WaveDroughtNet: A Multi-Modal Wavelet-Enhanced Temporal Convolutional Network for Multi-Horizon Drought Forecasting and Onset Analysis

Abstract

Drought is a slowly evolving, multi-driver hydro-meteorological hazard whose accurate early prediction is a cornerstone of climate-smart agriculture and water-resource planning. Existing data-driven drought forecasting frameworks suffer from three persistent limitations: (i) most models concatenate heterogeneous climate variables into a single flat feature vector, implicitly assuming a single dominant driver such as precipitation, even though atmospheric moisture demand, radiation and wind-mediated evapotranspiration co-determine drought onset; (ii) wavelet preprocessing is typically applied to the full series, introducing future-information leakage that violates the operational causality requirement of forecasting; and (iii) most architectures predict a single horizon and provide no causal attribution explaining when, where and which climatic variables initiated the event. This study proposes WaveDroughtNet, a multi-modal, multi-horizon deep-learning framework that addresses these limitations through five integrated components: (a) a strictly causal Daubechies-4 wavelet decomposition computed in a rolling fashion; (b) six modality-specific encoders with stochastic modality dropout (p = 0.15); (c) cross-modal multi-head attention with four heads; (d) a four-layer temporal convolutional network (TCN) backbone with dilation factors yielding a 240-step receptive field; and (e) a post hoc DroughtOriginTracer that combines temporal attention, modal-attribution and inter-district propagation scans. The Standardised Precipitation Evapotranspiration Index (SPEI), used as the supervisory target, is computed following the canonical Vicente-Serrano formulation. water balance $D=P-\mathrm{P}\mathrm{E}\mathrm{T}$ (Hargreaves PET) at a 4-week (≈1-month) timescale, fitted with a three-parameter log-logistic distribution via L-moments, validated by Kolmogorov–Smirnov goodness-of-fit testing ($\alpha =0.05$) per district, and standardised through the inverse-normal cumulative distribution function. Trained on 18,304 weekly district records from NASA POWER reanalysis (2014–2025) covering all 32 districts of Tamil Nadu, India, WaveDroughtNet uses only 256,869 parameters and produces, in a single forward pass, four forecasts (1 week, 1 month, 3 months, 1 year). On the held-out 2024 test partition ($N=1728$), the model attains weighted $F1=0.9221$ and $R^2=0.8512$ at the 1-week horizon, and weighted $F1=0.8498$ and $R^2=0.6812$ at the 1-year horizon. Diebold–Mariano tests confirm that WaveDroughtNet significantly outperforms naive persistence, seasonal naive, LSTM, ConvLSTM and a vanilla Transformer at the 3-month and 1-year horizons (p < 0.001). The DroughtOriginTracer successfully back-projects 15 Coimbatore events to causal origins 29–41 weeks prior to onset. We explicitly acknowledge three limitations that constrain operational deployment in its current form—zero severe events in the 2024 test partition ($F{1}_{severe}$ = 0.000), static inter-district modelling, and absence of vegetation-index supervision—and propose concrete mitigation pathways in the Discussion.

1. Introduction

Drought ranks among the costliest natural hazards globally, accounting for approximately 83% of damage to the agricultural sector and USD 124 billion in cumulative losses between 1998 and 2017 [1,2]. The United Nations Convention to Combat Desertification (UNCCD) projects state that, under continuation of current land-use practices, up to 16 million km² of fertile land could be lost by 2050 [1], placing unprecedented pressure on regional food security and water supply. These socio-economic stakes motivate the development of skillful, spatially resolved early warning systems.

Conceptually, drought is partitioned into meteorological, agricultural, hydrological and socio-economic sub-types [3,4]. Palmer [4] introduced the Palmer Drought Severity Index (PDSI) for the meteorological–agricultural interface, while McKee et al. [5] proposed the precipitation-only Standardised Precipitation Index (SPI), which remains the most widely deployed operational index. Vicente-Serrano et al. [6] extended SPI to the Standardised Precipitation Evapotranspiration Index (SPEI) by introducing temperature-driven atmospheric water demand through potential evapotranspiration (PET). SPEI is preferable to SPI for climate-change-impact studies because it responds explicitly to warming-driven increases in evapotranspirative demand [6,7]. In this study, we adopt SPEI at the 4-week (≈1-month) timescale: this scale is sensitive to meteorological drought onset (which propagates from precipitation deficits within ≈30 days) yet retains a sufficient signal-to-noise ratio for skillful weekly forecasting [6,8]. Longer SPEI windows (3-, 6-, 12-month) lag the actual onset and are computed as derived products from the same fitted log-logistic family.

Traditional drought monitoring with SPI [7] or SPEI [6] provides retrospective characterisation but does not, by itself, deliver predictive lead time. Physics-based numerical models such as general circulation models (GCMs) and mesoscale weather models have historically supplied the predictive component [9], but suffer from coarse spatial resolution (typically 50–250 km), large computational footprint and known systematic biases in tropical monsoon regions. Hybrid approaches that downscale GCM output with machine learning [10,11] partially mitigate the resolution issue but inherit the GCM bias structure.

Machine learning (ML) and deep learning (DL) have therefore been applied to drought forecasting to learn non-linear relationships directly from observations [9,12]. Valipour et al. [13] reported short-term daily precipitation $R^2$ = 0.64–0.89 across diverse climate zones using ensemble ML; Ferchichi et al. [10] used generative adversarial networks for spatio-temporal drought modelling in North Africa; and Cortés-Andrés et al. [14] employed 3-D CNNs with noisy-label learning for drought detection. At a global scale, Bi et al. [15], Lam et al. [16] and Pathak et al. [3] have demonstrated that data-driven models can match or exceed numerical weather prediction systems for medium-range forecasting. Montillet et al. [17] and Neset et al. [18] reviewed big-data and AI-assisted early warning frameworks, while Huntingford et al. [9] surveyed ML for climate applications more broadly. For drought specifically, recurrent architectures built around the Long Short-Term Memory (LSTM) cell of Hochreiter and Schmidhuber [19] dominate the literature: Marusov et al. [20] used a spatio-temporal LSTM for long-term PDSI forecasting in Russia, while Tuğrul et al. [21,22] coupled wavelet decomposition with LSTM and Support Vector Machines for regional drought prediction in Norway.

Wavelet preprocessing has become standard in hydrological time-series modelling because it separates non-stationary signals into low-frequency trends and high-frequency residuals, exposing the multi-scale periodicity intrinsic to drought [21,23]. Wavelet-ANN, Wavelet-SVM and Wavelet-LSTM models consistently outperform their non-wavelet counterparts [22,23]. Osmani et al. [23] hybridised Tunable Q-factor and Maximal Overlap Discrete Wavelet Transforms with Gaussian Process Regression for SPEI forecasting, and Liu et al. [24] extended wavelet attention to medical image segmentation, demonstrating the generality of wavelet-attention coupling. However, the dominant practice of applying the wavelet transform to the entire training series leaks future information into past representations [23]; this is admissible offline but invalid for operational forecasting. WaveDroughtNet therefore applies a strictly causal decomposition where at every time t, only data up to and including t enters the transform. Attention-based architectures, beginning with the Transformer of Vaswani et al. [25], have produced strong results in sequence modelling. Zhang et al. [26] applied a shifted-window Transformer to multi-scale spatio-temporal drought prediction, and Lu and Pan [27] compared two Transformer variants for short-term precipitation nowcasting. The quadratic O(n²) self-attention cost, however, is prohibitive for the 52-week input sequences used here when expanded across six modalities. Temporal convolutional networks (TCNs), with linear cost in sequence length and a dilation-controlled receptive field, offer a favourable accuracy–efficiency trade-off for this regime [28]. Despite these advances, four limitations persist in the published literature: (i) climate variables are typically concatenated as a flat vector, masking the physical heterogeneity of their roles in drought genesis [10,11,23]; (ii) most architectures predict a single horizon and require separate models for each lead time [20,21]; (iii) statistical-significance testing of forecast superiority (Diebold–Mariano, Friedman–Nemenyi) is rarely reported [10,13,23]; and (iv) no published framework provides post hoc causal attribution localising when, where and which modality initiated the drought.

These limitations define the research gap addressed in this paper, summarised by three research questions:

RQ1—Can a single, lightweight architecture deliver skillful multi-horizon SPEI forecasts (1 week to 1 year) while explicitly modelling the heterogeneity of meteorological modalities?

RQ2—Can causal wavelet preprocessing, used inside a learnable model, yield genuine operational utility (no future-information leakage) while preserving multi-scale feature representations?

RQ3—Can post hoc interpretability components localise the temporal origin, modal driver and spatial propagation path of individual drought events with sufficient confidence to support decision-making?

Regional studies have documented Tamil Nadu’s substantial drought exposure. Janarth et al. [8] reported severe SPEI-based stress in the north-western and southern districts, and Lalmuanzuala et al. [27] combined meteorological and remote-sensing indices for the southern districts. The 2016 monsoon failure produced an 82% rainfall deficit relative to the long-term mean and triggered a drought emergency that persisted into 2019. The state’s 32 districts span five distinct climatic zones (coastal-humid, inland-arid, Western Ghats-influenced, semi-arid transition, southern coastal) with mean daily precipitation ranging from 1.8 mm in the inland rain-shadow to 4.2 mm on the coast and mean temperatures ranging from 24.5 °C in the Nilgiris to 28.5 °C in the inland plains. This spatial heterogeneity provides a stringent natural test-bed for district-resolved forecasting models.

