ALBERT

Description: Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists of redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRCs). This works well for slowly varying homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, namely one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, with each of them containing exactly half of the original amount of water. The relative areas of the subgrid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity-dependent standard deviation (SD). The process ends when the amount of water in each subgrid cell is smaller than a fixed-bucket capacity, at which point the output of the cascade can be resampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that, on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model in the presence of intermittency and to the lower variance of its generator. However, both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale variability and extremes, the EVA model tends to produce fields that are slightly too smooth and block shaped compared to the observations. The complementary nature of the two approaches, and the fact that they produce errors of opposite signs, opens up new possibilities for quality control and bias corrections of downscaled fields.

Description: Weather radar has become an invaluable tool for monitoring rainfall and studying its link to hydrological response. However, when it comes to accurately measuring small-scale rainfall extremes responsible for urban flooding, many challenges remain. The most important of them is that radar tends to underestimate rainfall compared to gauges. The hope is that by measuring at higher resolutions and making use of dual-polarization radar, these mismatches can be reduced. Each country has developed its own strategy for addressing this issue. However, since there is no common benchmark, improvements are hard to quantify objectively. This study sheds new light on current performances by conducting a multinational assessment of radar's ability to capture heavy rain events at scales of 5 min up to 2 h. The work is performed within the context of the joint experiment framework of project MUFFIN (Multiscale Urban Flood Forecasting), which aims at better understanding the link between rainfall and urban pluvial flooding across scales. In total, six different radar products in Denmark, the Netherlands, Finland and Sweden were considered. The top 50 events in a 10-year database of radar data were used to quantify the overall agreement between radar and gauges as well as the bias affecting the peaks. Results show that the overall agreement in heavy rain is fair (correlation coefficient 0.7–0.9), with apparent multiplicative biases on the order of 1.2–1.8 (17  %–44  % underestimation). However, after taking into account the different sampling volumes of radar and gauges, actual biases could be as low as 10 %. Differences in sampling volumes between radar and gauges play an important role in explaining the bias but are hard to quantify precisely due to the many post-processing steps applied to radar. Despite being adjusted for bias by gauges, five out of six radar products still exhibited a clear conditional bias, with intensities of about 1 %–2 % per mmh−1. As a result, peak rainfall intensities were severely underestimated (factor 1.8–3.0 or 44 %–67 %). The most likely reason for this is the use of a fixed Z–R relationship when estimating rainfall rates (R) from reflectivity (Z), which fails to account for natural variations in raindrop size distribution with intensity. Based on our findings, the easiest way to mitigate the bias in times of heavy rain is to perform frequent (e.g., hourly) bias adjustments with the help of rain gauges, as demonstrated by the Dutch C-band product. An even more promising strategy that does not require any gauge adjustments is to estimate rainfall rates using a combination of reflectivity (Z) and differential phase shift (Kdp), as done in the Finnish OSAPOL product. Both approaches lead to approximately similar performances, with an average bias (at 10 min resolution) of about 30 % and a peak intensity bias of about 45 %.

Description: Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists in redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRC). This works well for slowly varying, homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, each of them containing exactly half of the original amount of water. The relative areas of the sub-grid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity dependent standard deviation. The process ends when the amount of water in each sub-grid cell is smaller than a fixed bucket capacity, at which point the output of the cascade can be re-sampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model to the presence of intermittency and to the lower variance of its generator. However, improvements are not systematic and both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale extremes and variability, the EVA model tends to produce fields that are slightly too smooth and blocky compared with observations.

