Severe haze or low-visibility events caused by abundant
atmospheric aerosols have become a serious environmental issue in many
countries. A framework based on deep convolutional neural networks
containing more than 20 million parameters called HazeNet has been
developed to forecast the occurrence of such events in two Asian megacities:
Beijing and Shanghai. Trained using time-sequential regional maps of up to
16 meteorological and hydrological variables alongside surface visibility
data over the past 41 years, the machine has achieved a good overall
performance in identifying haze versus non-haze events, and thus their
respective favorable meteorological and hydrological conditions, with a
validation accuracy of 80 % in both the Beijing and Shanghai cases, exceeding
the frequency of non-haze events or no-skill forecasting accuracy, and an F1
score specifically for haze events of nearly 0.5. Its performance is clearly
better during months with high haze frequency, i.e., all months except
dusty April and May in Beijing and from late autumn through all of winter in
Shanghai. Certain valuable knowledge has also obtained from the training,
such as the sensitivity of the machine's performance to the spatial scale of
feature patterns, that could benefit future applications using meteorological
and hydrological data. Furthermore, an unsupervised cluster analysis using
features with a greatly reduced dimensionality produced by the trained
HazeNet has, arguably for the first time, successfully categorized typical
regional meteorological–hydrological regimes alongside local quantities
associated with haze and non-haze events in the two targeted
cities, providing substantial insights to advance our understandings of this
environmental extreme. Interesting similarities in associated weather and
hydrological regimes between haze and false alarm clusters or differences
between haze and missing forecasting clusters have also been revealed,
implying that factors, such as energy-consumption variation and long-range
aerosol transport, could also influence the occurrence of hazes,
even under unfavorable weather conditions.
Introduction
Frequent low-visibility or haze events caused by elevated abundance of
atmospheric aerosols due to fossil fuel and biomass burning have become a
serious environmental issue in many Asian countries in recent decades,
interrupting economic and societal activities and causing human health
issues (e.g., Chan and Yao, 2008; Silva et al., 2013; Lee et al., 2017). For
example, rapid economic development and urbanization in China have caused
various pollution-related health issues, particularly in populated
metropolitan area such as the Beijing–Tianjin region and Yangtze River delta
centered in Shanghai (e.g., Liu et al., 2017). In Singapore, the total economic cost
caused by severe hazes in 2015 is estimated to be USD 510 million (0.17 %
of the GDP) or USD 643.5 million based on a wiling-to-pay analysis (Lin et al.,
2016). To ultimately prevent this detrimental environmental extreme from
happening requires rigid emission control measures in place through
significant changes in energy consumption and land and plantation
management. Before all of these measures can finally take place, it would be
more practical to develop skills to accurately predict the occurrence of
hazes to allow for mitigation measures to be implemented ahead of time.
Severe haze events arise from the solar radiation extinction by aerosols in
the atmosphere; this mechanism can be enhanced with the increase of relative
humidity that enlarges the size of particles (e.g., Kiehl and Briegleb, 1993).
Aerosols also need favorable atmospheric transport and mixing conditions to
reach places away from their immediate source locations, while their
lifetime in the atmosphere can be significantly reduced by rainfall removal.
In addition, soil moisture is also a key to dust emissions. Therefore,
meteorological and hydrological conditions are critical to the occurrence of
haze events in addition to particulate emissions. To forecast the occurrence of
such events using existing atmospheric numerical models developed based on
fluid dynamics and explicit or parameterized representations of physical and
chemical processes, first it is required for the models to accurately predict the
concentration of aerosols at a given geographic location and a given time in
order to correctly derive surface visibility (e.g., Lee et al., 2017, 2018).
However, the propagation of numerical or parameterization errors through the
model integration could easily drift the model away from the original track,
not to mention that a lack of real-time emission data alone would also
handicap such an attempt. Therefore, a more fundamental issue in practice is
whether these models could reproduce the a posteriori distribution of the possible
outcomes of the targeted low-probability extreme events. Ultimately, lack of
knowledge about the extreme events would, in turn, hinder the effort to
improve the forecasting skills.
Differing from the deterministic models, an alternative statistical
prediction approach could be adopted if the predictors of a targeted event
could be identified and a statistical correlation between them could be
established with confidence. However, this is a rather difficult task for
the traditional approaches, because it requires an analysis dealing with a
very large quantity of high-dimensional data to establish and generalize a
likely multi-variate and nonlinear correlation. Nevertheless, such attempts
can obviously benefit now from the fast-growing sectors of machine learning (ML) and
deep-learning (DL) algorithm development (e.g., LeCun et al., 2015). In addition,
technological advancement and continuous investment from governments and
other sectors across the world have led to a rapid increase in quantity
and substantially improved quality of meteorological, oceanic,
hydrological, land, and atmospheric composition data. These data might still
not be sufficient for evaluating and improving certain detailed aspects of
the deterministic forecasting models. However, rich information contained in
these data about favored environmental conditions for the occurrence of
extreme events such as hazes could already have great value for developing
alternative forecasting skills.
Many Earth science applications dealing with meteorological or hydrological
data need a trained machine not only to forecast values but also to recognize
patterns or images. However, this can easily lead to a curse of
dimensionality for many traditional ML algorithms. Fortunately, deep learning
that directly links a large quantity of raw data with targeted outcomes
through deep convolutional neural networks (CNNs) (Goodfellow et al., 2016)
offers a clear advantage in sufficiently training deep networks suitable for
solving highly nonlinear issues. In doing so, DL can also eliminate the
possible mistakes in data derivation or selection introduced by subjective
human opinion regarding a poorly understood phenomenon. Recently, DL
algorithms have been explored in various applications in atmospheric,
climate, and environmental sciences, ranging from recognizing specific
weather patterns (e.g., Liu et al., 2016; Kurth et al., 2018; Lagerquist et al., 2019;
Chattopadhyay et al., 2020), weather forecasting, including hailstorm detection
(e.g., Grover et al., 2016; Shi et al., 2015; Gagne et al., 2019), deriving model
parameterizations (e.g., Jiang et al., 2018), and beyond.
