The Delft Measures Rain Citizen-Science programme has been running for several years in the city of Delft, the Netherlands. Within this programme, interested citizens can apply to receive a low-cost Alecto WS5500 weather station, to measure local meteorological parameters in their own garden. Currently there are over 45 of these citizen-science weather stations spread across neighbourhoods in Delft, capturing rainfall variability in different urban microclimates. However, the scientific quality of these specific stations has never been tested, and from previous work we know that rigorous quality assurance is necessary in order to get meaningful (precipitation) data. Thus we have installed 8 Alecto stations in The Green Village outdoors urban climate field lab at the TU Delft. Stations have been explicitly installed in ways that a citizen might do: slightly tilted, next to a wall (simulating the limited open garden space of a Dutch urban residence), on top of a shed as well as free-standing. These different measurement setups, combined with a row of stations installed in the same way right next to one another, allow us to investigate the bias caused by less-than-ideal station installation, as well as systematic errors related to the tipping bucket mechanism and sensor drifts. Initial results show a general overestimation of the Alecto compared to reference stations and radar observations, and a discernible negative bias caused by sheltering effects of plants and, to a lesser extent by walls.@en

An experimental study aimed at identifying special rainfall regimes with the help of co-located disdrometers is performed. Eight potentially special events (i.e., four number-controlled events and four size-controlled events) are identified and examined. However, a detailed cross-check with additional, independent radar measurements reveals no clear evidence of special rainfall dynamics. The research underscores the difficulty of experimentally confirming seemingly straightforward questions about rainfall patterns and dynamics that have been theorized in the literature for several decades but never formally validated experimentally. The study also questions the reliability of previous claims and serves as a reminder to approach such problems with more caution, emphasizing the need for rigorous uncertainty analysis and multiple cross-checks between sensors to avoid misinterpretation.@en

Radar rainfall nowcasting has mostly been applied to relatively large (often rural) domains (e.g., river basins), although rainfall nowcasting in small urban areas is expected to be more challenging. Here, we selected 80 events with high rainfall intensities (at least one 1-km ² grid cell experiences precipitation >15 mm h ²¹ for 1-h events or 30 mm day ²¹ for 24-h events) in five urban areas (Maastricht, Eindhoven, The Hague, Amsterdam, and Groningen) in the Netherlands. We evaluated the performance of 9060 probabilistic nowcasts with 20 ensemble members by applying the short-term ensemble prediction system (STEPS) from Pysteps to every 10-min issue time for the selected events. We found that nowcast errors increased with decreasing (urban) areas especially when below 100 km ². In addition, at 30-min lead time, the underestimation of nowcasts was 38% larger and the discrimination ability was 11% lower for 1-h events than for 24-h events. A set of gridded correction factors for the Netherlands, CARROTS (Climatology-based Adjustments for Radar Rainfall in an Operational Setting) could adjust the bias in real-time QPE and nowcasts by 70%. Yet, nowcasts were still found to underestimate rainfall more than 50% above 40-min lead time relative to the reference, which indicates that this error originates from the nowcasting model itself. Also, CARROTS did not adjust the rainfall spatial distribution in urban areas much. In summary, radar-based nowcasting for urban areas (between 67 and 213 km ²) in the Netherlands exhibits a short skillful lead time of about 20 min, which can only be used for last-minute warning and preparation.

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In this study, we take a closer look at the important issue of μ–Λ relationships in raindrop size distributions (DSDs) by conducting a systematic analysis of 20 months of data collected by disdrometers in the Netherlands. A new power-law model for representing μ–Λ relationships based on the double normalization framework is proposed and used to derive separate μ–Λ relationships for stratiform and convective rain events. The sensitivity of the obtained relationships to measurement uncertainty is studied by applying two different quality control filters based on the mass-weighted mean drop diameter (Dm) and liquid water content (LWC). Our results show that there are significant differences in μ–Λ relationships between convective and stratiform rainfall types. However, the retrieved relationships appear to be quite robust to measurement noise and there is good agreement with other reference relations for similar climatological conditions.@en

