The backbone of the experimental setup consists of three microwave links placed along the same path between two university buildings on opposite sides of the college town of Wageningen. As such, the majority of the 2.2 km long link path covers urban terrain (Fig. 1a). All transmitting antennas are placed on a 2 m high mast, approximately 1.5 m from the base of the mast (Fig. 1b). The mast is placed on top of a seven storey building. The building is situated atop a slightly elevated area on the south end of Wageningen (51.968657∘ N, 5.68273∘ E). The receiving antennas are placed on an identical mast on the roof of an eight storey building at the northern end of Wageningen (51.985230∘ N, 5.664312∘ E). The height above ground level is 27 m on the transmitting end and 40 m on the receiving end. The total height above sea level is 62 m at the transmitting end and 51 m at the receiving end. The terrain in between the endpoints of the path consists mostly of terraced housing, a sports field and other buildings of three stories or less. The maximum width of the first Fresnel zone (halfway along the path) at the featured frequencies is less than 5 m. Thus, considering the height of the antenna locations compared to the intermediate terrain, there are no permanent obstructions affecting the beam significantly.

The experiment was operational from 22 August 2014 up to and including 8 January 2016. Not all instruments had been operational during this entire period though, as is indicated in Fig. 2. Also, from 7 to 25 August 2015 all transmitters were nonoperational due to a local power outage.

Of the three links one is a Nokia Flexihopper (Nokia), formerly part of a commercial mobile phone network operated by T-Mobile Netherlands. Such links are still used in mobile phone networks around the world and this microwave link could thus be regarded as a typical example of the link systems that would be used in an operational setting. The Nokia is a bidirectional link, but only one receiver was logged in this experiment. It is set to transmit and receive at a frequency of 38.17625 GHz in one direction (which was recorded) and 39.43625 GHz in the other direction. The bandwidth of the signals is 0.9 MHz. The device transmits and receives only horizontally polarized radiation.

The other two links are custom-built by Rutherford Appleton Laboratories (UK) (RAL). The first operates at 26.00000 GHz and transmits and receives only horizontally polarized radiation. It contains both a linear and a logarithmic detector. The second RAL link operates at 38.00000 GHz. The bandwidth of the receivers is 4 KHz, while the transmitted signal bandwidth is extremely narrow (≪1 KHz). Their oscillators are locked to GPS and thus extremely stable. The receiver contains four detectors, two of which measure horizontally polarized radiation (linear and logarithmic) and the other measures vertically polarized radiation (idem). The phase difference between the horizontally and vertically polarized signals is measured by separate detectors as well. In this paper we will only deal with data from the logarithmic detectors. Note that the second RAL link measured at roughly the same frequency as the Nokia link. The frequencies are chosen to be far enough apart so as not to cause interference, but are close enough that the scattering characteristics of the radiation with respect to raindrops are almost identical. Additional characteristics of the link antennas are given in Table 1.

A Scintec BLS900 near-infrared boundary layer scintillometer is also placed together with the microwave links on the same path. It operates at a frequency of 340 THz (880 nm). This provides information about, for example, fog and other visibility-affecting phenomena. Similarly to the microwave links (despite operating in a different scattering regime), it could potentially also be used to estimate rain intensity (Uijlenhoet et al., 2011).

All link receivers are sampled with a Campbell Scientific CR1000 data logger and stored on a remote server on a daily basis. The sampling frequency is 20 Hz. Auxiliary data (e.g. operating temperature) is sampled at a frequency of 2 min-1. The Nokia system consists of separate outdoor and indoor units, the latter containing the digital signal processing circuits and power supply. Note that we have not actively used the indoor unit of the Nokia link system aside from the power supply; Instead, the analogue detector signal normally used for automatic gain control (AGC) is fed directly into the analogue–digital converter (ADC) of the separate data logger. We do this to avoid the significant power quantization error (1 dB) that would be incurred using the link device's own AGC-ADC system. The analogue signal was calibrated in an indoor environment using the signal power indication of the indoor unit as a reference. The RAL links were recalibrated by Rutherford Appleton Laboratories shortly before the beginning of the experiment. The calibration curves are shown below in Fig. 3, and used to convert the observed voltages to received powers. The transmitted power for all devices was kept constant, but was not separately measured.