In certain applications, the targeted outcomes are the same features as the
input but at a different time, e.g., a given weather feature(s) such as
temperature or pressure at a given level. The forecasting can thus
proceed by using pattern-to-pattern correlation from a sequential training
dataset with spatial information preserving full CNNs such as U-net
(Ronneberger et al., 2015; Weyn et al., 2020). However, this is certainly not the case
for the applications where the environmental conditions associated with the
targeted outcome are yet known. For such applications, a possible solution
is to utilize a large quantity of raw data with minimized human intervention
in data selection to train a deep CNN to associate targeted outcomes with
favored environmental conditions. This study represents such an attempt,
where a DL forecast framework is trained to identify the meteorological and
hydrological conditions associated with the occurrences of severe hazes. The
DL framework has been developed to be initially targeted at the severe hazes in
Singapore (Wang, 2020) and now hazes in two megacities of China, Beijing
and Shanghai. In terms of particulate pollutant emissions, all of these cities
share certain sources, including fossil fuel combustion from transportation,
domestic, and industries. On the other hand, each city also has its own
unique sources, for instance, desert and perhaps anthropogenic dust for
Beijing and massive biomass burning in Singapore (Liu et al.,
2017; Lee et al., 2017, 2018, 2019). It is obvious that in addition to
meteorological and hydrological conditions, dynamical patterns of
anthropogenic activities leading to the emissions of particulate matters are
also important factors behind the occurrence of severe hazes. Nevertheless,
the major purpose of this study is to advance our fundamental knowledge
about the weather conditions favoring the occurrence of hazes and, through
an in-depth analysis on the forecasting results, to identify the limit of
such a machine and thus to provide useful information for establishing a
more complete forecasting platform for the task.
In the paper, the architecture involved, as well as the method and data used for training, are
described after this introduction, followed by a discussion of
training and validation results. Following this, an unsupervised cluster analysis that
benefited from the trained machine is introduced along with its results, which
further the understanding of the CNN's performance and summarize, for the
first time, the various typical meteorological and hydrological regimes
associated with haze versus non-haze situations in the two cities. The last
section concludes the effort and provides its major findings.
Network architecture, training methodology, and dataNetwork architecture
The convolutional neural network used in this study, the HazeNet (Wang,
2020), has been developed by adopting the general architecture of the CNN
developed by the Oxford University's Visual Geometry Group (VGG-Net)
(Simonyan and Zisserman, 2015). The actual structure and
hyper-parameters of HazeNet have been adjusted and fine-tuned based on
numerous test training runs. In addition, certain techniques that were not
available when the original VGG net was developed, e.g., batch normalization
(Ioffe and Szegedy, 2015), have been included as well. The current version
for haze applications of Beijing and Shanghai, though trained separately,
contains the same number of parameters, 20 507 161 (11 376 non-trainable),
owing to it having the same optimized kernel sizes. Figure 1 shows the general
architecture of a HazeNet version with 12 convolutional and 4 dense layers
(in total 57 layers).
Architecture of the 12 convolutional plus 4 dense layers of
HazeNet. Here “Conv” represents a unit containing zero padding and then a 2D
convolutional layer, followed by a batch normalization layer. There is a
flattened layer before the two dense layers. W stands for width, H stands for height, and N stands for the number of features of the input fields (i.e., 64, 96, and 16 for
Beijing and 64, 64, and 16 for Shanghai.
The network has been trained in a standard supervised learning procedure for
classification, where the network takes input features to produce
classification output that are then compared with known results or labels
based on observations. The coefficients of the network are thereafter
optimized in order to minimize the error between the prediction and the
observation or label. The loss function used in optimization is
cross-entropy (e.g., Goodfellow et al., 2017). Such a procedure is repeated until
the performance of the network can no longer be improved. In practice, the
training usually lasts about 2000 epochs (each epoch is a training cycle
that uses up the entire training dataset). This procedure is intended to
train a deep CNN to recognize and then associate input features (bundled
meteorological and hydrological conditions in this case) with a corresponding
class, i.e., severe haze events or non-haze events. As a result, the specific knowledge
about the favored meteorological and hydrological conditions
of severe hazes can thus be advanced.
Training data and methodology
The labels for the training are derived using the observed daily surface
visibility (hereafter referred to as “VIS”) obtained from the Global Surface Summary Of the
Day (GSOD) dataset consisting of daily observations of meteorological
conditions from tens of thousands of airports around the globe (Smith et al.,
2011). In the cases of Beijing and Shanghai, data are from observations in the
corresponding airports of these two cities during the time from 1979 to
2019, containing 14 975 samples. For simplicity, the discussions will be
mainly about the two-class training, where events with VIS ≤ the long-term
mean value of the 25th percentile or p25 of VIS (6.27 km in Beijing, 5.95 km in Shanghai; Fig. 2b; see also Fig. S1 in the Supplement) are
defined as class 1 or severe haze and events are otherwise classified as class 0 or non-haze cases.
Although p25 values vary interannually, their long-term means represent a
substantial reduction of VIS due to high particulate pollution (e.g., Lee et al.,
2017). Note that unlike in the case of Singapore (Wang, 2020), fog and mist
are more common low-visibility events in Beijing and Shanghai and thus have
been excluded from the labels of severe hazes by following GSOD fog marks.
The number of severe haze events that occurred during 1979–2019 defined in the
above procedure is 3099 and 2999 for Beijing and Shanghai, indicating a frequency
of 20.7 % and 20.0 %, respectively.
(a) The input feature defining domains for Beijing
(red box and dot, 32.25–48∘ N, 99.25–123∘ E; 64×96 grids with ERA5 data) and
Shanghai (white box and dot, 26–41.25∘ N, 109.25–125∘ E; 64×64 grids), made
using the Basemap library (a Matplotlib extension). (b) Annual means (solid
curves), 25th percentiles (dashed curves), and 25th percentile means
(solid straight lines) of surface visibility in Beijing (red) and Shanghai
(blue) between 1979 and 2019.
