Field work for this study was carried out at Früebüel (CH-FRU), a long-term Swiss FluxNet field site in Switzerland (Pastorello et al., 2020; Zeeman et al., 2010). The site is a permanent grassland located on a mountain plateau in the canton of Zug, Switzerland (47∘06′57.0′′ N, 8∘32′16.0′′ E), at an elevation of 982 m a.s.l. The annual mean temperature is 7.8 ∘C (years 2005 to 2019) and the annual mean rainfall is 1232 mm (SD =±372 mm). The site is moderately intensively managed with two to four management events per year, usually a combination of mowing and grazing, depending on vegetation growth (Imer et al., 2013). The dominant species are common ryegrass (Lolium multiflorum), meadow foxtail (Alopecurus pratensis), cocksfoot grass (Dactylis glomerata), dandelion (Taraxacum officinale), buttercup (Ranunculus sp.), and white clover (Trifolium repens) (Sautier, 2007). The soil at the site is a silt loam mixture (56 % silt, 37 % sand, 7 % clay), with a bulk density of 1.12±0.03 g cm-3 and an organic C content of 4.4±0.2 % (Stiehl-Braun et al., 2011). The main rooting horizon is within the top 20 cm of soil, with a high root density in the top 11 cm (Stiehl-Braun et al., 2011). A location map and an aerial photograph of the site can be found in Appendix A.

The site is equipped with an agrometeorological station, comprising a temperature and relative humidity sensor (CS215, Campbell Scientific Inc., Logan, USA) placed in an actively aspired radiation shield and a cup anemometer with a wind vane (A100R and W200P, Vector Instruments, North Wales, UK), all installed at a height of 1.15 m, and a 3D anemometer (R3-50, Gill Instruments Ltd., Lymington, UK) installed at a height of 1.80 m. Moreover, the site is equipped with a tipping bucket rain gauge (15188H, Lambrecht meteo GmbH, Goettingen, Germany) and a networked digital camera (NetCam SC, StarDot Technologies, Buena Park, CA, USA). Furthermore, a leaf wetness sensor (PHYTOS 31, Meter Group AG, Munich, Germany) that mimics thermodynamic and radiative properties of a leaf is installed horizontally at a height of 30 cm to measure close or in the canopy of the grassland vegetation. A visibility sensor (MiniOFS, Optical sensors Sweden AB, Gothenburg, Sweden) is installed at a height of 1 m to capture shallow radiation fog and rime events.

The ML system was composed of three individual MLs with additional sensors. The three MLs were placed in a row at 1.45 m intervals. The design of the ML system is presented in Sect. 2.2.1–2.2.2. Further information about the installation process (including photographs), data processing, and storage can be found in the Appendix. A description of the installation procedure and the soil monolith preparation can be found in Appendix B. How data were collected, stored, and delivered can be found in Appendix C. The description of the load cell data low-pass filtering can be found in Appendix D.

Three replications showed an almost perfect linear correlation (R2=0.9999) between target mass and load cell mass. Target mass was retrieved from the microcontroller after data filtering (see Appendix D). Data with a resolution of 0.1 g were used (Riedl, 2021). The root mean square errors (RMSEs) for comparisons of target mass to load cell mass of three replications were 0.43, 0.47, and 0.36 g, respectively. The standard errors (SEs) of the parameter estimates of three replications were ±0.13, ±0.14, and ±0.11 g, respectively.

NRW inputs occur during events with a finite time period, and thus for NRW input studies, the relative change in mass from the start to end of that time period is of interest. A 100 g change with the given ML size translated into a change of 2 mm water input. The residuals were in the range of ±0.25 g or ±0.005 mm equivalent water input, which represents the accuracy of the ML system (Riedl, 2021).

