Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Nourin Jahana , Madhurima Panjab , Muhammed Navas Ta , Tanujit Chakrabortyb,c
arXiv:2605.03795v1 [cs.LG] 5 May 2026
a
Department of Mathematics, Vellore Institute of Technology, Vellore, Tamil Nadu, India b SAFIR, Sorbonne University, Abu Dhabi, UAE c SCAI - Sorbonne Cluster for Artificial Intelligence, Paris, France
Abstract Urban air quality forecasting is challenging because pollutant concentrations are nonlinear, nonstationary, spatiotemporally dependent, and often affected by anomalous observations caused by traffic congestion, industrial emissions, and seasonal meteorological variability. This study proposes a Graph Convolutional Support Vector Regression (GCSVR) framework for robust spatiotemporal forecasting of urban air pollution. The model combines graph convolutional learning to capture inter-station spatial dependence with support vector regression to model nonlinear temporal dynamics while reducing sensitivity to outlier observations. The proposed framework is evaluated using air quality records from 37 monitoring stations in Delhi and 18 stations in Mumbai, representing inland and coastal metropolitan environments in India. Forecasting performance is assessed across multiple horizons and compared with established temporal and spatiotemporal benchmarks. The results show that GCSVR consistently improves predictive accuracy and maintains stable performance across seasons and outlier-prone pollution episodes. Statistical test further confirms the reliability of the proposed approach across the two cities. Finally, conformal prediction is integrated with GCSVR to generate calibrated prediction intervals, enhancing its practical value for uncertainty-aware air quality monitoring and public health decision-making. Keywords: Air quality; Graph convolutional networks; Support vector regression; Outliers; Spatiotemporal forecasting; Conformal prediction.
1. Introduction Air pollution is a major environmental and public-health challenge, especially in rapidly urbanizing regions where industrial activity, transport emissions, construction, population growth, and ∗
meteorological variability interact in complex ways (Li et al. (2008); He et al. (2020)). Reliable air quality forecasting is therefore essential for early warning, exposure reduction, traffic and industrial regulation, and public-health planning. However, forecasting pollutant concentrations is difficult because air quality data are often nonlinear, nonstationary, seasonally varying, and strongly dependent across both space and time (Panja et al. (2026); Nag et al. (2023)). These challenges are particularly acute in India, which contains several of the world’s most populous and fast-growing megacities, including Delhi and Mumbai. High population density, intense vehicular activity, industrial emissions, construction growth, biomass burning, and region-specific climatic conditions make air pollution monitoring and forecasting a pressing scientific and policy problem. Major atmospheric pollutants include particulate matter (P M ), carbon dioxide (CO2 ), carbon monoxide (CO), nitrogen dioxide (N O2 ), sulfur dioxide (SO2 ), and volatile organic compounds. In 2017, air pollution was associated with approximately 1.24 million deaths in India, with 51.4% occurring among individuals below 70 years of age; it also increases the risk of lung disease, stroke, and cardiovascular diseases (Balakrishnan et al. (2019)). Maternal exposure to particulate matter has further been linked to increased risks of preterm birth and low birth weight (Li et al. (2017)). To protect public health, countries define National Ambient Air Quality Standards (NAAQS) for major pollutants. In India, the Central Pollution Control Board (CPCB) specifies permissible limits of 60 µg/m3 for P M2.5 and 100 µg/m3 for P M10 . This study focuses on two major Indian urban agglomerations: Delhi and Mumbai. For Delhi, daily records from 37 monitoring stations during 2019–2023 show average P M2.5 and P M10 concentrations exceeding 100 µg/m3 and 200 µg/m3 , respectively, far above the prescribed limits. Pollution episodes intensify during winter because of temperature inversions, low wind speed, shallow boundary-layer conditions, and regional biomass burning (Guttikunda and Gurjar (2012)). For Mumbai, data from 18 monitoring locations during 2021–2024 indicate average P M2.5 and P M10 concentrations of 44.37 µg/m3 and 106 µg/m3 , respectively, with winter deterioration linked to reduced coastal ventilation, atmospheric stability, vehicular emissions, and construction dust. These elevated pollution levels are associated with increased risks of cardiovascular and respiratory diseases, stroke, lung cancer, and premature mortality (Patankar and Trivedi (2011)). Motivated by these public-health concerns, this study develops a spatiotemporal forecasting framework to improve urban air quality prediction and support timely warning and policy intervention. Air quality forecasting methods can be broadly grouped into traditional statistical models, machine learning approaches, and deep learning frameworks. Classical time series models, particularly 2
Auto-Regressive Integrated Moving Average (ARIMA), have long been used for pollutant forecasting because of their interpretability, modest data requirements, and ability to capture short-term temporal dependence. Seasonal ARIMA (SARIMA) further extends this framework by incorporating seasonal autoregressive and moving-average components, making it a common baseline for air quality data with periodic behavior (Hyndman and Athanasopoulos (2018)). However, ARIMA-type models are fundamentally linear and primarily temporal; they struggle to represent nonlinear pollutant dynamics, spatial dependence among monitoring stations, and irregular observations or outliers often present in real-world air quality records (Pak et al. (2018)). Classical spatiotemporal extensions, such as Space-Time Autoregressive Moving Average (STARMA) models (Pfeifer and Deutrch (1980)) and Generalized Space-Time Autoregressive (GSTAR) models (Cliff and Ord (1975)), partially address the spatial limitations of ARIMA by incorporating dependence across locations. Nevertheless, their linear structure, sensitivity to nonstationarity, and limited scalability restrict their effectiveness for modern urban air quality forecasting, where nonlinear, high-dimensional, and outlier-prone spatiotemporal patterns are common (Barman et al. (2025); Jakhmola et al. (2024)). The limitations of classical statistical models, particularly their linearity and limited ability to capture spatial dependence, have motivated the use of machine learning methods for air quality forecasting. These methods are data-driven and impose fewer distributional assumptions, making them suitable for nonlinear and noisy environmental data (Rybarczyk and Zalakeviciute (2018)). Among them, Support Vector Regression (SVR) (Vapnik et al. (1996)) has been widely used because its ϵ-insensitive loss fits a regression function within a specified tolerance margin, reducing sensitivity to isolated noisy or extreme observations compared with squared-error-based methods (Drucker et al. (1996)). Random Forests and SVR have often improved upon statistical baselines, especially when pollutant dynamics depend on complex nonlinear relationships (Stafoggia et al. (2019)). However, these models are commonly implemented separately at individual monitoring stations and therefore do not explicitly represent spatial interactions induced by atmospheric transport, shared emission sources, and regional meteorological conditions (Qi et al. (2019); Pak et al. (2020)). Moreover, although SVR provides some robustness to outliers, standard machine learning models do not naturally provide structured spatiotemporal learning or calibrated probabilistic forecasts (Pathak and Chakraborty (2026)), and their scalability can become restrictive in dense monitoring networks (Rybarczyk and Zalakeviciute (2018)). Deep learning has introduced air quality forecasting models with greater capacity to capture nonlinear and nonstationary temporal dynamics. Long Short-Term Memory (LSTM) networks 3
(Hochreiter and Schmidhuber (1997)) are among the most widely used architectures, as their gating mechanisms allow them to retain relevant long-range information and model complex temporal dependencies in pollutant concentration series. Several studies have reported strong LSTM performance for P M2.5 and P M10 forecasting in urban environments (Huang and Kuo (2018)). Other temporal deep learning models have further advanced the field: DeepAR enables probabilistic forecasting through an autoregressive recurrent structure (Salinas et al. (2020)); Transformer-based models use self-attention to capture long-range dependencies with high scalability (Wu et al. (2020)); and N-BEATS employs a feedforward basis-expansion architecture for flexible and interpretable time series forecasting (Oreshkin et al. (2019)). Despite these advances, such models are primarily temporal and typically process each monitoring station independently. As a result, they do not explicitly encode the spatial dependence among stations arising from pollutant transport, shared emission sources, and regional meteorological conditions (Pak et al. (2020)). Spatiotemporal learning models have been developed to overcome the limitations of purely temporal approaches. Fast Gaussian process models such as GpGp (Guinness (2018)) can capture spatiotemporal dependence and support probabilistic forecasting, but their linear structure and scalability constraints limit their use in large monitoring networks. Graph-based deep learning models offer a more flexible alternative. In particular, the Spatiotemporal Graph Convolutional Network (STGCN) (Yu et al. (2018)) combines graph convolutions with temporal gating mechanisms to jointly model spatial dependence and temporal dynamics. Related approaches, including STNN (Saha et al. (2020)) and DeepKriging (Nag et al. (2023)), further demonstrate the potential of deep spatiotemporal learning for environmental data. However, these models are often dataintensive and may be less stable when monitoring records are sparse, noisy, or affected by outliers. To overcome these challenges, this study proposes a Graph Convolutional Support Vector Regression (GCSVR) framework for robust spatiotemporal forecasting of urban air pollution. The proposed model combines graph convolutional learning to encode spatial dependence among monitoring stations with Support Vector Regression to provide nonlinear temporal prediction and structural robustness through the ϵ-insensitive loss function for limited air quality data with outlier observations. The proposed framework is further evaluated using air quality records from 37 monitoring stations in Delhi and 18 monitoring stations in Mumbai, representing inland and coastal metropolitan environments in India. Its forecasting performance is examined across multiple prediction horizons and compared with established temporal and spatiotemporal benchmark models. The empirical results show that GCSVR delivers accurate and stable forecasts across seasons and outlier-prone pollution 4
episodes in both cities. Additional statistical robustness analyses further support the reliability of the proposed approach. To quantify forecast uncertainty, conformal prediction is incorporated into the GCSVR framework, producing calibrated prediction intervals that enhance its practical value for air quality monitoring, public-health planning, and policy decision-making.
2. Proposed Methodology In this section, we present the proposed Graph Convolutional Support Vector Regression (GCSVR) framework for spatiotemporal forecasting of air pollutant concentrations in the presence of outliers. We first define the forecasting problem and then describe the main components of the proposed model. 2.1
Problem Formulation Consider an air quality monitoring network consisting of N stations. Let Xt = (Xt1 , Xt2 , . . . , XtN )⊤
∈ RN denote the vector of pollutant concentrations observed across all stations at time t, for t = 1, 2, . . . , T , where Xti is the pollutant concentration recorded at station i at time t. The historical observations are denoted by X1:T = (X1 , X2 , . . . , XT )⊤ ∈ RT ×N . The objective is to generate q-step-ahead forecasts, with q ≥ 1, given by (X̂T +1 , X̂T +2 , . . . , X̂T +q ), where each X̂T +h ∈ RN represents the predicted pollutant concentrations at all monitoring stations for horizon h = 1, 2, . . . , q. To achieve this, we develop a forecasting framework that combines graph convolutional networks (GCN) to encode spatial dependence among stations with Support Vector Regression (SVR) for nonlinear temporal prediction. The goal is to learn a mapping from historical spatiotemporal observations to future pollutant concentrations. 2.2
GCSVR Model The proposed GCSVR framework consists of two main modules: a spatial module and a tem-
poral forecasting module. The spatial module takes the historical pollutant observations and the monitoring-station network as inputs, where stations are represented as graph nodes and their spatial relationships are encoded through edges. Graph convolutional layers are then used to extract spatially informed representations by aggregating information from neighboring stations, followed by fully connected layers to obtain compact spatiotemporal features. These features encode the spatial dependence structure across monitoring locations and are subsequently combined with lagged temporal information in the SVR module. The resulting graph-enhanced representations are then
5
passed to the temporal module, where SVR is used to model nonlinear temporal relationships and generate station-specific forecasts. In this way, GCSVR combines graph-based spatial learning with SVR-based robust temporal prediction for air quality forecasting problem. 2.2.1
Spatial Module
Air pollutant concentrations exhibit spatially varying dependence across monitoring stations. To capture these spatial patterns, we employ GCNs, which provide a principled framework for learning representations from irregular graph-structured data. In the proposed GCSVR architecture, each monitoring station is represented as a node in an undirected graph G = (V, E), where V denotes the set of monitoring stations and E denotes the set of edges encoding spatial relationships between station pairs. The graph structure is represented by an adjacency matrix A ∈ RN ×N . Following the geographical locations of the stations, the entries of A are constructed using the weighted Haversine distance dij between stations i and j, with latitude–longitude coordinates (ϕi , λi ) and (ϕj , λj ), respectively, as follows: s dij = 2R sin
−1
2
sin
∆ϕij 2
2
+ cos(ϕi ) cos(ϕj ) sin
∆λij 2
! ,
(1)
where ∆ϕij = ϕi − ϕj , ∆λij = λi − λj , and R denotes the Earth’s radius. The similarity between monitoring stations is encoded through a weighted adjacency matrix A = (aij ) ∈ RN ×N , whose entries are computed using a Gaussian kernel: ! ! 2 2 d d exp − ij2 , if i ̸= j and exp − ij2 ≥ ϵ, σ̃ σ̃ aij = 0, otherwise.
(2)
Here, σ̃ 2 controls the decay rate of the edge weights with distance, while ϵ regulates the sparsity of the graph by removing weak connections. Thus, stations i and j are disconnected whenever their p geographical distance satisfies dij > −σ̃ 2 log ϵ. We represent the pollutant concentration measurements collected across N monitoring stations over T time steps as a sequence of spatiotemporal graphs G = {G1 , G2 , . . . , GT }, where each graph is defined as Gt = (Xt , A). Here, Xt ∈ RN denotes the vector of pollutant concentrations across all monitoring stations at time t, and A ∈ RN ×N encodes the spatial structure of the monitoring network (Panja et al. (2026)). To transform these non-Euclidean spatiotemporal graphs into spatially
6
informed node embeddings, we use GCN layers that perform localized convolutions over each node’s neighbourhood. GCNs extend the filtering principle of conventional CNNs to graph-structured data by applying polynomial filters that aggregate information from neighboring nodes. A graph filter of order d can be expressed using Chebyshev polynomials as
Pw (L) =
d X
wu Cu (L̃),
u=0
where Cu denotes the uth Chebyshev polynomial and L̃ = 2L/ζmax − IN is the normalized graph Laplacian. ζmax is the largest eigenvalue of L = D − A, where D is the diagonal degree matrix with P entries Dii = j Aij . Applying this graph filter to the input signal Xt gives: Xt′ = Pw (L)Xt .
(3)
Following Kipf (2016); Panja et al. (2026), we use a first-order approximation of the Chebyshev polynomial filter (d = 1), which reduces computational complexity while retaining effective local neighbourhood aggregation. The filtered graph signal can then be written as
Xt′ = w0 Xt + w1
2L − IN ζmax
Xt ,
(4)
where w0 and w1 are learnable filter parameters shared across all N monitoring stations. By stacking K first-order graph convolutional layers, spatial information can be propagated across multi-hop neighbourhoods. For each graph Gt = (Xt , A), t = 1, 2, . . . , T , the node embeddings are computed as i,(0)
ht
= Xti ,
i,(k)
ht
= g (k) W (k)
P
j,(k−1)
j∈N (i) ht
|N (i)|
i,(k−1)
+ B (k) ht
,
k = 1, 2, . . . , K,
i,(K) Zti = Dense ht , i,(k)
where ht
denotes the representation of station i at time t after the k th graph convolutional
layer, N (i) is the set of neighbouring stations connected to station i, W (k) and B (k) are learnable parameters, and g (k) (·) is a nonlinear activation function. The final output Zti represents the graph-enhanced spatial embedding of station i at time t. At each graph convolutional layer, the activation function g (k) and the learnable parameters W (k) , B (k) are shared across all nodes, 7
enabling localized 1-hop neighbourhood aggregation through a neural message-passing mechanism (Gilmer et al. (2017)). Repeating this operation for K layers allows each station to incorporate information from proi,(k)
gressively larger neighbourhoods. Specifically, ht
is obtained by combining the representation of
the neighbours of station i with its own representation from the previous layer. The final spatial representation Zti is then obtained by applying a fully connected dense layer to the K th −layer em⊤ i,(K) bedding ht . Thus, Zt = Zt1 , Zt2 , . . . , ZtN ∈ RN ×r provides a graph-enhanced representation of Xt , where Zti ∈ Rr denotes the spatial embedding of station i and r is the embedding dimension. Zt is enriched with spatial information propagated through K successive filtering operations. The use of first-order graph filters makes this construction computationally efficient and scalable for large monitoring networks (Yu et al. (2017)). 2.2.2
Temporal Module
The temporal module uses the graph-enhanced representations obtained from the spatial module i to generate pollutant forecasts at each monitoring station. Let Zt−1 ∈ Rr is an r-dimensional spatial
embedding for station i. For each station i = 1, 2, . . . , N , we construct a lagged temporal input from i ⊤ p i , Xi the observed pollutant series as xit = (Xt−p t−p+1 , . . . , Xt−1 ) ∈ R , where p is the input sequence
length. This local temporal history is concatenated with the corresponding graph-enhanced spatial embedding to form the SVR input vector i vti = xit ∥Zt−1 ∈ Rp+r , where ∥ denotes vector concatenation. The target variable is the one-step-ahead pollutant concentration yti = Xti . For each station i, an independent SVR model fi is trained to learn the nonlinear mapping fi : vti 7→ Xti . The one-step-ahead prediction is therefore given by X̂ti = fi (vti ). To obtain multi-step forecasts over a horizon q, we use a recursive forecasting strategy. Starting from the last observed sequence (XTi −p+1 , . . . , XTi ), the trained SVR model first produces X̂Ti +1 . This prediction is then appended to the input sequence and used to forecast the next step. Repeating this procedure yields q-step-ahead forecasts for all the stations: X̂Ti +1 , X̂Ti +2 , . . . , X̂Ti +q , i = 1, 2, . . . , N. Collecting the station-wise
8
predictions gives the multivariate forecast vector X̂T +h = (X̂T1 +h , X̂T2 +h , . . . , X̂TN+h )⊤ ∈ RN ,
h = 1, 2, . . . , q.
