Technical note: High accuracy weighing micro-lysimeter system for long-term measurements of non-rainfall water inputs to grasslands

Non-rainfall water (NRW), defined here as dew, hoar frost, fog, rime and water vapor adsorption, might be a relevant water source for ecosystems, especially during summer drought periods. These water inputs are often not considered in ecohydrological studies, because water amounts of NRW events are rather small and therefore difficult to measure. Here we present a novel micro-lysimeter (ML) system and its application which allows to quantify very small water inputs from 10 NRW during rainfree periods with an unprecedented high accuracy of ± 0.25 g, which corresponds to ± 0.005 mm water input. This is possible with an improved ML design paired with individual ML calibrations in combination with highfrequency measurements at 3.3 Hz and an efficient low-pass filtering to reduce noise level. With a set of ancillary sensors, the ML system furthermore allows differentiating between different types of NRW inputs: dew, hoar frost, fog, rime and the combinations among these, but also additional events when condensation on leaves is less probable, such as water vapor 15 adsorption events. In addition, our ML system design allows to minimize deviations from natural conditions in terms of canopy and soil temperatures, plant growth and soil moisture. This is found to be a crucial aspect for obtaining realistic NRW measurements in short-statured grasslands. Soil temperatures were higher in the ML compared to the control, thus further studies should focus to improve the thermal soil regime of ML. Our ML system has proven to be useful for highaccuracy, long-term measurements of NRW on short-statured vegetation like grasslands. Measurements with the ML system 20 at a field site in Switzerland showed that NRW input occurred frequently with 127 events over 12 months, with a total NRW input of 15.9 mm. Drainage water flow of the ML was not measured, therefore the NRW inputs might be conservative estimates. High average monthly NRW inputs were measured during summer months, suggesting a high ecohydrological relevance of NRW inputs for temperate grasslands.


Introduction 25
Non-rainfall water (NRW) inputs, defined here as dew, hoar frost, fog, rime and water vapor adsorption, provide water to plants. These different inputs form under different environmental conditions: Dew forms on plant surfaces when the temperature of the surface drops below the dewpoint temperature of the adjacent air (Beysens, 2018;Monteith, 1957), whereas dew forming directly on soil surfaces is design of a novel micro-lysimeter (ML) system with improved accuracy that was deployed at a Swiss mountain site (982 m elevation) where rainfall exceeds evaporation in average years . 110 Prolonged drought periods can occur even under such climatic conditions and are expected to increase by 1 to 9 days by 2085 (with RCP8.5, compared to the reference period 1980-2010) (Fischer and Schär, 2018).
It remains to be investigated whether the frequency and amount of NRW inputs are also high in summer. Groh et al. (2018) for example found that NRW inputs were on average higher in autumn and 115 winter months, i.e. from October until February. However, at another temperate site the second highest average NRW input was found in May. In general, higher NRW inputs and higher frequency of NRW inputs are expected to occur during spring, autumn and winter, when nights are longer than in summer, and when there is a higher probability for NRW inputs to occur. Thus, long-term measurements are important to observe such seasonal NRW input patterns and will allow to investigate the potential 120 effects of NRW inputs on grasslands during the main vegetation period in summer.
During drought periods, when rainfall input is absent, NRW inputs can be are the only available atmospheric water source. Thus, we hypothesize that NRW inputs to plants constitute an important water source during drought periods, even under temperate climate conditions with ample average rainfall in climates where rainfall exceeds evapotranspiration in the annual budget. 125 NRW might also influence plant water relations via these micro-environmental effects in periods and climates when soil water availability is not a limiting factor for plant growth. Thus, quantifying NRW inputs in different climates is considered to be of high relevance now and in the future.
Here we present an improved method that is suitable for automated long-term measurements of NRW inputs to short-statured grassland vegetation during dry spells and drought periods. 130

Field site Früebüel
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 135 982 m a.s.l.. The annual mean temperature is 7.8 °C (years 2005 to 2019), 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), 140 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. 145 The site is equipped with an agrometeorological station, comprising a temperature and a relative humidity sensor (CS215, Campbell Scientific Inc., Logan, USA) placed in an actively aspired radiation shield, 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 150 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, 155 Sweden) is installed at a height of 1 m to capture shallow radiation fog and rime events.

Methods
The ML system was composed of three individual ML with additional sensors. The three ML were placed in a row at 1.45 m intervals. The design of the ML system is presented in Section 2.2.1 -2.2.2. For better readability, abbreviations for dimensions were used before the corresponding value (d for  160 diameter, od for outer diameter, id for inner diameter, h for height or depth, t for thickness). 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. 165

