Identification of dry and rainy periods using telecommunication ...

12 nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011 

Identification of dry and rainy periods using telecommunication 

microwave links 

M. Kaufmann 1 and J. Rieckermann 1 

1 Eawag - Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland 

*Corresponding author, e-mail joerg.rieckermann@eawag.ch 

Abstract 

Microwave links from telecommunication networks (MWL) provide rainfall data at high spatial 

(


Figure 1 The pre-processing of received signal level (RSL) from Microwave Links (MWL) decomposes the 

RSL into the baseline (B) and the rain-induced attenuation (Atot). Pre-processing with an online-algorithm 

(left) only uses past information, but can be applied in real-time data analysis and operation. The corresponding 

offline algorithm uses both past and future observations. 

In this study, we therefore developed three novel methods to classify every measurement of 

the signal strength as either belonging to wet or dry periods: i) a moving window algorithm, 

ii) a statistical classification algorithm using random forests and iii) an algorithm based on a 

Gaussian factor graph, which is a rather novel signal-processing method. Our main innovations 

are that we suggest algorithms for offline and online data processing, compare their performance 

to that of others published algorithms in literature and investigate how the different 

methods cope with different data qualities, temporal and power resolution. Our results show 

minimal classification errors of precipitation for the random forest, although each algorithm 

has its pros and cons. Interestingly, the major influence factor is the quantization of the MWL 

signal. As expected, the results are very much dependent on the training procedure and data of 

the algorithms. 

CASE STUDY AREA IN ZURICH, CH 

MWL network: For our study, 14 links from a telecommunication network in the region of 

Zurich were available (Figure 2). For details see Rieckermann et al. (2009). The RSL was 

recorded as the instantaneous power from ten MWL with a “fine” quantization of 0.1 [dBm] 

and four with a “coarse” one (1 [dBm]: No. 2, 3, 6, 11) and a temporal resolution of about 2.5 

minutes. The RSL were recorded from April 2009 until May 2010. 

Rain gauges: Eleven rain gauges are present in the study area and the data were obtained from 

the local sewer operator, ERZ, and MeteoSwiss. We aggregated the tipping bucket recordings 

(volume: 0.1 mm) over ten minutes to account for the spatial and temporal variability of rainfall 

with regard to the path-averaged values of the MWL. This way, the measurable intensities 

were multiples of 0.6 mm/h. To evaluate the performance of the algorithms, we used the rain 

gauge closest to an individual MWL as the ground truth. This is naturally not exact, because, 

in addition to measurement errors, the measurements of point rainfall from a gauge do not 

correspond to the path-average rain intensities from MWLs. However, absolute values are not 

our primary interest in this study. Also, one rain gauge represents from less than 1 kilometre 

to up to 8 kilometres of MWL length, which is in the lower range of the values found in the 

literature (Berne and Uijlenhoet, 2007; Leijnse et al., 2007; Zinevich et al., 2008). 

Weather radar: Radar data are provided by MeteoSwiss (SMA) as a composite of the three 

Page 2 of 12


Figure 2 Location of the selected ORANGE microwave links and the location of the available rain gauges. 

weather radars in Switzerland (Germann et al., 2006). We deliberately chose not to use the 

radar data as ground truth in our study, because data from weather radars are rather uncertain 

(Krämer et al., 2005; Upton et al., 2005). However, to test their usefulness to inform the 

online and offline classification algorithms (see below), we filtered the data and set all radar 

measurements below 0.6 mm/h to zero. 

CLASSIFYING RECEIVED SIGNAL LEVELS INTO WET AND DRY 

PERIODS 

The moving window algorithm and its modification 

Schleiss and Berne (2010) proposed a method to separate dry from rainy periods based on the 

assumption that, during dry periods, the standard deviation of the received signal level is 

bounded by some constant value that does not change with time and only depends on the 

physical characteristics (i.e., frequency, length, type of antenna) of the MWL (Schleiss and 

Berne, 2010). This leads to a simple decision rule: IF (σ(t)) > σ0 THEN “Wet” (W) ELSE 