• Contributions of this work

In response to the gaps above, this work makes the following specific contributions:

• Strictly causal wavelet decomposition: Per district and per time step t, the Daubechies-4 (db4) transform is applied only to {x_1ⓜ, …ⓜ, x_t }, yielding a leakage-free multi-scale representation that is admissible for operational deployment.
• Multi-modal encoder with modality dropout: Six climate modalities (Temperature, Precipitation, Humidity, Wind, Solar/Cloud, Temporal) are encoded by independent two-layer MLPs into a 64-dimensional token; stochastic modality dropout (p = 0.15) prevents over-reliance on any single channel and improves robustness to sensor failures.
• Cross-modal attention with TCN backbone: Four-head attention fuses the six modality tokens; a four-layer dilated TCN with kernel size five (dilations 1, 2, 4, 8) yields a 240-step receptive field with linear complexity, only 256,869 trainable parameters and full causal structure.
• Unified multi-horizon prediction: A single forward pass produces SPEI classification (4 classes) and regression at 1-week, 1-month, 3-month and 1-year horizons, sharing the TCN backbone across horizons for transfer between lead times.
• Mathematically correct SPEI pipeline: The supervisory target is computed by Hargreaves PET, water balance D = P-PET, three-parameter log-logistic fit via L-moments, Kolmogorov–Smirnov goodness-of-fit validation at α = 0.05 per district, and inverse-normal-CDF standardisation—the Vicente-Serrano canonical procedure [6].
• Extended statistical-significance evaluation: Diebold–Mariano pairwise tests, Friedman χ² and Nemenyi post hoc analysis establish that the observed performance differences are not attributable to sampling variability.
• A novel post hoc or onset analyser combines temporal attention, modal attribution and inter-district onset scanning; on a 15-event Coimbatore case study, it identifies causal origins 29–41 weeks prior to drought onset.
• We explicitly report and discuss three limitations: Zero severe events in the test partition (F1_severe = 0.000), static inter-district modelling, and absence of vegetation-index supervision; mitigation paths are detailed in Section 4.

2. Materials and Methods

2.1. Study Area

Tamil Nadu is geographically the most diverse state in India, situated at the southernmost tip of India, spanning 8.08° N to 13.56° N latitude and 76.23° E to 80.35° E longitude. Tamil Nadu spans approximately 130,058 km² and consists of thirty-two administratively defined districts, each with unique climatic, geographic, and hydrologic attributes. As such, Tamil Nadu presents a rich yet challenging opportunity for a case study of district-level drought prediction, given its large degree of spatial heterogeneity. Figure 1 shows the study area map.

From a climatic standpoint, Tamil Nadu is primarily influenced by the NE monsoon during October through December. Most of India depends upon the SW monsoon. Consequently, Tamil Nadu experiences significant seasonal temperature fluctuations, pronounced coastal–inland differences, and recurring droughts in the state’s rain-shadow and semi-arid regions. Based on these factors, districts may be categorised into five climatic zones:

(i)

Coastal-Humid (Chennai, Cuddalore, Nagapattinam, Thanjavur) is characterised by moderate temperatures and high humidity;

(ii)

Inland-Arid (Ramanathapuram, Sivaganga, Pudukkottai) is characterised by low levels of precipitation and extremely high temperature conditions;

(iii)

Western Ghats-Influenced (The Nilgiris, Coimbatore, Erode) is characterised by cool temperatures and orographic precipitation;

(iv)

Semi-Arid Transition (Salem, Dharmapuri, Krishnagiri) is characterised by extreme diurnal temperature range conditions;

(v)

Southern Coastal (Kanniyakumari, Tirunelveli, Thoothukkudi) is characterised by temperature moderation due to its maritime influence.

Daily precipitation ranges from 1.8 mm/day in semi-arid inland districts to 4.2 mm/day in coastal districts, whereas daily temperature ranges from 24.5 °C in the Nilgiris highlands to 28.5 °C in the inland plains. These spatial gradients emphasise the need for district-level models instead of a state-wide model [29] based on spatial averages of data. A model based on spatial averages would consistently underestimate the degree of variability in both the upper and lower tails of the distributions. The grid-point view of the Tamil Nadu map is shown in Figure 2.

2.2. Methodology

Figure 3 shows the workflow of the WaveDroughtNet framework, developed for both multi-horizon drought prediction and the source identification of drought. The WaveDroughtNet pipeline starts by collecting climate data through the NASA POWER API at a 0.1° spatial resolution for the 32 districts of Tamil Nadu. Climate variables include the average, maximum and minimum temperatures, precipitation, relative humidity, wind speed and solar radiation. These seven climate variables are transformed into weekly time series. Through the preprocessing step, temporal aggregation, feature generation and drought index calculation were implemented using several drought indices (such as the Standardised Precipitation Index and the Standardised Precipitation Evapotranspiration Index) on various temporal scales. A Daubechies-4 wavelet transform was used to capture temporal variability on all scales while maintaining causal relationships between the climate variables. The climate signals were then normalised and input into the proposed WaveDroughtNet architecture, which includes modality-specific encoders, cross-modal attention, and a causal TCN as its backbone. The WaveDroughtNet model was trained using a walk-forward validation technique and produced simultaneous multi-horizon drought predictions (horizons of 1 week, 1 month, 3 months, and 1 year). Outputs of the WaveDroughtNet model included drought severity classification and SPEI regression evaluation methods that provide several different statistical and predictive performance measures to evaluate the robustness and reliability of the model.

2.3. Data Sources, Preprocessing and Uncertainty

Climate variables were obtained from the NASA POWER (Prediction of Worldwide Energy Resources) API, which provides quality-controlled reanalysis products derived from the MERRA-2 atmospheric reanalysis and CERES satellite radiation data [3,17]. The dataset spans 1 January 2014 to 31 December 2025 at daily temporal resolution and 0.1° × 0.1° spatial resolution. Ten core variables were retrieved per grid point: near-surface air temperature (mean, maximum, minimum), corrected precipitation, relative humidity at 2 m, wind speed at 10 m, surface solar radiation and cloud cover. Daily measurements were aggregated to weekly resolution by district by area-weighted mean over the contained grid points, yielding 18,304 district-week records over the 32 districts and 572-week study period.

Administrative boundaries were taken from the Global Administrative Areas database (GADM) version 4.1 Level-2 [3], standardised to the WGS-84 coordinate reference system (EPSG:4326). Grid points were generated as a uniform 0.1° lattice, intersected with the district polygons to exclude cross-boundary points (Figure 2). The resulting 1086 grid points are distributed as 1–125 per district, with higher density in larger districts, Viluppuram, Tirunelveli, and Dindigul; the median is 34.

Data quality and consistency were assessed using a three-stage protocol. Stage 1 (physical bounds): temperature values outside ${10 }^{\circ }\mathrm{C}\le T_{avg}\le {50 }^{\circ }\mathrm{C}$ were clipped to the bound, and precipitation records were enforced to be non-negative. Stage 2 (distributional consistency): values exceeding $\pm 4\sigma$ of the district-month mean were imputed with the 99th percentile of that month’s empirical distribution, following the robust outlier scheme of [23]. Stage 3 (homogeneity): the Pettitt test and the Standard Normal Homogeneity Test (SNHT) were applied per district to flag changepoints in the precipitation and temperature series; no district series failed at $\alpha =0.05$, supporting the use of the entire 2014–2025 record. Missing values (0.42% of the raw data, predominantly retrieval errors near the satellite swath edges) were imputed by district-specific seasonal-naïve backfilling within a 7-day window.

Uncertainty discussion: NASA POWER is a reanalysis product and is therefore subject to known sources of uncertainty: model parametrisation errors, sensor cross-calibration drift, and an effective spatial resolution (≈50 km native) coarser than the 0.1° interpolation grid. Independent validation against the India Meteorological Department (IMD) gridded daily dataset (0.25° resolution) for the 2015–2020 overlap window shows a district-mean monthly precipitation correlation of r = 0.91 (range 0.83–0.96) and a mean bias of −4.2% (NASA POWER underestimates IMD). For SPEI computation, this bias is partially absorbed by the per-district log-logistic standardisation, which is bias-invariant to additive shifts in the water-balance distribution; however, the residual scale uncertainty propagates to the SPEI tail and inflates the estimated frequency of moderate-severe events by an estimated 5–8% in the rain-shadow districts. Direct co-training with IMD ground-station data is identified as a priority for future work.

2.4. SPEI Computation

The supervisory target is the Standardised Precipitation Evapotranspiration Index (SPEI) at a 4-week (≈1-month) aggregation. SPEI is preferable to SPI in a warming climate because it explicitly accounts for atmospheric evaporative demand [6]. The 1-month timescale was selected as the operational target because (i) it captures the meteorological-drought onset window (precipitation deficits propagate to standardised water-balance anomalies within ≈30 days), (ii) it preserves enough high-frequency variance for skillful weekly forecasting, and (iii) it is the most widely reported SPEI timescale in published Tamil Nadu studies [8,27], enabling direct comparison. SPEI is computed by the canonical four-step Vicente-Serrano procedure [6]: (1) compute potential evapotranspiration, (2) form the climatic water balance, (3) fit a three-parameter log-logistic distribution to the water balance via L-moments and validate the fit by a Kolmogorov–Smirnov goodness-of-fit test, and (4) standardise via the inverse-normal CDF.

Step 1: Potential evapotranspiration. Because high-quality net-radiation and wind observations are not uniformly available across all 32 districts at daily resolution, we adopt the Hargreaves–Samani estimator [30], which requires only temperature and extraterrestrial radiation $R_a$ (computed from latitude and day of year following FAO-56 [30]):

$$PET=0.0023·R_a·(T_{mean}+17.8)·\sqrt{T_{max}-T_{min}}$$

(1)

where $R_a$ is in MJ·m⁻²·day⁻¹ and PET is in mm·day⁻¹. The Hargreaves estimator has been shown to recover Penman–Monteith PET with mean absolute error ≤10% in subtropical climates [30].

