Eight rainfall events recorded from May to September 2013 at Hong
Kong International Airport (HKIA) have been selected to investigate the
performance of post-processing algorithms used to calculate the rainfall
intensity (RI) from tipping-bucket rain gauges (TBRGs). We assumed a
drop-counter catching-type gauge as a working reference and compared rainfall
intensity measurements with two calibrated TBRGs operated at a time
resolution of 1 min. The two TBRGs differ in their internal mechanics, one
being a traditional single-layer dual-bucket assembly, while the other has
two layers of buckets. The drop-counter gauge operates at a time resolution
of 10 s, while the time of tipping is recorded for the two TBRGs. The
post-processing algorithms employed for the two TBRGs are based on the
assumption that the tip volume is uniformly distributed over the inter-tip
period. A series of data of an ideal TBRG is reconstructed using the virtual
time of tipping derived from the drop-counter data. From the comparison
between the ideal gauge and the measurements from the two real TBRGs, the
performances of different post-processing and correction algorithms are
statistically evaluated over the set of recorded rain events. The improvement
obtained by adopting the inter-tip time algorithm in the calculation of the
RI is confirmed. However, by comparing the performance of the real and ideal
TBRGs, the beneficial effect of the inter-tip algorithm is shown to be
relevant for the mid–low range (6–50

Application-driven requirements of rainfall data

Following the effort led in the last decade by the WMO and aiming at
quantifying the achievable accuracy of rainfall intensity measurements

Sound metrological procedures for the assessment of the uncertainty of
meteorological measurements have recently been introduced within the
framework of Europe-wide collaborative projects

Besides the inherent instrumental factors (e.g. the systematic mechanical bias of tipping-bucket rain gauges or the dynamic response bias of weighing gauges), post-processing of the raw data to obtain accurate rain intensity records at a pre-determined temporal resolution is common practice. In the case of tipping-bucket rain gauges (TBRGs), dedicated post-processing algorithms must be employed to achieve sufficient accuracy and to minimize the impact of sampling errors and the discrete nature of the measurement.

Various algorithms have been proposed to this aim and discussed in the
literature

This method

We compare and discuss in this paper the performance of different post-processing algorithms employed in the calculation of the rainfall intensity from tipping-bucket rain gauges. Data recorded at a field test site by two TBRGs using different mechanical designs are used, and a catching-type drop-counting gauge is assumed as the working reference. The comparison aims to highlight the benefits of employing smart algorithms in post-processing of the raw data and their ability to improve the accuracy of rain intensity measurements obtained from TBRGs.

The Hong Kong Observatory performs rainfall measurements at the weather
station of Hong Kong International Airport (HKIA). An Ogawa optical
drop-counting rain gauge, model Osaka PC1122 (OSK), is available at the field
site, providing rainfall measurements at the time resolution of 10

Based on the calibrated drop size volume (calculated in October 2013) of
63.93

Types of rain gauges employed for this comparison and their principal characteristics.

Due to the high accuracy and time resolution, we adopted the OSK drop-counter
gauge as a working reference, and compared its measurements with co-located
observations performed by two TBRGs manufactured by Logotronic MRF-C (LGO)
and Shanghai SL3-1 (SL3). The main characteristics of the instruments
employed in this study are summarized in Table

Shanghai SL3-1 (SL3): internal mechanism with a double layer of
tipping buckets

This is not a common solution for TBRGs, and the objective of the two layers of buckets employed seems to reside in the attempt to reduce the systematic mechanical bias, typical of traditional TBRGs. In a sense, this is a hardware type of correction similar to the use of a syphon or other mechanical solutions.

The three instruments are positioned in the western corner of the field test
site of the Hong Kong Observatory (depicted in Fig.

The western corner of the Hong Kong Observatory field test site where the SL3 (blue box), the LGO (red box) and the OSK (green box) are located. The distances of each instrument from the field site borders are also indicated.

In order to correct the systematic mechanical errors of the two TBRGs, both of them were subjected to appropriate dynamic calibration in the laboratory. The dynamic calibration consists of providing the gauge with a sufficient number of equivalent rainfall intensities, using calibrated constant flow rates. By comparing the reference values with those measured by the rain gauge under test, the parameters of a suitable correction curve (usually a power law) are derived. The measurements from the two TBRGs were corrected before performing any comparison with the drop-counter time series and/or with the ideal TBRG data obtained from the reference.

In this work, the computation of statistical estimators and deviations between paired observations was performed with no reference to any ancillary data (wind speed and direction, air temperature and absolute pressure, etc.), although it is known that some of them (especially the wind) may actually affect the accuracy of the measurement.

The field data available for this study cover a 5-month period of observations from May to September 2013. Eight significant events in this period were selected based on the total rainfall depth, after checking that the reference rainfall intensity values were lower than the given factory limits for the instruments under test.

Table

Total rainfall depth (

Reference rainfall intensity measured by the OSK drop counter (shaded grey background) and comparison of the accumulated reference (red continuous line) with the accumulated Logotronic (LGO) and Shanghai (SL3) measurements during the sample event of 22 May 2013.

Figure

Figure

Box plot of the reference rainfall intensity for each event (top of the graph) and the corresponding daily rain amount (lower part of the graph) for the OSK drop counter (reference) and the two TBRGs (SL3 and LGO). The explanation of the symbols used in the boxplot representation is shown on the right-hand side of the graph.