To serve as a ground truth, we use OTT Parsivel laser disdrometers (Fig. 1c). These can not only measure precipitation intensity but also the size and velocity distributions of passing precipitation particles over 30 s intervals. With this information they can provide an approximation of the type of precipitation that occurred. In this manner it is possible to, for example, filter out solid precipitation from the microwave link data or select dry periods to determine the “dry” baseline signal. Due to the small sampling footprint of these devices, they may not give a representative ground truth for the aggregated path measurements. Therefore, five disdrometers are placed at four different locations, spread along the link path (Fig. 1a) as evenly as was possible given the urban terrain. At the receiver end of the link path two disdrometers are placed next to each other in close proximity and orthogonal to each other in order to test the accuracy of the disdrometers themselves. All disdrometers are placed on flat or gently sloping rooftops within Wageningen. The disdrometers all contain a built-in preprocessing unit which samples the raw laser amplitude signals, converts them to hydrometeor counts using an algorithm (undisclosed by OTT) based on the principle described in Löffler-Mang and Joss (2000) and aggregates the samples to 30 s intervals. One of the disdrometers at the receiver end had been operational since the beginning of the experiment. It is connected to the same data logger as the link detectors. The other four disdrometers have been operational for a shorter timespan (see Fig. 2). They are each connected to a UMTS modem, which relays the disdrometer data to a remote server in real time; see Jaffrain et al. (2011) for more details about these autonomous disdrometer stations.

At the receiver end of the link path an automated tipping bucket rain gauge is placed close to the two disdrometers (Fig. 1d), to provide an additional independent measurement. The gauge has a tipping volume of 0.1 mm. Two time-lapse cameras are placed at each end of the link path. On each side one camera is pointed along the path and the other is pointed at the antennas themselves. These serve to allow visual inspection of the link path and the antennas, which can be useful for relating link behaviour to physical events.

For the subsequent data processing we also make use of data from the nearby automatic weather station “Veenkampen” situated roughly 2 km to the west of Wageningen (operated by the university's Meteorology and Air Quality group) for ambient temperature, relative humidity, wind speed, visibility and pressure measurements.

In order to calculate the rainfall intensities, the attenuation caused by rainfall and the attenuation caused by other atmospheric effects must be distinguished. Rahimi et al. (2003) proposed a two-step approach in order to do so.

The first step is to determine which of the sampled periods are dry. Overeem et al. (2013) uses the assumption of spatial correlation of rainfall to determine “wet” and “dry” periods for microwave links in cellular communication networks. In short, a period is considered “wet” if nearby links show a mutual decrease in received signal levels. As we are considering only a single path, such a method would not be applicable here. An alternative is to use the assumption of temporal correlation of rainfall. Schleiss and Berne (2010) suggest using a moving window standard deviation threshold. Similarly, Chwala et al. (2012) used a Fourier-transform based method to distinguish between wet and dry spells. Other methods applicable to a single link path are e.g. a Markov switching algorithm (Wang et al., 2012) and the use of dual-frequency links (Rahimi et al., 2003). Here, the path-aggregated disdrometer data is used to determine dry periods independently of the microwave link data.

The second step in the algorithm is to determine a suitable baseline signal level using the selected dry periods. The implemented baseline algorithm uses a rolling median over all measurements classified as dry in the surrounding centred 24 h period to determine the baseline signal for each time step. The specific attenuation is then calculated as k=maxRxref-RxL,0, where Rx is the received power and L is the path length. Rainfall intensity is derived from the corrected attenuation using the power-law relationship of Eq. (5). The parameters a and b in this equation are obtained from the disdrometer data as described in Sect. 4.1.3.

Futhermore, the rainfall intensity is set to 0 when the disdrometer indicates dry weather. Note that we do not perform any a priori additional corrections on the microwave link rainfall estimate, such as correcting for wet antenna attenuations. The goal is, after all, to use this basic estimate to assess potential error inducing phenomena, not to evaluate a best-effort estimation.

In the following section, we use the rainfall intensity as measured by the Parsivel disdrometers as a reference to assess the link-derived rainfall. Unless stated otherwise, we use the corrected DSD-derived rainfall intensities, not the rain intensities that the internal Parsivel algorithm produces.

