© The Author(s) 2023. Published by Science Press and EDP Sciences

Introduction

Climate change will affect future food security, energy production, human health, and sustainable development. In addition, climate change could also lead to an increase in hydrometeorological risks, such as floods, storm surges, landslides, avalanches, hailstorms, droughts, heatwaves, and forest fires [1]. In response to the threats posed by climate change, nature-based solutions (NbS) provide the potential for working closely with nature to adapt to future climate change, reduce the adverse impacts, and improve well-being [2]. NbS are defined as actions “inspired by, supported by, or copied from nature,” and designed to address a range of environmental challenges in an efficient and adaptable manner, while at the same time providing economic, social, and environmental benefits [3]. To some extent, NbS meet the triple challenge of minimizing climate change, restoring biodiversity and addressing food security and other development priorities [4]. Hence, they may be an effective solution for mitigating climate change. The European Commission recently adopted the concept of NBS in its “Horizon 2020” plan developed in 2015. For urban areas specifically, climate change raises multiple challenges, with larger cities being particularly vulnerable, as climate change will exacerbate the consequences of anticipated urban population growth in the coming decades [5]. Climate change manifests itself through changes in hydrology as well as meteorology. This can result in droughts affecting water supply reservoirs or flooding through storm intensification for example; both of which are very different situations that can lead to severe consequences in urban areas [6] and direct effects on water security and conflict [7]. Many research projects show that NbS can effectively reduce, mitigate, and prevent hydrological and meteorological risks [8]. Low impact development (LID) technologies are a form of NbS that minimizes the impact of increases in impervious surfaces by mimicking the pre-developed state of the watershed – hence making it a nature inspired approach [9]. A properly designed LID has the dual role of mitigating stormwater quantities and treating or enhancing stormwater quality. Green infrastructure (GI) is a term synonymous with LIDs. Both are essentially decentralized stormwater management practices, and examples include green roofs (GR), grassy swales (GS), infiltration trenches (IT), rain gardens also known as bioretention cells (BC), rain barrels (RB), and permeable pavements (PP) [10]. Water sensitive urban design (WSUD) is another term encompassing LIDs [11] while sustainable urban drainage systems (SUDS) is considered an NbS-style approach that includes sequences of stormwater practices and technologies that work together to form a management train [9].

Not surprisingly, there is a growing concern for the impact of climate change on urban hydrological processes, which many assess through precipitation output from climate models [12]. To suggest that LIDs are a possible tool for mitigating the impacts of climate change requires evidence-based projections and an understanding of how LIDs are impacted by changes in both small and large-scale hydrometeorology and vice versa. For example, future forecasts of precipitation frequency and the maximum number of consecutive days without precipitation are projected to increase. This will have a profound effect on regional intensity-duration-frequency (IDF) curves, which are the back-bone of LID design. IDF curves design LIDs to a sufficient size to combat flood events arising from storms of a specific return period. But outside of storm events, the LID plays an active role in the urban hydrological cycle throughout the year as an integrated component of the urban landscape. Climate change will also impact the range of temperatures experienced in urban settings, which will have a direct impact on evaporation levels in un-vegetated LIDs, and on evapotranspiration levels in vegetated LIDs. The changes to air temperature will also come with changes to water temperature, and water temperature changes can adversely impact water quality [13]. This coupled with the increases in heavy precipitation events can accelerate the transport of pathogens and other pollutants [14]. On the other hand, this may be offset by the dilution effect of increased flow in some regions [7].

While IDF curves serve as a guide to sizing LID capacity to manage flood events, computer modeling is a necessary tool in stormwater infrastructure design at both large and small spatial scales, and for event or continuous simulations in urban areas. A handful of models exist that incorporate LIDs into urban hydrological models. PCSWMM is a very popular urban stormwater model that has incorporated LID submodels to model the urban hydrology of catchments that contain such infrastructure [15]. It is a conceptual model that resides on quasi-physically based representations of hydrological processes in catchments with pervious areas, impervious areas, and LIDs. Like any conceptual urban hydrological computer model, the water balance and water dynamics are modelled with calibrated or default model parameters based on the literature, user experience, or developer recommendations. These parameters can dramatically impact simulation results [16] depending on the mathematical representation of the hydrological processes. PCSWMM’s representation of LIDs has given rise to numerous applications [17–19] in the literature with calibrations and validations on a wide variety of catchments.

LIDs are designed with the understanding of processes that occur at a small scale – much smaller than the scale of global climate models (GCM) that provide the projections in meteorology of future climates. Not surprisingly, most computer models for LIDs and urban hydrology are designed for small-scale processes that drive LID design and function. Thus, any study of urban hydrology under a changing climate should include a method for rectifying scale differences between the urban hydrological model (at the metre or sub-metre scale) and the km scale output of GCMs. Regional climate models (RCM) do provide output at finer resolutions than GCMs but their scales are still of the order of km. Downscaling methods are an approach for rectifying the differences in scales between GCM/RCM data and hydrological models by introducing complexity or heterogeneity in the meteorological data aligned with that of the hydrological model. While all models bring a certain degree of uncertainty to their output (both through underlying assumptions in the processes and in the data that are input to the model), downscaling methods come with an added level of uncertainty to any application [20]. A plethora of downscaling tools exist that may be categorized as either statistical or dynamic downscaling approaches. The choice of which method to use depends greatly on the circumstance and should be validated based on historical data [21]. Upscaling is considered the reverse process where the important processes at the watershed scale are exported through a set of mathematical equations to the larger scale [22]. Upscaling applications to groundwater and sub-surface water exist in the literature [23,24] and can use simple power laws to connect two different scales or more complex representations of individual processes interacting at several scales [25].