We use Support Vector Regression because it provides a nonlinear and regularized forecasting framework while reducing sensitivity to isolated anomalous observations through the ϵ-insensitive loss function Vapnik et al. (1996); Smola and Schölkopf (2004). Unlike squared-error loss, the ϵ-insensitive loss does not penalize prediction errors that fall within a tolerance tube of radius ϵ, making SVR particularly suitable for air quality series affected by noisy measurements and irregular pollution spikes. Using the radial basis function (RBF) kernel, the SVR forecasting function for station i is written as fi (vti ) =
n X
(αℓi − αℓ∗,i )K(vtiℓ , vti ) + bi ,
ℓ=1
where n is the number of training samples, αℓi and αℓ∗,i are Lagrange multipliers, and bi is the bias term. The RBF kernel is defined as 2 , K(vtiℓ , vti ) = exp −γ vtiℓ − vti where γ > 0 controls the kernel width. For each station i, the SVR dual optimization problem is n
max
αiℓ ,α∗,i ℓ
subject to
−
n
1XX i i ∗,i (αℓ − αℓ∗,i )(αm − αm )K(vtiℓ , vtim ) 2
ℓ=1 m=1 n n X X −ϵ (αℓi + αℓ∗,i ) + ytiℓ (αℓi − αℓ∗,i ) ℓ=1 ℓ=1 n X
(αℓi − αℓ∗,i ) = 0,
ℓ=1
0 ≤ αℓi , αℓ∗,i ≤ C,
ℓ = 1, 2, . . . , n,
where C > 0 controls the trade-off between model flatness and training error. The corresponding ϵ-insensitive loss function is
Lϵ (yti , fi (vti )) =
0,
if |yti − fi (vti )| ≤ ϵ,
|y i − f (vi )| − ϵ, otherwise. i t t This formulation enables the temporal module to learn nonlinear station-specific forecasting func9
Figure 1: Schematic representation of the proposed GCSVR framework.
tions from graph-enhanced lagged inputs while limiting the influence of small fluctuations and isolated outlier observations. Fig. 1 summarizes the proposed GCSVR framework. The monitoring stations and their geographical relationships are first represented as a graph using the adjacency matrix constructed from inter-station distances. The spatial module applies graph convolutional layers to generate station-specific embeddings that encode neighborhood-level spatial dependence. These graph-enhanced embeddings are then combined with local lagged pollutant observations and passed to the SVR-based temporal module. Finally, multi-step forecasts are obtained recursively for all monitoring stations, producing spatiotemporal predictions of future pollutant concentrations. During the implementation of GCSVR, the spatial module is first trained to generate GCNbased node embeddings for each monitoring station. These embeddings are then combined with the local lagged pollutant sequence of each station to construct the input features for the SVR module. Specifically, for station i, the SVR input vector consists of the recent temporal history of pollutant concentrations and the corresponding graph-enhanced spatial representation. A separate SVR model with an RBF kernel is trained for each monitoring station, using standardized input features and the ϵ-insensitive loss function. Multi-step forecasts are generated recursively: after producing a one-step-ahead forecast, the predicted value is appended to the input sequence and used to forecast the next time step. This implementation allows GCSVR to combine spatial information learned from the monitoring network with robust station-wise nonlinear temporal forecasting.
10
3. Experimental Evaluation This study evaluates the effectiveness of the proposed GCSVR framework by comparing its forecasting performance with several temporal and spatiotemporal benchmark models. The analysis uses daily air quality measurements from Delhi and Mumbai. For Delhi, data from January 1, 2019 to December 31, 2022 are used for model training, and forecasts are generated for selected periods in 2023. For Mumbai, data from January 1, 2021 to December 31, 2023 are used for training, and forecasts are generated for corresponding periods in 2024. To assess performance across different prediction settings, we consider three forecasting horizons: short-term, medium-term, and longterm, corresponding to 30, 60, and 90 days, respectively, using a rolling-window evaluation strategy. For the short-term setting, forecasts are produced separately for each month of the test year. For the medium-term setting, forecasts are generated over six non-overlapping two-month windows. For the long-term setting, the test year is divided into four non-overlapping three-month windows, corresponding to quarterly forecasting periods. The rolling-window evaluation design is summarized in Fig. 2, which illustrates how the in-sample period is progressively expanded and the out-of-sample year is evaluated under 30, 60, and 90-day forecasting windows for Delhi air quality data (see also Fig. 3 for the Mumbai dataset).
Figure 2: Rolling-window evaluation design for the Delhi air quality dataset.
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Figure 3: Rolling-window evaluation design for the Mumbai air quality dataset.
3.1
Data and Preliminary Analysis This study focuses on forecasting the daily concentrations of two major air pollutants, namely
P M2.5 and P M10 , using data collected from monitoring networks in Delhi and Mumbai. For Delhi, the data are obtained from 37 monitoring stations. The pollutant concentrations exhibit substantial spatial and temporal variability, with observed values ranging from 0.08 to 1000 µg/m3 for P M2.5 and from 1.00 to 1000 µg/m3 for P M10 . The corresponding mean concentrations are 102.06 µg/m3 and 204.02 µg/m3 , respectively, indicating pollution levels well above the prescribed air quality standards. For Mumbai, data are collected from 18 monitoring stations, with observed concentrations ranging from 0.85 to 833.80 µg/m3 for P M2.5 and from 0.841 to 985 µg/m3 for P M10 . The mean concentrations are 44.37 µg/m3 for P M2.5 and 106.6 µg/m3 for P M10 . Figs. 4 and 5 show the spatial distribution of air pollution monitoring stations in Delhi and Mumbai, respectively. The upper panels display the mean pollutant concentrations recorded at each station. Stations located close to one another generally exhibit similar concentration levels, suggesting spatial dependence in pollutant distribution. The lower panels present pairwise correlation heatmaps, where stations are reordered using hierarchical clustering based on their Haversine distances, as defined in Eq. (1). This ordering highlights spatial correlation patterns that may be less
12
visible in the original station arrangement. In both cities, geographically proximate stations tend to show stronger correlations, reflecting shared emission sources, local atmospheric conditions, and pollutant dispersion mechanisms. As expected, the diagonal entries of the correlation matrices are equal to one, representing perfect self-correlation. Overall, both P M2.5 and P M10 exhibit strong positive correlations across many station pairs, confirming the importance of explicitly modeling spatial dependence for accurate air quality forecasting. PM2.5 Monitoring Stations — Delhi, India
PM10 Monitoring Stations — Delhi, India
Mean daily PM2.5 (µg/m³) across 37 DPCC/CPCB stations (1826 days)
Mean daily PM10 (µg/m³) across 34 DPCC/CPCB stations (1826 days)
28.9°N
28.9°N
N 21
N 20
1
28.8°N 5
Mean Daily PM2.5 (µg/m³) 260
5
8
8 14
31
28.7°N 19
25
33
100
2
26
17
12
26
17
200
15 14
10
19
11
180
21
28
7
33 35
24
16
28.6°N
90 22
30
11
220
22 13
16 15
10
240
34 3 18
2 18
24
20
28.7°N
12 36
27
6 31
110
37 3
23 32 28
13
29
6 34
28.6°N
1
28.8°N
Mean Daily PM2.5 (µg/m³) 120
7
30 32
25
23
80 28.5°N
160 28.5°N
9
9
29
27
4
4
~20 km
~20 km
28.4°N
28.4°N 77.3°E
77.4°E
76.9°E
77.0°E
Pairwise PM2.5 Station Correlation — Delhi
0.82 0.93 0.93 0.95 0.83 0.93 0.94 0.92 0.93 0.81 0.96 0.96 0.96 0.95 0.97 0.96 0.98 0.95 0.97 0.93 1.00 0.95 0.89 0.96 0.88 0.91 0.93 0.95 0.94 0.96 0.93 0.82 0.93 0.93 0.93 0.69 0.93 0.75 0.91 0.91 0.93 0.79 0.91 0.89 0.87 0.90 0.78 0.94 0.92 0.93 0.91 0.95 0.94 0.94 0.90 0.94 1.00 0.93 0.92 0.87 0.94 0.83 0.89 0.93 0.95 0.93 0.94 0.91 0.80 0.93 0.91 0.90 0.67 0.93 0.80 0.93 0.93 0.94 0.83 0.93 0.95 0.94 0.94 0.79 0.97 0.96 0.97 0.94 0.98 0.96 0.98 0.96 1.00 0.94 0.97 0.96 0.89 0.97 0.86 0.91 0.93 0.96 0.94 0.97 0.94 0.79 0.94 0.92 0.92 0.70 0.93 0.82 0.92 0.92 0.92 0.82 0.91 0.92 0.92 0.93 0.78 0.94 0.94 0.95 0.93 0.96 0.93 0.96 1.00 0.96 0.90 0.95 0.94 0.88 0.95 0.88 0.90 0.92 0.93 0.93 0.95 0.93 0.78 0.92 0.92 0.92 0.71 0.91
0.50
0.82 0.94 0.94 0.95 0.85 0.94 0.94 0.92 0.94 0.81 0.97 0.96 0.97 0.96 0.98 0.98 1.00 0.96 0.98 0.94 0.98 0.96 0.90 0.97 0.89 0.93 0.95 0.97 0.95 0.98 0.95 0.82 0.95 0.95 0.95 0.71 0.95 0.79 0.92 0.93 0.95 0.82 0.93 0.91 0.89 0.92 0.80 0.96 0.94 0.96 0.94 0.97 1.00 0.98 0.93 0.96 0.94 0.96 0.94 0.88 0.96 0.86 0.92 0.95 0.96 0.94 0.97 0.93 0.81 0.93 0.95 0.94 0.70 0.95 0.80 0.93 0.93 0.95 0.84 0.94 0.93 0.92 0.93 0.79 0.97 0.95 0.97 0.96 1.00 0.97 0.98 0.96 0.98 0.95 0.97 0.96 0.90 0.97 0.88 0.93 0.96 0.97 0.95 0.97 0.94 0.80 0.95 0.95 0.94 0.69 0.96 0.82 0.92 0.92 0.93 0.86 0.92 0.90 0.90 0.92 0.78 0.94 0.92 0.93 1.00 0.96 0.94 0.96 0.93 0.94 0.91 0.95 0.94 0.88 0.93 0.89 0.92 0.93 0.94 0.92 0.94 0.92 0.79 0.93 0.93 0.91 0.67 0.93 0.78 0.91 0.91 0.93 0.80 0.92 0.92 0.91 0.91 0.81 0.96 0.94 1.00 0.93 0.97 0.96 0.97 0.95 0.97 0.93 0.96 0.94 0.88 0.96 0.84 0.90 0.93 0.95 0.93 0.96 0.92 0.80 0.92 0.93 0.93 0.70 0.93
0.25
0.81 0.92 0.93 0.94 0.81 0.92 0.94 0.93 0.94 0.79 0.96 1.00 0.94 0.92 0.95 0.94 0.96 0.94 0.96 0.92 0.96 0.94 0.87 0.95 0.85 0.89 0.92 0.94 0.94 0.95 0.93 0.81 0.92 0.91 0.92 0.71 0.92 0.80 0.93 0.94 0.96 0.83 0.94 0.94 0.92 0.93 0.81 1.00 0.96 0.96 0.94 0.97 0.96 0.97 0.94 0.97 0.94 0.96 0.95 0.89 0.96 0.85 0.91 0.94 0.96 0.95 0.97 0.92 0.81 0.93 0.93 0.93 0.69 0.95 0.72 0.80 0.78 0.80 0.65 0.78 0.78 0.74 0.74 1.00 0.81 0.79 0.81 0.78 0.79 0.80 0.81 0.78 0.79 0.78 0.81 0.78 0.71 0.81 0.74 0.74 0.79 0.79 0.80 0.80 0.77 0.83 0.76 0.78 0.83 0.67 0.77 0.80 0.91 0.90 0.91 0.81 0.90 0.91 0.91 1.00 0.74 0.93 0.94 0.91 0.92 0.93 0.92 0.94 0.93 0.94 0.90 0.93 0.93 0.88 0.93 0.85 0.89 0.91 0.93 0.92 0.93 0.92 0.76 0.92 0.90 0.89 0.69 0.91
0.00
0.78 0.90 0.90 0.90 0.79 0.88 0.91 1.00 0.91 0.74 0.92 0.93 0.91 0.90 0.92 0.89 0.92 0.92 0.94 0.87 0.92 0.90 0.84 0.90 0.83 0.86 0.88 0.91 0.90 0.91 0.91 0.74 0.90 0.87 0.87 0.67 0.88 0.81 0.93 0.94 0.94 0.81 0.91 1.00 0.91 0.91 0.78 0.94 0.94 0.92 0.90 0.93 0.91 0.94 0.92 0.95 0.89 0.94 0.92 0.86 0.92 0.85 0.88 0.89 0.91 0.92 0.93 0.91 0.78 0.92 0.89 0.90 0.70 0.90 0.82 0.94 0.94 0.95 0.85 1.00 0.91 0.88 0.90 0.78 0.94 0.92 0.92 0.92 0.94 0.93 0.94 0.91 0.93 0.91 0.93 0.92 0.87 0.93 0.86 0.91 0.93 0.93 0.94 0.93 0.93 0.80 0.94 0.94 0.93 0.69 0.95 0.77 0.85 0.86 0.86 1.00 0.85 0.81 0.79 0.81 0.65 0.83 0.81 0.80 0.86 0.84 0.82 0.85 0.82 0.83 0.79 0.83 0.84 0.78 0.82 0.83 0.84 0.83 0.83 0.83 0.83 0.82 0.64 0.84 0.85 0.81 0.54 0.85 0.82 0.95 0.96 1.00 0.86 0.95 0.94 0.90 0.91 0.80 0.96 0.94 0.93 0.93 0.95 0.95 0.95 0.92 0.94 0.93 0.95 0.94 0.88 0.95 0.86 0.92 0.94 0.95 0.96 0.95 0.94 0.80 0.95 0.94 0.94 0.70 0.96 0.85 0.97 1.00 0.96 0.86 0.94 0.94 0.90 0.90 0.78 0.94 0.93 0.91 0.92 0.93 0.93 0.94 0.92 0.93 0.91 0.93 0.92 0.87 0.92 0.87 0.91 0.92 0.93 0.94 0.93 0.94 0.80 0.95 0.93 0.93 0.71 0.94 0.84 1.00 0.97 0.95 0.85 0.94 0.93 0.90 0.91 0.80 0.93 0.92 0.91 0.92 0.93 0.92 0.94 0.92 0.93 0.91 0.93 0.92 0.87 0.94 0.87 0.92 0.93 0.95 0.94 0.93 0.93 0.80 0.96 0.93 0.92 0.72 0.95