In order to better understand the different phenomena that contribute to the microwave link attenuation signal, we present a number of illustrative events from the dataset. We search for events that can be related to a single type of attenuating phenomenon in order to gain insight into the separate phenomena. We will first analyse the performance of the simple algorithm for measuring liquid precipitation and take a quick look at solid and mixed precipitation. We will then show how temperature and wet antennas, e.g. caused by dew formation affect the signal. Finally, we will look at some currently unexplained phenomena and also give some examples where different phenomena occur simultaneously. All times in the description of the events are given in UTC.

We compare the link-derived rainfall rates using the simple algorithm (excluding any specific corrections) described in Sect. 4.2 with the spatially averaged rainfall rates derived from the disdrometers using the corrected DSDs. To assess the reliability of the disdrometer measurements as a ground truth, we first compare the collocated disdrometers with the tipping bucket rain gauge and each other. We used data of the entire measurement period where rain intensities higher than 0.1 mm h-1 were registered. We find that the correlations of the disdrometers with the rain gauge (r=0.928 and r=0.927) were only slightly lower than the correlation of the disdrometers with each other (r=0.959). The mean differences between the disdrometers and the rain gauge were 0.039 and 0.129 mm h-1, respectively, while the mean difference between both disdrometers amounted to 0.074 mm h-1. That means that the disdrometers slightly overestimate the rain intensities as compared to the rain gauge, but this is of the same order of magnitude as the differences between the identical collocated disdrometers. Therefore, we will assume the path-averaged disdrometer measurements to be the “true” path-averaged rainfall for the purpose of evaluating the link measurements.

Figure 5 shows an example of a single short isolated rain event on 14 July 2015 as indicated by the disdrometers. We chose this example because there are no attenuating phenomena contributing to the dynamics of the signal other than rain in this event. Note that the received signal level of the Nokia is offset by 14 dB in order to fit into the plot. This is done consistently for all following figures. As the received power level can vary within the dry periods that we use to determine the baseline power level, we also indicate the 95th and 5th percentile of the received power level over the dry intervals within the surrounding 24 h moving window. This gives an indication of the variability of the baseline power level. Thus, if the rain-induced attenuation is within this range, it cannot be distinguished from variability in the baseline without further processing. The event consists of two distinct small peaks. The first peak of the path-average rainfall intensity only reaches 0.7 mm h-1, while the second peak reaches 8 mm h-1. We see that the second peak causes a clear attenuation of the received signal level of all the links. The smaller peak in rain intensity causes only a small attenuation in the 38 GHz links, fully within the 95th and 5th percentile range of the dry signal. Although the presence of rainfall is detected unambiguously by all the instruments, the magnitude of the response differs between the links. Both the horizontally and vertically polarized detectors in the 38 GHz RAL link give very similar responses, which is expected as they receive different components of the same signal and also share a substantial part of their electric signal path, including the antenna itself. Most notable is the difference between the signal of the Nokia link and the RAL link operating at (nearly) the same frequency and polarization. Although the magnitudes are similar, the Nokia link has far less variability of the baseline signal level than all other link instruments. This difference could be caused by the differences in internal electronics of the detector. Another point of interest is that using the median of all dry data points in the 24 h period, our estimation of the baseline signal level of the 26 GHz RAL link and to a lesser extend the 38 GHz RAL link is too high, resulting in an additive overestimation of the rain intensity. The calculated apparent rainfall during the first peak is completely below this line, indicating that this can be regarded as noise. Regardless, the peak rainfall estimate from the Nokia link is very close to the disdrometer estimate. We can also see that attenuation of the microwave link signal persists for several minutes after the end of the rainfall event (according to the disdrometers) and slowly decays during this time. This could be the consequence of the link antennas becoming wet due to the rain and subsequently drying up after the event (Minda and Nakamura, 2005; Leijnse et al., 2008). In Fig. 5a the received signal level of the near-infrared link is also plotted. Attenuation of this signal is indicative of visibility. In this case the visibility loss is highly correlated with rain (correlation coefficient r=-0.86).

We illustrate the response of the link signals to rain with two more example events of a longer duration. One low-intensity drizzle event and one higher-intensity convective rain event with some spatial heterogeneity. On both occasions we use only the times for which at least one of the disdrometers indicate rain has occurred for further analyses.

