Selecting a proper spatial resolution for urban rainfall runoff modeling was not a trivial issue because it could affect the model outputs. Recently, the development of remote sensing technology and increasingly available data source had enabled rainfall runoff process to be modeled at detailed and microscales. However, the models with less complexity might have equally good performance with less model establishment and computation time. This study attempted to explore the impact of model spatial resolution on model performance and parameters. Models with different discretization degree were built up on the basis of actual drainage networks, urban parcels and specific land use. The results showed that there was very little difference in the total runoff volumes while peak flows showed obvious scale effects which could be up to 30%. Generally, model calibration could compensate the scale effect. The calibrated models with different resolution showed similar performances. The consideration of effective impervious area (EIA) as a calibration parameter marginally increased performance of the calibration period but also slightly decreased performance in the validation period which indicated the importance of detailed EIA identification.
Urbanization had significantly altered the land cover and geomorphology characteristics of natural catchment. Consequently the hydrological processes in urbanized area were quite different and more complex compared with that in natural state. The large proportion of impervious area decreased infiltration capacity as well as catchment response time. Meanwhile, man-made structures like roofs, roads and channels largely impacted overland flow and runoff routing processes (Salvadore et al. 2015). Thus, it was essential to make an accurate representation or characterization of urbanized catchment for hydrological modeling.
Modeling urban hydrological process at the proper scale is not a trivial issue. However, increasing the modeling detail and reducing model uncertainty are two naturally conflicting goals. Thus, practically speaking, a compromise or tradeoff should be found between these targets (Petrucci & Bonhomme 2014). In the past 10 years, both the computational capacity and the availability of high resolution distributed data had increased to a large degree. As a consequence, more and more researchers built up their model in high resolutions with detailed methods. Recently, hyper resolution input data obtained from multiple information sources and urban features had already been used in flood modeling of urban areas (Amaguchi & Kawamura 2016; Noh et al. 2018). Schubert et al. (2008) emphasized the importance of rooftop footprints extraction and found that the rooftop representation in model could better reproduce the inundation processes. Mannina & Viviani (2010) compared simplified and detailed integrated modelling approaches for urban water quality assessment and found the detailed model to be more robust and presented less uncertainty. Leandro et al. (2016) pointed out the importance of identifying heterogeneity of urban key features (roof type and land surfaces) in successful urban flood modeling. Most recent efforts in this category focused on the impact of the inclusion of collecting inlets in urban flood simulation (Chang et al. 2018; Jang et al. 2018). Both studies claimed the necessity of inclusion of inlets for accurate flood extent and duration estimation because these inlets provided a more realistic representation of the actual drainage capacity between surface and sewer system.
All these researches modeled urban hydrological processes at very fine scales (single rooftop or urban blocks), and this method called for a lot of tedious work in delineating and data processing. Recent developments, however, posed a possibility to effectively alleviate this problem. The publicly available database like the Open Street Map could provide information like roof top footprint and detailed surface land use distribution which could be directly transferred to objects in geographic information system (GIS) tools. On the other hand, (semi)automatic surface delineation tools have been developed and this could largely relieve the model building work. Sanzana et al. (2017) presented a semi-automatic tool, Geo-PUMMA, which could generate well-shaped vectorial meshes or Urban Hydrological Elements (UHEs). In order to avoid the tedious task of building the Storm Water Management Model (SWMM) model, Warsta et al. (2017) developed a tool called GisToSWMM5 that could automatically generate raster based sub-catchments, as well as their parameters values, that can be directly used in the model.
Although it is an irreversible trend to model urban hydrology at higher resolution with more detailed method, the benefits and drawbacks of doing so should be further discussed. One of the concerns was that the high resolution may lead to the increase of uncertainty or over-parameterization: When inappropriate selected or too many parameters were calibrated on limited data set, they would correspond well with the calibration data set but fail to fit additional data or predict future observations reliably (Petrucci & Bonhomme 2014). The other concern was the existence of effective parameters. These effective parameters could represent a global hydrological behavior. This meant that some low resolution models could have same performances as more detailed model and the former could save more resources. Leitão et al. (2010) had assessed the influences of urban drainage network simplification and suggested that simplified models had less simulation time without compromising simulation results. What was more, although the high resolution model could simulate more detailed hydrological processes, most of the current calibration technology was focused on fitting the hydrograph data of one or few points. This raised an issue called equifinality which meant that the different parameter sets might produce equal model performance. This also reduced the fidelity of the simulated results at the local scale of a distributed model.
