Mapping the Spatial Distribution of Noxious Weed Species with Time-Series Data in Degraded Grasslands in the Three-River Headwaters Region, China

Abstract

Noxious weeds (NWs) are increasingly recognized as a significant threat to the native alpine grassland ecosystems of the Qinghai–Tibetan Plateau (QTP). However, large-scale quantification of their continuous fractional cover remains challenging. This study proposes a pixel-level estimation framework utilizing time-series Sentinel-2 imagery. A Dynamic Mask Non-Stationary Transformer (DMNST) model was developed and trained using multi-temporal multispectral data to map the spatial distribution of NWs in the Three-River Headwaters Region. The model was calibrated and validated using field data collected from 170 plots (1530 quadrats). The results demonstrated that both the dynamic masking module and the non-stationary normalization significantly enhanced the prediction accuracy and robustness, particularly when applied jointly. The model performance varied across different combinations of spectral bands and temporal inputs, with the optimal configurations achieving a test R² of 0.770, MSE of 0.009, and RMSE of 0.096. These findings underscore the critical role of the input configuration and architectural enhancements in accurately modeling the fractional cover of NWs. This study confirms the applicability of Sentinel-2 time-series imagery for modeling the continuous fractional cover of NWs and provides a scalable tool for invasive species monitoring and ecological risk assessment in alpine ecosystems.

1. Introduction

Noxious weed species (NWs) have been persistently linked to grassland degradation driven by the interplay between anthropogenic activities and climatic variability, posing serious threats to ecosystems, species composition, and agricultural productivity [1,2,3]. These invasive species have the potential to modify habitats and interfere with ecological processes, resulting in pronounced ecological deterioration and considerable economic losses [4,5,6,7,8]. For example, NWs may exert allelopathic effects that inhibit the germination and early development of edible grasses and native plant species (NPSs), thereby obstructing the natural recovery of grassland ecosystems [9]. Their aggressive spread can further contribute to the decline of indigenous vegetation, the loss of biodiversity, and the disruption of ecosystem functionality, ultimately undermining ecological resilience and stability [9,10]. In agricultural contexts, NWs not only reduce land productivity but also escalate weed control expenditures, thereby intensifying the burden on land managers and jeopardizing the long-term sustainability of both pastures and natural ecosystems [11,12,13]. As such, the efficient monitoring and targeted management of NWs are essential for safeguarding the ecological integrity and sustainable development of grassland systems.

Accurate and timely spatial mapping is vital for the effective monitoring and management of NWs, as it facilitates the deployment of targeted control strategies. Nevertheless, due to the vast spatial extent of affected regions, the high labor and temporal costs, and the inaccessibility of certain remote landscapes, traditional field-based surveys are often impractical and inadequate for capturing the full spatial complexity of the NW distribution [14,15]. Recent advances in remote sensing technologies, coupled with the growing capacity of machine learning algorithms, have significantly enhanced the feasibility and accuracy of large-scale NW mapping, offering scalable and efficient alternatives to conventional survey methods [11,15,16,17,18].

In general, the remote sensing-based identification of NWs primarily exploits spectral, spatial, and temporal distinctions between NWs and native vegetation [2]. Spectral differentiation relies on the distinct spectral signatures exhibited by NWs, typically utilizing hyperspectral imagery to capture subtle reflectance differences [15,19,20]. Spatial differentiation analyzes the spatial distribution patterns of NWs in relation to the surrounding land cover and vegetation structure, often leveraging high-resolution imagery to enhance the detection accuracy [21,22,23]. Temporal differentiation, by contrast, capitalizes on phenological variations—such as seasonal or inter-annual growth dynamics—necessitating multi-temporal observations to acquire sufficient temporal depth [17,18,24]. Numerous studies have validated the effectiveness of remote sensing approaches in identifying various vegetation types, including trees, crops, and NWs [25,26,27,28,29,30]. However, hyperspectral and high-resolution multispectral imagery acquired from satellite or airborne platforms is typically limited in terms of the spatial coverage, which constrains the applicability in regional- to continental-scale studies [10]. In contrast, multi-temporal data from freely available satellite sources offer a more scalable and cost-effective solution for broad-scale vegetation mapping. For instance, time-series imagery and phenological metrics have been successfully applied to tasks such as sugarcane yield estimation and mangrove ecosystem classification [31,32,33].

Despite the notable success of phenological parameters in crop identification, their application in the mapping of NWs remains limited. At present, phenological features derived from multi-temporal remote sensing imagery are predominantly utilized in classification tasks, wherein each pixel is assigned a discrete categorical label [34,35,36,37,38,39,40]. However, regression-based approaches that aim to model pixel-level variables as continuous rather than categorical variables have received comparatively little attention [33,41,42]. This limitation is particularly critical given that many environmental variables—especially vegetation cover—exhibit inherently continuous spatial distributions [43]. For example, NWs and edible grasses frequently coexist within a single pixel, forming mixed vegetation signals. Since vegetation dynamics are more accurately characterized by continuous measures, there is a pressing need to extract more informative features from multi-temporal imagery to enable the continuous representation of vegetation variables—such as NW coverage—rather than relying exclusively on discrete classification frameworks.

In recent years, the rapid advancement of deep learning techniques has substantially expanded the application of time-series data in remote sensing, leading to significant progress across a wide range of research domains. Deep learning models have been utilized to extract salient features and recognize complex patterns from multi-temporal remote sensing imagery, thereby not only enhancing the predictive accuracy of vegetation-related variables but also capturing their spatiotemporal dynamics with greater fidelity [41,44,45,46,47,48,49]. These methodological developments present promising avenues to address the limitations of traditional phenology-based classification approaches, facilitating the continuous estimation of vegetation metrics such as the NW coverage. While hyperspectral and high-resolution imagery remains a prevalent tool for NWs classification, studies that incorporate time-series data to quantify their continuous fractional cover are still relatively scarce [14,16,50,51,52,53].

To address this research gap, the present study proposes a method for estimating the continuous fractional cover of NWs using multispectral time-series satellite data. In contrast to conventional approaches, the proposed method relies exclusively on publicly accessible multi-temporal multispectral imagery to generate continuous coverage maps of NWs. In addition, we developed a novel DMNST model. This model was trained on time-series Sentinel-2 imagery from 2019 to investigate the spatial distribution patterns of NWs in the TRHR on the QTP and to assess their responses to environmental drivers. To optimize the model performance, we systematically evaluated various combinations of spectral bands—including visible (VIS), red-edge (RE), near-infrared (NIR), and shortwave infrared (SWIR)—as well as alternative time-series configurations based on the seasonal completeness and temporal frequency. This study introduces a comprehensive framework for modeling the continuous fractional cover of NWs, offering new insights into their spatiotemporal dynamics and the underlying ecological mechanisms governing their expansion.

2. Materials and Methods

2.1. Study Area

The TRHR, situated in the hinterland of the QTP in western China (31°39′–36°12′ N, 89°45′–102°23′ E), encompasses the headwaters of three major Asian rivers: the Yangtze River, the Yellow River, and the Lancang (Mekong) River [54,55,56]. Commonly referred to as “China’s Water Tower,” the TRHR is characterized by a continental plateau climate, with an annual mean temperature ranging from −6 °C to −4 °C and total annual precipitation of between 260 mm and 780 mm [57,58,59,60,61,62]. The TRHR is dominated by glaciers, ice margins, mountains, highland plains and hills, with an altitude of 2600–6584 m [63]. Within this area, meadows account for 55.76%, steppes for 24.05%, alpine vegetation for 9.4%, forests for 1.08%, shrubs for 5.41%, deserts for 0.54%, and other types for 3.75% [64].

The study area is located within the core zone of the TRHR, with an average elevation exceeding 4000 m (Figure 1). The region exhibits marked climatic seasonality, characterized by long, cold winters, short, cool summers, and extended cold periods spanning nearly ten months (January–June and September–December), along with substantial diurnal temperature fluctuations [56,65]. The annual precipitation is primarily concentrated during the summer growing season (June–September), accounting for approximately 70–80% of the total annual rainfall [3,43,65]. Within the TRHR, alpine meadow constitutes the dominant grassland type, representing the most widespread and ecologically critical vegetation cover and serving as a key component of regional ecosystem services.

