Can stormwater runoff measurements be used for weather radar rainfall adjustment?

Urban areas are vulnerable to heavy rainfall due to impervious urban surfaces collecting stormwater into sewer systems. Accurate runoff modeling is crucial for water managers to successfully analyze, control, and utilize the capacity of urban drainage systems. Rainfall estimates with high accuracy and spatial and temporal resolution are prerequisites for urban hydrological applications and accurate runoff modeling (Schilling 1991; Berne et al. 2004; Tetzlaff & Uhlenbrook 2005; Ochoa-Rodriguez et al. 2015; Thorndahl et al. 2017). Rain gauges provide point measurements of rainfall with relatively high accuracy and temporal resolution. However, the spatial variability of rainfall might not be captured by rain gauges, which has been shown to affect runoff modeling in smaller urban areas significantly (Gires et al. 2012; Schellart et al. 2012; Ochoa-Rodriguez et al. 2015).

Weather radars have become a widely used technique for providing high-resolution rainfall estimates due to their ability to provide spatially distributed rainfall estimates in real time (Krajewski & Smith 2002; Krämer et al. 2007; Villarini et al. 2010; Thorndahl et al. 2013; Nielsen et al. 2014b). Weather radar rainfall estimates are derived indirectly from the measured reflectivity of the atmosphere and converted into rain rates, typically by applying a Z–R relationship with a two-parameter power law function (Marshall & Palmer 1948). For non-polarimetric weather radars, the conversion into rain rates relies only on the radar reflectivity measurement, whereas dual-polarimetric radars facilitate the possibility of including some of the dual-pol quantities in the rain rate estimations as well (Ryzhkov et al. 2005; Jorgensen et al. 2011). Regardless of the method used to convert rain rates, obtaining reliable precipitation estimates from indirect weather radar measurements taken at considerable distances from the radar and above the ground surface requires ground observations to adjust the derived rain rates. Several studies show that combining the advantages of weather radar and rain gauges by merging radar and rain gauge data increases the quality of rainfall measurements (Goudenhoofdt & Delobbe 2009; Wang et al. 2013, 2015; Thorndahl et al. 2014; McKee & Binns 2016; Ochoa-Rodriguez et al. 2019; Wijayarathne et al. 2020, 2021).

Proper adjustment of weather radar using rain gauges requires a high density of rain gauges (Thorndahl et al. 2017). However, in reality, the density is often too sparse, and installing new rain gauges in urban areas is often a significant challenge due to unfavorable surrounding conditions. Furthermore, rain gauges provide point measurements of rainfall accumulation over a small area (typically 200 cm²), whereas weather radar measurements provide area-distributed rainfall estimates over larger areas with bin or pixel sizes normally ranging from 0.01 to 16 km². These divergent measurement scales result in discrepancies in representativeness and, thus, rainfall estimates (Austin 1987; Schilling 1991; Ciach & Krajewski 1999; Krajewski & Smith 2002; Einfalt et al. 2004; Villarini et al. 2008; Peleg et al. 2013).

To overcome challenges with different spatial scales in radar-rain gauge merging, areal-averaged rainfall measurements are advantageous for bias adjustment. Areal-averaged rainfall measurements obtained through runoff measurements give measurements of the consequences of rainfall in the urban drainage system and thus the part of the rainfall of relevance for urban hydrological applications. Furthermore, adjusting radar with averaged rainfall measurements over time ensures mass balance and adjusts the rainfall depth to match the volume of the rainfall event. This gives a more stable bias adjustment and is vital for obtaining correct results in urban drainage modeling.

Marx et al. (2006) presented a method for weather radar adjustment using area-integrated rainfall derived from river runoff measurements. Their study showed improved modeled river discharge by applying a Z–R relationship derived from area-integrated precipitation. The study was performed on a larger rural area with a longer response time than most urban areas. Ahm & Rasmussen (2017b) presented a method for adjusting weather radar precipitation estimates using runoff-rainfall measurements from a small, fast-responding urban catchment. The runoff measurements were performed on a 1,395 m² well-defined catchment of a parking lot. The study demonstrated that runoff-rainfall measurements can be used for radar adjustment with high accuracy. However, the approach requires a well-defined and controlled catchment and a relatively costly flow measurement station.

