1. Introduction
Pasture grasslands are considered one of the most important ecological systems in the Iberian Peninsula, providing multiple agro-environmental services [
1], including biodiversity and meat production. Several studies [
2,
3] presented pasture grasslands as a spatial temporal-varying complex ecological system involving multiple variables. Thus, historical time-series analysis [
4] is considered an appropriate method to examine and characterise pasture grasslands complexity. In this work, we aim to assess the response of two different Vegetation Indices (VIs) time series to the temporal dynamics of temperature and precipitation in a semiarid area, characterised by a significant presence of bare soil and dead vegetation.
Multiple research studies [
5,
6] demonstrated that climate variables greatly influence vegetation growing. Among them, precipitation, and temperature [
7] have been pointed out as the most direct driver factors for plant growth. Based on this assumption, Gesner et al. [
8] showed that vegetation growth is strongly correlated to temporal and spatial patterns of precipitation in semiarid ecosystems, mainly because of the extreme precipitation events and seasonal shifts that affect vegetation dynamics. The temperature has also been pointed out as a critical driving factor in vegetation activity [
9]. In this way, Piao et al. [
10] reported that temperature showed positive effects on grasslands growth; decreasing, as temperature rises in high-cold areas. In the study area, two zones were selected to observe the interactions between climate and vegetation in two distinct semiarid zones. Both zones presented different precipitation regimes and annual temperatures. Ávila zone (ZAV) showed a lower annual mean precipitation and annual mean temperature in comparison to the Madrid zone (ZMA).
Researchers successfully applied remote sensing techniques in the agricultural [
11,
12] and environmental fields to monitor vegetation cover changes. Nowadays, satellites allow obtaining historical real-time acquisition data [
13] about the vegetation status in vast areas. Optical remote sensing techniques allow tracking vegetation cover due to its specific spectral behaviour in the visible (0.4–0.7 mm) and infrared (0.74–1.11, 1.3–2.5 mm) bands of the electromagnetic spectrum. However, alternative approaches, such as radar techniques, have been pointed out as a promising tool for vegetation monitoring, crop mapping and soil moisture estimation. Synthetic aperture radar (SAR) based on techniques are the most widely used [
14] in the agricultural field of study. Their principal advantages are the capacity to obtain information independent of the weather conditions, minimising the atmospheric effects, and the capacity to penetrate through the soil. However, they also present disadvantages compared to optical remote sensing techniques, such as possible speckle effects [
15], that could reduce the quality of SAR imagery and the disturbance of topography [
16] in hilly regions.
Vegetation indices (VIs) proved to be a powerful tool to characterise vegetation among all the optical remote sensing techniques. They are defined as a combination of two or more spectral bands related to vegetation status. It has been proved that VIs present a close relationship with climate [
17] across different biomes and bioregions [
18]. Significantly, the Normalised Difference Vegetation Index (NDVI) demonstrated an excellent indicator of the vegetation growth conditions [
19,
20] and the biophysical characteristics of ecosystems. Multiple studies revealed [
21,
22] that NDVI is an adequate tool to monitor rangelands conditions, being the most widely used spectral VI [
23] by ecologists and agriculturalists until nowadays. Its efficiency is based on its capacity to reduce variability caused by the reflectance of the soil background [
24], illumination, and view angle variation. NDVI values tend to increase during the growing season, showing the biomass increase due to the intense photosynthetic activity. On the contrary, there is a gradual reduction of NDVI values when there is a lack of water or the temperature is excessively higher.
Several authors [
25,
26,
27] pointed out that differentiated bare soil and dead vegetation are still challenging due to the disturbances in the VIs sensitivity. Regions with sparse vegetation tend to generate high reflectance values that might saturate sensors or produce biased biomass and vegetation cover estimations. Thus, a modified soil-adjusted vegetation index (MSAVI) [
28] was proposed as a solution to consider the soil background effect in semiarid areas. MSAVI has been successfully applied in numerous studies [
29,
30], especially in the estimation of above-ground biomass in semiarid areas.