Hydrology is a landscape-integrating phenomenon in which everything, processes and properties, are coupled and integrated with each other; and urban hydrology is no exception. Accurately assessing the functionality of an LID in a future climate should be aware of the uncertainty involved and scale of the processes being modeled/assessed. Otherwise, the effectiveness of small-scale LID processes may be under- or over-estimated in large-scale modelling exercises. Galster et al. [26] studied how impervious surfaces affected the scaling of river discharge with drainage area. Discharge and drainage areas are often related by a power equation that has been in use for decades for large watersheds. Their study showed that for small urban settings, the rate exponent in the power equation is very different from that of non-urban settings; but more importantly, where the urbanization occurs spatially in the landscape can have a profound effect on the scaling equation [26]. This is just one illustration of how existing relationships for rural watersheds cannot be extrapolated to urban settings. Because of the benefits of LIDs and NbS in general, there is an interest in wide scale implementation of NbS over larger catchment scales instead of just being relegated to small, urban areas [27]. But with this scale-up, there must be continued recognition of the interconnection between the LID and the rest of the catchment’s hydrological components, and therefore, must be understood at these larger scales. This is equally true for any study attempting to determine the impacts of climate change on LIDs or the potential for LIDs to mitigate climate change impacts.

This paper reviews the literature to date that assesses/considers LID performance under a changing climate for both water quantity and water quality treatment; and their inferred potential for mitigating these impacts. This review categorizes the literature in terms of the following criteria: (i) the type of LID used in the assessment; (ii) the spatial and temporal scale of the LID used in determining climate change impacts on LIDs; (iii) distinguishing between water quantity and water quality outcomes; (iv) the model used to determine LID output; (v) the nature and scale of the climate data used in the investigation. Note that in (ii) above, spatial scale refers to the spatial extent or size of the LID, while temporal scale refers to the time period used to model LID output; that is, short-term events vs. long-term continuous simulations. The literature review is synthesized and critiqued to determine reasonable directions for assessing the potential for LIDs in mitigating climate change impacts. To this end, the Authors present a case study that explores the pitfalls of one of the biggest obstacles to accurately determining LID function in future climates: scaling.

Literature review of LID potential in changing climates

Methodology

This review uses the PRISMA 2020 Protocol as a guideline for review papers (prisma-statement.org). The reviewed article was retrieved through databases from Web of Science, Google Scholar, Scopus, and the University of Victoria Libraries database. The keywords used in the search were: nature-based solution, climate change, low-impact development, water quantity, water quality, and uncertainty analysis. The selected time frame is January 1, 2002 to December 31, 2022 and the literature review framework is conducted in the following steps:

(1) Select relevant articles from the database. Note that the selected articles need to meet the research requirements of LID applications in changing climate.

(2) Distill and summarize the articled bases on criteria (i)–(v).

(3) Analyze the information to determine common approaches, trends, and gaps in studies with this focus.

Results and discussion

The literature search found only 55 articles were generated by the keywords, but out of that 55, only 18 articles either investigated or modelled performance or function of LIDs in future climates according to the five criteria noted above. These papers were written either as (1) a direct assessment of LID performance by modelling LIDs in future climate scenarios; or as (2) discussions on whether LIDs were suitable technologies for mitigating climate change through a general review of LID performance in the literature. Table 1 shows the distribution of the 18 journal papers based on the five criteria and the number of papers in each category. Note that papers that assess both permeable pavements and green roofs would be counted once in each category (so the sum of numbers across rows would not necessarily equal 18). The papers are summarized in the form of tables with attention to the five criteria but separated based on those taking approach (1), which are given in Table 2, and those papers categorized as approach (2), which are shown in Table 3.

Table 1 shows that of the studies conducted, bioretention cells account for the highest proportion of research on the topic, followed by permeable pavements, then green roofs and then other types at less than 10%. This is not surprising in these are the three most popular types of LID structures in stormwater management. Each has pros and cons based on their physical properties, costs and treatment ability [46]. The majority of studies were conducted at large scales with LID sizes exceeding 5 km². While the differences between each scale size in Table 1 may seem narrow, many of the large scale studies were working with LIDs well above the threshold for this category to the point of being unrealistically large for many locations. Depending on spatial construction limitations, rainfall patterns, targeted volume management, and efficacy of pollution removal, the size and the spatial distribution of bioretention cells may require an increase in size or other changes. But practically speaking, a 5-km² bioretention cell is not the norm for many urban applications as these are generally small, decentralized structures intended for at source treatment and distributed throughout a region [47].

Table 3 provided support for the benefits and disadvantages to three of the most popular forms of LIDs. Many of the type 2 studies were simulations designed to explore a very specific or niche aspect of the LID but ultimately, they confirm what the literature already shows regarding these LIDs: weather characteristics throughout the year are essential for managing vegetated structures, which provide the known benefits of vegetation but the disadvantages of pollutant leaching while vegetation is developing, maintenance and space constraints, and limitations on functionality if the location experiences winter conditions. Permeable pavements are very popular for altering surface hydraulic conductivity to allow infiltration and the sub-base can be designed with significant capacity over large areas. While they do not have the benefits or disadvantages of their vegetated counterparts, they are very prone to clogging that must be remediated mechanically and on an annual basis in some locations.