0.89 0.91 0.90 0.88 0.89 0.93 0.96 0.80 0.96 0.95 0.85 0.94 0.93 0.90 0.95 0.91 0.94 0.88 0.55 0.94 0.89 1.00 0.92 0.96 0.96 0.96 0.94 0.95 0.96 0.91 0.94 0.92 0.92 0.90 0.87 0.90 0.90 0.87 0.85 0.88 0.88 0.73 0.89 0.85 0.73 0.86 0.87 0.84 0.84 0.87 0.86 0.78 0.52 0.85 1.00 0.89 0.82 0.87 0.85 0.88 0.89 0.88 0.88 0.83 0.89 0.83 0.86 0.81
Source: Delhi PM2.5 daily data (1827 days) | Clustering: complete linkage on Haversine distance
0.75
0.93 0.93 0.93 0.91 0.91 0.97 0.92 0.77 0.93 0.96 0.88 0.96 0.95 0.90 0.93 0.95 0.96 0.92 0.60 1.00 0.85 0.94 0.90 0.95 0.95 0.93 0.89 0.89 0.94 0.88 0.91 0.89 0.91 0.90 0.56 0.56 0.56 0.56 0.56 0.58 0.56 0.44 0.59 0.61 0.57 0.60 0.62 0.55 0.56 0.60 0.60 0.58 1.00 0.60 0.52 0.55 0.51 0.57 0.57 0.57 0.56 0.58 0.57 0.51 0.58 0.57 0.51 0.54 0.85 0.87 0.86 0.86 0.85 0.92 0.89 0.71 0.89 0.91 0.85 0.92 0.91 0.88 0.86 0.90 0.93 1.00 0.58 0.92 0.78 0.88 0.85 0.91 0.91 0.90 0.85 0.87 0.89 0.86 0.85 0.89 0.88 0.90 0.92 0.93 0.92 0.90 0.90 0.97 0.94 0.77 0.95 0.96 0.88 0.97 0.95 0.91 0.92 0.95 1.00 0.93 0.60 0.96 0.86 0.94 0.90 0.96 0.95 0.94 0.92 0.91 0.94 0.89 0.91 0.91 0.92 0.90 0.93 0.94 0.94 0.90 0.89 0.95 0.92 0.77 0.94 0.94 0.85 0.95 0.94 0.89 0.90 1.00 0.95 0.90 0.60 0.95 0.87 0.91 0.88 0.94 0.92 0.92 0.91 0.90 0.91 0.86 0.90 0.89 0.88 0.87
0.50
0.87 0.87 0.87 0.87 0.87 0.90 0.94 0.77 0.94 0.94 0.86 0.93 0.92 0.88 1.00 0.90 0.92 0.86 0.56 0.93 0.84 0.95 0.88 0.93 0.93 0.92 0.91 0.93 0.94 0.86 0.90 0.90 0.89 0.87 0.88 0.89 0.88 0.86 0.86 0.91 0.92 0.75 0.91 0.89 0.81 0.91 0.90 1.00 0.88 0.89 0.91 0.88 0.55 0.90 0.84 0.90 0.86 0.89 0.90 0.92 0.89 0.90 0.90 0.87 0.86 0.87 0.87 0.87 0.90 0.93 0.92 0.90 0.89 0.96 0.93 0.78 0.94 0.95 0.87 0.96 1.00 0.90 0.92 0.94 0.95 0.91 0.62 0.95 0.87 0.93 0.90 0.95 0.94 0.93 0.90 0.92 0.93 0.88 0.91 0.92 0.91 0.91 0.91 0.93 0.92 0.90 0.90 0.96 0.94 0.79 0.95 0.97 0.89 1.00 0.96 0.91 0.93 0.95 0.97 0.92 0.60 0.96 0.86 0.94 0.91 0.96 0.96 0.94 0.91 0.92 0.94 0.89 0.91 0.91 0.91 0.90
0.25
0.82 0.82 0.81 0.83 0.79 0.86 0.84 0.68 0.86 0.88 1.00 0.89 0.87 0.81 0.86 0.85 0.88 0.85 0.57 0.88 0.73 0.85 0.82 0.87 0.86 0.84 0.81 0.82 0.85 0.80 0.81 0.82 0.84 0.82 0.89 0.92 0.91 0.89 0.89 0.95 0.94 0.80 0.95 1.00 0.88 0.97 0.95 0.89 0.94 0.94 0.96 0.91 0.61 0.96 0.85 0.95 0.90 0.97 0.96 0.93 0.91 0.93 0.95 0.88 0.92 0.91 0.90 0.90 0.90 0.92 0.91 0.90 0.89 0.94 0.96 0.78 1.00 0.95 0.86 0.95 0.94 0.91 0.94 0.94 0.95 0.89 0.59 0.93 0.89 0.96 0.91 0.97 0.96 0.96 0.95 0.95 0.95 0.91 0.92 0.92 0.92 0.90 0.73 0.77 0.76 0.73 0.76 0.78 0.78 1.00 0.78 0.80 0.68 0.79 0.78 0.75 0.77 0.77 0.77 0.71 0.44 0.77 0.73 0.80 0.76 0.79 0.79 0.78 0.77 0.77 0.79 0.73 0.77 0.76 0.74 0.74
0.00
0.89 0.90 0.89 0.88 0.89 0.92 1.00 0.78 0.96 0.94 0.84 0.94 0.93 0.92 0.94 0.92 0.94 0.89 0.56 0.92 0.88 0.96 0.89 0.94 0.94 0.95 0.93 0.96 0.95 0.91 0.91 0.92 0.91 0.90 0.94 0.96 0.95 0.93 0.92 1.00 0.92 0.78 0.94 0.95 0.86 0.96 0.96 0.91 0.90 0.95 0.97 0.92 0.58 0.97 0.88 0.93 0.91 0.95 0.95 0.94 0.91 0.90 0.94 0.89 0.91 0.90 0.93 0.91 0.89 0.90 0.89 0.89 1.00 0.92 0.89 0.76 0.89 0.89 0.79 0.90 0.89 0.86 0.87 0.89 0.90 0.85 0.56 0.91 0.85 0.89 0.87 0.89 0.89 0.90 0.87 0.86 0.90 0.86 0.86 0.85 0.88 0.84 0.90 0.91 0.91 1.00 0.89 0.93 0.88 0.73 0.90 0.89 0.83 0.90 0.90 0.86 0.87 0.90 0.90 0.86 0.56 0.91 0.87 0.88 0.87 0.89 0.88 0.88 0.86 0.86 0.90 0.86 0.84 0.83 0.90 0.84 0.93 0.96 1.00 0.91 0.89 0.95 0.89 0.76 0.91 0.91 0.81 0.92 0.92 0.88 0.87 0.94 0.92 0.86 0.56 0.93 0.90 0.90 0.87 0.92 0.89 0.90 0.89 0.87 0.91 0.86 0.87 0.85 0.89 0.86 0.94 1.00 0.96 0.91 0.90 0.96 0.90 0.77 0.92 0.92 0.82 0.93 0.93 0.89 0.87 0.94 0.93 0.87 0.56 0.93 0.90 0.91 0.88 0.93 0.90 0.91 0.90 0.88 0.91 0.86 0.89 0.87 0.90 0.86 1.00 0.94 0.93 0.90 0.89 0.94 0.89 0.73 0.90 0.89 0.82 0.91 0.90 0.88 0.87 0.93 0.92 0.85 0.56 0.93 0.87 0.89 0.87 0.89 0.87 0.89 0.88 0.85 0.89 0.84 0.86 0.86 0.89 0.83
1 20
6 14
3 37
34
32
23
28
2 26 27
36
12
17
13
18
33
30
35
16
15
9
7 25 22
11
10
4 29 24
1.00 0.84 0.85 0.82 0.77 0.82 0.81 0.78 0.80 0.72 0.80 0.81 0.78 0.82 0.80 0.79 0.82 0.82 0.80 0.75 0.82 0.82 0.74 0.79 0.85 0.80 0.81 0.79 0.78 0.81 0.83 0.78 0.81 0.83 0.83 0.64 0.81
0.87 0.88 0.87 0.87 0.87 0.91 0.89 0.76 0.91 0.90 0.82 0.91 0.90 0.86 0.88 0.88 0.90 0.85 0.51 0.90 0.82 0.92 1.00 0.92 0.91 0.91 0.87 0.87 0.89 0.87 0.87 0.90 0.90 0.89
11
0.75
4 27 10
0.82 0.92 0.92 0.94 0.84 0.92 0.92 0.90 0.93 0.78 0.95 0.94 0.94 0.94 0.96 0.94 0.96 0.94 0.96 0.92 0.95 1.00 0.89 0.95 0.88 0.91 0.94 0.95 0.95 0.96 0.93 0.80 0.94 0.92 0.92 0.68 0.93
Pearson Correlation (r) 1.00
0.89 0.93 0.92 0.89 0.89 0.95 0.94 0.79 0.97 0.97 0.87 0.96 0.95 0.89 0.93 0.94 0.96 0.91 0.57 0.95 0.87 0.96 0.92 1.00 0.97 0.95 0.93 0.93 0.95 0.90 0.93 0.92 0.92 0.91
30
0.74 0.87 0.87 0.88 0.78 0.87 0.86 0.84 0.88 0.71 0.89 0.87 0.88 0.88 0.90 0.88 0.90 0.88 0.89 0.87 0.89 0.89 1.00 0.89 0.81 0.87 0.89 0.90 0.88 0.89 0.88 0.73 0.88 0.87 0.87 0.66 0.88
0.87 0.90 0.89 0.88 0.89 0.95 0.94 0.79 0.96 0.96 0.86 0.96 0.94 0.90 0.93 0.92 0.95 0.91 0.57 0.95 0.85 0.96 0.91 0.97 1.00 0.96 0.92 0.93 0.96 0.90 0.92 0.91 0.92 0.92
28
0.79 0.94 0.92 0.95 0.82 0.93 0.92 0.90 0.93 0.81 0.96 0.95 0.96 0.93 0.97 0.96 0.97 0.95 0.97 0.94 0.96 0.95 0.89 1.00 0.86 0.93 0.94 0.97 0.95 0.97 0.93 0.81 0.94 0.94 0.93 0.70 0.95
0.89 0.91 0.90 0.88 0.90 0.94 0.95 0.78 0.96 0.93 0.84 0.94 0.93 0.92 0.92 0.92 0.94 0.90 0.57 0.93 0.88 0.96 0.91 0.95 0.96 1.00 0.94 0.95 0.95 0.92 0.92 0.91 0.92 0.90
32
0.85 0.87 0.87 0.86 0.83 0.86 0.85 0.83 0.85 0.74 0.85 0.85 0.84 0.89 0.88 0.86 0.89 0.88 0.86 0.83 0.88 0.88 0.81 0.86 1.00 0.87 0.88 0.87 0.86 0.86 0.88 0.79 0.87 0.88 0.86 0.60 0.87
0.88 0.90 0.89 0.86 0.87 0.91 0.93 0.77 0.95 0.91 0.81 0.91 0.90 0.89 0.91 0.91 0.92 0.85 0.56 0.89 0.89 0.94 0.87 0.93 0.92 0.94 1.00 0.94 0.93 0.88 0.91 0.90 0.88 0.86
15
0.80 0.92 0.91 0.92 0.84 0.91 0.88 0.86 0.89 0.74 0.91 0.89 0.90 0.92 0.93 0.92 0.93 0.90 0.91 0.89 0.91 0.91 0.87 0.93 0.87 1.00 0.93 0.94 0.91 0.92 0.91 0.76 0.92 0.94 0.90 0.67 0.94
0.85 0.88 0.87 0.86 0.86 0.90 0.96 0.77 0.95 0.93 0.82 0.92 0.92 0.90 0.93 0.90 0.91 0.87 0.58 0.89 0.88 0.95 0.87 0.93 0.93 0.95 0.94 1.00 0.94 0.90 0.92 0.91 0.89 0.89
14
0.81 0.93 0.92 0.94 0.83 0.93 0.89 0.88 0.91 0.79 0.94 0.92 0.93 0.93 0.96 0.95 0.95 0.92 0.93 0.93 0.93 0.94 0.89 0.94 0.88 0.93 1.00 0.96 0.95 0.94 0.94 0.82 0.94 0.94 0.93 0.71 0.95
0.89 0.91 0.91 0.90 0.90 0.94 0.95 0.79 0.95 0.95 0.85 0.94 0.93 0.90 0.94 0.91 0.94 0.89 0.57 0.94 0.88 0.96 0.89 0.95 0.96 0.95 0.93 0.94 1.00 0.91 0.92 0.89 0.93 0.90
9
0.79 0.95 0.93 0.95 0.83 0.93 0.91 0.91 0.93 0.79 0.96 0.94 0.95 0.94 0.97 0.96 0.97 0.93 0.96 0.95 0.95 0.95 0.90 0.97 0.87 0.94 0.96 1.00 0.95 0.96 0.95 0.80 0.96 0.94 0.93 0.70 0.96
Pearson Correlation (r) 1.00
7 23 21
0.78 0.94 0.94 0.96 0.83 0.94 0.92 0.90 0.92 0.80 0.95 0.94 0.93 0.92 0.95 0.94 0.95 0.93 0.94 0.93 0.94 0.95 0.88 0.95 0.86 0.91 0.95 0.95 1.00 0.95 0.94 0.80 0.94 0.93 0.93 0.71 0.95
0.84 0.86 0.86 0.86 0.86 0.89 0.91 0.73 0.91 0.88 0.80 0.89 0.88 0.87 0.86 0.86 0.89 0.86 0.51 0.88 0.83 0.91 0.87 0.90 0.90 0.92 0.88 0.90 0.91 1.00 0.87 0.85 0.91 0.87
6 13 19
0.81 0.93 0.93 0.95 0.83 0.93 0.93 0.91 0.93 0.80 0.97 0.95 0.96 0.94 0.97 0.97 0.98 0.95 0.97 0.94 0.96 0.96 0.89 0.97 0.86 0.92 0.94 0.96 0.95 1.00 0.93 0.80 0.94 0.94 0.93 0.69 0.95
0.86 0.89 0.87 0.84 0.86 0.91 0.91 0.77 0.92 0.92 0.81 0.91 0.91 0.86 0.90 0.90 0.91 0.85 0.58 0.91 0.89 0.94 0.87 0.93 0.92 0.92 0.91 0.92 0.92 0.87 1.00 0.89 0.88 0.90
2 33 25
0.83 0.93 0.94 0.94 0.82 0.93 0.91 0.91 0.92 0.77 0.92 0.93 0.92 0.92 0.94 0.93 0.95 0.93 0.94 0.91 0.93 0.93 0.88 0.93 0.88 0.91 0.94 0.95 0.94 0.93 1.00 0.81 0.95 0.93 0.94 0.73 0.94
0.86 0.87 0.85 0.83 0.85 0.90 0.92 0.76 0.92 0.91 0.82 0.91 0.92 0.87 0.90 0.89 0.91 0.89 0.57 0.89 0.83 0.92 0.90 0.92 0.91 0.91 0.90 0.91 0.89 0.85 0.89 1.00 0.86 0.92
24
0.78 0.80 0.80 0.80 0.64 0.80 0.78 0.74 0.76 0.83 0.81 0.81 0.80 0.79 0.80 0.81 0.82 0.78 0.79 0.80 0.82 0.80 0.73 0.81 0.79 0.76 0.82 0.80 0.80 0.80 0.81 1.00 0.79 0.78 0.84 0.64 0.79
0.89 0.90 0.89 0.90 0.88 0.93 0.91 0.74 0.92 0.90 0.84 0.91 0.91 0.87 0.89 0.88 0.92 0.88 0.51 0.91 0.86 0.92 0.90 0.92 0.92 0.92 0.88 0.89 0.93 0.91 0.88 0.86 1.00 0.88
16
0.81 0.96 0.95 0.95 0.84 0.94 0.92 0.90 0.92 0.76 0.93 0.92 0.92 0.93 0.95 0.93 0.95 0.92 0.94 0.93 0.93 0.94 0.88 0.94 0.87 0.92 0.94 0.96 0.94 0.94 0.95 0.79 1.00 0.94 0.92 0.71 0.96
12
0.83 0.93 0.93 0.94 0.85 0.94 0.89 0.87 0.90 0.78 0.93 0.91 0.93 0.93 0.95 0.95 0.95 0.92 0.92 0.91 0.93 0.92 0.87 0.94 0.88 0.94 0.94 0.94 0.93 0.94 0.93 0.78 0.94 1.00 0.95 0.72 0.96
8 29 17
0.83 0.92 0.93 0.94 0.81 0.93 0.90 0.87 0.89 0.83 0.93 0.92 0.93 0.91 0.94 0.94 0.95 0.92 0.92 0.90 0.93 0.92 0.87 0.93 0.86 0.90 0.93 0.93 0.93 0.93 0.94 0.84 0.92 0.95 1.00 0.76 0.93
8 31 20
77.4°E
0.83 0.86 0.86 0.84 0.84 0.91 0.90 0.74 0.90 0.90 0.82 0.90 0.91 0.87 0.87 0.87 0.90 0.90 0.54 0.90 0.81 0.90 0.89 0.91 0.92 0.90 0.86 0.89 0.90 0.87 0.90 0.92 0.88 1.00
5 18
0.64 0.72 0.71 0.70 0.54 0.69 0.70 0.67 0.69 0.67 0.69 0.71 0.70 0.67 0.69 0.70 0.71 0.71 0.70 0.67 0.69 0.68 0.66 0.70 0.60 0.67 0.71 0.70 0.71 0.69 0.73 0.64 0.71 0.72 0.76 1.00 0.69
5 19
77.3°E
Pearson correlation between 34 stations | Stations ordered by geographic proximity 11 10 27 4 30 28 32 15 14 21 23 7 9 19 13 6 34 3 31 26 22 25 33 2 24 16 12 17 29 8 18 5 20 1
0.81 0.95 0.94 0.96 0.85 0.95 0.90 0.88 0.91 0.77 0.95 0.92 0.93 0.93 0.96 0.95 0.95 0.91 0.93 0.93 0.93 0.93 0.88 0.95 0.87 0.94 0.95 0.96 0.95 0.95 0.94 0.79 0.96 0.96 0.93 0.69 1.00
1 21
77.2°E
Pairwise PM10 Station Correlation — Delhi
Pearson correlation between 37 stations | Stations ordered by geographic proximity 14 6 37 3 34 32 23 28 27 26 2 36 12 17 13 18 33 30 35 16 15 22 25 7 9 11 10 24 29 4 20 31 8 19 5 21 1
77.1°E
Source: PM10 data averaged over all available days
3 34
77.2°E
31
77.1°E
Source: PM2.5 data averaged over all available days
26
77.0°E
22
76.9°E
Source: Delhi PM10 daily data (1827 days) | Clustering: complete linkage on Haversine distance
Figure 4: Upper panel: Spatial distribution of monitoring stations across Delhi and average daily concentrations of P M 2.5 and P M 10 . Lower panel: Pairwise correlation heatmaps of P M 2.5 and P M 10 concentrations across monitoring stations, reordered according to geographical proximity using Haversine distance. For P M 10 , stations with unavailable records are excluded from the corresponding spatial and correlation plots.