Previous studies suggested that VIs response to climate differed at different timescales across the year’s seasons [
31,
32,
33]. A high correlation between precipitation and NDVI has been reported at a yearly scale [
6]. On the other hand, on a monthly scale, several studies revealed a delayed correlation between precipitation and NDVI [
8,
34]. Relationships between NDVI and temperature were also reported during specific periods. As an example, Tibetan Plateau (China) grasslands presented positive correlations during the growing season (May–September) [
35]. Found correlations presented spatial–temporal variations [
36], probably due to the differences in environmental factors or plant functional traits over which the correlations were calculated. In this way, researchers suggested that the optimal VI delayed response depends on the climate variable, shifting from one to two months in temperature and precipitation [
37].
In ecological systems, temporal variability is frequently measured as the standard deviation of the records in a time series, though, these systems present nonlinear characters as in any complex system. In particular, VIs time-series present time cycles, allowing agro-environmental system dynamics description [
38,
39,
40]. In this line, Eckmann et al. [
41] introduced recurrence plots (RPs) as a simple way to envision the periodic or chaotic behaviour of a dynamical system through its phase space. Recurrence Plots–Recurrence Quantification Analysis (RP–RQA) are able to measure temporal determinism and predictability [
42]. RPs are used to detect dynamical patterns in time series [
43], and Recurrence Quantification Analysis (RQA) quantifies and characterises the small-scale structures in RP. RPs can be visually interpreted to distinguish non-stationary dynamics with either smooth or abrupt transitions [
44] and finding the presence of periodic and non-periodic processes.
Furthermore, RPs can be extended to include multivariate relationships through Cross-Recurrence Plots (CRPs). CRP is defined as a bivariate extension of RP [
43]. It is computed to analyse two variables by comparing their states and studying the dependencies between two different systems; it may be regarded as a nonlinear cross-correlation function. Multiple works analyse the behaviour of the VIs time series through RPs analysis. Li et al. [
45] computed RPs to study the determinism and predictability of the NDVI series and its spatial patterns. Zurlini et al. [
46] showed the landscape changes after a burn through RPs methodology on Enhanced Vegetation Index (EVI) time series. Semeraro et al. [
47] showed the drought effects on a zone in the Amazon forest through RPs on MODIS EVI time-series.
Specifically, this study attempts to answer if: (i) VIs are an adequate tool to reflect the complexity of the relationships between vegetation and climate in grasslands, (ii) MSAVI performs better than NDVI to assess the vegetation response in a semiarid area and (iii) the recurrence plots methodology is a complementary tool to the study of the complexity of grassland ecosystems. This work is organised as follows: In
Section 2, we present the study plots and the methods used to relate and compare the VIs response to climate in two different zones. In
Section 3, we emphasise the main results of the paper. Then, in
Section 4, we discuss the remarkable outcomes of the research. Finally, we present the key conclusions of the paper in
Section 5.
3. Results
3.1. Soil Line Acquisition
The soil line was calculated for each studied plot in each zone, and the results are displayed in (
Figure 2). RED-NIR method’s linear regression displayed an R2 > 0.90 in all the cases. ZAV
s values were higher than ZMA in most cases. We could not detect significant differences between the
s values from ZAV and ZMA, even if the
s average in ZAV (1.40) tends to be higher than in ZMA (1.17).
3.2. Inter-Annual Analysis
In the time series, VIs, temperature, and precipitation values were higher in ZMA than ZAV (
Figure 3). VIs and precipitation displayed a descending trend over the years in both zones. In contrast, temperature showed an ascending trend in both zones. All the estimated slopes were non-statistically significant (
Supplementary Material Table S1).
Generally, an inverse relationship was observed between VIs and temperature fluctuations (
Figure 4). For instance, in 2009 and 2017, the temperature was remarkably higher in both zones; consequently, NDVI and MSAVI showed a severe fall. In contrast, we detected a direct relationship between VIs and precipitation. Usually, when precipitation was limited, VIs tended to be reduced. This tendency was observed over 2009 and 2017 in ZAV, and over 2003–2004 in ZMA, respectively.