2.2. Field Data Survey

The grassland vegetation in the study area can be broadly classified into two functional groups: native plant species (NPSs) and noxious weed species (NWs). The NPSs are predominantly represented by two genera—Kobresia Willd. and Stipa L.—encompassing six dominant species: Kobresia tibetica Maxim., Kobresia pygmaea (C. B. Clarke) C. B. Clarke, Kobresia humilis (C. A. Mey. ex Trautv.) Serg., Kobresia capillifolia (Decne.) C. B. Clarke, Stipa purpurea Griseb. and Stipa grandis P. A. Smirn. These native species constitute high-quality forage resources for the region’s primary livestock, especially yaks and Tibetan sheep. The NWs group includes seven prevalent invasive species: Ajania tenuifolia (Jacquem. ex DC.) Tzvelev, Oxytropis ochrocephala Bunge, Euphorbia fischeriana Steud., Aconitum pendulum Busch, Aster altaicus Willd., Leontopodium leontopodioides (Willd.) Beauverd and Potentilla chinensis Ser. [3,43]. Over the past few decades, the fractional cover of NPSs has steadily declined due to overgrazing and environmental change, while the invasion of NWs has accelerated, becoming a key ecological indicator of grassland degradation. Consequently, accurately mapping the NW coverage is essential for evaluating the grassland degradation and informing ecosystem management strategies in the TRHR [54,55,57,65].

The primary objective of the field survey was to quantify the key ecological indicators within the study area, including the fractional cover of NWs, NPSs, and non-vegetated surfaces (all expressed as percentages), and to identify the dominant species present within each plot. Field sampling was conducted in mid-August 2019, coinciding with the peak growing season of alpine grasslands in the TRHR. At each sampling location, a 30 m × 30 m plot was established, with a minimum spacing of 100 m between plots to minimize the spatial autocorrelation. Within each plot, nine 1 m × 1 m quadrats were symmetrically arranged along four transects radiating from the plot center to ensure spatial representativeness (Figure 2). The key ecological variables were measured and recorded within each quadrat. The geographic coordinates of each plot center were collected using a Trimble Geo 7X GPS device with sub-meter accuracy (~0.5 m). To minimize the anthropogenic disturbance and improve the data quality, all the sampling sites were located at least 100 m away from roads [3,43,65]. In total, 170 large plots were surveyed across the study area, yielding 1530 quadrat-level ecological observations. The final selection of sampling sites was informed by a combination of a literature review [3,43], local herders’ knowledge, and practical considerations regarding the research team’s operational capacity under high-altitude conditions. The median elevation of the sampling points was approximately 4200 m, with the majority of plots distributed between 4100 m and 4300 m. The spatial distribution of all the sampling sites is shown in Figure 1c, and the corresponding elevation distribution is illustrated in Figure 3. This field sampling framework ensured comprehensive coverage of the core elevational range of alpine grasslands in the Three-River Headwaters Region, while also incorporating representative samples from higher-altitude zones to support environmental gradient analysis.

2.3. Sentinel-2 Imagery Acquisition and Processing

To support long-term time-series analysis, Sentinel-2 imagery covering the entire study area for the year 2019 was acquired from the Google Earth Engine (GEE) platform (

Table 1. Specifications of Sentinel-2 spectral bands used for time-series analysis in 2019.

Dataset	Band Classification	Band IDs	Spatial Resolution	Resampled to	Time Range
Sentinel-2	Visible Bands	B2, B3, B4	10 m	30 m	2019
	Red-edge Bands	B5, B6, B7	20 m
	Near-infrared Bands	B8, B8A	10 m, 20 m
	Shortwave Infrared Bands	B11, B12	20 m

). These multispectral images, with spatial resolutions ranging from 10 m to 20 m, include a variety of spectral bands: visible bands (Bands 2, 3, 4), red-edge bands (Bands 5, 6, 7), near-infrared bands (Bands 8, 8A), and shortwave infrared bands (Bands 11, 12), along with quality assessment layers such as the cloud probability (MSK_CLDPRB), snow probability (MSK_SNWPRB), and scene classification (SCL) for identifying cloud shadows.

All the Sentinel-2 imagery used in this study had undergone radiometric calibration and atmospheric correction. To reduce the influence of environmental contaminants such as clouds, snow, and fog, a masking strategy was implemented using threshold-based filters applied to the cloud and snow probability bands. Pixels identified as low-quality observations due to cloud cover, snow, or shadow were excluded from subsequent analyses. To enhance the temporal consistency and data completeness, a temporal interpolation technique was applied to fill in the masked pixels, resulting in a high-quality, gap-filled dataset suitable for subsequent modeling and analysis.

2.4. Vegetation Index

In crop classification tasks using multi-temporal remote sensing data, vegetation indices often convey more informative and discriminative features than individual spectral bands and have consistently demonstrated superior performance [66,67,68,69,70]. To enhance the feature representation in this study, a suite of commonly used vegetation indices was derived, in addition to the original spectral bands. Specifically, 23 representative vegetation indices were extracted from the Sentinel-2 imagery, covering several functional categories: traditional near-infrared vegetation indices (e.g., NDVI, DVI, WDVI, RVI), chlorophyll-related indices (e.g., IRECI, PSSRa, MCARI), red-edge-based indices (e.g., S2REP, IRECI, RECI), soil-adjusted vegetation indices (e.g., SAVI, OSAVI, MSAVI), and atmosphere-corrected vegetation indices (e.g., EVI, ARVI). The corresponding formulas for these indices are summarized in

Table 2. The 23 common vegetation indices derived from the Sentinel-2 data.

Vegetation Indices Name	Formula	Bands	Reference
Enhanced Vegetation Index (EVI)	${\displaystyle \frac{2.5\times \left(B8-B4\right)}{\left(B8+6\times B4-7.5\times B2+1\right)}}$	B2, B4, B6	[71]
Ratio Vegetation Index (RVI)	$B8∕B4$	B4, B8	[72]
Modified Simple Ratio (MSR)	${\displaystyle \frac{\left(B8-B4\right)-1}{\sqrt{\left(B8/B4\right)+1}}}$	B4, B8	[73]
Transformed Vegetation Index (TVI)	$60\times \left(B8-B3\right)-100\times (B4-B3)$	B3, B4, B8	[74]
Difference Vegetation Index (DVI)	$B8-B4$	B4, B8	[75]
Weighted Difference Vegetation Index (WDVI)	$B8-0.5\times B4$	B4, B8	[76]
Normalized Difference Vegetation Index (NDVI)	$(B8-B4)∕(B8+B4)$	B4, B8	[77]
Normalized Difference Index 45 (NDI45)	$(B5-B4)∕(B5+B4)$	B4, B5	[78]
Transformed Normalized Difference Vegetation Index (TNDVI)	$\sqrt{\left(B8-B4\right)/\left(B8+B4\right)+0.5}$	B4, B8	[79]
Normalized Difference Red-Edge Index (NDRE)	$(B8-B5)/(B8+B5)$	B5, B8	[80]
Green Normalized Difference Vegetation Index (GNDVI)	$(B7-B3)/(B7+B3)$	B3, B7	[78]
Pigment Specific Simple Ratio (PSSRa)	$B7/B4$	B4, B7	[81]
Chlorophyll Index (CI)	$B4/B5-1$	B4, B5	[82]
Modified Chlorophyll Absorption Ratio Index (MCARI)	$\left(B5-B4\right)-0.2\times (B5-B3)\times (B5/B4)$	B3, B4, B5	[81]
Inverted Red-Edge Chlorophyll index (IRECI)	$(B7-B4)/(B5/B6)$	B4, B5, B6, B7	[83]
Red-Edge Chlorophyll Index (RECI)	${\displaystyle \frac{B8}{B4}}-1$	B4, B8	[84]
Soil Adjusted Vegetation Index (SAVI)	${\displaystyle \frac{1.5\times (B8-B4)}{(B8+B4+0.5)}}$	B4, B8	[85]
Optimized Soil-Adjusted Vegetation Index (OSAVI)	${\displaystyle \frac{(1+0.16)\times (B8-B4)}{(B8+B4+0.16)}}$	B4, B8	[86]
Modified Soil-Adjusted Vegetation Index (MSAVI)	$(2-NDVI\times WDVI)\times (B8-B4)∕8\times (B8+B4+1-NDVI\times WDVI)$	B4, B8	[87]
Perpendicular Vegetation Index (PVI)	$B8∕B4$	B4, B8	[88]
Sentinel-2 Red-Edge Position (S2REP)	$705+35\times ({\displaystyle \frac{B4+B7}{2}}-B5)\times (B6-B5)$	B4, B5, B6, B7	[89]
Infrared Position Vegetation Index (IPVI)	$B8∕(B8+B4)$	B4, B8	[90]
Atmospherically Resistant Vegetation Index (ARVI)	$B8-(2\times B4-B2)∕B8+(2\times B4-B2)$	B2, B4, B8	[91]

.