13
PM2.5 Monitoring Stations — Mumbai, India
PM10 Monitoring Stations — Mumbai, India
Mean daily PM2.5 (µg/m³) | 18 stations | 1461 days
Mean daily PM10 (µg/m³) | 17 stations | 1461 days
N
19.4°N
N
19.4°N
16
19.3°N
19.3°N
Mean Daily PM2.5 (µg/m³) 1 2
19.2°N
70
7
10
Mean Daily PM10 (µg/m³) 140
1 2
19.2°N 12
7
10
12
60
8
120
8
14
14
50 17
19.1°N
3 4
16
19.1°N 9
3 9
6
15
100
4
40
6
15
80
30 19.0°N
19.0°N
18
17
11
18.9°N
11
5 13
5 13
18.9°N ~15 km
~15 km
72.80°E 72.85°E 72.90°E 72.95°E
72.80°E 72.85°E 72.90°E 72.95°E
Source:PM2.5 averaged over all available days
Source:PM10 averaged over all available days
Pairwise PM2.5 Station Correlation — Mumbai
Pairwise PM10 Station Correlation — Mumbai
Pearson correlation between 18 stations | Stations ordered by geographic proximity
Pearson correlation between 17 stations | Stations ordered by geographic proximity
2
0.86
0.74
0.76
0.68
0.86
0.69
0.80
0.54
0.70
0.63
0.86
0.93
0.73
0.88
0.50
0.74
0.74
1.00
2
0.72
0.79
0.73
0.79
0.72
0.74
0.40
0.61
0.66
0.83
0.78
0.81
0.81
0.64
0.76
0.77
1.00
1
0.76
0.64
0.66
0.60
0.71
0.73
0.73
0.43
0.49
0.52
0.72
0.74
0.70
0.75
0.55
0.60
1.00
0.74
1
0.67
0.75
0.70
0.74
0.72
0.77
0.40
0.60
0.66
0.84
0.67
0.78
0.80
0.60
0.74
1.00
0.77
7
0.70
0.58
0.62
0.54
0.71
0.56
0.68
0.40
0.56
0.50
0.71
0.73
0.59
0.72
0.43
1.00
0.60
0.74
7
0.68
0.72
0.70
0.71
0.69
0.73
0.35
0.58
0.60
0.79
0.73
0.74
0.77
0.63
1.00
0.74
0.76
10
0.54
0.37
0.51
0.34
0.57
0.55
0.53
0.25
0.48
0.35
0.47
0.52
0.45
0.55
1.00
0.43
0.55
0.50
10
0.58
0.67
0.64
0.70
0.63
0.68
0.32
0.44
0.57
0.70
0.65
0.66
0.69
1.00
0.63
0.60
0.64
12
0.72
0.78
0.71
0.80
0.74
0.84
0.39
0.66
0.70
0.87
0.73
0.79
1.00
0.69
0.77
0.80
0.81
0.45
0.59
0.70
0.73
14
0.89
0.82
0.80
0.73
0.89
0.73
0.86
0.55
0.65
0.65
0.92
1.00
0.78
0.93
0.52
0.73
0.74
0.93
4
0.86
0.82
0.76
0.76
0.86
0.72
0.85
0.52
0.63
0.70
1.00
0.92
0.81
0.89
0.47
0.71
0.72
0.86
3
0.57
0.59
0.56
0.58
0.57
0.58
0.60
0.42
0.47
1.00
0.70
0.65
0.65
0.62
0.35
0.50
0.52
0.63
8
0.76
0.75
0.75
0.75
0.84
0.81
0.35
0.60
0.61
0.85
0.72
1.00
0.79
0.66
0.74
0.78
0.81
14
0.69
0.73
0.69
0.74
0.68
0.68
0.37
0.50
0.54
0.73
1.00
0.72
0.73
0.65
0.73
0.67
0.78
4
0.78
0.83
0.78
0.85
0.78
0.88
0.41
0.69
0.71
1.00
0.73
0.85
0.87
0.70
0.79
0.84
0.83
3
0.54
0.66
0.58
0.65
0.60
0.72
0.32
0.53
1.00
0.71
0.54
0.61
0.70
0.57
0.60
0.66
0.66
9
0.55
0.56
0.52
0.59
0.53
0.65
0.23
1.00
0.53
0.69
0.50
0.60
0.66
0.44
0.58
0.60
0.61
16
0.36
0.37
0.34
0.40
0.28
0.34
1.00
0.23
0.32
0.41
0.37
0.35
0.39
0.32
0.35
0.40
0.40
15
0.72
0.79
0.72
0.78
0.81
1.00
0.34
0.65
0.72
0.88
0.68
0.81
0.84
0.68
0.73
0.77
0.74
6
0.69
0.73
0.74
0.73
1.00
0.81
0.28
0.53
0.60
0.78
0.68
0.84
0.74
0.63
0.69
0.72
0.72
0.75
9
0.64
0.48
0.58
0.50
0.70
0.47
0.55
0.38
1.00
0.47
0.63
0.65
0.45
0.60
0.48
0.56
0.49
0.70
17
0.52
0.47
0.47
0.46
0.52
0.38
0.47
1.00
0.38
0.42
0.52
0.55
0.42
0.52
0.25
0.40
0.43
0.54
15
0.84
0.78
0.77
0.63
0.81
0.78
1.00
0.47
0.55
0.60
0.85
0.86
0.77
0.88
0.53
0.68
0.73
0.80
6
0.70
0.70
0.67
0.63
0.64
1.00
0.78
0.38
0.47
0.58
0.72
0.73
0.83
0.74
0.55
0.56
0.73
0.69
18
0.85
0.74
0.80
0.70
1.00
0.64
0.81
0.52
0.70
0.57
0.86
0.89
0.68
0.85
0.57
0.71
0.71
0.86
11
0.68
0.70
0.62
1.00
0.70
0.63
0.63
0.46
0.50
0.58
0.76
0.73
0.69
0.66
0.34
0.54
0.60
0.68
17
0.79
0.85
0.80
1.00
0.73
0.78
0.40
0.59
0.65
0.85
0.74
0.75
0.80
0.70
0.71
0.74
0.79
13
0.79
0.74
1.00
0.62
0.80
0.67
0.77
0.47
0.58
0.56
0.76
0.80
0.68
0.78
0.51
0.62
0.66
0.76
11
0.77
0.80
1.00
0.80
0.74
0.72
0.34
0.52
0.58
0.78
0.69
0.75
0.71
0.64
0.70
0.70
0.73
5
0.77
1.00
0.74
0.70
0.74
0.70
0.78
0.47
0.48
0.59
0.82
0.82
0.76
0.79
0.37
0.58
0.64
0.74
13
0.75
1.00
0.80
0.85
0.73
0.79
0.37
0.56
0.66
0.83
0.73
0.75
0.78
0.67
0.72
0.75
0.79
16
1.00
0.77
0.79
0.68
0.85
0.70
0.84
0.52
0.64
0.57
0.86
0.89
0.71
0.89
0.54
0.70
0.76
0.86
5
1.00
0.75
0.77
0.79
0.69
0.72
0.36
0.55
0.54
0.78
0.69
0.76
0.72
0.58
0.68
0.67
0.72
0.50
0.50
0.25
0.25
0.00
16
Pearson Correlation (r) 1.00
0.75
2
0.77
1
1.00
7
0.78
10
0.81
8
0.65
12
0.45
4
0.42
14
0.77
3
0.83
9
0.68
16
0.69
6
0.68
15
0.76
17
0.71
11
8
5
0.88
13
0.75
2
0.72
1
0.55
7
1.00
10
0.77
8
0.93
12
0.89
4
0.62
14
0.60
3
0.52
9
0.88
17
0.74
6
0.85
15
0.66
18
0.78
11
0.79
5
0.89
13
12
Pearson Correlation (r) 1.00
Source: Mumbai PM2.5 daily data (1461 days) | Clustering: complete linkage on Haversine distance
0.00
Source: Mumbai PM10 daily data (1461 days) | Clustering: complete linkage on Haversine distance
Figure 5: Upper panel: Spatial distribution of monitoring stations across Mumbai and average daily concentrations of P M 2.5 and P M 10 . Lower panel: Pairwise correlation heatmaps of P M 2.5 and P M 10 concentrations across monitoring stations, reordered according to geographical proximity using Haversine distance. For P M 10 , one station with unavailable records is excluded from the corresponding plots.
3.2
Performance Evaluation Measures The experimental evaluation uses six performance measures to assess the forecasting accuracy
and uncertainty quantification of the proposed model. Four deterministic metrics, namely Mean Absolute Error (MAE), Mean Absolute Scaled Error (MASE), Root Mean Squared Error (RMSE), and Symmetric Mean Absolute Percentage Error (SMAPE), are used to evaluate point forecast accuracy from complementary perspectives, including absolute error, scale-free error, squared-error sensitivity, and relative percentage error (Hyndman and Athanasopoulos (2018)). In addition, two
14
probabilistic metrics, namely the Continuous Ranked Probability Score (CRPS) and Pinball Loss, are used to evaluate the quality of predictive distributions and quantile forecasts. These measures extend the assessment beyond point prediction by examining whether the model provides wellcalibrated uncertainty estimates, including performance in the tails of the predictive distribution. Pinball Loss evaluates accuracy at specified quantile levels, whereas CRPS summarizes the overall agreement between the predictive cumulative distribution and the observed outcome, following the principle of proper scoring rules (Gneiting and Raftery (2007)). The mathematical definitions of these metrics are given below. For station i, let XTi +h and X̂Ti +h denote the observed and predicted pollutant concentrations at forecast horizon h = 1, 2, . . . , q, respectively. The deterministic forecast accuracy measures are defined as i
MAE i
P = 1q qh=1
XTi +h − X̂Ti +h
,
r
2
RMSE =
1 Pq h=1 q
XTi +h − X̂Ti +h
1 Pq i i h=1 XT +h −X̂T +h q 1 PT i i t=2 Xt −Xt−1 T −1
|
i
MASE = , SMAPEi = 1q
|
| , |
2|XTi +h −X̂Ti +h | × 100%, i h=1 |X i T +h |+|X̂T +h |
Pq
q denotes the forecast horizon, T is the number of training observations, and i indexes the monitoring station. For the probabilistic evaluation, Q̂iT +h (ρ) denote the predicted ρ-level quantile for station i at horizon h. The Pinball Loss at quantile level ρ ∈ (0, 1) is defined as 1 PLiρ = q
q X
o n i i i i max ρ XT +h − Q̂T +h (ρ) , (ρ − 1) XT +h − Q̂T +h (ρ) .
h=1
The Continuous Ranked Probability Score (CRPS) is given by q
CRPSi =
1X q
Z ∞
h=1 −∞
i 2 FT +h (x) − 1{x ≥ XTi +h } dx,
where FTi +h denotes the predictive cumulative distribution function for station i at horizon h. In this study, Pinball Loss is evaluated at ρ = 0.8, corresponding to the 80th predictive quantile (Gneiting et al. (2023)). Lower values of all six metrics indicate better forecasting performance. 3.3
Implementation of the Proposed GCSVR The proposed GCSVR framework is implemented in two stages: spatial feature extraction using
GCN and temporal forecasting using SVR. First, the monitoring network is represented as a weighted graph, where nodes correspond to monitoring stations and edge weights are derived from inter-
15
station Haversine distances. The adjacency matrix is constructed from the pairwise distance matrix using a Gaussian kernel. The spatial module is implemented as a two-layer GCN using the GCNConv module from PyTorch Geometric. For each time step, the node feature matrix consists of the previous 24 days of pollutant observations at each station. The first GCN layer maps the 24-dimensional input features to a 64-dimensional hidden representation, followed by ReLU activation and dropout with a rate of 0.2. The second GCN layer produces a 32-dimensional spatial embedding for each station. The GCN is trained for 100 epochs using the Adam optimizer with learning rate 0.001 and weight decay 5×10−4 , minimizing the mean squared error between the predicted and observed next-day pollutant concentrations across all stations. After training, the GCN is frozen and used as a spatial feature extractor. In the temporal forecasting stage, a separate SVR model is trained for each monitoring station using the SVR implementation from scikit-learn. For each station, the SVR input is formed by concatenating two components: the 24-dimensional local lagged pollutant sequence and the 32-dimensional GCN-derived spatial embedding for that station. The resulting 56-dimensional feature vector combines station-specific temporal dynamics with spatial information aggregated from neighbouring stations. This concatenation is important because the GCN embedding captures inter-station spatial dependence, while the local lagged sequence preserves the recent temporal behaviour of the target station. Before SVR training, all input features are standardized. The SVR is fitted using an RBF kernel with C = 100, gamma = scale, and ϵ = 0.1. Multi-step forecasts over 30, 60, and 90-day horizons are generated recursively: each predicted value is appended to the input sequence, the oldest value is removed, and the updated sequence is used to forecast the next time step. For future horizons, spatial embeddings are computed using the most recently available input window passed through the trained GCN. 3.4
Experimental Results The experimental results are presented first for the Delhi dataset, as it provides a particularly
challenging testbed for evaluating the robustness of the proposed GCSVR framework. Delhi is one of the most polluted capital cities in the world, and its pollutant concentration series exhibit pronounced nonlinearity, strong seasonal variation, spatial heterogeneity, and frequent extreme or anomalous observations. These characteristics make the Delhi dataset especially suitable for assessing whether the proposed model can maintain stable forecasting accuracy under outlier-prone and
16
high-pollution conditions. We therefore use Delhi as the primary case study for detailed model comparison, horizon-wise evaluation, seasonal analysis, and robustness assessment. The Mumbai results are subsequently used to examine the generalizability of the proposed framework in a climatically distinct coastal urban environment. 3.4.1
Results on Delhi dataset
Tables 1 and 2 report the 30-day forecasting results for PM2.5 and PM10 , respectively. The proposed GCSVR model is compared with nine benchmark models: ARIMA, LSTM, DeepAR, Transformer, N-BEATS, STARMA, GSTAR, GpGp, and STGCN. Forecasting performance is evaluated using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS, with lower values indicating better performance across all metrics. The experimental setup and benchmark results for the competing models are adopted from Panja et al. (2026) to ensure a consistent and directly comparable evaluation protocol across the same Delhi air quality dataset. For PM2.5 , GCSVR achieves the strongest overall performance across the majority of monthly windows and metrics, with frequent best results in MAE and RMSE, and consistently competitive results across the remaining measures. The improvements are particularly evident during high pollution periods, where competing models exhibit larger errors. However, there are instances where alternative models, such as N-BEATS or ARIMA, achieve comparable or slightly better results for specific metrics, indicating that the advantage of GCSVR is not uniform across all conditions. A similar pattern is observed for the probabilistic metrics, where GCSVR generally attains lower CRPS and Pinball Loss values, while remaining competitive rather than strictly dominant. A similar pattern is observed for PM10 , where GCSVR again shows strong and stable performance across most evaluation metrics and months. While some baselines achieve marginal improvements in isolated metrics for specific periods, these gains are not systematic and typically occur in limited cases rather than across multiple metrics or time windows. Tables 3 and 4 extend the evaluation to the 60-day forecasting horizon. GCSVR maintains a clear and consistent advantage across both PM2.5 and PM10 , achieving the lowest or near lowest errors across all evaluation metrics. The improvement is not confined to a subset of measures but is observed across both deterministic and probabilistic criteria, indicating that the model preserves accuracy as well as distributional alignment over extended horizons. Compared to the 30-day horizon, GCSVR continues to provide stable gains with only mild performance degradation, demonstrating that the combined spatial embeddings and local temporal dynamics effectively support longer-term forecasting. Tables 5 and 6 further evaluate performance at the 90-day hori-
17
zon. GCSVR continues to deliver strong and reliable forecasts for both pollutants, maintaining competitive performance across metrics and windows. Table 1: 30 day-ahead forecasting performance for P M2.5 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN
MAE MASE RMSE SMAPE Pinball Loss CRPS
54.88 0.96 71.18 31.20 35.68 78.95
160.54 2.85 174.93 152.10 128.43 113.95
164.82 2.93 178.87 160.70 131.86 113.95
93.72 1.63 114.86 60.40 74.32 113.43
61.72 1.10 78.46 36.50 41.03 89.85
95.87 1.67 112.01 69.40 76.03 110.15
63.48 1.10 82.27 39.50 47.16 94.29
86.09 1.49 107.61 53.30 66.68 111.56
66.51 1.16 84.94 39.01 49.42 96.64
49.71 1.94 64.27 26.91 24.86 36.25
FEB
MAE MASE RMSE SMAPE Pinball Loss CRPS
36.26 1.23 45.68 32.00 17.44 50.74
91.75 3.11 101.86 127.70 73.40 71.20
96.10 3.27 105.83 139.70 76.88 71.21
37.45 1.27 50.23 33.10 24.60 54.57
38.97 1.35 49.71 34.00 20.09 54.71
73.25 2.47 88.40 89.10 58.44 72.02
70.54 2.40 85.35 83.80 56.29 71.81
37.82 1.31 49.05 33.50 21.67 53.89
36.04 1.23 47.79 31.87 22.58 52.50
36.98 1.41 46.43 31.81 18.49 27.19
MAR
MAE MASE RMSE SMAPE Pinball Loss CRPS