The training and validation of HazeNet also need the input features with the
same sample dimension of the labels. These input data are derived from
hourly maps of meteorological and hydrological variables covering the data
collection domain (Fig. 2a), obtained from ERA5 reanalysis data
produced by the European Centre for Medium-range Weather Forecasts or ECMWF
(Hersbach et al., 2020). These data are distributed in a grid system with a
horizontal spatial interval of 0.25∘. Up to 16 features are derived
from the original hourly data fields covering the analysis domain
for Beijing (64×96 grids) and Shanghai (64×64 grids),
including daily mean of surface relative humidity (REL), daytime change and daily standard deviation of 2 m temperature (DT2M
and T2MS, respectively), daily mean of 10 m zonal and meridional wind
speed (U10 and V10, respectively), daily mean of total column water (TCW),
daily mean (TCV) and daytime change (DTCV) of total column water vapor,
daily mean of planetary boundary layer height (BLH), daily mean soil water
volume in soil layer 1 and 2 (SW1 and SW2, respectively), daily mean of
total cloud cover (TCC), daily mean geopotential heights at 500 (Z500) and
850 (Z850) hPa pressure levels and their daytime changes (D500 and
D850, respectively). All input features have been normalized into a range of
[-1, +1] (Fig. S2 in the Supplement).
Before the training, the entire samples of labels alongside corresponding
input features were randomly shuffled first then split in the following way: two-thirds of the
samples went to the training set, and one-third of the
samples went to the validation set, each is duly used
for its designated purpose throughout the entire training process without
switching. The above procedure treats each event as an independent sample. For
the convenience of being able to compare performance or restart training based on a
saved machine, a saved training dataset and a holdout validation
dataset that has never been used in training were produced following the
above procedure and used for the purpose.
The number of samples used in training HazeNet is rather limited compared to deep-learning standards. However, to associate 16 joint two-dimensional maps with
targeted labels even with the current number of samples is still a demanding
task that requires a deep CCN to accomplish. Furthermore, the targeted severe hazes
are low-probability events. Their frequency of appearance is about 20 % in the
Beijing and Shanghai cases. Therefore, a trained machine would easily bias
toward the overwhelming non-haze events. To resolve these issues, a
combination of class weight and batch normalization has been implemented in
HazeNet, which both use corresponding Keras functions. The class weight is used to
change the weight of training loss of each class, normally by increasing the
weight of the low-frequency class. The class weight coefficient was calculated
based on the ratio of class 0 to class 1 frequency. Batch normalization
(Ioffe and Szegedy, 2015) is an algorithm to renormalize the input
distribution at certain step (e.g., for each mini batch) to eliminate the shift
of such distributions during optimization. The above approaches have
effectively reduced the overfitting while overcoming the data imbalance issue,
making the long training of a deep CNN possible (Wang, 2020). Entire
training events have been conducted using a NVIDIA Tesla V100-SXM2 GPU cluster,
costing 25 and 17 s per epoch for the machines in Beijing and Shanghai,
respectively.
Kernel size optimization
As in the cases of other CNNs, there are many hyperparameters of HazeNet that
need to be determined or optimized. These have been done through numerous
testing training events. In practice, the deep architecture of
HazeNet and the long training procedure have actually made the performance
less sensitive to many hyperparameters of the network. One hyperparameter,
however, is specifically interesting to explore in its application using a
large quantity of meteorological maps, i.e., the kernel size of the first
convolutional layer, where the input data (meteorological and hydrological
maps) are convoluted and then propagated into the subsequent layers.
(a, d) Weight coefficients of the first filter set
(WN,1), (b, e) partial output for each feature (ZN,1),
and (c, f) the output (Z) of the first convolution layer
(CONV2d_1) with two selected kernel sizes (ks): (a–c)20×20 and (d–f)3×3. Here W represents the filters and Z the
output of convolution; the subsets of Z before the feature dimension is
merged can be expressed as ZN,i=WN,iks,ks⋅fNTks,ks, with the order of input
features N=1, … 16 and i representing the convolutional layer
index, i.e., 1 is the first layer or CONV2d_1. For the first
layer, input feature size is (h,w)=(64,64), the set of filters is 92, and
thus the final output Z has a dimension of (h-ks+1, w-ks+1, 92). Shown are the
results from the training for Shanghai haze cases.
Meteorological maps or images often contain characteristic patterns with
different spatial scales. Intuitively, preserving these patterns could be
important in predicting the targeted extremes. Apparently, a larger kernel
size produces smoother output images from the first convolutional layer,
while a smaller kernel size can preserve many spatial details of the
meteorological maps, as demonstrated by the layer output shown in Fig. 3.
In practice, however, the patterns produced by the latter configuration
might be too complicated for the networks to recognize and to perform
classification, whereas patterns resulting from a relatively larger kernel
size for the first convolutional layer might be more suitable for the task.
The actual result suggests that HazeNet configured with a first-layer kernel
size of 20 to 26 or close to 5–6∘ in spatial resolution
consistently produces a better performance (about a 10 % improvement in
F1 score) than that using a smaller kernel size of 3 or 6. As a result, a kernel size
of 20 has been adopted as the default configuration for the first two
convolutional layers in this study.
Training and validation results of haze forecasting
Currently, it is still difficult to find any practical score for forecasting
the occurrence of severe hazes for comparison. Therefore, the performance of
HazeNet has mainly been measured by using certain commonly adopted metrics
for classification that are largely derived from the concept of the so-called
confusion matrix (e.g., Swets, 1988; Table A1), including accuracy, precision, recall, F1 score, equitable threat score (ETS), and
Heidke skill score (HSS) (Appendix A). Unless otherwise indicated, the discussions on the
performance scores are hereafter referring to the severe haze class (or
class 1) and are obtained from validation rather than training. In all the
cases, the performance metrics referring to non-haze or class 0 have much
better scores. Also note that, unless otherwise indicated, results shown in
this Section are obtained using 16 features.
