For the analysis here, rain gauges from the Netatmo brand of PWSs were used. These PWSs have a large coverage over the Netherlands which has slightly increased since 2018 (around one PWS per 9 km² area in 2024; Fig. a). This rain gauge type uses a tipping bucket mechanism with a nominal volume of 0.101 mm according to the manufacturer . These gauges can also be calibrated manually by the owner by changing – via software – the volume per tip, resulting in deviating tipping bucket volumes (approximately 13.5 % is manually calibrated according to ). The diameter of the collecting funnel is 13 cm (leading to an orifice area of 133 cm²). According to the manufacturer, the accuracy is 1 mm h⁻¹ for a measurement range of 0.2 to 150 mm h⁻¹, and the PWS operates best for temperatures between 0 and 50 °C . However, it is unclear what this accuracy exactly entails, thereby showing the need for this study.

The default rain gauge processing software records the number of tips over approximately 5 min intervals, which is communicated wirelessly to an indoor module. Next, the data are transmitted via Wi-Fi to the Netatmo platform. The Netatmo software resamples this to regular 5 min intervals by assigning the data to the next full 5 min interval. When within a 5 min interval no data are transferred, this time interval is not included by Netatmo (see the supporting information in Table  for an example). When there is a connection failure between the rain gauge module and the indoor module, the rainfall will likely be attributed to a timestamp when there is a connection again, potentially aggregating it over a longer time interval than approximately 5 min (see the supporting information in Table  for an example). However, when the connection of the indoor module is also temporarily interrupted, data are lost.

The PWSs were evaluated against data from AWSs from the KNMI. The KNMI operates a network of 33 AWSs across the Netherlands, which are relatively homogeneously distributed with approximately one AWS per 1000 km² area (Fig. a). These AWSs estimate cumulative rainfall every 12 s by measuring the displacement of a float placed in a reservoir. The data are archived at a lower resolution, i.e. every 1, 10 min, and hourly. Here, AWS data with resolutions of 10 min and 1 h are used. The 10 min dataset contains unvalidated rainfall data, while the hourly data have been validated . The collecting funnel has a diameter of 16 cm (corresponding to an orifice area of 201 cm²) and the device is heated for temperatures below 4 °C. In addition, these stations are placed in open locations using an English setup or Ott windscreen to reduce errors from wind-induced undercatch . Nevertheless, these data are not an absolute truth. compared the AWS network and manual rain gauge network over the Netherlands and concluded that the AWS network underestimates rainfall at 5 %–8 % annually, with a higher underestimation in winter (7.7 %) than in summer (5.0 %). The undercatch is non-linear with intensity, with larger intensities resulting in less underestimation. These uncertainties are not taken into account in this research.

Rainfall data at 5 min intervals from multiple PWSs were extracted using the Netatmo API . Note that the API only provides access to data from PWSs that were operational at the time of access, which was in February 2024. We do not have access to data from stations that were previously in operation but no longer online at the time of access. Two search radii were employed to find all operational PWSs within that range. One radius of 10 km around an AWS was used to quantify the quality of the PWSs, and a radius of 20 km was used to filter the PWS data using a quality control algorithm. and showed that the decorrelation distance for precipitation over the Netherlands is around 50 km for 1 h accumulation intervals. Comparing PWSs within 10 km of an AWS can therefore be assumed to limit spatial sampling errors with respect to a larger search radius.

First, all PWSs within 20 km around each AWS were identified. Second, AWSs that had at least five PWSs within 10 km since 1 January 2018 were kept in the dataset. Next, the 10 closest available PWSs located within 10 km of the AWS were selected (Fig. , purple crosses) for the comparison with the AWS nearby. Note that the selection of PWSs varies per selected rainfall event due to temporary station outages and changing data and station availability over time. This procedure resulted in 11 AWSs with a cluster of 5 to 10 PWSs around it (see Fig. b for the selected AWSs and the used PWSs). All PWSs within 20 km were used to filter the data (Fig. , orange dots and purple crosses) using the quality control algorithm developed by and described below (Sect. ).

