilled).
Table 11.
Summary of results for different exfiltration rate scenarios with reference values of parameters that are subject to the sensitivity analysis (both WHC
soil_filter and AWHC
trench are set to 10%, average TWU
potential is used); determining performance criterion shows which of the three performance criteria used (
Table 6) is critical for the optimization (i.e., two other criteria are fulfilled).
Exfiltration rate in mm.h-1 |
Determining performance criterion |
Adrained in m2
|
Ared/ABC in m2.m-2
|
TWUcover in % |
180 |
Frequency of surcharge |
167 |
54.6 |
73.1 |
18 |
Frequency of surcharge |
69 |
23.1 |
59.9 |
1.8 |
Emptying duration |
14 |
5.5 |
16.4 |
1.8 + underdrain |
Frequency of surcharge |
112 |
37.0 |
68.1 |
Table 12.
Effect of changing the studied parameters values (WHCsoil_filter, AWHCtrench and TWUpotential) on Adrained.
Table 12.
Effect of changing the studied parameters values (WHCsoil_filter, AWHCtrench and TWUpotential) on Adrained.
|
Tested parameters |
|
WHCsoil_filter
|
AWHCtrench
|
TWUpotential
|
Reference value |
10% |
10% |
Average |
Tested values |
5% |
15% |
5% |
15% |
Low |
High |
Exfiltration |
Change in Adrained compared to reference value in % |
180 mm.h-1
|
0.0 |
0.0 |
+7.2 |
-7.2 |
0.0 |
0.0 |
18 mm.h-1
|
-1.4 |
0.0 |
+7.2 |
-13.0 |
-1.4 |
0.0 |
1.8 mm.h-1
|
-7.1 |
0.0 |
-21.4 |
+14.3 |
-21.4 |
+7.1 |
1.8 mm.h-1 + underdrain |
0.0 |
0.0 |
+6.3 |
-10.7 |
0.0 |
0.0 |
Table 13.
Effect of changing the studied parameters values (WHCsoil_filter, AWHCtrench and TWUpotential) on TWUcover.
Table 13.
Effect of changing the studied parameters values (WHCsoil_filter, AWHCtrench and TWUpotential) on TWUcover.
|
Tested parameters |
|
WHCsoil_filter |
AWHCtrench |
TWUpotential |
Reference value |
10% |
10% |
Average |
Tested values |
5% |
15% |
5% |
15% |
Low |
High |
Exfiltration: |
Change in TWUcover compared to reference value in % |
180 mm.h-1
|
+1.4 |
-1.2 |
-23.4 |
+11.5 |
+25.2 |
-11.5 |
18 mm.h-1
|
+2.8 |
-3.3 |
-22.5 |
+7.3 |
+37.7 |
-15.2 |
1.8 mm.h-1
|
+11.0 |
-17.7 |
-36.0 |
+25.0 |
+38.4 |
-14.6 |
1.8 mm.h-1 + underdrain |
+2.2 |
-2.1 |
-23.8 |
+10.4 |
+30.8 |
-12.6 |
Table 14.
Summary of results for different exfiltration scenarios with values of WHCsoil_filter, AWHCtrench and TWUpotential neglected.
Table 14.
Summary of results for different exfiltration scenarios with values of WHCsoil_filter, AWHCtrench and TWUpotential neglected.
|
Tested parameters |
|
WHCsoil_filter |
AWHCtrench |
TWUpotential |
Reference value |
10% |
10% |
Average |
Tested value |
neglected |
neglected |
neglected |
Exfiltration: |
Change in Adrained compared to reference value in % |
180 mm.h-1
|
+7.2 |
18 mm.h-1
|
+13.0 |
1.8 mm.h-1
|
-50.0 |
1.8 mm.h-1 + underdrain |
+6.3 |