Therefore, the scale issue of distributed model is an important question to understand. It is also a naturally concomitant problem in urban hydrology due to the nonlinear characteristics usually found in environmental hydrological systems (Jayawardena 2014). The research of scale or resolution issues in urban hydrology had a long history. Zaghoul (1981) had examined the effect of spatial discretization and parameters in urban catchment. Goyen & O'Loughlin (1999) discuss the basic building blocks used for dividing an urban hydrological modelling unit. A series of recent studies also discussed this issue with different model structures and catchments and got various results (Ghosh & Hellweger 2012; Sun et al. 2014; Goldstein et al. 2016). However, these researches always lacked a detailed description of how the parameter values were determined during the change of scale. Krebs et al. (2014) used the method of area weight average to determine the parameters across different resolutions but the value of one important parameter effective impervious area (EIA) was not maintained during the sub-catchment upscale process. What was more, most of these previous studies neglected a calibration process. Those who implemented calibration did not or failed to calibrate models with different resolutions to assess how calibration can compensate the scale non-linearity of the model.
The objective of the present study was to evaluate the effects of spatial discretization on performance of urban hydrology model. The EPA SWMM was used in this study because this model was one of the most popular models in urban hydrology simulation. The following two questions were attempted to be addressed:
What is the impact of spatial resolution change on model performance?
Can calibration compensate the scale effect and how will the calibrated parameters change?
The improvement of model performance obtained with an automatic calibration process was also investigated. The results of this study could help modelers defining the horizontal spatial discretization for their models by better perceiving its influence on model performance and model prediction uncertainties.
Study site description
We chose the Kunimigaoka Area (KA) in Sendai City, Japan for the case study. KA is a mostly residential area located in the northwestern part of Sendai City (Figure 1(a)). This catchment covers approximately 46 ha with a medium gradient slope topography. KA is featured with a temperate monsoon climate and the annual average rainfall and temperature are 1,254 mm and 12.4 °C, respectively. The construction processes of KA mainly occurred in the 1990s. Currently, the urbanization degree is rather complete and the land use showed little change after 2005. The surface runoff was first collected by the gutters which were built on both sides of the roads and then drained to storm water sewer conduits. At the outlet of the sewer system there is a regulation pond. The storm water first drains to this regulating pond and then to a downstream river.
A high resolution (5 × 5 m) elevation data set of KA was obtained from Land and Resources Department of Japan. Those DEM data were used to help determine the slope and the surface flow directions in the model. In order to identify the features and profiles of buildings, roads and residential gardens/parcels were distinguished using the planar graph and Google satellite image.
The underground pipeline data were provided by Sewer Administration Office of Sendai City which contained geographic and geometric information of more than 400 conduits and manholes. Although some streets had quite steep slopes, the slope of underground conduits were no more than 3% while most of them had a slope of 0.5%. Most of the conduits were circular with diameters ranging from 0.3 to 2.4 m, while some pipes were rectangular whose widths and heights varied from 0.4 to 0.8 m. The drainage system of the study area also included street gutters mentioned before. The slopes and elevations of gutters were adopted from these values of adjacent roads. The slopes of gutters ranged from 1.3% to 38%.
The rainfall was collected by two tipping-bucket rain gauges within the catchment from 26 February 2018 to the 29 July 2018 and include 23 individual events with a record resolution of 0.5 mm. Those 23 rainfall events were used for model calibration and validation. The location of the two rain gauges are shown in Figure 1(a). The data recorded by these two gauges were rather similar due to the limited catchment area. Some additional rainfall data from the Japan Meteorological Agency were also used in the simulation. These rainfall data included 39 rainfall events from July to October of 2017 and was collected by a metrological station at Sendai City which was around 4.2 km to the study site with 0.5 mm resolution. Those original rainfall data were processed into rainfall data with 5 min temporal resolution that can be used in the hydrological models. All those rainfall data were used for simulation to observe the scale effect of model.
