=Paper=
{{Paper
|id=Vol-3389/XCBR102
|storemode=property
|title=A Case-based Explanation Method for Weather Forecasting
|pdfUrl=https://ceur-ws.org/Vol-3389/ICCBR_2022_Workshop_paper_102.pdf
|volume=Vol-3389
|authors=Moisés Fernando Valdez-Ávila,Gerardo Arturo Pérez-Pérez,Humberto Sarabia-Osorio,Carlos Bermejo-Sabbagh,Mauricio G. Orozco-del-Castillo
|dblpUrl=https://dblp.org/rec/conf/iccbr/Valdez-AvilaPSB22
}}
==A Case-based Explanation Method for Weather Forecasting==
https://ceur-ws.org/Vol-3389/ICCBR_2022_Workshop_paper_102.pdf
A Case-based Explanation Method for Weather
Forecasting
Moisés Fernando Valdez-Ávila1,2 , Gerardo Arturo Pérez-Pérez1,2 ,
Humberto Sarabia-Osorio1,2 , Carlos Bermejo-Sabbagh1,2 and
Mauricio G. Orozco-del-Castillo1,2,*
1
Tecnológico Nacional de México/IT de Mérida, Department of Systems and Computing, Merida, Mexico
2
AAAIMX Student Chapter at Yucatan, Mexico (AAAIMX), Association for the Advancement of Artificial Intelligence,
Mexico
Abstract
This paper presents an explainable Artificial Intelligence of Things (AIoT) solution that combines the
information provided by an environmental Internet of Thigs (IoT) sensor with the potential of artificial
intelligence to obtain climate predictions using forecasting techniques. We propose a recurrent artificial
neural network that provides personalized weather predictions (humidity, pressure, and temperature)
based on the concrete environmental time series collected through a sensor installed in a wearable or
mobile device locations of the user. However, as neural networks are black-box models which do not
allow users to better understand the complex dynamics associated with climatology and the reasons
that support a weather prediction, we propose a cased-based reasoning approach to explain how (future)
predictions could be dependent of past time series windows.
Keywords
Explainable Artificial Intelligence, Weather Forecasting, Artificial Neural Networks, Time Series, Artificial
Intelligence of Things
1. Introduction
The current rise of the Internet of Things (IoT) technology has produced a wide range of sensing
solutions that are progressively being integrated into our daily life devices such as mobile phones
or wearables [1]. The combination of such sensing capabilities with Artificial Intelligence (AI)
is producing Artificial Intelligence of Things (AIoT) applications that provide an enhanced user
experience [2].
Within the climate prediction field, a variety of efforts has been made to develop complex
models to perform seasonal climate prediction [3, 4], however, this process is inevitably subject
to many error sources [4]. Climate forecasting has been usually divided into two different
approaches: deterministic and probabilistic forecasting. Deterministic forecasting aims to
provide a quantitative estimate of the future value of climate variables. Probabilistic forecast, on
ICCBR XCBR’22: 4th Workshop on XCBR: Case-based Reasoning for the Explanation of Intelligent Systems at ICCBR-2022,
September, 2022, Nancy, France
$ mauricio.orozco@itmerida.edu.mx (M. G. Orozco-del-Castillo)
0000-0001-7761-9635 (M. F. Valdez-Ávila); 0000-0003-2693-4146 (G. A. Pérez-Pérez); 0000-0002-1003-3303
(H. Sarabia-Osorio); 0000-0002-6053-1175 (C. Bermejo-Sabbagh); 0000-0001-5793-6449 (M. G. Orozco-del-Castillo)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
the other hand, aims to provide the probability distribution for the future state of the variables.
Since a forecast of the occurrence probability for a given event can bring greater economic
value than a single deterministic forecast with uncertain accuracy [5], these methods tend to be
preferred.
Time series forecasting is the prediction of future data values based on some collected data
[6] and has been an area of great interest in science, engineering, and business. Traditional time
series forecasting is usually approached by the analysis of its internal structure: autocorrelation,
trend, seasonality, etc., to capture the pattern of long-time behavior of the system [6]. These
models predict future values of a target 𝑦𝑖 (𝑡) for a given observed value 𝑖 at a time 𝑡. In
climatology, these observed values usually represent measurements from individual weather
stations [7]. While this applies to univariate forecasting, the same components can be extended
to multivariate models without loss of generality [8].