(a, b) Validation accuracy (a) and loss (b) of HazeNet with 16 features for the Beijing and Shanghai cases; kernel
size for the first filter is 20×20. (c, d) Prediction outcomes in
reference to haze events (or class 1) of Beijing and Shanghai with 16
features. TP stands for true positive, TN stands for true negative, FP stands for false
positive, and FN stands for false negative prediction outcomes. (e) Scores of performance metrics shown as means over the last 100 epochs for Beijing and
Shanghai with 16 and 9 features, respectively.
In order to train a stable machine, training events with 2000 epochs or longer
have been conducted instead of using certain commonly adopted skills such as
early stop. As a result, the validation performance metrics of the trained
machines all appeared to be stabilized by approaching the end of training
(Fig. 4). These scores were consistent with the results of ensemble training
with the same configuration but different randomly selected training and
validation datasets and were also comparable among training events with different
configurations. Overfitting has been clearly overcome due to such a long
training procedure and the adoption of class weight and batch
normalization. In a two-class classification (haze versus non-haze), trained deep
HazeNet can always reach an almost perfect training accuracy (e.g., 0.9956 for
Beijing cases) and a validation accuracy of 80 % (frequency of non-haze
events or no-skill forecasting accuracy) in both Beijing and Shanghai cases
(Fig. 4a). At the same time, the performance scores for predicting
specifically severe hazes are also very reasonable, e.g., for Beijing cases
either precision or recall exceeds 0.5 (they normally evolve in opposite
directions), leading to a nearly 0.5 F1 score (Fig. 4c–e). The corresponding
scores in training are obviously much higher, e.g., with precision, recall, and
F1 as 0.9804, 0.9980, and 0.9880, respectively for Beijing cases, owing to
the deep and thus powerful CNNs. HazeNet performed slightly better than
several known deep CNNs, such as Inception Net V3 (Szegedy et al., 2015), ResNet50
(He et al., 2015), and VGG-19 (Simonyan and Zisserman, 2015), for the same haze
forecasting task (Wang, 2020). Nevertheless, as indicated previously, a
nearly perfect validation performance is not realistic since meteorological
and hydrological conditions are not the only factors behind the occurrence
of haze events.
(a) Monthly counts of predicted TP, FP, and FN outcomes
and (b) performance scores for each month. All results are taken from validation of
Beijing cases with 16 features.
Looking into the specific prediction outcomes in reference to severe haze,
the trained machine has produced a considerably higher ratio of true positive
(TP) outcomes than in the Southeast Asian cases (Wang, 2020) despite a
number of outcomes of false positive (FP, i.e., false alarm) and false
negative (FN, i.e., missing forecast). In forecasting the severe hazes in
Beijing, the trained machine performs reasonably well throughout all months
except for April and May (the major dusty season), producing an F1
score, ETS, and HSS that all exceed or are near 0.5, as well as the number of TP
outcomes higher than that of FN outcomes (Fig. 5). HazeNet actually performs
better in months with more observed haze events. For Beijing, the lowest
haze season is during the dusty April and May when all the major performance
metrics are lower than 0.4, and the machine produces more missing forecasts
than true positive outcomes. The relatively poor performance in spring
suggests that the weather and hydrological features associated with
dust-dominated haze events during this period might differ from the
situations in the other seasons when hazes are mainly caused by local
particulate pollution. For Shanghai cases, HazeNet performs better during
late autumn and all of winter (from November to February) when haze occurs
most frequently (not shown). The worst performance comes from the monsoon
season (July to October), the season with the fewest haze cases.
Reducing the number of input features
One recognized advantage of
deep CNN in practice is its capacity to directly link the targeted outcome
with a large quantity of raw data and thus avoid human misjudgment in selecting
and abstracting input features due to a lack of knowledge about the
application task. Nevertheless, for an application such as this one that
uses a large number of meteorological and hydrological variables (or
channels in machine learning terms), reducing the number of input features
with a minimal influence on the performance can still benefit the efforts
to establishing physical or dynamical causal relations and other features.
There are certain available methods to rank features and then reduce those found to be
unimportant. These do not work straightforwardly for deep CNNs (e.g.,
McGovern et al., 2019). In previous efforts, this has been done by testing the
sensitivity of the full network performance in real training with either a
single feature only or all but one feature (Wang, 2020), which apparently
is also a demanding task. Here, another attempt has been made to use a
trained (then saved) machine to examine the sensitivity of the network to
various features (Appendix B).
The sensitivity analyses using trained machines for Beijing and Shanghai
have obtained largely consistent results, indicating that the network is
more sensitive to the same nine features compared to the other seven (Fig. S3). However, the
highest-ranking features differ, with daytime change of column vapor
(DTCV) and soil water content in the second soil layer (SW2) as the most
sensitive features for Beijing, while relative humidity (REL) and planetary
boundary layer height (BLH) are the most sensitive for Shanghai. Most importantly, training events using
only the top nine most sensitive features have produced a performance
equivalent to or even better than the same training event with 16 features
(Fig. 4e). With a reduced number of features, many further
analyses can be conducted with lower workload that produce results that are
easily understood.
Identifying and categorizing the typical regional meteorological
and hydrological regimes associated with haze events
A major purpose of this study is to identify the meteorological and
hydrological conditions favoring the occurrence of severe hazes in the
targeted cities. When using a dataset with a large number of samples, this
type of analyses could be better accomplished by applying, e.g., cluster
analysis (e.g., Steinhaus, 1957), a standard unsupervised ML algorithm that
groups data samples into various clusters in such a way that samples in the
same cluster are more similar to each other than to those in other clusters.
Specifically for this study, the derived clusters would likely represent
various regimes in terms of combined meteorological and hydrological
conditions for associated events. However, applying cluster analysis
directly to a large number of samples, each with a feature volume of
∼50000, is not an easy task. A dimensionality reduction is
apparently needed to reduce the feature volume of data.
In practice, a trained CNN is actually an excellent tool for this purpose.
It encodes (downscales) the input with large feature volume into data with a
much smaller size in the so-called latent space (i.e., the output of the layer
before the output layer of the CNN) but equal predictability for the targeted events.