33.32 1.70 38.68 38.60 7.21 39.74
56.96 2.78 61.09 108.50 45.57 47.91
60.59 2.98 64.47 120.90 48.47 47.91
25.88 1.35 30.17 31.90 7.76 34.81
25.90 1.24 31.38 30.00 7.90 35.24
36.81 1.79 42.52 59.10 27.62 45.98
31.18 1.53 35.75 44.70 20.59 42.02
31.99 1.75 36.87 38.20 8.40 38.08
30.40 1.60 35.75 36.24 8.75 38.21
20.22 0.77 24.62 26.27 10.11 17.76
22.49 2.52 27.92 32.20 10.43 37.21
47.35 2.75 53.81 93.50 37.86 43.49
51.54 1.94 57.56 108.50 41.23 43.48
33.61
APR
MAE MASE 1.22 RMSE SMAPE Pinball Loss CRPS
38.34 45.10 10.21 37.75
22.44 1.20 28.55 33.00 14.01 37.15
50.17 2.68 57.09 107.10 40.11 43.67
37.83 2.02 45.31 68.90 29.17 43.50
36.48 2.16 41.67 48.40 10.56 39.32
38.27 2.18 43.10 48.92 10.37 40.42
21.27 0.81 26.56 31.48 10.63 13.37
MAY
MAE MASE RMSE SMAPE Pinball Loss CRPS
35.10 1.43 42.79 48.40 11.73 41.50
45.77 1.83 56.97 85.80 36.55 44.36
49.80 2.00 60.38 100.40 39.83 44.35
39.24 1.63 45.89 53.70 11.32 42.15
30.31 1.22 37.60 44.20 14.87 38.98
42.19 1.69 52.70 80.10 33.20 44.11
35.32 1.42 45.30 59.30 26.50 43.11
40.23 1.72 47.76 53.70 11.32 43.95
42.47 1.75 49.82 55.87 12.32 45.37
28.82 1.04 34.28 39.74 13.41 21.00
JUN
MAE MASE RMSE SMAPE Pinball Loss CRPS
23.59 2.20 27.23 45.10 6.85 26.06
22.77 1.99 27.32 58.40 18.11 27.51
26.79 2.39 30.91 75.10 21.39 28.16
53.82 5.22 55.83 78.80 11.10 39.23
33.72 3.08 40.94 54.00 8.16 33.94
27.43 2.47 30.66 85.50 21.94 27.80
24.78 2.24 28.29 73.60 19.80 27.49
54.13 5.34 57.68 78.00 11.37 41.02
27.94 2.66 32.84 52.91 9.29 31.62
12.77 0.49 16.33 27.63 6.39 15.44
JULY
MAE MASE RMSE SMAPE Pinball Loss CRPS
23.00 3.20 26.16 53.20 5.07 21.87
12.98 1.63 15.84 41.20 9.72 18.25
16.23 2.00 19.05 55.30 12.71 20.49
64.44 8.76 65.33 99.60 12.90 40.58
17.71 2.47 21.69 43.00 4.55 20.01
20.32 2.47 23.09 81.20 16.09 20.95
16.44 1.99 19.42 60.20 12.50 20.20
60.83 8.39 63.79 94.60 12.18 40.44
32.21 4.60 34.43 69.07 10.02 25.73
9.33 0.37 11.61 27.36 4.67 14.00
AUG
MAE MASE RMSE SMAPE Pinball Loss CRPS
20.00 3.25 22.20 44.00 4.66 20.38
16.06 2.30 19.01 45.90 12.54 21.45
19.67 2.87 22.42 61.10 15.63 23.31
60.41 10.15 61.48 90.70 12.17 39.88
18.38 2.98 22.64 38.40 5.59 21.37
20.52 3.06 24.71 67.40 15.65 24.02
25.65 3.84 28.93 94.20 20.45 23.97
58.39 9.78 59.55 89.20 11.75 38.91
51.29 8.63 52.64 82.54 11.40 35.56
9.99 0.40 12.98 27.82 5.00 14.45
SEPT
MAE MASE RMSE SMAPE Pinball Loss CRPS
22.48 2.46 26.80 49.90 5.11 24.43
20.76 2.15 25.72 57.10 15.62 26.35
24.06 2.50 29.06 70.30 18.66 26.68
53.97 6.01 57.04 84.10 10.95 39.72
19.66 2.12 24.10 44.80 7.06 23.40
22.97 2.41 30.48 67.70 16.80 27.57
22.30 2.34 29.16 63.90 15.88 27.29
52.60 5.84 56.34 82.50 10.66 40.13
56.07 6.25 59.07 85.41 12.39 40.62
11.54 0.47 15.37 32.31 5.77 14.35
OCT
MAE MASE RMSE SMAPE Pinball Loss CRPS
35.69 1.93 47.38 35.90 26.47 56.05
75.37 4.19 85.49 111.30 60.30 63.26
79.84 4.45 89.45 124.00 63.87 63.27
35.38 1.98 42.93 35.70 18.36 47.22
41.20 2.25 52.15 44.90 29.21 56.02
67.20 3.72 83.63 90.90 53.67 64.94
65.33 3.63 81.76 86.90 52.13 64.86
33.87 1.89 42.76 34.00 18.59 49.04
36.12 1.98 46.58 36.89 24.77 52.69
24.56 1.01 32.35 28.80 12.15 19.79
NOV
MAE MASE RMSE SMAPE Pinball Loss CRPS
102.46 1.77 119.19 49.30 79.49 142.51
216.26 3.74 228.49 159.30 173.01 148.22
219.77 3.80 231.84 164.40 175.82 148.23
147.62 2.52 164.44 81.10 117.81 147.73
119.58 2.06 137.38 61.80 93.07 145.81
141.29 2.42 157.71 81.10 112.22 147.36
143.39 2.46 159.42 81.80 114.07 147.19
136.72 2.32 153.82 72.50 108.65 146.60
142.82 2.44 159.83 77.45 114.85 147.55
61.55 2.55 79.49 28.15 30.78 45.69
DEC
MAE MASE RMSE SMAPE Pinball Loss CRPS
74.03 1.97 94.04 39.80 50.95 106.68
176.33 4.76 186.95 151.90 141.06 123.46
181.01 4.89 191.37 159.90 144.81 123.46
106.47 2.85 122.82 66.10 85.07 122.15
68.77 1.84 89.40 35.90 46.63 105.74
97.15 2.59 123.92 58.20 71.73 124.31
106.11 2.86 133.80 68.30 84.21 125.80
96.54 2.55 116.90 56.80 74.21 120.71
81.80 2.20 102.78 46.32 65.71 124.10
43.23 1.70 54.44 21.26 21.26 31.02
18
Table 2: 30 day-ahead forecasting performance for P M10 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN
MAE MASE RMSE SMAPE Pinball Loss CRPS
99.31 1.23 126.85 35.90 73.38 148.08
276.07 3.46 294.14 175.50 220.85 181.85
275.41 3.45 293.53 174.60 220.33 181.85
165.16 2.05 192.87 70.50 131.76 181.60
87.24 1.10 112.07 30.80 49.21 126.42
121.40 1.49 147.81 47.10 95.66 166.91
82.99 1.02 110.33 29.70 58.43 133.98
86.54 1.09 109.86 30.30 44.33 125.78
94.94 1.18 123.03 34.22 66.80 140.99
74.04 1.71 94.76 25.15 37.02 53.72
FEB
MAE MASE RMSE SMAPE 25.40 Pinball Loss CRPS
59.32 1.25 77.99 172.10 42.62 96.23
218.02 4.72 228.33 169.00 174.42 143.51
216.10 4.68 226.50 49.80 172.88 143.52
102.77 2.14 122.29 29.50 81.67 135.78
68.89 1.50 83.55 96.70 34.85 101.07
157.65 3.38 175.50 93.30 126.07 144.43
153.76 3.32 171.40 52.60 122.95 144.32
106.83 2.22 125.72 85.05 137.02
57.98 1.23 74.10 24.96 38.28 92.88
55.45 1.23 70.56 24.32 27.72 41.60
MAR
MAE MASE RMSE SMAPE Pinball Loss CRPS
51.41 1.29 62.16 29.60 14.42 73.61
159.77 3.93 166.91 169.10 127.82 105.90
154.64 3.80 162.02 158.10 123.71 105.90
52.33 1.23 63.41 31.30 37.08 82.38
52.00 1.31 64.42 29.50 14.23 75.46
54.18 1.30 64.10 33.40 34.13 80.74
51.87 1.26 61.11 31.60 30.48 77.35
60.80 1.61 71.00 34.40 18.40 78.00
49.95 1.26 60.05 29.01 16.54 72.26
48.03 1.08 59.68 27.87 24.02 36.58
APR
MAE MASE RMSE SMAPE Pinball Loss CRPS
59.82 1.37 75.86 30.90 43.18 96.36
181.01 4.18 191.41 164.50 144.81 122.26
179.36 4.14 189.86 161.40 143.49 122.26
71.49 1.61 88.30 37.90 53.27 108.53
67.72 1.54 85.42 36.10 51.59 108.55
151.14 3.46 165.07 117.10 120.90 122.69
106.86 2.45 124.18 68.50 83.76 122.69
61.34 1.42 74.55 31.90 38.60 92.03
55.68 1.31 66.76 29.03 27.75 82.19
48.28 1.08 59.68 27.87 24.02 36.58
MAY
MAE MASE RMSE SMAPE Pinball Loss CRPS
71.01 1.12 91.48 38.00 35.98 90.80
176.32 2.81 199.93 167.30 141.06 122.60
170.78 2.72 195.07 155.40 136.63 122.60
79.39 1.24 107.15 42.90 53.76 108.91
71.75 1.15 92.81 38.60 33.77 90.80
117.99 1.86 147.03 77.90 91.62 122.96
88.82 1.41 118.57 49.30 61.73 119.12
78.77 1.23 105.91 42.50 52.29 107.33
78.42 1.25 97.83 41.91 36.63 96.06
70.10 1.56 93.68 36.28 35.05 51.30
JUN
MAE MASE RMSE SMAPE Pinball Loss CRPS
67.66 2.00 81.88 45.10 20.16 80.27
117.99 3.36 129.68 150.10 94.39 84.39
114.96 3.27 126.93 142.20 91.96 84.39
47.59 1.42 58.79 36.00 20.32 63.00
43.32 1.27 56.31 33.40 23.77 62.06
87.20 2.46 100.34 90.00 69.76 83.63
74.67 2.11 89.19 70.90 59.68 83.14
69.23 2.09 82.67 47.00 23.20 81.28
72.83 2.17 82.26 48.73 19.06 77.44
37.74 0.85 49.41 28.33 18.87 31.75
JULY
MAE MASE RMSE SMAPE Pinball Loss CRPS
101.08 5.72 108.53 81.10 20.77 74.62
60.00 3.21 65.60 120.10 48.00 47.71
57.24 3.05 63.07 110.20 45.79 47.70
72.83 4.37 77.47 69.50 14.95 58.41
30.07 1.65 36.78 36.90 10.36 38.46
38.87 2.01 46.32 62.10 30.43 46.71
31.80 1.66 38.07 46.70 22.67 43.11
96.52 5.83 103.92 79.90 20.41 72.39
125.26 7.09 128.13 93.13 26.11 83.19
22.24 0.50 27.88 27.86 11.12 25.12
AUG
MAE MASE RMSE SMAPE Pinball Loss CRPS
60.84 2.86 69.72 42.60 14.02 67.48
108.73 4.88 116.57 146.70 86.98 77.86
105.64 4.73 113.71 138.40 84.51 77.86
48.29 2.23 56.02 37.20 16.72 60.84
47.00 2.03 59.81 39.20 35.18 68.49
71.27 3.16 87.31 71.80 56.80 79.02
84.91 3.80 97.19 94.80 67.91 78.59
60.04 2.88 69.23 43.10 15.76 67.32
42.14 1.90 51.87 32.29 18.73 58.65
30.60 0.67 38.89 26.72 15.30 28.81
SEPT
MAE MASE RMSE SMAPE Pinball Loss CRPS
82.97 4.60 94.06 60.70 16.86 78.86
92.66 5.68 102.86 130.70 74.08 70.71
91.22 5.59 101.53 126.70 72.92 70.71
52.34 3.08 63.62 46.50 13.99 62.09
68.16 3.89 81.38 53.40 14.91 69.93
48.30 2.95 60.46 48.50 26.92 65.91
47.63 2.90 58.86 46.60 24.25 64.31
66.26 3.91 78.06 53.70 14.97 69.96
89.70 5.15 101.05 63.63 19.36 84.24
33.31 0.77 40.63 32.87 16.66 28.91
OCT
MAE MASE RMSE SMAPE Pinball Loss CRPS
56.62 1.54 76.41 25.00 38.14 93.92
214.64 6.00 225.67 176.90 171.71 139.86
206.32 5.75 217.78 162.80 165.06 139.86
81.46 2.17 101.38 37.90 62.31 119.26
94.69 2.61 114.30 47.60 74.59 133.38
120.44 3.27 148.51 66.20 95.89 141.47
118.95 3.29 147.03 65.60 94.70 141.89
67.79 1.80 88.08 30.20 47.51 105.70
60.10 1.64 79.08 26.74 40.09 95.93
39.38 0.92 50.89 20.10 19.69 32.04
NOV
MAE MASE RMSE SMAPE Pinball Loss CRPS
160.63 2.00 181.25 49.20 124.79 222.28
370.52 4.64 387.20 182.20 296.41 237.70
365.48 4.57 382.37 176.90 292.38 237.70
230.28 2.86 255.63 78.10 183.96 237.70
114.14 1.43 137.63 31.90 73.64 178.26
164.50 2.04 183.15 51.80 125.90 216.77
163.94 2.04 182.67 51.80 125.97 219.46
101.36 1.28 123.56 27.60 49.25 159.67
139.78 1.74 161.36 40.51 105.57 206.01
91.44 2.12 116.45 25.74 45.72 67.62
DEC
MAE MASE RMSE SMAPE Pinball Loss CRPS
111.36 2.02 139.68 36.60 83.53 174.92
320.05 5.87 329.61 184.50 256.04 202.04
311.54 5.71 321.36 174.50 249.23 202.04
174.14 3.12 191.44 66.20 139.30 200.90
82.85 1.54 100.84 24.70 39.40 128.38
131.11 2.36 163.30 45.00 95.89 189.84
148.68 2.71 183.15 55.20 117.67 201.10
112.51 2.02 139.38 36.10 80.35 171.97
134.13 2.43 155.58 46.92 108.21 190.48
62.34 1.43 79.39 18.87 31.17 45.88
19
Table 3: 60 day-ahead forecasting performance for P M2.5 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN–FEB
MAE RMSE MASE SMAPE Pinball Loss CRPS
73.48 86.23 1.72 46.50 21.51 83.42
132.20 148.60 3.11 152.00 105.76 95.40
131.90 148.33 3.10 151.30 105.52 95.40
66.52 89.53 1.54 47.40 50.69 94.09
59.28 77.12 1.39 45.20 45.07 83.66
80.56 96.46 1.87 81.50 62.52 87.92
100.35 113.61 2.36 57.00 23.37 99.12
58.53 78.81 1.36 39.90 39.18 85.74
62.00 84.09 1.44 43.58 46.61 92.50
43.18 56.12 1.70 29.68 21.59 32.46
MAR–APR
MAE RMSE MASE SMAPE Pinball Loss CRPS
35.03 40.90 1.82 43.70 8.10 40.07
59.96 65.06 3.02 131.80 47.97 45.49
55.51 60.99 2.78 114.10 44.41 45.50
29.62 34.89 1.58 39.20 8.60 36.68
35.06 41.08 1.84 42.80 8.89 40.11
50.95 57.72 2.56 111.50 40.47 45.67
50.86 58.23 2.55 112.70 39.91 45.84
37.44 42.69 2.07 46.50 9.54 40.96
34.42 39.94 1.81 43.28 9.65 39.48
21.29 26.53 0.82 29.88 10.64 20.09
MAY–JUN
MAE RMSE MASE SMAPE Pinball Loss CRPS
37.54 42.70 2.14 57.70 11.64 37.77
40.38 49.77 2.23 97.10 32.29 36.76
38.31 48.09 2.11 88.10 30.63 36.77
46.70 51.41 2.71 66.60 11.17 41.25
22.53 32.55 1.24 39.10 15.27 32.45
43.36 50.27 2.41 127.60 34.65 36.00
22.15 30.71 1.23 38.70 13.32 29.82
49.65 54.99 2.95 68.60 11.69 43.42
50.80 55.57 2.92 69.57 19.84 43.61
19.36 26.50 0.77 33.07 9.68 20.22
JULY–AUG
MAE RMSE MASE SMAPE Pinball Loss CRPS
30.37 33.44 4.07 60.90 6.55 26.97
21.33 24.35 2.68 74.00 16.98 22.71
18.44 21.69 2.30 59.70 14.57 22.46
60.75 61.90 8.17 93.40 12.21 39.78
24.10 28.32 3.25 51.00 5.82 24.77
29.51 32.59 3.77 132.80 23.60 22.95
12.67 16.06 1.60 38.10 9.45 18.45
62.11 64.19 8.35 93.60 12.50 41.13
62.03 63.43 8.33 93.83 13.47 40.81
9.98 13.02 0.40 28.72 4.99 16.43
SEPT–OCT
MAE RMSE MASE SMAPE Pinball Loss CRPS
36.12 51.27 2.63 55.00 26.24 46.88
54.88 69.38 3.95 107.90 43.73 47.82
52.05 66.93 3.74 97.40 41.36 47.83
44.53 50.97 3.32 59.80 14.96 45.98
40.25 55.78 2.91 64.00 30.90 47.67
58.62 76.23 4.25 120.70 46.10 49.68
34.86 49.13 2.54 52.40 24.12 45.92
44.33 51.34 3.34 59.40 14.66 46.10
34.29 41.26 2.52 49.63 15.37 39.24
20.45 28.78 0.84 34.97 10.22 19.47
NOV–DEC
MAE RMSE MASE SMAPE Pinball Loss CRPS
90.77 111.64 1.91 46.50 71.38 131.98
204.62 217.05 4.30 169.40 163.70 136.38
200.48 213.17 4.21 162.30 160.39 136.39
127.97 146.81 2.67 74.50 102.18 135.65
132.34 149.75 2.78 80.80 105.13 136.02
159.92 175.57 3.35 117.80 127.54 136.20
157.59 173.31 3.31 113.50 125.72 136.15
120.80 139.69 2.50 68.20 96.23 134.78
107.25 127.11 2.24 57.87 85.93 134.44
55.38 73.02 2.28 26.19 27.66 41.60
Table 4: 60 day-ahead forecasting performance for P M10 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN–FEB
MAE RMSE MASE SMAPE Pinball Loss CRPS
94.47 113.55 1.53 35.10 30.47 124.50
252.19 269.06 3.99 183.00 201.75 163.35
245.01 262.36 3.88 171.80 196.01 163.35
135.51 163.79 2.11 61.20 107.88 162.62
95.19 116.76 1.53 35.40 34.42 124.74
120.61 147.89 1.88 61.00 91.92 152.08
116.70 143.09 1.83 56.50 90.83 153.03
101.61 130.47 1.58 40.70 74.52 149.54
82.81 110.99 1.30 32.34 60.41 131.16
70.85 90.67 1.67 26.66 35.43 53.55
MAR–APR
MAE RMSE MASE SMAPE Pinball Loss CRPS
61.48 73.69 1.43 33.40 19.10 83.08
168.41 178.80 3.87 167.10 134.73 113.16
164.51 175.13 3.78 159.10 131.61 113.16
62.63 78.19 1.39 35.80 45.14 95.51
61.36 75.55 1.42 33.80 28.45 87.98
103.94 125.97 2.35 76.30 79.35 115.24
95.72 117.40 2.18 67.70 72.03 114.65
57.14 70.86 1.32 32.20 32.15 85.66
54.37 65.85 1.27 30.45 24.67 77.98
49.65 61.83 1.10 27.80 24.83 39.67
MAY–JUN
MAE RMSE MASE SMAPE Pinball Loss CRPS
71.99 89.34 1.48 43.60 30.71 86.48
145.59 167.01 2.95 155.20 116.47 104.87
143.09 164.85 2.90 149.30 114.47 104.87
83.16 113.32 1.65 56.00 64.84 104.04
67.01 95.91 1.35 42.90 50.75 98.39
129.13 150.33 2.61 128.80 103.25 103.80
111.88 134.00 2.27 100.80 89.01 103.36
67.53 87.32 1.40 41.70 33.56 87.12
75.81 90.26 1.57 45.48 32.42 86.72
61.15 80.33 1.37 36.00 30.58 47.43
JULY–AUG
MAE RMSE MASE SMAPE Pinball Loss CRPS
58.10 65.40 2.90 50.40 13.75 59.61
87.62 97.74 4.18 142.70 70.09 64.63
82.17 92.87 3.90 125.20 65.73 64.63
59.70 67.62 3.05 52.50 15.87 61.12
42.82 54.78 2.04 40.70 21.15 57.72
76.47 91.86 3.62 110.10 60.88 66.10
77.41 93.15 3.69 112.70 61.64 66.26
70.26 78.60 3.65 58.20 17.58 66.90
104.24 111.69 5.22 73.42 22.79 82.76
26.53 34.68 0.58 27.63 13.27 30.52
SEPT–OCT
MAE RMSE MASE SMAPE Pinball Loss CRPS
64.76 81.32 2.38 40.50 27.79 85.45
153.86 174.76 5.74 156.20 123.08 109.81
148.98 170.42 5.55 145.10 119.15 109.81
67.84 87.21 2.50 42.70 38.93 92.85
77.56 97.58 2.88 47.90 42.61 101.60
119.55 151.29 4.44 93.70 89.79 115.41
118.63 150.95 4.42 92.00 88.02 116.21
70.16 88.90 2.62 43.80 35.99 92.69
74.00 89.91 2.74 44.80 29.03 91.66
40.59 51.29 0.94 28.81 20.30 35.39
NOV–DEC
MAE RMSE MASE SMAPE Pinball Loss CRPS
114.94 139.63 1.71 35.00 87.31 180.03
342.22 356.98 5.07 179.80 273.77 220.48
338.54 353.46 5.01 175.80 270.84 220.48
202.89 226.80 2.97 72.60 162.18 220.48
156.01 177.83 2.30 52.30 121.19 209.88
204.62 226.54 3.00 81.90 160.86 216.08
188.63 210.06 2.79 72.00 148.22 219.38
186.24 208.70 2.71 64.90 134.06 215.31
164.65 191.68 2.43 54.60 146.36 219.38
73.43 96.63 1.70 21.21 36.72 55.74
20
Table 5: 90 day-ahead forecasting performance for P M2.5 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
JAN–FEB–MAR
APR–MAY–JUN
JULY–AUG–SEPT
OCT–NOV–DEC
Metric
ARIMA
LSTM
DeepAR
Spatio-Temporal Model
Trans.