“Dry” (D), where σ(t) is the standard deviation of the received signal level RSL(t) in the moving 

window Wt=[t-w, t], w>0, and σ0 is a threshold parameter that has to be estimated from the 

data. For our investigation, we chose a length of Wt, �Wt = { 20, 30 min}. The threshold σ0 

was computed from previously recorded data. Typically, several months of previously recorded 

data are required, because the fraction of rainy periods is small: σ0= q1-r{�ˆ (t)} where 

q is the quantile and r is the fraction of rainy periods, which we determined to 7.2% based on 

SMA rain data from May to December 2009. The attenuation baseline B(t) is then estimated 

in real-time using the following algorithm: 

(1): For each time index t � D, set B(t)= RSLWt 

(2): For each time index t � W, set B(t)=B(t-k), where k is the smallest value such that tk 

� D. 

We label this original algorithm by Schleiss and Berne (2010) “S1a” for �Wt= 20 min and 

“S1b” for �Wt= 30 min. We found that S1a and S1b show quite high class errors for the W 

category, which is probably because the temporal resolution of the RSL used in the original 

method was 6 seconds, while we have a typical resolution of two or three minutes. To improve 

the detection of rain, we thus modified the above decision rule by introducing an additional 

threshold for the mean of the moving window, mean(RSLWt) and �Wt= 20 min (S2). 



� 

� 

RSL(t) 

Figure 3 (Left) A simple classification tree with categories D and W based on the attributes RSL(t), σ(t), 

min(RSLWt), max(RSLWt) for a backward-looking moving window of length �Wt= 20 min. (Right) Illustration 

of different moving windows to construct the attributes for a case of RSL(t). Online versions of 

algorithms only use past data, i.e. backward-looking windows. An observation is classified as D, if i) the 

attribute RSL(t)� 39.81 [dBm] (�), ii) RSL(t)� 39.81 AND σ(t)� 0.3202 AND max(RSL(t))< -40.81(�), etc. 

Regressive classification trees and random forests 

The aim of a regressive classification tree is to predict a classification for a “case” based on its 

attributes (also: “variables”) (Breiman et al., 1984) (Figure 3, left). Here, we classify an observation 

RSL(t) based on attributes computed from past (online) or both past and future (offline) 

data (e.g., σ(t), min(RSLWt), etc.) (Figure 3, right). We used the rpart package in the 

statistical computing language R, which maximizes the mean decrease in the Gini-index (GI) 

(Gini, 1921) at every split. To every end-node a classification (W or D) is assigned, when the 

splitting stops. This occurs by default, when a maximum of 20 observations at every node is 

reached (Atkinson, 2000). 

A random forest basically consists of many regressive trees, it again relies on a training-set 

with in total m classified cases. Each tree of the forest is then constructed using a different 

bootstrap sample, which is drawn with replacement from the original data (Breiman, 2001). 

The criteria for building the classification forest are the same as for the single classification 

tree. After the construction of the random forest, each new observation is classified by all 

trees of the forest, where each tree give a votes and the final category is assigned based on the 

majority of the votes. As the sum of all decreases in GI over the whole tree for an attribute 

(e.g., min(RSLWt)) gives an estimate of its importance, the mean decrease in GI (�Gini) is a 

measure of the sensitivity of the classification to this attribute (Breiman, 2001). While we 

used rpart for the classification tree, the R package randomForest was used for the construction 

of random forests to analyze the MWL data. 

For the offline random-forest algorithm, we calculated the following attributes from forwardbackward-looking 

windows (Figure 3, right) (the online versions only relied on past data) 

with �Wt= {15, 30, 120 min}: i) RSL, ii) standard deviation (std), iii) slope of a fitted regression 

line (slope) and autocorrelation (lag=1) (autocor) (all relative), iv) min(RSL) (min), v) 

max(RSL) (max), vi and vii) the 10%- and the 90%-Quantile (q10, q90; only for 

�Wt= 120min) (all absolute), viii) the last rain intensity obtained by the weather radar 

(RTS_past) and a binary variable (0 or 1) depicting whether it had rained in the previous 10 - 