Table 2 provides the type of literature that attempts to model LIDs in future climate scenarios to either determine the impacts of climate change on LIDs. Most of the studies were done on event-based timescales, which is not surprising as LIDs are designed starting with IDF curves as are most stormwater infrastructure. The design storms are of a specific return period and modelled with time steps as small as minutes. Interestingly though, it suggests that the infrastructure’s role and interaction with the landscape outside of the events for which they are designed (of the order of 2 to 5-yr return for permeable pavement to 100-yr design storms for bioretention cells) is less important. But continuous simulations are often needed to determine maintenance and operational performance over the lifespan of the LID. They can be time-consuming exercises particularly when using GCM/RCM precipitation data for meteorological input but alternatively, may be less affected by climate model uncertainty than event-based exercises that rely on accurate estimates of rainfall intensity at short time scales. In some cases, the studies were unclear as to what time scale was involved in the simulation. Furthermore, some studies lacked clarity in terms of the actual LID area modeled, or resolution of the modelling exercise. The temporal and spatial scale of the study, whether in current climates or future climates, will significantly affect the estimates of both water quantity and quality mitigation by the LID. The processes that support the treatment, work at a variety of timescales but for the most part, are studied and modelled at small spatial scales for both vegetated and un-vegetated LIDs.

Uncertainty analysis is an effective tool for analyzing scale problems. Some of the literature mentioned the uncertainty arising from the scale and spatial distribution of the LID in the simulations. Sensitivity analysis is often used in analyzing the impacts of temporal heterogeneity (that may exist in precipitation time series data) and spatial heterogeneity (such as the study area scope and LID implementation size). A recent study conducted an uncertainty analysis and suggested that climate change caused wide ranges of uncertainties in LID performance but the uncertainty in LID water quality performance was more significant than that of LID hydrologic performance. Scenario analysis under the climate change conditions showed that the hydrological results varied depending on the rainfall scenarios [38]. Further research showed that hydrological results varied with rainfall scenarios, while water quality outcomes were strongly influenced by temporal rainfall distribution [39]. Effective (net) rainfall patterns were found to have a significant impact on the runoff hydrograph of an LID, and therefore would affect the outcomes of any climate change study [29]. In spite of this, an LID focused case study in central Shanghai, China suggested that LIDs could effectively mitigate flooding projected from global climate model (GCM) precipitation estimates [28].

The literature has already shown that the spatial distribution of the urban area and placement of the LID is an important factor in urban or peri-urban catchment hydrology. Different percent coverages of LIDs in a catchment afforded different mitigating response for water quantity as well as water quality; but that location was also important and suggested that placing LIDs in the downstream region of the catchment was optimal. In addition, spatially distributed information such as slope and soil type will influence the effectiveness of LID implementation [48,49] and different resolutions in the data input to the same model will also result in varying output [50–52].

Spatial scale is coupled to temporal scale. LID measures with limited retention capacity should be adopted for shorter return period design storms [36]. The effectiveness for mitigating peak flows by permeable pavement and bioretention cells varied non-linearly with the extent of implementation but that both LID types were found to significantly reduce runoff volume and peak discharge for short return period events, but not for longer return periods storms [37]. As well, the prevalence of small scale studies in the literature suggested a need for more research that supports climate change impacts with research at the appropriate scales [53].

The repeated theme of scale issues is noted in many of the studies and many authors indicated an understanding of the inherent uncertainty arising from using forced inputs from GCMs or RCMs onto smaller scale hydrological models, even if they did not quantify it outright. Even modest reductions in impervious cover can have a significant impact on reducing stormwater runoff and pollutant loads related to increased precipitation but cautioned that due to the uncertainty in future precipitation patterns and magnitudes, the effectiveness of such measures cannot be accurately predicted [54]. Others noted that the LIDs are modelled as static systems in long term, continuous simulations, which is entirely unrealistic given that all LIDs are plagued by clogging over time; and thus, assessing the effect of LIDs on mitigating water quality in future climates might be overestimated [38].

Another commonality found in the literature review was the predominance of the use of the SWMM model (or hybrid thereof) to model the LID in the study. A review on LID effectiveness noted that many studies modelling future water quality use the SWMM model or some version of SWMM. This model is based on small scale processes relevant to the urban landscape that is proliferated with stormwater infrastructure such as pipes and catchbasins [55]. The need for an LID component was recognized years ago and added based on a simple representation of a generic LID [56]. Like any model, it is based on various concepts and assumptions that simplify reality, and is not without its own deficiencies, particularly where vegetated LIDs, such as BRs and GRs, are concerned. Despite this, the SWMM model seems to be the model of choice for use in climate change impacts in areas with LIDs in the literature, and will likely continue to be a model of choice for many urban applications in future climates.

As a small scale model, SWMM’s LID model performance is particularly vulnerable to errors leading to overestimation or underestimation in performance if applied at too large a scale. When scaling up, or down, the degree of heterogeneity either decreases or increase, respectively. SWMM uses averages over fundamental hydrological response units that define the catchment’s hydrology and the LIDs it contains. The literature shows that determining the ramifications of scaling with this model for climate change studies, particularly on the uncertainty in the outcomes, is often ignored. To further explore the extent to which the SWMM model and its LID component can be upscaled for use with RCM data, the authors conduct a case study that applies the PCSWMM model to increasing areas of a region, in order to model LID performance in a future climate, while assessing the information heterogeneity at each scale. Information theory or diversity indices are measures of the heterogeneity in a layer of information (input to the model). The authors propose that studying information loss when upscaling can be used as an indicator of the scalability of a model. This may allow the user to determine whether the loss is acceptable at a certain scale.

Case study: The implication of scale in LID mitigation assessment in future climates

This case study is intended to illustrate the drawbacks in addition to those already identified in the literature that are related only to spatial scaling when using an urban centered hydrological model like SWMM, which is the predominant choice in the literature. We use PCSWMM 7.5.3399 Professional 2D (based on SWMM vs. 5.1.015) with ArcGIS to conduct a simple LID modelling exercise in an actual catchment given regional climate model data. The assessment is only conducted for one future climate scenario, and only examines peak flowrates and total volumes output by PCSWMM. In addition, the case study uses only one type of LID, a bioretention cell, as it is the one of the most complicated types of LID in terms of structure and modelling requirements.