This functionality of CNN has been used in developing various generative DL
algorithms from variational autoencoders (VAEs) to different generative
adversarial networks (GANs) (e.g., Forest, 2019). Therefore, the trained
HazeNet for Beijing and Shanghai using 9 instead of 16 features, which benefited
from the effort of reducing the number of input features as described at the
end of Sect. 3, have been used here to produce data with reduced size
suitable for clustering (Fig. 6; see also Appendix C). The new
sample feature set with a size of 14975×512 produced from this
procedure was then used in cluster analysis.
A diagram of the cluster analysis procedure. Here 96, 64,
and 9 represent the number of longitudinal grids, latitudinal grids, and
features (variables) or the size of the input feature volume of a trained
HazeNet for Beijing cases, respectively, while 512 is the size of the output from the
dense layer before the output layer of HazeNet or the size of new feature volume.
In order to provide useful information for understanding the performance of
the trained networks, the clustering has been performed for each of the
prediction outcomes rather than just haze versus non-haze events (Appendix C). In this configuration, haze-associated regimes are represented by
derived clusters of TP plus FN outcomes, while non-haze regimes are represented by clusters of
TN plus FP outcomes. Since the clusters were derived using the indices of samples as
the record for members, the actual feature maps of the members in any
cluster can thus be conveniently retrieved and used to identify the
representative regimes in terms of combined nine meteorological and
hydrological features. Here the clustering results have been analyzed using
the feature maps in both normalized (machine native) and unnormalized
(original reanalysis data) format. The characteristics of various regimes
can be easily identified from the former as they represent anomalies to
climatological means. An added benefit is to advance the understanding of
the performance of the trained networks. The analysis using the latter maps
aims to better appreciate the conventional regional and local meteorological
and hydrological patterns associated with various regimes. The feature maps
used in both analyses have been averaged across each cluster for clarity.
Maps of the nine features in a normalized format for four clusters of
true positive (TP) outcomes, three clusters of false negative (FN) outcomes, and
four clusters of false positive (FP) outcomes. Here, TP plus FN covers haze events.
Results shown are cluster averages for Beijing cases (location marked by navy dot).
Results based on normalized feature maps
As shown in Fig. 7, the four clusters of true positive (TP) cases in Beijing
exhibit a clear similarity in general feature patterns closely surrounding
Beijing (marked by a navy dot in the Fig. 7). These common
patterns include an isolated small positive relative humidity (REL) center
covering Beijing, associated with mild daytime change (DT2M) and
standard deviation (T2MS) of surface temperature and zonal wind
(U10) and a lower boundary layer height (BLH). Weatherwise, Beijing and its
immediate surrounding area appear to be located between two sharply
different air masses occupying the northwestern and southeastern
part of the domain, respectively (weather systems usually progress from northwest to
southeast in this region). When relating this to the other feature
characteristics, it is likely that Beijing and its nearby area do not
experience a drastic weather system change such as a front when haze
occurs; hence, the high REL – a critical condition for aerosol to effectively
scatter sunlight – can be easily formed, aided by a stable boundary layer
with mild surface wind to allow aerosols to be well mixed vertically near
the ground without being significantly reduced through advection
diffusion. In addition, relatively high soil water content could fuel the
humidity in the air, and thin while stable low clouds, if present (judged
based on temperature change), could signal a lack of persistent
precipitation. Altogether, these conditions apparently allow the haze to
easily form, persist, and effectively scatter sunlight, thus reducing
visibility. These conditions are also noticeably contrast with those
associated with non-haze events represented by TN outcomes (Fig. S4).
Note that as each cluster consists of a collection of 3D data volumes or
images, any two clusters could be sufficiently differentiated should only
one of their images differ based on the clustering derivation algorithm,
even though statistically speaking, they very likely belong to the same
population (i.e., should be tested statistically). As shown in Fig. 7, the
distinctions between TP clusters are largely reflected by the two
different air masses distant from Beijing in both strength and spatial
extent, particularly from DTCV patterns, likely representing different types
of systems or background regimes. Specifically, a strong DTCV anomalous
center seen in the cluster 1 and 4 patterns occupies most of the domain west of
Beijing and directly influences Beijing and its nearby area. In contrast,
DTCV distributions in cluster 2 and 3 are much weaker, where Beijing and its
immediate neighboring area even appear to be more influenced by the
southeastern system. In addition, surface wind distributions of the first two
clusters clearly differ from those of cluster 3 and 4, and the patterns of
BLH alongside SW1 and SW2 over Beijing and its immediate neighboring area of
cluster 3 also suggest a land–atmosphere exchange condition differing from
that of others. The combinations of these differences across various TP
clusters apparently clearly define the various regimes of surrounding weather
systems and their influence on Beijing. For the TP clusters of Shanghai,
the above similarities and differences among various clusters also
exist, except that clusters 1, 2, and 4 maintain more similarities in their
feature patterns of distant air masses from Shanghai, while cluster 3 offers
certain evident diversity in many feature patterns compared to other
clusters (Fig. S5). Even more interestingly, the distribution of the number
of members within various TP clusters evidently does not differ in different
months (Table S1) (note that the number of haze events itself differs
seasonally; see Fig. 5). Therefore, it is very likely that the characteristic
weather conditions favoring haze occurrence and being captured by HazeNet
cannot be simply differentiated by location (Beijing versus Shanghai) and
season.
On the other hand, among three FN clusters (also associated with haze events
but missed in prediction), only the first cluster (the major cluster of FN)
displays certain similarity to TP clusters across various features. Even for
this cluster, the characters of the air masses distantly surrounding Beijing
differ substantially from those of TP clusters, as seen from the patterns of
temperature (DT2M, T2SM), wind (particularly V10), and column water (DTCV)
that reflect a much weaker weather system to the west. The patterns of BLH,
SW1, and SW2 also differ from those of TP, indicating a different near-site
boundary layer and hydrological condition. Such differences appear to be
even more evident in the two other (minor) clusters, e.g., the size and
strength of high relative humidity center covering Beijing are even more
different. This result suggests a possible reason for HazeNet's inaccurate
forecasting of these haze events, i.e., that haze might occur under unfavorable
weather and hydrological conditions owing to, e.g., certain energy-consumption
scenarios. Again, the distribution of members of these latter two clusters
does not exhibit clear seasonality (Table S1). Interestingly, first two of
the four FP clusters display more a clear similarity in their
normalized feature patterns to those of TP than FN in Beijing and its
immediate surrounding area (Fig. 7). As in FN cases, however, two other
clusters differ more evidently. All of these could explain the false alarms reported by the machine, i.e., the machine could have simply been confused by such
similarities between certain TP and FP members. Nevertheless, these could
also suggest an alternative reason behind the incorrect forecasts, i.e., that
certain pollution mitigation measures could have been in place. The results
of FP clusters and the last FN cluster reported alongside a TP for Shanghai cases also
share some similar characteristics as analyzed here (Figs. S5 and S6).