A zero-point offset calibration combined with data filtering (see Appendix D) gave us not only a more accurate zero-point offset, but also a more accurate span value. An accurate span value reduced fluctuating values from load cell readings and gave us stable measurements when mass changed over time. The precision was determined by repeatedly loading and unloading calibration mass on the weighing platform three times and noting the difference to test for repeatability. The precision was ±0.28 g, equivalent to ±0.005 mm water input. With a base mass over 18.5 kg, the precision was slightly lower, with ±0.45 g equivalent to ±0.009 mm water input. The digital resolution of the ML system was 0.01 g, which corresponds to 0.0002 mm equivalent water input and is thus 2 orders of magnitude better than the physical resolution provided by our ML system. Regular loading/unloading experiments following Nolz et al. (2013) showed deviations in the range between ±<0.1 g (±<0.002 mm) and ±0.4 g (±0.008 mm) and thereby confirmed high accuracy also under field conditions. Thus, the data acquisition of the ML system was accurate enough to provide high accuracy.

Our ML system allowed differentiation among different types of NRW events when the ML measurements were combined with ancillary sensors. During a combined dew and fog event (Fig. 4a), we measured an increase in mass on the ML and an increase in leaf wetness (uncalibrated sensor voltage), while visibility was partially below 1000 m (intermittent fog event). During a dew-only event, we measured an increase in mass on the ML, besides increased leaf wetness, while visibility stayed above 1000 m throughout the event (Fig. 4b). During a potential water vapour adsorption event, there was only an increase in mass on the ML, whereas no condensation occurred on the leaf wetness sensor, while the visibility stayed well above 1000 m (Fig. 4c). Wind speed remained low (<1 m s-1) during the whole potential water vapour adsorption event. Mass increases on the ML could be attributed to hoar frost if air temperature was below 0 ∘C or to rime during events with reduced horizontal visibility <1000 m and temperatures below 0 ∘C. The highest water gain of the NRW input events shown in Fig. 4 was 0.4 mm and originates from the combined dew and fog event; the water input from the dew-only event was 0.2 mm, and the lowest water input with 0.06 mm came from the potential water vapour adsorption event.

Canopy temperature did not differ significantly (t test, p>0.05, n=30) between ML vegetation and control (Fig. 5a and b). The standard deviation of temperature data between the ML surface and the control was <0.5 ∘C throughout the observation period. The variance of canopy temperature between the ML vegetation and the control was not statistically significantly different (F test, p>0.05, n=30). Soil temperature in ML pot 1 was higher than in the control plot at the beginning of the dew formation period (Fig. 5c) but equalled control soil temperatures towards the end. Dew formation started at 18:53 and ended at 06:07 UTC (Fig. 5d). Dew water input was 0.24 mm, showcased for ML 1, even though dew formation occurred during that night on all three MLs installed at the site (Riedl, 2021).

Plant heights of Trifolium pratense, Plantago major, and Rhinanthus alectorolophus did not differ between ML pots and the control (t test, p>0.05, n=3); also, variability did not differ (F test, p>0.05, n=3). Additional measurements of mean and maximum vegetation height on 14 August 2019 also showed no statistically significant difference (t test, p>0.05, n=3; data not shown; Riedl, 2021).

WFPS data of ML pot 1 and ML pot 2 were very similar and closely matched the control (Fig. 7a). WFPS values of ML pot 3 showed a higher dynamic but closely followed the temporal pattern of the control and ML pots 1 and 2. The differences between WFPS of ML pots and the control were constant over time (Engle–Granger two-step co-integration test; p<0.05). This indicates that soil moisture data of ML pots and the control were in general not significantly different. However, during a prolonged no-rainfall period in summer (Fig. 7a, marked with the red box), WFPS of ML pots decreased more quickly in comparison to the control. Since lower soil moisture values can result in a lower heat capacity of the soil, we assessed whether lower WFPS values inside ML pots may have an influence on soil temperature during non-rainfall periods (Fig. 7b).