In general, we detected that both VIs showed similar inter-annual variations in both zones. However, there were unusual VIs changes in certain years, i.e., in 2007, VIs showed a remarkable rise, even when temperature and precipitation did not show a notable change of trend.
3.3. Intra-Annual Analysis
The VIs phases were closely related to the Mediterranean climate seasons (
Table 2), being (P1 and P2) the cold season, (P4) the hot season and (P3 and P5) the transitional periods. Chow’s test revealed that all of them were significantly different from each other (
Supplementary Material Table S2). We found that VIs, temperature, and precipitation were higher in ZMA than ZAV on an intra-annual scale (
Figure 5). We also observed that VIs and precipitation were notably different between zones in P2 and at the beginning of P3 and P5. It should be noted that ZMA VIs declined faster in P3 and increased quicker in P5 than ZAV VIs. NDVI dispersion was generally greater than MSAVI. At the same time, VIs and precipitation showed a higher data dispersion in ZMA than ZAV. Both variables reached their dispersion peak in the same period of the year (P3 and P5).
Based on the box plots results, it was observed that P1 and P4 phases did not show any variation along the time, being stable and less dispersed than the other phases. For this purpose, linear regression analysis between VIs and climate variables was conducted only in the phases in which a trend was observed in VIs (
Figure 6 and
Supplementary Material Figure S1). In this way, the most critical vegetation–climate driving factors were detected. Generally, the temperature was identified as the potential driving factor in the vegetation–climate system as it showed R
2 > 0.9 in all the studied phases in both zones. We observed that the temperature trend varied throughout the year, being positive in P2 and negative in P3. Instead, precipitation showed lower R
2 values than temperature, being the highest (>0.7) in P3, and maintained the same positive trend in all the phases. From this point, we detected that both indices showed similar behaviour, though, generally, MSAVI showed better results, suggesting that its dynamics would be more distinct than NDVI. Thus, NDVI analysis and results are presented in the
Supplementary Material.
3.4. Time-Series Correlation
Pearson’s coefficients analysis revealed that all correlation coefficients between VIs and meteorological time-series were statistically significant along the time (
Table 3 and
Supplementary Material Table S3). The corresponding Pearson’s coefficients for temperature showed a negative relationship, whereas precipitation displayed a positive relationship. The temperature was the most correlated variable, and partial coefficients indicated that temperature is the main driving factor in the relationships between climate variables and VIs.
Cross-correlation showed the sinusoidal behaviour of the climate variables and the seasonality of VIs (
Figure 7 and
Supplementary Material Figure S2). The Lagτ varied between variables and zones, i.e., MSAVI-PCP showed an Lag of −2 (16 days) in ZAV, while Lag was of −3 (24 days) in ZMA. The Lag also fluctuated depending on the VI used, NDVI could not differentiate precipitation lags between zones; meanwhile, MSAVI distinguished them.
3.5. Correlation by Phase
Pearson correlation coefficients by phases (
Table 4 and
Supplementary Material Table S4) indicated that VIs dynamics varied over a year. Correlation coefficients varied between zones, being the highest difference in P3 and P5. The temperature was the most correlated climate variable, achieving values higher than 0.7 in P3 and P5 in both zones and VIs. As expected, there were some inaccuracies in the precipitation; thus, it was not possible to obtain high correlations values (<0.5). However, in P3, MSAVI showed significant results (0.270 in ZAV and 0.248 in ZMA), most likely due to the decrease of MSAVI data dispersion during the dry season.
A fluctuating lag was observed in cross-correlation coefficients by phases, pointing out the different VIs dynamics during a year (
Table 5 and
Supplementary Material Table S5). The most correlated variable was the temperature. Precipitation did not achieve higher correlation values, though a lag was needed in all the cases. As a result, the correlation by phase method improved the correlations in all the precipitation cases. Overall, cross-correlation by phases was significant in P3 and P5, allowing us to achieve better correlation coefficients than time-series analysis, regardless of VI and zone.