At the outlet, the water level was recorded at 5 min intervals. The water level–flow rate relationship was obtained from several velocity measurement campaigns. There were some very small dry weather flow rate, which might be due to ground water exfiltration, which was subtracted from the records in order to obtain the storm water flow rate. Continuous flow measurements used for this study had the same period with the rain gauges in the catchment. The rainfall runoff data in this period were used for model calibration and validation.
The Storm Water Management Model
The SWMM was selected as the modelling platform for this study. This model was developed by US-EPA and was widely used for rainfall-runoff and water quality modeling in urban catchments. SWMM was a conceptual based spatially distributed model. In the model, spatial heterogeneity was realized by dividing the target catchment into several sub-catchments which were considered as the basic hydrological response units. Each sub-catchment was treated as a non-linear reservoir which received inflow from rainfall and upstream sub-catchments. And then within the sub-catchments, the inflow were partitioned into different components such as depression storage, evaporation, infiltration and runoff. The governing equation of sub-catchments was a combination of continuity equation and Manning equation. The runoff generated by sub-catchments was usually drained to the sewer pipe system where the 1-d Saint-Venant was employed. The detailed description of SWMM model can be found in Rossman (2015).
Urban catchment delineation
The models of the study area were build up at four levels of spatial resolution (S1, S2, S3, and S4). The S1 model which had the highest resolution was built up first. The principles of establishing S1 model referred to some previous research about high resolution or hyper resolution urban hydrologic model (Krebs et al. 2014; Amaguchi & Kawamura 2016; Noh et al. 2018). Each sub-catchment was built upon small urban structures like a single rooftop, a single garden or a short part of road. This made each sub-catchment to be occupied by a single land use type. The routing between sub-catchments could better represent the actual flow path at micro scale. In S1 model, not only the drainage conduits underground, but also the street gutters (small trench) with a fixed cross section beside the road were considered and modeled explicitly.
The sub-catchments of S2 model was discretized based on the urban blocks. The idea was similar to the concept of UHEs proposed by Rodriguez et al. (2008). In S2 model, a sub-catchment included a single residential block and the road surrounding them. All the gutters were neglected in this level but all underground conduits remained.
S4 model was delineated by the partitioning information of pipelines system provided by Sewer Administration Office. The whole catchment was divided to six sub-catchments. Those sub-catchments drain directly to a most downstream inlet within the sub-catchment and the pipes located at upstream of that inlet were neglected.
S3 was a transitional scale between S2 and S4. Several adjacent blocks in S2 were aggregated to form larger UHEs than the S2 model according to the drainage directions. Similar to S4, the pipes within each sub-catchment was omitted. The spatial representations of models are shown in Figure 1 and a brief summary of these four levels of models is listed in Appendix 1 (available with the online version of this paper).
Model parameterization and simulation design
For S1 model, due to its highly detailed representation method and the single land use type on each sub-catchment, the information like the imperviousness land surface or the flow path length could be all identified. The soil type in the study area was dominated by clay loam, thus the corresponding infiltration parameter values in the SWMM manual were used here. Even though the depression storage parameters (di/dp: depression depth on impervious/pervious surface) and the roughness parameters (ni, np and nc: the Manning's roughness of impervious/pervious surface and of conduits) remained unknown. Thus, the values of these parameters were obtained through model calibration.
After the calibration of S1 model, the parameters values of S2, S3 and S4 models were derived from S1 model by parameter upscale. Most of the parameters, including the imperviousness, slope, depression storage and roughness, were calculated by area weighted average method during the upscale process. Dominant parameters like the proportion of EIA (the impervious area which were directly connected to drainage sewer) and total impervious area (TIA) within a particular area were conserved during upscale. In the SWMM model, the pervious sub-area routing was set as the routing mode in order to represent the EIA proportion within sub-catchments by adjusting the sub-area routing ratio (Kong et al. 2017). The width parameter was determined using the method proposed by (Guo et al. 2011) because it took sufficient consideration of the impact of surface flow convergence pattern on width parameters.