NBeats
STARMA
GSTAR
GpGp
Proposed STGCN
GCSVR
MAE
87.20
108.92
108.36
52.24
50.23
77.69
80.22
50.66
51.90
38.24
RMSE
97.95
127.48
127.00
75.09
66.30
90.16
92.99
68.84
73.24
51.67
MASE
2.47
3.10
3.09
1.48
1.43
2.20
2.28
1.45
1.47
1.50
SMAPE
59.70
143.60
142.00
41.70
47.90
110.70
110.30
40.20
41.39
29.99
Pinball Loss
27.03
87.13
86.69
36.48
38.46
60.86
63.74
29.13
34.91
19.12
CRPS
83.53
82.09
82.09
77.78
68.19
73.70
75.95
69.47
74.53
31.05
MAE
44.46
47.61
43.16
40.92
25.30
52.92
47.06
47.07
45.87
20.84
RMSE
50.55
55.62
51.84
58.00
30.93
59.96
54.56
52.37
51.03
28.01
MASE
2.55
2.63
2.38
2.39
1.42
2.95
2.62
2.81
2.64
0.82
SMAPE
59.90
116.20
96.50
58.00
40.80
157.20
133.60
63.50
61.84
32.24
Pinball Loss
10.97
38.09
34.52
10.34
10.78
42.32
37.29
11.54
11.83
10.42
CRPS
43.12
39.28
39.29
39.77
37.64
39.09
39.06
43.32
42.44
20.89
MAE
37.00
20.14
19.75
61.16
41.07
31.89
29.92
61.83
63.09
11.69
RMSE
40.83
24.13
23.78
62.78
47.51
35.94
34.54
64.02
64.92
15.23
MASE
4.64
2.36
2.31
7.69
5.17
3.80
3.56
7.76
7.92
0.46
SMAPE
68.30
64.30
62.50
93.20
69.80
146.50
132.70
93.10
94.02
33.50
Pinball Loss
7.71
15.84
15.51
12.32
8.72
25.46
23.72
12.43
13.71
5.85
CRPS
30.49
23.50
23.49
40.74
34.56
23.93
24.10
41.48
42.08
16.73
MAE
99.14
158.91
157.95
98.80
136.28
163.98
163.83
96.85
96.12
45.70
RMSE
126.15
180.61
179.76
125.13
161.44
190.17
189.36
123.31
128.35
63.65
MASE
2.66
4.29
4.26
2.65
3.68
4.43
4.43
2.58
2.91
1.85
SMAPE
64.30
151.40
149.20
63.90
110.10
157.20
157.30
61.80
65.22
27.84
Pinball Loss
78.49
127.12
126.36
76.57
108.97
131.16
131.07
74.97
75.82
22.85
CRPS
114.80
115.44
115.44
114.58
115.60
117.16
116.93
114.31
114.41
32.16
Table 6: 90 day-ahead forecasting performance for P M10 in Delhi, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
JAN–FEB–MAR
APR–MAY–JUN
JULY–AUG–SEPT
OCT–NOV–DEC
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
MAE
111.07
219.16
215.14
109.07
110.28
128.22
118.87
84.76
73.02
GCSVR 68.22
RMSE
128.20
237.79
234.10
129.64
129.64
149.21
139.84
113.21
98.71
87.30
MASE
2.04
3.94
3.86
1.92
2.02
2.28
2.12
1.50
1.31
1.65
SMAPE
44.00
174.70
167.80
52.20
43.80
86.60
73.20
37.20
31.84
28.71
Pinball Loss
29.99
175.32
172.12
85.71
32.37
99.53
93.41
59.62
46.66
34.11
CRPS
125.56
146.24
146.24
144.56
126.52
136.51
136.65
127.41
110.51
54.20
MAE
69.36
162.31
155.56
65.89
69.75
150.98
123.69
68.75
72.40
55.08
RMSE
85.71
180.11
174.06
88.02
95.17
169.22
144.79
86.74
86.75
75.60
MASE
1.49
3.45
3.29
1.39
1.47
3.20
2.62
1.48
1.56
1.23
SMAPE
40.00
169.50
154.00
38.70
42.40
152.90
112.20
42.50
41.43
32.26
Pinball Loss
33.59
129.85
124.44
43.33
52.72
120.78
98.34
38.58
27.46
27.54
CRPS
89.98
111.26
111.26
96.81
104.82
110.78
110.55
92.48
89.62
45.16
MAE
67.13
89.83
84.03
57.10
44.69
84.31
86.80
70.51
101.56
30.20
RMSE
76.53
100.04
94.82
66.28
56.63
98.63
103.53
80.25
109.53
38.50
MASE
3.48
4.48
4.18
3.03
2.21
4.20
4.35
3.82
5.27
0.67
SMAPE
54.90
144.20
125.70
50.80
45.60
130.20
130.80
57.80
71.70
31.13
Pinball Loss
14.92
71.86
67.20
15.10
29.33
67.22
68.49
16.98
22.03
15.10
CRPS
65.28
65.90
65.90
60.97
62.90
67.20
68.62
68.29
82.83
33.28
MAE
181.14
296.82
292.10
162.13
246.24
259.03
263.90
155.14
137.84
68.16
RMSE
212.44
317.30
312.89
194.85
274.96
293.93
297.78
188.18
171.56
92.33
MASE
3.24
5.32
5.23
2.86
4.41
4.63
4.73
2.72
2.81
1.61
SMAPE
74.10
177.60
171.40
61.40
122.30
135.20
139.80
57.40
50.71
22.97
Pinball Loss
144.49
237.46
233.68
128.70
196.98
207.09
211.09
122.13
109.33
34.08
CRPS
195.50
195.37
195.37
195.27
196.71
198.95
198.78
193.24
192.65
52.48
21
Across all horizons, a consistent pattern emerges. Temporal models such as ARIMA remain relatively stable but lack the capacity to capture spatial dependencies, limiting their overall performance. Deep learning-based temporal models, including LSTM and DeepAR, tend to exhibit higher errors and greater variability, particularly as the forecasting horizon increases, due to their data-intensive nature. Overall, the results indicate that GCSVR not only achieves strong pointwise accuracy but also maintains stable performance as the forecasting horizon increases. While all models experience performance degradation at longer horizons, GCSVR exhibits a more gradual increase in error and retains a consistent advantage across both pollutants and evaluation metrics. This behavior is particularly important in air quality forecasting, where reliable long-term predictions are required despite the presence of strong temporal variability and spatial heterogeneity.
Figure 6: Delhi 30-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS. Each box plot shows the distribution of forecast errors across evaluation windows for a given model. The dashed vertical line separates temporal benchmark models from spatiotemporal models, while the horizontal dotted line indicates the lowest median error among all models for each metric.
22
Figure 7: Delhi 60-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS.
Figs. 6, 7, and 8 provide a distributional comparison of model performance across the 30, 60, and 90-day forecasting horizons. Across all six evaluation metrics, GCSVR consistently yields lower and more compact error distributions, indicating both higher accuracy and greater stability across forecasting windows. This pattern is observed for both deterministic metrics, such as MAE, MASE, RMSE, and SMAPE, and probabilistic metrics, including Pinball Loss and CRPS. The horizontal dotted reference lines further highlight that GCSVR attains the lowest median error in most metric panels, supporting its robustness under outlier-prone pollution conditions. Among the competing methods, N-BEATS generally provides the strongest alternative performance, whereas DeepAR, STARMA, and STGCN show comparatively larger errors and greater variability across several metrics. Overall, the box plots reinforce the tabular results and demonstrate the consistent advantage of combining graph-based spatial embeddings with SVR-based robust temporal forecasting. 3.4.2
Results on Mumbai dataset
Delhi exhibits more frequent and severe outlier pollution episodes because of its landlocked geography and high pollution burden, whereas Mumbai’s coastal setting allows relatively better pollutant dispersion and more moderate air quality conditions. To show generalization, Tables 7 23
and 8 report the monthly forecasting results for PM2.5 and PM10 in Mumbai, respectively, while Tables 9– 12 extend this analysis to 60-day and 90-day horizons. The proposed GCSVR framework demonstrates superior, maintaining high predictive stability despite the distinct meteorological profile of the Mumbai coast. The model is particularly effective during the monsoon and post-monsoon phases, where its forecasts are more accurate than those of the baseline models. While GCSVR provides the most consistent performance, certain benchmarks demonstrate localized competitiveness. Among spatiotemporal models, GpGp emerges as a strong alternative for PM2.5 during the late monsoon, frequently achieving the second-best performance across multiple metrics. However, its accuracy is seasonally dependent; whereas GCSVR remains resilient during the monsoon onset, GpGp exhibits a significant increase in error margins, indicating lower robustness to rapid shifts in atmospheric conditions. Similarly, the statistical STARMA and GSTAR models perform competitively during the summer months, occasionally matching the proposed model in point accuracy. Nevertheless, these models fail to maintain this performance during the winter transition, where their predictive skill deteriorates significantly compared to the GCSVR baseline. The evaluation of temporal deep learning architectures reveals a notable disparity between model complexity and longitudinal reliability. N-BEATS is the most robust temporal competitor, consistently outperforming LSTM and DeepAR and achieving competitive results during the mid-year window. In contrast, while the Transformer model exhibits high predictive precision during the first quarter, it displays significant instability in the latter half of the year, with error magnitudes occasionally exceeding those of GCSVR by a factor of three. This suggests that self-attention mechanisms, while effective for short-term dependencies, may lack the spatial regularities required for stable long-term forecasting in coastal environments. This instability is further highlighted in the STGCN model, which experiences a performance collapse in long-term PM10 forecasts. Across the 60-day and 90-day horizons, the structural advantages of GCSVR become more pronounced; while traditional models like STARMA and GSTAR record relative errors exceeding 130% in winter quarterly windows, GCSVR maintains a reliable equilibrium between point accuracy and probabilistic quality. These results confirm the efficacy of the proposed framework for air pollution forecasting across varying urban topographies.
24
Figure 8: Delhi 90-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS.
Tables 9–12 summarize the 60 and 90-day forecasting results for both pollutants. Across these longer horizons, GCSVR continues to achieve the lowest or near-lowest values across most evaluation periods and metrics. Its advantage is most pronounced during the summer and post-monsoon windows, where MAE, SMAPE, Pinball Loss, and CRPS jointly indicate superior performance. In contrast, STARMA and GSTAR show severe deterioration during winter quarterly forecasts, with SMAPE values exceeding 130% for both pollutants. STGCN also exhibits a major failure in Table 10, where its March–April MAE reaches 160.98. The Transformer remains competitive in selected winter periods but becomes unstable in summer. N-BEATS is the strongest temporal benchmark across the longer horizons, whereas DeepAR frequently records high Pinball Loss values. Overall, the Mumbai results confirm the generalizability of GCSVR in a coastal metropolitan setting. Across monthly, bimonthly, and quarterly forecast windows for both P M2.5 and P M10 , GCSVR provides the most reliable balance between point accuracy and probabilistic forecast quality. N-BEATS and GpGp emerge as the strongest temporal and spatiotemporal competitors, respectively, but neither matches the stability of GCSVR across seasons, pollutants, and forecast horizons.
25
Table 7: 30 day-ahead forecasting performance for P M2.5 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN
MAE MASE RMSE SMAPE Pinball Loss CRPS
15.37 1.63 18.36 31.02 7.75 12.29
25.90 2.73 30.86 54.90 12.95 14.39
23.20 2.43 27.46 46.91 10.94 15.43
8.20 1.20 11.28 17.53 5.04 6.04
17.86 0.81 25.57 35.47 9.63 13.47
18.00 1.84 21.13 35.12 9.00 14.91
16.71 1.73 19.60 32.80 8.36 12.67
20.62 2.28 24.22 40.73 10.31 15.05
19.92 1.13 23.33 38.55 10.66 14.73
18.59 1.94 22.16 36.65 8.87 13.81
FEB
MAE MASE RMSE SMAPE Pinball Loss CRPS
15.33 1.69 18.72 36.55 7.09 11.90
25.83 2.78 30.65 61.42 12.91 14.20
23.16 2.51 27.23 52.13 13.16 14.16
13.55 1.99 16.76 25.63 4.65 9.59
20.02 0.90 25.94 52.45 14.78 14.57
19.07 1.99 22.50 43.59 9.53 14.61
17.15 1.84 20.35 40.03 8.57 12.67
15.43 1.73 18.94 37.17 7.72 12.77
19.10 1.15 22.20 43.19 8.47 14.28
17.28 1.84 20.39 40.79 9.18 13.30
MAR
MAE MASE RMSE SMAPE Pinball Loss CRPS
17.34 1.88 19.81 43.82 5.52 12.59
23.16 2.57 28.12 58.46 11.58 11.72
20.96 2.33 24.92 51.05 15.84 12.50
10.30 1.51 13.59 23.21 5.66 7.44
12.09 0.54 16.05 33.91 4.77 8.71
16.94 1.87 20.27 42.51 8.47 13.31
14.32 1.58 17.43 37.78 7.16 10.67
17.54 1.94 19.84 44.70 8.77 13.19
18.22 1.07 21.25 44.74 7.00 13.89
13.50 1.48 16.40 35.83 6.76 10.12
APR
MAE MASE RMSE SMAPE Pinball Loss CRPS
13.37 1.41 15.58 33.61 4.49 10.51
22.67 2.49 27.73 55.90 11.33 10.31
19.36 2.12 23.52 45.56 15.56 10.65
27.47 3.96 29.00 60.67 5.56 22.23
14.72 0.66 18.70 44.61 10.15 10.48
13.44 1.41 16.50 32.95 6.72 11.97
11.69 1.27 14.83 29.71 5.85 8.97
12.01 1.28 14.29 30.32 6.01 11.22
14.19 0.81 16.89 33.69 5.86 10.37
11.33 1.21 14.44 29.95 5.97 8.61
MAY
MAE MASE RMSE SMAPE Pinball Loss CRPS
23.58 2.54 30.62 63.11 6.76 15.83
26.92 3.02 36.82 69.99 13.46 16.13
25.00 2.79 34.14 65.83 24.52 16.66
20.24 2.94 20.95 61.74 4.05 17.21
16.64 0.74 40.37 46.23 6.87 14.94
12.73 1.46 20.90 38.80 6.36 12.31
16.39 1.77 23.98 47.89 8.20 11.89
19.44 2.24 26.32 56.02 9.72 14.70
26.39 1.53 33.66 67.75 7.55 21.08
14.06 1.61 22.54 40.26 7.09 11.62
JUN
MAE MASE RMSE SMAPE Pinball Loss CRPS
25.23 2.72 26.76 91.05 5.16 15.61
22.49 2.53 27.71 83.28 11.24 15.20
26.63 2.97 30.81 90.31 29.81 19.14