We adopted the catching-type drop-counter gauge as the working reference for
this work due to the high sensitivity of the measurement. Indeed, the
instrument provides the number of generated drops with a time resolution of
10

Both the SL3 and LGO rain gauges provide records of the time stamp of each tip. This feature allows one to use various algorithms to calculate the 1 min rainfall intensity values for the two investigated TBRGs.

The first, traditional and widely applied method to derive the 1 min
rainfall intensity (RI

The second method used to obtain the 1 min rainfall intensity values
(RI

For both the TBRGs, the two values of the 1 min RI derived from the two
post-processing algorithms described above (generally indicated in
Eq.

In order to assess the ability of the employed algorithm to describe the inner variability of the considered events and to capture their finer details, we calculated the correlation coefficients between all the derived time series and the reference ones. In particular, for each event, we calculated the RMSE error of paired deviations between the measured and ideal/reference RI signals.

In an effort to homogenize the dataset, we considered the standardized value
of the generic rainfall intensity value (RI

We first evaluated the accuracy of the investigated RI algorithms using TBRG
measurements by comparing their performance with the working reference.
Figure

One-minute relative deviations (

Two different regions of this graph show different behaviours of the relative
deviations calculated with the inter-tip approach. At
low values of the RI, the relative deviations of all the TBRGs exhibit a
large variability, whereas this scatter suddenly decreases just above the
RI value of 6

One-minute relative deviations (

It emerges from the graph in Fig.

The behaviour of the ideal TBRG is clearly different, since it is not
affected by instrumental mechanical errors (ideal mechanics), and the average
value of

Note from Fig.

As the rainfall rate increases, the
variability of

Figure

In Fig.

Taylor diagram representation of pattern statistics of the various RI series. The radial distance from the origin is proportional to the normalized standard deviation of the RI signal; the blue contour lines highlight the RMSE difference from the OSK reference (black dot) for each recorded event; the azimuthal position indicates the correlation coefficient between the RI signal and the reference. Crosses indicate the statistics of each single event, while the dots indicate the average values of the whole campaign (colours according to the legend).

In the same figure, the benefit of using the inter-tip time algorithm instead
of the tip counting is evident: the correlation coefficients of the two real
TBRGs increase using the former one for both TBRGs. Therefore, the beneficial
effect in terms of deviations of the measured RI from the reference is
highlighted. In fact, note the reduction of the RMSE difference from the
reference, approaching the value of the ideal TBRG. This reduction can be
quantified in about 1

Also, the RI time series of the ideal TBRG shows a normalized standard
deviation approximately equal to 1, that is, the same as the reference, and a
mean correlation coefficient greater than 0.99. However, the average value of
the RMSE between the synthetic TBRG and the reference continues to show a
relevant value slightly below 2

In order to evaluate the effectiveness of the post-processing algorithms on
the accuracy of the measurements over different ranges of rainfall intensity,
we plotted the standard deviation of the relative error (

Standard deviation of the relative error for the ideal and
investigated TBRGs when adopting the inter-tip time algorithm (Ttip) and
the tip-counting method (raw) with respect to the ideal gauge for both the
SL3

It is evident from the graph that the raw counting of the number of tips results, for both the investigated TBRGs, in a continuous trend of linear (in a log–log scale) reduction of the error variance with increasing RI. This reflects the fact that the random attribution of one tip to the wrong minute does not strongly affect the derived RI since the number of tips per minute is relatively high.

At very low values of RI, there is little difference between the results
obtained by employing the simple counting of tips or the inter-tip algorithm,
with respect to the ideal TBRG. By increasing the RI, but still below the threshold
intensity corresponding to the sensitivity of the gauges, the effectiveness
of the inter-tip time algorithm is relevant and results are very near to the
ideal gauge. This effectiveness decreases beyond the sensitivity value and,
when the RI increases beyond 50–60

The raw data recorded during a dedicated monitoring campaign have been analysed using two different post-processing algorithms to calculate 1 min RI series. The results allow one to compare the performance of the inter-tip time algorithm with the more common tip-counting method when using two different types of TBRGs. The field reference chosen for this comparison is a catching-type, optical drop counter that, although calibrated in the laboratory, is still subject to unknown uncertainties in field operation (wind, wetting, splashing, etc.). Notwithstanding this residual uncertainty, comparison of the two gauges with a virtual TBRG obtained from the reference measurements was able to show relevant differences in the calculated 1 min rainfall intensity and the relationship of such differences with the rainfall rate itself.

In particular, the main benefit of adopting the inter-tip time method as a post-processing algorithm to calculate rainfall intensity from the raw data resides in a better representation of the inner variability of rainfall events. The measured RI series shows an improved correlation coefficient and a lower RMSE with respect to the reference, closely approaching the performance of an ideal TBRG, which is not affected by mechanical biases.

In terms of accuracy, the inter-tip time algorithm contributes its greater
beneficial effects in the range of low to mid RI values. In the very low RI
range, below the threshold value of 6

Beyond that threshold value, a step change is observed since at least one tip
per minute is recorded when RI > 6

The data presented in this paper are available on request from the corresponding author.

This research is supported through funding from the European Metrology Research Programme – project MeteoMet 2 (ENV58-REG3). Edited by: G. Vulpiani Reviewed by: R. Uijlenhoet and three anonymous referees