Study area

The research location is located in Saanich, which is situated on Vancouver Island, British Columbia and is shown in Figure 1A. Saanich includes a mix of rural and urban landscapes and communities extending north up to the Saanich Peninsula. The climate is a temperate coastal climate where the temperature rarely falls below 0°C and much of the precipitation falls as rainfall. The terrain in this area is characterized by undulating land with several rocky outcrops resulting from glaciers. The elevation of the area varies from sea level to 229 m above sea level. Daily rainfall data for 2022 were obtained from the “VICTORIA INT’L A” meteorological station in Saanich, BC on Vancouver Island (station number: 1018620) from Environment Canada, and the location is shown in Figure 1A (source data taken from climate.weather.gc.ca/climate_normals/index_e.html). The RCM precipitation data were obtained from the Climate Change Data Portal website (canadaccdp.ca). Daily precipitation for the period of 2020–2029 generated by PRECIS RCM for downscaled climate projections at a resolution of 50 km under RCP4.5, were used. Other data sources such as landuse GIS data were obtained from the District of Saanich, a municipality on Vancouver Island (www.saanich.ca/EN/main/local-government/development-applications/land-use-contracts.html). The soil data were obtained from the BC Soil Survey at www2.gov.bc.ca/gov/content/environment/air-land-water/land/soil/soil-information-finder, and shown in Figure 1B. The digital elevation model (DEM) was obtained from the USGS at a 30×30 m resolution (DEM data layer GMTED2010N30W150) from earthexplorer.usgs.gov/ and shown in Figure 1C. Model parameters based on soil type have been calibrated in previous studies [56] for catchment C3 and the data sources used for modelling are shown in Table S1 in the Supplementary information. Figure 1B shows the research area boundaries for catchments C1 to C5 modelled in PCSWMM within the Saanich region. Table 4 shows the physical characteristics of each catchment as they are input into PCSWMM. C1 is the smallest catchment with 3.01 km² of area, while C5 is the largest research area with 51.43 km².

Figure 1 Geographic information system layer datasets used in the case study simulation. (A) Research area in Saanich on lower Vancouver Island, British Columbia, Canada; (B) catchment boundaries for C1 to C5; (C) soil type up to catchment C5; (D) slope data (derived from DEM data).

Table 4 shows that as the research area (and scale) increases, the flow length also increases linearly. This is because flow length is determined in PCSWMM according to the maximum flow length in the study area. In addition, the slope is expressed as a single value by PCSWMM calculated using an area weighted average. Thus, not surprisingly, the average slope gradually decreases with increasing study area. The observed values of the soil-related data (suction head, conductivity as well as initial deficit) in PCSWMM are relatively stable in different upscaling scenarios. Model parameters in Table 4 had been calibrated in previous studies [56].

Catchment scaling scenarios

The scenarios span a range of circumstances including continuous simulations of 2022 peak flows and runoff volumes, as well as 40% catchment imperviousness when there are no LIDs implemented in the catchment (‘No LID in Catchment’ scenarios in Table 5), and various LID implementation scenarios (shown as ‘LIDs in Catchment’ in Table 5) in a future climate. Table 5 shows 29 simulation scenarios and using two types (Type A and Type B) of continuous time series rainfall data. Scenarios under rainfall time series data Type A use 2022 meteorological data from the airport in Saanich. The number in the scenario name indicates the catchment modelled; for example, A1 represents the simulation using actual rainfall data in 2022 corresponding with catchment C1 with 40% imperviousness and there is no LID infrastructure in the catchment. A1R also involves 2022 precipitation data but with the actual and current levels of imperviousness in the catchment (shown in Table 6) and no LIDs implemented in catchment C1. A1S1 is a scenario with LID implemented in the C1 catchment with 40% impervious area, and is used to evaluate the LID performance for mitigating water quantity in current climates. The number that increases in the naming convention shown in A1S1, A2S1… to A5S1, correspond to catchments C1, C2… to C5, respectively, as an exercise exploring the scaling up process with LID implementation in current climates (Type A time series simulation scenarios). Scenarios that begin with the letter B represent a 20-year simulation using future Representative Concentration Pathway 4.5 (RCP 4.5) precipitation data, where the interval is selected as the near future from 2020–2039 and the number B1 to B5 refers to catchments C1 to C5. Therefore, the B1 scenario uses catchment C1 without LID practices in place and with 40% imperviousness under RCP 4.5 20 year rainfall simulation. Similarly, B1S1 involves LID practices implemented in the catchment with a 40% impervious area under RCP 4.5 20 year rainfall simulation. Beyond that, B#S2 scenarios for every catchment # involve LID implemented at a fixed percentage of 10% for each of catchment. Overall, these simulation scenarios are able to help us to explore the differences resulting from LID implementation when scaling up, and the differences arising from using Type A and Type B rainfall. The latter can also help to evaluate the LID performance in current rainfall in comparison to that in a future climate. Note that the LID area is fixed at about 0.3 km² for 10 (out of 29) simulation scenarios (A1S1 to A5S1 and B1S1 to B5S1). This helps to observe the impact of the LID and impervious area signal on output under the 2022 rainfall and the RCP 4.5 rainfall, as the overall catchment areas increases (but the LID and impervious areas are fixed).

We compare the output results of PCSWMM simulations, such as peak flow and total volume for current and future climate change in a variety of urbanization and LID implementation levels by computing a mitigating factor shown in Eq. (1) that calculates the role of LID for mitigating water quantity metrics (peak flow rate or total volume):

(1)

where O is the performance metric describing the percent reduction (or increase) associated with the computed output (either peak flow rate or total volume) for each scenario; S_NoLID is the scenario’s computed output when no LID is implemented; and S_LID is the scenario’s computed output after with LID implemented in various scenarios.