Traditional time series forecasting methods tend to focus on parametric models informed by
the expertise in a given domain, including autoregressive, exponential smoothing, or structural
models [7]. However, in recent years machine learning (ML) methods have provided a means to
capture dynamics of time series directly from the data, instead of domain expertise information
[9]. The increasing data availability and computing power have positioned ML-based time
series forecasting models as the next generation of time series forecasting models [7]. One of
the main techniques in ML is artificial neural networks (ANNs), which have proven to be a
reliable tool for time series analysis [10], and numerous ANNs design choices have emerged
given the diversity of time series problems across multiple domains [7]. Of these designs, the
most commonly used one in time series forecasting is recurrent neural networks (RNNs) [11].
This is due to the natural interpretation of time series data as sequences of inputs and targets
[7].
Although ML approaches have demonstrated very good prediction performance, they have
a significant limitation regarding its explainability. Neural network models are considered
as “black boxes”, because their internal processes are difficult to interpret with respect to the
predictions they produce [12]. Solving this problem is a requirement to audit the reasoning
behind incorrect prediction taken by AI systems and foresee the data patterns that may led
to a climate event. Assuming that ANNs achieve better performance than white-box models,
in this paper we propose a post-hoc sliding-window method that enables the explanation of
an ANN forecasting model for the weather prediction domain. This way, instead of using a
transparent or white box model with lower performance than an ANN, we enable the use of
these black-box prediction models but augmented with explanation capabilities. The post-hoc
explanation system follows an explanation-by-example approach implemented through Case-
based Reasoning (CBR). Here, time series are split into different time-window cases that serve
as explanation cases for the outcome of the ANN prediction model.
In this paper we focus on the combination of an environmental sensor for mobile devices, such
as the BOSCH Sensortec BME6801 capable of sensing several weather variables [13, 14], with
the potential of AI to compute climate predictions using forecasting techniques. Our ultimate
goal is to provide an AIoT solution that brings the user the possibility to obtain personalized
predictions based on the historical environmental data collected through the sensors installed
1
https://www.bosch-sensortec.com/products/environmental-sensors/gas-sensors/bme680/
2
Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
in a wearable or mobile device. Moreover, the aim to provide explainable predictions that
improves the user’s acceptance of the predictions. This way, instead of receiving a generic
climate prediction based on the nearby weather stations (that can be relatively far), this AIoT
solution provides personalized weather predictions based on the concrete locations of the user,
incorporating an explanation mechanism that lets the user understand the previous climate
values that led the AI to make a concrete forecasting prediction.
Paper runs as follows. Section 2 presents the background of this work. Then, Section 3
describes our case-based explanation method. Section 4 presents the evaluation results and
section 5 concludes the paper and opens lines of future work.
2. Background
In a recent work [15], scientists have used eXplainable Artificial Intelligence (XAI) to estimate
precipitation from satellite images. The aim of this research was to exploit the high potential of
ANNs used with satellite images to capture spatial information and inform numerical modeling
and forecasting, which could help to mitigate weather risks. Using XAI techniques, insights
gained from long-range planning (LRP) have given scientists confidence that the ANN generated
predictions based on a physically reasonable strategy, and thus helped build more confidence
in their predictions. Furthermore, if scientists want to improve the model by testing different
model architectures, knowing how physically consistent the different model decision strategies
are, provides a criterion for distinguishing between models [16]. This consequence of using
XAI techniques goes well beyond the prediction performance obtained by using models such as
ANNs by themselves without any explicability.
Some works have focused on conterfactual explanations, but not many have aimed at time
series. Despite this, conterfactual explanations has become very popular, with more than 100
methods proposed, one of these is the native guide method [17]; this explainability method
defines some key properties of good counterfactual explanations such as proximity, sparsity,
plausibility, and diversity.
Like weather forecasting, with respect to climate prediction at subseasonal, seasonal, and
decadal timescales, empirical statistical models exhibit limited predictive skill due to the complex
and non-stationary nature of the relationship between large scale modes and regional climate.
