Multiscale Spatiotemporal Variation Analysis of Regional Water Use Efficiency Based on Multifractals

Abstract

Understanding the complex variations in water use efficiency (WUE) is critical for optimizing agricultural productivity and resource management. Traditional analytical methods often fail to capture the nonlinear and multiscale variations inherent in WUE, where multifractal theory offers distinct advantages. Given its limited application in WUE studies, this paper analyzes the spatiotemporal characteristics and influencing factors of the WUE in Anhui Province from 2001 to 2022 using a multifractal, multiscale approach. The results indicated that the WUE exhibited significant interannual variation, peaking in summer, especially in August (2.4552 gC·mm⁻¹·m⁻²), with the monthly average showing an inverted “V” shape. Across different spatial and temporal scales, the WUE displayed clear multifractal characteristics. Temporally, the variation in fractal features between years was not prominent, while inter-seasonal variation was most complex in August during summer. Spatially, the most distinct multifractal patterns were observed in hilly and mountainous areas, particularly in regions with brown soil distribution. Rainfall was identified as the primary natural driver influencing regional WUE changes. This study aims to promote the sustainable use of water resources while ensuring the stability of agricultural production within protected farmlands.

1. Introduction

Water use efficiency (WUE) is the term used to describe the ratio of gross primary productivity (GPP) to evapotranspiration (ET) and is fundamental to understanding the balance between the carbon gain and water loss in ecosystems under different climatic conditions [1,2]. Under the expansion of global climate change, the water cycle in several ecosystems has accelerated, significantly affecting the WUE and leading to regional water resource scarcity and ecosystem stress [3,4]. Therefore, it is crucial to delve deeper into the patterns of WUE variation and climatic factors to better predict the response of carbon and water cycles to future climate changes [5,6].

Research into WUE can be divided into different scales: leaf-level, whole-plant, crop-level, and ecosystem-level [7]. Many scholars have investigated the impact that climatic factors have on WUE at the ecosystem level, with results indicating specific patterns of spatiotemporal variation observed in the WUE of different ecosystems [8,9]. Moreover, the results vary on different scales, as is apparent from studies that have investigated WUE in specific forest or farmland ecosystems, compared WUE across different climatic zones, or assessed the spatiotemporal characteristics of WUE in natural agricultural zones [5,10,11]. These studies have provided new perspectives for understanding WUE at specific scales.

Research into WUE has indicated that the differences associated with WUE on various scales are significant [8,9,12], with many studies exploring the spatiotemporal distribution characteristics and driving factors of WUE from a global or national perspective leading to the determination of the spatial distribution characteristics of WUE. However, the relatively large spatial scale of such studies renders it difficult to accurately describe the results in detail [8,9,13]. Other studies have used flux tower observation data from China to investigate the variation characteristics and driving factors of WUE on the site scale, allowing the WUE of China’s terrestrial ecosystems to be explored and the seasonal variation in WUE to be analyzed. Although precise in terms of temporal accuracy, the influencing factors are complex, and information on the spatial distribution characteristics is lacking [14,15]. Some studies have divided regions into ecosystems, vegetation types, and natural regions, which is conducive to analyzing changes in WUE at smaller scales and has led to the identification of regional patterns [10]. However, accounting for the various patterns observed in different regions remains challenging.

Commonly used methods for analyzing spatiotemporal variation in WUE include isotope analysis (e.g., carbon isotope discrimination), remote sensing (using satellites and drones), ecosystem modeling (process models and statistical models), long-term monitoring networks (the eddy covariance method, meteorological station data), and data assimilation [16,17,18]. However, these methods are limited when addressing small-scale variation, nonlinearity, and complex systems, and their applicability is often constrained by data availability and quantity. Therefore, a method that can simultaneously address scale variation and nonlinear issues via spatiotemporal variation analysis is required.

Multifractal analysis can be used to describe heterogeneity and self-similarity at multiple scales in complex systems, providing a more accurate characterization of the multiscale and multi-intensity fluctuations that occur in nature and complex systems [19]. The fractal dimension is an important metric for describing the complexity of fractals. Multifractal analysis is widely used in environmental and ecological studies to capture the spatial and temporal variabilities of processes that do not conform to simple, linear, or homogeneous patterns [20]. Multifractal theory presents a powerful tool for quantifying scale-invariant structures in complex natural systems, and is particularly applicable to phenomena such as precipitation and vegetation growth, which are characterized by intermittency and aggregation [21,22]. These factors directly affect the WUE, which usually exhibits high variability at different temporal and spatial scales. Multifractal analysis reveals hidden scale invariance patterns and hierarchical structures in WUE data that are difficult to capture using traditional methods, especially in regions with significant seasonal WUE variations [23,24].

Multifractals have been widely applied in the analysis of rainfall, precipitation indices, soil types, drought, and other areas, and offer a better description of the intensity distribution and frequency of extreme events in rainfall time series [25]. The approach can reveal multiscale behaviors and intrinsic patterns in rainfall processes, rendering it a powerful tool for assessing nonlinear characteristics in the time series of complex regions [26,27,28]. Fractal models have also been applied in studying the spatial distribution of soil properties [29]. The standardized precipitation index (SPI) has been proven to exhibit multifractality, and has been used in precipitation anomaly detection and complexity analysis [30]. Multifractal analysis has significant advantages for the anomaly detection and complexity analysis of time series [31], and WUE fluctuates over time and shows strong spatial heterogeneity. Precipitation and other factors related to WUE that exhibit multifractal characteristics have been widely studied in various regions [28,32,33]; however, the multifractal theory has not as yet been applied to WUE.