40 min (rain_10_40_past) (information on past rainfall). Our expectation was that information 

on past precipitation could improve the classification. Intrinsic MWL variables, such as 

the cross-correlation between the two communication channels were also calculated, but finally 

not used in the classification, because it often resulted in zero standard variation in the 

intervals, for which the correlation coefficient is not defined. We constructed various random 

forests based on different attributes [in brackets] as online (ON) or offline version: RF1 [all 

attributes], RF2 [same as RF1, ON], RF3 [all-{RTS_past, rain_10_40_past}], RF4 [same as 

RF3, ON]. RF5 [{RSL, min}], RF6 [same as RF5, ON] consider only the most informative 

RSL (t) 

Page 4 of 12 

time (t)


attributes, which we selected based on a high �Gini value. A table with the list of all used 

variables for RF1-RF6 is provided in Table A2. As the moving window algorithm repeatedly 

misclassified small rain amounts (see below), we introduced the additional category “light 

rain” (L) (D: 0, Light: 0.6, W> 0.6 [mm/h]). For training, we compiled sets of 1000 dry and 

1000 rainy cases, randomly sampled out of the desired analysis period. Although this does not 

correspond to the observed distribution of dry and wet periods, it improves the detection of 

wet periods, which are more relevant in our application. 

Stochastic state space model of the baseline using a Gaussian factor graph 

Here, we used a rather new model-based signal processing methodology which is based on 

factor graphs and algorithms for message passing, which include an element of forgetting to 

ensure a decreasing confidence in remote parts of the baseline model. For an introduction on 

the use of factor graphs in model-based signal processing see Loeliger et al. (2007) and on the 

idea of forgetting (Loeliger et al., 2009). The underlying idea of the algorithm developed by 

Reller et al. (2011) is to reconstruct the baseline and to classify the RSL(t) either as belonging 

to the baseline (ck=1, i.e., Dry weather) or not (ck=0) (see Eq. 2). Important assumptions are 

that the data belonging to the baseline are locally smooth and that there is some periodicity in 

the observed signal over consecutive days (Figure A1). Therefore, the baseline is composed 

from two linear state space models on different time scales, which are referred to as the “fast" 

and the “slow" model. As an example, we briefly describe the fast model, which is formulated 

as a second order linear state space model of a straight line (Eqs. 1 and 2), where a time interval 

is defined �k = tk-tk-1, with timestamp t and observations indexed with k=1,..K. The state 

vector of the straight line, Xk, contains the RSL(tk) and the line slope at time t (Reller et al., 

2011). 

� k 

Xk � AkXk-1 

(1) 

Yk= CXk+ Zk 

(2) 

where �� 1 

� k � 

Ak 

� �� , C � �1, 0�, 

Zk is Gaussian noise and �k is a forgetting factor on the state 

�0 

1 � 

Xk, which has a similar, but not the same, effect as state noise. Yk are the observed RSL. Details 

of the algorithm, such as the slow model, the message passing and the choice of threshold 

parameters for classification are described in Reller et al. (2011). Due to limited time, we 

were only able to adjust the threshold parameter, but not to optimize the algorithm extensively. 

Figure 4 shows the results for a single rain event on 17.07.2009 and MWL 8. In the 

lower part of the figure, the observed RSL and modeled baseline are plotted with the timestamps 

where the fast and slow baseline models are connected (�t= 6 hours). In the upper 

part, the baseline components are displayed and the residual signal is compared to the rain 

intensity measured by the gauge, which are in good agreement (not scaled). 

Performance evaluation and comparison of the algorithms 

The classification of every single RSL measurement was compared to the rain intensity that 

was measured at that time at the corresponding rain gauge of the MWL. The methods were 

applied to two different analysis periods: Period A (01.07.2009-31.10.2009) contains only 

liquid precipitation events. Period B (01.07.2009-31.12.2009) in addition contains snowfall 

and sleet. To evaluate the above algorithms, we computed the class errors for W and D based 

on the confusion matrix which contains True Positives, False Positives, False Negatives and 

True Negatives: 



R [mm/h]; Residuals [dBm]; RSL [dBm]; B [dBm] 