To address this issue, data-driven ML methods that leverage information from the entire globe
have shown improvements in predictive skill [18]. A number of studies have highlighted the
potential of ANNs in predicting climate across a range of scales because of their ability to
capture nonlinear relations [19], while more recent studies have used XAI methods to explain
these ANNs and their strategies to increase trust and generate new knowledge [20]. Mayer and
Barnes [21] used XAI to show that ANNs can identify when favorable conditions that lead to
enhanced predictive skill of regional climate are present in the atmosphere or not. In a decadal
climate prediction application, Toms et al. [22] used simulated data from climate models to
explore sources of decadal predictability in the climate system. The results showed that there are
several regions where surface temperature is practically unpredictable, whereas there are also
regions of high predictability. Such an analysis could motivate further mechanistic investigation
to physically establish new climate teleconnections, illustrating how XAI methods can help
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
Figure 1: Global schema of the RNN-CBR twin
advance climate science [16]. Further XAI applications have focused on analyzing the impacts
of climate change on the energy consumption in building, explaining the underlying reasons
behind the predictions [23].
3. Method
The main contribution of this paper is the use of CBR for the generation of explanations associ-
ated to the prediction of the ANN. CBR systems are claimed to have a “natural” transparency
as they are based on the reuse of previous experiences or examples. Therefore, we propose a
particular solution for the explanation of the outcomes of the ANN to the experts, where this
opaque, black-box ML system is explained by a more interpretable, white-box CBR system,
following the so-called twin-systems approach [24]. This approach is illustrated in Figure 1,
where the dataset is used as the input of the ANN and to create the explanatory cases pro-
vided by the CBR system. Explanatory cases are generated from the weather series using a
sliding-window method over the whole time series: 𝐶𝑡 = ⟨[𝑡 − 𝑤𝑠, 𝑡], 𝑅𝑡+1 ⟩ where 𝑤𝑠 is the
window size and 𝑅𝑡+1 is the solution of the case, which corresponds to the meteorological
reading for the next day. Analogously, given a query time stamp 𝑡𝑞 , the ANN will predict the
time series values for that date: 𝑃 𝑟𝑒𝑑(𝑡𝑞 ). Then, the query for our CBR system will be the time
window 𝑄 = [𝑡𝑞 − 1 − 𝑤𝑠, 𝑡𝑞 − 1]. Next, the prediction given by the ANN for 𝑡𝑞 is explained
by means of the most similar explanatory cases to the current time window 𝑄, following the
explanation-by-example paradigm illustrated in Figure 1.
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
3.1. Dataset and model
The historical dataset of the meteorological variables was recorded by the Mexican National
Water Council (Comisión Nacional del Agua, CONAGUA) ground station located at the city of
Mérida; among the data provided, the following variables were found, simulating the values that
can be also obtained by the BOSCH BME680 sensor: temperature (T), vapor pressure (P), and
relative humidity (H). The range dates of the records were from January 1, 2000 to September 30,
2018, where there is a daily record of temperatures with minimum, maximum, and average units,
resulting in nine readings provided for each day. A RNN using LSTM cells was trained over
the dataset of time windows and weather labels. 70% of the dataset was used during training,
while the remaining 30% was used for testing purposes. The dataset is then divided into time
windows with 𝑤𝑠 = 14, obtaining explanation cases with 14 days of weather evolution.
3.2. Time windows correlation
Under the assumption that time windows with similar climate will present similar outcomes for
the next days, we could reuse previous time windows to explain new ones in the future, without
the use of an ANN. To do so, we need to define several similarity metrics for the retrieval.
Let us define the Combined Correlation Index (CCI), which provides a way to measure how a
given time window case C is related to a target query window Q:
1
CCI(C, Q) = (𝜌(C, Q) − 2‖(C, Q)‖ + 3), (1)
4
where 𝜌 is the function that calculates the Pearson correlation coefficient, and the double bars
represent the normalized Euclidean distance between those vectors. In our particular case, we
define CCIf as the CCI of a given meteorological feature f (temperature, vapor pressure, or
humidity), Cf represents a fixed window for comparison of different (sliding) windows Qf ,
vectors of 14 values registered daily for the same aforementioned meteorological feature. The
normalized Euclidean distance is simply the Euclidean distance between all possible vectors
(windows) in the time series, but normalized so it is defined in the range [0, 1]. CCI is defined
in the range [0, 1], where higher values indicate a greater similarity between time windows,
and viceversa. The correlation component deals with the morphological similarity of the time
windows, while the Euclidean distance component deals with the proximity between the time
series in the given time windows.
