Scale effect challenges in urban hydrology highlighted with a distributed hydrological model

Abstract

Abstract. Hydrological models are extensively used in urban water management, development and evaluation of future scenarios and research activities. There is a growing interest in the development of fully distributed and grid-based models. However, some complex questions related to scale effects are not yet fully understood and still remain open issues in urban hydrology. In this paper we propose a twostep investigation framework to illustrate the extent of scale effects in urban hydrology. First, fractal tools are used to highlight the scale dependence observed within distributed data input into urban hydrological models. Then an intensive multi-scale modelling work is carried out to understand scale effects on hydrological model performance. Investigations are conducted using a fully distributed and physically based model, Multi-Hydro, developed at Ecole des Ponts ParisTech. The model is implemented at 17 spatial resolutions ranging from 100 to 5 m. Results clearly exhibit scale effect challenges in urban hydrology modelling. The applicability of fractal concepts highlights the scale dependence observed within distributed data. Patterns of geophysical data change when the size of the observation pixel changes. The multi-scale modelling investigation confirms scale effects on hydrological model performance. Results are analysed over three ranges of scales identified in the fractal analysis and confirmed through modelling. This work also discusses some remaining issues in urban hydrology modelling related to the availability of high-quality data at high resolutions, and model numerical instabilities as well as the computation time requirements. The main findings of this paper enable a replacement of traditional methods of "model calibration" by innovative methods of "model resolution alteration" based on the spatial data variability and scaling of flows in urban hydrology.

Multi-hydro hydrological modelling of a complex peri-urban catchment with storage basins comparing C-band and X-band radar rainfall data

“…Multi-Hydro is designed in such a way that its spatial resolution can be optimised with regard to all the available data and to the scaling of urban hydrology flows. This is an innovative method of model resolution alteration that can replace the traditional model calibration methods (Ichiba et al 2018).…”

“…The first step in the implementation of the model is rasterisation, i.e., allocating a single category of land use to each pixel in the domain. There are two different methods of performing this operation using MH-AssimTool (Ichiba et al 2018). The first is based on the order of priority of the six land use categories listed above, from the most to the least permeable.…”

“…Thus, a process is implemented once the "Gully" pixels have first been allocated. The two methods of data rasterisation are compared by Ichiba et al (2018). The results indicate that applying the majority rather than the priority order rule leads to a much better representation of catchment heterogeneity.…”

Technical note: Laboratory modelling of urban flooding: strengths and challenges of distorted scale models

“…At intermediate levels, such as when a single street or single crossroads are represented, scale factors of the order of 10-20 were used (Lee et al, 2013;Mignot et al, 2013;Rivière et al, 2011) which are generally deemed not to lead to excessive scale effects (Chanson, 2004). In contrast, when it comes to the experimental analysis of flooding at the level of an entire urban district, the spatial extent of the prototype to be represented becomes considerably larger (∼ 10 2 -10 3 m), as summarized in Table 1 To analyse river flooding at the level of an entire urban district (1 km × 2 km), Ishigaki et al (2003) also used a scale factor of 100; but in this case, despite a particularly large experimental facility (10 m × 20 m), the model Reynolds number was of the order of 7 × 10 3 , with water depth lower than 1 cm and being even lower than this amount in some streets. Ishigaki et al (2003) reported that the observed flow became "laminar" in some parts of the model, hence exacerbating scale effects.…”

“…In contrast, when it comes to the experimental analysis of flooding at the level of an entire urban district, the spatial extent of the prototype to be represented becomes considerably larger (∼ 10 2 -10 3 m), as summarized in Table 1 To analyse river flooding at the level of an entire urban district (1 km × 2 km), Ishigaki et al (2003) also used a scale factor of 100; but in this case, despite a particularly large experimental facility (10 m × 20 m), the model Reynolds number was of the order of 7 × 10 3 , with water depth lower than 1 cm and being even lower than this amount in some streets. Ishigaki et al (2003) reported that the observed flow became "laminar" in some parts of the model, hence exacerbating scale effects. This questions the validity of the upscaled lab observations and highlights a difficulty in the design of experimental models for analysing urban flooding, namely the substantial difference between the characteristic length in the horizontal direction (e.g.…”