24 

0 

-24 

-48 

Measured rain intensity [mm/h] 

Residual (dBm) of: 

- only fast model (upper, dark grey line) 

- the combination of fast and slow model (lower, black line) 

B ± threshold for only the fast model (grey lines) or the 

combination of the fast and slow model (black lines) [dBm] 

RSL (dBm) 

-72 

17.07. 12:00 17.07. 16:00 17.07. 20:00 18.07. 00:00 18.07. 04:00 


Timestamp of the connection between 

the two sub-models 

Figure 4 Signal decomposition of MWL No. 8 with a Gaussian Factor graph. (Bottom) RSL and baseline 

model, (Top) Fast and slow baseline components, Residual attenuation and Measured rain intensities. 

Type I errors: dry class error (false rainfall alert) = False Positives / n_dry (3) 

Type II errors: wet class error (missed rain) = False Negatives / n_wet (4) 

RESULTS AND DISCUSSION 

Moving window algorithms 

The results for period A demonstrate that the original algorithm (S1a and S1b) is prone to 25.4 - 64.9% of 

type II errors ( 

Figure 5, left), which is unsatisfactory. It is remarkable that type II errors of the MWL with a 0.1 dBm 

quantization were about half of those with a coarse quantization. For the coarse quantization MWL, we 

found that the wet class errors decreased with increasing �Wt. In contrast, our modified algorithm, S2, 

presented lower wet class errors and higher dry class errors. Furthermore, S2 showed a superior performance 

regarding the true detections of dry and wet periods for all the investigated MWL in our study 

area ( 

Figure 5, right). Period B included events with snowfall and ice particles, which have a different 

influence on millimeter microwave attenuation (Brussaard and Watson, 1994). Therefore, 

the wet 

Figure 5 (Left) Class errors for S1a, S1b and S2 for ten MWL with a fine (0.1 dBm) and four with a coarse 

(1.0 dBm) quantization for period A. (Right) Proportion of the RSL measurements that were classified as 

wet by a rain gauge for the methods S1a, S1b and S2 for period A (mean over all 14 links). The class errors 

were calculated without offset.


class error for S1a and S1b increased to approximately 45% (coarse quantization: 75%). In 

contrast, the wet class error for S2 only increased to 20 % (coarse quantization: 30%). As expected, 

the dry class error did not experience important changes. 

Regressive classification trees and random forests 

Similar to the above algorithms, we developed individual classifiers for the 14 MWL based 

on Random forests and the various attributes computed from period A data. As described 

above, we classified dry (D) and rainy periods, split into light (L) and strong (W). The direct 

comparison with S1-S2 shows rather favourable results for the random forest algorithms RF1- 

RF6, because less than 5% of all rainy cases {L,W} were misclassified as dry (results not 

shown). We found that the mean class errors for RF1- RF6 (averaged over all 14 links) for 

class W were about 20%, with 30-50% errors for L, light rains, which means that many light 

rains are wrongly classified as strong and vice versa. Also, the online algorithms perform 

competitively against the offline algorithm, because the class error for W is very similar and 

errors for the two other classes only increase slightly (e.g., D: RF1/RF2 = 19.9%/22.2%). For 

period B, the class errors (averaged over all links and over RF1-RF6) showed an increase of 

9.9 % (D), 3.9 % (L) and 8.5 % (W) (absolute values). Figure 6 shows the average �Gini for 

the offline algorithm RF1, which indicates the potential of the different attributes to identify 

dry or wet periods. First of all, we found that the important attributes depend on the quantization 

of the MWL. Second, min(RSL) (for �Wt= {15,30}) and the RSL itself are very informative 

for the MWL with 0.1 dBm resolution. Third, for the coarse MWL, the by far most informative 

attribute is the radar rainfall (RTS_past) and the attributes calculated based on the 

RSL unfortunately do not contain much information. Interestingly, attributes computed from 

�Wt=120min are very informative for the coarse MWL, but not for the fine ones. The online 

algorithms (RF2, RF4 and RF6) which only use past information show similar patterns. 