An enhanced CCI can be obtained using the original CCI values, so that:
CCIf + (Cf , Qf ) = (CCIf (Cf , Qf ) + ℎ)2 , (2)
where ℎ corresponds to an “enhancement value” which increases higher CCI values (those over
0.5), while decreasing lower ones. In our paper, since CCI is in the range [0, 1], ℎ = 0.5, and
CCIf + is in the range [0.25, 2.25].
With this in mind, we define the full combined correlation index, FCCI, between two windows
Cf and Qf as the sum of the CCIf + computed for every meteorological feature (humidity,
temperature and vapor pressure: H, T and P, respectively). This is mathematically defined as
follows:
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
Figure 2: threshold being applying to the data.
Figure 3: Results of applying the threshold.
FCCI(Cf , Qf ) = CCIH + (CH , QH ) + CCIT + (CT , QT ) + CCIP + (CP , QP ). (3)
This value can also be normalized, dividing each FCCI result between the highest FCCI en-
countered, therefore FCCI is defined in the range [0, 1].
3.3. Retrieval process
The retrieval process begins with the thresholding of the FCCI values to filter the windows
with the greatest similarity results. To threshold the correlations results we define a minimum
similarity value 𝑠𝑚𝑖𝑛 which was empirically defined a value of 0.7. The values of FCCI for all
the time series are shown in Figure 2, with the 𝑠𝑚𝑖𝑛 threshold overlaid as an horizontal yellow
line. The resulting data after the threshold was applied is shown in Figure 3.
However, the calculated FCCI values yield undesirable high frequency components as shown
in Figure 3. To solve this problem, a low pass filter can be applied over the FCCI time series
to smooth the readings. In our case, we performed a filtering phase which consisted of the
multiple application of a simple moving average filter (MAF). After iteratively applying this
filter until the resulting signal no longer changes, we obtain a smoothed time series for the FFCI.
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
Figure 4: FFCI time series after several filtering iterations. After successive iterations, the time series
converges into a smooth signal.
Smoothed time series can be seen in Figure 4.
The first numerical derivative of this time series is also obtained, helping in the identification
of peaks and valleys in the FFCI, which will be used to segment it into groups of ascending and
decreasing curves to obtain the maximum and minimum values.
The highest FFCI values are used to identify the 𝑘 most similar explanation cases to the
time-window query 𝑄. These are the cases that are presented to the user in order to explain the
prediction given by the ANN model. An example showing the windows of humidity, pressure,
and temperature, for the highest FFCI value with respect to the time-window query, is presented
in the left-hand side of Figure 5. For visual comparison purposes, we also identified the window
corresponding to the lowest FFCI value, and is shown on the right-hand side of this same figure.
Notice how we also included the prediction of the ANN for the 15th day, as well as the real value
of the 15th day, the following value of these two windows for each climate feature, respectively.
4. Evaluation
Even though a visual inspection of the plots of the windows shows an evident difference between
the highest and the lowest FCCIs, respectively, we proposed a quantitative approach to measure
this difference. When a window is retrieved from any of the absolute highest peaks (maximum
or minimum) in the FFCI signal, we calculated the mean absolute error (MAE) between the
ANN prediction for the 𝑡𝑞 date and the actual values in the solution of the case, 𝑅𝑡 , containing
the readings of the day represented by the explanation case, particularly:
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
High FCCI Low FCCI
Humidity
(a) (b)
Vapor Pressure
(c) (d)
Temperature
(e) (f)
Figure 5: Example of explanation through the comparison of meteorological features between the Q
and the most similar explanation case (left column). Right column compares with the most dissimilar
one (right column). Both according to the FFCI time readings).
1 ∑︁
MAE(pred(𝑡𝑞 ), 𝑅𝑡 ) = |pred(𝑡𝑞 )[𝑉 ] − R𝑡 [𝑉 ]|, (4)
|TS|
𝑉 ∈{TS}
where pred(𝑡𝑞 ) is a vector containing the outputs of the ANN for each climate variable 𝑉
represented by the time series TS or the case, concretely: {H, P, T}, representing humidity,
pressure, and temperature, respectively. 𝑅𝑡 is another vector containing the three actual values
of a given time window for each climate feature obtained from the explanation case. We
calculated the MAEs of the 𝑘 = 20 highest and lowest FFCI values, respectively, which are
shown in Table 1.