ML design
A ML consisted of an inner part (Fig. 1a) and an outer part (Fig. 1b,item (a), in what follows referenced as Fig. 1b:a). The outer part ( Fig. 1b:a) was made by a cylindrical PVC-U tube (VINK Schweiz GmbH, Dietikon, Switzerland; 45 cm outer diameter x 42 cm height, 44.64 cm inner diameter) with an open top and a closed bottom. The bottom was closed with a PVC-XT disk (VINK Schweiz GmbH,Dietikon,170 Switzerland; 46 cm diameter, 0.3 cm thick), which was welded with a PVC-U welding rod to the cylindrical tube for waterproof closure. The outer part protected the inner part ( Fig. 1b:b-q) from confounding factors like soil pressure, infiltrating water and biota. The core elements of the inner part were a cylindrical pot ( Fig. 1b:b), filled with a soil monolith (for simplicity called ML pot within this paper) containing the original grass sward. The ML pot was made of a cylindrical PVC-U tube (VINK 175 Schweiz GmbH, Dietikon, Switzerland; 25 cm outer diameter x 25 cm height, 24.8 cm inner diameter), of which the bottom was closed with a PVC-XT disc (VINK Schweiz GmbH, Dietikon, Switzerland; 26 cm diameter, 0.3 cm thick) that was welded in the same way as the outer part. The ML pot was mounted by means of three custom made sockets (Fig. 1b:c) on a weighing platform , secured with machine screws. The weighing platform consisted mainly of three parts, the load plate ( Fig. 1b:d), a 180 load cell (Fig. 1b:e), and a base plate (Fig. 1b:f). The load plate was made of aluminum (AlSi1MgMn, 29 cm diameter, 1 cm thick), likewise the base plate (35 cm diameter, 1 cm thick). Between the load plate and the base plate, a PW15AHY temperature-compensated load cell with 20 kg capacity (HBM, Darmstadt, Germany) was mounted. To allow bending of the load cell, two rectangular spacing washers (Fig. 1g, 2.5 x 3.1 cm, 0.1 cm thick) were mounted between load cell and load plate, and between load 185 cell and base plate. To mount the load cell and the spacing washers to the load plate and the base plate, two countersunk head screws were used. The weighing platform was standing on three equidistant adjustable support feet ( Fig. 1b:h, M6×1 machine screws, 15.5 cm height) integrated in the base plate. This allowed to level the weighing platform, which is important for accurate load cell measurements. A counter nut above the base plate ( Fig. 1b:i) fixed the position of the weighing platform. 190 load cell, f) base plate, g) spacing washer, h) adjustable support feet, i) counter nut for adjustable support feet, j) cover lid, k) water guide, l) water and dirt protection, m) float switch, n) bilge pump, o) soil moisture and temperature sensor, p) drainage-195 water outlet, and q) optional sensor or drop counter to quantify drainage for applications that do not specifically target drought conditions.

Drainage water flow
To avoid stagnating water inside of ML pots, a passive drainage water flow path was made. The 200 drainage-water was guided away from the load cell to a reservoir to protect the load cell from suspended matter. Suspended matter can be carried along with drainage water and could impede the function of the load cell by blocking the load cell bending. Drainage water beyond soil field capacity was allowed to flow out from the bottom of the ML pot via drainage-water outlets. Three drainage-water outlets (Fig. 1b:j; 0.8 cm diameter) were drilled equidistantly into the lateral side of the ML pot as close as possible 205 to the bottom. The drainage-water outlets were protected with a metal mesh to prevent erosion of ML soil during heavy rainfall events. Excessive water could follow a passive drainage path from the top of the load plate, guided by a water guide ( Fig. 1b: Rainfall could enter also in the gap between the ML pot and the outer part of the ML system. To minimize this water collection, a cover lid ( Fig. 1b:o) made of a PVC-XT ring (47 cm outer diameter, 26 cm inner diameter) was constructed. The cover lid had an inclination of 7° towards the outside. This was done by putting the cover lid in a heated oven at 90 °C and then pressing it towards a custom-made wooden fit with the desired form, till it had cooled down. The slanted cover lid resulted in a preferred 220 water flow towards the surrounding and thereby prevented water flow towards the inside of the ML system. Furthermore, it protected the ML pot from incident solar radiation, also minimizing potential heating effects. Wiring of the load cell, the float switch, the bilge pump as well as the soil temperature and moisture sensors (see Section 2.2.8) were bundled and led out close to the top of the outer part of the ML system (schematically shown with an arrow in Fig. 1b). 225 In the design as used here, i.e. to quantify NRW inputs during dry spells rainfree and drought periods in summer, drainage water was allowed to freely drain from the ML pots. Thus, rainfall periods had to be excluded from analysis (see section 2.2.3). During dry spells and drought periods, we assumed that no drainage occurs or that the drainage rate is lower than the NRW input rate during dry spells and drought periods, when NRW inputs potentially are important as an additional water source to plants. However,230 to use the ML system more universally during and shortly after rainfall periods, it is recommended to add an additional sensor ( Fig. 1b:p) to quantify drainage water flow (see Appendix E). For applications without such an additional sensor, it should be kept in mind that, depending on soil type, up to 41.5 hours after intensive rainfall that saturated the soil monolith completely drainage water losses can occur (see Fig. F1 and Table F1). 235

Calculation of NRW amounts and differentiation of NRW inputs
We differentiated six types of NRW events with ML and ancillary sensors, i.e., (1) dew only, (2) hoar frost only, (3) fog only, (4) rime only, (5) combined dew and fog events, and (6) combined hoar frost and rime events. During all six event types, a mass increase was expected on the ML. The NRW amounts (NRWamount) were calculated using equation (1): 240 where MLmax1m is the maximum value of the one-minute mean ML mass (all three ML values averaged every minute) over a time period of 24 hours (from 12:00 to 12:00 UTC), MLmin1m is the minimum value of the one-minute mean ML mass over the same time period. The resulting NRWmass (in grams) was then converted to mm. If rainfall occurred during an analyzed 24-hour period, that period was 245 excluded, except when the rain event occurred directly after the NRW input event. Rain events were determined by the rain gauge measurements at the site. Time periods with a snow cover as determined visually from digital images were not considered in the analysis. To distinguish between different types of NRW inputs, we used the information from all ancillary sensors. Often dew and fog or hoar frost and rime occurred in combination, e.g. after sunset, dew formation occurred, when the atmosphere cooled 250 further down till the atmosphere got highly saturated, fog started to form. We termed such events combined dew and fog events, or hoar frost and rime events, respectively. The leaf wetness sensor was used to sense condensation (during dew only and hoar frost only events), NRW droplet interception and impaction (during fog, rime, combined dew and fog, combined hoar frost and rime events), and to sense an absence of condensation (during events when less condensation is expected to occur, e.g. water 255 vapor adsorption or dew formation on soil). The visibility sensor was used to distinguish between events with reduced visibility below 1000 m (fog, rime events), and events without reduced visibility (dew only, hoar frost only events). To distinguish between fog and rime events from dew and hoar frost events, the temperature sensor of the nearby agrometeorological station was used. When temperature dropped below 0 °C, NRW inputs were attributed to rime and hoar frost. 260