Gaussian factor graphs 

For the data from period A, we found that, for the fine (coarse) MWL, the factor graph produces 

2% (7%) of type I errors, and misclassifies about 35% (32%) of the W class (Figure 7). 

For period B, this is about 1% (5%) higher (absolute values). Nevertheless, the Factor Graph 

is a very elegant algorithm, because it can cope very well with pronounced signal fluctuations 

and even large gaps of missing data (Reller et al., 2011). In addition, the available MATLAB 

implementation is very fast compared to current implementations of the other algorithms. The 

classification performance could be further optimized by tuning, eventually also accompanied 

by a post-processing to filter out unrealistically frequent and small rain events. 

�Gini 

180 

160 

140 

120 

100 

80 

60 

40 

20 

0 

min15_fut 

min30_past 

min15_past 

min30_fut 

RSL 

RTS_past 

min120_past 

std120_past 

std30_past 

min120_fut 

std30_fut 

std120_fut 

max15_fut 

q10_120_fut 

q10_120_past 

std15_past 

std15_fut 

max15_past 

autocor120_past 

slope30_fut 


slope120_fut 

slope30_past 

max30_fut 

autocor120_fut 

slope120_past 

max30_past 

slope15_past 

0.1 dB-Links 

1 dB-Links 

slope15_fut 

q90_120_past 

rain_10_40_past 


autocor30_fut 

max120_fut 

max120_past 


autocor15_fut 

Figure 6 Mean Gini-decrease for algorithm RF1. �Gini is the average decrease over ten 0.1 dBm and four 

1.0 dBm links.


Dry Wet 

Figure 7 Class errors for two categories Dry and Wet. For the Random Forest, the two Wet classes were 

merged to one. 

DISCUSSION 

In general, our results indicate that all algorithms are able to successfully identify dry and wet periods 

based on MWL signals. In Figure 7 we compare the online algorithms S1a, S1b and S2 to RF4, which is 

based on similar attributes. For the factor graphs, only an offline algorithm was available. We found that 

the quantization had a great influence and therefore provide separate bars for the MWL with fine (bold) 

and coarse (shaded) quantization (Figure 7). In general, it can be seen that S2 shows smaller type II errors 

than S1a or S1b and out of the type II errors, less correspond to heavy rains ( 

Figure 5, right). However, we also notice that the cost of fewer type II errors lies in higher 

misclassification rates for dry periods. Based on our results, we find that the choice of one 

specific algorithm strongly depends on the user’s preferences and the available resources. 

First, the absolute performance can be adjusted according to the user’s preference by varying 

the respective tuning parameters. For the original (S1) and extended (S2) moving window 

algorithms, the fraction of wet periods is a physically-based parameter and should therefore 

not necessarily be changed. For the random forests, the composition of the training set and 

the weights assigned to each class can be can be tuned. For the Factor graph, the threshold 

parameter could be further adjusted to lower the misclassification rate for the wet classes, 

which would automatically lead to an increased D misclassification. Second, such parameters 

could be optimized by introducing a cost or preference function. Ideally, this should be defined 

by the user of the algorithms and will be different for online and offline algorithms as 

the user is probably interested in different kind of rainfall data (e.g., real-time information to 

control waster water infrastructure vs. generated time series for the dimensioning of waste 

water infrastructure). This should also consider the absolute deviation from observed rainfall 

volumes. 

CONCLUSIONS 

In this study, our goal was to develop an appropriate offline and online algorithm for the preprocessing 

of MWL data to support urban drainage applications. We compared novel algorithms 

based on moving windows, random forests and factor graphs, which is a rather novel 

technique from signal processing to those reported in literature. Our results show that an appropriate 

online and offline algorithm strongly depends on the quantization and temporal 

resolution of the MWL data, which greatly depends on the deployed instruments. With regard 



to the individual algorithms we conclude that i) the improved moving window algorithm is 

easy to implement and provides an instant prediction of the baseline and the rain-induced attenuation. 