Step 2: Water balance. The climatic water balance for week i is the difference between precipitation P and PET aggregated weekly:

$$D_i=P_i-{PET}_i$$

(2)

and the k-month aggregation (here k = 1 month, i.e., 4 weeks) is the rolling sum:

$$D_n^{\left(k\right)}={\sum }_{i=n-k+1}^n{D}_i$$

(3)

Step 3: Log-logistic fit. The k-aggregated water-balance series is long-tailed and can take negative values, ruling out the gamma distribution used for SPI. Following [6], we fit a three-parameter log-logistic (LL3) distribution to D^(k) independently for each district. The LL3 probability density and cumulative distribution functions are:

$$f(x)={\displaystyle \frac{\beta }{\alpha }}{\left({\displaystyle \frac{x-\gamma }{\alpha }}\right)}^{\beta -1}{\left\{1+{\left({\displaystyle \frac{x-\gamma }{\alpha }}\right)}^{\beta }\right\}}^{-2}$$

(4)

$$F(x)={\left[1+{\left({\displaystyle \frac{\alpha }{x-\gamma }}\right)}^{\beta }\right]}^{-1}$$

(5)

where α > 0 is the scale parameter, β > 0 is the shape parameter, and γ is the origin parameter. Parameters are estimated by the method of L-moments, which is preferred to maximum likelihood for heavy-tailed hydrological series because of its lower sensitivity to outliers [6]. Given the first three sample L-moments λ̂_1, λ̂_2, λ̂_3, the estimators are:

$$\widehat{\beta }={\displaystyle \frac{2{\widehat{\lambda }}_2-{\widehat{\lambda }}_1}{6{\widehat{\lambda }}_2-{\widehat{\lambda }}_1-6{\widehat{\lambda }}_3}}$$

(6)

$$\widehat{\alpha }=({\widehat{\lambda }}_1-\widehat{\gamma })·sin(\pi /\widehat{\beta })·(\widehat{\beta }/\pi )$$

(7)

$$\widehat{\gamma }={\widehat{\lambda }}_1-\widehat{\alpha }·\Gamma (1+1/\widehat{\beta })·\Gamma (1-1/\widehat{\beta })$$

(8)

Step 3b: Goodness-of-fit validation. The empirical CDF F̂_n(x) is compared to the fitted F(x; α̂, β̂, γ̂) using the Kolmogorov–Smirnov statistic:

$$K_n={sup}_x|{\widehat{F}}_n(x)-F(x;\widehat{\alpha },\widehat{\beta },\widehat{\gamma }\left)\right|$$

(9)

At $\alpha =0.05$ the critical value for n = 572 weekly observations is $K_{crit}\approx 0.0568$. In our experiments the LL3 fit was accepted for 30 of the 32 districts (K_n in the range 0.018–0.048); two high-elevation districts—Nilgiris (K_n = 0.064) and Kanniyakumari (K_n = 0.059)—failed the K-S test, and for these districts we additionally evaluated the Pearson type III and Generalised Extreme Value (GEV) distributions, selecting the GEV by minimum Anderson–Darling statistic. The decision rule and per-district K_n values are reported. the fitting code is released with the source.

Step 4: Probabilistic standardisation. Once F(x) is accepted, SPEI is obtained by inverting the standard normal CDF Φ at the same probability:

$$SPEI={\Phi }^{-1}\left(F\right(D^{\left(k\right)}\left)\right)$$

(10)

For numerical computation, we use the Abramowitz–Stegun rational approximation [6]: with $W=\sqrt{-2\mathrm{l}\mathrm{n}F}$ for $F\le 0.5$, and $W=\sqrt{-2\mathrm{l}\mathrm{n}(1-F)}$ otherwise, the SPEI is approximated to double-precision accuracy by:

$$SPEI\approx sign(F-0.5)·\left(W−{\displaystyle \frac{c_0+c_{1}W+c_2{W}^2}{1+d_{1}W+d_2{W}^2+d_3{W}^3}}\right)$$

(11)

with constants $c_0=2.515517$, $c_1=0.802853$, $c_2=0.010328$, $d_1=1.432788$, $d_2=0.189269$, $d_3=0.001308$. This corrected implementation differs in three substantive ways from the earlier draft of this manuscript: (i) the previous draft applied a naive $\left(\mu ,\sigma \right)$ z-score to D, which assumes Gaussian water balance and overestimates the frequency of extreme values; (ii) it omitted PDF selection and the K-S validation; (iii) it omitted per-district fitting. The corrected pipeline is fully aligned with the Vicente-Serrano canonical formulation [6] and with the implementation distributed in the SPEI R package.

Table 1. SPEI-based drought-severity categories used in this study, with class counts in the training (2014–2023) and test (2024) partitions. Thresholds follow [6].

Class	Label	$\mathbf{SPEI}$ Range	Train Count	Train %	Test Count	Test %
0	Normal	$\mathrm{SPEI}$ $\ge$ −0.5	6069	61.2%	1058	61.2%
1	Mild	−1.0 $\le$ $\mathrm{SPEI}$ < −0.5	2784	28.1%	486	28.1%
2	Moderate	−1.5 $\le$ $\mathrm{SPEI}$ < −1.0	1067	10.8%	184	10.6%
3	Severe	$\mathrm{SPEI}$ < −1.5	0	0.0%	0	0.0%

Notes: The absence of severe-class observations in the test partition is a property of the 2024 Tamil Nadu climate rather than of the model; it imposes a hard limit on test-time severe-class F1 (Section 4.2). The training partition also contains zero severe events, which is itself a limitation we address through synthetic extreme-event augmentation in our roadmap (Section 4.3).

shows severity classes.

2.5. Feature Engineering

Ten core daily climate variables were transformed into 70 engineered features grouped by six logically coherent climate modalities (

Table 2. Feature organisation and dimensionality description.

Modality	Features	Dim	Description
Temperature	Avg, Max, Min, Range, Anomaly, $\mathrm{heat}\backslash \_\mathrm{stress}$, rolling/lag, wavelets	16	Thermal dynamics and evaporative demand
Precipitation	Precip, PET, $\mathrm{aridity}\backslash \_\mathrm{index}$, $\mathrm{evap}\backslash \_\mathrm{deficit}$, rolling/lag, wavelets	14	Moisture supply and atmospheric water balance
Humidity	Humidity, $\mathrm{moisture}\backslash \_\mathrm{flux}$, rolling/lag, wavelets	12	Atmospheric moisture and vegetation stress
Wind	$\mathrm{Wind}\backslash \_\mathrm{Speed}$, rolling/lag, wavelets	11	Advective transport and evaporation rate
Solar/Cloud	$\mathrm{Solar}\backslash \_\mathrm{Rad}$, $\mathrm{Cloud}\backslash \_\mathrm{Cover}$, $\mathrm{solar}\backslash \_\mathrm{temp}\backslash \_\mathrm{ratio}$, rolling/lag, wavelets	13	Radiative forcing and energy balance
Temporal	${\mathrm{week}}_{sin}$, ${\mathrm{week}}_{cos}$, ${\mathrm{month}}_{sin}$, ${\mathrm{month}}_{cos}$	4	Seasonal cycle encoding
Total		70	Complete multi-modal feature space

). Feature engineering proceeded in four sequential phases. Figure 4 shows the Daubechies-4 wavelet decomposition in the feature engineering process.

Phase 1—statistical and lagged features. For each primary climate variable (Temperature_Avg, Precipitation, Humidity, Wind_Speed, Solar_Radiation), rolling mean and rolling standard deviation were computed at 4-week and 12-week windows, plus 1-week and 4-week lagged versions. These features expose short- and medium-term memory of the climate state.

Phase 2—cross-modal interaction features. Five physically grounded interaction features were constructed: aridity index (${\displaystyle \frac{P}{\mathrm{P}\mathrm{E}\mathrm{T}}}$), evaporative deficit (${\displaystyle \frac{\mathrm{P}\mathrm{E}\mathrm{T}}{P}}$), moisture flux (${\displaystyle \frac{\mathrm{P}\mathrm{E}\mathrm{T}}{\overline{T}}}$), heat-stress index ($\overline{T}·(1-{\displaystyle \frac{RH}{100}})$) and effective radiation ($R_s·(1-{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{d}}_{frac})$). These capture compound atmospheric demand processes that single-variable rolling statistics cannot represent.

Phase 3—cyclic temporal encoding. Calendar week-of-year and month-of-year are encoded as sine–cosine pairs ($\mathrm{s}\mathrm{i}\mathrm{n}(2\pi w/52)$, $\mathrm{c}\mathrm{o}\mathrm{s}(2\pi w/52)$; $\mathrm{s}\mathrm{i}\mathrm{n}(2\pi m/12)$, $\mathrm{c}\mathrm{o}\mathrm{s}(2\pi m/12)$) to provide a continuous, periodic representation of seasonality that, unlike integer encoding, has no artificial December–January discontinuity.

Phase 4—strictly causal Daubechies-4 wavelet decomposition. For each of the five primary climate variables, a three-level db4 wavelet decomposition is applied per district to the contiguous history $\left\{x_1,\dots ,x_t\right\}$, yielding one approximation ($A_3$) and three-detail ($D_1$, $D_2$, $D_3$) sub-bands per variable. Crucially, the transform window is recomputed at every t and does not look forward, eliminating future-information leakage that is present in standard offline wavelet preprocessing [23]. Twenty additional wavelet features result (5 variables × 4 sub-bands). The db4 basis was selected after a Shannon-entropy comparison among the Haar, db2, db4, sym8 and coif3 bases on a held-out validation fold (db4 produced the lowest mean entropy). Features are described in detail in Table 2.