Soil monolith preparation
To retrieve an undisturbed soil monolith with intact grass vegetation, we used an empty ML pot that was placed upside down at the place of interest from where the monolith was to be retrieved. First, we trenched the soil with a long spade around the ML pot. Then we removed the soil around the ML pot 265 with small shovels, which allowed pressing the ML pot into the soil. We continued until the top of the ML pot was at ground level. Finally, the contact with the soil could be cut at the bottom with a spade. The reversed soil monolith was carefully taken out from the ML pot and transferred with the help of three people to a second ML pot to be upright again and was ready for installation on the weighing platform. The weighing platform was levelled out by adjusting the three adjustable standing feet with a 270 prolonged hexagon socket wrench. The final position was fixed with the counter nut by using an open end wrench.

Data collection, storage and delivery
Data from all sensors were collected by an Arduino-type MEGA 2560 PRO microcontroller (RobotDyn, Zhuhai, China), which was installed on a custom-made printed circuit board (PCB). The voltage signal 275 coming from the load cells was digitised by a 24-bit analog-to-digital converter for weigh scales (LM711, SparkFun Electronics, Niwot, USA). For each load cell, a separate analog-to-digital converter was used. After collecting and processing the data of the load cells and the other sensors, the data were stored as one-minute averages on a micro-SD card (

Load cell data low-pass filtering
Load cell data are prone to noise. To cancel the noise related to temperature fluctuations, the load cells used four strain gauges in a Wheatstone bridge configuration. Thus, noise visible in the data mostly originated from electrical noise, fluctuations in wind speed and atmospheric pressure. To minimize this 290 noise, we used a data filtering algorithm on the microcontroller. The microcontroller measured the load cells nominally at 3.3 Hz in combination with the retrieval of measurements from other sensors. The raw load cell data were then stored in an averaging window (ring memory) with a size of 100 values, where the oldest values were replaced by the newest ones. The upper and lower 15% of these values within the averaging window were discarded, and the remaining values were averaged. From the low-295 pass filtered signal, one-minute means were stored on the micro-SD card. For data delivery via IoT, these mean values were further averaged over five-minute intervals to comply with the allowed IoT bandwidth for data transfers.

Load cell calibration and determination of accuracy
In this study, weighing accuracy denotes the difference between the measured mass (determined with a 300 ML) and the control (calibrated mass). Precision reflects the reliability of the measurements, and it specifies to what extent the experiment can be repeated. On the other hand, resolution is the smallest distinguishable unit for an observable change in mass and thus determines the upper limit of precision. For NRW studies, high accuracy is indispensable, which requires instruments with high resolution paired with high precision. 305 Calibration runs for ML and the determination of the accuracy of the measurements were performed in a laboratory with closed windows and doors to avoid any influence of turbulence on load cell readings. Raw data were filtered as described in Appendix D during load cell calibration of the ML. A two-point calibration was performed on every single ML using calibration mass. For mass increases up to 500 g, 310 calibration mass complying with the OIML F1 standard (Mettler Toledo, Greifensee, Switzerland) were used. The maximum permissible error of these calibration mass is ± 2.5 mg. For mass increases of 1000 g, custom made mass of steel were used. Their mass was determined on a laboratory scale (XS4002S DeltaRange, Mettler Toledo, Switzerland) which was calibrated and certified for determining mass up to 4.1 kg with an accuracy of ± 0.01 g. First, a zero-point calibration was carried out, then the span was 315 set to 15045.2 g, as this was the approximate mass which most moist ML pots had. The offset from the zero-point calibration was used together with the span calibration value in the code running on the microcontroller. The absolute accuracy of the load cells was tested on 2 nd April 2019, by loading calibration mass on the weighing platform, in the range of 0 kg to 19.5 kg. The mass was increased stepwise by 500 g. The maximum mass was set to 19.5 kg to avoid an overload damage of the load cell. 320 Three repetitions were performed. A linear regression was performed in order to assess the relationship between target mass and load cell mass. Moreover, a relative calibration was performed on 7 th April 2019. We investigated the accuracy of a load cell with relative mass changes. A base mass, ranging from 10 kg to 19.5 kg, was loaded on the weighing platform, then a 100 g calibration mass was added to the base mass. Accuracy of relative mass changes was determined with three replications. To test 325 accuracy also under field conditions, we regularly performed a loading/unloading experiment after Nolz et al. (2013), by loading 5 to 10 g calibration mass on the ML and noting the mass before and after the loading. Because masses can be calibrated with certified standards as was done here, we use the term accuracy in this context, which goes beyond (relative) precision.