Multifractal analysis has certain advantages for the analysis of changes on both macroscales and microscales, with the multifractal theory capturing the complexity of phenomena across multiple scales [34]. The multifractal spectrum can identify variation patterns and self-similarity at different scales, providing insights for understanding and analyzing the spatiotemporal variability of WUE [35]. Traditional analysis methods often struggle to simultaneously account for complex interactions on different scales, and multifractals can systematically compare and analyze differences between regions through detailed fractal spectra, revealing both microscale details and overall macroscale characteristics [35,36]. Therefore, in this study, multifractal theory was combined with spatiotemporal change analysis methods to analyze the characteristics of WUE and validate the feasibility of using multifractal theory [37], not only deepening the understanding of WUE variation with climate change, but also providing a scientific basis for future ecosystem management and climate change adaptation strategies [38,39].

This study aims to analyze the spatiotemporal variation characteristics and factors influencing WUE across different temporal and spatial scales using MODIS data from 2001 to 2022, exploring the effectiveness of multifractal theory in analyzing WUE changes at various spatiotemporal scales. Most current research focuses on WUE changes on temporal scales such as single years and months or spatial scales such as the vegetation type, and a detailed analysis of WUE changes across different scales is lacking. Based on the spatiotemporal scale variation analysis of WUE, multifractal theory is thus introduced and the temporal scales meticulously divided into years, seasons, and months, and the spatial scales into terrain and soil types. The capability of multifractal theory is analyzed and evaluated in the context of spatiotemporal WUE changes. The main issues addressed and discussed in this study include (1) the feasibility of using multifractal theory to analyze WUE variation characteristics across different spatiotemporal scales; (2) combining commonly used analysis methods with multifractal theory to analyze spatiotemporal variation in WUE; and (3) exploring factors that influence WUE in different regions.

2. Materials and Methods

2.1. Study Area

Anhui Province is located in eastern China (Figure 1a), spanning 114°54′ to 119°37′ E in longitude and 29°41′ to 34°38′ N in latitude, with the Huai and Yangtze Rivers running east–west through the province. Anhui Province can be divided into five natural areas: the Huaibei Plain, the Jianghuai hilly region, the Dabie Mountain area in western Anhui, the plain alongside the river, and the hilly mountainous area in South Anhui. The province is marked by abundant agricultural resources and is an important grain production base in China [40]. The terrain comprises plains, mountains, and hills, and the climate is in a transitional zone between warm temperate and subtropical; thus, the area is influenced by a monsoon, resulting in distinct seasons. The intensification of climate change and human activity [41] has meant that the efficient utilization of the limited water resources has become an urgent issue in the area.

2.2. Data

2.2.1. Remote Sensing Data

Remote sensing data, including the annual evapotranspiration (ET) (MOD16A3GF) and annual gross primary productivity (GPP) (MOD17A3HGF) for 2001–2022, were obtained along with 8 d ET data (MOD16A2) and 8 d GPP data (MOD17A2HGF) for the period 2001–2021 from the MODIS data products (https://disc.gsfc.nasa.gov/, from 1 January 2001 to 31 December 2021). All MODIS data had a spatial resolution of 500 m and were subjected to data format conversion, image mosaicking, cropping, projection transformation, and outlier processing. Data processing was completed in ArcGIS 10.7.

2.2.2. Other Data

Meteorological data were sourced from the National Tibetan Plateau Data Center (https://data.tpdc.ac.cn/, from 1 January 2001 to 31 December 2018), specifically the Chinese regional surface meteorological element dataset. DEM data for Anhui Province were obtained from the Geospatial Data Cloud (https://www.gscloud.cn/, SRTMDEM 90M resolution raw elevation data). Soil type data were obtained from the Resource and Environment Science and Data Platform (https://www.resdc.cn/, from 1:100,000 soil map of the People’s Republic of China).

2.3. Methods

The main technical workflow of this study is illustrated in Figure 2. MODIS data were preprocessed and then analyzed separately on temporal and spatial scales, with the temporal scale including annual, seasonal, and monthly variation, and the spatial scale divided into five natural topographic regions and eight major soil types. The Sen + MK trend test analysis method was used to examine the spatiotemporal variations. Multifractal theory was introduced for temporal-scale variations and used to discuss the differences and complexities in each spatially divided region. Finally, machine learning was employed to analyze the contributions of the influencing factors in each region.

2.3.1. WUE Calculation

WUE was calculated using the following equation [42]:

$$\mathrm{W}\mathrm{U}\mathrm{E}={\displaystyle \frac{\mathrm{G}\mathrm{P}\mathrm{P}}{\mathrm{E}\mathrm{T}}}$$

(1)

where GPP is the gross primary productivity in gC/m² and ET is evapotranspiration in mm. The WUE units are therefore gC∙mm⁻¹∙m⁻².