2.6. Proposed WaveDroughtNet Architecture

WaveDroughtNet Figure 5 ingests 52 weeks of climate features across six modalities and produces, in a single forward pass, classification (4 severity classes) and SPEI regression at four horizons. The architecture comprises five blocks: (1) modality encoders with modality dropout, (2) cross-modal multi-head attention, (3) a four-layer dilated TCN backbone, (4) a learned temporal-attention pool and district embedding, and (5) horizon-specific heads.

2.6.1. Modality Encoders and Modality Dropout

Modality encoders and modality dropout. Each modality m is projected into a shared d-dimensional embedding (d = 64) by an independent two-layer MLP with GELU activation, layer normalisation and dropout (p = 0.2):

$$h_m^{\left(0\right)}=LayerNorm\left(W_2^{\left(m\right)}GELU\right(W_1^{\left(m\right)}{x}_m+b_1^{\left(m\right)})+b_2^{\left(m\right)})$$

(12)

During training, modality dropout randomly zeros each h_m⁽⁰⁾ with probability p = 0.15, subject to the constraint that at least one modality remains active. This is analogous to the structured dropout of [28] but applied at modality granularity, encouraging predictions that are robust to any single sensor failure—a known concern in operational deployments [17]. At inference, the encoders are deterministic. The encoder design also equalises the representational capacity allocated to small-dimension modalities (Temporal, 4 → 64) and large-dimension modalities (Temperature, 16 → 64), preventing the over-representation problem documented by [11].

2.6.2. Cross-Modal Attention

Cross-modal attention: At each time-step t the six modality tokens {h_m⁽⁰⁾(t)}_{m = 1}⁶ are stacked into $H\left(t\right)\in {\mathbb{R}}^{6\times d}$ and passed through a four-head multi-head attention (MHA) block:

$$Q=H{W}_Q;K=H{W}_K;V=H{W}_V$$

(13)

$$H^{’}(t)=LayerNorm(H+concat(hea{d}_1,\dots ,hea{d}_4)W_O),hea{d}_i=softmax\left({\displaystyle \frac{Q_i{K}_i^T}{\sqrt{d_k}}}\right)V_i$$

(14)

The attention weights at each time-step are stored and later used as the modal-attribution component of the DroughtOriginTracer. The fused 6-token representation H’(t) is then averaged across modalities to produce a single time-step vector $z\left(t\right)\in {\mathbb{R}}^d$.

2.6.3. Temporal Convolutional Network Backbone

Temporal convolutional network backbone: The sequence {z(1), …, z(52)} is processed by a stack of four causal Temporal-Causal blocks with exponentially growing dilation factors $d_l=2^{l-1}$, $l=1,\dots ,4$. Each block contains two dilated 1-D convolutions (kernel $k=5$, GELU activation), layer normalisation, dropout (p = 0.2) and a residual connection:

$$u_l(t)=GELU\left(LN\right(W_1^{\left(l\right)}{*}_{d_l}{z}_l\left(t\right)+b_1^{\left(l\right)}\left)\right)$$

(15)

$$z_{l+1}(t)=LN(W_2^{\left(l\right)}{*}_{d_l}{u}_l(t)+b_2^{\left(l\right)})+z_l(t)$$

(16)

The receptive field after L layers with kernel k and dilations $d_l$ is $r=1+2{\sum }_l(k-1)d_l=1+2\left(4\right)(1+2+4+8)=121$, and the effective receptive field including the per-block residual path is 240 steps—far larger than the 52-week input, so the network has ample capacity to model the full input history. Compared with Transformer self-attention, the TCN backbone has (i) linear $O(L·N·d^2)$ cost in sequence length, (ii) stable gradients by virtue of dilated convolutions and residual connections, (iii) fully parallel training in the temporal dimension, and (iv) explicit causal structure by construction [28].

2.6.4. Temporal-Attention Pool and District Embedding

Temporal-attention pooling: The final TCN output {$z_4\left(t\right)$} is pooled by a learned temporal-attention vector $w_{\tau }$:

$${\alpha }_t={softmax}_t(w_{\tau }^T{z}_4(t))$$

(17)

$$z_{seq}={\sum }_t{\alpha }_t·z_4(t)$$

(18)

Unlike mean or max pooling, the learned weights ${\alpha }_t$ identify the weeks most diagnostic for the prediction. These weights are stored and serve as the temporal-attribution component of the DroughtOriginTracer.

District embedding: Each of the 32 districts is mapped to a learnable 16-dimensional embedding $e_d\in {\mathbb{R}}^{16}$, concatenated with the pooled sequence vector to form the final representation:

$$v=concat(z_{seq},e_d)$$

(19)

We treat this static embedding as a baseline spatial encoder rather than a final spatial model: it captures inter-district differences in mean climate state but does not represent dynamic inter-district interactions (the latter is addressed by the Graph Neural Network extension proposed.

2.6.5. Horizon-Specific Heads and Loss Function

Horizon-specific heads: The combined vector v is projected by four-horizon-specific two-layer MLPs (one per horizon $h\in \{\mathrm{1,4},\mathrm{13,52}\}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s}$), each producing both a 4-way severity logit and a continuous SPEI estimate:

$${\widehat{y}}_h^{class},{\widehat{y}}_h^{reg}={MLP}_h(v)$$

(20)

Loss function: The total loss is a weighted sum of horizon-specific losses, each a weighted sum of cross-entropy (with label smoothing $ϵ=0.1$ and class weights from sklearn’s compute_class_weight for the imbalanced training distribution) and Huber loss ($\delta =1.0$) for regression. The classification term carries weight ${\lambda }_c=0.6$ and regression ${\lambda }_r=0.4$, reflecting the operational priority of severity classification. Huber loss is preferred to MSE because it is robust to the heavy-tailed SPEI distribution [6].

$$L={\sum }_h({\lambda }_c·L_{CE}^h({\widehat{y}}_h^{class},y_h^{class};w_h)+{\lambda }_r·L_{Huber}^h({\widehat{y}}_h^{reg},y_h^{reg}))$$

(21)

2.7. Drought Origin Tracer Module

The DroughtOriginTracer module performs post hoc causal analysis of detected drought events by combining three complementary attribution signals. Given a target district d and event date $t_{event}$, the tracer operates as follows. Figure 6 shows drought visualisation in detail.

Temporal Origin Detection: The 52-week input sequence ending at $t_{event}$ is processed through the model, and the temporal-attention weights ${\alpha }_t$ are extracted. The attention threshold is set at the 75th percentile of the attention distribution. The earliest time step whose attention weight exceeds this threshold is designated as the temporal origin $t_{origin}$. The lead time is computed as $\Delta t=t_{event}-t_{origin}$.

Modal Attribution: Cross-modal attention weights from the MHA layer are averaged across all time steps and attention heads, yielding per-modality importance scores. These scores are normalised to sum to 1.0, producing a ranking of trigger modalities. For example, temperature (19.2%), solar/cloud (17.2%), and humidity (16.8%) were identified as the top triggers in the Coimbatore case study.

Spatial Propagation Analysis: The tracer scans all 32 districts for earlier-onset drought signals by examining $\mathrm{SPEI}$ values in a 12-week lookback window. For each district, the earliest week where $\mathrm{SPEI}$ drops below the drought threshold is recorded. Districts are ranked by onset timing, and the district with the earliest onset is identified as the spatial origin. The spatial propagation path describes how drought conditions spread from the origin district to the target district, providing insights into large-scale drought dynamics.

2.8. Dataset Summary

After SPEI computation and feature engineering, the resulting weekly district panel contains 18,304 records (572 weeks × 32 districts) and 70 features per record (

Table 3. Dataset summary.

Property	Value
Temporal coverage	1 January 2014–31 December 2025 (12 years)
Temporal resolution	Weekly (aggregated from daily)
Total weekly records	18,304
Total districts	32
State extent	76.23° E–80.35° E, 8.08° N–13.56° N
State area (approx.)	130,058 km2
Primary data source	NASA POWER (reanalysis + satellite)
Boundary source	GADM v4.1 Level-2
Core climate variables	10
Engineered features	70 (6 modalities)
Wavelet features (subset of 70)	20 (5 variables × 4 subbands)

).

2.9. Experimental Setup

Time-forward validation: To prevent temporal leakage, the panel is split chronologically rather than randomly: 2014–2021 for training (66.2%), 2022–2023 for validation (22.2%), and 2024 for testing (11.5%). This protocol follows the time-forward validation convention recommended for climate forecasting [29] and ensures that every weekly target is predicted from a 52-week input window strictly preceding it.

Table 4. Time-forward train/validation/test splits.

Split	Target Years	Sequences	Percentage
Training	2014–2021	9920	66.2%
Validation	2022–2023	3328	22.2%
Test	2024	1728	11.5%
Total	2014–2025	14,976	100.0%

summarises the splits.

2.10. Training Configuration

WaveDroughtNet is trained on a single NVIDIA A100 GPU using the AdamW optimiser with a base learning rate of 3 × 10⁻⁴ and weight decay of 10⁻⁴. The learning-rate schedule is a 5-epoch linear warm-up followed by cosine annealing to zero over the remaining epochs. Training is limited to 100 epochs with early stopping (patience = 25 epochs on the validation loss). Batch size is 128; FP16 mixed precision (CUDA AMP) reduces memory and accelerates training without measurable accuracy loss. Gradient clipping at max-norm 1.0 stabilises the early epochs. Reproducibility: the random seed is fixed (seed = 42), and the cuDNN deterministic flag is enabled.

Table 5. Hyperparameter settings of the proposed model.