A similar event selection procedure was used as described by , which defines an event as a certain time period rather than by the beginning and end of rainfall. Rainfall observations from the 10 min dataset of the AWSs were employed to make a selection of events between 2018 and 2023 using a moving window approach. Only the 10 largest rainfall accumulations were selected, as these are the most important ones for pluvial flood forecasting. Analysis shows that, on average, the 10 highest 1 h rainfall accumulations for the selected AWSs account for 12.5 % of the annual rainfall. The hourly dataset (clock hour) was employed to perform a consistency check on this selection. For selected events with rainfall differences of more than 10 % with the validated hourly dataset, the values of the validated hourly dataset were used instead. These deviations occurred in less than 0.4 % of the total number of selected events. Note that the selected events can contain time steps without any rain observed.

For every selected AWS based on the methodology in Sect. , the 10 largest rainfall events per meteorological season (winter, spring, summer, and autumn) and accumulation interval (1, 3, 6, and 24 h) were selected to draw statistically meaningful conclusions. This results in a total of 11 stations × 4 seasons × 4 accumulation intervals × 10 events = 1760 individual events for the analysis. The events were selected in such a way that, for the same station and accumulation interval, no overlapping time series were included.

The statistics of the selected events are shown in Fig. . A clear seasonality is observed here, especially for 1 h intervals (Fig. a), with the highest rates during summer (June–July–August, JJA) and the lowest rates during winter (December–January–February, DJF) and medians of 14.65 and 6.17 mm h⁻¹, respectively. This is in line with the Dutch climate, where the highest rainfall intensities occur during summer and are typically characterized by convective rainfall .

Based on the return periods provided by , over 75 % of the selected observed rainfall accumulations in winter, spring, and autumn have a return period of less than 0.5 years, while in summer this is around 25 % (Fig. a). Most extreme events occur during the summer months, with multiple events having a return period of over 5 years and one event exceeding a return period of 100 years. Rainfall rates during the autumn months (September–October–November, SON) are slightly higher than in spring (March–April–May, MAM), with medians of 9.40 and 8.33 mm h⁻¹, respectively (Fig. a). However, spring appears to have two extreme outliers, with return periods that exceed 10 years. Note that these return periods are calculated based on annual statistics, which are dominated by rainfall events from March to October. Because winter has the lowest intensities, return periods then based on annual statistics are low.

The rainfall observed by a cluster of PWSs is averaged, effectively representing the rainfall over an area while comparing it with a point measurement (AWS), which has a limited spatial footprint. With an increasing domain area, the variation of areal precipitation becomes smaller than that of point precipitation. To account for the reduction in the magnitude of rainfall extremes over an area as compared to a point, areal reduction factors (ARFs) can be applied. The ARF estimates areal rainfall percentiles from point rainfall percentiles. and more recently parameterized the ARF based on weather radar for the Netherlands. This reduction factor is a function of duration, area, and return period, with rarer events having a stronger areal reduction. Equations (1a), (2), (3b), (4), and (5) of are used to estimate the ARF. The inverse of the ARFs will be used to adjust the values of the PWSs to a point observation.

As stated by , the key advantage of the QC algorithm of over QC algorithms such as those developed by and is that no auxiliary data are required. This makes it particularly suitable for regions lacking access to (real-time) reference data. For that reason, we decided to use the QC of . The high-influx (HI) and faulty zero (FZ) filters from the personal weather station quality control (PWSQC) algorithm of were applied to filter the PWS dataset. HI data can be caused by sprinklers, addition of liquids into the gauge, or tilting of the gauge. In addition, a high influx can result from a temporary connection interruption between the rain gauge module and the indoor module, assigning the rain to the timestamp when the connection is re-established. Disaggregating this type of high influx using reliable rainfall time series from nearby stations could potentially solve this issue. The HI filter uses four parameters:

d, the maximum distance over which neighbouring PWSs are selected that likely capture similar rainfall dynamics;

Over time, the availability of PWSs changes due to factors such as connection failure. To analyse the availability of PWSs, a dataset comprising operational PWSs on 1 January 2018 within 10 km from an AWS was employed. This dataset contained 178 PWSs. Time series from the PWSs were extracted for each selected event according to the method described in Sect. . In total, 95.8 % of the PWSs were available for all selected events during the 6 consecutive years. From these available PWSs, 3.5 % of the total time steps did not contain any data due to either missing data or irregular data transfers that were longer than 5 min. In addition, 0.7 % of the PWSs did not have five neighbours within 10 km. Applying the quality control algorithm leads to more data being discarded. For the remaining PWSs with enough neighbours, 8.9 % of the total data are either discarded (i.e. flagged as FZ or HI), have a temporal resolution beyond 5 min, or are missing.