Evaluation of the effects of ML size on plant growth, canopy temperatures and soil moistures and temperatures
Plant growth in the ML system was evaluated by comparing individual plant heights in the ML pots versus the control (surrounding). Plant heights were measured from ground level to maximum standing height. Plant heights of Trifolium pratense, Plantago major and Rhinanthus alectorolophus were 335 measured at CH-FRU on 26 July 2019, with three replications per species and treatment (ML pot, control). To test for a statistically significant difference between plant heights of ML pots and the control (surrounding) we used a t-test (n=3). To compare canopy temperatures of ML and the control (surrounding) during a NRW input period, we used a thermal camera (testo 882, Testo AG, Lenzkirch, Germany), with a thermal sensitivity of ±0.05 °C. Thermal infrared images were taken from 18:27 to 340 05:15 (UTC) of ML vegetation and of the control (surrounding) at CH-FRU during a dew night on 24 to 25 June 2019. Thermal images of the control (surrounding) were taken in a distance of ca. 100 cm from the ML system, to exclude any potential influences of the ML system on its immediate surrounding. To compare thermal images of the ML surface with the control, we compared the variance (F-test). Data were bootstrapped to reduce sample size from > 30k to 30 samples using the scikit-learn machine 345 learning package of Python (Pedregosa et al., 2011). Soil moisture and temperature data of ML pots and the control (surrounding) were retrieved by soil temperature and moisture sensors ( Fig. 1b:q; 5TM, Meter Group AG, Munich, Germany), installed at a soil depth of 15 cm. As a control, one additional sensor was placed outside the ML system at the same depth in the surrounding. We measured over a period from beginning of May till mid October 2019. Soil moisture data were compared as water filled 350 pore space (WFPS). WFPS was used to make soil moisture values better comparable, by minimizing the effects of soil texture, e.g. different gravel content, that might be present in close proximity of the sensors. Higher or lower gravel content could bias soil saturation. WFPS was calculated relative to a saturation point (100%), which was reached, when the soil was heavily saturated with water after long and intensive rainfall. To test if the difference of WFPS values of ML pots and the control 355 (surrounding) stayed constant over time, we used a cointegration test after Engle and Granger (1987), which can be used to test for co-movement of two non-stationary variables. To test if the WFPS time series were non-stationary, we used an Augmented Dickey-Fuller (ADF) test. To perform all statistical tests, we used the programming language Python and used the Statsmodels package (Skipper et al., 2010) of Python. 360

Accuracy of the ML system
Three replications showed an almost perfect linear correlation (R 2 =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. The root mean square errors (RMSE) for comparisons of 365 target mass to load cell mass of three replications were 0.43, 0.47 and 0.36 g, respectively. The standard error (SE) 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, thus for NRW input studies, the relative change in mass from start to end of that time period is of interest. A 100 g change with the given ML size translated to a change of 2 mm water input. The residuals were in the range of ± 0.25 g or ± 0.005 375 mm equivalent water input, which represents the accuracy of the ML system. A zero-point offset calibration combined with data filtering (see Appendix D) gave us not only a more 380 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 for 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 385 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 two orders of magnitude better than the physical resolution provided by our ML system. Regular loading/unloading experiments after 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 390 of the ML system was accurate enough to provide high accuracy.

Differentiation among different types of NRW inputs
Our ML system allowed differentiating 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, an increase in leaf wetness (uncalibrated sensor voltage), 395 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 vapor 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). Potential effects of wind speed fluctuations that 400 exert a force on the ML and could thereby be confounded with water vapor adsorption, could be excluded by nearby wind measurements. Wind speed during the water vapor adsorption period remained below 1 m s-1. Wind speed remained low (< 1 m s -1 ) during the whole potential water vapor 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 405 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 vapor adsorption event.

Influence of ML system design on plant canopy temperature
Canopy temperature did not differ significantly (t-test, p > 0.05, n = 30) between ML vegetation and 420 control (Fig. 5a, b). The standard deviation of temperature data between 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 significant different (F-test, p > 0.05, n = 30). Soil temperature in the ML pot 1 was higher than in the control plot at the beginning of the dew formation period (Fig. 5c), but equaled control soil temperatures towards the end. Dew formation started at 18:53 425 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 ML installed at the site.

Influence of ML system design on plant growth
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 showed 440 also no statistically significant difference (t-test, p > 0.05, n = 3; data not shown).

Influence of ML system design on soil moistures and temperatures
WFPS data of ML pots 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 450 over time (Engle-Granger two step cointegration 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 norainfall period in summer (Fig. 7a, marked with red box), WFPS of ML pots decreased faster 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 455 temperature during non-rainfall periods (Fig. 7b).
Soil temperature of ML pot 1 and the control (Soil temperature in the surrounding) ( 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 (same pattern as of ML pot 1 was also evident on 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 460 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 period from May till October 2019 prolonged no-rainfall period, the hourly mean soil temperature deviations of ML pot 1 from the control ranged between -0.14 °C around 465 sunrise and 2.57 °C in the later afternoon (Fig. 7c). Thus, during most of the night when NRW input occurs, the temperature differences between the soil of ML pots and the control are typically less than 1 °C Over the period from May-October 90 % of nocturnal one-minute soil temperature deviations (sunset-sunrise) were lower than 2.90 °C, 50 % were lower than 0.69 °C.

NRW inputs over one year
There were a total of 127 NRW input events at CH-FRU over one year (2 nd May 2019 12:00 UTC to 2 nd May 2020 11:59 UTC; Fig. 8). The most frequent event was dew formation with 85 events, followed by hoar frost formation with 21 events, and combined dew and fog events with 13 events. Less frequent were fog only events (5 in total), combined hoar frost and rime events (2 events), and rime events only 480 (1 event). The frequency of the events can be found in Table 2. Eleven NRW events were observed when leaf wetness remained low, potentially indicating water vapor adsorption events or dew formation on soil. Potential water vapor adsorption events occurred during two time periods: period 1 in July 2019, period 2 in April 2020. During period 1, a single potential water vapor adsorption event occurred, whereas during period 2 ten such events occurred. During both periods rainfall was low, ten days before 485 the event in period 1 the cumulative rainfall was only 9.6 mm, 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 vapor adsorption periods was rather low, with WFPS of ca. 45 %. This indicates a potential water vapor gradient from the atmosphere to the soil, favorable for water vapor adsorption. The cumulative NRW input over 12 months was 15.9 mm, which corresponds to 490 roughly 1% of the 1580 mm annual precipitation collected during the third warmest year in Switzerland since weather recordings started in 1864 (MeteoSchweiz, 2020