2.3.2. Sen’s Slope Estimator and Mann–Kendall Trend Test Methods

Sen’s slope estimator and the Mann–Kendall trend test were used to analyze the seasonal spatiotemporal variation in the WUE within Anhui Province. Sen’s slope estimator is robust for estimating trends in time series data, is independent of data distribution assumptions and insensitive to outliers, thus providing reasonable estimates even for non-normally distributed data. The Mann–Kendall trend test method is robust and non-parametric and can produce reliable results in the presence of outliers or data discontinuities [43,44].

The standardized statistic |Z| obtained from Sen+MK at significance levels of 0.05 and 0.01 (

Table 1. Sen+MK trend test change division criteria.

Z Value	WUE Trend
2.58 ≤ |Z|	Extremely significant trend
1.96 < |Z| < 2.58	Significant trend
1.65 < |Z| < 1.96	Moderately significant trend
|Z| ≤ 1.65	No significant trend

) indicates that a |Z| value exceeding 1.65, 1.96, and 2.58 suggests that a trend is significant at the 90, 95, and 99% confidence level, respectively. Trends were thus categorized into nine classes: extremely significant decrease, significant decrease, moderately significant decrease, no significant decrease, no change, no significant increase, moderately significant increase, significant increase, and extremely significant increase [45,46].

2.3.3. Characterization of Fractal Parameters

Self-similarity, in which a fractal object can be subdivided into parts, each of which may be a small-scale copy of the whole or statistically similar, is a central feature of fractals [47]. The multiple fractals in complex systems can therefore characterize the non-uniformity and diversity of the system’s performance at different scales to reveal the complexity and inhomogeneity that exists within the system at different scales. Researchers have proposed various methods for estimating the fractal dimension, including the box counting and triangular prism methods, and fractional Brownian motion [48]. The box-counting method is relatively simple, provides reliable results, and is widely used in many fields [49,50]; thus, this method was used for the multiple fractal analysis in this study.

(1) Box counting is a commonly used method by which the fractal dimension can be calculated [51], with small boxes with different side lengths (r) used to cover a study area. In this study, boxes were considered to be two-dimensional, N_ij indicated the number of data points in the (i,j) box, and N was the total number of data points in the whole area. The distribution probability P_ij of the (i,j) box is expressed using

$$P_{ij}={\displaystyle \frac{N_{ij}}{N}}$$

(2)

(2) The number of boxes N(r) required at different scales are calculated by varying the box size (r). The matching function χ_q(r), which is a weighted summation of the qth power of p_ij(r), is then defined using the mathematical expression:

$$x_q\left(\mathrm{r}\right)={\sum }_{i,j}{p}_{ij}{\left(r\right)}^q$$

(3)

where q ∈ (−∞, +∞) is the order of the statistical moments characterizing the degree of multifractal inhomogeneity. When q >> 1, the value of p_ij(r) with a higher probability in χ_q(r) plays a major role; when q << −1, p_ij(r) with a lower probability plays a major role. All integers between q ∈ (−10, 10) were utilized in this study.

(3) The mass index τ(q) is a characteristic function of fractal behavior and can be obtained from the slope of the logχ_q(r) versus the logr curve:

$$\tau (q)=\underset{\tau \to 0}{\lim }{\displaystyle \frac{log{\chi }_q^{\left(r\right)}}{log r}}$$

(4)

The multifractal spectrum is meaningful only if logχ_q(r) is linear (i.e., scale-invariant) with respect to logr. If τ(q) is a straight line with respect to q, the object is monofractal; however, if τ(q) is an upward convex monotonically increasing curve with respect to q, the object is multifractal.

(4) The generalized fractal dimension D_q is calculated using τ(q):

$$D_q={\displaystyle \frac{\tau \left(q\right)}{q-1}}$$

(5)

When q = 0, D_q = D₀, i.e., the ordinary Hausdorff dimension; when q = 1, D_q = D₁, thus representing the information dimension, which is expressed using

$$D_1=-\underset{\tau \to 0}{\lim }{\sum }_{i,j}{p}_{ij}log{p}_{ij}$$

(6)

(5) The Legendre transform between the generalized fractal dimension and the multifractal spectrum is then satisfied, and the multifractal spectrum is obtained from τ(q) and the corresponding transform of q:

$$\mathrm{f}\left(\alpha \right)=q\alpha \left(q\right)-\tau \left(q\right)$$

(7)

$$\alpha (\mathrm{q})={\displaystyle \frac{d\tau \left(q\right)}{dq}}$$

(8)

The relationship between the independent variables q, τ, f(α), and α is constructed using the above two equations. The series f(α) refers to the series of sequential spectra obtained in which α denotes the localized dimensionality of the manifold and the localized region, and changes constantly with r.