Quantifying the magnitude and frequency of extreme precipitation events is key in translating climate observations to planning and engineering design. Past efforts have mostly focused on the estimation of daily extremes using gauge observations. Recent development of high-resolution global precipitation products, now allow estimation of global extremes. This research aims to quantitatively characterize the spatiotemporal behavior of precipitation extremes, by calculating extreme precipitation return levels for multiple durations on the global domain using the Multi-Source Weighted-Ensemble Precipitation (MSWEP) dataset. Both classical and novel extreme value distributions are used to provide insight into the spatial patterns of precipitation extremes. Our results show that the traditional Generalized Extreme Value (GEV) distribution and Peak-Over-Threshold (POT) methods, which only use the largest events to estimate precipitation extremes, are not spatially coherent. The recently developed Metastatistical Extreme Value (MEV) distribution, that includes all precipitation events, leads to smoother spatial patterns of local extremes. For durations of 5 and 10 days, however, there are less events per year to fit the distribution (37 and 22 on average, respectively), leading to larger inter-annual variability and possible overestimation of the extremes. While the GEV and POT methods predict a consistent shift from heavy to thin tails with increasing duration, the MEV method predicts a relatively constant heaviness of the tail for any precipitation duration, opening up an important research question on what is the ‘correct’ tail behavior of extreme precipitation for different durations. The generated extreme precipitation return levels and corresponding parameters are provided as the Global Precipitation EXtremes (GPEX) dataset. These data can be useful for studying the underlying physical processes causing the spatiotemporal variations of the heaviness of extreme precipitation distributions.

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The raindrop size distribution (DSD) is a statistical description of the number and
size distribution of raindrops within a specified volume of air. DSDs play a central
role in radar remote sensing and are essential for understanding the scattering and
absorption of electromagnetic radiation as it travels through the air and interacts with
falling rain. They form the mathematical backbone for linking radar observations
to physical quantities such as rainfall intensities, liquid water content, and kinetic
energy. Yet, in most remote sensing applications, the DSD in the target volume is
likely to be unknown. Therefore, parameterized DSD models have been created to act
as substitutes for direct measurementswhen observations are unavailable, incomplete,
or impractical. Over time, a large number of models have been proposed, each with
their own intricacies and constraints. Understanding these mathematical constructs
and the assumptions behind them is essential for interpreting radar measurements and
improving quantitative rainfall estimation.@en

Raindrop size distributions (DSDs) play a crucial role in quantitative rainfall estimation using weather radar. Thanks to dual polarization capabilities, crucial information about the DSD in a given volume of air can be retrieved. One popular retrieval method assumes that the DSD can be modeled by a constrained gamma distribution in which the shape (μ) and rate (Λ) parameters are linked together by a deterministic relationship. In the literature, μ-Λ relationships are often taken for granted and applied without much critical discussion. In this study, we take another look at this important issue by conducting a detailed analysis of μ-Λ relations in stratiform rain and quantifying the accuracy of the associated DSD retrievals. Crucial aspects of our research include the sensitivity of μ-Λ relations to the temporal aggregation scale, drop concentration, inter-event variability, and adequacy of the gamma distribution model. Our results show that μ-Λ relationships in stratiform rain are surprisingly robust to the choice of the sampling resolution, sample size, and adequacy of the gamma model. Overall, the retrieved DSDs are in a rather decent agreement with ground observations (correlation coefficient of 0.57 and 0.74 for μ and Dm). The main sources of errors and uncertainty during the retrievals are calibration offsets in reflectivity (Zhh) and differential reflectivity (Zdr). Measurement noise and differences in scale between radars and disdrometers also play a minor role. The raindrop concentration (NT) remains the most difficult parameter to retrieve, which can be off by several orders of magnitude. After careful data filtering and removal of problematic Zhh/Zdr pairs, the correlation coefficient for the retrieved NT values remained low, only slightly increasing from 0.12 into 0.24.