505
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 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 until 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 510 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 for 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 515 ( Fig. 9) was not very strong, but when durations were binned into ten 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 hours, we first started with a square-root regression through the origin, = ⋅ √ , the slope of the fit was 0.042 ± 0.001 mm h-1/2 ( Fig. 9 dotted line, R2 = 0.98, p < 0.001), but for durations > 2 hours it closely corresponded to a conventional linear regression slope of 520 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 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 now shown). 525

Accuracy of the ML system 535
The high accuracy of our newly developed ML system allowed capturing even very small NRW events such as the potential water vapor 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 less than 100 g (equivalent to 2 mm water input), which is true for most NRW 540 events. The accuracy of our ML system was four orders of magnitude better than reported for many other studies (see Table 3). Feigenwinter et al. (2020) could achieve on average (depending on calibration date) the same accuracy, although with a lower depth of the ML pot (6.5 cm) and a lower weighing capacity (7kg). 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 545 filtering as well as ancillary data. For example, wind measurements were crucial to exclude possible effects of wind. temperature measurements were crucial to differentiate 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 increase thereby mass., although nocturnal wind speeds are in general much lower than during daytime (Groh et al., 2018). However, 550 NRW inputs occur during conditions with low wind speed, the probability for 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. With high frequency data filtering, we obtained one stable decimal place, which enabled exact calibration. A further factor promoting high accuracy was a load-cell specific calibration. Factory calibration is the same for all load cells of the 555 same model, but when an individual calibration is made, the differences among individual load cells are substantial, and hence 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 560 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. 565 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 were weighing 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 labor intensive and consequently unsuitable for long-term 570 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 575 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 .

Quantification and differentiation among different types of NRW inputs
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 hydro ecological relevance. 585 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., although we could 590 not estimate the water input ratios of dew, hoar frost and fog, rime during combined events. A leaf wetness sensor allowed differentiating between events in which condensation occurred (dew, hoar frost) in contrast to events when condensation on leaves was less probable (water vapor adsorption and/or dew formation on soil). Potential water vapor adsorption events occurred during periods with low rainfall, when soil was drying out, which increased the vapor pressure deficit gradient between soil and 595 atmosphere, promoting water vapor adsorption. However, the NRW inputs of the potential water vapor adsorption events were rather low (0.03 -0.13 mm). Thus, it is not unlikely that a leaf wetness sensor might react slightly different 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 if the leaf wetness sensor is suitable to 600 differentiate between dew and water vapor 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 differentiating between NRW events and rainfall events, and a networked digital camera allowed to observe persisting snow cover. The installation of three ML allowed exclusion of possible effects by insects, snails and lizards arriving on or departing 605 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 is 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 610 multiple ML further had the advantage that spatial variation in soils, species composition and leaf area could be reduced in comparison to single ML deployments.

Effect of ML size on plant growth, canopy temperatures, soil moisture and soil temperatures
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.  615 6), representing more natural conditions than many, rather shallow ML systems, an issue crucial for accurate measurements of NRW inputs to grasses and forbs. short-statured vegetation. We did not find any significant differences in canopy temperatures between our ML pots and of the control (surrounding) (Fig. 5a). Furthermore, we found in general no significant difference in soil moisture between ML and the control (surrounding), only during a prolonged drought period soil moisture values 620 of ML pots were decreasing faster. In this study, this had however 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, this lower soil moisture during prolonged drought periods can result in reduced evaporation rates and increased water vapor adsorption rates. Furthermore, this can influence plant growth and development. Thus, the ML 625 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 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 630 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 to avoid 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, 635 2004;Ninari and Berliner, 2002), the open soil surface in grasslands is rather small, ideally zero under good management practices. Higher soil temperatures could underestimate water vapor adsorption, because it lowers the vapor 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 640 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 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 645 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 daytime 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 650 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-hour 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 655 mass onto the load cell and would thus decrease load cell accuracy (Kaseke et al., 2012). Overall, ML design is always a tradeoff between representing the surrounding 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 ML 660 and the control. Thus, we conclude that our novel ML design is suitable for quantifying nocturnal NRW inputs on grasses and forbs in grasslands reliably and accurately at high temporal resolution.

NRW inputs at CH-FRU
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. which can be justified for applications during dry spells and drought periods, Under conditions with water lost via drainage, NRW 670 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 675 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 the Appendix E and F for more details). Nevertheless, depending on soil characteristics and conditions, drainage water flow could persist for longer time (Fig. F1 and Table F1). Under such conditions under conditions when drainage water flow persists for a longer time, the ML system provides conservative 680 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 the 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 685 reliable quantitative estimates of drainage losses can be obtained. but clearly limits the application of our ML system during and shortly after rainfall periods. Under conditions with water lost via drainage flow, NRW inputs would be underestimated.
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, thus there 690 was also a high probability for NRW inputs to occur 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 695 water status have still 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 vapor pressure 700 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 705 and measuring NRW inputs with high accuracy are crucial steps to address ecohydrological processes, but further investigations are necessary to understand physiological effects on grasslands.