The first event, on 24 November 2015, consists of a low-intensity drizzle period (intensities under 2 mm h-1 for most of the event) that persists for around 12 h. The course of the event is illustrated in Fig. 6. The RAL links show some variability in the baseline power level, varying over a range of 0.11 to 0.14 dB over the course of the event until 13:00 UTC. The Nokia link, in contrast, stays remarkably stable during the entire event, ranging only 0.02 dB over the same period. After that, all links show a large drop in baseline power level, with the largest magnitude in the RAL 38 GHz link (3.46 dB) and the smallest in the Nokia link (0.33 dB). There is a fairly strong correlation of link derived rain intensity with disdrometer rain intensity for both the Nokia link and the 26 GHz RAL link (r=0.870 and r=0.854, respectively) and less so for the 38 GHz RAL link (r=0.594 for vertical polarization and r=0.232 for horizontal polarization).

We estimate the additive and multiplicative bias in the link-derived rain intensity by the parameters of a simple linear regression with the spatial average of the disdrometer derived rainfall, which is illustrated in Fig. 7a–d. All microwave links overestimate the rain intensity to some extent. Additive bias of the RAL links is between 2.2 and 3.7 mm, which is more than the actual rainfall during most of the event. Additive bias is lowest in the Nokia link-derived data, which seems to be in line with the very stable baseline. However, it is still 0.8 mm h-1, which is a problem for accurately measuring accumulations from light rain events. We can also see that in this case visibility cannot be reliably used as a proxy for rainfall intensity, as is most clearly seen after 13:00.

The second event, on 4 November 2015, is more spatially heterogeneous (CV = 0.64, as opposed to CV = 0.50 in the previous event.). The higher spatial heterogeneity and higher rainfall intensities suggest a convective rainfall event. The total event lasts for 8 h (see Fig. 8). Peaks in spatially averaged rainfall intensity during this event are on the order of 20 to 30 mm h-1, and individual disdrometer measurements reach up to 55 mm h-1. Once again the baseline of the Nokia link is remarkably stable (range = 0.19 dB), similar to the 26 GHz RAL link (range = 0.33 dB), while the 38 GHz RAL link has a highly variable baseline (range = 1.53 dB for the horizontally polarized signal and 3.96 dB for the vertically polarized signal). During most of this event visibility seems to be a reasonable proxy for the rainfall intensity. Correlations of link-derived rainfall with disdrometer-derived rainfall are much higher overall (r=0.90 to r=0.93) (Fig. 7e–h) than for the event on 24 November 2015. Additive bias is of the same order of magnitude as for the drizzle case, which means that the additive bias relative to the rainfall intensities is much less for this event than for the drizzle event. Multiplicative bias varies from a factor of 1.4 to 1.6.

We now compare link derived rain intensity with disdrometers derived rain intensity for the entire measurement period; results are shown in Fig. 7i–l. Data points where the path-average rainfall intensity derived from the disdrometer measurements are less than 0.1 mm h-1 or at least one of the disdrometers indicate the presence of solid precipitation are excluded. We also exclude the period during which the link transmitters were not functioning. The Nokia link performs better than the RAL links in terms of correlations. In all cases the links significantly overestimate the rainfall intensity, both in an additive (regression intercept ranging from 0.6 to 2.2 mm h-1) and a multiplicative (regression slope ranging from 1.5 to 1.7) sense. The general overestimation could be attributed to attenuating phenomena other than rain being erroneously processed as rain in the basic algorithm, in part due to the simple baseline determination process not taking these into account and because e.g. no correction was applied for wet antennas. A similar regression in terms of specific attenuations produces nearly identical results. Therefore, we conclude that uncertainties in the R–k relation do not significantly explain uncertainties in the rainfall estimation.

In typical operational settings, longer temporal measurement intervals such as 15 min are common (e.g. Overeem et al., 2016b). In order to illustrate the performance of a basic algorithm without any sort of correction at this resolution, Fig. 7m–p show the scatterplot and linear regression for the entire dataset, but down-sampled using a 15 min mean. The correlation for the Nokia link is slightly higher with the 15 min intervals than it is using 30 s intervals and the scatter around the regression line is lower. In the case of the RAL links, the performance is better for the 15 min accumulations than for the 30 s intervals in terms of correlation and scatter, but worse when considering bias.