2.5. Proposed Dynamic Masked Non-Stationary Transformer Regression Method

The continuous fractional cover of NWs is a critical indicator for assessing grassland ecosystem functioning, as its spatial distribution reflects the competitive dynamics among vegetation communities and the extent of ecological degradation. Accurate quantification of the NW coverage is therefore essential for evaluating the ecological stability of grassland systems [43]. However, estimating the continuous distribution of NWs at large spatial scales remains a considerable challenge. This difficulty arises primarily from two factors: (1) the heterogeneous and patchy coexistence of NWs and NPSs within individual pixels, and (2) the limited spectral resolution of single-date multispectral imagery, which hampers the ability of conventional classification approaches to detect subtle within-pixel variations in the NW abundance.

These limitations collectively constrain the accuracy of large-scale NW coverage estimation using traditional remote sensing methods. To address these challenges, we propose a novel self-attention-based regression framework—Dynamic Masked Non-Stationary Transformer (DMNST)—which exploits the temporal richness of Sentinel-2 time-series imagery to model the fractional cover of NWs with enhanced spatial continuity and sensitivity to subtle vegetation dynamics.

2.5.1. Model Definition

The self-attention mechanism constitutes the core component of the Transformer architecture [92]. By modeling the global temporal dependencies, it dynamically captures the long-range spatiotemporal correlations within input sequences and adaptively assigns attention weights to enhance the estimation accuracy. For the task of continuous fractional cover regression, the final predictions are obtained through a linear projection layer.

In this study, a Transformer model based on an encoder-only architecture was designed to align with the characteristics of the input dataset. The model comprises several key components, including a feature normalization module, positional encoding layer, dynamic masking module, multi-head self-attention layer, layer normalization, feed-forward neural network, regression output layer, and a de-normalization module to restore the predicted values to their original scale.

2.5.2. Network Architecture

An encoder-based architecture for the Self-Attention Transformer Network was adopted, as illustrated in Figure 4. Given the spectral and temporal properties of the time-series remote sensing data, the word-embedding step—commonly used in natural language processing (NLP)—was omitted. In NLP tasks, the input sequences typically have variable lengths; thus, padding and masking modules are employed to ensure a uniform input size and to ignore artificial padding during attention computation. In contrast, the time-series data for each pixel in this study are of a fixed length, eliminating the need for padding and static masks.

However, remote sensing observations are often affected by atmospheric disturbances such as clouds and fog, which can cause spectral distortion or missing data at specific time steps. These low-quality observations are typically filled with predefined values (e.g., −9999), reflecting the unreliability of spectral information under such conditions. To mitigate this issue, a dynamic masking module was introduced to automatically identify and exclude corrupted timestamps from the attention mechanism, ensuring that only high-quality inputs contribute to the model learning.

In addition, while a positional encoding module was employed to enable the model to learn temporal dependencies, the temporal behavior of vegetation in remote sensing imagery is often highly non-stationary due to variations in the climate and phenology. Traditional Transformer models often struggle to capture such non-stationary patterns effectively, thereby limiting the predictive performance. To address this challenge, a Normalization module was incorporated to enhance the stability and predictability of non-stationary time series, while a De-normalization module was appended to restore the predicted values to their original scale and alleviate potential over-stabilization effects.

2.5.3. Model Variants for Ablation Analysis

To examine the respective contributions of the dynamic masking and non-stationary temporal modeling components, three simplified variants of the proposed DMNST model—which integrates both modules—were developed for the ablation analysis. These variants maintain a consistent Transformer-based encoder architecture and are trained under identical experimental settings, enabling a fair comparison of the module-level contributions.

Transformer (Baseline): This configuration excludes both the dynamic masking and non-stationary enhancement mechanisms. This baseline reflects a conventional Transformer model adapted to the remote sensing regression task without specialized handling of the data quality or temporal dynamics.

Dynamic Masked Transformer: In this variant, the dynamic masking mechanism is retained to filter out corrupted or low-confidence observations from the attention process, ensuring that only valid temporal inputs influence the model.

Non-Stationary Transformer: This configuration incorporates mechanisms to enhance the model’s robustness against temporal heterogeneity in vegetation dynamics, such as phenological shifts or abrupt changes. By refining how the temporal patterns are represented and learned, this variant aims to stabilize training on seasonally variable signals. Meanwhile, the dynamic masking component is omitted, and potentially unreliable time steps remain in the sequence.

Together, these ablated models serve to disentangle the roles of each proposed enhancement within the full DMNST architecture. Their comparative performance, reported in Section 3.4, provides insight into the individual and synergistic effects of addressing data quality and temporal non-stationarity in satellite time-series regression.

2.5.4. Loss Function and Experimental Setting

Given the regression nature of this task, the mean squared error (MSE) was employed as the loss function to evaluate the model’s performance. The network was optimized using the Adam optimizer, with L2 regularization (weight decay set to 1 × 10⁻⁴) applied to reduce the risk of overfitting. The initial learning rate was set to 0.0001, with a batch size of 10 and a total of 1000 training epochs.

The input to the model consists of multi-temporal Sentinel-2 imagery, with each sample comprising a time series of selected spectral bands across multiple timestamps. The number of spectral bands varies depending on the specific band combination strategy (ranging from 2 to 33 bands; see

Table 3. Performance metrics (R², MSE, and RMSE) of the optimized DMNST model under selected input feature combinations on the test set. The results highlight the varying predictive performance of the different spectral and vegetation index configurations.

Feature Combinations	Test R2	Test MSE	Test RMSE
NIR	0.149	0.034	0.184
VIS	0.483	0.021	0.143
SWIR + 2BVIs	0.555	0.018	0.133
2BVIs	0.567	0.017	0.131
RE	0.584	0.017	0.129
23CVIs + VIS	0.588	0.016	0.128
RE + 2BVIs	0.598	0.016	0.126
23CVIs + RE	0.607	0.016	0.125
NIR + 2BVIs + VIS	0.613	0.015	0.124
23CVIs + NIR + VIS	0.615	0.015	0.124
23CVIs + NIR + RE + VIS	0.618	0.015	0.123
SWIR + VIS	0.625	0.015	0.122
23CVIs + NIR + RE	0.626	0.015	0.122
23CVIs + NIR	0.637	0.014	0.12
2BVIs + VIS	0.643	0.014	0.119
23CVIs	0.645	0.014	0.119
RE + 2BVIs + VIS	0.649	0.014	0.118
SWIR	0.650	0.014	0.118
NIR + 2BVIs	0.651	0.014	0.118
23CVIs + SWIR	0.658	0.014	0.117
NIR + SWIR	0.660	0.014	0.116
NIR + RE	0.662	0.013	0.116
NIR + RE + 2BVIs + VIS	0.666	0.013	0.115
RE + VIS	0.669	0.013	0.115
NIR + RE + 2BVIs	0.670	0.013	0.114
23CVIs + NIR + RE + SWIR	0.671	0.013	0.114
SWIR + 2BVIs + VIS	0.674	0.013	0.114
23CVIs + NIR + SWIR	0.675	0.013	0.114
NIR + SWIR + 2BVIs	0.676	0.013	0.113
23CVIs + RE + VIS	0.676	0.013	0.113
RE + SWIR + VIS	0.677	0.013	0.113
23CVIs + NIR + RE + SWIR + VIS	0.665	0.013	0.115
23CVIs + RE + SWIR + VIS	0.692	0.012	0.111
23CVIs + RE + SWIR	0.692	0.012	0.111
RE + SWIR + 2BVIs + VIS	0.694	0.012	0.11
23CVIs + SWIR + VIS	0.695	0.012	0.11
NIR + RE + SWIR + 2BVIs	0.695	0.012	0.11
NIR + RE + VIS	0.695	0.012	0.11
RE + SWIR	0.695	0.012	0.11
23CVIs + NIR + SWIR + VIS	0.698	0.012	0.109
NIR + SWIR + 2BVIs + VIS	0.702	0.012	0.109
NIR + RE + SWIR + 2BVIs + VIS	0.705	0.012	0.108
RE + SWIR + 2BVIs	0.711	0.011	0.107
NIR + VIS	0.713	0.011	0.107
NIR + SWIR + VIS	0.719	0.011	0.106
NIR + RE + SWIR	0.730	0.011	0.104
NIR + RE + SWIR + VIS	0.770	0.009	0.096