Soil temperature of ML pot 1 and the control (soil temperature in the surroundings) (Fig. 7b) showed the same increasing trend, while deviation of WFPS of ML pots from the control (Fig. 7a, marked in red) increased with time (the same pattern as that of ML pot 1 was also evident in ML pot 2 and ML pot 3, data not shown). From this we conclude that soil temperatures inside ML pots during the most relevant hours of the day when dew forms (during the night before sunrise) were not strongly influenced by a lower water content and its resulting lower heat capacity. Nocturnal temperature minima almost perfectly agreed between ML pot 1 and the control, while the daily temperature range of ML pot 1 was double compared to the control (Fig. 7b). Over the prolonged no-rainfall period, the hourly mean soil temperature deviations of ML pot 1 from the control ranged between -0.14 ∘C around sunrise and 2.57 ∘C in the later afternoon (Fig. 7c). Over the period from May to October 90 % of nocturnal 1 min soil temperature deviations (sunset–sunrise) were lower than 2.90 ∘C, and 50 % were lower than 0.69 ∘C.

There were a total of 127 NRW input events at CH-FRU over 1 year (2 May 2019, 12:00 UTC, to 2 May 2020, 11:59 UTC; Fig. 8). The frequency of the events can be found in Table 2. Eleven NRW events were observed when leaf wetness remained low, potentially indicating water vapour adsorption events or dew formation on soil. Potential water vapour adsorption events occurred during two time periods: period 1 in July 2019 and period 2 in April 2020. During period 1, a single potential water vapour adsorption event occurred, whereas during period 2 10 such events occurred. During both periods rainfall was low: 10 d before the event in period 1 the cumulative rainfall was only 9.6 mm, and in period 2 the cumulative rainfall between 14 March, the last bigger rainfall event with 12.3 mm, and 23 April was only 13.7 mm. The soil moisture during both potential water vapour adsorption periods was rather low, with a WFPS of ca. 45 %. This indicates a potential water vapour gradient from the atmosphere to the soil favourable for water vapour adsorption. The cumulative NRW input over 12 months was 15.9 mm, which corresponds to roughly 1 % of the 1580 mm annual precipitation collected during the third-warmest year in Switzerland since weather recordings started in 1864 (MeteoSchweiz, 2020).

The mean NRW input over all events was 0.12 mm, with the highest single input of 0.4 mm by a fog event and the lowest input of 0.021 mm by a hoar frost event. On a monthly basis, the months with the highest NRW inputs were September with 2.64 mm, August with 2.35 mm, and June with 2.32 mm. The cumulative NRW input from May till September was 9.7 mm. At the monthly scale, NRW inputs can be remarkable: in April 2020, the month with the least rainfall (51.8 mm), the contribution of NRW input to the monthly hydrological input was 3.5 %. The average monthly NRW input was highest in September with 0.088 mm, when the nights were longer than in summer, and thus the probability of NRW inputs was increasing with the duration of the night. However, observed average monthly NRW inputs ranked second and third in terms of amount in June and August, when nights were much shorter than in September. The relationship between NRW input as a function of actual NRW input duration (Fig. 9) was not very strong, but when durations were binned into 10 bins of equal widths, a clear trend of increasing NRW inputs with increasing NRW input duration emerged. Because no NRW input is expected if the duration of NRW input is 0 h, we first started with a square-root regression through the origin, y=b⋅x, the slope of the fit was 0.042±0.001 mm h-1/2 (Fig. 9, dotted line), but for durations >2 h it closely corresponded to a conventional linear regression slope of 0.008±0.001 mm h-1 (Fig. 9, black line, R2=0.86, p<0.001; the intercept should be ignored because it has no physical meaning in this context). Despite this rather clear dependence on the actual duration of NRW input, there was no significant correlation found between average monthly NRW input duration and potential NRW input duration given by the time between sunset and sunrise (R2=0.16, p>0.1; data not shown; Riedl, 2021).