Summary and conclusions
The aim of this study was to develop a high accuracy ML system for the quantification of NRW inputs that overcomes existing drawbacks. The ML system comprised a comparatively large and deep ML pot 710 in the size class of 25 cm diameter× 25 cm depth in combination with an unprecedented weighing accuracy. This ML size allowed natural plant growth and such a ML system can therefore be used in different ecosystems with most short to mid-size statured grasses and forbs or similar vegetation up to ca. 40 cm. Ancillary sensors allowed differentiating among different types of NRW inputs. However, further methodical improvements are necessary to distinguish between the fraction of dew, hoar frost 715 and fog, rime water inputs during combined events. Our study shows that the ML system represents natural conditions very well. The plant height was not significantly different between ML pots and the control (surrounding). Plant canopy temperatures of ML pots were close to canopy temperatures of the surrounding during a nocturnal period when NRW input took place. However, additional continuous canopy temperature measurements in follow-up studies could allow to more clearly distinguish dew 720 formation from water vapor adsorption and to identify if canopy temperature drops below dewpoint temperature. If this is not the case, and other factors like rainfall and fog can be excluded, a weight increase might then be related to water vapor adsorption. Furthermore, canopy temperature measurements would clarify if a leaf wetness sensor alone is sufficient to distinguish between dew and water vapor adsorption events. Soil temperatures were higher in ML pots, especially during the day. 725 This could influence the hydraulic characteristics of soil water, the heat balance of the soil and in consequence lead to biased latent and sensible heat fluxes. Thus, further ML studies should primarily focus to get rid of soil temperature differences between ML pots and the surrounding soil. In addition, the ML system could be further improved by adding water flow or water droplet sensors at the ML pot outlets to measure drainage water flow (see Appendix E), with the goal to avoid underestimation of 730 NRW inputs shortly after intensive rainfall events or during soil conditions when drainage water flow persists for longer time (see Appendix F). With our ML system, we were able to resolve mass changes on a 15 kg pot with an accuracy of ± 0.25 g, which corresponds to ± 0.005 mm of water input. This accuracy allows determining typical water gains by dew, hoar frost, fog, rime or water vapor adsorption on the order of 0.021 to 0.4 mm in a single night. The study revealed that, NRW inputs occurred 735 frequently and provided on average of all NRW events 0.12 mm of water. Such quantitative estimates will be essential to assess the role that NRW inputs might have on temperate grasslands during summer drought conditions. However, longer-term NRW input measurements would allow to see whether the seasonal pattern of NRW inputs are constant over time, or if they are influenced by weather conditions and thus vary from season to season. Moreover, the effects of NRW inputs on plant physiology in 740 grassland ecosystems have still to be elucidated more carefully, to assess the importance of such water inputs during ongoing climate change such as projected prolonged heat periods in the months of main vegetation growth.
Afterwards the ML pot was gently pressed into the soil. b) The contact of the monolith with the soil was cut at the bottom with a spade. C) The monolith was removed from the ML pot and carefully transferred to a second ML pot. d) Monolith ready for installation at the weighing platform. e) Empty ML pot on a weighing platform. The weighing platform is standing on the 755 adjustable support feet.

f) Lateral view of an installed ML. g) Top view of an installed ML.
To retrieve an undisturbed soil monolith with intact grass vegetation, we used an empty ML pot that was placed upside down at the place of interest from where the monolith was to be retrieved. First, we trenched the soil with a long spade around the ML pot. Then we removed the soil around the ML pot with small shovels, which allowed pressing the ML pot into the soil. We continued until the top of the 760 ML pot was at ground level. Finally, the contact with the soil could be cut at the bottom with a spade. The reversed soil monolith was carefully taken out from the ML pot and three people collaborated to transfer it to a second ML pot to be upright again. The ML pot was then ready for installation on the weighing platform. The weighing platform was levelled out by adjusting the three adjustable standing feet with a prolonged hexagon socket wrench. The final position was fixed with the counter nut by 765 using an open-end wrench.

Appendix C: Data collection, storage and delivery
Data from all sensors were collected by an Arduino-type MEGA 2560 PRO microcontroller (RobotDyn, Zhuhai, China), which was installed on a custom-made printed circuit board (PCB). The voltage signal coming from the load cells was digitised by a 24-bit analog-to-digital converter for weigh scales 770 (LM711, SparkFun Electronics, Niwot, USA). For each load cell, a separate analog-to-digital converter was used. After collecting and processing the data of the load cells and the other sensors, the data were stored as one-minute averages on a micro-SD card (MicroSD 16 Gb, Kingston Technology Company Inc., Fountain Valley, USA) inserted in the slot of a micro-SD breakout board (MicroSD card breakout board 254, Adafruit Industries, New York, USA). Then, the data were transferred to our data server 775 every five minutes by using Internet of Things (IoT) technology. To send the data, a breakout board (RFM9X LoRa Radio, Adafruit Industries, New York, USA) connected to the open TheThingsNetwork was used. TheThingsNetwork uses a Long Range Wide Area Network (LoRaWAN) protocol. A realtime clock (DS3231 for PI, HiLetgo, Shenzhen, China) was installed on the PCB to obtain exact timestamps. 780

Appendix D: Load cell data low-pass filtering
Load cell data are prone to noise. To cancel the noise related to temperature fluctuations, the load cells used four strain gauges in a Wheatstone bridge configuration. Thus, noise visible in the data mostly originated from electrical noise, fluctuations in wind speed and atmospheric pressure. To minimize this noise, we used a data filtering algorithm on the microcontroller. The microcontroller measured the load 785 cells nominally at 3.3 Hz in combination with the retrieval of measurements from other sensors. The raw load cell data were then stored in an averaging window (ring memory) with a size of 100 values, where the oldest values were replaced by the newest ones. The upper and lower 15% of these values within the averaging window were discarded, and the remaining values were averaged. From the lowpass filtered signal, one-minute means were stored on the micro-SD card. For data delivery via IoT, 790 these mean values were further averaged over five-minute intervals to comply with the allowed IoT bandwidth for data transfers.

