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 wellbeing. One of its major goals 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:
Contributing to the restoration of the natural water regime by reducing runoff frequency and total runoff volume [
14]; reducing the frequency of runoff events to around 15 days per year has been proposed as a target in southeastern Australia [
15]. In the same region, a target of retaining 77–93% of the annual runoff volume has been proposed by [
16];
Providing enough water for trees; computing a tree water balance is a complicated task with many uncertainties and depends on many factors including tree species and its climatic region [
17];
Sufficient pretreatment of stormwater; at least 80% of stormwater runoff volume is recommended to be captured and pretreated through the soil filter in the bioretention cell [
18,
19,
20];
Prevention of waterlogging tree roots; various authors [
18,
21,
22] recommended between 24 and 48 h as the trench emptying duration.
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 has limited space available space for BGI both on the surface and underground [
23]. Conflicts of interest with transport, buried infrastructure, and historic preservation are common and lead to constrictions of the BGI design [
24]. Thus, the use of the bioretention cell with the open retention space near the tree trunk is often the only possible solution in dense urban environments and/or historical parts of cities. 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 [
25]. Therefore, an adequate ratio of the drained area (reduced by the runoff coefficient) A
red to bioretention cell area A
BC is a crucial parameter for BC-T performance [
26].
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 an 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 [
27]. 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 of 45 considering the value of the runoff coefficient of paved surfaces to be 0.90) to ensure treatment of 90% of the mean annual runoff. Christchurch City, New Zealand [
18], analyzed several scenarios with a goal to capture 80% of stormwater runoff. They found that 350 m
2 of a 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). Simulations of bioretention cell performance with 10-year rainfall data in Kansas City, Missouri, USA, proved that if bioretention cell surface area is only 5% of A
red (i.e., an A
red/A
BC ratio of 18 considering the runoff coefficient of paved surfaces to be 0.90), the cumulative runoff volume is reduced by 53% [
22]. Hamburg City, Germany, recommends connecting 15–21 m
2 of the drained area to 1 m
2 of bioretention cell area [
28] (i.e., A
red/A
BC ratio 13.5–19 considering the runoff coefficient of paved surfaces to be 0.90). Having a 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 [
29], resulting in an A
red/A
BC ratio of 18–45 (considering a 0.90 runoff coefficient for paved surfaces). The authors of [
26] declared that the A
red/A
BC ratio for bioretention cells should be between 5 and 15, because 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 reasons for this may be the different study locations, climatic data, different setups of bioretention cells, ambient soil characteristics, and/or the 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 BC-T water balance. Data needed for the calculation 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 are 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 [
30]) 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 [
31].
The uptake of water by a tree is a complex problem. At a single root scale, root hydraulic properties and planting media are of main concern; however, at the whole tree root system scale, single root processes affect each other and are integrated [
32]. The primary source of water for a tree in BC-T is water held by the soil or substrate the tree is planted in [
9]. The maximum amount of the held water available to the tree is limited by available water-holding capacity. It is defined as the amount of water held between the field capacity and the permanent wilting point of the soil [
33].
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, and tree characteristics—type of tree, size of tree, diameter of crown, canopy structure, internal water storage, etc. [
34,
35,
36]) 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 [
37] 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 [
38], by 50% (2–5% of biochar in the soil, [
39]), or even by 100% (9% of biochar in the soil, [
40]). 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 omitting tree water uptake and available water-holding capacity data in the calculation of the water balance is unknown.
The goals of this paper are (i) to study the sensitivity of the tree water uptake rate and water-holding capacity in the water balance calculation used for the BC-T design (permissible Ared/ABC ratio), and (ii) to recommend a possible simplification of the water balance used for the BC-T design in engineering and landscaping practice.
4. Discussion
Several counteracting factors affect the optimization of BC-T: (i) volume of water held by the soil filter, (ii) volume of water held by the trench substrate, (iii) water needed for the tree uptake TWUpot, and (iv) exfiltration rate from the underground trench to the ambient soil.
The volume of water held by the soil filter WHCSF decreases as a higher amount of water percolates into the underground trench and is available to cover the AWHCTR. On the other hand, more water in the trench must be exfiltrated. A higher volume of water held by the trench substrate AWHCTR means more water is available for tree uptake and less water is exfiltrated from the trench. However, less retention volume is available during heavy rainfall events. A higher value of the amount of water needed for the tree uptake TWUpot helps to restore the free retention volume in the underground trench. However, it is a slow process so it is significant only under very low exfiltration conditions. The exfiltration rate from the underground trench to the ambient soil determines which of the above-mentioned processes will be crucial during the optimization procedure.
The A
red/A
BC ratio was found to be in the range of 4.5–58 which is consistent with the studies [
11,
18,
26,
27,
28,
29] (identified A
red/A
BC in the range 5–45). However, it is highly dependent on exfiltration conditions (48–58 when the exfiltration rate is 180 mm·h
−1, 18–23 when the exfiltration rate is 18 mm·h
−1, 4.5–7 when the exfiltration rate is 1.8 mm·h
−1, and 31–39 when an underdrain is applied). It corresponds with the findings of [
11,
56].
A
red/A
BC should be 36 when the exfiltration rate is 34 mm·h
−1 and only 11 when the exfiltration rate is 1 mm·h
−1 [
11]. However, the A
red/A
BC value for 1 mm·h
−1 stated by [
11] is substantially higher than our finding for the exfiltration rate of 1.8 mm·h
−1 (11 compared to 4.5–7). This difference can be explained by different climatic data used for the analysis. While the annual rainfall depths in Melbourne, Australia, and Prague, Czech Republic, are similar (515 vs. 532 mm·y
−1), the rainfall distribution during the year is different (Melbourne: minimum 33, maximum 60 mm per month; Prague: minimum 23, maximum 77 mm per month); thus, the retention space of BC-T has to be accommodated accordingly.
Further, the risk of the soil filter clogging must be discussed [
26]. A higher A
red/A
BC leads to faster clogging and, therefore, higher costs associated with its more frequent replacement.