The high accuracy of our newly developed ML system allowed us to capture even very small NRW events such as the potential water vapour adsorption event with 0.06 mm shown in Fig. 4c. It was possible to capture NRW events with an accuracy of ±0.25 g with pots that weigh roughly 15 kg in total. This corresponds to an accuracy of ±0.005 mm of water inputs. The accuracy would be even higher with a relative mass change of less than 100 g (equivalent to 2 mm water input), which is true for most NRW events. The accuracy of our ML system was 4 orders of magnitude better than reported for many other studies (see Table 3). Feigenwinter et al. (2020) were able to achieve on average (depending on the calibration date) the same accuracy, although with a lower depth of the ML pot (6.5 cm) and a lower weighing capacity (7 kg). The high accuracy of our ML system was achieved by a combination of factors, such as using a state-of-the-art load cell in combination with continuous high-frequency data filtering as well as ancillary data. For example, temperature measurements were crucial for differentiating between hoar frost and dew events and fog and rime events. Ancillary wind measurements could be used to exclude periods with high wind speeds, because high wind could act as a force on ML and thereby increase mass. However, NRW inputs occur during conditions with low wind speed, and the probability of dew formation decreases below 5 % when wind speeds are smaller than 0.4 m s-1 or bigger than 1.9 m s-1 (Zhang et al., 2014). Thus, wind is not a big bias source for NRW quantification. A further factor promoting high accuracy was a load-cell-specific calibration. Factory calibration is the same for all load cells of the same model, but when an individual calibration is made, the differences among individual load cells are substantial, and hence the highest accuracy always requires a load-cell-specific calibration by the user. Construction details that promoted accuracy were the frictionless gap construction between ML pot and cover lid as well as the three adjustable support feet on which the weighing platform was centred on the load cell. This is needed because after burial, a ML system may accidentally tip, twist, and be thrown out of balance (Uclés et al., 2013). The low-cost microcontroller had enough computing power to continuously process data from multiple sensors while consuming little energy. Thus, our ML system could also be powered by solar panels. During or after freezing temperature conditions the ML system should be controlled, because expanding water in the reservoir or the ML pot could break PVC parts of the ML system. However, this did not occur during this study period.

The precision (repeatability of the measurements) of our ML system was ±0.005 mm equivalent water input. With a base mass over 18.5 kg, the precision was lower, with ±0.009 mm equivalent water input. However, in the field, ML pots weighed less than 18.5 kg, even when soil was moist. This precision was unprecedented, only topped by manual ML weighing on an electronic balance (Jia et al., 2014). Manual weighing is, however, very labour intensive and consequently unsuitable for long-term NRW studies.

The digital resolution (smallest distinguishable unit) of our ML system was 0.0002 mm. This resolution was in the range reported by Uclés et al. (2013). Comparison of accuracies, precisions, and resolutions with other studies is often hampered, because the distinct terms “accuracy”, “precision”, and “resolution” are often misconceived. The load cell capacity of 20 kg in our ML system is relatively large compared to other ML studies. NRW input studies with ML had a load cell capacity in the range from 0.3 kg (Brown et al., 2008), 1.5 kg (Kaseke et al., 2012), 3 kg (Uclés et al., 2013), 6 kg (Maphangwa et al., 2012; Matimati et al., 2013), up to 7 kg (Feigenwinter et al., 2020).

NRW inputs occurred rather frequently over the entire year of observation (Fig. 8). NRW inputs could be measured on approximately every third day on average. The highest NRW inputs occurred during the months of main grass growth (April–September), indicating a potential hydroecological relevance. Ancillary sensors allowed differentiation of different NRW inputs. Differentiation among different types of NRW inputs is important for various research disciplines; e.g. the prediction of fog events poses a major challenge for numerical weather prediction for meteorologists (Westerhuis et al., 2020). Thus, it is important to measure the frequency and water inputs of fog events during the whole year.