Appendix E: Drainage water flow of ML pots
The ML pots were designed to avoid stagnation of water that potentially could impede plant growth by creating anaerobic conditions in the rooting zone. For that reason, a passive drainage water flow path 795 allowed drainage of excess water beyond field capacity. However, to further develop this ML system and use it during and shortly after rainfall periods or to improve the measurements during other periods when the soil cannot hold excessive water universally, it is recommended to quantify drainage water flow. This is because NRW inputs increase the mass of ML pots, whereas drainage water flow out of the ML pots reduces their mass. Therefore, if drainage water flow during NRW inputs is non-zero, this 800 would lead to an underestimation of the NRW inputs, as long as no additional sensor is added to the ML pots to quantify this drainage flow.
To assess the required specification of such an additional sensor and to quantify how long drainage water flow of the ML system persists, we investigated three consecutive events (see Table E1): 1) A high intensity, high amount and high duration rainfall event (Fig. E1a, event 1); 805 2) an evapotranspiration event from sunrise until sunset (Fig. E1a, event 2), and 3) a NRW input event (Fig. E1a, event 3).   During event 1, the total amount of rainfall was 128.5 mm. The highest hourly rainfall intensity occurred on 28 July 2019 at 10 UTC with 16.8 mm h -1 , which classifies as "heavy rain" > 4 mm h -1 (Met Office, 2012). ML mass increased as soon as the rainfall event started and increased with the same rate during the rainfall input until ca. 11 UTC. Afterwards the rate of ML mass change, i.e. the slope of 830 the ML mass increase was flattening compared to the cumulative curve of rainfall input: From the beginning of the rainfall event until sunset, the water input was 101.6 mm, whereas the ML system showed an increase of only 36.2 mm. The difference of 65.4 mm most likely corresponds to the losses from drainage water flow, because of soil saturation during such high intensity rainfall with excessive water being lost. However, WFPS did not reach the 100% mark (Fig. E1b). Note that the 100% WFPS 835 reference was determined from the full year of measurements and is thus relative to spring conditions. Therefore, it is not surprising that this mark was never reached during dry summers, even after heavy precipitation. During such a high rainfall water input, drainage water flow of the ML system was on the order of 64 % of the rainfall amount. However, water might not only be lost via drainage water flow, but also by evapotranspiration during daytime. To quantify solely drainage water loss, the nighttime 840 period (when no evapotranspiration is expected) was further investigated. We separated the nighttime period in period ev1a, when rainfall occurred, and period ev1b, when no rainfall occurred (Fig. E1a, gray shaded periods).
During the ev1a period (Fig. E1a, period ev1a), from sunset until the end of the rainfall event, the water input was 26.9 mm, whereas the ML system showed only an increase of 0.3 mm. The difference of 26.6 845 mm (98 %) might be caused by losses from drainage water flow. The water loss rate was 3.6 mm h -1 . The 34 % higher drainage water loss compared to the daytime period might be due to the lower water holding capacity of the more saturated soil. During the ev1b period, starting after the ev1a period until sunrise (Fig. E1a, period ev1b), no further water gains and losses were expected, because evapotranspiration was absent during nocturnal conditions with low average wind speed (< 0.6 m s -1 ). 850 During period ev1b, the ML system showed a water loss of 0.07 mm, which corresponds to an average water loss of 0.05 mm h -1 . This water loss can clearly be attributed to drainage water flow. The rate of drainage water loss was however strongly reduced (by 98%) compared to the ev1a period. Thus, drainage water flow of the ML system reached very low values within only 1 hour and 33 minutes after this extraordinary high rainfall, showing that even the current ML system can handle high drainage 855 water flows well.
During event 2 with no rain but evapotranspiration, the ML system indicated a water loss of 2.25 mm, which corresponds to an average evapotranspiration rate of 0.15 mm h -1 . Potentially a drainage water loss could have occurred in the morning hours on July 29. However, the drainage water loss most likely was < 0.05 mm h -1 , similar to the drainage water flow rate during the ev1b period, just before event 2, 860 shortly after the rainfall event. Since no new rain fell, we expect the drainage water flow rate to decrease with time. In fact, one hour before sunset, a further reduced ML mass loss of only 0.005 mm h -1 was recorded. This very low water loss can be either attributed to drainage water loss, or to evapotranspiration as it occurred during daytime. We conclude that the drainage water loss could at maximum be 0.005 mm h -1 , but was most likely lower due to concurrent evapotranspiration. Thus, the 865 ML system readings were no longer significantly affected by potential drainage water flow after only 15 hours after rainfall.
During event 3, a very large dew event of 0.28 mm occurred, which was above the 95 th percentile of all NRW events during the 12 months period considered in this study. Such a large dew event is unlikely to be recorded under conditions when at the same time also a large drainage water flow would have 870 occurred. If this would have happened, the dew water input should have been lower. Thus, it is very unlikely that drainage water flow still occurred during that dew event.
Overall, these three events showed that drainage flow can occur occurred under rainfall conditions and shortly after rainfall events. The current ML system handled large drainage flows well and effectively, i.e. water drained fast, avoiding long-lasting "memory" effects. Drainage flow was lower than 0.005 875 mm h -1 one hour before sunset during event 2, only 15 hours after the last rainfall. However, at other sites with different soil characteristics different drainage flow patterns might occur (See Appendix F) and our ML system might therefore provide conservative NRW inputs and accentuated evapotranspiration rates. Nevertheless, if If the current ML system were to be used for high rainfall conditions, potential drainage water flow need to be quantified using additional sensors. Without such 880 additional sensors, NRW inputs could be underestimated if the NRW input occurs shortly after a rainfall event and drainage water flow indeed occurs. Consequently, the current ML system is expected to give conservative estimates of NRW inputs, especially if NRW inputs happen directly after a rainfall event.