), while the temporal length of the sequence is determined by the selected time-combination scheme (ranging from 8 to 72 timestamps; see

Table 4. Definitions of temporal sampling interval strategies used for Sentinel-2 time-series data.

Interval Code	Description
interval_1	Retain all time steps (no temporal downsampling)
interval_2	Retain 1 out of every 2 time steps
interval_3	Retain 1 out of every 3 time steps
interval_4	Retain 1 out of every 4 time steps

). The Transformer architecture consists of six encoder layers, each incorporating a multi-head self-attention mechanism with eight attention heads. The input features are embedded into a 512-dimensional space, and each encoder layer includes a feed-forward network with a hidden layer size of 2048. The final output layer generates a single continuous value representing the predicted fractional cover of NWs.

All the experiments were conducted on a Windows 10 platform equipped with an AMD Ryzen 5 3600 processor, 64 GB of RAM, and an NVIDIA GeForce RTX 2070 GPU to accelerate the training. The model was implemented in Python 3.10 using the PyTorch 2.0.1 deep learning framework.

2.6. Accuracy Assessment

To ensure a comprehensive evaluation, the DMNST model was independently executed three times. Its performance in estimating the continuous fractional cover of NWs was assessed using three widely adopted metrics: the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE), as defined in Equations (1)–(3) [43]. Specifically, the R² reflects the degree of correlation between the predicted and reference values, while the MAE and RMSE quantify the magnitude of the estimation errors, with the RMSE being more sensitive to larger deviations. The model-derived continuous estimates of the NW coverage were subsequently validated against field-measured reference data to assess the accuracy and reliability.

$$R^2=1-{\sum }_{i=1}^n{\left(O_i-P_i\right)}^2/{\sum }_{i=1}^n{\left(O_i-\overline{P}\right)}^2,$$

(1)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^n\left|O_i-P_i\right|,$$

(2)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^n{\left(O_i-P_i\right)}^2},$$

(3)

where O_i denotes the observed percentage cover of NWs, P_i denotes the predicted percentage cover of NWs, $\overline{P}$ represents the mean of predicted values, and N is the total number of samples.

3. Results

3.1. Effect of Input Feature Combinations on Model Performance

To evaluate the influence of different input feature combinations on the model performance, a systematic assessment was conducted based on the optimized DMNST model. The input features were derived from ten spectral bands (B2–B12) of Sentinel-2 imagery and grouped into four primary spectral categories: visible (VIS; B2–B4), red-edge (RE; B5–B7), near-infrared (NIR; B8, B8A), and shortwave infrared (SWIR; B11, B12).

In addition, two categories of vegetation indices were incorporated into the feature space: (1) two basic vegetation indices (2BVIs), including the NDVI and EVI; and (2) a comprehensive set of 23 commonly used vegetation indices (23CVIs), such as the TNDVI, GNDVI, and IRECI. In total, 48 distinct feature combinations were constructed for the model evaluation.

The predictive performance associated with each feature combination is quantitatively summarized in Table 3. Moreover, the coefficient of determination (R²) on the test set was employed to visualize and compare the model performance across all the combinations (Figure 5), providing an intuitive understanding of the relative predictive strength of each input feature set.

3.1.1. Overall Performance Analysis of Feature Combinations

The feature combination that integrated all four spectral domains—visible (VIS), red-edge (RE), near-infrared (NIR), and shortwave infrared (SWIR)—achieved the best overall performance, yielding the highest R² value of 0.770 on the test dataset (Figure 5). This result highlights the effectiveness of spectral fusion in capturing the comprehensive spectral responses of NWs, including the pigment absorption, canopy structural characteristics, and moisture content. The integration of diverse spectral information substantially enhanced the model’s estimation accuracy, underscoring the importance of multi-domain spectral inputs in improving the predictive performance for fractional cover regression tasks.

In contrast, the feature combinations derived from a single spectral domain exhibited substantially lower predictive performance. The models using only the VIS, RE, NIR, or SWIR bands produced test R² values below 0.6, indicating that isolated spectral inputs are insufficient to fully capture the complex physiological and structural characteristics of NWs. In comparison, multi-band fusion provides a more holistic spectral representation, leading to improved model accuracy.

A limited subset of vegetation indices also yielded moderate performance. For instance, the feature combination of NIR + VIS + 2BVIs achieved an R² of 0.613, which was comparable to the result obtained using the full set of 23CVIs (R² = 0.615). This finding suggests that incorporating an excessive number of indices may introduce redundancy, increase the model complexity, and elevate the risk of overfitting.

Further analysis indicated that the vegetation indices primarily perform a complementary role. When used in isolation, the 2BVIs and 23CVIs achieved R² values of 0.567 and 0.645, respectively. While these indices enhanced the model’s sensitivity to phenological variation, they were consistently outperformed by combinations that incorporated raw spectral bands. This highlights that the vegetation indices alone lack the spectral diversity required for high-precision regression tasks.

Notably, the SWIR bands contributed meaningfully to the performance gains. Combinations such as SWIR + VIS and SWIR + NIR consistently achieved R² values above 0.62, underscoring the importance of the SWIR in capturing the vegetation water content, biophysical traits, and stress-related signals.

In summary, integrating the VIS, RE, NIR, and SWIR spectral information—supplemented with key vegetation indices—substantially improves the DMNST model’s performance in estimating the fractional cover of NWs. These findings underscore the value of spectral fusion strategies for spatiotemporal monitoring of NWs’ dynamics and their ecological implications.

3.1.2. Comparative Analysis of Representative Feature Combinations

To further investigate the influence of different input feature combinations on the model performance, four representative configurations were selected, each corresponding to a distinct feature engineering strategy: multispectral fusion, index-constrained selection, high-dimensional stacking, and partial-spectrum fusion. The predictive effectiveness of these configurations was assessed using scatter plots comparing the estimated and observed fractional coverage of NWs (Figure 6), providing a visual basis for the performance comparison.

The configuration that combined the VIS, RE, NIR, and SWIR bands demonstrated the highest accuracy, achieving an R² of 0.770 and an RMSE of 0.096 on the test set. As illustrated in Figure 6a, the predicted values were well aligned with the 1:1 reference line, particularly within the low-to-moderate coverage range (0.2–0.5), indicating that integrating full-spectrum information effectively captured the spectral responses of NWs across multiple biophysical dimensions.

The second configuration combined the RE and SWIR bands with two representative biophysical vegetation indices (2BVIs) while excluding the NIR domain. As shown in Figure 6b, this setup yielded slightly reduced predictive performance (R² = 0.711, RMSE = 0.107) compared to the full-spectrum fusion strategy. The absence of NIR likely constrained the model’s ability to characterize key vegetation properties such as the canopy density and moisture content—attributes that are critical for accurately estimating the fractional cover of NWs. As a result, the model tended to slightly underestimate the NW coverage, especially in regions where the actual fractional coverage of NWs was relatively high.