Hydrometeorological data and PRECIS data

Figure 2A shows the precipitation data for 2022. This data series is mainly used to explore the impact that LIDs might have to mitigate a high level of imperviousness in the current climate. We also use this data series to explore the information loss and normalized information loss between the actual spatial data and PCSWMM’s representation of the spatial data in the various scenarios. Figure 2B shows the precipitation data series from PRECIS for RCP4.5 climate change scenario from 2020 to 2040. Figure 2C shows the PRECIS data but only for 2022. In comparison to Figure 2A, the distribution of precipitation is fairly similar between the observed data for the region and the PRECIS data. Figure 2D shows the boundary of the single grid cell represented by the PRECIS data. Also shown in this figure is the C5 catchment for scale.

Figure 2 (A) Total precipitation rainfall distribution for 2022 rainfall; (B) PRECIS RCP4.5 20 year simulation precipitation; (C) PRECIS RCP4.5 scenario precipitation for 2022; (D) C5 catchment location vs. the PRECIS grid cell associated with the future climate precipitation data.

In addition, Canadian Climate Normal data from 1981 to 2010 (https://climate.weather.gc.ca/climate_normals/index_e.html) for the Victoria International Airport were obtained to conduct a comparison between current and future precipitation time series, as shown in Table 6. The results show that the 2022 precipitation is lower than the Climate Normal, indicating that 2022 was likely a dry year. However, the average annual rainfall and peak value of rainfall in the next 20 years is predicted by PRECIS to be significantly higher than the Climate Normal by a factor of nearly 1.5. This meteorological difference reflects a significant change in rainfall and peak values under future climate conditions.

Spatial information representation in PCSWMM

PCSWMM will convert the irregular subcatchment shape to a rectangular reservoir for further simulation. This representation is shown in Figure 3. This process effectively reduces the calculation time but also greatly reduces the amount of heterogeneity in a catchment by reducing nearly all spatial heterogeneity to an average over space. PCSWMM determines soil related parameters for each soil type in the catchment but then uses an area weighted average to produce one soil type for the whole catchment. Landuse is one type of input that gets reduced to either two or three different types: pervious, impervious, and LID. The figure shows the way in which each catchment is converted to its PCSWMM representation with respect to physical topology and landuse. For the purposes of this case study, we assume that the LIDs are optimally maintained, and that clogging does not affect the performance of the LID in the 20-year simulation. The impact of the clogging factor on the simulation can be found in Ref. [56]. The specific modelling parameters of the LID are for the bioretention cell type and are derived from low impact development stormwater management [57] and shown in Table S2 in the Supplementary information.

Figure 3 PCSWMM Land use conversion process from actual shown on the left to scenarios involving no LIDs, and for scenarios involving LIDs shown on the right for (A) catchment C1, (B) C2, (C) C3, (D) C4, (E) C5. Note that the left most figures in each row show the actual landuse GIS data, the middle figure represents PCSWMM’s representation in the A1R to A5R scenarios, and rightmost figures represent model circumstances in the BS1 to BS2 scenarios.

With the exception of the landuse layer, all other geographic information (soil and slope) is represented as a single value in PCSWMM. Regarding the implementation of LID, the soil will be classified into LID soil and catchment soil, and the slope of the original catchment will not change after the implementation of LID.

Shannon diversity index for information loss in scaling

The Shannon diversity index (SHDI) is a measure of information diversity in a system. With regard to modelling catchment hydrology, the index would estimate the degree of heterogeneity in each layer of information used by the model in determining the watershed’s hydrological output such as soil maps or landuse maps. To measure the diversity in landuse, soil, and slope, which are inputs to PCWMM, SHDI was calculated using Eq. (2) for the actual catchment as well as PCSWMM’s representation of the catchment (with or without LIDs) in its modelling process. Shannon entropy formula as well as upper limit of SHDI is given by Singh (2011):

(2)

(3)

where p(x_i) is the probability associated with the occurrence of x_i where x_i represents one of the different categories that exist in that layer with N different types of categories (such as landuse classes, soil types, and ranges of slope). The probability is simply computed as the areal proportion of the catchment having a value of x_i to the entire research area. SHDI_max is the upper limit of SHDI in each layer. If there is only one category in a region, the SHDI is 0, indicating that the category is the only one that exists in the area. If the proportion of various categories is exactly equal, the distribution of diversity in the catchment layer follows a uniform distribution and the SHDI is the largest value possible reaching an upper limit. Furthermore, we use Eq. (3) to normalize the SHDI given the number of different categories describing the heterogeneity in a watershed’s layer. This process can provide a relative measure of SHDI when comparing values between different layers. This is necessary because it is not meaningful to directly compare SHDI values for two different types of information (soil SHDI cannot be compared to slope SHDI). The NSHDI of Eq. (4) ranges from 0 to 1 as SHDI approaches infinity, with higher values indicating greater diversity and lower values indicating lower diversity. When the GIS layers contain only one category (N = 1), the SHDI equals SHDI_max and both are equal to 0. This is meaningless in terms of the SHDI, and subsequently, results in Eq. (4) being undefined; thus, 1 is added to the denominator, which does not change the range as SHDI approaches infinity.

(4)

A second expression was created to calculate the information loss produced by the PCSWMM model, especially in the conversion process from the real GIS data to its representation in the model. Eq. (5) describes the index NILI for the information loss measurement.

(5)

where NILI is the normalized information loss index for each layer, NSHDI_actual is the normalized SHDI for the data layer created from the GIS data at the scale available, and NSHDI_model is the same information layer as it is represented in the model; in this case study, the PCWMM model.