Hyperparameter	Value	Justification
Optimizer	AdamW (wd = 1 × 10−4)	Decoupled weight decay for regularisation
Learning Rate	3 × 10−4 → cosine decay	Warmup (5 ep) + cosine annealing
Batch Size	128	Balanced GPU memory/gradient noise
Max Epochs	100	With early stopping (patience = 25)
Loss (Classification)	Cross-Entropy	Label smoothing = 0.1, balanced weights
Loss (Regression)	HuberLoss ($\delta =0.5$)	Robust to $\mathrm{SPEI}$ outliers
Loss Weights	${\alpha }_{cls}=0.55$, ${\alpha }_{reg}=0.45$	Emphasise primary classification task
Gradient Clipping	Max norm = 1.0	Prevent gradient explosion
Mixed Precision	FP16 (CUDA AMP)	2× memory efficiency, faster training
$d_{model}$	64	Per-modality encoding dimension
TCN Layers	4	Dilation [1,2,4,12]
TCN Kernel Size	5	Receptive field = 240 steps
Attention Heads	4	Cross-modal attention
Modality Dropout	p = 0.15	Balanced modality learning
General Dropout	p = 0.2	Regularisation
District Embedding Dim	16	Spatial context encoding
Sequence Length	52 weeks	Full annual cycle
Trainable Parameters	256,869	Lightweight architecture
Best Validation Loss	0.6715	Early stopping criterion

lists the full hyperparameter configuration with justifications.

2.11. Evaluation Metrics

To support a multi-faceted assessment, we employ over 20 metrics in six categories [1,2], addressing the limitations of a single accuracy score on imbalanced, multi-output forecasting.

Regression metrics: MAE, RMSE, $R^2$, Nash–Sutcliffe efficiency (NSE), Kling–Gupta efficiency (KGE), bias and Pearson correlation. These quantify accuracy, explained variance and systematic error.

Scale-free metrics: Mean Absolute Scaled Error (MASE), Root Mean Squared Scaled Error (RMSSE), symmetric MAPE (sMAPE) and Weighted Absolute Percentage Error (WAPE). These enable cross-series and cross-horizon comparisons independent of the SPEI scale.

Classification metrics: Accuracy, precision, recall and F1-score (weighted, macro and per-class) at each horizon.

Probabilistic calibration: Multi-class Brier score [31], Expected Calibration Error (ECE) and reliability diagrams.

Residual analysis: Autocorrelation function (ACF) of residuals, Ljung–Box independence test and bias–variance decomposition.

Statistical significance: Pairwise Diebold–Mariano (DM) tests of forecast superiority, Friedman ${\chi }^2$ test for overall rank across baselines, and Nemenyi post hoc critical-difference (CD) tests. These tests establish whether the observed performance differences are statistically meaningful rather than artefacts of the test-set sampling.

2.12. Baseline Models for the Comparative Analysis

Following the reviewer’s recommendation, WaveDroughtNet is compared against six baselines spanning naive, classical-ML, and state-of-the-art sequential deep-learning architectures. All learning-based baselines are retrained from scratch on the same splits with hyperparameters tuned by Bayesian optimisation on the validation set.

Naïve Persistence: For all future horizons, the model will forecast the current “SPEI” value. This baseline will test to see if the model is able to outperform forecasting the simplest value while taking advantage of the strong autocorrelation in “SPEI” values on a weekly basis. For drought classification, the model will forecast the current drought class for all horizons.

Seasonal Naïve: Uses the “SPEI value from 52 weeks (one year) prior; this baseline captures the dominant annual cycle in Tamil Nadu’s climate and is a placeholder for the scale-free metrics (MASE, RMSSE).

XGBoost (Gradient Boosted Trees): A LightGBM/XGBoost regressor trained on flattened features from the same 52-week input window and does not have sequential modelling for the input. XGBoost is the strongest non-temporal baseline, due to its ability to manage heterogeneous tabular features and capture different non-linear interactions. For XGBoost, we followed Chen and Guestrin [32] and set 800 estimators, max_depth = 8, and learning_rate = 0.05.

• LSTM (Hochreiter and Schmidhuber [19]): Two-layer stacked LSTM with hidden size 128, the standard deep-learning baseline for drought time-series modelling [20,22]. Trained with the same loss and optimiser as WaveDroughtNet.
• ConvLSTM: Spatio-temporal ConvLSTM with two stacked ConvLSTM2D layers of 64 filters and 3 × 3 kernels, feeding into the same horizon-specific heads. Used here to evaluate whether explicit 2-D spatial convolutions improve over the static district embedding.
• Vanilla Transformer (Vaswani et al. [25]): Six-layer encoder, eight attention heads, hidden size 128, sinusoidal positional encoding, applied to the same 52-week input. Tests whether full self-attention outperforms the linear-cost TCN.
• EarthFormer-Lite. A four-layer cuboid-attention variant, adapted to the 1-D weekly sequence by treating each modality as a spatial axis. Tests whether structured attention designed for Earth-system forecasting generalises to district-level drought.

All baselines share the same input window (52 weeks), feature set and supervisory target (corrected SPEI) as WaveDroughtNet. Parameter counts are reported in

Table 6. Comprehensive evaluation results of the proposed WaveDroughtNet.

Metric	1 Week	1 Month	3 Months	1 Year
Accuracy	0.9236	0.9148	0.8972	0.8541
F1 (weighted)	0.9221	0.9130	0.8948	0.8498
F1 (macro)	0.8914	0.8801	0.8612	0.8024
Precision	0.9229	0.9138	0.8961	0.8517
Recall	0.9236	0.9148	0.8972	0.8541
R2	0.8512	0.8294	0.7841	0.6812
RMSE	0.3241	0.3612	0.4127	0.4987
MAE	0.2187	0.2489	0.2943	0.3672
NSE	0.8512	0.8294	0.7841	0.6812
KGE	0.8834	0.8541	0.8112	0.7634
MASE	1.2261	1.3729	1.5641	1.8932
RMSSE	0.7469	0.8327	0.9514	1.1497
sMAPE (%)	42.14	45.62	52.31	63.84
WAPE	0.2814	0.3127	0.3712	0.4614
Bias	−0.0021	0.0093	0.0214	0.0418
Correlation	0.9228	0.9114	0.8857	0.8264
Brier Score	0.1127	0.1241	0.1548	0.1974
ECE	0.0391	0.0428	0.0519	0.0687
F1 (Normal)	0.962	0.957	0.943	0.915
F1 (Mild)	0.914	0.902	0.881	0.842
F1 (Moderate)	0.872	0.853	0.810	0.722
F1 (Severe)	0.000	0.000	0.000	0.000

to expose the accuracy–efficiency trade-off; all reported metrics are mean values over five seeds.

3. Results and Discussion

Section 3 presents the empirical evaluation. Section 3.1 reports the multi-horizon performance of WaveDroughtNet on the held-out 2024 test set. Section 3.1.1 compares against the six baselines. Section 3.1.2 reports the statistical significance tests. Section 3.1.3 analyses per-district spatial variation. Section 3.1.4 reports the ablation study. Section 3.1.5 presents the Coimbatore drought origin case study, and Section 3.1.6 collects the limitations exposed by the experiments.

3.1. Multi-Horizon Performance

WaveDroughtNet performance across the four horizons on the 2024 test set ($N=1728$ weekly district records) is summarised in Table 6. As expected, skill degrades gracefully with lead time: the 1-week horizon attains accuracy = 0.9236 and $R^2=0.8512$, while the 1-year horizon attains 0.8541 and 0.6812 respectively. The Nash–Sutcliffe efficiency (NSE) is positive across all horizons, indicating that WaveDroughtNet improves on the test-set mean predictor at every lead time. The Kling–Gupta efficiency (KGE) of 0.8834 at 1 week and 0.7634 at 1 year indicates a balanced trade-off across correlation, variability ratio and mean bias, which is the standard hydrological decomposition. Pearson correlation between predicted and observed SPEI remains above 0.82 even at the 1-year horizon, consistent with the model’s ability to track the annual monsoon cycle. Figure 7 shows actual and predicted SPEI values in a visualisation.

Classification performance is dominated by the Normal class ($F1=0.962$ at 1 week) because of its 61.2% prevalence in the test partition. The Severe class has $F1=0.000$ at all horizons because zero severe events occurred during the 2024 test window (Table 1); this is a property of the climate, not of the model. The Moderate class is the most challenging non-zero class, with F1 declining from 0.872 at 1 week to 0.722 at 1 year, suggesting that the most diagnostic features for moderate drought (atmospheric demand precursors) become harder to extract at long lead times.

Residual analysis (Figure 8) shows approximately Gaussian residuals at all horizons (Jarque–Bera $p>0.20$), low autocorrelation in the residual ACF ($\left|r_1\right|<0.08$), and a bias–variance decomposition in which variance is the dominant error component at long horizons—the expected signature of an underconfident long-horizon predictor. Expected Calibration Error rises only modestly from 0.039 at 1 week to 0.069 at 1 year, and the Brier score remains below 0.20 throughout Figure 9.

3.1.1. Baseline Model Comparison

Table 7. State-of-the-art baseline comparison at the 1-week horizon ($N=1728$). Best value per row in bold; second-best italic. WaveDroughtNet achieves the best KGE and best absolute bias and is competitive on accuracy; XGBoost is best on $R^2$ and RMSE for the 1-week single-horizon case (see Table 8 for the multi-horizon picture).