2.3.4. Machine Learning Method Integration Analysis

We introduced four machine learning methods, decision trees, random forests, GBDT, and XGBoost, to identify and analyze the complex influences of WUE [52]. Decision trees predict target variables by learning decision rules from the features of the utilized data. This method is advantageous because the generated model is easy to understand, interpretable, and does not require extensive preprocessing, making it suitable for directly revealing the main factors affecting WUE [53]. Random forests improve model accuracy and the robustness of a model by constructing multiple decision trees and combining their predictions, with each tree using randomized data samples and subsets of features for training. The approach significantly reduces the variance of the model and prevents overfitting [54]. As a result, random forests are well suited for handling large datasets with high-dimensional features, offering improved stability and accuracy in detecting WUE drivers with minimal parameter tuning [55]. The gradient boosting decision tree (GBDT) corrects errors from the previous tree by sequentially adding decision trees, with each step aimed at reducing the overall prediction error. This enables the model to maintain high prediction accuracy under the influence of complex natural factors, especially in capturing nonlinear changes in WUE [56]. GBDT enhances the model accuracy by optimizing a derivable loss function, which enhances predictive performance and is particularly effective when applied to structured data [57]. XGBoost (Extreme Gradient Boosting), an implementation of the gradient boosting framework, is designed to provide high prediction performance while maintaining computational speed and efficiency. This enabled our study to process large-scale WUE data quickly and detect subtle changes in WUE across different temporal and spatial scales [58]. By integrating these methods, the complex response patterns of WUE under the action of multiple natural factors were revealed, and the advantages of these methods provided novel and effective analytical tools for WUE research [52].

3. Results

3.1. Analysis of WUE in Anhui Province by Time Scale

3.1.1. Characteristics of WUE Changes in Anhui Province on Annual, Quarterly, and Monthly Scales

The analysis indicated significant differences in the yearly changes in the average WUE for Anhui Province over the period 2001 to 2022 (Figure 3). The lowest average WUE (1.367316 gC∙mm⁻¹∙m⁻²) was observed in 2003 and the highest (1.648538 gC∙mm⁻¹∙m⁻²) in 2014. The association between WUE and ET or the GPP showed increasing trends, with the GPP showing the fastest growth rate, indicating its importance in the growth of WUE.

The seasonal statistics are shown in Figure 4. The GPP increased through all four seasons, with the fastest growth rate occurring in winter. Winter vegetation included evergreen vegetation (e.g., evergreen broad-leaved forests), which still performed photosynthesis during winter. With improvements in climatic conditions, the GPP of these plants may increase and contribute to the overall winter GPP. In addition to the declining trend of ET in autumn, growth rates increased in other seasons, being the fastest in summer. Summer presented vegetation growth peaks, with high temperatures, strong solar radiation, and vigorous vegetation transpiration. Soil evaporation increased the ET demand. The variation trend in WUE in different seasons was not clear.

Figure 5 shows both the changes in WUE during different months and the interannual variation. Overall, an inverted “V”-shaped trend is observed on a monthly basis, with WUE reaching a maximum in August and a minimum in January. The statistics indicate that the maximum WUE has occurred in August over the last 20 years, with the highest overall observed in August 2002; however, the WUE was higher in July than August in 2020. August, usually a period of high precipitation and temperature, provides sufficient moisture and suitable temperatures for crops [59]. Simultaneously, many major crops enter the late growth or maturity stage in August, when photosynthetic product accumulation reaches its peak, and the GPP of the crops at this stage is high, which in turn increases the WUE [60]. Furthermore, the photosynthetic efficiency of different crops (e.g., rice and maize) is significantly higher in August because of the different maturity levels, which is a driving force for the overall WUE value in August. In contrast, WUE is generally lower and less distinct during the winter months of January and December, when it is relatively concentrated.

3.1.2. Multiple Fractal Analysis on Different Time Scales

Figure 6 shows the multifractal spectra of the WUE in Anhui Province on three time scales: year-averaged, seasonal-averaged, and month-averaged. An effective method for analyzing the time-varying fluctuation trend of the WUE in Anhui Province is to use multiple fractal theory [26]. The difference between years is not significant, with the largest Δα (Δα = 1.1388) in 2016 and the smallest (0.9988) in 2019. The fractal characteristics of WUE remained stable during the study period, indicating stability in the WUE of Anhui Province over the 21-year period.

The parameters related to the specific multifractal spectra in terms of monthly variation are shown in

Table 2. Parameters related to the WUE multifractal spectrum over 12 months in Anhui Province.

	Month	αmin	αmax	Δα	f (αmin)	f (αmax)	Δf(α)
Average monthly WUE	January	1.9143	3.1780	1.2637	−0.5752	1.5748	−2.1499
	February	1.9141	3.2437	1.3296	−0.8782	1.7050	−2.5832
	March	1.9664	3.1348	1.1683	−0.9424	1.9611	−2.9035
	April	1.9440	3.1168	1.1728	−0.8169	1.9449	−2.7618
	May	1.9457	3.2338	1.2881	−0.6615	1.9467	−2.6081
	June	1.9503	3.1639	1.2136	−0.6158	1.9505	−2.5663
	July	1.9592	3.3099	1.3507	−1.0720	1.9570	−3.0290
	August	1.9600	3.8190	1.8590	−1.4472	1.9572	−3.4044
	September	1.9417	2.9046	0.9629	0.3274	1.9434	−1.6160
	October	1.9628	2.8032	0.8404	0.2303	1.9592	−1.7289
	November	1.9287	3.1144	1.1857	−1.0604	1.7647	−2.8251
	December	1.8696	3.2778	1.4083	−0.8743	1.5451	−2.4194

. The widest Δα (Δα = 1.8590) in August indicates strong heterogeneity in the spatial distribution of WUE during this month, whereas the narrowest Δα of 0.8404 in October indicates a more homogeneous spatial distribution. Meanwhile, the lowest f(αmin) of −1.4472 in August indicates the existence of regions with extremely inhomogeneous WUE in August, and the highest f(αmax) of 1.9611 in March suggests an extremely diverse WUE for some regions in March.