This paper presents a method for weather radar adjustment using wet stormwater detention ponds. Stormwater detention ponds have the advantage of reacting rapidly to rainfall and are commonly found in urban areas, providing ample opportunities for ground observations. We derive catchment runoff-rainfall measurements from water levels measured in a stormwater detention pond. The approach is independent of rain gauges in the catchment for determining the catchment-specific runoff coefficient and takes into account both mass balance and time series dynamics in its performance evaluations, as both factors are critical for achieving accurate and reliable representations of urban hydrological processes in urban drainage applications.

The drainage system in Frejlev primarily consists of a separated sewer system, and a mainly residential area of 0.34 km² within the town discharges separated stormwater to a stormwater detention pond located north of the town. The stormwater detention pond is the only drainway for stormwater in the catchment shown in Figure 1. The pond has a permanent water table, two inlets, and an outlet with a flow regulator with a maximum discharge of 36 L/s to the receiving nearby stream Hasseris Å.

The transducer records the water level every 5 min and is installed at the center of the stormwater detention pond to minimize the effects of wind setup. Due to signal noise in the water level measurements, a weighted moving average filter with the binomial expansion of [1/2, 1/2]ⁿ is applied to the water level data prior to further data analyses. The resulting signal smoothing is illustrated for a subset of the time series in Figure 2.

The City of Aalborg and its surroundings have a total of nine meteorological tipping bucket rain gauges available for this study (see Figure 5). The rain gauges are of the model series RIMCO and are a part of the national network of rain gauges managed by The Water Pollution Committee of The Society of Danish Engineers. The tipping bucket rain gauge measures precipitation by detecting the tipping of an internal bucket, which occurs every time the bucket fills with water. Each tip is equivalent to 0.2 mm of precipitation, and the temporal resolution of the rain gauge data is 1 min (Madsen et al. 1998; Mikkelsen et al. 1998).

The weather radar data is adjusted by applying a daily mean field bias (MFB) adjustment. As previously described, the two rain gauges located near the pond catchment (Figure 5) are only used as validation observations of the rainfall and hence not for MFB adjustment of the weather radar data. The MFB is derived based on observations from the remaining seven rain gauges within and near Aalborg (Figure 5).

The daily bias adjustment based on rain gauges located near Aalborg is not expected to be valid for the entire quantitative range of the weather radar because the rain gauges only cover a small and very local part of the weather radar range. Rather, it is regarded as a local adjustment of the radar data specific to the city of Aalborg and its surroundings, including the catchment in Frejlev.

The inflow to the pond is dependent on the catchment runoff, whereas the outflow is dependent on the pond water level and is affected by the hydraulic characteristics of the flow regulator in the outlet, which is represented by its rating curve. Thus, determining the rating curve of the pond outlet is essential for deriving the inflow from Equation (3).

The rating curve (dashed line in Figure 6) is established as the 99th percentile of the dataset. This is chosen due to residual noise after smoothing, which might lead to erroneously high outflow values if fitted to the highest measured outflow. Furthermore, we force an intersection in origin. Thus, estimated outflows greater than 0 m³/s at a water level corresponding to the bottom elevation of the flow regulator are considered noise and therefore filtered out.

Using this method, the rating curve for the outflow through the flow regulator can only be described up to the highest measured water level. It is therefore important that a wide range of water levels are present in the measurements, with it potentially becoming necessary to update the rating curve with higher water levels if these are measured.

As described by Lallam et al. (2018), the description of the individual factors' influence on the runoff coefficient is complex due to the many influencing variables. Several studies have also indicated that a definitive determination of the runoff coefficient is challenging (e.g., Jensen 1990; Thorndahl et al. 2006; Chen & Adams 2007). Multiple studies have however demonstrated that the runoff coefficient can be determined experimentally at catchment scale (e.g., Merz et al. 2006; Ahm et al. 2013; Xu & Zhao 2016; Machado et al. 2022).

Merz et al. (2006) studied the spatial variability of the runoff coefficient by analyzing 50,000 rainfall events and different catchments in Austria. The study showed that differences in regions and climates have a greater impact on the spatial variability of the coefficient than rainfall depth and catchment-specific parameters such as geology. By studying the impact of urbanization, Xu & Zhao (2016) showed that the runoff coefficient is affected and increased significantly with changed imperviousness and infiltration in the catchment. Ahm et al. (2013) showed that the runoff coefficient can be estimated experimentally using flow measurements and weather radar data as a constant parameter. Machado et al. (2022) demonstrated, through a study of five different catchments, that experimentally determined runoff coefficients significantly differ from tabulated values due to variations in catchment characteristics and hydrological processes. This study illustrates the necessity of determining the runoff coefficient based on experimental studies in the catchment for accurate estimates of the catchment runoff-rainfall.