The method performs unsatisfactory with a low temporal or power resolution, ii) 

the power of the random forest algorithm is its flexibility, because it can readily consider 

various types of information. However, this supervised learning method requires a comprehensive 

ground truth and, to cope with seasonal variations, ideally a whole year of data should 

already be available. In our case study, offline and online algorithms performed similarly and 

results were more robust to a coarse quantization than the moving window algorithm, iii) the 

Factor graph is a very elegant solution, as it decomposes the observed signals by means of 

stochastic state-space estimation. Although it performed well, even without intensive tuning, a 

post processing step is suggested for MWL with a coarse quantization to avoid the prediction 

of too many small rain rates. This is the preferred method for low temporal resolution data, 

because of its underlying dynamic system model. 

ACKNOWLEDGEMENTS 

We thank Michal Piotrowski and Johannes Graf, ORANGE SA and Maciej Rudnicki from Alcatel-Lucent for kind provision of the MWL 

data and ERZ for rainfall information. Dr. Marcel Dettling provided valuable advice regarding statistical classification using random forests. 

We are most grateful to Prof. Loeliger, Christoph Reller, Juan Pablo Marín Díaz from the Signal and Information Processing Laboratory 

(ISI) of ETH for developing and implementing the novel factor graph algorithm. 

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Appendix 

Table A1 Coordinates (in CH1903+ datum) and operating information on the MWL used in our study. 

The operation of the shaded link finished early (07.10.2009). 

ID Band A Easting 

A Northing 

B Easting 

B Northing 

Length Precision Quantization 

No. of 

channels 

[GHz] [m] [m] [m] [m] [m] [dBm/km] [dBm] [-] 

1 23 686'678 245'929 682'375 242'720 5'368 0.019 0.1 1 

2 23 681'022 249'720 679'900 246'950 2'989 0.335 1 1 

3 23 681'022 249'720 684'005 248'145 3'373 0.296 1 1 

4 23 679'900 246'950 687'883 244'409 8'378 0.012 0.1 1 

5 23 687'292 251'528 682'330 256'182 6'803 0.015 0.1 1 

6 38 682'580 248'400 682'853 247'657 792 1.263 1 1 

7 38 681'552 248'965 681'342 248'164 828 0.121 0.1 1 

8 38 679'455 245'037 681'291 247'127 2'782 0.036 0.1 2 

9 38 685'101 248'105 684'538 245'285 2'876 0.035 0.1 1 

10 38 686'678 245'929 684'004 246'127 2'681 0.037 0.1 1 

11 38 686'549 244'845 685'868 245'322 831 1.203 1 2 

12 38 681'690 249'449 682'580 248'400 1'376 0.073 0.1 1 

13 58 682'853 247'657 682'870 247'348 309 0.388 0.1 1 

14 58 687'292 251'528 687'457 251'109 450 0.266 0.1 1 

RSL (dBm) 

-40 

-45 

-50 

-55 

-60 

-65 

-70 

01.06.2009 08.06.2009 15.06.2009 22.06.2009 29.06.2009 

Figure A1 Observed variations of the RSL for MWL 1 during June 2009. Cycling pattern represents 

normal variations during dry weather. In contrast, precipitation causes strong attenuation of up to -80.8 

dBm (19.06.2009). 



Table A2 Attributes that were used for the different random forests (RF1-RF6). ON=Online algorithm, 

using only past information. 

Attribute All attributes 


All attributes w/o past 

rainfall information 

The most informative 

attributes 

RF1 RF2 (ON) RF3 RF4 (ON) RF5 RF6 (ON) 

RSL X X X X X X 

std15_past X X X X 

min15_past X X X X X X 

max15_past X X X X 

slope15_past X X X X 

autocor15_past X X X X 

std15_fut X X 

min15_fut X X X 

max15_fut X X 

slope15_fut X X 

autocor15_fut X X 


min30_past X X X X X X 




std30_fut X X 

min30_fut X X X 

max30_fut X X 




min120_past X X X X 




q10_120_past X X X X 

q90_120_past X X X X 

std120_fut X X 

min120_fut X X 

max120_fut X X 



q10_120_fut X X 

q90_120_fut X X 

rain_10_40_past X X 

RTS_past X X


Figure A2 Close-up of the factor graph (adapted from Reller, 2011). The grey boxes depict noise terms.

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