Therefore, it is worth indicating again that meteorological or hydrological
conditions are not the only factors determining the occurrence of hazes.
Other factors such as abnormal energy-consumption events or long-range
transport of aerosols could all cause haze to occur even under unfavorable
weather and hydrological conditions. This could well be the reason for some
of the missing forecasts (FN outcomes) when haze occurred under unfavorable
conditions, as suggested above, or for false alarms (FP outcomes) when low-aerosol events occurred even under a weather condition favorable to haze.
Future improvement of the measurement skill could benefit from this knowledge.
Results based on original unnormalized feature maps
Utilizing feature maps in their original unnormalized format represented by
actual physical quantities could provide a convenient way to appreciate the
conventional regional and local meteorological and hydrological patterns
and implement additional analysis, if necessary, of the
possible impact of seasonality or trends associated with various events. Note
that the visual differences between unnormalized feature maps, particularly
in cluster mean format, might be too subtle for the naked eye to recognize.
Feature maps associated with severe haze events in
Beijing represented by four clusters of TP-predicted outcomes (four top rows) and three clusters of FN-predicted outcomes (three
lower rows). Shown are cluster means of unnormalized data
of relative humidity (REL) (ratio), daytime change (DT2M), and daily
standard deviation (T2MS) of 2 m temperature (degrees), 10 m winds
U10 and V10 (m/s), daytime change of column water vapor or DTCV
(kg/m2), planetary boundary height (BLH) (m), and soil water
content in soil level 1 (SW1) and level 2 (SW2) (kg/m2).
For haze events in Beijing (i.e., TP and FN outcomes; Fig. 8), the associated
cluster mean regional meteorological and hydrological patterns of most
features except DTCV contain two regions with sharply contrasting
quantities, roughly separated by a line linking the southwest and northeast
corner of the domain, likely due to the typical progression direction of
weather systems in this region aside from a meridional variation of general
climate. In comparison, the as same as is shown in the previous analysis using
normalized feature maps, the patterns of the first FN cluster share many
characteristics with those of TP clusters. The differences among TP and FN
clusters are more evident in DTCV (specifically cluster 1 and 4 versus
cluster 2 and 3), SW1, SW2, and surface winds, particularly for the second
and third FN clusters. FP clusters also display a similarity to those of
TP clusters (Fig. S7), whereas TN clusters show more visible differences,
particularly in patterns of meridional wind (V10) and daily change of column
water vapor or DTCV (Fig. S8).
The general regional meteorological and hydrological conditions during haze
events in the southeastern portion, in contrast to the northwestern portion of the
domain, include a higher relative humidity, lower variation of surface
temperature, largely northward or northwestward wind, lower planetary
boundary layer height, and higher soil water content, and quantity wise
these are all in sharp contrast to the situation in the other half of the
domain. Based on the surface wind direction, Beijing and its immediate
surrounding area is clearly located between two air masses that both feature
anticyclonic surface winds. The strengths of these two centers differ,
particularly in the last two FN clusters, implying regimes with systems
that have different strengths or that are in different development phases. Such a
difference is also clearly related to the visually recognizable
cross-cluster difference in DTCV patterns, represented by a strong negative
center in the middle of the domain with varying extent and strength across
different clusters. Consistent with the analysis result using normalized
feature maps, all of these indicate a stable weather condition over Beijing and
its neighboring area during haze events while surrounded by two (or more)
different weather systems. It is known that dust can cause low-visibility
events in Beijing. During dust seasons, the condition of the northwestern
half of the domain, represented by a dominant eastward wind and lower soil
water content, likely favors dust transport from desert to Beijing. However,
the details would need an in-depth analysis since most clusters
have members that are rather well distributed through different months (Table S1).
Cluster means of features associated with haze events (TP
and FN) in Beijing and Shanghai versus means of all clusters of non-haze
events of TN and FP. The number of cluster members in each cluster
is listed in parentheses.
The cluster means of nine features for haze events (TP plus FN) versus non-haze
(TN plus FP) at the grid point of Beijing are also derived and listed in
Table 1 for reference. Specifically, the common local conditions associated
with hazes in Beijing in comparison to those with non-haze events include a
higher humidity, less drastic variations in surface temperature, a
northwestward rather than southeastward wind, a lower planetary boundary
layer height, and higher soil water content. Again, the most recognizable
cross-cluster differences appear in DTCV (i.e., cluster 1 versus others),
followed by surface wind (cluster 1 and 2 versus 3 and 4). In most of the
local features, variabilities of FN clusters tend to be larger than those of
TP clusters. Notably, such differences in local feature quantities for FN
clusters are not necessarily more evident than in the regional maps over
distant air masses. One interesting result of the local weather conditions
shown in Table 1 is that the cluster means of TN are sharply different to
those of TP and FN, while the cluster means of FP and those of TP + FN are
likely to be statistically indifferent outside of DTCV, providing
evidence to support the assumption that FP outcomes might simply represent
the non-haze events caused by reasons other than weather and hydrological
conditions.
The same as Fig. 8 except for Shanghai with four clusters
for TP outcomes and three clusters for FN outcomes.