Since we can only suspect that data are likely not missing when a 5 min time step is not included, a minimum availability criterion was set to limit a biased comparison. A minimum percentage of time steps should be valid before aggregating the data. The criterion set has a large impact on the availability (Table ). By requiring a data availability of 100 % before aggregation, 40.9 % of the dataset is retained, while a lower required availability (92 %) almost doubles (79.7 %) the remaining stations of the original dataset. Lower criteria potentially result in underestimation of rainfall due to missing data. Based on these results, a data availability requirement of 83 % was chosen (e.g. at least 10 out of 12 5 min intervals within 1 h) to keep a large part of the original dataset (83.7 %), which is also in line with .

The data quality of the PWSs was evaluated by comparing the PWS data to those of the selected AWSs, using the relative bias, the coefficient of variation (CV) of the residuals, the Pearson correlation coefficient (r), and the slope of the linear regression relationship. Note that the evaluation metrics were calculated over the total rainfall within a time interval and over the average of the cluster of PWSs.

The relative bias was defined as follows: 1Bias=∑i=1nRPWS,i∑i=1nRAWS,i-1, with n the total number of events for each season and time interval and RAWS and RPWS the rain recorded by the AWS and PWS, respectively. Values above zero indicate an overestimation and values below zero an underestimation of the PWS data. The CV is used to describe the dispersion of rainfall, with values closer to zero suggesting greater consistency with the mean of the reference and higher values indicating more dispersion, defined as follows: 2CV=1n∑i=1nRres,i-R‾res2RAWS‾, with the overbar indicating the arithmetic mean and 3Rres=RPWS-RAWS. The Pearson correlation coefficient describes the strength of the linear relation between the PWSs and the AWS, with values ranging between -1 and 1, and it was calculated between all events within a season and aggregation interval (including zeroes): 4r=covRPWS,RAWSsdRPWSsdRAWS. The linear regression line, fitted through the origin, is defined as follows: 5RPWS‾=a*RAWS‾, with a the slope calculated over all events: 6a=∑i=1nRAWS,iRPWS,i∑i=1n(RAWS,i)2. Values close to 1 indicate strong agreement with the reference dataset.

The PWSs in this study were selected based on the closest distance from an AWS without considering the uniformity of the distribution around the AWS. Figure  shows that the average cluster distance to an AWS is around 4.4 km and that the average inter-gauge PWS distance of all pairs within a cluster is around 5 km. This indicates that, overall, the selected stations are not clustered in one location and represent a larger area. Variation in the distance to the AWSs in Fig. a can be explained by the location of the selected AWSs. Higher PWS network densities and associated shorter distances to the closest PWSs can be found in urban regions. However, most of the AWSs are located in rural regions. In addition, variability in Fig.  also partially results from fluctuating data availability and the number of available PWSs, which increases over the years. The average number of PWSs within a cluster is 8.75.

Figure  shows a substantial decline in ARFs with larger area sizes and shorter durations, with the largest reductions for short durations. The decline becomes more prominent for longer return periods. For an area of 79 km² (based on a radius of 5 km towards an AWS) and a duration of 1 h, the ARF according to varies between 0.88 and 0.82 for return periods of 2 and 50 years, respectively, while for 24 h the ARF varies between 0.96 and 0.92 for return periods of 2 and 50 years, respectively. The reduction becomes larger for a radius of 10 km. For example, the ARFs are 0.78 and 0.70 for a duration of 1 h and return periods of 2 and 50 years, respectively. To convert the areal estimate from the PWSs into a point observation (reflecting the AWS), the PWS cluster average is adjusted using the inverse of the ARF, with the area based on a 10 km radius (the maximum distance between a PWS and an AWS used in the PWS selection procedure).

The relative bias of the non-adjusted PWS cluster average over multiple accumulation intervals was quantified by comparing it with AWSs nearby for the selected rainfall events (Table , each row indicating different accumulation intervals). Results indicate that, without applying any ARF or DBC factor, on average, significant biases are present in rainfall observations from the PWSs. The underestimation is largest for accumulation intervals of 1 h (around 36%). The magnitude of the bias decreases over longer intervals towards an average underestimation of around 19% for accumulation intervals of 24 h. In addition, a seasonal dependency is visible for the bias.