In NDVI and temperature, ℓ varied in both zones from zero in P2 to 5 (40 days) in P5. In the MSAVI case, temperature ℓ showed a similar pattern to the NDVI case, varying only in the P5 phase on ZMA. Concerning precipitation, in the NDVI case, an ℓ of 2 (16 days) was found in all the phases studied for both zones. Though, MSAVI showed different precipitation ℓ depending on the zone and the phases. Precipitation ℓ was 3 (24 days) in the phases when the VI increases (P2 and P5) in both zones. In P3, with a decreasing trend in the VI, the precipitation ℓ was 2 in Avila and 1 in Madrid. This fact pointed out a higher precipitation MSAVI sensitivity and recognised ℓ as a variable able to distinguish different zones in the same phase.
MSAVI performance was better than NDVI in winter and at the beginning of the spring (P2). It was remarkable because precipitation dispersion reached its peak during this phase. This fact might reveal that MSAVI might improve NDVI results in the springtime at a correct time scale. It is recommendable to analyse both series from a dynamic point of view, emphasising the behaviours of MSAVI in both zones.
3.6. RPs Characterisation and Recurrence Diagonal Profile
The Optimizeparam function was computed to estimate the parameters of RPs and showed that the embedding dimension (m) increased in all VI series for both zones (
Table 6 and
Supplementary Material Table S6). In the case of NDVI, m was 2 for both zones, then for the MSAVI case, m was 6 for ZAV and 8 for ZMA. The τ ranged from 8 to 11 varying between zones. The same dimensionality increase was detected in the climate variables where precipitation showed a higher dimension than the temperature in ZMA, pointing out a higher precipitation complexity than temperature.
NDVI RPs showed a noisy behaviour, characterised by many isolated points. Meanwhile, MSAVI RPs showed white stripes on a large scale (
Figure 8 and
Supplementary Material Figure S3). Furthermore, we could observe that MSAVI RPs present small-scale structures and periodic patterns (diagonal line like-shapes). This kind of structure is visible in the temperature RP, where we could observe the temperature seasonality through diagonal-like structures. At the visual inspection, we did not detect significant temperature changes between the two zones.
In contrast, precipitation RP showed a distinct pattern in each zone. In ZAV, we could observe a block-like structure, whereas, in ZMA, we could distinguish a more line-like pattern. This difference was likely due to the different precipitation regimes in each zone.
We found that the profile tendency varied between VIs and zones (
Figure 9 and
Supplementary Material Figure S4). NDVI showed a more distinctive RR drop on the first days (0–8 days) in both zones. In contrast, MSAVI maintained higher values of RR until 16 days. As expected, temperature showed similar behaviour in the two zones. Meanwhile, PCP showed a different maximum lag. Both PCP profiles showed lower values of RR from eight days till the end. We speculate that different maximum lags are a consequence of the different PCP distribution in both zones.
3.7. CRPs Characterisation and CRPs Diagonal Profile
Once RPs were constructed, the maximum m and τ for the two time series were selected as the parameters to the construction of CRPS (
Table 7 and
Supplementary Material Table S6), then a RR of 5% was selected for all of them.
We detected the seasonal temperature effect on the VIs dynamics in the CRPs (
Figure 10 and
Supplementary Material Figure S5). In the case of NDVI-TEMP, we could not distinguish between zones. However, MSAVI-TEMP showed a different pattern in each zone, probably due to the distinct MSAVI dynamics that distinguish between different CRP patterns. Cross-recurrence profile allowed us to distinguish the interactions between VIs and climate variables in the LOC and the surroundings lags. The temperature did not show a difference between zones. As we observed in TEMP-VIs CRPs, the LOC was non-existent (
Figure 10 and
Supplementary Material Figure S5), and the surrounding regions were similar. Then it was expected that RR was near zero on the first lags. We believe that this fact was due to the temperature seasonality not being detected on the first lags.