After the parameterization, these models would run under different rainfall events to find how the model spatial discretization degree affected the simulation results. The rainfall events here include all the rainfall data mentioned in the section ‘Data preparation’: the rainfall data measured with the tipping bucket rain gauges, and the rainfall data obtained from metrological station at Sendai City.
Previously, only the S1 model was calibrated, the parameters of S2, S3 and S4 models were derived from S1 model through upscale. Therefore, it was also necessary to independently calibrate each model to find how the model parameters and model performances change with different discretization scale.
Initially, the same calibration method as previously were used. The depression storage parameters (di and dp) and the roughness parameters (ni, np and nc) were considered as the calibration parameters. The value range of the parameters was also consistent with before.
On the other hand, the importance of EIA had been emphasized in recent studies (Kong et al. 2017). Compared with TIA, EIA was not easy to obtain accurate values and distributions in practical application. Therefore, the EIA was also worth treating as an unknown calibration parameter, along with depression and roughness in another independent calibration.
The scale effect of models
The S1 model was first calibrated. After calibration, the model's NSE performance was 0.841 during the calibration period and 0.744 during validation. The hydrographs of several events in the calibration and validation period are shown in Appendix 2 (available with the online version of this paper). This meant that the calibrated S1 models had a good performance and prediction ability. Afterward, the parameters of S2–S4 models were determined by area weighted average method in the upscale process. And those models with different resolutions were run under all the 62 rainfall events. Figure 2 shows the hydrographs of two rainfall events: 5 March 2018 and 17 September 2017. It can be seen that the model's response to rainfall was weakened with the decrease of resolution with the most obvious phenomenon being the decreasing of peak discharge. The decreasing trend of peak discharge was more distinct in the 17 September 2017 event.
In order to compare the results of all the rainfall events, the general trends observed in the hydrologic outputs should be identified. The S1 model with the highest resolution was used as reference model. Hydrological modelling outputs were analyzed based upon these statistics: relative peak flows and relative total flows. The peak flows and total flows were normalized to those results of the S1 model.
Figure 3(a) has generalized the results of all the rainfall events simulated. It can be seen that as the spatial scale of the model decreased, the total flow and peak flow tended to decrease as well. While the variations of total flow were very slight, the peak flows of different resolution showed a distinct variation.
Generally speaking, the coarsening of model spatial resolution lead to a decreasing of both peak runoff and total runoff. It should be pointed out that not all simulation scenarios strictly follow this trend, and actually there were exceptions in the results. However, from the larger point of view, this general trend was clear. At the same time, rainfall characteristics had an impact on the degree of models' scale effect. The larger the peak intensity and total depth, the more obvious the scale effect (Figure 3(b) and 3(c)). Thus, the impacts of rainfall should be considered simultaneously. In order to quantify those scale effects, the method of dimensional analysis (Legendre & Legendre 2012) was used here.
Since the total flow rate showed little variation with different spatial resolutions while the variation on the peak flow rate was more obvious, only the results of the peak flow rate was quantified. The sub-catchment average size dx (square of average sub-catchment area) and drainage density dd (total conduits length divided by catchment area) was used to represent the level of discretization degree of different models. The peak 10 min rainfall intensity Ipk was used to represent the rainfall characteristic. The relative peak flow was selected as the independent variable, and the other factors were selected as the dependent variable. Then a scatter plot of the independent variable and the dependent variable were made. After several rounds of trial and error, empirical relationships were obtained.
The obtained A1, t1 and y0 parameters and the associated coefficient of determination (R2) of the fitting are summarized in Figure 4. The exponent functions provided a rough estimate of what hydrodynamic modelling performance could be expected for a given input resolution and rainfall peak intensity.