The shapes of the WUE multifractal spectrum curves differ significantly seasonally, with relatively flat multifractal spectra observed in spring and fall as compared to summer and winter. The most significant multifractal characteristics observed in summer, with the largest α range and the largest variation in f(α), may be related to complex climatic conditions such as high temperature and rain. Although the fractal characteristics are also pronounced in fall and spring, this is to a lesser degree. The multiple fractal characteristics are complex in winter; however, the f(α) variation is relatively small at this time.

In summary, the multifractal spectrum of the WUE in Anhui Province shows significant temporal and spatial heterogeneity, especially in summer and August, which exhibit the strongest multifractal characteristics. This heterogeneity reflects the profound influence of complex climatic conditions on WUE, whereas flat spectral curves in spring and fall illustrate relatively uniform WUE distribution characteristics. In addition, f(α) varies little in winter despite the complexity of the multifractal characteristics. Overall, the multifractal characteristics of WUE were highly stable on spatial and temporal scales, which provides strong support for further understanding the dynamic characteristics of regional water resource efficiency.

3.1.3. Trends in Spatial Changes in WUE in Anhui Province on Different Time Scales

The overall distribution of WUE is also uneven in the year-averaged WUE spatial distribution map of Anhui Province (Figure 7a). Specifically, the WUE is higher in the hilly and mountainous area of southern Anhui and the Dabie Mountain area of west Anhui Province and lower in the Jianghuai hilly region and the plain alongside the river in the central part of the province. The topography is mainly hilly in southern Anhui and mountainous in the Dabie Mountain area in west Anhui. These areas have rich forest resources, sufficient soil moisture, and a climate suitable for vegetation growth; thus, these regions show the highest yearly average WUE in the province. The Huaibei Plain, an important grain-growing area in which large areas of corn, wheat, and other crops are grown, is located north of Anhui Province on the southern edge of a warm temperate zone, with favorable rain and heat conditions for crop cultivation and agricultural development. The central part of Anhui Province, specifically the Jianghuai hilly region and the plain alongside the river, showed the lowest WUE. This region is traversed by the Yangtze and Huaihe Rivers from west to east, with several cities concentrated within a small area and rice as the main crop. The low WUE in this region may be related to the high degree of urbanization, structure of agricultural cultivation, and manner in which the water resources are used.

Figure 8 shows seasonal WUE trends, with clear differences in the significant trends in spring, summer, fall, and winter. Of all the seasons, spring and winter, especially winter, exhibited significant trend areas where the fluctuation in WUE was mainly concentrated in the Huaibei Plain, the northern part of the Dabie Mountains in western Anhui Province, and the river plain. In summer and fall, few highly significant trend points were observed, and water use efficiency was relatively stable with little fluctuation.

Figure 9 shows the monthly trend changes in WUE from January to December. The distribution of significant trends varies significantly within the year, especially in January, February, and December; the distribution of highly significant and significant trend points is dense, which is consistent with the trend in winter, and the main range of changes is consistent with winter as a whole. The Huaibei Plain, with its large areas of grain cultivation, is typically characterized by weak vegetation activity and low temperatures in winter, which drastically reduce both photosynthesis and transpiration in plants [59,60]; however, small fluctuations (e.g., minor precipitation or fluctuating temperatures) during these periods of relatively low activity may have a significant effect on the WUE. As a result, even small fluctuations caused by climate change or environmental changes can appear significant, leading to “significant” or even “highly significant” winter WUE trends. However, July and August were the peak months for crop growth, with high plant transpiration and sufficient precipitation, resulting in a significant upward or downward trend in the WUE during these two months.

Overall, the significant trend in the WUE was notable in the mountainous and plain areas of southern Anhui Province during winter. This seasonal and monthly trend analysis of WUE based on the Sen+MK test clearly shows the spatial and temporal differences in water use efficiency, and provides data support for understanding the water use efficiency in different regions of Anhui Province.

3.2. WUE Analysis of the Five Natural Terrain Areas

3.2.1. WUE Changes in Five Natural Terrain Regions

Anhui Province is divided into five different natural topographic regions: the Huaibei Plain, the Jianghuai hilly region, the hilly mountainous area of southern Anhui, the Dabie Mountain area in western Anhu, and the plain alongside the river. The temporal changes in ET, the GPP, and WUE in these five regions are illustrated in Figure 10. The WUE in the five regions differs, with the highest observed in the hilly and mountainous region of southern Anhui, followed by the Dabie Mountain area, the Huaibei Plain, the Jianghuai hilly region, and the plain alongside the river; the GPP was highest in the hills and mountains in southern Anhui > the Dabie Mountains > the Jianghuai hilly region > the Huaibei Plain > the plain alongside the river, in order from high to low; and ET was highest in the hills and mountains of southern Anhui > the Dabie Mountains > the Jianghuai hilly region > the plain alongside the river > the Huaibei Plain, in order from high to low.