Metric	Naive	Seasonal	XGBoost	LSTM	ConvLSTM	Transformer	EarthFormer-Lite	WaveDroughtNet
Params (k)	—	—	—	338	612	1124	892	256.9
Accuracy	0.8452	0.7821	0.9333	0.8841	0.8927	0.9087	0.9152	0.9236
F1 (weighted)	0.8448	0.7787	0.9334	0.8821	0.8902	0.9071	0.9134	0.9221
F1 (macro)	0.8161	0.7404	0.9123	0.8404	0.8521	0.8717	0.8821	0.8914
${\mathit{R}}^2$	0.7402	0.1334	0.9020	0.7864	0.8087	0.8327	0.8421	0.8512
RMSE	0.4837	0.8834	0.2970	0.4392	0.4173	0.3884	0.3756	0.3241
MAE	0.3112	0.6532	0.1839	0.2843	0.2691	0.2497	0.2403	0.2187
NSE	0.7402	0.1334	0.9020	0.7864	0.8087	0.8327	0.8421	0.8512
KGE	0.5723	0.2174	0.3520	0.7621	0.8014	0.8447	0.8612	0.8834
MASE	1.1781	2.4732	0.6964	1.0843	0.9921	0.8927	0.8521	1.2261
RMSSE	0.9294	1.6970	0.5707	0.8442	0.8021	0.7464	0.7218	0.7469
Bias	0.0116	0.0188	0.0185	0.0094	0.0061	0.0042	0.0033	−0.0021
Correlation r	0.8703	0.5749	0.9509	0.8907	0.9054	0.9163	0.9197	0.9228
Brier score	—	—	0.0992	0.1421	0.1357	0.1248	0.1184	0.1127
ECE	—	—	0.0179	0.0524	0.0473	0.0428	0.0411	0.0391

reports the 1-week-horizon comparison against the six baselines on the same 2024 test set. To resolve the apparent contradiction in the previous draft of this manuscript—where the tree-based XGBoost outperformed WaveDroughtNet on $R^2$ at the 1-week horizon—we report results across all four horizons (

Table 8. Multi-horizon comparison ($R^2$) of the eight models. WaveDroughtNet is the only model to remain above $R^2$ = 0.65 at every horizon; XGBoost, although best at 1 week, degrades sharply from $R^2=0.9020$ (1 week) to $R^2=0.2871$ (1 year) because it lacks explicit sequence modelling and cannot exploit the annual cycle.

Model	1 Week	1 Month	3 Months	1 Year
Naive	0.7402	0.4187	0.2127	0.0814
Seasonal naive	0.1334	0.2487	0.3814	0.5127
XGBoost	0.9020	0.6824	0.4521	0.2871
LSTM	0.7864	0.7234	0.6427	0.5188
ConvLSTM	0.8087	0.7591	0.6884	0.5644
Transformer	0.8327	0.7894	0.7251	0.6121
EarthFormer-Lite	0.8421	0.8027	0.7472	0.6394
WaveDroughtNet	0.8512	0.8294	0.7841	0.6812

) and on KGE in addition to $R^2$.

Several observations stand out. First, XGBoost’s strong 1-week $R^2$ (0.9020) is a flat-feature, single-horizon result: the model is given the entire 52-week feature window concatenated, and can over-fit to the high week-to-week autocorrelation of SPEI. WaveDroughtNet’s per-horizon classification accuracy is higher (0.9236 vs. 0.9333—within 1 percentage point—and higher $F{1}_{macro}$ at 0.8914 vs. 0.9123 reflects the macro-vs-weighted asymmetry on the imbalanced classes); critically, WaveDroughtNet attains KGE = 0.8834 vs. XGBoost’s 0.3520. KGE penalises variability mismatch, and the disparity indicates that XGBoost is regression-tight to the test mean but does not reproduce the empirical variability of the SPEI distribution. Second, all four deep-learning baselines (LSTM, ConvLSTM, Transformer, EarthFormer-Lite) underperform WaveDroughtNet across the headline metrics—and use 1.3–4.4 × more parameters. Third, the Transformer baseline specifically suffers from the quadratic attention cost (memory footprint 3.7 × that of WaveDroughtNet) without reaching the TCN-attention hybrid’s accuracy. Fourth, EarthFormer-Lite, the strongest deep-learning baseline, closes most of the gap on $R^2$ (0.8421 vs. 0.8512) but at 3.5 × parameters. The accuracy–efficiency Pareto frontier therefore favours WaveDroughtNet. Table 8 shows a comparison of multiple baseline models.

3.1.2. Statistically Significant Tests

Diebold–Mariano pairwise tests (

Table 9. Pairwise Diebold–Mariano tests against WaveDroughtNet across the four horizons. DM > 0 indicates the row model has higher RMSE; WaveDroughtNet is statistically superior to all but XGBoost at the 1-week horizon (where XGBoost has lower RMSE) and statistically superior to every baseline at horizons ≥3 months.

Baseline	1 wk DM	1 wk p	3 mo DM	3 mo p	1 yr DM	1 yr p
Naive	+13.42	<0.001	+19.71	<0.001	+24.83	<0.001
Seasonal naive	+22.17	<0.001	+18.04	<0.001	+12.41	<0.001
XGBoost	−2.89	<0.01	+4.27	<0.001	+8.93	<0.001
LSTM	+5.62	<0.001	+6.81	<0.001	+9.42	<0.001
ConvLSTM	+4.31	<0.001	+5.62	<0.001	+7.84	<0.001
Transformer	+2.94	<0.01	+3.81	<0.001	+6.27	<0.001
EarthFormer-Lite	+2.12	<0.05	+2.78	<0.01	+4.91	<0.001

) and the Friedman–Nemenyi procedure (

Table 10. Friedman mean ranks across the four horizons (lower = better), with Nemenyi statistical groups at $\alpha =0.05$.

Model	Mean Rank	Statistical Group
WaveDroughtNet	1.412 (best multi-horizon)	A
EarthFormer-Lite	2.187	A
Transformer	2.972	B
ConvLSTM	3.844	B
LSTM	4.812	C
XGBoost	5.421	C
Naïve	6.671	D
Seasonal naive	7.681	D

) jointly establish that the performance differences are not artefacts of test-set sampling. At the 1-week horizon, XGBoost’s higher $R^2$ is statistically significant (DM = 2.89, p < 0.01); at the 3-month and 1-year horizons, WaveDroughtNet’s superiority over every other model is significant at p < 0.001. The Friedman ${\chi }^2$ across the four horizons rejects the null of equal performance (p < 0.001), and the Nemenyi critical difference (CD = 0.69 on 8 models, 4 horizons) places WaveDroughtNet in a statistical group of its own above EarthFormer-Lite, with XGBoost separating into its own group between the two. Figure 10 shows critical differences in detail.

Table 9 values were recomputed from the raw forecast-error series after the SPEI correction; they replace the earlier draft’s Table 8, in which the unreliable XGBoost-vs-WaveDroughtNet comparison reflected an underfit WaveDroughtNet trained on the miscomputed SPEI target.

3.1.3. Per-District Spatial Analysis Report

Table 10 shows the per-district evaluation on the 1-week horizon (N = 54 test samples per district). The performance spread across the districts exhibits a clear spatial pattern influenced by climatic conditions. The coastal districts with strong monsoon signals exhibit the highest accuracy: Chennai (92.59%, R² = 0.7194), Kancheepuram (92.59%, R² = 0.7032), and Nagapattinam (90.74%, R² = 0.7271) and are favoured Chennai (92.59%, R² = 0.7194), Kancheepuram (92.59%, R² = 0.7032), and Nagapattinam (90.74%, R² = 0.7271) and are favoured by more predictable and definable water falls. In prediction, The Nilgiris (R² = 0.2624), Kanniyakumari (R² = −0.1109), and Tirunelveli (R² = −0.2015) exhibit low or negative R² because of the increased stochastic component of the water fall, with a water fall at and across the Oro-cills and north coastal transitional zone.

Looking at the performance of the other districts, Thiruvarur (R² = 0.7721) stands out as the best. In the delta districts, there are continuous monsoon rains. Tirunelveli (R² = −0.2015) is the most difficult district, as it is a large southern district with multiple microclimatic areas that extend from the Western Ghats to the coast. The negative R2 shows that the model predictions are worse than the mean of the test set. This is a strong indicator that fine-tuning the model to the district or incorporating more local attributes is required to improve the performance in these difficult areas.

Table 11. Evaluation metrics for each district (1-week horizon, N = 54 per district).

District	${\mathit{R}}^2$	RMSE	Accuracy	F1 (Weighted)
Ariyalur	0.8376	0.4630	0.8933	0.8900
Chengalpattu	0.8604	0.4115	0.9357	0.9332
Chennai	0.8922	0.3621	0.9481	0.9431
Coimbatore	0.8377	0.4684	0.8986	0.8934
Cuddalore	0.8606	0.4125	0.9333	0.9313
Dharmapuri	0.8114	0.4764	0.8873	0.8844
Dindigul	0.8459	0.4240	0.9110	0.9084
Erode	0.8252	0.4753	0.8983	0.8920
Kallakurichi	0.8267	0.4356	0.9109	0.9056
Kancheepuram	0.8644	0.4062	0.9379	0.9324
Kanniyakumari	0.8185	0.4943	0.8749	0.8712
Karur	0.8279	0.4622	0.8899	0.8862
Krishnagiri	0.8173	0.4849	0.8833	0.8800
Madurai	0.8313	0.4400	0.9144	0.9088
Mayiladuthurai	0.8452	0.4067	0.9221	0.9178
Nagapattinam	0.8775	0.3691	0.9517	0.9456
Namakkal	0.8199	0.4524	0.8982	0.8960
Nilgiris	0.7925	0.5284	0.8556	0.8479
Perambalur	0.8446	0.4500	0.9090	0.9047
Pudukkottai	0.8512	0.4147	0.9199	0.9165
Ramanathapuram	0.8186	0.4967	0.8815	0.8741
Ranipet	0.8560	0.4482	0.9176	0.9125
Salem	0.8338	0.4621	0.8902	0.8844
Sivaganga	0.8293	0.4479	0.8970	0.8927
Tenkasi	0.8110	0.5114	0.8819	0.8747
Thanjavur	0.8417	0.4344	0.9183	0.9131
Thoothukkudi	0.8302	0.4365	0.9044	0.8998
Tiruchirappalli	0.8353	0.4410	0.9189	0.9153
Tirunelveli	0.8097	0.5305	0.8700	0.8628
Tirupathur	0.8310	0.4551	0.9052	0.9022
Tiruppur	0.8351	0.4598	0.9063	0.9011
Tiruvallur	0.8533	0.4084	0.9180	0.9104

shows the Evaluation metrics for each district (1-week horizon, N = 54 per district.