It is important to make a distinction between the sources of bias in order to avoid correcting non-instrumentally related errors. Due to the setup of this study, which makes use of PWSs within a maximum 10 km distance from an AWS, the bias can be divided into two categories: (1) bias resulting from the spatial variation in rainfall extremes and (2) an instrumental bias.

The ARF accounts for the spatial variability of rainfall extremes and illustrates that the bias is partially caused by category 1. The ARF was applied to compensate for the spatial variation of rainfall extremes and to fairly compare the rainfall measured by a cluster of PWSs with one AWS. The largest areal reductions are visible for 1 h accumulation (Fig.  and Table ), reducing the relative bias on average over all seasons from -36 % to -22 %. During the winter months on average, the lowest rainfall intensities and the least spatial variability of rainfall occur (Fig. ), resulting in the smallest areal reduction. The ARFs have a limited effect on the 24 h events, with an average reduction of 2 percentage points in the bias over all seasons. The remaining bias for time intervals of 3 h over all seasons and longer is on average around 16 %.

The remaining biases are part of the second category and indicate the need for a DBC factor to adjust the instrumental biases. To compensate for this instrumental bias, the DBC factor of 1.22 was applied. After application of this DBC factor, the underestimation for 1 h intervals over all seasons decreases to an average of 5 %, while for 3 h and longer intervals it converges towards zero or in a slight overestimation of the rain. The remaining bias is within the expected uncertainty of rainfall observations. This is supporting evidence that the DBC factor of 1.22 works effectively.

A small part of the dataset obtained from Netatmo (5.38 % of the selected events' total time steps) was not included, suggesting either that data were missing or that the system suffered from connection issues, resulting in irregular data transfer (longer than approximately 5 min). It is expected that the effect of this on the bias will be limited, as most of the data are likely not missing. Rather, the effect is caused by irregular data transfer and/or connection interruption between the rain gauge and the indoor module (see the supporting information in Tables  and ).

For the selected events, a seasonal dependency is visible for the performance of the PWSs (Figs.  and ). The seasonal effect is most pronounced for shorter accumulation intervals (1 h and 3 h), with the best performances of the PWSs in winter and autumn and the worst performances in summer and spring (Fig. ). Events in winter show the lowest variability of the PWS observations compared with the AWS observations (e.g. average CV values of 0.30 and 0.21 for accumulation intervals of 1 h and 3 h, respectively). While the CV is larger for autumn (0.41 and 0.26), the correlation between the PWSs and AWSs is higher during autumn compared to winter (Fig. b). Winter in the Netherlands is mainly characterized by larger, more persistent rainfall systems, which have a longer decorrelation distance (80 km for 1 h aggregations) . In addition, the error bars for winter are smaller compared with the other seasons, showing that there is more consistency between the individual PWSs (see Fig.  and the supporting information in Fig.  for a complete overview of all of the seasons and accumulation intervals). For that reason, it is expected that the spatial sampling errors were minimized during winter, indicating that other factors, such as solid rain, caused the lower correlation.

Figure a shows that, for all seasons, the CV decreases over longer accumulation intervals. For 1 h intervals the CV varies between 0.30 and 0.54 over the different seasons, while for 24 h the CV shows lower variability, with values varying between 0.14 and 0.27. Similarly, the correlation coefficient increases from values ranging from 0.43 to 0.74 for 1 h intervals to a range from 0.75 to 0.86 for 24 h intervals. This indicates that, for longer accumulation intervals, rainfall observations from PWSs exhibit less variability and more agreement with those from AWSs. Data transferring and processing errors decrease for longer accumulation intervals, as the effect of attributing rainfall to an erroneous time stamp decreases. This takes place for example when the connection between the indoor and outdoor modules is temporarily interrupted, potentially attributing rainfall to a timestamp when there is a connection again and as a consequence aggregating it over a longer time interval than approximately 5 min (see the supporting information in Table ). Within a cluster of PWSs, variation in rainfall is observed. However, using the average rainfall of each PWS cluster shows great agreement with the AWS. Overall, the average of the cluster of PWSs largely follows the 1:1 line, with slopes of the fitted lines indicating slight underestimation or overestimation by varying between 0.97 and 1.03 for 24 h. A seasonal effect is limited on the slope for durations of 3 h and longer. Furthermore, high correlations, low CV values, and low biases are found for both winter and autumn, indicating that there is good agreement with the AWSs (Fig. ).