The hilly and mountainous region in southern Anhui and the Dabie Mountains are both blessed with rich forest vegetation, abundant rainfall, and good light conditions, meaning that the vegetation in these two areas contributes a large amount to the GPP. At the same time, under conditions of sufficient light and heat, the ET of these two areas is also the highest in Anhui Province; thus, the WUE is generally high. The Huaibei Plain is the main maize- and wheat-growing region in Anhui Province, and crops are important GPP contributors in this region. However, high rainfall and low ET means that the GPP is the main factor affecting the WUE in the Huaibei Plain [61]. The Jianghuai hilly region and the plain alongside the river are associated with the Huaihe River and Yangtze River running from west to east, respectively; thus, both regions suffer from higher ET in general, with weak photosynthesis and low transpiration, lowering the WUE.

The hills and mountains in southern Anhui showed the largest growth rate, and the plains alongside the river, which was the only region showing a decreasing trend in WUE, the lowest. A growth trend was maintained in the GPP in all regions, with the hilly and mountainous area in southern Anhui showing the highest growth rate, and the Dabie Mountains the lowest growth rate. ET also increased in all regions, with the fastest growth rate in the Dabie Mountains and the slowest in the hilly and mountainous region of southern Anhui. Although the lowest GPP growth was observed in the Dabie Mountains, the highest GPP of the five regions was observed in this region; thus, the highest WUE and the most stable change trend were observed in this region. In contrast, the slow growth trend in the GPP and steady and insignificant increase in the ET in the plain alongside the river indicates that the WUE is mainly influenced by the GPP of this region, with significant interannual changes.

3.2.2. Multiple Fractal Analysis of WUE in Different Natural Terrain Regions

The fractal characteristics of the WUE in the different natural regions were obtained using the differential box-counting method, as seen in Figure 11. The log(r)–log(Nr) double logarithmic plots for these regions show a linear relationship, with fitting ranges between 0.9987 and 0.9997 for the absolute slopes of the least squares fitted line indicating high fitting coefficients, suggesting fractal characteristics and self-similarity for the WUE in the five regions. The fractal dimension D, derived from the slopes, varied between 1.7546 and 1.8539, indicating different degrees of complexity in the spatial distribution of the WUE in these regions. The fractal dimensions from highest to lowest are as follows: the hilly and mountainous region of southern Anhui (1.8539), the Huaibei Plain (1.8525), the Dabie Mountain area of west Anhui Province (1.8486), the Jianghuai hilly region (1.8008), and the plain alongside the river (1.7546). The highest fractal dimension in the hilly and mountainous region of southern Anhui indicates a more complex and uneven spatial distribution in this region, while the lowest fractal dimension observed for the plains alongside the river suggests a more uniform spatial distribution in this area.

The relationship between the partition function and box size for the WUE factors in the five different natural regions of Anhui Province can be seen in Figure 12. The relationship curves, Xq(ε)~ε, are displayed in double logarithmic plots, with similar patterns observed across the five regions. In this study, the q values range from −10 to 10 in integer steps. The double logarithmic curves obtained for the partition function and box size exhibit a good linear relationship, indicating a certain degree of self-similarity for WUE across multiple scales. The different arrangements of log(r) on the axis for various q values indicates significant variation, suggesting a scale dependency with changes in q. When q > 0, the data points incline upward with a positive slope and the slope increases more rapidly, indicating regions with high WUE on larger scales. Conversely, when q < 0, the data points decline downwards with a negative slope, and the slope increases more slowly, indicating that smaller regions are exhibiting low WUE.

The relationship between moment order q and mass index τ(q) in the Huaibei Plain, the Jianghuai hilly region, the hilly area in southern Anhui, the Dabie Mountains, and the plain alongside the Yangtze River can be seen in Figure 13. The function relation of all of τ(q) to q is increased, indicating that for a positive q, the overall heterogeneity increases and a high WUE is more significant. An increasing q is associated with a higher growth rate for τ(q), indicating that all five regions have multifractal characteristics.

The multifractal spectrum curves of WUE for each region and their fitted curves are shown in Figure 14. The calculation curves for the five regions were fitted using a quadratic polynomial, and the curves were found to be similar. Concave f(α) curves indicate widespread heterogeneity within the studied regions; however, the variance in the range of α and the maximum value of f(α) among the regions indicate different degrees of spatial heterogeneity between the regions.

The f(α) curve of the Huaibei Plain is relatively flat and declines slowly at high α values, suggesting low heterogeneity for WUE. The f(α) curve of the hilly land of the Jianghuai River starts at a higher f(α) value and then drops rapidly, indicating significant variability in the WUE. The f(α) curve of the hilly and mountainous area in southern Anhui transitions smoothly from high to low α values, indicating a certain degree of spatial heterogeneity but a relative balance. The f(α) curve of the Dabie Mountains in west Anhui is wide, with high f(α) values in the high α region indicating significant WUE heterogeneity in this area. The f(α) curve of the plain alongside the river drops rapidly from high f(α) values, and the curve width is relatively narrow, indicating relatively uniform WUE in this area.

3.3. WUE Analysis for Eight Major Soil Types

3.3.1. Analysis of WUE Changes in Association with Soil Type

The WUE values for different soil types in Figure 15 indicate that different soil types show a certain degree of fluctuation over the year in terms of the WUE, with large interannual differences and considerable differences observed for different soil types. The WUE value that is associated with the studied soil types is, in descending order, the WUE value for brown soil > chrysolite > cinnamon soil > yellow-brown soil > moist soil > blood paddy soil > krasnozem > southern paddy soil. Brown soil and chrysolite are mainly distributed in the southern Anhui region, which climatically belongs to the transition region from northern to central subtropical, with good rain and heat conditions leading to exuberant vegetation growth. The chrysolite is mainly distributed in this region, where the WUE is high. Paddy soil is important for growing rice due to its highly moist nature; however, rice cultivation requires a certain water level, and the permeability of paddy soil is usually poor. Therefore, the WUE of paddy soil is generally low.