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Conventionally, Micro Rain Radars (MRRs) have been used as a tool to calibrate reflectivity from weather radars, estimate the relation between rainfall rate and reflectivity, and study microphysical processes in precipitation. However, limited attention has been given to the reliability of the retrieved drop size distributions (DSDs) from MRRs. This study sheds more light on this aspect by examining the sensitivity of retrieved DSDs to the assumptions made to map Doppler spectra into size distributions, and investigates the capability of an MRR to assess polarimetric observations from operational weather radars. For that, an MRR was installed near the Cabauw observatory in the Netherlands, between the International Research Center for Telecommunications and Radar (IRCTR) Drizzle Radar (IDRA) X-band radar and the Herwijnen operational C-band radar. The measurements of the MRR from November 2018 to February 2019 were used to retrieve DSDs and simulate horizontal reflectivity Z_e, differential reflectivity Z_DR, and specific differential phase K_DP in rain. Attention is given to the impact of aliased spectra and right-hand-side truncation on the simulation of polarimetric variables. From a quantitative assessment, the correlations of Z_e and Z_DR between the MRR and Herwijnen radar were 0.93 and 0.70, respectively, while those between the MRR and IDRA were 0.91 and 0.69. However, Z_e and Z_DR from the Herwijnen radar showed slight biases of 1.07 and 0.25 dB. For IDRA, the corresponding biases were 2.67 and-0.93 dB. Our results show that MRR measurements are advantageous to inspect the calibration of scanning radars and validate polarimetric estimates in rain, provided that the DSDs are correctly retrieved and controlled for quality assurance.

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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 38ĝ€¯GHz dual-polarized CML of 1.85ĝ€¯km path length at a high temporal resolution (4ĝ€¯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 10.5281/zenodo.4923125 . 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.

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A new type of rainfall sensor (the intervalometer), which counts the arrival of raindrops at a piezo electric element, is implemented during the Tanzanian monsoon season alongside tipping bucket rain gauges and an impact disdrometer. The aim is to test the validity of the Poisson hypothesis underlying the estimation of rainfall rates using an experimentally determined raindrop size distribution parameterisation based on Marshall and Palmer (1948)'s exponential one. These parameterisations are defined independently of the scale of observation and therefore implicitly assume that rainfall is a homogeneous Poisson process. The results show that 28.3 % of the total intervalometer observed rainfall patches can reasonably be considered Poisson distributed and that the main reasons for Poisson deviations of the remaining 71.7 % are non-compliance with the stationarity criterion (45.9 %), the presence of correlations between drop counts (7.0 %), particularly at higher arrival rates (ρa>500 m−2s−1), and failing a χ2 goodness-of-fit test for a Poisson distribution (17.7 %). Our results show that whilst the Poisson hypothesis is likely not strictly true for rainfall that contributes most to the total rainfall amount, it is quite useful in practice and may hold under certain rainfall conditions. The parameterisation that uses an experimentally determined power law relation between N0 and rainfall rate results in the best estimates of rainfall amount compared to co-located tipping bucket measurements. Despite the non-compliance with the Poisson hypothesis, estimates of total rainfall amount over the entire observational period derived from disdrometer drop counts are within 4 % of co-located tipping bucket measurements. Intervalometer estimates of total rainfall amount overestimate the co-located tipping bucket measurement by 12 %. The intervalometer principle shows potential for use as a rainfall measurement instrument.@en

The use of spectral polarimetric filters in the range-Doppler domain shows great promise for clutter mitigation in weather radar applications. One limitation of these filters is that they cannot deal with situations in which ground clutter and precipitation overlap. In this letter, we propose a new signal recovery technique based on kriging in the spectral domain to recover the precipitation in clutter-contaminated areas. Using synthetic radar data, we test our new method and compare its performance to that of Gaussian model adaptive processing and bilinear interpolation. Our results indicate that kriging is the most accurate and robust technique out of the three.@en

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 %.

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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.

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The adequacy of the gamma model to describe the variability of raindrop size distributions (DSD) is studied using observations from an optical disdrometer. Model adequacy is checked using a combination of Kolmogorov–Smirnov goodness-of-fit test and Kullback–Leibler divergence and the sensitivity of the results to the sampling resolution is inves-tigated. A new adaptive DSD sampling technique capable of determining the highest possible temporal sampling resolution at which the gamma model provides an adequate representation of sampled DSDs is proposed. The results show that most DSDs at 30 s are not strictly distributed according to a gamma model, while at the same time they are not far away from it either. According to the adaptive DSD sampling algorithm, the gamma model proves to be an adequate choice for the majority (85.81%) of the DSD spectra at resolutions up to 300 s. At the same time, it also reveals a considerable number of DSD spectra (5.55%) that do not follow a gamma distribution at any resolution (up to 1800 s). These are attributed to transitional periods during which the DSD is not stationary and exhibits a bimodal shape that cannot be modeled by a gamma distribution. The proposed resampling procedure is capable of automatically identifying and flagging these periods, providing new valuable quality control mechanisms for DSD retrievals in disdrometers and weather radars.