The third configuration incorporated all ten spectral bands together with 23 commonly used vegetation indices (23CVIs), forming a high-dimensional input structure. Despite offering the most comprehensive information base, this configuration exhibited reduced performance (R² = 0.665, RMSE = 0.115). As illustrated in Figure 6c, the scatter plot showed substantial dispersion, particularly within the mid-range coverage interval (0.3–0.6). These results suggest that excessive feature stacking may introduce redundancy and increase the risk of overfitting, ultimately impairing the model’s generalization capability.

The fourth configuration utilized the RE, NIR, and SWIR bands, excluding the VIS bands and all the vegetation indices. As shown in Figure 6d, this setup achieved an R² of 0.730 and an RMSE of 0.104. Although the performance was reasonably strong, notable deviations were observed at both the low and high ends of the coverage distribution. These discrepancies suggest that the absence of visible-band information limited the model’s capacity to capture reflectance features associated with the leaf pigmentation and surface color, which are essential for distinguishing subtle variations in the NW coverage.

In summary, the model performance is strongly influenced by the structure and dimensionality of the input features. Full-spectrum fusion (VIS + RE + NIR + SWIR) emerged as the most effective strategy, enabling comprehensive spectral representation for high-accuracy estimation. The selective inclusion of vegetation indices can further enhance the performance when appropriately constrained. In contrast, excessive feature stacking or the exclusion of critical spectral domains may introduce redundancy and reduce the model accuracy. These findings highlight the importance of balancing spectral diversity and feature compactness when designing remote sensing models for accurate and scalable monitoring of NWs’ dynamics.

3.1.3. Comprehensive Evaluation of Feature Fusion Strategies

The experimental results presented above confirm that the strategy used to construct the input features plays a critical role in accurately modeling the fractional coverage of NWs. In particular, feature combinations that integrate multiple spectral domains—especially those incorporating the VIS, RE, NIR, and SWIR bands—consistently yielded the highest predictive performance across all the experiments. These findings highlight the superior effectiveness of multispectral fusion in capturing the vegetation heterogeneity and enhancing the model generalization.

Moreover, the inclusion of a small set of essential vegetation indices—particularly the two basic vegetation indices (2BVIs; NDVI and EVI)—further enhanced the model’s sensitivity to phenological dynamics. When combined with the spectral bands, these indices served a complementary role in improving the prediction accuracy. In contrast, the indiscriminate addition of a large number of high-dimensional indices, such as the 23 commonly used vegetation indices (23CVIs), did not lead to substantial performance gains. Instead, it frequently introduced feature redundancy and increased the model complexity, thereby elevating the risk of overfitting.

Additionally, the results indicate that models constructed with excessively high feature dimensionality—such as those integrating all 10 spectral bands together with the 23CVIs—were more susceptible to noise interference, leading to increased prediction errors and reduced model stability. Therefore, in the feature construction process, it is recommended to prioritize the inclusion of representative spectral bands and key vegetation indices. This should be complemented by appropriate feature selection or dimensionality reduction techniques to effectively control the model complexity and enhance both the robustness and generalizability.

Finally, the feature combinations that relied solely on a single spectral domain—such as NIR or SWIR—consistently exhibited inferior predictive performance compared to the multisource fusion strategies. This finding reinforces the notion that limited spectral information is inadequate for capturing the complex spectral signatures of NWs, thereby constraining the model’s ability to achieve high-precision estimation.

In summary, this section underscores the critical importance of multispectral feature integration and the selective inclusion of vegetation indices in enhancing the model performance. These findings offer both theoretical insight and practical guidance for the design of input features in deep learning-based remote sensing models for vegetation mapping.

3.2. Impact of Temporal Combination Strategies on Model Performance

To systematically evaluate the influence of temporal information on the regression performance, two temporal configuration dimensions were designed: sampling interval and observation month filtering. In this experiment, the input feature set was fixed to the optimal combination identified in Section 3.1.2, specifically the VIS, RE, NIR, and SWIR bands. This choice ensures a consistent feature foundation across the different temporal strategies.

Four temporal interval strategies (interval_1 to interval_4) were constructed by subsampling from the 72 Sentinel-2 observations acquired in 2019, as summarized in Table 4. These simulate different temporal resolutions.

In parallel, five month-based filtering strategies were designed to exclude low-quality or off-season observations, focusing on the phenological relevance of the vegetation dynamics. These retention strategies are defined in

Table 5. Definitions of temporal observation window strategies based on monthly filtering (retention codes).

Interval Code	Description
retain_Jan_Dec	Retain all observations from January to December (full year)
retain_Feb_Nov	Retain observations from February to November; exclude January and December
retain_Mar_Oct	Retain observations from March to October; exclude early and late months
retain_Apr_Sep	Retain observations from April to September (core growth season)
retain_May_Sep	Retain observations from May to September (peak growing season)

.

By combining these dimensions, 20 composite configurations (e.g., interval_3 + retain_May_Sep) were constructed to form a comprehensive temporal input strategy set. The regression performance of each configuration is summarized in

Table 6. Regression performance of different temporal input strategies for estimating NW fractional coverage.

Temporal Input Strategy	Test R2	Test MSE	Test RMSE
interval_2 + retain_May_Sep	0.665	0.013	0.115
interval_1 + retain_Apr_Sep	0.696	0.012	0.110
interval_1 + retain_May_Sep	0.701	0.012	0.109
interval_2 + retain_Apr_Sep	0.705	0.012	0.108
interval_3 + retain_Apr_Sep	0.710	0.011	0.107
interval_4 + retain_Mar_Oct	0.713	0.011	0.107
interval_3 + retain_May_Sep	0.719	0.011	0.106
interval_1 + retain_Mar_Oct	0.721	0.011	0.105
interval_4 + retain_Feb_Nov	0.722	0.011	0.105
interval_4 + retain_Apr_Sep	0.725	0.011	0.104
interval_3 + retain_Mar_Oct	0.728	0.011	0.104
interval_3 + retain_Jan_Dec	0.728	0.011	0.104
interval_3 + retain_Feb_Nov	0.729	0.011	0.104
interval_1 + retain_Feb_Nov	0.731	0.011	0.103
interval_4 + retain_Jan_Dec	0.736	0.010	0.102
interval_2 + retain_Mar_Oct	0.736	0.010	0.102
interval_2 + retain_Jan_Dec	0.745	0.010	0.101
interval_4 + retain_May_Sep	0.746	0.010	0.100
interval_2 + retain_Feb_Nov	0.759	0.010	0.098
interval_1 + retain_Jan_Dec	0.770	0.009	0.096

and visualized in Figure 7.

For the sampling interval dimension, four temporal interval strategies were defined based on the 72 Sentinel-2 observations spanning the full calendar year of 2019 (Table 4). Specifically, interval_1 retains all the available time steps (i.e., no downsampling), while interval_2, interval_3, and interval_4 retain one observation every two, three, and four time steps, respectively. These configurations were designed to simulate the varying temporal resolutions and evaluate their impact on the model’s ability to learn the time-dependent vegetation dynamics. The definitions of the interval strategies are summarized as follows.

For the month filtering dimension, five retention strategies were constructed to mitigate the influence of low-quality observations from the non-growing seasons—particularly winter—when the cloud contamination, snow cover, and low solar angles frequently degrade the data quality (Table 5). Beginning with the full annual span (January to December), successive subsets were defined by progressively excluding marginal or low-activity months. For example, retain_May_Sep retains only the observations from May to September, thereby concentrating on the peak growing season while minimizing the temporal noise. The definitions of the month-based retain strategies are summarized as follows.

For example, the configuration interval_4 + retain_Mar_Oct refers to a setting in which one observation is retained every four time steps, and only those falling within the March to October period are utilized. This strategy balances temporal representativeness and data quality by capturing the major phenological phases of vegetation growth while excluding low-value observations typically associated with non-growing seasons.

3.2.1. Overall Performance Analysis of Temporal Combinations

To quantitatively evaluate the impact of different temporal combination strategies on the model performance, this study assessed the regression metrics—including the coefficient of determination (R²), mean squared error (MSE), and root mean square error (RMSE)—across 20 distinct temporal configurations on the test dataset. As presented in Table 6 and Figure 7, the predictive performance varied substantially among the different combinations. The highest R² reached 0.770, while the lowest dropped to 0.665, resulting in a maximum difference exceeding 0.10. These results underscore the critical importance of the temporal feature design in modeling the fractional coverage of NWs.