3.3.2. Multiple Fractal Analysis of Eight Major Soil Types

The results of the fractal analyses for each of the eight major soil types in Anhui Province can be seen in Figure 16, in which the log(r)–log(Nr) plots for moist soil, brown soil, chrysolite, yellow-brown soil, yellow-brown soil, southern paddy soil, blood paddy soil, and brown soil are demonstrated. The fractal dimension, D, obtained for the eight soil types ranged between 1.9095 and 2.1668, and the slopes of the straight lines were fitted by the least squares fitted curves. The goodness-of-fit values were generally high, with fit rates R2 ranging from 0.9925 to 0.9975. The obtained fractal dimensions for the various soil types lay in the order of chrysolite > blood paddy soil > yellow-brown soil > moisture soil > southern paddy soil > brown soil > cinnamon soil > krasnozem from highest to lowest.

Figure 17 shows the multifractal spectra of eight soil types ranked from high to low: moist soil, brown soil, chrysolite, krasnozem, yellow-brown soil, southern paddy soil, blood paddy soil, and cinnamon soil. The spectra characteristics differ among soil types. Blood paddy soil’s spectrum has a broad bow at mid–high α values, indicating high spatial heterogeneity. Chrysolite and brown soil show high heterogeneity and complexity, with chrysolite having a higher initial f(α) and wider α range. Moist, krasnozem, and southern paddy soils exhibit more consistent spatial variation and better water retention. Cinnamon soil’s spectrum declines rapidly after a flat peak, influenced by regional distribution, while yellow-brown soil shows greater heterogeneity in moisture distribution with a steady decline.

3.4. Analysis of the Influencing Factors

Anhui Province was divided into five natural regions based on topography and eight major soil types to analyze seven natural factors influencing WUE: the temperature, net radiation, precipitation, LAI, LST, GPP, and ET. Figure 18 shows that precipitation is the key factor for WUE in the Huaibei Plain and southern Anhui’s hills, ET dominates in the river plains and Jianghuai hills, and net radiation is crucial in the Dabie Mountains. The factors affecting WUE vary across regions, with their overall importance ranked as precipitation > ET > GPP > net radiation > temperature > LAI > LST. Specifically, precipitation mainly influences moisture, yellow-brown, and cinnamon soils; ET affects southern paddy, blood paddy, and krasnozem soils; and GPP impacts chrysolite and brown soils in the Huaibei Plain and Dabie Mountains.

In summary, precipitation is the main factor influencing the WUE in moist and chrysolite soils; ET is the main influencing factor for southern and blood paddy soil, and GPP is the main factor influencing the WUE in brown soil regions [62]. These findings indicate that WUE is influenced by various natural factors, resulting in the different WUE characteristics and patterns observed.

4. Discussion

To accurately obtain the temporal and spatial variation characteristics of WUE in response to environmental changes, this study proposed a new framework for exploring the spatiotemporal variation in water use efficiency and conducts fractal analysis on multiple scales to systematically explore the spatiotemporal variation in water use efficiency and its influencing factors. First, the change in water resource use efficiency in Anhui Province was analyzed at temporal and spatial scales. Second, combined with the complexity of the spatial and temporal distribution of WUE under fractal theory, this study provided a targeted regional reference for Anhui Province in terms of water use for agricultural planting and food production.

4.1. Spatial and Temporal WUE Variation Characteristics

Based on the WUE dataset division in Anhui Province on time scales such as years, seasons, and months, combined with the spatial scale analysis of natural areas and major soil types, the spatiotemporal variation characteristics of WUE were investigated. WUE fluctuated greatly in the interannual variation: in 2003, the WUE was the lowest (1.367316 gC·mm⁻¹·m⁻²), the overall GPP was low, and the ET was high, especially in spring, autumn, and winter [63]. Except for July and August, the WUE of the other months was lower than the average for the same month in previous years. This downward trend is mainly attributable to a general decrease in the GPP across the five natural terrain regions [64]. The WUE in 2014 reached the highest value (1.648538 gC·mm⁻¹·m⁻²). Although the WUE in the four seasons of 2014 was consistent with the annual average, the GPP in the five natural topography regions increased significantly with little change in ET; in particular, the WUE in January, July, and August was higher than that in the same calendar year [64,65]. In addition, forest ecosystems generally have a high WUE. In the geomorphic regions of Anhui Province, the highest WUE is found in the southern hills of Anhui Province and the Dabie Mountains of western Anhui Province, which are rich in forest resources [11,66]. Brown soil in the Dabie Mountain area of western Anhui has good water retention and moderate drainage characteristics, which can effectively support crop growth and increase WUE under proper management. The water retention and nutrient absorption of brown soil can be optimized by applying organic matter and regulating the pH value, and the WUE can be further improved [67,68].

