Improved Extreme Rainfall Events Forecasting Using
Neural Networks and Water Vapor Measures
Matteo Sangiorgio1, Stefano Barindelli2, Riccardo Biondi3, Enrico Solazzo2, Eugenio
Realini4, Giovanna Venuti2, and Giorgio Guariso1
1 Department Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy
2 Department of Civil and Environmental Engineering, Politecnico di Milano, Milan, Italy
3 Department of Geosciences, Università degli Studi di Padova, Padova, Italy
4Geomatics Research & Development srl (GReD), Lomazzo (CO), Italy
Abstract. In the last few years, many studies claimed that machine learning
tools would soon overperform the classical conceptual models in extreme rain-
fall events forecasting. In order to better investigate this statement, we imple-
ment advanced deep learning predictors, such as the deep neural nets, for the
forecasting of the occurrence of extreme rainfalls. These predictors are proved
to overperform more simple models such as the logistic regression, which are
traditionally used as a benchmark for these tasks. Also, we evaluate the value of
the information provided by the Zenith Tropospheric Delay. We show that add-
ing this variable to the traditional meteorological data leads to an improvement
of the model accuracy in the order of 3-4 %. We consider an area composed by
the catchments of four rivers (Lambro, Seveso, Groane, and Olona) in the Lom-
bardy region, northern Italy, just upstream from the metropolitan area of Milan,
as a case study. Data of convective extreme rainfall events from 2010 up to
2017 (more than 600 extreme events) have been used to identify and test the
Keywords: Nowcasting, Extreme Rain Events, Deep Neural Networks, Global
Navigation Satellite System, Zenith Tropospheric Delay.
Many researchers in the field of meteorology claim that machine learning tech-
niques will soon overperform the traditional physically based models in weather fore-
Also, black box models seem to be well suited for real-time application, since they
are faster due to the lower computational effort required with respect to the traditional
meteorological nowcasting methodologies, which are based on physically based mod-
In particular, extreme events are very difficult to predict with classical Numerical
Weather Prediction (NWP) models because they usually affect very small and loca l-
ized areas and the convection is triggered by peculiar and local conditions, requiring
both high-resolution NWP and high temporal and spatial resolution observations.
In this work, we deal with the problem of forecasting the occurrence of extreme lo-
cal rainfall events 30 minutes ahead.
The considered area, located in Lombardy region, Northern Italy, is composed by
the hydrological basin of four torrential rivers (Lambro, Seveso, Groane, and Olona).
This is a high-risk territory due to the high frequency of severe and short thunder-
storms, which usually trigger flash floods. The situation is even more critical due to
the presence of the metropolitan area of Milan, where the flows coming from the four
considered rivers are drained, causing severe damage. In 2014, for instance, floods
produced damages evaluated in several million euros in the Milan municipality.
In this work, we adopted advanced machine learning tools, the Deep Neural Net-
works (DNNs hereafter), which receive as input some meteorological variables sam-
pled inside and around the study area and return as output the prediction about the
occurrence of an extreme event.
In addition to the classical meteorological variables (temperature, pressure, hu-
midity, wind speed), we also included the Zenith Tropospheric Delay (ZTD), which
seems to be promising since it is a proxy of water vapor in the atmosphere, a funda-
mental variable in rain events genesis    .
This represents a novel element of this research since it is one of the first attempts
to use the ZTD in a black box model for prediction of severe storms  . We quan-
tify the impact of ZTD repeating the task twice: the first time without considering
ZTD, the second including it within the model inputs.
Developing a black box model for this environmental problem could become an
innovative nowcasting product exploitable also by Civil Protection Agencies to face
This work is part of the Lombardy based Advanced Meteorological Predictions and
Observations (LAMPO) project (http://www.geolab.polimi.it/projects/lampo-
2.1 Extreme Event Definition
The objective of this work is to identify machine learning models able to forecast
the occurrence of extreme rainfall events 30 minutes ahead.
We consider a rainfall event as extreme if it persists for more than 25 minutes
within the study area and if the radar reflectivity factor is greater than 50 dBZ.
2.2 Machine Learning Models
the task we are dealing with is a binary classification task.
As it is well-known, while developing machine learning tools, it is important to
start with some simple models which will be considered as a benchmark for more
complex (and hopefully more performing) ones. In this case, we adopted a logistic
regression (see Fig. 1) as a baseline model, using its Python implementation provided
by Scikit-learn library .
The logistic regression is a linear classifier which splits the feature space (which in
this case is a high-dimensional one) with a linear manifold and classifies each sample
according to its position relative to a linear decision boundary.
Given the complexity of almost all the real-world applications, it is unlikely that
the decision boundary is actually a linear one. For this reason, we introduced a more
advanced machine learning model which can efficiently deal with problems where
classes are not linearly separable: a DNN  (see Fig. 1).