From an overall perspective, the configuration interval_1 + retain_Jan_Dec, which retained all the observations throughout the year and employed the highest sampling density, achieved the best performance, with a test R² of 0.770 and the lowest RMSE of 0.096. These results indicate that complete, high-frequency temporal sequences are most effective in capturing the spectral dynamics of NWs across their full growth cycle, thereby enhancing the model’s ability to learn vegetation trends and improving the regression accuracy. In contrast, the interval_2 + retain_May_Sep configuration—characterized by both sparse sampling and a restricted observation window—yielded the weakest performance, with an R² of only 0.665 and an RMSE of 0.115. This suggests that simultaneously reducing the temporal span and resolution may result in the loss of critical phenological information, thereby impairing the model’s capacity to represent the vegetation dynamics accurately.

Further analysis based on the retention strategies revealed systematic differences in the model performance. Among all the configurations, those using retain_Jan_Dec achieved the highest average R² (0.745), followed by retain_Feb_Nov (0.735) and retain_Mar_Oct (0.725). These results suggest that moderately excluding non-growing season observations—such as those from January and December—can effectively reduce the noise and enhance the model stability. Although the retain_May_Sep strategy, which focuses exclusively on the peak growing season, yielded a slightly lower average R² of 0.707, it still demonstrated strong predictive performance, highlighting the modeling value of high-quality seasonal data.

From the perspective of the sampling frequency, the temporal resolution also had a substantial impact under a fixed month filtering window. For instance, under the retain_Jan_Dec condition, the interval_1 configuration achieved the highest R² (0.770), outperforming interval_2 (R² = 0.745), interval_3 (R² = 0.728), and interval_4 (R² = 0.736). This trend suggests that higher-frequency observations enhance the model’s sensitivity to short-term fluctuations in vegetation conditions, while sparser sampling may fail to capture critical phenological transitions, thereby reducing the prediction accuracy.

In summary, the temporal combination strategies not only define the structure of the time-series inputs but also directly influence the model’s capacity to characterize the seasonality, periodicity, and phenological dynamics. The results indicate that full-year, high-frequency observations represent the optimal configuration for maximizing the predictive accuracy. Nevertheless, strategically reducing the sampling interval or limiting the observation period can still yield competitive performance while enhancing data efficiency. Therefore, temporal configurations should be flexibly tailored to specific task requirements and computational constraints to achieve an optimal balance between model performance and operational efficiency.

3.2.2. Comparative Analysis of Representative Temporal Combinations

To further evaluate the impact of the temporal combination strategies on the model fitting performance, four representative configurations were selected, each reflecting a distinct temporal design strategy: full-year high-density observation, growing-season–focused sampling, inactive-period exclusion, and sparse seasonal input. Their predictive accuracy was assessed using scatter plots comparing the estimated and observed fractional coverage of noxious weeds in the test dataset (Figure 8).

The first configuration, interval_1 + retain_Jan_Dec, retained all 72 Sentinel-2 observations across the full calendar year without subsampling. As shown in Figure 8a, this full-coverage, high-frequency strategy yielded the best performance, achieving an R² of 0.770 and an RMSE of 0.096. The predicted values were tightly aligned with the 1:1 reference line across the entire coverage spectrum, particularly within the low-to-moderate range (0.2–0.5), indicating that a complete time series effectively captured the seasonal spectral dynamics and ensured robust model fitting.

The second configuration, interval_4 + retain_May_Sep, retained only one observation every four time steps, limited to the peak growing season (May to September). Despite its compressed temporal span and sparse sampling density, it still produced competitive results (R² = 0.746, RMSE = 0.100), as illustrated in Figure 8b. The scatter plot revealed tightly clustered predictions within the mid-range interval (0.3–0.6), although slight underestimation occurred at higher coverage levels, likely due to insufficient representation of extreme cases in the training data.

The third configuration, interval_2 + retain_Feb_Nov, excluded January and December to avoid interference from extreme winter conditions while maintaining a moderate sampling frequency across February to November. As shown in Figure 8c, this setting achieved near-optimal performance (R² = 0.759, RMSE = 0.098) while substantially reducing the number of input samples. The predictions were evenly distributed and exhibited low variance across all the coverage ranges, demonstrating that the exclusion of low-quality temporal segments can enhance the data efficiency without compromising the predictive accuracy.

The fourth configuration, interval_2 + retain_May_Sep, represented the weakest performer. As depicted in Figure 8d, it combined a limited seasonal window with a reduced sampling frequency, resulting in the lowest R² (0.665) and the highest RMSE (0.115). The scatter plot showed substantial deviations and outliers, particularly in high-coverage regions (>0.6), where the predictions were consistently underestimated. These results indicate that excessive compression in both the temporal resolution and observational span impairs the model’s capacity to capture critical phenological transitions.

In summary, the comparative results demonstrate that full-length, high-frequency temporal input remains the most effective strategy for maximizing the predictive performance. However, selectively excluding redundant months or applying moderate reductions in the sampling frequency during key phenological periods can still yield satisfactory accuracy while significantly reducing the data volume and computational cost. These findings underscore the value of the temporal configuration as a flexible and practical tool for balancing the model precision and resource efficiency in remote sensing applications.

3.2.3. Overall Evaluation of Temporal Combination Strategies

The experimental results collectively underscore the pivotal role of the temporal combination strategies in the regression-based modeling of the noxious weed fractional coverage. Variations in both the sampling interval and observation month selection significantly affect the model’s ability to capture the vegetation growth dynamics and ultimately determine the predictive accuracy. Across the 20 evaluated configurations, several consistent patterns emerged.

First, complete and densely sampled time-series inputs substantially enhance the model’s capacity to capture temporal variations in the NW coverage. For example, the interval_1 + retain_Jan_Dec configuration, which incorporates all the available time steps without omission, achieved the best performance (R² = 0.770, RMSE = 0.096). This highlights the importance of full-year, high-frequency observations in delivering comprehensive temporal signals—particularly advantageous for applications requiring high accuracy and model stability.

Second, moderately excluding non-growing season observations—especially winter months such as January and December—can effectively reduce the spectral noise without compromising the prediction accuracy. For instance, the interval_2 + retain_Feb_Nov strategy yielded near-optimal results (R² = 0.759, RMSE = 0.098), despite a substantial reduction in the input volume. This demonstrates the effectiveness of a quality-over-quantity approach in enhancing the model robustness and generalization.

Third, temporal strategies that focus exclusively on the growing season while employing lower sampling frequencies can still achieve satisfactory performance with reduced data requirements. For example, interval_4 + retain_May_Sep retained only one image every four time steps during the May–September period, representing approximately 11% of the total samples used in the optimal configuration. Despite this reduction, it attained strong results (R² = 0.746, RMSE = 0.100), illustrating an effective trade-off between accuracy and computational efficiency—well suited for rapid-response or resource-constrained applications.

Finally, excessive temporal compression leads to significant performance degradation. The interval_2 + retain_May_Sep configuration, although covering the core growing season, combined sparse sampling with a limited temporal span. It yielded the poorest performance (R² = 0.665, RMSE = 0.115), indicating that concurrently reducing both the temporal density and coverage diminishes the model’s ability to capture critical phenological transitions, thereby weakening its predictive capacity.

In summary, temporal information serves not only as a foundational component of remote sensing modeling but also as a critical driver of the model’s capacity to learn phenological dynamics. The findings indicate that, whenever feasible, full-year and high-frequency observations should be prioritized to maximize the predictive accuracy. Alternatively, carefully designed temporal strategies—such as excluding redundant months or applying sparse sampling during informative periods—can achieve high efficiency with a minimal loss in accuracy. These results provide both theoretical insight and practical guidance for designing scalable and effective time-series remote sensing models for noxious weed monitoring.