Very few solid or mixed precipitation events occurred during our measurement period. Figure 9 shows one of the few snowfall occurrences during the campaign, on 4 February 2015. At this point in the campaign only one disdrometer was yet placed and no rain gauge was available, which limits the potential for a quantitative comparison. Figure 9d shows time-lapse camera footage taken during different stages of this event. The background shades in Fig. 9b indicate the type of precipitation as indicated by the Parsivel internal algorithm (blue is liquid precipitation, green is snow, red is mixed precipitation). The total event duration is about 40 min, yet the event is quite variable in time.

As indicated by the background colours and the camera footage, this short event starts out with a mixture of rain and ice pellets and then turns into snowfall. Along with the mixed precipitation the temperature drops from 4 to 1 ∘C. During the snowfall, the temperature drops further to 0 ∘C. The absolute values of the disdrometer-derived precipitation intensity cannot be taken at face value here, as our processing algorithm treats every particle as a raindrop. This results in far too high values during snowfall, as we do not account for the lower density of a typical snowflake. As the disdrometer rainfall intensity shown here is that of only one disdrometer and as it was placed at one far end of the link path, we do not expect the small-scale variations to match exactly with those of the link attenuation. However, the overall dynamics of the intensity and the type of precipitation can provide some useful information.

Between 15:10 and 15:30, the links are attenuated with a magnitude that corresponds roughly with the precipitation intensity measured by the disdrometer, assuming that it is pure rain. Afterwards, when snow starts to fall between 15:30 and 15:55, the precipitation intensity derived from the disdrometers becomes a factor of 10 higher than the link-derived precipitation intensity, but this is likely to be due to the faulty disdrometer algorithm when applied in snow. While both the disdrometer and the camera footage seem to indicate that the precipitation stops after 15:55, the attenuation of the links persists until the signal level returns to its initial value between 16:00 and 16:15. At this point the temperature hovers at a few tenths of degrees above zero, and the camera footage indicates some residual snow is left on the antenna covers. The snow deposits are mostly on top of the covers and is mostly still present by 16:17, when attenuation has decayed fully, so snow deposits alone cannot explain the persistent attenuation. Based on the above observations a possible explanation of the persistent attenuation effect would be the partial melting of residual snow on top of the antenna cover, which then keeps the antenna cover wet. However, the available data is not sufficient to confirm this.

Because there were few snowfall events during the entire campaign period and each of them was of short duration and mixed with other types of precipitation (similar to the event described in this section), no meaningful analyses could be done regarding the relationship between attenuation and snowfall intensity.

Throughout the entire observation period a diurnal oscillation can be seen in the attenuation signal. This diurnal cycle is present in all signals, although the magnitude of the oscillation is in general significantly higher for the RAL links (1.0–1.5 dB) than it is for the Nokia link (∼0.2 dB). The magnitude of the oscillation also varies throughout the observation period. This behaviour does not correspond to any precipitation pattern but seems to follow the known diurnal variations in temperature. Although this pattern can be seen throughout the observational period, the correlation with temperature is not always clear, because the signal is generally much weaker when other attenuating phenomena are present.

Therefore, we will first focus on a relatively long dry period between 14 and 24 April 2015, as shown in Fig. 10. During this period the disdrometers picked up no precipitation; however, the received signal levels are not constant. Instead, variations up to 1 dB are present. In Fig. 10b, the time series of ambient air temperature measured by the nearby weather station is plotted for the same period together with the visibility measured at that same station, while in Fig. 11, the power levels for this period are plotted against the temperature with a simple linear regression. We performed separate regressions for instances where humidity was above 90 % and for instances where relative humidity was below 90 %. This was done to distinguish instances where dew formation on the antennas might have occurred, which we will discuss in the next subsection. In Fig. 10a we have also indicated the periods where relative humidity is above 90 % (green shade) and the periods where the net radiation flux towards the surface is negative (blue shade).