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Urban pluvial flooding is one of the most costly natural hazards worldwide. Risks of flooding are expected to increase in the future due to global warming and urbanization. The complexity of the involved processes and the lack of long-term field observations means that many crucial aspects related to urban flood risks still remain poorly understood. In this paper, the possibility to gain new insight into urban pluvial flooding using citizen flood observations is explored. Using a ten-year dataset of radar rainfall maps and 70,000 citizen flood reports for the city of Rotterdam, we derive critical thresholds beyond which urban pluvial flooding is likely to occur. Three binary decision trees are trained for predicting flood occurrences based on peak rainfall intensities across different temporal scales. Results show that the decision trees correctly predict 37%–52% of all flood occurrences and 95%–97% of all non-flood occurrences, which is a fair performance given the uncertainties associated with citizen data. More importantly, all models agree on which rainfall features are the most important for predicting flooding, reaching optimal performance whenever short- and long-duration rainfall peak intensities are combined together to make a prediction. Additional feature selection using principal component analysis shows that further improvement is possible when critical rainfall thresholds are calculated using a linear combination of peak rainfall intensities across multiple temporal scales. The encouraging results suggest that citizen observatories, although prone to larger errors and uncertainties, constitute a valuable alternative source of information for gaining insight into urban pluvial flooding.

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For pluvial flood risk assessment in urban areas it is important to be able to calculate how often a specific area is at risk of flooding. This is especially evident in urban areas subject to contribution from multiple sources, e.g. surcharging drainage system, surface runoff, overflowing rivers, etc. In this study extreme event statistics are assessed by simulation of rainfall impact and consecutive statistics of flood response in order to estimate return periods of flooding. The model applied is an integrated hydraulic model which includes relevant hydrological processes that contribute to urban flooding. The setup is analysed based on a small urban catchment in Aalborg Denmark. Results show that it is possible to estimate return periods of flood volume, flood extent and local water levels based on simulation and that rainfall and hydrological conditions critical to flooding can be identified.@en

An intervalometer is an extremely simple measurement device that measures the intervals between the impact of raindrops on a surface. In our case, we used a piezo-electric element put in a small 3D-printed holder. When a raindrop hits the surface, a voltage is generated that is detected by a simple CPU, such as that of an Arduino. A softwarr-based signal filter is applied to filter out frequencies that are too far removed from the Eigenfrequency of the element. Once an impact is detected, a transistor shorts out the the piezo, after which it is ready for the next drop. It takes about 20 ms to register a drop. The design follows the open hardware philosophy and all codes, including those for 3D printing, can be found at https://github.com/nvandegiesen/Intervalometer/wiki/Intervalometer. The intervalometer has been tested under different climatic conditions. The main focus here is on a campaign in Tanzania. It turned out that the intervalometer gives surprisingly consistent results and with some calibration, rainfall rates can be determined. Because the arrival rates are known in great detail, one can check to see if the Poisson assumption, underlying many rainfall models, is valid. For tropical Tanzania, it turned out that only under rare drizzle-like conditions does Poisson hold.@en

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.

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A novel algorithm is put forward to separate radar target and moving clutter based on a combination of the low-rank matrix optimization (LRMO) and the decision tree. Similar to the moving object detection in the field of automated video analysis, the proposed separation method, which is carried out in the range-Doppler domain, makes use of different motion variations of radar target and clutter in the spectrogram sequence. The technique is very general, but the focus of this paper is on narrowband moving clutter suppression in a weather radar. The first step in implementing this method is the generation of a range-Doppler spectrogram sequence. Then, the LRMO is applied to the obtained sequence to divide target and moving clutter into foreground and background. From the foreground sequence which is obtained by solving the LRMO, foreground frequency and spectral width are combined in a decision tree to obtain a filtering mask to mitigate the narrowband moving clutter and noise. Data collected by a polarimetric Doppler weather radar known as the IRCTR Drizzle Radar are used to validate the performance of the proposed algorithm. Moreover, its effectiveness in removing narrowband moving clutter is quantitatively assessed through comparisons with another clutter mitigation method.

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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.

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