The use of a visibility sensor allowed us to assess the contribution of fog and rime. A leaf wetness sensor allowed differentiation between events in which condensation occurred (dew, hoar frost), in contrast to events when condensation on leaves was less probable (water vapour adsorption and/or dew formation on soil). Potential water vapour adsorption events occurred during periods with low rainfall, when soil was drying out, which increased the vapour pressure deficit gradient between soil and the atmosphere, promoting water vapour adsorption. However, the NRW inputs of the potential water vapour adsorption events were rather low (0.03–0.13 mm). Thus, it is not unlikely that a leaf wetness sensor might react slightly differently than a true plant leaf despite the care that was taken to design leaf wetness sensors to match the radiative and thermodynamic properties of plant leaves, and these events were small dew events. Further investigations are needed to clarify whether the leaf wetness sensor is suitable for differentiating between dew and water vapour adsorption events. Air temperature measurements from the agrometeorological station were necessary to differentiate between dew vs. hoar frost formation and between fog vs. rime. Rainfall measurements allowed differentiation between NRW events and rainfall events, and a networked digital camera allowed us to observe persisting snow cover. The installation of three MLs allowed exclusion of possible effects by insects, snails, and lizards arriving on or departing from a ML pot. If it is assumed that these animals have no preference for a particular ML pot and thus their arrival and departure form a random process, such effects only contribute to the noise that is filtered out during data filtering and thus should not bias our NRW input estimates. In deserts or arid regions (with low vegetation cover), additional sensors (e.g. infrared video cameras) would be needed to detect depositing materials like dust and sand that accumulate on the ML over time. The installation of multiple MLs furthermore had the advantage that spatial variation in soils, species composition, and leaf area could be reduced in comparison to single ML deployments.

Our ML system had a larger area and a deeper ML pot than most other ML systems developed and used in earlier studies on NRW quantification (Table 4). This allowed unimpaired plant height growth (Fig. 6), representing more natural conditions than many, rather shallow ML systems, an issue crucial for accurate measurements of NRW inputs to grasses and forbs. We did not find any significant differences in canopy temperatures between our ML pots and the control (surroundings) (Fig. 5a). Furthermore, we found in general no significant difference in soil moisture between the ML and the control (surroundings); only during a prolonged drought period did soil moisture values of ML pots decrease more quickly. In this study, this however had no influence on plant standing height because measurements of plant height (before the drought period) and measurement of overall vegetation height (after the drought period) were not statistically different. However, lower soil moisture during prolonged drought periods can result in reduced evaporation rates and increased water vapour adsorption rates. Furthermore, this can influence plant growth and development. Thus, the ML system can be used to reliably measure NRW inputs as long as the difference in soil moisture during prolonged drought periods does not influence plant height or canopy architecture. WFPS values of ML pots were in general not higher than the control, suggesting a sufficient drainage by the drainage-water outlets. This is crucial, because saturation at the bottom of a ML could lead to oxygen limitation for root growth (Ben-Gal and Shani, 2002). In contrast to Kidron and Kronenfeld (2017), Evett et al. (1995), and Ninari and Berliner (2002), we also did not observe substantially lower nocturnal soil temperatures, the time when NRW inputs actually take place, which is important for avoiding an overestimation of dew formation on soils. On the other hand, afternoon and close-to-sunset soil temperatures of ML pots were higher compared to those in the control (Fig. 7). Thus, potentially, the ML system could underestimate dew formation on soils shortly after sunset, but dew formation on soils is rare (Agam and Berliner, 2004; Ninari and Berliner, 2002) and the open soil surface in grasslands is rather small, ideally zero under good management practices. Higher soil temperatures could underestimate water vapour adsorption, because it lowers the vapour pressure deficit between soil and atmosphere. Therefore, our estimates of NRW inputs on soils should be conservative estimates, given that the slightly elevated temperatures actually do reduce (not increase) NRW inputs on soil inside the ML pots. The higher soil temperatures in the afternoon were not related to a lower water content nor its associated heat capacity. Kidron et al. (2016) provided a possible explanation for the diurnal temperature difference between a ML pot and the control. They termed it a “loose stone effect”: the ML pot might act as a loose stone, i.e. through the air gap between the ML pot and the outer part of the ML system more efficient longwave radiational cooling can occur in comparison to the bulk soil. However, Ninari and Berliner (2002) found that the lateral soil temperature gradient was small compared to the vertical soil temperature gradient and that wrapping the ML pots with insulation material did not reduce temperature deviations. We thus think that insufficient ML pot depth has most likely caused the soil temperature alterations observed mainly during day-time when dew formation is absent. Ninari and Berliner (2002) suggested that the minimum ML depth should be the depth at which the temperature is constant during the entire day. For a dry loess soil in the Negev desert, a sufficient ML pot depth would be 50 cm (Ninari and Berliner, 2002). At CH-FRU, a ML pot depth of approximately 95 cm would be necessary in order to have soil temperature gradients over 24 h periods <0.5 ∘C. With a depth of 95 cm, there would be the risk that all the advantages any ML system entails would be lost. Although constructing deeper ML pots would be possible, even with double or triple the current ML pot depth, deeper ML pots would exert more dead mass onto the load cell and would thus decrease load cell accuracy (Kaseke et al., 2012). Overall, ML design is always a trade-off between representing the surroundings and feasibility of construction and installation. The ML system was not constructed with the depth suggested by Ninari and Berliner (2002); however, the aim of this study was to measure NRW inputs to grasslands, for which canopy temperatures are more important. We found only a small difference in canopy temperature between the ML and the control. Thus, we conclude that our novel ML design is suitable for quantifying nocturnal NRW inputs on grasses and forbs reliably and accurately at high temporal resolution.