Figure  shows that, for certain individual events, the PWSs report rainfall amounts which deviate strongly from those observed by the AWSs. We investigated the causes of some of these outliers further, which are indicated with orange circles.

It can be seen in Fig. c that one of the selected events showed (almost) no precipitation measurements according to the cluster of PWSs, while the AWS nearby recorded precipitation. These outliers occurred during winter and were also observed for the 6 h accumulation interval. In the Netherlands, winter has on average around 34 d with a minimum temperature below 0 °C , which is outside the optimal temperature range of the PWSs. For the event with the outliers in Fig. c, the maximum temperature was below -1.4 °C. It is not possible to unambiguously determine whether precipitation is solid based solely on temperature. However, a temperature-based flag can provide end users with an indication that the rainfall observations may be subject to uncertainty. Flags were assigned to time series where the corresponding AWS recorded temperatures below freezing. If these events were discarded by a temperature filter that filters stations when temperatures are below a certain threshold for a certain duration, the values of r and CV for 6 h for winter would have improved to 0.83 and 0.18, respectively. For 24 h this would have been r=0.88 and CV = 0.12. However, as these are only two points and the two intervals have some overlap in time at the same location, no statistically valid conclusion can be drawn from this.

During summer and spring, the highest rainfall accumulations were observed by the AWSs, with intensities exceeding 35 mm h⁻¹. An example of the low performance of PWSs for two high rainfall events in summer can be seen in Fig. b. These events likely skew the overall performance during these months. A large spread is observed within the cluster, especially for the highest event in summer in Fig. b, indicating a large variation in the spatial rainfall distribution. This suggests that the differences between the cluster of PWSs and AWSs are not necessarily only related to instrumental limitations but are rather due to the spatial rainfall distribution. In addition, tipping bucket mechanisms are known for having difficulties in recording higher rainfall intensities. PWSs only send rainfall data to the Netatmo platform twice every 10 min, which is considerably lower than the recording interval of AWSs (12 s). More than one-third of the rainfall during these events fell within 10 min, exceeding intensities of 75 mm h⁻¹ during that interval. However, it is unknown whether the rain was evenly spread within these 10 min or mostly occurred during a shorter period of time and whether this measurement range of the PWSs was indeed exceeded.

Adjusting the PWS dataset with ARFs and correcting for the instrumental bias using a DBC factor reduces the bias. The remaining bias can indicate either that e.g. a higher DBC factor is required to correct for the substantial underestimation or that the ARFs are not able to fully account for the spatial variability of the rainfall.

The quality control algorithm of utilized in this research improves the overall performance of the PWSs (see the supporting information in Fig. ). However, there are some limitations to this algorithm. The algorithm works only if there are enough neighbouring stations within 10 km, limiting its usefulness for less densely populated regions. That said, for this study only a small percentage (0.66 %) was discarded from this dataset due to an insufficient number of neighbouring PWSs. While the number of currently active PWSs is quite high in Europe, they are not evenly distributed (see Fig.  for the network density of PWSs across Europe). For that reason, regions with a less dense network of PWSs are expected to have a higher percentage of discarded stations due to insufficient neighbours (around 35 % within Europe). Alternatively, other data sources (such as gauges or weather radars operated by national meteorological or hydrological services) can be employed for quality control, such as those employed in the QC algorithm by . In addition, insufficiently calibrated PWSs which record higher rainfall at each time stamp are not discarded by the HI filter if a certain threshold is not reached. These differences become more apparent when accumulated over longer periods. With a dynamic bias correction factor, this could have been adjusted.

Another limitation of a quality control algorithm that does not use auxiliary data is that if all PWSs provide faulty observations, these timestamps are not flagged, consequently giving a wrong signal. This was observed for two events during winter for the 6 and 24 h accumulation intervals, when none of the stations recorded any precipitation during an event, while the AWSs did observe precipitation (e.g. Fig. c). During winter, solid precipitation can occur, which can result in an undercatch by the PWSs, as these are not heated and consequently work best for temperatures above the freezing point. Results from also suggested that PWSs are not able to capture solid precipitation. Quality control algorithms based on a reference dataset, such as from , would have filtered these PWSs. Alternatively, a temperature filter could be developed without using auxiliary weather stations. The temperature module present at the PWS can be utilized for this.