Traditionally, the runoff coefficient is estimated through in situ flow measurements and rainfall depth measured with rain gauges or disdrometers as done by, e.g., Ahm & Rasmussen (2017a) and Machado et al. (2022). However, this paper aims to develop a method for adjusting weather radar rainfall against catchment runoff-rainfall without the need for rain gauges located in the catchment. Instead, the runoff coefficient is derived from the daily bias-adjusted weather radar-measured precipitation and the runoff measured as the inflow to the stormwater detention pond divided by the catchment area. In this process, it is assumed that the hydrological processes in the catchment can be described by a constant factor, regardless of seasonal variations, rain intensity, antecedent soil moisture, and rainfall duration. While this assumption might seem overly simplistic, determining how the runoff coefficient varies requires data taken over several years. Additionally, as urban catchments continue to develop and change over time, this may not lead to an accurate description of the runoff coefficient. Therefore, we derive the runoff coefficient as a constant value for all rain events as the slope of a linear regression fitted to the measured runoff and the daily bias-adjusted radar rainfall measurements with an intersection in origin.

The performance of the weather radar precipitation estimates is evaluated by comparing hourly and daily accumulated rainfall measurements at the two independent validation rain gauges in Frejlev (shown in Figure 1), with the weather radar precipitation estimates in the corresponding radar pixels.

To validate the bias adjustment method, including the pond measurements, we identify rainfall events as rainfall days over Frejlev within the data period from 4 April 2022 to 19 December 2022 and 16 March 2023 to 11 December 2023. We define events as days with radar-measured rainfall in the catchment and more than 2 mm of runoff measured in the stormwater pond. This threshold is selected to overcome potential problems with tailing effects after rainfall events leading to the inclusion of days without rainfall. Within the measurement period, this resulted in a total of 133 days. To avoid systematic bias related to seasonal effects, rain intensity, or rain depth, the 133 days were randomly divided into two datasets containing 80% (106 days) and 20% (27 days). The dataset containing 80% is used only to determine the site-specific runoff coefficient. This ensures that the runoff coefficient is independent of the remaining 20% of the data, which is used for validation of the bias adjustment method including the catchment runoff-rainfall measurements.

The runoff coefficient might be a result of averaging large spatial variation of rainfall over the catchment and, thus, not only imperviousness and micro-hydrological effects. In Figure 7, the minimum and maximum daily weather radar rainfall depths over the catchment are shown as horizontal lines. The average spatial variation in weather radar rainfall over the catchment for the 106 days is 0.73 mm/day, while the 95th percentile variation is 1.96 mm/day, and the maximum observed variation between two pixels covering the catchment is 3.94 mm/day. In comparison, the average variation between the two rain gauges in the catchment is 0.70 mm/day, the 95th percentile variation is 3.94 mm/day, and the maximum difference is 25.8 mm/day. This highlights the limited spatial variability in rainfall across the catchment for most events, while also demonstrating the potential challenges associated with the use of rain gauges: Rain events may go unrecorded due to blockages or outages of the rain gauge, leading to the high maximum difference in observed daily rainfall between the two rain gauges. As shown in Figure 7, the spatial variation in weather radar rainfall over the catchment is not considerable for the majority of the events indicating that the derived runoff coefficient does not primarily result from spatial rainfall variations over the catchment.

A generally good performance is observed for daily and hourly accumulated bias-adjusted rainfall measurements for the 27 validation days when comparing weather radar estimates with rain gauges. The results show that the performance is increased significantly by bias adjusting the weather radar for all performance parameters, and high performance is obtained when bias adjusting using only the seven rain gauges near Aalborg. This is indicated by the high NSE, low RMSE, and the slope of the regression line being close to 1. Including the catchment runoff-rainfall measurement in the bias adjustment results in a slight improvement, and especially daily rainfall less than 5 mm is better represented when including the catchment runoff-rainfall. However, due to the good performance when bias adjusting only against the seven rain gauges near Aalborg, it is difficult to significantly improve weather radar performance when also including the catchment runoff-rainfall measurements. A slight improvement is nevertheless obtained for all three performance parameters for daily accumulated rainfall when including the catchment runoff-rainfall in the bias adjustment, and for hourly accumulated rainfall, a minor enhancement is obtained for NSE and RMSE while the regression line is slightly more distant from the bi-sector. This improvement illustrates the potential for using catchment runoff-rainfall measurements derived from stormwater detention ponds for bias adjustment of weather radar rainfall.