NRW inputs occurred on approximately one-third of the nights and were thus a frequent water input. The NRW inputs measured by our ML system represent conservative estimates under certain conditions, because drainage-water flow from the ML pots was not measured. Under conditions with water lost via drainage, NRW inputs would be underestimated. Especially during and shortly after intensive rainfall periods, when drainage-water flow is more likely (see Appendix F, Fig. F1, and Table F1), the application of the ML system is limited. During transition periods, shortly after rainfall, e.g. during nights when the sky clears after rainfall, NRW inputs may be underestimated. Therefore, we excluded such periods (see Eq. 1) from the analysis and limited our analysis for dry periods. Our longer-term NRW estimates might thus be conservative estimates if rainfall periods are included in the total hydrological input. At our site, drainage-water flow from the ML pots reached low levels rather quickly after rainfall events (see Appendices E and F for more details). Nevertheless, depending on soil characteristics and conditions, drainage-water flow could persist for a longer time (Fig. F1 and Table F1). Under such conditions, the ML system provides conservative estimates of NRW inputs, because we set NRW input to 0 mm when there is rainfall and/or drainage flow percolating out of the soil monolith. A possible modification of the ML system to also quantify such drainage flow accurately is suggested in Appendix E, with an additional sensor as indicated in Fig. 1b:p. We used three outlets (Fig. 1b:j) to ascertain that drainage is not hindered, but if a sensor to quantify drainage is added, the ML pot should only have one drainage hole with a sensor, from which reliable quantitative estimates of drainage losses can be obtained.

NRW inputs were especially high under conditions when rainfall was absent, e.g. in April, the month with the lowest rainfall. NRW inputs were not influenced by potential NRW input duration, and thus there was also a high probability of NRW inputs occurring during summer months, the main growth period of temperate grasses and forbs. In fact, the monthly average NRW inputs were similar to the NRW inputs that were measured in spring and autumn months, when NRW inputs are expected to be highest. This indicates a high ecohydrological relevance of NRW inputs for temperate grassland ecosystems, especially during hot and dry periods. However, the effects of these frequent NRW inputs on plant–water status still have to be investigated.

Besides studying the effects of NRW inputs on temperate grassland species during hot days with low soil moisture, a special focus should be directed to the effects of NRW inputs during periods with high soil moisture, when no soil water stress is present. NRW inputs could be beneficial even under such conditions, when simultaneously atmospheric demand is high (high energy input, high vapour pressure deficit). NRW inputs could reduce leaf temperatures by the re-evaporative cooling effect and thereby reduce water stress during early morning hours and consequently increase productivity (Dawson and Goldsmith, 2018). However, leaf wetting by NRW inputs could also be disadvantageous during periods with no soil water stress. Leaves covered by water droplets from NRW inputs could show reduced gas exchange due to lower gas diffusivity through the water layer. Thus, the development of the ML system and measurement of NRW inputs with high accuracy are crucial steps to address ecohydrological processes, but further investigations are necessary to understand physiological effects on grasslands.