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.

High-resolution rainfall fields contain numerous zeros (i.e. pixels or time steps with no rain) which are either real or artificial – that is to say associated with the limit of detection of the rainfall measurement device. In this paper we revisit the enduring discussion on the source of this intermittency, e.g. whether it requires specific modelling. We first review the framework of universal multifractals (UM), which are commonly used to analyse and simulate geophysical fields exhibiting extreme variability over a wide range of scales with the help of a reduced number of parameters. However, this framework does not enable properly taking into account these numerous zeros. For example, it has been shown that performing a standard UM analysis directly on the field can lead to low observed quality of scaling and severe bias in the estimates of UM parameters. In this paper we propose a new simple model to deal with this issue. It is a UM discrete cascade process, where at each step if the simulated intensity is below a given level (defined in a scale invariant manner), it only has a predetermined probability to survive and is otherwise set to zero. A threshold can then be implemented at the maximum resolution to mimic the limit of detection of the rainfall measurement device. While also imperfect, this simple model enables explanation of most of the observed behaviour, e.g. the presence of scaling breaks, or the difference between statistics computed for single events or longer periods

Abstract.We are used to the weather-climate dichotomy, yet the great majority of the spectral variance of atmospheric fields is in the continuous "background" and this defines instead a trichotomy with a "macroweather" regime in the intermediate range from ≈ 10 days to 10-30 yr (≈ 100 yr in the preindustrial period). In the weather, macroweather and climate regimes, exponents characterize the type of variability over the entire regime and it is natural to identify them with qualitatively different synergies of nonlinear dynamical mechanisms that repeat scale after scale. Since climate models are essentially meteorological models (although with extra couplings) it is thus important to determine whether they currently model all three regimes. Using last millennium simulations from four GCMs (global circulation models), we show that control runs only reproduce macroweather. When various (reconstructed) climate forcings are included, in the recent (industrial) period they show global fluctuations strongly increasing at scales > ≈ 10-30 yr, which is quite close to the observations. However, in the preindustrial period we find that the multicentennial variabilities are too weak and by analysing the scale dependence of solar and volcanic forcings, we argue that these forcings are unlikely to be sufficiently strong to account for the multicentennial and longer-scale temperature variability. A likely explanation is that the models lack important slow "climate" processes such as land ice or various biogeochemical processes.

Abstract. The Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech (hmco.enpc.fr) has made a data set of optical disdrometer measurements available that come from a campaign involving three collocated devices from two different manufacturers, relying on different underlying technologies (one Campbell Scientific PWS100 and two OTT Parsivel 2 instruments). The campaign took place in JanuaryFebruary 2016 in the Paris area (France). Disdrometers provide access to information on the size and velocity of drops falling through the sampling area of the devices of roughly a few tens of cm 2 . It enables the drop size distribution to be estimated and rainfall microphysics, kinetic energy, or radar quantities, for example, to be studied further. Raw data, i.e. basically a matrix containing a number of drops according to classes of size and velocity, along with more aggregated ones, such as the rain rate or drop size distribution with filtering, are available.Link to the data set: https://zenodo.org/record/1240168 (DOI: https://doi.org/10.5281/zenodo.1240168).