Results and discussion

PCSWMM catchment simulations with and without LIDs, in 2022 and RCP4.5 scenarios

Figure 4A and B show the impact of LIDs implemented in 2022 for mitigating peak flow and total volume as the catchment increases. The authors used Eq. (1) to evaluate the performance of the LIDs at each catchment scale. In this section, 20 simulation scenarios (shown in Table 5) were compared for LID impacts on peak and volume under 2022 actual rainfall and in RCP 4.5 climate. These include A1 to A5, B1 to B5, A1S1 to A5S1, as well as B1S1 to B5S1. Note that LID area is fixed at about 0.3 km² for 10 (out of 29) simulation scenarios.

Figure 4 (A) LID mitigating performance vs. increasing area for peak flow and total volume for 2022; (B) computed peak flows and volumes computed with LIDs and without LIDs implemented in 2022; (C) LID mitigating performance for the RCP 4.5 scenarios; (D) corresponding peak flows and volumes with and without LIDs under RCP4.5. Note that (A) and (B) are computed with 2022 rainfall simulations (A1 to A5) and (A1S1 to A5S1); (C) and (D) are computed using (B1 to B5) and (B1S1 to B5S1) in RCP4.5.

On the surface, comparing Figure 4B and D show that peak flows and total volumes will increase by an order of magnitude in the future climate. Furthermore, the small LID of roughly 0.3 km² for the whole region has a discernable impact on total volumes in 2022 and in RCP4.5 but much less so on peak flows as the LID area starts to fall below 1% of the catchment area. Figure 4A and C show the linear reduction in impact for total volumes as the catchment grows in size and the rapid decline on mitigating peak flows. Figure 4C and D were computationally intensive, taking hours to run because of the daily timestep over 20 years of data. But in actuality, the graphs show that a simple linear relationship between flow (or volume) and precipitation would have produced an equally reasonable result with the same level of uncertainty. This is because of how PCSWMM represents urban catchments and LIDS and Figure 4 is a manifestation of this representation. Regardless of the type of LID and whether they are vegetated or not, they are all effectively modelled as tanks in PCSWMM that store water to a designed depth (capacity) whose volume increases as the area of the LID increases. In PCSWMM, vegetation impacts the surface storage portion of the tank and is rendered static. However, this aspect of the LID is not a highly influencing factor on flowrates and volumes and for continuous simulations, it is the sub-surface storage that has the greatest impact on mitigating volumes and to some degree, peaks [56]. Thus, Figure 4B and D show linear increases in peaks and volumes as the LID becomes less and less impactful as the catchment grows. If the results are to be accepted at face value, it suggests that LIDs are excellent at mitigating total volumes in future climates and can potentially mitigate peak flows by almost 50%, depending on the scale. Mitigating the increase in extreme rainfall intensity and total rainfall brought about by future climate change will depend on the space available to provide the storage capacity need by the LID. Scenarios B#S2 were run simply to see the mitigation percentages when every catchment C1 to C5 is implemented with an LID equal to 33.3% of its area. Because the LID effectively becomes a reservoir (more closely emulated by a rain barrel than a bioretention cell), the mitigation is exactly the same for every catchment in RCP4.5 - peak flows are reduced by 49% with the LID and total volumes are reduced by 86% in the future. While an obvious and computationally expensive exercise, because of the simplistic representation of the catchment in these continuous simulations, a simple linear expression would suffice to scale up the impacts of climate change when implementing LIDs. Note that an LID area of 17 km² within a 51 km² catchment is not realistic or practical.

SHDI computations for measuring the information loss in upscaling real and PCSWMM’s representation of spatial data

In this section, Eq. (2) and AR1 to AR5 simulation scenarios were used to calculate the SHDI of the actual data and of the PCSWMM transformation of that data, for three important variables affecting the catchment’s hydrology: land use, soil type and slope. Figure 5 shows the SHDI and the maximum SHDI calculated with Eq. (3) for each data type. Depending on the distribution of information for land use, soil type or slope, when increasing the catchment area (i.e. scaling up), the number of different categories of land use or soil type or slope may increase or decrease depending on the heterogeneity in the area. For this particular region, as can be seen in Figure 1, increasing the area introduces more categories of soil data and land use type into the system and this is seen in Figure 5 as the SHDI value changes as the scale changes. Slope on the other hand stays relatively constant indicating that the region as a whole is relatively homogenous with respect to slope.

Figure 5 SHDI change vs. catchment size for (A) actual land use and PCSWMM land use, (B) soil, and (C) slope. Note that PCSWMM LU values are computed with respect to the A1R to A5R scenarios while all other SHDI values are computed from the actual GIS data.

Note that in Figure 5B and C, no PCSWMM SHDI values are shown. This is because PCSWMM uses one average value for the entire catchment, is therefore zero and does not change with scale. This means that the information entropy of the model is at the minimum value and that all possible states of the system are deterministic. The process of converting the catchment from the irregular shape of the real watershed to a rectangular shape leads to an inherent loss of information immediately before the simulation begins. Figure 5A shows that PCSWMM only has two or three land use types; two if there is no LID and 3 if one exists, as can be seen in Figure 3. What is non-intuitive is how the SHDI value for PCSWMM LU shows greater diversity than the actual landuse layer for the smaller catchments. This higher level of diversity is entirely artificial and is an artefact of the representation of landuse in PCSWMM.

Given the shortcomings of comparing SHDI values between different data types, Figure 6 shows the NSHDI values for all the layers in which SHDI is not zero (computed using Eq. (4)).