For the case of Shanghai, the general weather conditions associated with
haze events are likely stable, with characters similar to the cases of
Beijing, except that Shanghai appears to be located between a northwest
air mass with anticyclonic surface wind and a southeast air mass with cyclonic
wind (Fig. 9). Quantities of most feature patterns display a sharply
southeast versus northwest contrast. DTCV maps display a negative center
over a large area, its distribution and extent vary significantly among
different clusters in particular for the first two FN clusters. The patterns
of soil water content in both soil layers exhibit a sharp meridional
contrast that is much higher in the southern part of the domain than in the northern
part, areas largely separated by the Yellow River. Local quantities of all the
features associated with haze events (TP plus FN) in Shanghai display clear
differences with those of non-haze prediction outcomes (TN) (Table 1). The
most recognizable cross-cluster differences for TP appear in U10 of cluster 4 and V10 of cluster 3, differing from the cases of Beijing, and DTCV
(particularly for cluster 3) for FN. Like the cases of Beijing, the cluster
mean of the FP outcomes is not statistically different to that of haze (TP
and FN) when compared to predicted non-haze (TN) events. Again, this result implies that
even when a weather pattern favoring haze appeared and was correctly recognized
by HazeNet, haze
still could not to occur due to other factors such as energy-consumption variations.
It is worth indicating that the current analysis discussed here is only
applied to the included features of clustering, and the presented figures in
cluster-wise averaging format might have effectively smoothed out certain
variability among members. A full-scale analysis would necessarily go beyond
this to provide further synoptical or large-scale hydrological insights and
better define different regimes.
Summary and conclusions
Following an earlier preliminary attempt at forecasting haze in Singapore,
a deep convolutional neural network containing more than 20 million
parameters, HazeNet, has been further developed to test forecasting of
the occurrence of severe haze events during 1979–2019 in two metropolitan areas
in Asia, Beijing and Shanghai. By training the machine to recognize regional
patterns of meteorological and hydrological features associated with haze
events, the study advances our knowledge about this still poorly known
environmental extreme. The deep CNN has been trained in a supervised
learning procedure using time-sequential maps of up to 16 meteorological
and hydrological variables or features as inputs and surface visibility
observations as the labels.
Even with a rather limited sample size (14 975), the trained machine has
displayed a reasonable performance measured by commonly adopted validation
metrics. Its performance is clearly better during months with high haze
frequency, i.e., all months except dusty April and May in Beijing and from late
autumn through all of winter in Shanghai. Relatively large spatial patterns
appear to be more effective than the smaller ones for influencing the
performance of forecasting. On the other hand, in-depth analysis of
performance results has also indicated certain limitations of the current
approach of solely using meteorological and hydrological data in performing
forecasts.
The trained machine has also been used to examine the sensitivity of the CNN
to various input features and thus to identify and then remove features
ineffective to the performance of the machine. In addition, to further
categorize typical regional weather and hydrological patterns associated
with severe haze versus non-haze events, an unsupervised cluster analysis
has been subsequently conducted and has benefited from using features with greatly
reduced dimensionality produced by using the trained machine.
The cluster analysis has, arguably for the first time, successfully
categorized major regional meteorological and hydrological patterns
associated with severe haze and non-haze events in Beijing and Shanghai into
a limited number of representative groups, with the typical feature patterns
of these clustered groups derived. It has been found that the typical
weather and hydrological regimes of haze events in Beijing and Shanghai are
rather stable conditions represented by anomalously high relative humidity,
low planetary boundary layer height, and mild daily temperature change that are
likely associated with a thin low cloud cover over the haze-occurring
regions. The result has further revealed rather strong similarities in
associated meteorological and hydrological regimes between haze and false
alarm clusters and differences between haze and missing forecasting
clusters, implying that factors such as energy-consumption variations, long-range transport of aerosols could influence the occurrence of
hazes even under unfavorable weather conditions.
Due to the exploratory nature of this specific effort, several aspects could
be further optimized, including the rather arbitrary though statistically
meaningful labeling. In addition, an in-depth analysis of weather regimes would
necessarily involve the use of certain features that are not included in the
current clustering; however, this exceeds the extent of this paper and can
only be discussed properly in a future work. Nevertheless, this study has
demonstrated the potential of applying deep CNNs with extensive
multi-dimensional and time-sequential environmental images to advance our
understanding of poorly known environmental and weather extremes. Using this
methodology, the results and experience obtained from this study could
benefit future improvement efforts regarding these skills. Aside from this use, the trained machines can
be used in many other types of machine learning and deep-learning
applications, as has been partially demonstrated here.
Performance metrics
Several commonly used performance metrics have been used in this study. They
are largely derived based on the so-called confusion matrix (Swets, 1988) as
defined in the following Table A1.
Here, “positive” or “negative” is referring to the outcome of a given event or class in the
classification, e.g., severe haze or non-haze events. Hence, the prediction
outcome TP is a correct forecast of a severe haze, while TN is a correct
forecast of a non-haze event, FP represents a false alarm, and FN represents a missing
forecast. The context of outcomes changes when the designated class is
switched. The major performance metrics used in this paper include
A1accuracy=TP+TNN,A2precision=TPTP+FP,A3recall=TPTP+FN,A4F1 score=2⋅precision⋅recallprecision+recall,ETS=TP-HitrandomTP+FP+FN-Hitrandom,
where
Hitrandom=TP+FN⋅TP+FPN,HSS=2⋅TP⋅TN-FP⋅FNTP+FP⋅FP+TN+TP+FN⋅TP+TN.
Here, F1 score is the F score with β=1 (van Rijsbergen, 1974), ETS
represents equitable threat score (or Gilbert skill score; Gilbert, 1884;
range =[-1/3,1]), HSS represents Heidke skill score (Heidke, 1926; range
=[-∞,1]), and N is the number of total outcomes. Note that
“accuracy” has the same value for all the classes and thus is a good metric for the
overall classification. The values of all the other metrics differ depending on
the referred class.
Confusion matrix for measuring the prediction outcomes of
a given class.