Description: Weather radar has become an invaluable tool for monitoring rainfall and studying its link to hydrological response. However, when it comes to accurately measuring small-scale rainfall extremes responsible for urban flooding, many challenges remain. The most important of them is that radar tends to underestimate rainfall compared to gauges. The hope is that by moving to higher resolution and making use of dual-polarization, these mismatches can be reduced. Each country has developed its own strategy for addressing this issue. But since there is no common benchmark, improvements are hard to quantify objectively. This study sheds new light on current performances by conducting a multinational assessment of radar's ability to capture heavy rain events at scales of 5 min up to 2 hours. The work is performed within the context of the joint experiment framework of project MUFFIN (Multiscale Urban Flood Forecasting), which aims at better understanding the link between rainfall and urban pluvial flooding across scales. In total, 6 different radar products in Denmark, the Netherlands, Finland and Sweden were considered. The top 50 events for each country were used to quantify the overall agreement between radar and gauges and the errors affecting the peaks. Results show that the overall agreement between radar and gauges in heavy rain is fair, with multiplicative biases in the order of 1.41–1.66 (i.e., radar underestimates by 29–39.8 %) and correlation coefficients of 0.71–0.83 across countries. However, the bias increases with intensity, reaching 45.9 %–66.2 % during the peaks. Only part of the bias (i.e., roughly 13 %–30 % depending on the radar product) can be explained by differences in measurement areas between gauges and radar. Radar products with higher spatial and temporal resolutions agreed better with the gauges, highlighting the importance of high-resolution radar for urban hydrology. However, for capturing peak intensity and reducing the bias during the most intense part of a storm, the ability to combine measurements from multiple overlapping radars to help mitigate attenuation seemed to play a more important role than resolution. The use of dual-polarization and phase information (e.g., Kdp) in the experimental Finnish OSAPOL product also seemed to provide a slight advantage in heavy rain. But improvements were hard to quantify and similarly good results were achieved in the Netherlands by applying a simple Z–R relation together with a mean field bias-correction.

Description: A detailed analysis of how intermittency modulates the rate at which sub-daily rainfall extremes depend on temperature is presented. Results show that hourly extremes tend to be predominantly controlled by peak intensity, increasing at a rate of approximately 7 % per degree in agreement with the Clausius–Clapeyron equation. However, rapid increase of rainfall intermittency upward of 20–25 degrees Celsius is shown to produce local deviations from this theoretical scaling, resulting in lower correlations between rainfall and temperature. On the other hand, rapidly decreasing intermittency with temperature between 10–20 degrees can result in higher net scaling rates than expected, potentially exceeding Clausius–Clapeyron. In general, the importance of intermittency in controlling the scaling rates of precipitation totals with temperature grows as we progress from hourly to daily aggregation time scales and beyond. Thermodynamic effects still play an important role in controlling the maximum water holding capacity of the atmosphere and therefore peak rainfall intensity. But the observational evidence shows that beyond a few hours, storm totals become increasingly dominated by dynamical factors such as event duration and internal intermittency. The conclusion is that Clausius–Clapeyron scaling alone can not be used to reliably predict the net effective changes in rainfall extremes with temperature beyond a few hours. A more general scaling model that takes into account simultaneous changes in intermittency and peak intensity with temperature is proposed to help better disentangle these two phenomena. The model is applied to a large number of high-resolution rain gauge time series in the United States. Results show that the new model with intermittency greatly improves the representation of rainfall extremes with temperature, producing a much more consistent and reliable picture of extremes across scales than what can be achieved using Clausius–Clapeyron only.

Description: A detailed analysis of how intermittency (i.e., the alternation of dry and rainy periods) modulates the rate at which sub-daily rainfall extremes depend on temperature is presented. Results show that hourly extremes tend to be predominantly controlled by peak intensity, increasing at a rate of approximately 7 % per degree in agreement with the Clausius–Clapeyron equation. However, a rapid increase in intermittency upward of 20–25 °C is shown to produce local deviations from this theoretical scaling, resulting in lower scaling rates. On the other hand, rapidly decreasing intermittency with temperature between 10 and 20° can result in higher net scaling rates than expected, potentially exceeding Clausius–Clapeyron. In general, the importance of intermittency in controlling the scaling rates of precipitation with temperature grows as we progress from hourly to daily aggregation timescales and beyond. Thermodynamic effects still play an important role in controlling the maximum water-holding capacity of the atmosphere and therefore peak rainfall intensity, but the observational evidence shows that, beyond a few hours, storm totals become increasingly dominated by dynamical factors. The conclusion is that Clausius–Clapeyron scaling alone cannot be used to reliably predict the net effective changes in rainfall extremes with temperature beyond a few hours. A more general scaling model that takes into account simultaneous changes in intermittency and peak intensity with temperature is proposed to help better disentangle these two phenomena (e.g., peak intensity and intermittency). The new model is applied to a large number of high-resolution rain gauge time series in the United States, and results show that it greatly improves the representation of rainfall extremes with temperature, producing a much more consistent and reliable picture of extremes across scales than using Clausius–Clapeyron only.

