**1. Introduction**

The changes in hydrology and water resources caused by climate change have stimulated hydrologists to pay attention to and study the impacts in this field, which have become one of the popular issues at home and abroad [1–3]. Runoff change is mainly affected by climate change and underlying surface conditions [4–6]. The most important manifestations of climate change on runoff are the changes in rainfall amount and temporal and spatial distributions [7]. Climatic and hydrological processes have highly non-linear and unstable characteristics due to the complex exchange process of the Earth's atmosphere system [8–10] and the difference in watersheds' geographical and human environment characteristics; these characteristics cause great difficulties in the simulation and prediction of hydrological changes. Therefore, studying the multi-scale evolution law in the interaction process between meteorology and hydrology has scientific significance for the management and optimal regulation of water resources in river watersheds.

**Citation:** Wu, L.; Wang, S.; Bai, X.; Chen, F.; Li, C.; Ran, C.; Zhang, S. Identifying the Multi-Scale Influences of Climate Factors on Runoff Changes in a Typical Karst Watershed Using Wavelet Analysis. *Land* **2022**, *11*, 1284. https://doi.org/ 10.3390/land11081284

Academic Editor: Ilan Stavi

Received: 6 July 2022 Accepted: 8 August 2022 Published: 10 August 2022

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Most of the previous studies have focused on the correlation between meteorological factors and runoff, but limited analysis has been conducted on the multi-temporal characteristics of runoff and major meteorological elements [6,11–17]. In addition, the traditional hydrological research methods, such as linear correlation, the Pearson correlation coefficient, the linear trend method and the multiple regression method, can only reveal the variation characteristics on a single time scale. The evolution relationship and interaction characteristics of the two hydrometeorological variables on multi-time-scales are impossible to demonstrate. Spectral analysis and spatial coherency can reveal the scale-dependent relationships between the variables but are only applicable to stationary systems. Hydrometeorological series behavior belongs to non-stationary systems [18]. Wavelet analysis can deal with non-stationary data series and thereby provide an opportunity to analyze the temporal patterns of hydrometeorological series at multiple scales.

The climatic factor is the driving factor of runoff change; therefore, different time scale correlations must exist between runoff and the climatic factor in its oscillation frequency. Wavelet analysis, especially cross wavelet analysis, had been gradually applied to the analysis and study of runoff changes and meteorological factors in river watersheds on multi-time-scales in recent years [19–21] and had also been used to determine the overall and scale-dependent similarities of the temporal patterns of soil moisture [22]. Multiresolution analysis (MRA) can study signals represented at different resolutions [23]. This method can be used to decompose a signal into a progression of successive approximations and details in increasing order of resolution [24]. Continuous wavelet transform (CWT) is a common tool for analyzing localized intermittent oscillations in time series, and it is often desirable to examine two time series together that may be expected to be linked in some way. We can show the strength of sequence signals at different time scales by analyzing the wavelet power spectrum. cross wavelet transform (XWT) will expose their common power and relative phase in time–frequency space and can reflect that two sequences have the same energy spectrum region after wavelet transform, thus revealing the significance of the interaction between the two sequences in different time–frequency domains. Wavelet transform coherence (WTC) can find significant coherence although the common power is low [19]. In this field, CWT has been recently used to determine the effect of climatic phenomena on stream flow regimes [25–28], runoff processes [29–31], surface–groundwater interactions and the hydrogeological behavior of karst systems [32,33]. Furthermore, XWT, which has strong signal coupling and resolution ability, can show the common high-energy region and phase correlation of two time-series data. However, XWT has a great unsolved shortcoming that cannot find significant coherence when analyzing the low-energy regions of two time series' data in the time–frequency domain, and its functional defects in the low-energy areas must be compensated for by WTC [34]. In view of this, the coupling of MRA, CWT, XWT and WTC will be generally applied in the field of hydrometeorology.