Figure 6 Change in NSHDI as area increases. Note that PCS values pertain to PCSWMMs representations in A1R to A5R, while others are computed from actual GIS data.

Figure 6 shows that for areas less than 40 km², the real slope dataset has the highest NSHDI values, followed by the real soil dataset, followed by PCSWMM’s land use layer. The fact that actual slope has the greatest diversity as compared to all other spatial data may seem counter-intuitive given that slope remained fairly constant as catchment scale increases. But SHDI is a measure of the proportion of cells in a grid that belong to a specific category. If the distribution is uniform, the SHDI tends to its maximum value. If it is distributed with most values residing in one or two categories, then SHDI and NSHDI values are smaller.

As the scale increases, the dominance of NSHDI values for these three layers also changes. The results indicate that for actual data, slope NSHDI is relatively stable with a slight decrease with increasing spatial scales, while the soil NSHDI gradually increases. When the scale increases, the value of NSHDI for soil will tend to approach the slope value. This suggests that with increasing spatial scales in this region, the relevance of soil heterogeneity will gradually increase, thus increasing the uncertainty with any lumped representation of the soil in the model. This is true for any NSHDI values computed from actual data that increase with increase in scale. The key here is how the model represents that heterogeneity—for all scales PCSWMM has no heterogeneity in soil or slope. It only has heterogeneity in landuse and that heterogeneity is constant across scales. The NSHDI of actual landuse in fact increases with scale suggesting that a model with a constant NSHDI will inherently provide over- or under-estimates of predictions.

To explore the issue further, Eq. (5) was used to calculate the information loss due to the PCSWMM model in any of the scenarios. The NILI values for landuse, soil type and slope vs. catchment area are shown in Figure 7. The Figure shows that NILI value for landuse is negative for smaller scales, suggesting that the diversity of the landuse was enriched in the process of transforming real data into the PCSWMM model. The difference between the actual and model values gradually decreases as the scale increases. This finding suggests that for a homogeneous catchment in small scale studies, PCSWMM may overexpress and transform land use types artificially. For NILI soil, increasing scale will gradually increase and introduce uncertainty into model simulation. This value will exceed NILI slope and become the most significant factor leading to uncertainty in the study area at a large scale. In addition, NILI slope has the highest degree of information loss relative to the other two but the uncertainty remains relatively constant at all scales. As a result, as the scale increases, the accuracy of the soil layer is reduced, while the slope layer will always have a high degree of information loss. Ultimately, it is how the model uses slope, soil type and landuse in computing the hydrological output that determines the significance of information loss. Research has shown that for peak flows, PCSWMM was highly sensitive to slope and less so, to landuse and soil type; while for total volumes, PCSWM output was highly sensitive to soil related parameters [56]. Thus, because of the degree of information loss with scale, the uncertainty associated with PCSWMM output will also vary with scale.

Figure 7 The normalized information loss in slope, landuse and soil type between actual spatial data and PCSWMM representations. There is no LID implementated in A1R to A5R simulation scenarios.

Relationship between NILI and PCSWMM output under RCP 4.5

In this section, scenarios B1 to B5, and B1S1 to B5S1 were selected to explore the relationship between information loss and PCSWMM’s prediction under future climate change. Figure 8 is a plot of how total volumes are mitigated by LIDs in RCP4.5 with catchment area, superimposed on a graph of information loss versus catchment area. However, information loss in this figure is computed using the following variation of Eq. (5):

Figure 8 The RCP4.5 scenario LID performance for mitigating climate change impact on total volume by PCSWMM vs. catchment area. Also shown is the information loss for the landuse and soil layers from scenarios B1–B5 scenarios B1S1–B5S1 vs. catchment area. NILI for LID areas of 10% for all catchments as in B1S2–B5S2 are also shown.

(6)

Figure 8 shows that LID mitigation of total volumes decreases with scale alongside the increases in uncertainty (NILI value) in landuse and soil type. As noted earlier, the LID mitigating performance decreases with scale as information loss increases. With regard to the two simulation scenarios belonging to PCSWMM (No LID and LID implemented), when facing 20 years of rainfall under climate change, the figure suggests that the computed NILI value for soil and landuse has a potential relationship with LID mitigating performance. Figure 8 results indicate that as the scale increases, the NILI values of soil gradually increase. This is because when implementing LID at a fixed scale, the proportion of engineering soil in the LID gradually decreases with increasing scale. When the NSHDI value without LID implementation is zero and the computed NSHDI LID soil value decrease with spatial scale, the overall NILI value will gradually approach zero with the increase in scale. Therefore, combining this with the LID mitigating performance curve in Figure 4C, we can conclude that as the NILI soil value gradually approaches zero with an increase in scale, the ability of the LID to mitigate future climate change (as modelled) will also decrease with the increase in scale. In addition, we observed that the NILI value of landuse has the same changing trend if implementing LID at a fixed size, where the trend gradually increases from negative to positive values. This is because, unlike soil data, PCSWMM divides catchments into impervious, pervious, and LID areas (if LID is implemented), making the complexity of expressing LID implementation higher than that of the soil data (a single value). Therefore, for landuse when there is no LID implemented in the catchment, the proportion of impervious and pervious areas is 40% and 60%, respectively, and the NSHDI values for all B scenarios without LIDs is 0.3974. But the landuse NSHDI value with LIDs at fixed value (B1S# scenarios) will gradually decrease from 0.4376 to 0.336 with the increase in scale. Therefore, the range of change in NILI landuse by the model will gradually increase with the scale. The figure also shows the NILI landuse values in scenario B#S2 (where every catchment has an LID area of 10% of the catchment area). The NILI value never changes, which corresponds to the LID mitigating performance as constant. The NILI is a measure of the model’s ability to use the heterogeneity in a catchment no matter the scale. It speaks to the complexity of the model as well at the uncertainty that may be generated as it conceptualizes the spatial characteristics of the catchment. While the NILI and the LID mitigating performance are only peripherally connected, together they demonstrate that the PCSWMM’s application at multiple scales can be replicated with a simple relationship between the scale metric (in this case area) and the total volume.