Description: Urban drainage systems are challenged by both urbanization and climate change, intensifying urban pluvial flooding impacts. Urban pluvial flooding impacts can be reduced by improving infrastructure and operational urban flood management strategies. This study investigated the relation between heavy rainfall and urban pluvial flooding in Rotterdam with the aim to identify parameters and thresholds that can be used as predictors of urban pluvial flooding. The focus of the investigation was on an area of 16 km2. Datasets for this research included historical crowdsourced flooding reports, overflow pumping volumes, open spatial data and rainfall data at different temporal and spatial resolutions. Threshold values, (which can be used as part of early warning systems), were derived from historical flooding data and rainfall depths over sub daily durations. Threshold values of rainfall depth were found to be 6 mm (±3 mm) in 15 min and 11 mm (±6 mm) in 60 min. Surprisingly, the derived thresholds are only approximately half of the theoretical drainage system design capacity. Furthermore, a threshold value of 70 % (±4 %) imperviousness was found above which flooding incidents significantly increase. Results also suggested a strong dependence on spatial aggregation scale, as it highly influences correlation coefficients and parameter density values. Elevation differences did not appear to contribute to urban pluvial flooding, based on a flow path analysis for the study area. Finally, we showed that antecedent rainfall does not explain additional variance in reports, meaning it is not an influential urban pluvial flooding predictor, at least not on a daily temporal resolution.

Description: Urban catchments are typically characterised by a more flashy nature of the hydrological response compared to natural catchments. Predicting flow changes associated with urbanisation is not straightforward, as they are influenced by interactions between impervious cover, basin size, drainage connectivity and stormwater management infrastructure. In this study, we present an alternative approach to statistical analysis of hydrological response variability and basin flashiness, based on the distribution of inter-amount times. We analyse inter-amount time distributions of high-resolution streamflow time series for 17 (semi-)urbanised basins in North Carolina, USA, ranging from 13 to 238 km2 in size. We show that in the inter-amount-time framework, sampling frequency is tuned to the local variability of the flow pattern, resulting in a different representation and weighting of high and low flow periods in the statistical distribution. This leads to important differences in the way the distribution quantiles, mean, coefficient of variation and skewness vary across scales and results in lower mean intermittency and improved scaling. Moreover, we show that inter-amount-time distributions can be used to detect regulation effects on flow patterns, identify critical sampling scales and characterise flashiness of hydrological response. The possibility to use both the classical approach and the inter-amount-time framework to identify minimum observable scales and analyse flow data opens up interesting areas for future research.

Description: Commercial microwave links (CMLs) in telecommunication networks can provide relevant information for remote sensing of precipitation and other environmental variables, such as path-averaged drop size distribution, evaporation, or humidity. The CoMMon field experiment (COmmercial Microwave links for urban rainfall MONitoring) mainly focused on the rainfall observations by monitoring a 38 GHz dual-polarized CML of 1.85 km path length at a high temporal resolution (4 s), as well as a co-located array of five disdrometers and three rain gauges over 1 year. The dataset is complemented with observations from five nearby weather stations. Raw and pre-processed data, which can be explored with a custom static HTML viewer, are available at https://doi.org/10.5281/zenodo.4923125 (Špačková et al., 2021). The data quality is generally satisfactory for further analysis, and potentially problematic measurements are flagged to help the analyst identify relevant periods for specific study purposes. Finally, we encourage potential applications and discuss open issues regarding future remote sensing with CMLs.