ObservedPositiveNegativePredictedPositiveTrue positive or TPFalse positive or FPNegativeFalse negative or FNTrue negative or TNExamining the network's sensitivity to features using
trained machine
A method has been adopted in this study to use a trained machine to examine
the sensitivity of the network to a random perturbation applied to the
values of different features. The saved machine contains all the
coefficients in different network layers and can be used to predict output
from any of these layers using the same input features for training or
validation. The sensitivity of the network to a given feature is determined
by comparing the prediction using input feature maps containing random
perturbation applied to the map of this feature with the prediction using
original input feature maps. The sensitivity is measured by the content loss
between these two predictions, with img1 with M×N pixels as the unperturbed and img2 as
perturbed network output:
content loss=1M×N∑i,jM,N(img1i,j-img2i,j)2.
The perturbation is applied as random patches with the addition of -0.2 or 0.2
to 10 % of the pixels of the input map of the targeted feature in each
sample, while maps of all the other features remain unperturbed. To reduce
the workload, only the validation input set corresponding to the class 1 events
(about 1020 samples) is used. Therefore, the sensitivity tested here is
actually the sensitivity of the network to a given feature in predicting
class 1 events. To preserve the spatial information of the perturbed field,
the output of the 9th layer, or the “MaxPooling” layer following the
second convolutional layer (Fig. 1), is used as the prediction. It has a size
of (15, 31, 92) for Beijing cases and (15, 15, 92) for Shanghai cases when a
kernel size of 20×20 is adopted. A higher content loss resulting from Eq. (B1)
represents a higher sensitivity.
Cluster analysis
The cluster analysis of this study was conducted in the following three
steps (see also Fig. 6).
Firstly, the trained and saved HazeNet for both the Beijing and
Shanghai cases with nine input features have been used to perform prediction
using the entire 14 975 input samples in the original raw data format, i.e., with a
feature volume size of 64×96×9 for Beijing and 64×64×9 for Shanghai for each
sample. The prediction results were then summarized into various outcomes,
i.e., as true positive (TP), true negative (TN), false positive (FP), or false
negative (FN), in referring to the haze class. In the meantime, the output of
the second dense layer just before the output layer or the latent space (see
Figs. 1 and 6) was further used to form a new data of each sample with
a reduced feature volume of 512. This new dataset, with a size of 14 975 by
512, was then ready for clustering.
The second step is to perform clustering using the new dataset
with reduced size resulting from the previous step. For this purpose, it
should be conducted separately for different types of samples or events,
e.g., categorizing all the samples for haze into characteristic groups with
similarities and identical features, and the same for all samples of non-haze events. In order to provide additional
information to further the understanding of the network's performance, the
clustering was actually conducted for different prediction outcomes, by
taking corresponding samples from the new dataset. In this case, TP plus FN
would lead to haze events, and TN plus FP would lead to non-haze events. The clustering
calculations were done by directly using the k-mean (Steinhaus, 1957)
function of the scikit-learn library (https://scikit-learn.org/stable/modules/clustering.html#clustering, last access: 2 September 2021).
For Beijing cases, the trained machine with nine features produced 2591 TP,
11368 TN, 508 FP, and 508 FN outcomes, and it produced 2407 TP, 11 484 TN, 492 FP, and
592 FN outcomes for Shanghai. The cluster analysis was performed separately for each
of these outcomes in an unsupervised learning procedure to let the machine
categorize corresponding samples into groups based on similarities among
them. In practice, similarity is judged by the so-called inertia for a
cluster with members of xi and mean of μ:inertia=∑iN(xi-μ)2.The clustering is to seek a grouping with minimized inertia within each
cluster. The overall measure is the summation inertia that decreases almost
exponentially with the increase of number of clusters. In practice, the
cluster analysis was first tested with various given number of clusters
ranging from 1 to 100 to examine the values alongside decay of the inertia.
This provided a base to identify the smallest possible number of cluster
centers with reasonably low inertia in actual cluster analysis. This has
actually been decided by using square root of the inertia weighted by the
number of samples to put the varying number of samples across various
outcomes in consideration. An optimized number of clusters was chosen with a
weighted inertia lower than 1/e of that of the single-cluster case. For TN,
due to the large sample number, this criterion was set to be half of 1/e. As
a result, the optimized number of clusters for TP, FN, FP, and TN outcomes
is 4, 3, 4, and 15 for Beijing and 4, 3 3, and 10 for Shanghai,
respectively.
The members of each cluster derived from step (ii) were recorded
by the actual sample indices with the date included. Therefore, actual samples
of input data grouped into various clusters can be conveniently identified
with corresponding feature maps retrieved, either in a normalized or unnormalized format
(i.e., in original quantity as in reanalysis
dataset), and used for further analyses. In practice, cluster-averaged maps
for various features were performed beforehand.
Code and data availability
The Python script for network architecture, training, and validation is
rather straightforward and simple, basically consisting of directly adopted
function calls from Keras interface library (https://github.com/keras-team/keras, last access: 2 September 2021) with a TensorFlow-GPU (https://www.tensorflow.org, last access: 2 September 2021) as the backend or from scikit-learn library
(https://scikit-learn.org/, last access: 2 September 2021). All the data used here for the analyses are
publicly available: GSOD data from https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ncdc:C00516, last access: 2 September 2021; ERA5 reanalysis data from https://climate.copernicus.eu/climate-reanalysis, last access: 2 September 2021.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-21-13149-2021-supplement.
Competing interests
The author declares that there are no conflicts of interest.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
This study is supported by L'Agence National de la Recherche (ANR) of France
under “Programme d'Investissements d'Avenir” (ANR-18-MPGA-003 EUROACE).
The author thanks the European Centre for Medium-range Weather Forecasts for
making the ERA5 data publicly available under a license generated (and
service offered) by the Copernicus Climate Change Service and the National
Center for Environmental Information of the US NOAA for making the GSOD data
available. All of the related computations have been accomplished using the GPU
clusters of French Grand Equipment National de Calcul Intensif (GENCI)
(project 101056) and the CNRS Mesocenter of Computing of CALMIP (project p18025). Constructive comments and suggestions from two anonymous reviewers led to the improvement of the manuscript.
Financial support
This research has been supported by the Agence Nationale de la Recherche (grant no. ANR-18-MPGA-003 EUROACE).
Review statement
This paper was edited by Yun Qian and reviewed by two anonymous referees.
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