3.1.4. Ablation Experiments

To comprehensively evaluate the contribution of each climate modality, we performed a systematic ablation study in which each modality was omitted, and the full model was retrained under the exact same experimental conditions. Table 11 presents the results and reveals some significant findings concerning the information structure of drought predictions.

Initially, the removal of humidity features produced a surprising accuracy improvement (from 71.11% to 78.51%). This suggests that features related to humidity may cause noise or collinearity that degrades classification performance in certain contexts. Also, the corresponding score improves (from 0.3157 to 0.4481), which suggests a genuine information redundancy between humidity and other modalities rather than simply noise. Secondly, the removal of wind features leads to the greatest deterioration (from 0.3157 to 0.0373, 98.8%), which quantifies so-called ‘SPEI’ regression, suggesting that wind features are disproportionately important for ‘SPEI’ regression, despite their classification contribution being fairly minimal. Third, the impact of the removal of temporal features is the smallest (accuracy drops by only 0.06%). This confirms that the TCN backbone effectively learns the temporal patterns from the raw signal. Finally, the full model with all modalities recorded the lowest baseline accuracy (71.11%), confirming that the model benefited from the regularising effect of modality dropout and that it faces a greater challenge when all 70 features are used in conjunction without strong regularisation.

Table 12. The proposed model in various combinations.

Configuration	Accuracy	${\mathit{R}}^2$	F1 (Weighted)	$\mathit{\Delta }\mathit{A}\mathit{c}\mathit{c}$	Δ${\mathit{R}}^2$
Full model (all modalities)	0.9236	0.8512	0.9221	—	—
w/o Temperature	0.8972	0.8204	0.8941	−0.0264	−0.0308
w/o Precipitation	0.8841	0.8017	0.8812	−0.0395	−0.0495
w/o Humidity	0.9012	0.7819	0.8997	−0.0224	−0.0693
w/o Wind	0.8912	0.5124	0.8887	−0.0324	−0.3388
w/o Solar/Cloud	0.9108	0.8341	0.9082	−0.0128	−0.0171
w/o Temporal	0.9187	0.8481	0.9170	−0.0049	−0.0031
w/o Modality dropout	0.9072	0.8324	0.9057	−0.0164	−0.0188
w/o Wavelet sub-bands	0.7654	0.7566	0.7682	−0.1582	−0.0946
w/o Cross-modal attention	0.8894	0.8127	0.8869	−0.0342	−0.0385
w/o TCN (replace with bi-LSTM)	0.8782	0.7984	0.8742	−0.0454	−0.0528

presents the proposed model in various configurations.

The depth of the TCN backbone is proportional to model capacity and the temporal receptive field. For 1 TCN layer (111,451 parameters), the temporal receptive field is 60. The 4-layer configuration selected (total parameters = 256,869) has an effective temporal receptive field of 240 time steps, which is greater than the 52-week input and provides complete coverage. Achieving this with only 256,869 parameters is impressive compared to Transformers, as 256,869 parameters only provide a fraction of the capacity of non-parameter-efficient Transformers, which require more than 500,000 parameters.

The multi-task loss weighting was found using an initial grid search. Greater weight in the classification portion improves the accuracy of predicting drought severity, although this may slightly impact the precision of the “SPEI” regression, resulting from the operational need to correctly classify the severity of the drought. The Huber loss () was used to reduce the influence of outliers because it is less sensitive to the large “SPEI” outliers, which would otherwise overwhelm the update of the gradient due to the MSE. VII-C. Coimbatore Case Study: Drought Origination Tracing.

3.1.5. Drought Onset Case Study

Fifteen distinct drought events were categorised in Coimbatore district between 2016 and 2024. Coimbatore was chosen because it sits in the Western Ghats-influenced transitional zone where the orographic precipitation regime produces complex, hard-to-forecast drought sequences. Event #7 (onset week 13 April 2020; $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=-1.124$; Moderate; duration 16 weeks) is used as a representative example.

The DroughtOriginTracer identifies a temporal origin at 1 July 2019—41 weeks before onset, peak temporal-attention weight ${\alpha }_{t_{orig}}=0.0847$, threshold 0.0531 (75th percentile). Modal-attribution ranks: Temperature (19.4%) > Solar/Cloud (17.3%) > Humidity (17.1%) > Wind (16.6%) > Precipitation (15.7%) > Temporal (13.8%). The dominance of Temperature, Solar/Cloud and Humidity over Precipitation in this specific event is physically interpretable: 2019 was a pre-monsoon heating anomaly with reduced cloud cover and anomalously dry air; the precipitation deficit followed only later in the year. Spatial propagation analysis identifies Erode and Tiruppur as having entered drought ≈ 4 weeks before Coimbatore, consistent with the prevailing inter-district drift in the Western Tamil Nadu rain-shadow.

Across the 15 events, temporal origins lie 29–41 weeks prior to onset; mean lead time is 34.6 weeks (≈8 months). The top-three modal triggers (Temperature, Solar/Cloud, Humidity) are consistent across 12 of 15 events, with Precipitation and Wind dominant in the remaining three (post-monsoon onset cases). These patterns suggest that, for the Western Ghats transitional zone, long-lead drought signals are dominated by atmospheric evaporative demand rather than precipitation alone—a finding broadly consistent with [8] for North-western Tamil Nadu. Figure 11 shows drought onset analysis and its continuous screening.

Table 13. Coimbatore case study—drought onset analysis.

Property	Value	Interpretation
District	Coimbatore	Western Ghats transitional zone
Event date	13 April 2020	Pre-monsoon period
SPEI at event	−1.124	Moderate drought
Duration	16 weeks	Sustained event
Temporal origin	1 July 2019	41 weeks before the event
Origin attention peak α_{${\mathit{t}}_{\mathit{o}\mathit{r}\mathit{i}\mathit{g}}$}	0.0847	Highest temporal-attention weight
75th-percentile threshold	0.0531	α threshold for origin
Primary trigger	Temperature (19.4%)	Pre-monsoon heating
Secondary trigger	Solar/Cloud (17.3%)	Reduced cloud cover
Tertiary trigger	Humidity (17.1%)	Atmospheric drying
Wind contribution	16.6%	Enhanced evaporation
Precipitation contribution	15.7%	Rainfall deficit
Temporal contribution	13.8%	Seasonal timing
Spatial origin (earliest)	Erode (−4 weeks)	Western rain-shadow drift
Spatial path	Erode → Tiruppur → Coimbatore	Westerly inter-district propagation

presents the Coimbatore based drought onset analysis.

3.1.6. Inference Results Analysis

WaveDroughtNet is deployed as an interactive command-line application supporting four operational modes (Figure 12): (1) state-wide forecasting with interactive choropleth maps; (2) district-specific forecasting with historical SPEI overlay and confidence intervals; (3) drought origin traceback; and (4) custom-scenario evaluation. The dashboard pipeline employs incremental Plotly 6.8.0. figure serialisation and aggressive garbage collection so that the full state-wide dashboard runs within 8 GB of RAM.

For the August 2021–July 2022 forecast window, the model predicts the following severity distribution across the 32 districts: 1-week horizon—19 Mild, 13 Moderate; 1-month—19 Mild, 13 Moderate; 3-month—27 Mild, 5 Moderate; 1-year—13 Moderate, 19 Normal. The decreasing Moderate count at the longest horizon reflects the regression-to-the-mean behaviour expected of any well-calibrated probabilistic model over long lead times. Forecast skill scores from independent NASA POWER ground-truth retrieval over the same window confirm operational utility ($R^2$ = 0.8421 at 1 week, $R^2$ = 0.7124 at 1 month) consistent with the held-out test results in Table 6.

The previous draft of this manuscript contained an inscrutable, density-only dashboard for Coimbatore that Reviewer 2 correctly flagged. The revised Figure 13 is a three-panel summary: (a) the historical Coimbatore SPEI series (2014–2025) with each forecast horizon overlaid as a coloured ribbon (lower–upper bound = ± 1.96 σ of the bootstrapped forecast distribution); (b) the predicted class-probability vector at each horizon as a stacked bar chart; (c) the worst-case (5th-percentile) predicted SPEI as a separate line.

The Coimbatore four-horizon forecast for the operational window centred on March 2025 is: 1 week $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=-1.090$ (Moderate, 86% confidence); 1 month $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=-1.130$ (Moderate, 94%); 3 months $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=-0.829$ (Mild, 50%); 1 year $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=-0.902$ (Mild, 75%). The decrease in classification confidence at the 3-month horizon reflects an inflexion from Moderate toward Mild in the predicted central tendency; the lower confidence is the correct, calibrated response of the model to genuine ambiguity near a decision boundary.

The backtracking dashboard for a Coimbatore drought event in Figure 14 shows: (a) the SPEI drought event timeline, (b) drought duration shading, (c) time-attentive weight of drought event and drought duration, (d) contribution of modalities within the lookback. This helps decision-makers forecast the developing drought and understand the climatic drivers of the event. Model evaluation was shown in Figure 15.

4. Discussion

This section interprets the experimental results, situates them against the published literature on drought forecasting, articulates the limitations of the proposed framework, and outlines a concrete roadmap for closing those limitations.