27.00 3.98 27.13 91.78 5.40 25.54
17.04 0.77 21.19 74.02 4.08 12.25
4.90 0.54 6.17 33.61 2.45 8.59
4.96 0.57 6.28 34.01 2.48 5.07
21.07 2.44 23.00 83.30 10.53 14.29
31.28 1.85 32.62 101.90 6.28 26.20
7.00 0.74 8.28 40.76 2.77 6.27
JULY
MAE MASE RMSE SMAPE Pinball Loss CRPS
24.77 2.75 27.27 96.48 5.28 15.65
20.30 2.33 24.97 90.04 10.15 12.79
29.30 3.37 33.58 102.16 32.94 21.34
26.53 3.97 26.67 92.36 5.31 24.98
7.08 0.32 12.69 49.05 3.95 5.60
6.41 0.69 9.16 45.52 3.21 9.27
7.77 0.86 10.38 59.43 3.88 6.62
5.59 0.61 8.30 39.34 2.79 9.60
32.21 1.97 33.70 110.97 6.66 27.53
6.57 0.71 9.31 44.91 3.57 6.35
AUG
MAE MASE RMSE SMAPE Pinball Loss CRPS
23.22 2.60 24.30 92.96 4.68 14.58
12.33 1.39 15.14 79.98 6.16 5.98
27.47 3.18 31.24 97.43 31.25 19.07
22.73 3.45 23.91 77.59 4.56 18.72
7.21 0.33 9.30 46.53 2.67 5.13
6.24 0.69 8.01 41.74 3.12 9.09
7.55 0.85 9.39 55.15 3.78 6.54
5.28 0.61 6.56 36.98 2.64 9.22
29.40 1.82 30.73 103.80 5.91 24.76
5.12 0.59 6.80 35.62 2.28 5.60
SEPT
MAE MASE RMSE SMAPE Pinball Loss CRPS
20.68 2.36 22.03 78.13 4.15 13.75
11.76 1.29 14.19 68.28 5.88 5.54
23.63 2.75 27.61 82.58 27.33 15.69
24.89 3.82 25.20 85.04 4.98 22.68
13.02 0.61 15.31 59.66 2.87 9.41
7.19 0.77 8.71 38.95 3.59 9.38
8.61 0.95 10.28 53.88 4.30 7.08
5.23 0.57 6.52 28.22 2.62 9.42
27.57 1.73 28.71 92.96 5.59 23.38
4.89 0.60 6.12 28.42 2.52 5.66
OCT
MAE MASE RMSE SMAPE Pinball Loss CRPS
15.84 1.85 17.85 62.45 4.23 11.68
14.99 1.68 18.13 73.89 7.50 9.02
21.98 2.59 26.36 74.89 22.96 13.45
15.66 2.44 18.07 47.99 5.28 10.69
10.02 0.47 14.52 47.50 5.45 7.57
14.89 1.68 18.29 72.47 7.44 12.52
14.58 1.64 17.80 70.59 7.29 10.95
10.70 1.23 13.85 48.86 5.35 11.13
23.73 1.52 25.92 79.12 5.48 18.51
10.31 1.22 13.27 48.07 6.58 8.50
NOV
MAE MASE RMSE SMAPE Pinball Loss CRPS
17.27 2.04 20.67 36.85 11.56 13.33
28.25 3.32 33.83 66.13 14.13 17.12
27.57 3.27 32.93 65.06 9.27 17.20
37.65 5.80 40.80 60.34 30.12 29.40
28.32 1.35 34.03 71.54 21.38 19.95
25.23 2.98 28.52 57.37 12.62 17.97
24.23 2.91 27.62 55.07 12.12 18.56
17.93 2.11 21.04 40.20 8.96 13.95
20.37 1.31 24.01 42.42 13.06 15.39
21.15 2.49 25.32 47.21 12.62 16.28
DEC
MAE MASE RMSE SMAPE Pinball Loss CRPS
16.19 1.87 19.44 35.42 9.16 12.48
26.64 3.13 31.87 62.17 13.32 13.57
25.89 3.06 30.77 58.30 10.85 15.17
43.00 6.54 47.39 64.80 34.40 32.79
17.05 0.81 21.73 40.93 10.35 12.11
20.01 2.31 24.03 43.30 10.01 14.77
19.04 2.18 22.63 39.70 9.52 14.13
15.50 1.86 17.56 35.71 7.75 12.06
20.82 1.31 23.60 44.20 13.60 15.98
14.63 1.79 17.96 33.53 8.98 11.86
26
Table 8: 30 day-ahead forecasting performance for P M10 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN
MAE MASE RMSE SMAPE Pinball Loss CRPS
32.66 1.55 38.76 27.61 16.77 25.35
59.47 3.02 67.97 65.10 29.73 46.96
57.00 2.89 64.24 59.59 10.23 48.35
37.42 2.15 42.51 37.81 8.12 27.08
35.39 0.76 52.25 30.69 23.17 27.11
36.59 1.86 43.75 32.50 18.30 30.25
36.13 1.81 42.49 31.46 18.06 27.22
30.73 1.53 37.08 26.47 15.37 25.86
40.47 1.05 46.97 33.81 22.52 30.91
36.63 1.76 43.90 31.64 17.90 27.18
FEB
MAE MASE RMSE SMAPE Pinball Loss CRPS
33.11 1.56 40.14 28.32 16.83 24.94
60.62 3.06 69.81 65.63 30.31 46.90
57.91 2.94 65.76 59.39 10.76 49.08
28.36 1.64 32.44 23.67 17.76 18.98
37.17 0.80 47.51 35.38 22.67 26.53
36.70 1.85 44.66 32.07 18.35 29.10
36.56 1.83 43.88 32.70 18.28 27.01
28.66 1.44 35.40 25.13 14.33 24.43
40.43 1.04 47.70 33.78 22.30 30.62
30.31 1.50 37.79 27.34 17.34 22.75
MAR
MAE MASE RMSE SMAPE Pinball Loss CRPS
35.14 1.70 40.34 34.75 12.65 25.63
50.14 2.54 59.12 61.13 25.07 35.08
44.66 2.26 52.66 50.10 10.09 35.26
25.89 1.49 30.18 23.78 11.24 17.50
33.81 0.73 40.95 33.23 10.38 23.74
35.00 1.78 41.60 34.84 17.50 27.21
31.65 1.58 37.67 32.49 15.82 22.99
35.24 1.79 40.24 35.17 17.62 26.60
51.18 1.32 60.55 48.00 21.41 35.98
29.52 1.48 35.16 31.02 13.26 22.15
APR
MAE MASE RMSE SMAPE Pinball Loss CRPS
28.12 1.35 35.37 24.95 13.11 22.70
51.23 2.52 62.95 58.81 25.61 37.54
46.80 2.28 57.42 49.43 8.33 37.91
36.20 2.08 41.66 35.41 8.35 26.30
30.93 0.67 43.10 29.63 20.60 22.96
33.39 1.65 44.05 31.42 16.70 27.04
31.19 1.55 42.26 29.49 15.60 23.91
26.41 1.32 34.09 23.99 13.21 23.53
32.11 0.84 39.35 28.06 14.76 22.90
27.26 1.36 36.49 24.99 16.01 21.59
MAY
MAE MASE RMSE SMAPE Pinball Loss CRPS
37.19 1.82 42.38 37.68 10.34 25.98
37.30 1.80 47.76 45.50 18.65 25.55
33.76 1.61 43.19 38.86 11.60 25.50
43.38 2.48 46.07 46.96 8.92 34.28
30.72 0.67 42.88 33.95 19.60 22.74
31.65 1.59 39.31 33.64 15.82 25.16
30.50 1.49 38.50 31.78 15.25 22.35
40.95 2.09 46.31 41.51 20.47 28.82
36.61 0.95 43.50 37.33 12.03 26.32
26.53 1.31 34.16 28.11 12.56 20.78
JUN
MAE MASE RMSE SMAPE Pinball Loss CRPS
47.28 2.32 52.15 62.61 11.49 30.76
35.33 1.77 43.42 54.53 17.67 20.23
33.03 1.64 40.37 49.43 25.10 23.22
77.41 4.49 78.29 93.50 15.48 70.78
29.87 0.65 39.10 44.84 11.40 21.22
23.56 1.17 28.95 37.95 11.78 22.19
21.67 1.06 27.22 34.26 10.83 17.27
40.92 2.08 46.12 57.58 20.46 28.75
52.15 1.37 57.11 66.14 12.42 40.75
23.00 1.16 28.41 36.87 11.24 18.93
JULY
MAE MASE RMSE SMAPE Pinball Loss CRPS
52.62 2.58 59.81 74.27 12.98 34.68
38.42 1.96 48.37 62.41 19.21 25.48
37.22 1.91 46.02 60.68 32.96 28.18
71.92 4.22 73.10 94.89 14.38 64.54
26.95 0.59 40.73 50.63 13.53 20.35
22.72 1.14 33.47 41.97 11.36 23.10
26.52 1.32 38.05 50.65 13.26 21.46
37.52 1.90 45.30 61.40 18.76 28.07
65.81 1.75 70.13 85.88 15.47 52.28
19.76 0.96 29.67 41.66 12.00 17.22
AUG
MAE MASE RMSE SMAPE Pinball Loss CRPS
55.16 2.75 58.25 78.82 12.20 34.85
35.24 1.83 41.91 61.57 17.62 21.33
36.81 1.91 42.19 61.40 35.39 27.47
67.23 3.99 67.75 84.16 13.45 62.51
39.98 0.88 50.98 61.94 11.86 28.81
24.75 1.33 29.74 46.69 12.37 23.05
21.06 1.07 26.22 43.65 10.53 17.36
43.29 2.30 46.51 67.37 21.65 30.26
64.25 1.72 66.48 86.53 14.21 54.10
20.04 1.04 24.60 43.62 8.65 17.21
SEPT
MAE MASE RMSE SMAPE Pinball Loss CRPS
45.91 2.27 49.23 66.78 10.29 29.16
37.38 1.95 43.79 59.72 18.69 22.38
36.11 1.89 40.71 57.12 35.69 26.43
78.72 4.76 79.17 101.84 15.74 73.98
26.76 0.59 33.95 45.46 6.81 19.31
20.19 1.04 24.63 40.48 10.10 21.51
20.38 1.06 24.84 41.12 10.19 17.06
26.70 1.41 30.19 47.18 13.35 22.11
62.25 1.68 65.27 81.15 13.80 51.64
11.42 0.57 15.44 27.81 7.52 13.04
OCT
MAE MASE RMSE SMAPE Pinball Loss CRPS
37.55 1.87 42.91 51.54 11.49 25.61
39.78 2.09 48.87 58.10 19.89 22.64
36.26 1.91 43.87 51.10 29.72 25.85
70.44 4.32 73.83 86.60 14.09 58.15
22.76 0.51 36.36 38.97 16.10 17.86
39.21 2.02 49.02 71.80 19.60 30.05
35.58 1.86 45.34 61.66 17.79 27.33
24.28 1.26 30.10 37.88 12.14 22.10
52.58 1.44 57.08 65.54 13.36 41.01
23.51 1.21 32.50 40.23 17.11 19.94
NOV
MAE MASE RMSE SMAPE Pinball Loss CRPS
33.86 1.81 39.86 27.90 24.56 25.26
61.66 3.24 69.51 61.46 30.83 46.90
56.67 2.97 63.45 53.10 10.97 45.85
16.65 1.02 20.30 14.12 11.75 11.48
36.29 0.82 45.34 32.42 27.14 25.84
55.37 2.89 61.94 50.43 27.69 37.77
50.63 2.69 57.04 46.10 25.32 37.56
33.89 1.76 39.57 27.97 16.95 25.94
38.80 1.10 44.62 32.79 27.69 28.94
26.81 1.37 33.16 21.39 15.20 20.04
DEC
MAE MASE RMSE SMAPE Pinball Loss CRPS
33.39 1.78 41.22 26.34 22.57 25.60
61.62 3.25 71.22 59.27 30.81 45.89
58.21 3.06 65.73 52.63 11.11 47.43
23.77 1.47 35.09 18.11 18.91 18.83
30.57 0.69 39.37 22.95 15.87 22.03
37.51 1.97 47.31 29.74 18.76 28.56
38.96 2.04 48.08 30.74 19.48 28.96
25.48 1.35 31.67 19.14 12.74 22.52
42.20 1.20 48.57 34.70 30.67 31.98
24.47 1.28 29.73 17.86 10.77 18.31
27
Table 9: 60 day-ahead forecasting performance for P M2.5 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN-FEB
MAE RMSE MASE SMAPE Pinball Loss CRPS
16.76 19.91 1.82 36.32 8.11 12.90
25.20 30.73 2.72 55.42 12.60 14.10
22.56 27.13 2.41 48.26 11.95 14.98
11.73 15.33 1.72 23.58 7.90 8.56
18.83 25.71 0.86 41.00 11.49 13.91
22.44 26.26 2.28 50.51 11.22 17.17
19.81 23.45 2.06 43.49 9.91 15.13
22.62 26.33 2.54 47.06 11.31 15.87
19.58 23.26 1.14 40.80 10.07 14.30
18.45 22.17 1.98 40.47 10.37 13.93
MAR-APR
MAE RMSE MASE SMAPE Pinball Loss CRPS
16.68 19.07 1.78 41.16 5.46 12.31
22.57 27.68 2.49 55.83 11.29 11.09
19.76 23.87 2.17 47.36 15.53 11.61
11.95 14.25 1.75 29.91 3.96 8.22
12.81 16.54 0.57 35.97 6.01 9.14
17.67 21.69 1.90 45.70 8.83 13.92
16.24 20.13 1.78 44.07 8.12 12.35
18.80 21.21 2.08 45.64 9.40 13.71
17.86 20.61 1.03 42.65 6.24 13.01
16.61 19.94 1.85 43.63 9.07 12.53
MAY-JUN
MAE RMSE MASE SMAPE Pinball Loss CRPS
27.87 33.07 3.02 83.79 6.60 17.71
30.48 38.77 3.41 86.40 15.24 18.68
27.58 34.87 3.07 82.19 28.47 18.78
24.50 25.14 3.56 78.40 4.90 21.34
15.48 31.54 0.69 53.85 5.04 12.53
9.10 15.93 1.04 37.83 4.55 10.47
11.58 18.25 1.26 44.89 5.79 8.66
22.35 27.60 2.57 74.75 11.18 15.36
28.50 33.86 1.67 84.55 6.81 22.80
12.11 18.95 1.37 45.59 5.40 10.60
JULY-AUG
MAE RMSE MASE SMAPE Pinball Loss CRPS
27.94 29.64 3.12 102.07 5.76 17.45
26.21 31.83 3.00 97.46 13.10 16.85
29.95 33.90 3.42 102.27 33.20 21.30
25.46 26.16 3.81 86.53 5.09 22.16
7.21 11.98 0.33 50.09 4.50 5.68
8.12 10.86 0.88 63.28 4.06 9.64
9.44 12.04 1.04 81.10 4.72 7.41
5.76 8.28 0.64 40.14 2.88 9.50
32.68 34.10 1.99 110.10 6.66 27.65
7.06 9.56 0.75 48.49 3.83 7.20
SEPT-OCT
MAE RMSE MASE SMAPE Pinball Loss CRPS
21.84 23.54 2.53 78.46 4.65 14.63
14.43 17.94 1.59 70.70 7.22 7.13
25.00 29.18 2.90 82.13 27.12 15.88
19.73 21.31 3.03 65.45 5.02 13.73
13.63 16.39 0.64 60.12 4.17 9.45
12.24 15.95 1.35 65.42 6.12 11.48
13.69 17.33 1.54 82.53 6.85 10.58
8.77 11.75 0.94 41.31 4.38 10.63
25.08 26.95 1.58 84.95 5.45 19.82
8.35 11.17 0.99 40.78 4.48 8.01
NOV-DEC
MAE RMSE MASE SMAPE Pinball Loss CRPS
18.63 21.83 2.19 39.27 12.24 14.13
27.07 32.93 3.17 60.88 13.53 15.99
26.40 31.76 3.12 60.81 9.91 16.39
40.52 44.42 6.24 62.99 32.42 31.12
26.94 32.71 1.29 66.71 20.07 18.98
31.89 35.48 3.80 80.37 15.94 22.26
30.55 34.28 3.70 76.30 15.28 24.06
20.27 23.43 2.39 45.00 10.13 15.27
20.05 23.54 1.27 41.64 12.34 15.07
22.29 26.47 2.61 50.14 14.18 16.59
Table 10: 60 day-ahead forecasting performance for P M10 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
GCSVR
JAN-FEB
MAE RMSE MASE SMAPE Pinball Loss CRPS
35.67 42.30 1.69 29.92 18.98 27.10
60.79 70.05 3.08 65.58 30.39 48.43
58.25 66.41 2.95 60.33 10.57 49.77
30.14 35.41 1.73 28.52 11.42 20.50
44.87 61.07 0.97 42.34 32.81 33.11
54.02 63.87 2.73 55.59 27.01 39.76
49.70 58.73 2.53 49.00 24.85 38.53
32.79 39.44 1.64 28.03 16.40 26.74
41.46 48.88 1.07 34.65 22.48 31.24
38.40 45.83 1.88 33.03 20.44 30.68
MAR-APR
MAE RMSE MASE SMAPE Pinball Loss CRPS
32.69 39.30 1.58 30.66 13.55 24.82
52.03 62.97 2.58 60.83 26.01 37.55
46.66 57.02 2.31 50.78 9.26 37.62
28.35 33.26 1.63 27.50 9.58 19.49
34.82 43.95 0.75 32.25 13.87 24.58
45.90 55.74 2.27 48.87 22.95 33.01
43.04 52.68 2.14 46.59 21.52 31.80
34.19 40.78 1.75 32.36 17.10 26.27
160.98 202.37 4.13 115.50 82.52 114.60
32.85 40.66 1.63 31.80 16.94 25.09
MAY-JUN
MAE RMSE MASE SMAPE Pinball Loss CRPS
46.05 51.15 2.25 53.31 11.54 30.45
35.48 45.63 1.74 48.81 17.74 23.01
32.98 42.04 1.60 43.94 17.62 24.07
60.54 63.76 3.47 70.52 12.20 49.29
29.19 41.17 0.63 38.87 18.40 21.84
28.28 36.19 1.41 36.62 14.14 24.00
26.83 34.90 1.32 34.19 13.41 20.13
50.77 55.98 2.60 57.49 25.39 33.80
43.56 50.60 1.14 51.02 12.11 31.81
26.84 35.29 1.32 35.66 15.08 22.85
JULY-AUG
MAE RMSE MASE SMAPE Pinball Loss CRPS
58.48 63.15 2.87 80.64 13.61 37.30
37.53 46.38 1.93 62.20 18.77 24.60
36.39 43.98 1.87 60.50 33.49 27.31
70.29 71.19 4.12 90.01 14.06 63.91
27.50 38.89 0.60 58.42 15.95 20.29
25.94 35.24 1.28 54.75 12.97 24.03
30.62 39.96 1.52 71.59 15.31 23.35
47.69 53.33 2.44 72.01 23.85 32.13
63.76 67.80 1.70 85.10 14.72 50.19
18.26 26.65 0.88 40.91 11.35 18.08
SEPT-OCT
MAE RMSE MASE SMAPE Pinball Loss CRPS
48.63 52.75 2.41 65.83 11.84 31.16
38.54 46.54 2.00 58.46 19.27 22.53
36.36 42.56 1.89 54.64 32.03 25.84
66.26 68.94 4.01 88.53 13.25 55.77
28.95 36.77 0.64 45.34 9.41 20.45
33.97 43.90 1.73 69.62 16.98 27.88
34.41 44.41 1.77 71.88 17.21 26.60
34.72 39.60 1.83 52.99 17.36 25.39
56.39 60.32 1.52 72.59 13.53 44.30
18.14 26.40 0.92 34.87 12.44 18.34
NOV-DEC
MAE RMSE MASE SMAPE Pinball Loss CRPS
37.14 43.72 1.98 30.35 26.91 27.38
62.43 70.69 3.27 60.69 31.21 48.30
57.99 65.12 3.03 53.44 11.21 47.59
19.11 27.53 1.17 15.12 14.33 14.51
36.15 45.91 0.82 29.80 23.48 25.73
73.80 81.23 3.86 74.30 36.90 50.64
68.40 76.11 3.63 67.63 34.20 53.46
34.07 40.55 1.77 27.31 17.04 26.13
39.93 46.95 1.12 33.03 27.91 29.66
31.48 38.51 1.65 23.34 15.83 24.44
28
Table 11: 90 day-ahead forecasting performance for P M2.5 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
JAN-FEB-MAR
APR-MAY-JUN
JULY-AUG-SEPT
OCT-NOV-DEC
Metric
ARIMA
LSTM
DeepAR
Spatio-Temporal Model
Trans.