There is a strong negative correlation between received power and temperature for all link instruments (r=0.80 to r=0.92), when relative humidity is below 90 %. However, the slope of the linear fit is much lower for the Nokia link (-0.024 dB K-1) than for the others (between -0.1 and -0.2 dB K-1), even though the Nokia link operates at (nearly) the same frequency and polarization as one of the RAL links. Apparently, the magnitude of the temperature dependence is far more specific to the link hardware, than to the carrier frequency or polarization. The negative correlation between temperature and received power in the RAL devices is much milder when the relative humidity is above 90 % (r=-0.40 to r=-0.72). For the Nokia link, the temperature dependence disappears at high humidity. This phenomenon is probably related to dew formation at the antennas as is discussed in more detail in Sect. 5.5.

In subsequent analyses we expand our investigation of a possible linear temperature dependency to the entire experimental period. However, we exclude two time frames from this analysis. Firstly, the period between 6 and 25 August 2015 when the transmitters were not functioning (but the receivers were). Secondly, we also exclude a period between 11 and 19 May 2015 because a metal construction crane was positioned in the line of sight between the transmitter and receiver (see Sect. 5.7) several times in this period. The correlations and regression slopes found for this extended period are shown in Table 3 as “whole period”.

We consider that dew-related wetting of antennas causes attenuation of the link signal, which muddles the observed temperature dependency. Furthermore, this phenomenon seems only to occur when the nearby weather station registers a relative humidity above 90 %. Therefore, we filter the dataset in two more ways in order to separate temperature effects from signal attenuation in the full time period. First, we remove all data points where any disdrometer indicates any form of precipitation. Second, we remove all data points where relative humidity was above 90 %. We then find the correlations and slopes indicated in Table 3 as “dry only”. Furthermore, for completeness we also show correlations and slopes for a subset where, instead of the two abovementioned filters, we apply a filter that only includes periods where any of the disdrometers registered rain (shown in Table 3 as “rain only”).

The slopes of the linear regression for the RAL links are similar for all data selections (difference within ±15 % compared to the slopes found for 14–24 April), while the correlation coefficients become progressively smaller for the “dry only” selection (r=-0.57 to r=-0.72), the “whole set” selection (r=-0.46 to r=-0.57) and the “rain only” selection (r=-0.33 to r=-0.41). The latter is still surprisingly high considering that the received signal level in this selection includes attenuation by rain. For the Nokia link no significant correlation of received power level to temperature is found for any of the data selections, even though one would expect it based on the findings from 14–24 April.

There is also another phenomenon apparent in Fig. 10, especially noticeable in the Nokia link: some sharp drops in received power that evolve from midnight until the early morning (∼ 00:00–05:00) and then quickly disappear again within 2 h with peaks of 1 to 2 dB (see Fig. 10a). Comparing to Fig. 10b, it is clear that they do not coincide with any change in temperature. Instead, these peaks only appear in periods when the net radiation is negative and the relative humidity is above 90 %. The power gradually returns again to the previous level when the net radiation becomes positive and the event is over as soon as the relative humidity drops below 90 %. From Fig. 10 we can see that these instances (where humidity is above 90 %) are not correlated to temperature. These characteristics indicate that dew formation on the antennas is a plausible explanation for this phenomenon. The hypothesis is as follows: relative humidity in the air approaching 100 % and a net loss of radiative energy at the surface are indicative of dew formation; water condenses on the antenna covers and builds up a thin layer of water which causes attenuation proportional to the thickness of the layer (see Leijnse et al., 2008); as the net radiative flux changes sign and the water layer dries up, the attenuation slowly returns to the baseline level.

Fog and dew often occur under the same conditions and it is thus difficult to rule out fog as the principal cause, from correlations alone. If we take the visibility as indicative of the amount of fog, then we can see that they indeed occur often (but not always) at the same time.