At present, the implications of climate and anthropic pressures on the short- to longterm changes in the water resources of a Mediterranean karst were assessed by using wavelet analysis [23], and the non-stationary relationships of ocean and atmosphere mean conditions and freshwater discharge, which were integrated at the continental scale, were studied by using XWT [27]. In addition, the impacts of rainfall, air temperature and evapotranspiration on the annual runoff in the source region of the Yangtze River were investigated in the time domain by using wavelet analysis and multiple regression [17]. WTC was used to determine the overall and scale-dependent similarities of the temporal patterns of soil moisture in the karst catchments of Southwestern China [32]. CWT analysis was used to detect the trends and periodicity in sediment discharge, whilst WTC was used to detect the temporal covariance between sediment discharge and water discharge, rainfall, potential evapotranspiration and vegetation index in two typical karst watersheds in southwest China [33] and to assess the relative importance of catchment properties in modulating streamflow and modes of variability in West Africa and Central Africa [35].

Karst landforms are developed in highly heterogeneous carbonate rocks that are easily eroded by flowing water, widely distributed in Southwest China and generally have different hydrogeological characteristics from non-karst areas [36]. Thus, the karst watersheds are characterized by broken surfaces, low runoff coefficients, serious underground leakage, thin surface soil and poor regulation and water conservation capacities [37–40]. The unique two-dimensional/three-dimensional hydrogeological structure can accelerate the hydrological process [41,42]. In particular, rainfall drains rapidly to underground systems through numerous cracks and fissures [40,43–46]. The soil–epikarst system plays important roles in runoff generation due to the large storage capacity and high infiltration rate of karst carbonate fissures and fractures [2]; consequently, runoff changes in karst areas are sensitive to climatic factors, and small climatic fluctuations will cause large fluctuations in runoff. The appearance, storage and circulation of water in karst aquifers are apparently different from those of water in non-karst areas. The special hydrological process in karst areas will lead to the influence of climate change on runoff with time lag or advance at different time scales. In addition, the hydrometeorological evolution in karst areas has obvious seasonal and multi-scale characteristics. Significant differences exist in the evolution and influence relationships at different scales, especially the intrinsic relationship between monthly and seasonal rainfall, evaporation, temperature and runoff; their vibration energy distribution characteristics and correlations in time and frequency domains are extremely complex. Numerous studies have focused solely on non-karst watersheds. On the contrary, the impacts of climatic factors on runoff (surface runoff) changes have rarely been identified for karst watersheds. Specifically, the research on the time-varying characteristics of climate and runoff and their coupling relationship in karst trough valley watersheds is scarce. Therefore, the objectives of this study are to (1) analyze the multiscale temporal variability effects of runoff with climatic factors, (2) characterize the coupling relationship between runoff and climatic factors in common high- and low-energy regions and high-correlation regions at different time scales and (3) provide a theoretical basis and technological support for water resource safety management in karst watersheds.

#### **2. Study Site**

The Yinjiang River watershed (108◦21 21–108◦47 27 E, 27◦53 17–28◦13 57 N), which is located in northeast of Guizhou Province (Figure 1a), is a typical karst watershed of a trough valley, SW China. It covers an area of 691.56 km2, with the karst area of 376.77 km2 and non-carbonate rocks area of 314.79 km2, accounting for 54.68% and 45.32% of the total watershed area, respectively. Elevation in the study area decreases from southeast to northwest, ranging in a large scope with an elevation range of 439–2466 m above sea level and a mean elevation of 1033 m above sea level (Figure 1b).

The southeast part of the watershed is dominated by non-karst areas, and the karst is widely distributed in the middle and northwest parts of the watershed. A small number of banded non-karst regions are concentrated in the western, central and northern parts of the watershed. Six types of lithology are present, namely, homogenous limestone, interbedded limestone and clastic rock, clastic rock of limestone interlayer, non-carbonatite, homogenous dolomite, mixture of homogeneous limestone and dolomite (Figure 1c). A karst valley with a geographical background of a syncline structure in the center of the valley with steep bedding slopes exists on both sides. The land surface is steep and broken with numerous underground cracks, causing a severe underground loss of rainfall and runoff. The middle part of the watershed is a typical deep-cut karst trough valley, and the middle part of the trough is a karst valley with a synclinal structure as its geological background. Both sides of the trough are steep beddings or inversion slopes, and the top of the trough is over 1000 m above sea level; thus, it has a good ecological three-dimensional climate characteristic.

**Figure 1.** Location and overview of the study area. Study area location in China (**a**), topography (**b**) and lithology (**c**) in Yinjiang River watershed.