3.3. Analysis of Noxious Weed Coverage and Its Elevation-Dependent Distribution Patterns

Figure 9a illustrates the spatial distribution of the fractional noxious weed coverage across the study area. Overall, the weed coverage levels remain relatively low throughout most regions. To further examine the spatial heterogeneity and elevation-dependent trends in the NWs’ expansion, a series of analytical visualizations was developed, including the pixel-wise distribution of weed coverage (Figure 9b), the distribution of pixel counts across different elevation intervals (Figure 9c), and the variation in the mean coverage and standard deviation within each elevation band (Figure 9d). Together, these analyses reveal the spatial patterns and topographic dependencies that characterize the proliferation of noxious weeds in the region.

Figure 9b shows the distribution of the pixel counts across different coverage intervals. Overall, the NWs exhibited a clear tendency toward moderate levels of coverage, with the majority of pixels concentrated within the 30–50% range. Specifically, the 30–40% interval accounted for the highest proportion of pixels (32.7%), followed by the 40–50% range (25.3%). In contrast, pixels with coverage below 10% or above 70% were relatively rare, each comprising less than 5% of the total. This distribution pattern suggests that NWs are broadly distributed across the study area but typically occur at intermediate densities, indicating a moderate and widespread expansion trend rather than localized high-intensity infestations.

Figure 9c further illustrates the elevation-based distribution of the NW pixels. The results indicate that NWs are predominantly concentrated within the 4200–4800 m elevation range, with the peak pixel density observed between 4300 and 4500 m. This pattern suggests that mid-elevation zones—particularly those dominated by alpine meadows and alpine shrub lands—offer the most favorable ecological conditions for NW proliferation. In contrast, the pixel counts decline sharply at elevations below 4100 m and above 4900 m, likely due to a combination of topographic constraints, climatic limitations (e.g., low moisture and temperature), and land-use variability. Overall, the distribution of NWs exhibits a characteristic enrichment trend within mid- to high-elevation landscapes.

Figure 9d presents the mean and standard deviation of the NW coverage across different elevation intervals. Within the 4200–4700 m band, the mean coverage remains relatively high (approximately 39–40%) with a low standard deviation, indicating that NWs are not only abundant but also uniformly distributed at these elevations. In contrast, both the coverage levels and spatial consistency decline in the 4100–4200 m and 4800–5000 m bands, where the increased standard deviation reflects greater spatial heterogeneity and ecological uncertainty at the distributional margins. These results suggest that mid-elevation zones are not only hotspots of NW abundance but also areas of stable and consistent infestation, likely shaped by selective environmental pressures and relatively homogeneous habitat conditions.

In summary, the spatial distribution of NWs within the study area exhibits a strong elevation-dependent pattern, with the 4200–4800 m range identified as the core expansion zone for these invasive species. Accordingly, future management and control efforts should prioritize this elevational belt by implementing enhanced monitoring and targeted interventions in high-coverage patches, thereby improving the effectiveness of strategies aimed at suppressing further NW proliferation.

3.4. Ablation Study

To quantitatively assess the individual contributions of the dynamic masking and non-stationary modeling components within the DMNST framework, an ablation study was conducted by comparing the full model with three simplified variants: Transformer (Baseline), Dynamic Masked Transformer, and Non-Stationary Transformer. All the models share the same encoder-only Transformer backbone and were trained under identical experimental conditions.

Importantly, each variant was evaluated using the optimal input configuration identified in Section 3.1 and Section 3.2—specifically, the VIS, RE, NIR, and SWIR spectral bands combined with the full-year, high-frequency time series (interval_1 + retain_Jan_Dec). This setup ensured that the performance differences are attributable solely to architectural changes, rather than to variation in the input data quality or quantity.

The models were assessed using three standard regression metrics: MSE, RMSE, and R². The results are summarized in

Table 7. Performance comparison of the DMNST model and its three ablated variants using the optimal input configuration (VIS + RE + NIR + SWIR bands; interval_1 + retain_Jan_Dec).

Model	Test R2	Test MSE	Test RMSE
Transformer (Baseline)	0.696	0.012	0.110
Dynamic Masked Transformer	0.722	0.011	0.105
Non-Stationary Transformer	0.729	0.011	0.104
DMNST	0.770	0.009	0.096

.

The baseline Transformer model, which excludes both dynamic masking and target normalization, exhibited the weakest performance (R² = 0.696), highlighting its limited ability to address spectral noise and seasonal variability in vegetation dynamics. Incorporating either enhancement independently led to modest improvements: the Dynamic Masked Transformer demonstrated improved robustness to cloud-contaminated inputs (R² = 0.722), while the Non-Stationary Transformer better adapted to temporal non-stationarity (R² = 0.729).

The DMNST model, integrating both modules, significantly outperformed all the variants, achieving the lowest MSE (0.009), lowest RMSE (0.096), and highest R² (0.770). These results suggest a synergistic effect when temporal filtering and non-stationary modeling are applied in concert. Beyond the improved accuracy, the full model also exhibited enhanced robustness across the full spectrum of NW coverage values.

In summary, this ablation analysis underscores the effectiveness of each architectural enhancement and their combined contribution to the DMNST model. The dynamic masking module suppresses unreliable observations arising from atmospheric interference, while the non-stationary normalization facilitates more stable learning from temporally complex vegetation signals. Together, they provide a robust framework for accurate and scalable regression modeling of the NW fractional coverage using satellite time-series data.

4. Discussion

4.1. Integrated Evaluation of Feature and Temporal Combinations

This study confirms that both the spectral and temporal input designs play a central role in determining the model performance for NW fractional coverage estimation. Regarding the spectral configurations, the fusion of the VIS, RE, NIR, and SWIR bands yielded the best predictive results (R² = 0.770, RMSE = 0.096), effectively capturing the pigment, structural, and moisture-related vegetation traits. In contrast, using only a single spectral domain (e.g., NIR or VIS) significantly reduced the accuracy.

For the vegetation indices, introducing all 23 common indices (23CVIs) brought about marginal improvement and added complexity. A simpler integration of the NDVI and EVI (2BVIs) with the four spectral bands performed better, indicating that excessive stacking of indices may introduce redundancy and noise. While the DMNST model’s attention mechanism supports high-dimensional input, overly complex feature spaces can hinder the training stability and generalization.

The temporal configurations exhibited similarly critical influence. Full-year, high-frequency sampling (interval_1 + retain_Jan_Dec) provided the richest phenological signals and achieved the best performance. However, streamlined alternatives—such as removing non-growing months (interval_2 + retain_Feb_Nov) or limiting observations to the main growth season (interval_4 + retain_May_Sep)—also retained strong accuracy (R² = 0.759–0.746) while reducing the computational burden. Over-compressed strategies, like interval_2 + retain_May_Sep, underperformed (R² = 0.665), emphasizing the need for sufficient temporal coverage.

In conclusion, the optimal input strategies should prioritize multispectral fusion and phenologically relevant time series. Selective integration of vegetation indices and informed temporal downsampling strike a practical balance between accuracy and efficiency. These findings jointly offer methodological guidance for designing streamlined yet effective remote sensing models. for vegetation monitoring.

4.2. Performance of the DMNST Model in Mapping Continuous Coverage of NWs

In this study, a Dynamic Masked Non-stationary Transformer (DMNST) model was developed to estimate the continuous fractional coverage of noxious weeds (NWs) across alpine grassland regions, using Sentinel-2 time-series imagery as the input. The model achieved strong predictive performance, with a coefficient of determination (R²) of 0.770, a mean absolute error (MAE) of 0.009, and a root mean square error (RMSE) of 0.097 on the test dataset (Table 3). These results demonstrate the model’s robust regression capability and its effectiveness in capturing spatially continuous vegetation dynamics.

Compared to previous studies that employed convolutional neural networks (CNNs) and high-resolution WorldView-2 imagery to classify Euphorbia virgata in heterogeneous grassland ecosystems in the United States—with reported classification accuracies reaching up to 96.1% [93]—the predictive accuracy achieved in this study was relatively lower. This discrepancy is primarily attributed to differences in the spatial resolution of the input imagery. While high-resolution data are well suited for fine-scale vegetation identification, particularly when paired with texture-sensitive models such as CNNs, they also entail considerable data volumes and computational costs, limiting their applicability for large-scale, continuous mapping tasks.