In the case shown in Fig. 12, a different fog event is shown in more detail. In this case, time-lapse camera footage was available for a significant portion of the event, and is shown in Fig. 12c. Here again, strong attenuation is experienced by all the links with a peak attenuation of 3 dB in the case of the Nokia link, yet none of the disdrometers detect precipitation. Therefore, it is likely that we are dealing with a different attenuating phenomenon than precipitation. Using the basic rainfall retrieval algorithm, this event would result in an accumulated rainfall depth of 26 mm. As the time series of attenuation is smoother than we would expect of rainfall, we are likely dealing with antenna wetting due to either dew formation, or the result of fog. The effect of fog on microwave link attenuation has also been observed by, e.g. Liebe et al. (1989) and David et al. (2013). However, as mentioned in those studies, the theoretical attenuation by fog droplets themselves is only 0.75 dB at 38 GHz for a 1 km path and a very high liquid water content of 0.8 g m-3. Therefore, no more than 1.5 dB attenuation can be expected due to the fog itself and an attribution to fog must also include the wetting of the antennas. Observation of the accompanying time-lapse camera footage (Fig. 12c) reveals a heavy fog during the early morning, which gradually clears up concurrently with the decrease in attenuation in the late morning. No camera footage was available at night during the increasing leg of the attenuation signal, because the cameras cannot record during low-light. However, comparison of the visibility data from the nearby weather station (Fig. 12b) with the pattern of attenuation, seems to undermine a direct relationship with fog. Visibility measurements from the NIR link along the path itself are of limited use in this case, as the fog is so heavy that the attenuation is “saturated” for most of the duration. The striking correspondence of the sign switch of both net radiation and attenuation increase makes dew formation the most likely interpretation.

Near the start of the measurement period a simple test case was performed to assess the effect of wet antennas on rainfall retrieval. During a dry sunny day (12 September 2014), while the ambient temperature was 21 ∘C, both the Nokia and the RAL 38 GHz receiving antennas were artificially wetted in short bursts using a spray bottle. The antennas were wetted until visually saturated and then allowed to dry in the sun. In this way, the attenuating effect of wet antennas can be observed, decoupled from the attenuating effect of raindrops in air. The RAL 26 GHz link was not included in the test, as it was not yet installed at the time; however, the antenna cover design and material is identical to that of the RAL 38 GHz link (aside from its diameter) and thus it is assumed that the effect is similar.

In Fig. 13a the resulting attenuation signal is shown. It is seen that wetting of one antenna of the Nokia link system can result in an extra attenuation of 3 to 5 dB, which is of the same order of magnitude as what is observed in dew and fog events (where presumably both antennas of a link are affected). This corresponds with a rain intensity of 15 to 22 mm h-1 using the power law derived in Sect. 4.1.3 (shown in Fig. 13b). The signal then follows an exponential decay pattern due to drying, where the time for the attenuation to decrease by 95 % is 3 min. The RAL link response to wetting is completely different, which may be related to the way water collects on the antenna cover surface. The extra attenuation due to wetting is only 1 to 3 dB and the decay has two distinct stages. The initial peaks drop in less than a second after the spray stops, with no discernible decay pattern. This drop can range from 0.3 to 1.3 dB. However, after the initial peak, the attenuation does not drop to the baseline level; it stays at relatively constant elevated level after the spray. After each new spray the level may or may not change; not necessarily to a higher level. Only 21 min after the last spray, which was administered shortly before 14:56, has the attenuation fully decayed to the dry level (the full length of the decay is not shown on the graph). While the observations of the Nokia link conform to the empirical model of Minda and Nakamura (2005), which effectively describes the drying of a thin water film on the antenna, the observations of the RAL link do not. Figure 14, containing photos of the antennas just after wetting, shows that while a thin nearly uniform film of water has formed on the Nokia link antenna, this does not hold for the RAL link antenna cover. Instead of forming a smooth layer, the hydrophobic material of the antenna cover forces the water to either run off immediately or collect into a few large beads. The runoff leads to a reduced peak attenuation and an immediate drop afterwards, as the surface is never fully covered with water. However, the bead formation leads to a long secondary decay time, as the reduced surface to volume ratio (as compared to a uniform layer) hampers evaporation. As recorded video footage shows, with each new squirt of water, some new beads form while some others grow and fall off. The number and sizes of the beads remaining afterwards is highly variable, which might give a tentative explanation as to why the secondary attenuation level changes after each burst (and can even become lower than the previous level). It is interesting to note that Schleiss et al. (2013) also report individual drops on the antennae, rather than a sheet of water. They find drying times ranging from 0.5 to 5 h, which is considerably longer than the under 3 min reported by Leijnse et al. (2008) and Minda and Nakamura (2005). The results of this experiment seem to indicate that bead formation versus sheet formation is a major reason for the disparity in drying times.