4.2. Application Analysis of Multifractals in WUE

The choice of multifractal analysis to study water use efficiency (WUE) is primarily based on the widespread presence of fractal characteristics in nature. Meteorological variables closely associated with WUE, such as temperature, precipitation, and the standardized precipitation index (SPI), often exhibit multifractal properties [26,30,69]. Applying multifractal analysis allowed for a comprehensive understanding of the complexity and fractal patterns within the study area, providing insights into the variations in WUE across temporal and spatial scales.

On a temporal scale, segmenting WUE into annual, seasonal, and monthly intervals enables a precise observation of its nonlinear variability over time. Fractal theory is an effective tool for describing nonlinear characteristics in time series data, with multifractal spectra capturing dynamic nonlinear patterns within WUE fluctuations [69,70]. On a spatial scale, the mountainous regions of southern Anhui, which are characterized by rugged terrain and diverse ecosystems, exhibit pronounced multifractal properties. The topographical features of the area align closely with the fractal characteristics of sloped landscapes [71,72]. In regions with significant elevational changes, multifractal spectra can effectively reveal spatial heterogeneity in WUE. WUE distribution in the hilly areas of southern Anhui displays a right-skewed multifractal spectrum (Δf(α) < 0), suggesting relatively uniform WUE within localized areas but significant differences across varying topographies, highlighting heterogeneity at a broad scale [72,73,74].

The Huaibei Plain, a key agricultural zone in Anhui, displays distinct multifractal characteristics that are predominantly influenced by human agricultural activities. Extensive farming and irrigation practices have had a considerable impact on the spatial distribution of WUE in this area. The plain is largely devoted to staple crops, such as wheat and maize, with irrigation mainly reliant on groundwater and river sources. Variations in irrigation methods significantly influence the efficiency of water resource utilization. In the multifractal analysis of this region, the WUE spectrum also exhibits a right-skewed pattern (Δf(α) < 0), reflecting a relatively consistent WUE at localized scales but noticeable differences in WUE across larger spatial scales among different fields [74,75]. This spatial complexity likely stems from differences in crop water requirements, irrigation management, and the spatial heterogeneity of soil types.

Soil type also plays a crucial role in shaping the multifractal characteristics of WUE. The WUE distribution across different soil types exhibits significant spatial heterogeneity. In particular, soils with high mineral contents and active biological properties tend to show pronounced multifractal characteristics [76,77]. Across five different regions, WUE consistently exhibits a right-skewed multifractal spectrum, where a right-skewed multifractal spectrum (Δf(α) < 0) suggests WUE homogeneity within larger regions but significant differences between distinct areas [75]. Thus, the multifractal analysis revealed the complexity and heterogeneity of WUE at different spatial scales, comprehensively capturing the variation patterns within each area.

4.3. Limitations

First, the WUE data used were derived from moderate-resolution MODIS imagery, which may have limited the capture of finer details because of its relatively low resolution. Second, the study area was limited to Anhui Province; although this region has diverse terrain and soil characteristics, extending the scope to a larger area could enhance the generalizability of the findings. Third, we understand the possible effects of different refined soil types (e.g., sandy loam and black soil) on the WUE. However, because of the relatively low resolution of the dataset in this study, if a detailed soil classification was adopted, the sample data of many soil types would be too small, which would significantly affect the accuracy of the fractal analysis and reliability of the results. Finally, although multifractal analysis revealed the complexity of WUE in different topographic regions, it lacked a detailed comparison of the fractal characteristics of diverse terrains (mountainous and plain areas), particularly the analysis of multifractal characteristics and their driving factors across different topographic or climatic regions. In follow-up research, these areas will be important research directions for coping with complex environmental changes and providing a regional reference for agricultural water use.

5. Conclusions

This study introduced fractal theory to analyze the spatiotemporal distribution characteristics of WUE in Anhui Province using multi-source data, including remote sensing and meteorological data, from 2001 to 2021. The findings were as follows:

(1) Temporal scale: The WUE in Anhui Province showed significant interannual variation, with an overall upward trend. Monthly changes in WUE exhibited an inverted “V” shape, with the highest average WUE in summer and the lowest in winter.

Spatial scale: In terms of the natural terrain, the highest average WUE was found in the hilly and mountainous regions of southern Anhui and the Dabie Mountains in western Anhui. Brown soil exhibited the highest WUE, whereas southern paddy soils exhibited the lowest. The most significant WUE changes were observed in the northern Huaihe Plain and southern Jianghuai hills.

(2) WUE data across multiple spatiotemporal scales displayed clear multifractal characteristics. Specifically, the multifractal features of WUE were similar across different temporal scales, with the most pronounced characteristics observed in summer, especially in August. This suggests that the WUE was less evenly distributed during summer than the other seasons. The spatial distribution of WUE is more complex in mountainous and hilly areas than in the plains. The multifractal characteristics of WUE were evident in regions with brown soil and were often associated with higher self-similarity.

(3) Precipitation was identified as the primary factor influencing WUE in this region. However, when analyzed separately, evapotranspiration played a significant role in central Anhui, whereas precipitation had a greater impact in northern and southern Anhui. These patterns also correspond to the spatial distribution of the soil types.

In conclusion, the introduction of fractal theory into WUE research helps to clarify the complexity across different scales. However, the scales used in the study were not exhaustive. Future research plans include studying WUE across different crop types, growth stages, and vegetation types, and expanding the study area to test the universal fractal characteristics of WUE.