NBeats
STARMA
GSTAR
Proposed
GpGp
STGCN
GCSVR
MAE
17.37
25.00
22.07
11.26
19.34
24.53
21.84
23.36
19.12
18.64
RMSE
20.47
30.57
26.68
14.76
26.34
28.39
25.57
26.96
22.69
22.43
MASE
1.88
2.70
2.37
1.65
0.88
2.53
2.30
2.63
1.12
2.03
SMAPE
39.55
56.84
49.21
23.48
46.60
65.51
56.41
50.07
42.15
44.54
Pinball Loss
7.67
12.50
13.11
7.15
12.51
12.26
10.92
11.68
8.83
10.82
CRPS
13.09
13.49
14.21
8.19
14.25
18.14
16.71
16.23
13.87
14.35
MAE
23.99
27.52
24.06
36.09
12.71
11.59
10.18
19.13
44.56
11.09
RMSE
29.47
35.59
31.14
38.42
26.51
19.00
17.43
24.64
57.42
17.72
MASE
2.57
3.04
2.64
5.21
0.57
1.27
1.14
2.14
2.59
1.20
SMAPE
68.91
74.95
68.40
87.26
46.18
44.13
37.19
60.59
115.74
39.85
Pinball Loss
6.10
13.76
23.75
7.29
7.39
5.79
5.09
9.56
18.46
5.69
CRPS
15.87
15.18
15.90
28.97
10.47
11.54
8.40
14.05
31.96
10.05
MAE
28.32
28.08
29.30
25.54
7.91
10.31
11.35
6.16
30.66
7.55
RMSE
29.73
33.63
33.20
26.11
12.93
12.79
13.67
8.53
32.30
9.81
MASE
3.17
3.19
3.33
3.82
0.36
1.12
1.25
0.66
1.87
0.78
SMAPE
100.20
96.85
98.39
86.55
52.31
87.34
102.98
39.28
103.75
46.66
Pinball Loss
5.78
14.04
32.60
5.11
5.16
5.15
5.67
3.08
6.26
4.09
CRPS
17.72
17.72
20.68
22.55
6.26
10.24
8.43
9.69
25.40
8.13
MAE
18.46
30.07
23.50
32.34
21.16
38.32
37.89
29.31
21.23
18.50
RMSE
21.98
35.11
28.47
37.85
29.83
43.80
43.40
34.32
25.08
23.07
MASE
2.16
3.58
2.77
5.04
1.00
4.59
4.54
3.53
1.34
2.15
SMAPE
48.01
95.41
61.19
58.23
56.41
134.53
132.99
87.13
53.88
48.78
Pinball Loss
9.94
15.03
14.40
23.45
14.34
19.16
18.95
14.66
9.99
11.16
CRPS
13.88
24.02
14.83
22.29
15.99
27.87
31.33
21.12
15.38
14.34
Table 12: 90 day-ahead forecasting performance for P M10 in Mumbai, averaged across all monitoring stations. The proposed GCSVR model is compared with temporal and spatiotemporal benchmark models. The best and secondbest results are highlighted in bold and italic, respectively. Temporal Model Period
JAN-FEB-MAR
APR-MAY-JUN
JULY-AUG-SEPT
OCT-NOV-DEC
Metric
Spatio-Temporal Model
Proposed
ARIMA
LSTM
DeepAR
Trans.
NBeats
STARMA
GSTAR
GpGp
STGCN
MAE
36.31
57.09
54.26
28.81
48.29
61.21
56.80
34.53
39.29
GCSVR 40.19
RMSE
42.77
66.90
63.18
33.90
63.55
70.98
66.24
41.17
46.39
47.87
MASE
1.73
2.88
2.74
1.66
1.04
3.07
2.87
1.75
1.01
1.96
SMAPE
32.09
63.38
57.62
27.01
50.72
73.53
65.81
31.11
34.37
37.42
Pinball Loss
17.86
28.54
10.30
11.20
36.36
30.61
28.40
17.27
20.04
23.39
CRPS
27.15
44.47
45.57
19.60
35.32
43.54
44.06
27.23
29.27
31.39
MAE
39.15
41.26
37.39
48.07
31.86
39.33
35.84
40.72
40.76
35.12
RMSE
45.92
53.87
48.50
53.33
44.21
49.06
45.85
48.02
47.95
44.64
MASE
1.91
2.03
1.82
2.76
0.69
1.90
1.75
2.08
1.07
1.77
SMAPE
43.27
53.58
45.66
55.56
38.48
54.38
48.16
45.03
44.33
41.38
Pinball Loss
12.37
20.63
13.76
10.34
20.03
19.66
17.92
20.36
13.55
19.95
CRPS
27.62
27.87
28.92
35.69
23.65
29.72
26.82
29.36
28.35
28.72
MAE
60.22
36.68
35.48
72.16
30.12
30.02
34.58
53.32
64.00
17.78
RMSE
63.87
44.76
42.30
72.96
41.16
37.70
42.07
57.85
68.00
25.49
MASE
2.95
1.88
1.82
4.23
0.66
1.49
1.72
2.73
1.70
0.86
SMAPE
81.48
60.51
58.66
93.36
72.00
72.84
92.85
76.27
84.15
40.99
Pinball Loss
13.78
18.34
33.30
14.43
19.62
15.01
17.29
26.66
14.56
11.34
CRPS
37.95
23.66
26.35
66.09
21.83
25.32
25.46
34.63
50.55
19.59
MAE
38.31
56.20
51.57
32.31
65.43
93.91
91.70
34.59
43.51
31.56
RMSE
45.72
66.71
60.25
42.14
80.26
105.52
103.81
41.85
51.24
40.00
MASE
1.99
2.94
2.69
1.98
1.47
4.89
4.80
1.78
1.21
1.63
SMAPE
38.28
61.76
53.42
36.38
77.38
133.29
127.56
34.13
43.36
32.90
Pinball Loss
22.27
28.10
17.54
14.33
51.37
46.96
45.85
17.30
22.88
21.43
CRPS
27.45
39.87
41.30
23.76
48.64
68.08
76.25
26.57
30.69
25.89
29
Figure 9: Mumbai 30-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS. Each box plot shows the distribution of forecast errors across evaluation windows for a given model. The dashed vertical line separates temporal benchmark models from spatiotemporal models, while the horizontal dotted line indicates the lowest median error among all models for each metric.
Figs. 9, 10, and 11 provide a visual comparison of the ten forecasting models on the Mumbai dataset across 30, 60, and 90-day horizons for both P M2.5 and P M10 . The figures summarize model performance using the metrics considered. Consistent with the tabulated results, GCSVR shows the strongest overall performance across pollutants, metrics, and forecast horizons. Its box plots are generally lower and more compact across the MAE, RMSE, SMAPE, Pinball Loss, and CRPS panels, indicating both higher accuracy and greater stability as the forecast horizon increases. In contrast to most competing models, the variability of GCSVR increases only modestly with longer horizons, highlighting its robustness across short-, medium-, and long-term forecasting settings. Among the benchmark models, N-BEATS emerges as the strongest temporal alternative and performs particularly well in terms of MASE. By contrast, STGCN, Transformer, DeepAR, and LSTM display comparatively larger errors and greater variability across several metrics. Overall, these box plots reinforce the numerical results and show that GCSVR provides the most reliable balance between forecasting accuracy and robustness on the Mumbai dataset.
30
Figure 10: Mumbai 60-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS.
Figure 11: Mumbai 90-day forecasting horizon: comparison of model performance for P M2.5 (upper panel) and P M10 (lower panel) using MAE, MASE, RMSE, SMAPE, Pinball Loss, and CRPS.
31
4. Statistical Tests for Model Robustness
Figure 12: MCB test results for P M2.5 forecasting in Delhi across the six evaluation metrics. In each panel, models are ordered according to their mean ranks, with lower ranks indicating better performance. For example, the label ‘GCSVR: 1.09’ indicates that the proposed GCSVR model obtains a mean rank of 1.09 under the MAE metric. The same labeling convention is used for all models and metrics. The shaded region represents the critical-distance interval derived from the MCB test; models outside this region are statistically inferior to the best-ranked model at the chosen significance level.
To assess whether the observed performance differences are statistically meaningful, we apply two complementary tests: the Multiple Comparison with the Best (MCB) test (Koning et al. (2005)). The MCB test is particularly useful in this setting because the models are evaluated repeatedly across multiple forecasting windows, pollutants, horizons, and performance metrics. Rather than 32
comparing models using a single average error value, the test ranks the competing methods within each forecasting task and then compares their average ranks across tasks. The MCB test compares F competing models across D forecasting tasks by assigning ranks based on their performance for each metric and then computing the mean rank of each model. The model with the lowest mean rank is treated as the reference model.
Figure 13: MCB test results for P M10 forecasting in Delhi across the six evaluation metrics. In each panel, models are ordered according to their mean ranks, with lower ranks indicating better performance.
Statistical significance is assessed using the critical distance r CD = δθ
F (F + 1) , 6D
33
where δθ denotes the critical value of the Tukey distribution at significance level θ. Models whose mean ranks fall outside the critical-distance region of the best model are considered statistically inferior. Thus, the MCB test provides a formal statistical validation of whether the apparent improvements of GCSVR over the benchmark models are due to consistent performance gains rather than random variation across forecasting windows.
Figure 14: MCB test results for P M2.5 forecasting in Mumbai across the six evaluation metrics. In each panel, models are ordered according to their mean ranks, with lower ranks indicating better performance.
Figs 12–15 present the MCB results for P M2.5 and P M10 in Delhi and Mumbai across the six evaluation metrics. For Delhi P M2.5 , GCSVR obtains the lowest mean rank for nearly all metrics, with values of 1.09 for MAE, 2.32 for MASE, 1.05 for RMSE, 1.00 for SMAPE, 2.09 for Pinball 34
Loss, and 1.00 for CRPS. N-BEATS, ARIMA, and GpGp are the closest competing models. For Delhi P M10 , GCSVR ranks first across all six metrics, confirming its robust advantage under the more outlier-prone Delhi pollution setting.
Figure 15: MCB test results for P M10 forecasting in Mumbai across the six evaluation metrics. In each panel, models are ordered according to their mean ranks, with lower ranks indicating better performance.
For Mumbai, the results remain broadly consistent, though the performance gap is narrower because the coastal environment produces comparatively less severe pollution variability. For P M2.5 , GCSVR achieves the lowest mean rank for MAE (2.64), RMSE (2.73), SMAPE (2.82), and CRPS (3.05), while N-BEATS and GpGp remain strong alternatives. For P M10 , GCSVR again attains the best ranks for MAE, RMSE, SMAPE, and CRPS. However, N-BEATS performs best under 35
MASE, and the Transformer achieves the best rank for Pinball Loss. Overall, the MCB analysis supports the main empirical findings: GCSVR is the most reliable model for deterministic forecast accuracy and overall probabilistic calibration, particularly in the more polluted and outlier-prone Delhi dataset. 4.1
Uncertainty Quantification using Conformal Prediction Beyond point forecasting, uncertainty quantification is essential for air quality monitoring be-
cause policy decisions often depend on the likelihood of future pollutant concentrations exceeding safety thresholds. To provide prediction intervals for the proposed GCSVR forecasts, we use conformal prediction, a distribution-free and model-agnostic approach introduced by Vovk et al. (2005). Unlike parametric uncertainty models, conformal prediction constructs prediction intervals directly from the empirical distribution of forecast errors and therefore does not require strong assumptions about the underlying data-generating process. For station i, let X̂ti = GCSVR(vti ) denote the point forecast obtained from the GCSVR model, where vti is the graph-enhanced lagged input vector defined in the temporal module. To account for possible heterogeneity in forecast uncertainty, we define the normalized conformity score as
γti =
Xti − X̂ti U(vti )
,
where U(vti ) > 0 denotes an uncertainty scaling function evaluated at the same input. This score measures the forecast error relative to the estimated local uncertainty level. To adapt the conformal interval to the temporal nature of air quality data, we compute the conformal quantile using a rolling calibration window of length υ. For a future time point t, define the rolling calibration index set as Ct = {s : t − υ ≤ s < t}. For a desired coverage level 1 − ρ, the conformal quantile is computed as the empirical (1 − ρ)-quantile of the recent conformity scores: ( κit = inf
) 1 X i ω: 1{γs ≤ ω} ≥ 1 − ρ , |Ct | s∈Ct
where ρ ∈ (0, 1) is the significance level, so that smaller values of ρ correspond to wider prediction intervals. The conformal prediction interval for station i at time t is then given by h
i X̂ti − κit U(vti ), X̂ti + κit U(vti ) .
36
Thus, the final interval expands the GCSVR point forecast by a data-driven conformal margin. This provides calibrated uncertainty bounds while preserving the flexibility of the GCSVR framework for nonlinear and spatiotemporally dependent air quality forecasting. Fig. 16 shows that the GCSVR forecasts closely follow the observed P M2.5 and P M10 concentrations at the selected Delhi monitoring stations during the April–June 2023 window, including periods with sharp pollution fluctuations. Fig. 17 shows that the GCSVR forecasts capture the overall temporal evolution of P M2.5 and P M10 concentrations in Mumbai during the October–December 2024 window. The conformal prediction bands provide adaptive uncertainty bounds around the forecasts, widening during more volatile episodes and remaining narrower during relatively stable periods. Thus, integrating GCSVR with conformal prediction provides uncertainty-aware prediction intervals alongside point forecasts, supporting more informed decision-making for air quality monitoring and public health planning.
Figure 16: Delhi conformal prediction results for the April–June 2023 forecasting window. The left panel shows the predicted values (blue line) and observed values (red dots) of P M2.5 concentrations at two monitoring stations: (A) Lodhi Road IMD and (B) Nehru Nagar. The right panel presents the corresponding results for P M10 at the same stations.
37
Figure 17: Mumbai conformal prediction results for the October–December 2024 forecasting window. The left panel shows the predicted values (blue line) and observed values (red dots) of P M2.5 concentrations at two monitoring stations: (A) Borivali East, IITM and (B) Navy Nagar, Colaba. The right panel presents the corresponding results for P M10 at the same stations.
5. Policy Implication India continues to face a severe air pollution burden, with annual average P M2.5 concentrations far exceeding international health-based guidelines (IQAir (2024)). This problem is particularly acute in large urban centres such as Delhi and Mumbai, where rapid urbanization, transport emissions, industrial activity, construction, biomass burning, and adverse meteorological conditions interact to produce persistent and episodic pollution events. The public-health implications are substantial, as long-term exposure to ambient air pollution is strongly associated with respiratory illness, cardiovascular disease, stroke, premature mortality, and disability-adjusted life years (World Health Organization (2021); Sagheer et al. (2024); World Heart Federation (2024)). These risks highlight the need for reliable, data-driven forecasting systems that can support early warning, exposure reduction, and targeted policy intervention. The proposed GCSVR framework contributes to this need by combining geometric deep learning with machine learning principles for robust environmental forecasting. By integrating graph convolutional spatial representation with SVR-based temporal prediction, the model captures inter-station 38
dependence while reducing sensitivity to anomalous pollutant observations. This is particularly relevant for cities such as Delhi, where extreme pollution episodes and outlier values are frequent, and for Mumbai, where coastal dispersion produces different but still complex pollution dynamics. The resulting forecasts can help environmental agencies identify high-risk periods, allocate monitoring resources, issue timely public-health advisories, and design short-term mitigation strategies such as traffic regulation, construction control, and industrial emission management. From the perspective of modern environmental modeling, the proposed framework offers a scalable and statistically grounded tool for spatiotemporal risk assessment. Its integration with conformal prediction further provides uncertainty-aware prediction intervals, allowing decision-makers to assess not only expected pollution levels but also the reliability of those forecasts. Although developed for two major air pollutant forecasting in Delhi and Mumbai, the GCSVR framework is model-agnostic and can be adapted to other environmental and risk-sensitive domains involving nonlinear, spatially dependent, and outlier-prone data.
6. Discussion Predicting air quality in densely populated urban environments remains challenging because pollutant concentrations are governed by nonlinear, nonstationary, and spatially dependent processes. In cities such as Delhi and Mumbai, P M2.5 and P M10 levels are influenced by interactions among emission sources, monitoring locations, meteorological conditions, and human activity. Delhi experiences severe winter pollution episodes driven by low wind speeds, temperature inversions, stubble burning, and festive-season emissions, whereas Mumbai’s winter deterioration is often linked to wind stagnation, moisture-driven pollutant trapping, construction dust, vehicular emissions, industrial activity, and open waste burning (Mangaraj et al. (2024)). These persistent and episodic pollution events pose serious risks to public health and urban sustainability, particularly in rapidly growing metropolitan regions. This study proposed a Graph Convolutional Support Vector Regression (GCSVR) framework for robust spatiotemporal forecasting of urban air pollution. The model combines graph convolutional learning to encode spatial dependence among monitoring stations with SVR-based temporal forecasting, whose ϵ-insensitive loss reduces sensitivity to anomalous observations and extreme pollution spikes. Empirical analysis using daily P M2.5 and P M10 data from 37 monitoring stations in Delhi and 18 stations in Mumbai shows that GCSVR effectively captures nonlinear, nonstationary, and outlier-prone spatiotemporal dynamics. Across multiple forecasting horizons, the proposed model 39
delivers accurate point forecasts and calibrated prediction intervals, supporting uncertainty-aware air quality assessment and evidence-based policy planning. Statistical robustness analyses further confirm the reliability and generalizability of the framework across two climatically distinct urban environments. The study also has limitations that motivate future research. The current framework relies mainly on historical pollutant concentrations and a distance-based graph structure, without explicitly incorporating meteorological, traffic, land-use, or emission-source variables. Future work can extend GCSVR by integrating domain-informed covariates such as boundary-layer height, wind speed and direction, temperature, humidity, vehicular emissions, industrial activity, and biomass-burning indicators. Dynamic or causally informed graph structures could further improve the model’s ability to represent changing pollutant transport mechanisms across seasons and cities. Finally, linking spatiotemporal pollution forecasts with public-health impact models would allow the framework to estimate pollution-attributable morbidity and mortality, transforming it from a forecasting tool into a broader decision-support system for urban environmental governance.
Data and code availability All data supporting the findings of this study are derived from publicly available sources, particularly from the Central Pollution Control Board (CPCB) website (https://airquality.cpcb.gov. in/ccr/). The code for GCSVR is publicly available at https://github.com/ctanujit/GCSVR.
Author contributions All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Nourin Jahan and Madhurima Panja. The first draft of the manuscript was written by Nourin Jahan, after which all authors contributed by adding sections and providing comments on earlier versions of the paper. All authors read and approved the final manuscript.
Acknowledgment Nourin Jahan would like to acknowledge SAFIR, Sorbonne University Abu Dhabi and Tanujit Chakraborty would like to acknowledge Ms. Donia Besher for her comments on the paper.
40
Funding The authors declare that no funds were received during the preparation of this manuscript.
Declarations The authors declare no competing interests.
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