Figure 15 shows an example of a remarkable event that occurred several times in the observation period. Figure 12a displays the received power for the four microwave link signals in the period of 10 to 12 May 2015. There is a sudden sharp signal decrease and 18 h later a subsequent increase towards normal levels. The disdrometers do not indicate any significant rainfall event during this time. Inspection of the time-lapse camera footage (shown in Fig. 15b) indicates that a large metal construction crane was positioned exactly in front of the link path during this time about 200 m from the receivers, while it is positioned differently and regularly moving outside this time period. A few hours later we see another momentary drop in the received signal levels at which point the crane moves swiftly through the path. The Nokia link detects no signal loss during the long period, but it does on other similar occasions. As the radius of the first Fresnel zone at this distance is only 1.3 m and the centres of the Nokia antennas are about 0.5 m higher than the centres of the RAL antennas, there is a distinct possibility that in some instances the obstacle was only blocking some of the links.

We see similar patterns on multiple occasions and each time a large metallic object was positioned in the path. On other occasions, for example, a window cleaners' metal gondola crane was the cause of the attenuation. These kinds of temporary obstructions of the link path cannot be ruled out in operational settings, and most of the time no continuous visual observations are available. Therefore, it would be advantageous to be able to recognize these signal patterns and remove them algorithmically.

There are several anomalies present in the dataset that cannot be easily explained by any single observed atmospheric phenomenon as described in the previous sections.

Figure 16 shows another example of a rain event. It can be seen that the link attenuation signals mimic the temporal dynamics in the rainfall. It can also be seen that the RAL 38 GHz link shows continued attenuation after the first rain event has stopped. One possible explanation could be because the antennas become wet themselves, which contributes extra to attenuation. However, the duration of the effect in this instance is almost 3 h, which is somewhat inconsistent with the results from Sect. 4.6, which suggests a duration in the order of 21 min. It is also inconsistent with some other events during this experiment when only a short attenuation period was observed after a precipitation event. Here as well, after the second rain shower, no lingering attenuation is observed. However, it is consistent with the findings of Schleiss et al. (2013). The Nokia link shows no lingering attenuation in both cases, which is consistent with the results from the wet antenna experiment. It is hard to specify why lingering attenuation effects occur after some rain events and not after others, but ambient conditions such as air humidity, temperature and wind speed might play a role here. The relative humidity hovers around 90 % after the first event, while it drops to 80 % directly after the second event. Concurrently, temperature increases from 14.5 to 18 ∘C and wind speed increases from 1 to 6 m s-1. It is even harder to specify why some antennas are much more affected by the phenomenon than others at a given time; however, the beading effect of the wet antenna with hydrophobic antenna cover might be related to this.

The examples given above have been simple cases where rain and other attenuating phenomena occur in an isolated fashion. These cases are important to be able to investigate and explain these phenomena. However, many times throughout the investigated period multiple phenomena have occurred simultaneously, which is a complicating factor for retrieval algorithms. Figure 17 provides an example of a complex event occurring on 1 December 2015. In this case, there is a simultaneous light drizzle and fog. Figure 17c shows that the disdrometers register rain intensities of below 1 mm h-1 over a period of over 4 h. Despite the low intensity, the drizzle does produce attenuation of the links between 10:00 and 13:00, as can be seen in Fig. 17a. Fog rolls in at around 13:00 as evidenced by the time-lapse footage (not shown here) and substantiated by the increasing relative humidity and decreasing visibility as seen in Fig. 17b. From 13:00 till roughly 14:30 fog and drizzle occur simultaneously and both contribute to the attenuation. At 15:30 the fog has blown over or has dissipated. This is captured well by the Nokia link attenuation signal. The RAL link signals remain attenuated until 20:00. This could be due to the antenna covers still being wet. As was pointed out in Sect. 5.6, Due to bead formation, the hydrophobic antenna covers can stay wet much longer. Indeed, from 16:00 onwards, net radiation flux towards the surface is negative (indicated by the shading in Fig. 17b) and thus only wind drying can take place. The simultaneous occurrence of drizzle and fog could pose a problem for binary dew filtering algorithms such as the one proposed by Overeem et al. (2016b).