4.1. Positioning Against Prior Work

Wavelet-based hybrid forecasting: Osmani et al. [23] reported a wavelet-Gaussian-Process SPEI forecaster with $R^2$ = 0.81 at the 1-month horizon for Iran. WaveDroughtNet attains $R^2=0.8294$ at the equivalent horizon on Tamil Nadu data, while additionally (i) eliminating future-information leakage through the causal transform, (ii) extending the maximum horizon from 1 month to 1 year, and (iii) providing post hoc origin attribution. The wavelet-LSTM comparison of Tuğrul et al. [22] reported $R^2$ ≈ 0.78 on a Norwegian dataset at the 1-month horizon; the TCN + wavelet combination used here exceeds that figure while using approximately 30% fewer parameters.

Deep multi-horizon drought modelling: Marusov et al. [20] used spatiotemporal LSTMs for long-term PDSI forecasting and reported skillful predictions out to 18 months; their architecture, however, predicts a single horizon per trained model. WaveDroughtNet’s single-pass multi-horizon design reduces both training and inference cost by a factor of four for the four horizons reported here. Shifted-window Transformers [26] have been used for multi-scale spatio-temporal drought prediction; we show in Table 7 that a vanilla Transformer baseline does not match WaveDroughtNet on Tamil Nadu data, and the cuboid-attention EarthFormer-Lite variant closes most but not all of the gap at 3.5 × parameter cost.

Regional Tamil Nadu studies: Janarth et al. [8] used SPEI to monitor multi-year drought across Tamil Nadu and identified the north-western and southern districts as the most vulnerable. Our spatial analysis (Table 11) is consistent: the lowest predictive $R^2$ is observed in Tirunelveli and Tenkasi (the south), and the Nilgiris (the north-west), where the orographic precipitation regime increases the local variability of SPEI. Lalmuanzuala et al. [27] used the conventional SPEI with no deep-learning forecaster; the proposed framework therefore advances the regional state of the art by providing a predictive forecasting capability that is mathematically aligned with the established SPEI standard.

Statistical-significance reporting: A recurring shortcoming of the wavelet-ML drought literature [10,13,23] is the absence of paired statistical-significance tests of forecast superiority. We report Diebold–Mariano and Friedman–Nemenyi tests (Table 9 and Table 10) so that the magnitude of WaveDroughtNet’s advantage at long horizons can be evaluated against test-set sampling variability rather than read from point estimates alone.

4.2. Limitations

We articulate four limitations that constrain operational deployment of WaveDroughtNet in its current form. Each is paired with the corresponding mitigation strategy in Section 4.3.

L1—Zero severe events in the test partition. The 2024 Tamil Nadu climate was relatively mild and contained zero $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}<-1.5$ events (Table 1), so the test-time $\mathrm{F}{1}_{\mathrm{s}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}}$ is necessarily zero (Table 6). The training partition also contains zero severe events, which we expose explicitly here rather than relying on the previous draft’s interpretation that the model ‘has been trained to detect all four categories’. A model that has not been observed performing on a class for which it has no training data cannot be claimed to be validated for extreme-event prediction. This is the most consequential limitation of the present study; mitigation requires synthetic extreme-event augmentation (e.g., by importing severe events from neighbouring states with similar climatology) and a longer operational test window that captures the next major drought year (likely 2026–2027 per IMD’s regional outlooks).

L2—Static inter-district modelling. The 16-dimensional learnable district embedding captures inter-district differences in mean climate state but does not represent dynamic inter-district interactions. Drought is a spatially propagating hazard driven by large-scale atmospheric forcing (the Indian Summer Monsoon and the North-East Monsoon for Tamil Nadu) and by regional hydrological connectivity (the Cauvery, Vaigai and Tamiraparani river basins span multiple administrative districts). Ignoring this connectivity limits the model’s physical realism and is the most likely source of the predictive performance gap between coastal districts (Chennai 0.8922) and Western Ghats-influenced districts (Nilgiris 0.7925, Coimbatore 0.8377). Mitigation: a Graph Neural Network (GNN) extension with nodes = districts and edges = (i) Queen-style geographic adjacency, (ii) river-basin co-membership, and (iii) shared climatic-zone membership, replacing the static embedding with a graph attention layer.

L3—No vegetation-index supervision. The current feature space relies entirely on meteorological variables from NASA POWER. Agricultural drought is defined by soil-moisture deficit and vegetation stress, which are most directly captured by satellite-derived indices such as NDVI, EVI and the Vegetation Condition Index (VCI) from MODIS and Sentinel-2/3. The current scope of WaveDroughtNet is therefore strictly meteorological drought (SPEI), and the manuscript’s earlier framing as broadly ‘climate-smart agriculture’ has been narrowed in the Introduction to avoid over-claiming. A planned MODIS/Sentinel-3 OLCI extension will add NDVI, EVI and VCI as a seventh modality and a vegetation-stress regression head.

L4—Reanalysis-only ground truth. NASA POWER is itself a reanalysis product (MERRA-2 + CERES) with uncertainty (Section 2.3, paragraph on uncertainty). Independent comparison against IMD ground-station data shows a 0.91 correlation and a −4.2% mean bias; the residual scale uncertainty inflates estimated moderate-to-severe event frequencies by an estimated 5–8%. Mitigation: co-training with IMD’s gridded 0.25° daily product (1980–present) and a multi-task auxiliary loss that penalises NASA-POWER–IMD disagreement is on our roadmap for the next manuscript.

4.3. Recommendations and Future Work

The limitations above translate to four concrete extensions of WaveDroughtNet that we are pursuing in subsequent work:

• R1—Synthetic extreme-event augmentation. Importing severe-event windows from climatologically similar districts in Andhra Pradesh, Karnataka and Kerala (matched by 30-year SPEI percentiles) and using time-warping data augmentation should deliver a training set with non-trivial severe-class support without leaking spatial test information. We expect $F{1}_{severe}$ in the range 0.4–0.6 on a synthetic test partition based on the analogous severe-event augmentation in [10].
• R2—Graph-augmented spatial modelling. Replacing the static district embedding with a two-layer Graph Attention Network (GAT) over a multi-relational district graph (geographic + hydrological + climatic edges) is expected to raise per-district $R^2$ in the Nilgiris and Tirunelveli by ≥ 0.05 and to enable principled inference of cross-district drought propagation. Implementation is straightforward because the existing TCN output already serves as a node representation.
• R3—Vegetation-index multi-modal extension. Adding NDVI, EVI and VCI from the MODIS MOD13Q1 (16-day, 250 m) and Sentinel-3 OLCI products as a seventh modality and a dedicated vegetation-stress regression head transitions the model from meteorological to combined meteorological–agricultural drought. The current architecture trivially accommodates a seventh modality because of the modality-encoder design.
• R4—Multi-source ground-truth co-training. A multi-task loss that penalises NASA-POWER–IMD precipitation disagreement, together with optional supervision from in situ Tamil Nadu State Land Use Research Board (TNSLURB) soil-moisture sensors, will reduce the reanalysis-only uncertainty discussed in L4. We are currently negotiating a research data-sharing agreement with IMD’s Regional Meteorological Centre, Chennai.
• R5—Operational deployment study. Beyond the technical extensions above, we plan a 12-month operational pilot in co-operation with the Tamil Nadu Department of Agriculture, measuring forecast utility against grower decision-making in two case-study districts (Coimbatore and Cuddalore). The pilot will deliver the kind of independent operational evaluation that closes the loop between forecasting accuracy and real-world value.

5. Conclusions

This study presents WaveDroughtNet, a multi-modal, wavelet-enhanced temporal convolutional network for multi-horizon meteorological drought forecasting across the 32 districts of Tamil Nadu, India. The framework integrates five components—strictly causal Daubechies-4 wavelet decomposition, modality-specific encoders with stochastic modality dropout, cross-modal multi-head attention, a four-layer dilated TCN backbone, and a post hoc DroughtOriginTracer—into a single 256,869-parameter model that produces, in a single forward pass, classification and regression outputs at four horizons (1 week, 1 month, 3 months, 1 year). The supervisory SPEI target is computed by the canonical Vicente-Serrano procedure—Hargreaves PET, water balance, three-parameter log-logistic fit via L-moments, Kolmogorov–Smirnov goodness-of-fit validation at $\alpha =0.05$ per district, inverse-normal-CDF standardisation.

On the held-out 2024 test set ($N=1728$), WaveDroughtNet attains weighted $F1=0.9221$ and $R^2=0.8512$ at the 1-week horizon and weighted $F1=0.8498$ and $R^2=0.6812$ at the 1-year horizon, with Diebold–Mariano and Friedman–Nemenyi tests establishing statistically significant superiority over six baselines (naive persistence, seasonal naive, XGBoost, LSTM, ConvLSTM, vanilla Transformer, EarthFormer-Lite) at the 3-month and 1-year horizons. The DroughtOriginTracer successfully back-projects 15 Coimbatore drought events to causal origins 29–41 weeks prior to onset, identifying Temperature, Solar/Cloud and Humidity as the dominant atmospheric-demand triggers for the Western Ghats transitional zone.

We have additionally been explicit about four operational limitations—zero severe events in the test partition ($F{1}_{severe}$ = 0.000), static inter-district modelling, absence of vegetation-index supervision and reanalysis-only ground truth—and have paired each with a concrete mitigation strategy in Section 4.3. Future work will integrate synthetic extreme-event augmentation, a graph attention layer over a multi-relational district graph, a MODIS/Sentinel vegetation-index modality, IMD ground-station co-training, and a 12-month operational pilot with the Tamil Nadu Department of Agriculture. The combination of parameter efficiency, post hoc interpretability and statistically validated multi-horizon skill, together with the corrected SPEI pipeline, positions WaveDroughtNet as a transparent and reproducible step toward operational climate-resilience decision support.