Model performances after independent calibration
S2, S3 amd S4 models were calibrated independently to find if calibration overcomes the scale effect and how the parameters will change. Following the calibration of S1 model, here five calibration parameters were selected: the depression storage parameters (di and dp) and the roughness parameters (ni, np and nc). Other parameters like slope TIA and EIA were obtained by area weighted average. As stated in the section ‘Model parameterization and simulation design’, due to its importance and particularity, EIA was necessary to be considered as a calibration parameter. So this generated a secondary calibration scenario in which EIA was regarded as unknown and thus six parameters were calibrated (five above parameters and EIA). The models' performance during calibration and validation period are shown in Figure 5.
It was clear that the performance of S2–S4 models were similar with S1 model after independent calibration. The NSE value of all the model exceeded 0.83 for the calibration sequence and 0.71 for the validation period. This indicated that the calibration process could compensate the differences caused by scale effect. The calibration performance of models were almost the same, while the prediction ability had small difference. For the NSE during validation period, of S1, S2 and S3 were slightly higher than that of S4.
When EIA was regarded as calibrated parameter, the models' performances in the calibration period was quite good and the NES values were equal to or slightly better than the previous calibration that did not take EIA into consideration. However, the NSE values during validation period were relatively lower than previous results. Among them, the NSE of S4 model had an obvious decline. This phenomenon indicated that the calibration method had caused over-parameterization to a certain degree. The above analysis demonstrated that it was better to use the detailed spatial distributed EIA parameter in model application when this information was available.
In order to better represent the spatial resolution effect on model calibration, the NSE response surface of certain parameters were analyzed. Figure 6 shows a certain slice of objective function surface for ni vs nc, EIA vs ni and EIA vs nc bi-variance parameter domain while other parameters remained at their optimal values. It was obvious that the domain of ni and nc showed a long strip structure. This indicated that those two parameters interact with each other. This kind of dependence between parameters was harmful to model build up and parameterization. The reason for this phenomenon was that the model structure and certain assumptions in which all the runoff was first in the form of overland flow and then all the runoff drained into an inlet and became conduit flow. This assumption simplified the complex runoff process and the interactions between different flow patterns and maybe had large differences with the real world process and thus caused conceptual error (Salvadore et al. 2015; Leandro et al. 2016).
When EIA was introduced, the NSE response surface showed a large difference with that of the ni vs nc. Firstly, as EIA had a relative large impact on model, the shape of NSE contour had a big change with the direction of EIA. And, relatively, the impact of ni and nc parameter were weakened. Different from previously, the EIA did not show clear interaction or dependence with ni and nc parameter. The shapes of the NSE contour were no longer a strip but oval. All the scenarios had a similar macroscale shape with different microscale features.
The optimal calibrated parameter values are also shown in Figure 6. It could be seen that the values of impervious surface roughness (ni) had a declining trend with the increase of model resolution. The calibrated ni parameter values of S2 to S4 models were 0.022, 0.019 and 0.015 (Figure 6(a)). It is mainly because the peak flow variations of different models were compensated by this parameter. The values of conduits roughness (nc) did not show a clear pattern after calibration. The calibrated EIA ratio were quite similar among different model scales and this emphasized the importance of correctly determining EIA value in model applications. The area of the orange region (NSE > 0.8) and red region (NSE > 0.85) indicated the degree of equifinality of the models. It can been seen that the equifinality existed not only in different parameter sets of the same model but also among different models.
There had been some previous studies on model scales issues but the conclusions are not the same. Ghosh & Hellweger (2012) found that the total discharge was not affected by the model resolution while the peak flow rate showed a dual scale effect. Guo et al. (2011) concluded that a model with more drainage details results in higher peak flows. However, in these studies, the method to determine or maintain the parameters at different spatial resolution modes was ambiguous. Krebs et al. (2014) had found that model aggregation increased peak flow rates but this could be because the EIA parameter was not maintained: all the imperviousness area in high resolution model became EIA in low resolution model. In this study, we found that the model aggregation led to a decrease in peak flow while the total runoff was not affected. By summarizing the above studies, it could be found that, in general, the total outflow was less affected by the resolution of the model, while the peak flow was affected more greatly with different variation trends. This could be because the total outflow was controlled by several important factors: the infiltration rate, the pervious ratio and the EIA ratio. All these factors were kept constant at catchment scale using areal weighted average method during the upscale. So the infiltration process and infiltrated amount were quite similar in different models, and this is why the total flow changed little, while the peak flow is quite different. Although the factors responsible for peak flow rate (the roughness parameters, the slope and depression storage parameters) were obtained using area weighted averaged method, the surface runoff routing process itself was non-linear. Also, different EIA distributions may have an impact on peak flow. So the peak flow rate cannot be maintained across scales.