Conclusions

The literature review indicated that many studies combining climate change with LIDs mostly focus on bioretention cells, followed by permeable pavements and green roofs. In terms of spatial scale, most studies are conducted with large areas of LIDs of over 5 km²; even though LIDs are normally used as small, decentralized structures used for source control. In terms of time scales, most studies are event-based applications and research with continuous long-term simulations is lacking. The most recognized research gap is how LIDs are modeled (in terms of processes), and on what spatial and temporal scales (which greatly affect the outcomes). Little attention was paid to the interactions between LIDs, the meteorology or other hydrological components in a catchment. Nearly all the literature reviewed used statistical downscaling methods to reduce GCM and RCM data and use the results as rainfall input to a SWMM model or a hybrid version, and often ignoring the ramifications of the scaling process.

Various work attempt to reflect on the different types of LIDs and their effectiveness in potentially mitigating climate change; however, the study outcomes were always climate and location specific scenarios with little recognition of the uncertainty in LID model parameters or the dynamic nature of LIDs. The resolution of the GCM and RCM models, both in time and space, is too low for proper plot scale evaluation (the scale of many LIDs). The performance of LIDs is highly dependent on rainfall data both in overall quantities and in the distribution over the event or longer. Coarse rainfall distributions will introduce further uncertainty into the system, both spatially and temporally. This root of uncertainty will largely lead to overestimation or underestimation of the performance of the LID, thus leading to unreliable model simulation results.

In order to illuminate the consequences of scaling and any associated uncertainty, the authors used the SHDI with a PCSWMM application to a series of nested catchments. The index is used to quantify the information loss in representing geographic spatial information by the model. The results showed that slope derived from a 30 × 30 m DEM had a higher level of information loss as compared to that found for soil and landuse at any scale. Slope in PCSWMM is a significant factor in peak flow estimates and suggests that any misrepresentation at small or large scales may provide inaccurate estimates of flood projections. Due to the uneven spatial distribution of actual soil data in the study area, upscaling led to the poorest representation of soil diversity by PCSWMM and led to the highest source of uncertainty as compared with the other two types of spatial data considered. This suggests that PCSWMM’s conversion of soil distribution coupled with upscaling may lead to high uncertainty in processes related to soil in the model.

Data availability

Data sources are given in the manuscript and simulation results are available upon request.

Acknowledgments

We are grateful to Computational Hydraulics International (CHI) in Guelph, Ontario for providing the PCSWMM model with no cost for research purposes.

Funding

This work was supported by the National Science and Engineering Research Council of Canada (RGPIN-2022-04352).

Author contributions

Z.Z. and C.V. designed the research. Z.Z. conducted the simulations and analyzed the results. Both authors interpreted the results and wrote the manuscript.

Conflict of interest

The authors declare no conflict of interest.

References

All Tables

All Figures

	Figure 1 Geographic information system layer datasets used in the case study simulation. (A) Research area in Saanich on lower Vancouver Island, British Columbia, Canada; (B) catchment boundaries for C1 to C5; (C) soil type up to catchment C5; (D) slope data (derived from DEM data).
In the text

	Figure 2 (A) Total precipitation rainfall distribution for 2022 rainfall; (B) PRECIS RCP4.5 20 year simulation precipitation; (C) PRECIS RCP4.5 scenario precipitation for 2022; (D) C5 catchment location vs. the PRECIS grid cell associated with the future climate precipitation data.
In the text

Figure 3 PCSWMM Land use conversion process from actual shown on the left to scenarios involving no LIDs, and for scenarios involving LIDs shown on the right for (A) catchment C1, (B) C2, (C) C3, (D) C4, (E) C5. Note that the left most figures in each row show the actual landuse GIS data, the middle figure represents PCSWMM’s representation in the A1R to A5R scenarios, and rightmost figures represent model circumstances in the BS1 to BS2 scenarios.

In the text

Figure 4 (A) LID mitigating performance vs. increasing area for peak flow and total volume for 2022; (B) computed peak flows and volumes computed with LIDs and without LIDs implemented in 2022; (C) LID mitigating performance for the RCP 4.5 scenarios; (D) corresponding peak flows and volumes with and without LIDs under RCP4.5. Note that (A) and (B) are computed with 2022 rainfall simulations (A1 to A5) and (A1S1 to A5S1); (C) and (D) are computed using (B1 to B5) and (B1S1 to B5S1) in RCP4.5.

In the text

	Figure 5 SHDI change vs. catchment size for (A) actual land use and PCSWMM land use, (B) soil, and (C) slope. Note that PCSWMM LU values are computed with respect to the A1R to A5R scenarios while all other SHDI values are computed from the actual GIS data.
In the text

	Figure 6 Change in NSHDI as area increases. Note that PCS values pertain to PCSWMMs representations in A1R to A5R, while others are computed from actual GIS data.
In the text

	Figure 7 The normalized information loss in slope, landuse and soil type between actual spatial data and PCSWMM representations. There is no LID implementated in A1R to A5R simulation scenarios.
In the text

	Figure 8 The RCP4.5 scenario LID performance for mitigating climate change impact on total volume by PCSWMM vs. catchment area. Also shown is the information loss for the landuse and soil layers from scenarios B1–B5 scenarios B1S1–B5S1 vs. catchment area. NILI for LID areas of 10% for all catchments as in B1S2–B5S2 are also shown.
In the text