To determine if the MAEs of the prediction of the ANN against the actual value for each win-
dow corresponding to the highest FCCIs are indeed statistically lower than those corresponding
to the lowest FCCIs, i.e., if there is a high contrast of the central tendencies of both samples
implying that they come from truly distinct populations, we proposed to use the Mann-Whitney
U-test. Also called the Mann-Whitney-Wilcoxon, Wilcoxon rank-sum test or simply U-test [25],
the Mann-Whitney U-test is appropriate for samples which do not follow a normal distribution.
The result of the U-test is the z statistic, which represents a measure of how large the contrast
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
Highest FCCIs Lowest FCCIs
W FCCI MAE W FCCI MAE
6744 1.000 .2923 3996 .4179 .3640
6447 .9500 .2893 1507 .4170 .3982
6388 .9455 .2956 3715 .4170 .4023
6456 .9448 .2936 4685 .4169 .3920
6446 .9380 .3061 3696 .4169 .3909
6104 .9264 .3063 3714 .4163 .3661
6805 .9222 .3118 3246 .4155 .4018
6062 .9211 .2647 14 .4121 .3471
5670 .9204 .2954 1506 .4107 .4454
5781 .9201 .3232 1101 .4105 .3890
1741 .9198 .2888 4011 .4100 .4076
4972 .9198 .2867 3687 .4084 .4004
225 .9195 .3070 3995 .4079 .3385
5825 .9192 .3257 4349 .4030 .3213
5782 .9170 .3302 1099 .4016 .3947
5749 .9170 .3108 3257 .3921 .3761
6410 .9159 .2863 1811 .3840 .3799
5790 .9117 .3262 4809 .3834 .4322
5761 .9105 .2974 3697 .3741 .4167
5762 .9104 .3113 1841 .3521 .3711
Table 1
The values of the 𝑘 = 20 highest and lowest FCCI values, including the corresponding window number
(W) and MAE, according to Equation 4.
between the central tendencies of two samples is [26]. Usually 𝑧 would show a significant
difference to the 0.05 level if it had a value of 1.96 and any greater value corresponds to an even
greater difference. The 𝑧 statistic resulting from comparing both the 20 highest and 20 lowest
values of FCCI was 5.28, showing a clear difference between these two sets.
5. Conclusions
This paper proposes a RNN for weather forecasting of three climatological variables: humidity,
vapor pressure, and temperature. Using 14-day windows extracted from the time series of these
variables, the RNN forecasts the corresponding values for the 15th day. More importantly, we
also propose a XAI CBR-based methodology to illustrate how in similar cases the RNN yields
similar predictions to the actual values of the climatological variables.
The similarity between two different time windows, a query and a fixed case, was calculated
with a proposed index, the FFCI, also proposed in this work, which takes into account both 1)
the Euclidean distance between the time series and 2) their morphological aspect through the
Pearson correlation coefficient.
The 20 cases corresponding to the highest and lowest values of the FCCI, and their respective
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Moisés Fernando Valdez-Ávila et al. ICCBR’22 Workshop Proceedings
15th value, were statistically compared using the Mann-Whitney U-Test, yielding a 𝑧 statistic
of 5.28, well over the 1.96 value commonly associated with a 95% confidence. This means
that the 14-day time period prior to a given date has a clear impact on the forecast of the
climatological variables of the following day. As future work, an optimization method could be
applied to determine the number of days which most affect the forecasting of future variables
of climatological variables.
The main conclusion of this work is that XAI CBR-based techniques can be used to determine
if there is a statistically significant impact of the past values of climatological variables when
trying to forecast future ones. Furthermore, these methodologies could be used to determine
the optimal number of previous days which affect the behavior of climatological variables in
the future. This can eventually help us to better understand complex processes related to the
dynamics of climatology.
Acknowledgments
This research is a result of the Horizon 2020 Future and Emerging Technologies (FET) programme
of the European Union through the iSee project (CHIST-ERA-19-XAI-008, PCI2020-120720-2).
Supported by the BOSCH-UCM Honorary Chair on Artificial Intelligence applied to Internet of
Things of the Universidad Complutense de Madrid. It is also part of projects 10428.21-P and
13933.22-P of the Tecnológico Nacional de México/IT de Mérida.
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