The deep neural network here considered has a traditional fully connected structure
 and has been implemented in Keras  with TensorFlow backend.
Fig. 1. Representation of the considered model's architectures.
To find the best combination of hyper-parameter (learning rate, batch size, regular-
ization rate, activation functions shape, number of hidden layers, number of neurons
for each layer, class weights) values, we implemented a traditional grid search ap-
The dataset used to identify the classifiers has been split into training (70 % of the
samples), validation (15 %) and test (15 %) sets, as it is common practice in the neu-
Since we are dealing with a classification task, we considered the binary cross-
entropy as loss function and the overall classification accuracy as validation metrics.
Early stopping and L2 norm weight regularization have been used to avoid overfit-
ting on training data. The performances, in terms of overall accuracy and confusion
matrix, are then evaluated on the test set.
2.3 Meteorological Variables
Several classical meteorological variables are measured every 10 minutes: temper-
ature, air pressure, wind speed, and relative humidity. In addition, another variable
has been considered: the Global Navigation Satellite System (GNSS) derived ZTD
estimated from the observations of the permanent geodetic station of Como. ZTD
represents the zenithal delay in the transmission of the GNSS signal from the satellite
to the ground receiver caused by the troposphere . It is the sum of a delay caused
by the troposphere gases in hydrostatic equilibrium, called Zenith Hydrostatic Delay
(ZHD) and a delay caused by the presence of water vapor called Zenith Wet Delay
(ZWD). Since the temporal variations of the first term are very small, the ZTD could
be considered a proxy of the presence of water vapor in the atmosphere , which is
a fundamental variable in rain events genesis.
Each sample in the dataset is thus formed by an input vector, whose elements are
the meteorological variables, and by an output value, a boolean variable which repre-
sents the occurrence (or not) of the rainfall extreme event.
The dataset considered in this work covers the period from 2010 to 2017 and con-
tains 656 extreme events (together with thousands of cases where the extreme events
did not occur).
The baseline situation (i.e., using logistic regression with traditional meteorological
variables only) guarantees an overall classification accuracy of 72.5 % corresponding
confusion matrix is reported in Fig. 2.
Fig. 2. Confusion matrix obtained with the logistic regression considering traditional mete-
orological variables only.
As already stated in the previous section, given the complexity and the nonlinear
nature of the processes which occur in the atmosphere, it is very unlikely that a simple
model such as the logistic regression would turn out to be the best approach to deal
with the considered problem.
This idea is confirmed by the performances obtained with a more complex model:
a DNN with three hidden layers, each one composed by ten neurons: the overall accu-
racy grows up to 79.0 % (see Fig. 3 for the confusion matrix).
Fig. 3. Confusion matrix obtained with the DNN considering traditional meteorological var-
To evaluate the importance of including ZTD estimates, we repeated the identifica-
tion of the two models with the new set of input variables.
Fig. 4 and 5 show the confusion matrices computed with the logistic regression and
the DNN, respectively. Looking at the comparison between the models, the results
exhibit almost the same trend when the ZTD is included or not in the inputs: adopting
complex models like the DNNs, the overall accuracy in the forecasting of extreme
events increases of 6.5 % and 8.5 % for the cases without and with the ZTD, respec-
tively (see Table 1).
Fig. 4. Confusion matrix obtained with the logistic regression, including the ZTD in the in-
put variable set.
Fig. 5. Confusion matrix obtained with the DNN, including the ZTD in the input variable
The performances computed in terms of overall accuracy, which are reported in
Table 1, allow quantifying the value of the information provided by the ZTD meas-
ured at Como. In fact, considering the logistic regression, including the ZTD within
the input set increases the accuracy from 72.5 % to 74.0 % (+1.5 %). The advantage is
even more evident when adopting a DNN: the overall accuracy grows from 79.0 % to
Table 1. Overall accuracy of the models identified in the study.
Model Overall accuracy
Logistic regression without ZTD 72.5 %
DNN without ZTD 79.0 %
Logistic regression with ZTD 74.0 %
DNN with ZTD 82.5 %
In this paper, we showed how machine learning techniques can be effectively used
to forecast extreme rainfall events. In particular, the results demonstrate that complex
nonlinear models, such as the DNNs, overperform the logistic regression, which has
been used as a benchmark. For the considered case study, this advantage can be quan-
tified in the range of 5-10 %.
In addition, we confirm the results recently obtained in  and : including the
ZTD in the input set leads to an increase of the model accuracy, especially when
adopting a DNN, of the order of 3-4 %.
This fact seems interesting because the ZTD station, located in Como, is on the
border of our study area. We would expect even better performances in case the sta-
tion where ZTD is measured was localized closer to the center of the study area or if
there were some stations inside and/or outside the considered boundary.
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