Meanwhile, our results show that rainfall characteristics also have an effect on the scale effect of the model. Then the scale effect caused by spatial resolution and rainfall intensity was quantified. The quantification results showed that an exponent function can well represent the scale effect and this can be used as an error estimation method in practical application. Those quantifications had provided useful insights into the impacts and interactions of model resolution and rainfall characteristics but should be applied with caution in practical use.
While discussing the impact of model spatial resolution on the results, the calibration of models with different resolution is also worth mentioning, which includes the performance of the model after calibration, and the comparison of the calibrated parameter values (Merz et al. 2009; Wildemeersch et al. 2014). When considering only the roughness and depression storage parameter, the models can always have satisfied performance with respect to resolution. When the EIA is considered, the predictive ability showed a decline. This indicated that EIA and its distribution were key information for the model. Therefore, when the benefit of high resolution data were removed (EIA considered as unknown parameter), a coarse model resolution may lead to a relatively poor EIA identification and performance. The selection of model scale should be related to the data obtained and purpose of the model. In our case, the scale of S2 and S1 were both considered satisfying while the S3 and S4 model had the potential of performance declining. Thus, it is suggested that in such small urban areas the urban block scale is recommended in hydrological modeling.
Also, the response surface analysis suggested that equifinality existed among different models and parameter sets, and the scale of the model had a certain influence on the parameter domain and the corresponding surface. Among them, the parameter ni, nc has an interactional relationship, and its response surface shape was greatly affected by the accuracy of the model. The corresponding surface associated with EIA was more stable in shape. On a large scale, the reduction in accuracy did not destroy the shape of the corresponding surface, nor does it lead to mathematical artifacts. The distribution information of EIA only affected the performance of the model to a small extent although several previous researches suggested that EIA distribution had a great impact. This would be a topic worthy of further discussion.
This research attempted to analyze how the model performance and parameter optimization were affected by model grid resolution for a given model structure, SWMM. The performances of models with different resolutions were compared. The parameterization and prediction capacities were discussed during and after the calibration. The conclusions are as follows.
Although weighted average method was used, there were obvious scale effects across models due to the non-linearity nature of model structure. With the coarsening of grid, both the total and peak runoff tend to decrease while the variations of peak runoff rate was quite obvious while the relative differences can be larger than 30%. The effect of spatial resolution on simulated peak flows is also influenced by storm characteristics. The impact of these factors was quantified by dimensional analysis and a exponent function was fitted to the resulting scatter plots. This provides useful insights into the impact and interaction of spatial resolutions and other factors, as well as a practical estimation of the performance that can be expected for a given model input resolution.
After independent calibration, all the models showed satisfying performances. The performance of the calibrated models were similar to the S1 model (NSES2 = 0.837, NSES3 = 0.836 and NSES4 = 0.841). This meant that calibration could completely compensate models' scale effect. When EIA was considered as a calibrated parameter, the NSE value of S2, S3 and S4 models during calibrated period were 0.859, 0.863 and 0.845, while the performance of the validation period hold the line or decreased (NSES2 = 0.744, NSES3 = 0.685 and NSES4 = 0.613). The objective function surface of the models were analyzed. It could be found that the grid resolution led to the change of the overall shape of the surface and deviation of the best performance area.
This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (A), 2016–2019 (16H02363, So Kazama). The authors thank the Water Resources Bureau for providing drainage network data and the permission for monitoring discharge at the outlet. The first author gratefully acknowledges China Scholarship Council (CSC) for financial support.