Cumulative summed weather radar rainfall estimates adjusted with and without the pond are compared to one of the rain gauges (5057) in Frejlev (Figure 10(b)). In three of the presented four events, no significant improvement is observed from this comparison when including the catchment runoff-rainfall estimate. In the 1 July 2023 event, the daily accumulated rainfall is changed significantly by including the catchment runoff-rainfall resulting in a better fit with the rain gauge in the catchment. An improvement in the daily accumulated rainfall measurement is observed in the four selected events, showing that catchment rainfall measurements can supplement rain gauges in the bias adjustment of weather radar measurements. In Figure 10, it is furthermore shown that the time series dynamics are well captured by the bias-adjusted weather radar measurements. Only one of the two rain gauges (5057) is shown in Figure 10; however, a comparison with the other gauge (5058) gives similar results.

The results of this study demonstrate that catchment runoff-rainfall estimates derived from stormwater detention ponds can complement rain gauges when bias-adjusting weather radar data. Catchment rainfall estimates do not necessarily outperform rain gauges in achieving the highest performance for bias-adjusted radar data. However, the results demonstrate that the value of runoff-rainfall measurements for adjusting weather radar measurements equals that of gauge observations. The density of ground observations is in many areas limiting the performance of weather radar rainfall estimates; hence, increasing the density by use of opportunistic rainfall sensors has a significant potential. In Denmark, several thousand stormwater detention ponds function as drainways for urban areas and roads, and implementing the presented method in already established ponds will thus increase the ground observation network density significantly. Dense ground observation networks consisting of opportunistic rainfall sensors have been shown to improve weather radar rainfall estimates and facilitate spatially distributed weather radar bias adjustment (Nielsen et al. 2024; Overeem et al. 2024). Furthermore, it is a significant benefit that the catchment runoff-rainfall measurements are easily achievable and can increase the density of ground observations and thereby improve weather radar bias adjustment in urban areas. Runoff-rainfall estimates derived from stormwater detention ponds include a mass balance consideration in the radar adjustment, making the adjustment more robust and potentially leading to more accurate results in urban drainage modeling.

Due to signal noise, the established rating curve leads to uncertainties in the catchment runoff-rainfall estimates. This is primarily the case at water levels near the level of the flow regulator. Including the catchment runoff-rainfall estimates however improves the radar rainfall estimates on days with daily accumulated rainfall less than 5 mm (Figure 8), indicating that the uncertainties in the rating curve at lower water levels do not result in significant rainfall estimate uncertainties. The rating curve expresses the outflow up to the highest measured water level and must thus be updated if higher water levels are measured. Extrapolation of the rating curve might lead to increased uncertainties as the throttling of water through the flow regulator is expected to be greater with increased water level in the pond. Alternatively, the rating curve for a stormwater pond outflow can be established by closing the outlet, filling the pond, and then measuring the water level while the outlet is opened, and the water level sinks during dry weather and hence without inflow. This will result in a fully established rating curve for the entire pond capacity with fewer uncertainties. However, when adjusting using catchment runoff-rainfall estimates, the derived daily bias factors indicate no significant systematic errors in the estimated runoff.