To further develop the usability of the current ML system for conditions with abundant rainfall, we suggest to continuously measure drainage water outflow. The amounts of drainage water flow from the 885 pot size used in this ML are however too small for using conventional tipping bucket devices which would work adequately with large lysimeters. Suited Potential approaches to quantify the small amounts of drainage flow from a ML system are by installing a water flow sensor or a drip counter at the ML pot drainage water outlets. or by adding an additional weighing platform to the ML system, on which drainage water is collected and continuously measured. The maximum rainfall intensity reported above 890 was 16.8 mm h -1 . With a ML pot diameter of 25 cm (see Section 2.2.1 of the main text), and the extreme assumption that 100% of precipitation contributes to drainage water flow, such an addition must be able to process 13.7 ml min -1 . If the maximum drainage water flow is however only expected to be <15% of precipitation, then a sensor capable of measuring up to 2000 µl min -1 would be an adequate choice. 895 An additional weighing platform would increase costs and maintenance labor substantially. We thus We recommend using a water flow sensor or a drip counter instead. One option is a liquid flow sensor (SLF3S-0600F, Sensirion AG, Staefa, Switzerland) that is capable to detect low flow rates of up to ±2000 µl min -1 . A drip counter can be constructed with two gold electrodes attached to the ML pots drainage water holes with a small gap. If a water droplet passes the gap, an electric circuit is closed 900 which can be counted as a water drop by a datalogger (Meter Group AG, 2020). Calibration of a drip counter is recommended for accurate measurements of drainage water amount. Sensors measuring drainage water flow would allow to correct for drainage water outflow and would thereby increase the usability of the current ML system for times during and shortly after rainfall events.
Appendix F: Duration of drainage water flow after heavy rainfall (saturated soils) 905 Drainage water flow was not quantified in the application of the ML system described here, because the goal was to quantify NRW inputs during dry conditions without saturated soils. To estimate the duration of drainage water flow from the bottom of the ML pot, we used the approach by Zhan et al. (2016) with modifications following Freeze and Cherry (1979) and model input parameters from Rawls et al. (1991) listed in Table F1. The full equation set used here is provided in what follows. 910 The relation between the unsaturated hydraulic conductivity , the volumic water content and the porewater pressure head can be described by the following formula: We simulated the drying of the 25 cm deep soil monolith using a finite difference approach with Δz* = 0.01 m and Δt = 10 minutes. The procedure carried out at each timestep was: (1) to compute the drainage water loss across the bottom of the soil monolith Per using Zhan et al.'s (2016) where k' is the dimensionless ratio of the unsaturated hydraulic conductivity normalized by its value at saturation (ks), k' = k/ks. and γ is the slope angle. For the simulations we assumed γ = 0°; thus, in case of a sloping surface the drying of the soil monolith takes less time (td) than what we present in Figure F1.
(2) This amount of water was removed from the lowest soil layer θ(z*=0).
(3) Then the updated soil 935 water content profile θ(z*) was converted to an updated pressure head profile Ψ(z*) using the relationship in Eq. ( (4) Then the drainage flow rate for all soil layers was computed with Eq. (F5), and the respective amount was transferred from each layer to its lower adjacent layer. (5) Then the θ(z*) profile was 940 converted to Ψ(z*) and the change over time from Eq. (F3) was added, and then the θ(z*) profile was updated accordingly before the next timestep was simulated.
The threshold for the end of the drainage period was set to one drop of water per day percolating out of the soil monolith's bottom (0.05 mm d -1 , or 0.35 µm at the Δt = 10 minutes timestep).
The results for different soil textures are shown in Figure F1. Given the initial condition that the soil 950 monolith is completely water saturated at t = 0 our results show rather conservative estimates how long water is percolating out of the ML pot after heavy rainfall or long rainfall that saturated the entire soil volume (which typically takes a few days to a week with precipitation). best estimate for each soil type for completely saturated soils, and whiskers show the range that results when the parameter range given by Rawls et al. (1991) in Table F1 are used. Symbols show the reduced td when the average water content of the soil monolith is 90% of its saturation (yellow circles), 80% (green circles), or 70% (blueish circles). Because the system is highly nonlinear, the parameters given in Table F1 are not resulting in the full range of td, hence we added the maximum that can be obtained with intermediate model parameters for each soil type (dashed whiskers) and the 70%, 80% and 90% two-sided confidence interval 960 (gray bars of varying width, see legend) for all td resulting by combination of parameter values within the bandwidth given in Table F1.
Most soils on average fall dry within less than 24 hours; the absolute maximum was modeled for silty clay which can produce drainage up to 41.5 hours. At the sandy end short maximum td are realistic because of easy drainage of soils with high sand content, whereas the results at the clay side show a 965 range from no drainage up to 30.0-41.5 hours can be explained by the high capillary retention of water that retains more water inside the soil volume without generating drainage water flow. The modeling however is based on a traditional micropore flow approach, whereas macropore flow (e.g. Alaoui and Eugster, 2004) is not explicitly represented in the model. But the range of parameter estimates in Table  F1 seems to include also macropore flow via parameter combinations that result in td = 0 hours, which is 970 most likely not realistic, but should be interpreted that in the presence of macropore flow (wormholes, dry cracks in clay) the drainage is restricted to very short intervals even after soils were fully saturated). Thus, in reality most but not all soils will most likely not produce measurable drainage after one day or so. Adding a sensor to measure drainage water flux (item q in Fig. 1b) is recommended if in contrast to this study the entire hydrological soil water budget shall be quantified, and not only the NRW gain 975 during dry and drought periods.