In contrast, although Sentinel-2 imagery has only moderate spatial resolution, its wide spatial coverage, high revisit frequency, and long-term data availability make it well suited for regional-scale temporal modeling. Compared to previous studies that employed 30 m hyperspectral imagery to estimate the fractional coverage of native and invasive herbaceous species in alpine meadows—with reported accuracies of approximately 65% [94]—the DMNST model developed in this study achieved superior predictive performance. These results highlight both the feasibility and the practical applicability of the DMNST approach for mapping continuous noxious weed coverage at landscape scales.

Furthermore, the findings of this study are consistent with a growing body of literature emphasizing the effectiveness of temporal features in vegetation classification tasks [42,44,45]. For example, Ref. [95] demonstrated that integrating high-spatial-resolution and high-temporal-resolution remote sensing imagery enabled accurate parcel-scale crop classification using deep learning, achieving an accuracy of 0.80. This reinforces the importance of incorporating spectral–temporal information to enhance the classification performance in remote sensing applications. Time-series data have also shown increasing potential in a range of tasks, including vegetation mapping, crop type identification, and continuous variable estimation [46,96,97,98,99,100,101,102].

While high spatial and spectral resolution imagery may yield higher accuracies for fine-grained tasks such as crop classification [15,93,103,104,105,106], time-series remote sensing data offer distinct advantages for long-term ecological monitoring [46,101,102]. Most hyperspectral and high-resolution sensors have only been in operation for a relatively short duration and lack consistent long-term observational records. In contrast, multispectral platforms such as Sentinel-2 and Landsat have provided systematic global coverage for decades, offering temporally consistent and historically extensive datasets. Compared to hyperspectral sensors, these platforms enable longer time series and more stable data continuity, supporting long-term ecological trend analysis and retrospective assessment. Therefore, multispectral time-series data remain indispensable for regional-scale ecological modeling and monitoring.

Despite the strong predictive performance of the DMNST model in estimating the noxious weed coverage, misclassification issues were observed in relation to certain land cover types. For example, field surveys confirmed that the central portion of the study area includes perennial rivers. However, the model erroneously predicted low weed coverage in these regions, misinterpreting water bodies as areas with sparse NW presence. This misclassification likely resulted from limited spatial representation in the training dataset. The sampling locations were constrained to accessible areas, leading to a lack of representative samples for non-vegetated classes such as water bodies and perennial snow. As a result, the model was unable to adequately learn their spectral–temporal signatures, which contributed to the classification errors during inference. To mitigate this issue, water and perennially snow-covered areas were masked prior to the model training to reduce the interference from spectrally irrelevant land cover types. This finding underscores the critical importance of ensuring representative and balanced training samples in large-scale remote sensing applications. Future research should prioritize the inclusion of underrepresented land cover types—particularly those prone to misclassification—in order to improve the model generalizability and ensure consistency between the predicted outputs and the actual land surface conditions.

4.3. Limitations

Although the proposed DMNST model demonstrated strong overall performance in estimating the fractional coverage of noxious weeds—particularly under the optimized multi-band and temporal sampling configurations—the results across various feature and temporal combinations reveal several limitations and potential biases that warrant further investigation and methodological refinement.

First, regarding the spectral feature combinations, although the integration of the VIS, RE, NIR, and SWIR bands achieved the highest coefficient of determination (R² = 0.770), several other combinations exhibited systematic underestimation in high-coverage regions (>0.6) and overestimation in low-coverage regions (<0.3). These trends, also evident in the scatter plots (Figure 6), suggest that the model’s predictive response to samples with varying vegetation density remains imbalanced. This issue is particularly pronounced in combinations such as RE + SWIR + VIS and NIR + RE + SWIR, indicating the presence of either insufficient feature selection or redundant spectral representations in the high-dimensional space.

Such deviations may stem from two primary factors. First, the spectral similarities between NWs and background vegetation in certain bands can lead to inadequate spectral separability, especially in mixed or sparse infestation zones (e.g., cropland margins or shrub edges), making the model prone to misclassification. Second, high-dimensional inputs may contain multicollinearity and redundancy, potentially causing the model to overfit intermediate coverage samples while lacking generalization capacity for extreme values. Additionally, the differences in sensitivity among the spectral bands to plant structural, moisture, and pigment properties may contribute to the inconsistent representation across phenological stages.

Second, from a temporal perspective, the variations in the observation windows and sampling frequencies also significantly influence the model performance. While the full-year configuration (interval_1 + retain_Jan_Dec) achieved the best overall results, slight underestimation was still observed in high-coverage areas. In combinations that used only growing season data or excluded winter months (e.g., interval_3 + retain_May_Sep, interval_1 + retain_Mar_Oct), the model performed well for moderate values but remained unstable in handling extreme coverage cases. This may be attributed to the inherently imbalanced distribution of the training samples, as high-coverage zones are naturally rare in alpine ecosystems, limiting the model’s capacity to learn such patterns. Moreover, although excluding low-activity seasons helps reduce noise, it may also impair the model’s ability to fully characterize the phenological cycle.

Beyond the feature and temporal strategy-related structural errors, the limited availability of ground truth samples is another factor contributing to the prediction uncertainty in certain regions. Although this study ensured representative and quality-controlled sample selection, the overall sample size was still insufficient to fully capture the spectral and spatial variability of NWs, particularly in ecologically complex or extreme scenarios.

Furthermore, the study area—located in the Qinghai–Tibet Plateau (QTP) alpine grassland ecosystem—is characterized by high elevation, rugged terrain, and low oxygen availability, all of which restrict the sample accessibility and collection frequency. Ultimately, 170 ground plots were collected. While this sample size sufficed for local-scale modeling with high predictive accuracy, the limited ground truth data may introduce greater uncertainty when extending the model to broader spatial domains, potentially affecting the stability and generalizability. This is consistent with prior findings suggesting that deep learning-based geoscience models are often constrained by the availability and representativeness of reference data [107,108,109,110,111].

Given the considerable challenges associated with large-scale field surveys in geospatial remote sensing—such as the complex terrain, limited accessibility, and high labor costs—numerous studies have proposed alternative or complementary strategies to address the scarcity of in situ samples. Among these, UAV-based image acquisition has emerged as a widely adopted method due to its high spatial resolution, flexible deployment, and controllable flight paths, making it particularly effective for plot-scale sampling in areas that are difficult to access [112,113]. Additionally, manual interpretation of high-resolution satellite imagery serves as a valuable supplementary approach [114]. By integrating expert knowledge of vegetation types, topographic features, and ecological context, researchers can generate large-scale auxiliary labeled datasets, thereby improving the representativeness and spatial extent of training samples.

5. Conclusions

Accurately mapping the continuous coverage of noxious weeds (NWs) at large scales is essential for ecological risk assessment and the targeted management of invasive species. To address this need, this study proposed a predictive framework that integrates Sentinel-2 time-series imagery with a Dynamic Masked Non-Stationary Transformer (DMNST) model. Two key objectives were pursued: (1) estimating the pixel-level fractional NW coverage, and (2) evaluating the utility of multi-temporal remote sensing inputs in supporting regional-scale weed monitoring.

The proposed DMNST model exhibited robust regression performance across diverse spectral and temporal configurations, with the optimal setting achieving an R² of 0.770. The attention-based architectures demonstrated strong capacity for capturing the spatiotemporal dynamics of vegetation. Among the spectral features, the fusion of the VIS, RE, NIR, and SWIR bands provided the highest accuracy, underscoring the importance of integrating pigment-, structure-, and moisture-sensitive bands for modeling NWs characterized by seasonal variation and spatial heterogeneity.

Temporal analysis showed that full-year time series yielded the most stable results, while reduced configurations—such as retaining only peak-season observations—also maintained competitive accuracy with a reduced data volume. These findings highlight the flexibility of the temporal design in balancing performance and efficiency.

In summary, the DMNST model combined with Sentinel-2 data provides an effective and scalable solution for continuous weed mapping. The framework offers a solid foundation for dynamic monitoring of invasive species across heterogeneous landscapes. Future efforts may enhance the generalizability by integrating additional data sources such as UAV imagery, hyperspectral data, climate variables, and terrain features.