Uncertainties regarding catchment-specific parameters, including the runoff coefficient, will naturally lead to uncertainties when estimating catchment runoff-rainfall. However, since this method adjusts weather radar using the part of the rainfall event relevant for the urban drainage system, the uncertainties regarding the runoff coefficient will not necessarily lead to increased uncertainties in urban drainage model results. The scatter plot in Figure 7 highlights the uncertainties associated with estimating the runoff coefficient as a constant parameter. For rainfall events with a depth <2 mm/day, the figure indicates a strong dependency of the runoff coefficient on the rain depth; however, if the runoff coefficient were indeed significantly larger for smaller rain events, as implied by the figure, incorporating the catchment runoff-rainfall derived with the constant runoff coefficient would reduce the performance evaluation for these smaller rain events. Nevertheless, Figure 8(c) and 8(d) demonstrate that including the catchment runoff-rainfall improves the performance of daily rainfall estimation for rain events with depths < 5 mm. This shows that despite the scatter observed in Figure 7 for light rain, deriving the runoff coefficient as a constant parameter does not reduce the accuracy of estimated rainfall when the pond measurements are included in the bias adjustment. A catchment's runoff coefficient is typically unknown and requires relatively costly flow measurement equipment to determine. Due to the lack of knowledge, the parameter is often used as a calibration parameter in urban drainage models. Therefore, the measure of the runoff coefficient obtained through this method is an advantage in setting up urban drainage models.

The derived MFB factors range from 0.95 to 2.55 when including the catchment runoff-rainfall in the bias adjustment. Various factors influence the MFB corrections, such as variations in drop size distributions between rainfall events. Notably, this study does not identify trends in the derived MFB corrections depending on rain depth. On 7 out of the 27 validation days, the MFB factors change by over 10% when including the catchment runoff-rainfall in the bias adjustment (Figure 8(b)). For all seven events, the rainfall depth is < 5 mm/day, highlighting that the impact of including local catchment runoff-rainfall is most significant on smaller events. Figure 8(c) and 8(d) demonstrate that reducing bias factors for smaller rain events by incorporating catchment runoff-rainfall improves the estimated daily rainfall. This impact is also demonstrated on time series scales on one of these 7 days (1 July 2023) in Figure 10. Hence, the largest contribution occurs during small events, where the uncertainty in estimating the runoff coefficient and pond outflow is greatest, which demonstrates that these uncertainties do not necessarily lead to uncertainties in the calculated catchment runoff-rainfall.

Validation of the bias-adjusted radar rainfall based on meteorological rain gauges near the catchment shows that including the catchment runoff-rainfall as a supplement to rain gauge measurements improves the weather radar rainfall estimate performance. This improvement may be caused by more ground observations being included, and thus, a comparable improvement could possibly be achieved by including a rain gauge in the area. However, the improvement shows that catchment runoff-rainfall measurements are as valuable as rain gauge measurements for weather radar bias adjustments. Consequently, opportunistic rainfall measurements from stormwater ponds are highly relevant and valuable supplements to rain gauges, increasing the density of ground observations usable for bias adjustment of weather radar measurements for urban hydrological applications.

Since the measuring equipment is inexpensive and easy to install, and since there are many stormwater ponds in urban areas, the method developed for weather radar bias adjustment is very scalable. Measuring the stormwater pond geometry with differential GPS is time-consuming. It has been shown by Zhao et al. (2023) that photogrammetry based on drone recordings of stormwater ponds is a fast and inexpensive method for achieving hypsometric curves with high accuracy. Applying photogrammetry instead of measuring ponds with a differential GPS increases the scalability of the presented method. This and the results presented in this paper show that the method has a high potential for increasing the density of ground observations and thus obtaining better weather radar products.

The paper demonstrates that stormwater runoff measurements derived from stormwater ponds can be used for bias-adjusting weather radar measurements over urban areas. Implementing runoff-rainfall derived through the presented approach is shown to improve the performance of weather radar rainfall estimates to be used as input to urban drainage models. The approach has the additional benefit of deriving the runoff coefficient for the catchment when bias-adjusted radar rainfall is available, which also improves the input to urban drainage models.

The presented method is highly scalable and the required resource effort for establishing and maintaining the measurement station is similar to the effort required for installing and maintaining a tipping bucket rain gauge. By comparing the runoff-rainfall estimates to independent rain gauge-measured rainfall, it is demonstrated that the derived runoff-rainfall estimates provide precise and accurate rainfall estimates (NSE = 0.96 and RMSE = 1.43 mm). Hence, a catchment runoff-rainfall measurement can substitute for a tipping bucket rain gauge and increase the density of ground observations significantly. The paper demonstrates that stormwater pond-derived runoff-rainfall contributes positively to weather radar adjustment and is as valuable for weather radar adjustments as rain gauge measurements.

This research was supported by the Foundation for Development of Technology in the Danish Water Sector in the project RADIATE.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.