In contrast to the temperature, CRPs of precipitation and VIs were able to characterise a different dynamic in each zone. In this case, we observed that NDVI-PCP CRPs showed vertical lines in ZAV and diagonal-like structures in ZMA. In MSAVI-PCP CRPs, the most distinct region zone occurred during 400–600 time-units, where ZMA presented an isolated point structure, while ZAV did not show any recurrence in that timeframe. This fact might be explained due to the increase of dimensionality produced by the precipitation in the CRPs. VIs-PCP recurrence profile showed an evident maximum lag of 16 days in the ZMA. In contrast, the ZAV presented a lower RR in precipitation, and the maximum lag was not evident, presenting a more stable recurrence profile. This difference can be explained because the CRQA analysis detected a higher number of precipitation events coupled to the MSAVI index, showing a more evident maximum lag. in the ZMA zone.
3.8. Recurrence Quantification Analysis of RPs and CRPs
Now, we present the values of DET, LT, ENTR, LAM and TT. The DET is related to the system’s random or periodic behaviour based on the density of recurrence points, being higher when the system shows more periodical behaviour. The MSAVI presented a higher DET in both zones, being ZMA the highest. DET obtained in precipitation RP was higher in ZAV than ZMA.
Concerning CRPs, MSAVI-TEMP showed a higher DET than NDVI-TEMP. Both of them showed a higher DET than PCP CRPs. MSAVI-PCP showed a DET increase in comparison to NDVI-PCP in ZMA. We believe that MSAVI could characterise better precipitation data dispersion, allowing us to improve the NDVI results in ZMA.
The LT is interpreted as the system’s predictability time, increasing when the predictability time is longer. The LT values in both VIs obtained were low. Temperature showed a higher LT than precipitation, suggesting that temperature predictability time was higher than precipitation. In CRPs, we observed similar results, being the LT of VIs-TEMP higher than VIs-PCP.
The ENTR value refers to the disorder of the system. MSAVI RPs showed a higher value than NDVI, higher in ZMA than ZAV. Concerning climate variables, temperature showed a higher ENTR than precipitation in their separate RPs and their CRPs with VIs.
The LAM value refers to the chaos–chaos transitions and is directly related to the detection of laminar states. The MSAVI LAM was higher than NDVI. Generally, temperature showed higher LAM values than precipitation. We also noticed that when precipitation was involved, LAM values tended to decrease in the CRPs, being temperature the highest in both cases.
The TT represents the average length of vertical structures and indicates how long the state will be trapped at the same time. The MSAVI showed a higher value of TT in both zones. In the climate variables RPs, Temperature TT was higher than precipitation TT. The same phenomenon happened in the CRPs, where TT was higher in VIs-TEMP than VIs-PCP.
4. Discussion
Concerning
s values, we obtained different values of
s in each zone. According to [
60]’s findings,
s increased when soil moisture grew. As shown in
Table 1, ZAV topsoil was more clayey and less sandy than ZMA soil. Thus, a higher water holding capacity (WHC) was expected in ZAV than ZMA, explaining the differences between zones. We could not obtain significant differences between the
s values from ZAV and ZMA, most likely because of the litter and non-photosynthetic material influence [
61].
Temperature and precipitation yearly tendencies found in this work are consistent with what was reported in previous studies, where the temperature is increasing, and precipitation is decreasing in semiarid zones due to the climate change effect [
62,
63]. We detected specific years when VIs dramatically dropped (2005, 2009, and 2017). These years coincide with drought periods [
64,
65] that happened in Spain (2004–2008 and 2016–2017). These phenomena most likely negatively affected the vegetation growth; thus, VIs values decreased during this time. We expected a non-significant result in the trend slope because environmental works suggested a significant data quota is needed to obtain trustworthy climate trends at a yearly scale [
66].
We obtained different inter-annual trends depending on the climate variable. An inverse relationship between temperature and VIs was found, in agreement with previous research [
67], pointing out that NDVI and other optical indices are generally inversely related to temperature. In contrast, the precipitation was directly related to VIs. This fact ties nicely with previous studies [
68] wherein precipitation events were related to vegetation growth, leading to increased VIs values.
Both VIs used the same NIR-RED spectral bands, leading to a similar performance [
11]. However, the soil factor’s addition in the MSAVI case was expected to increase the sensitivity in semiarid areas [
27,
28,
69]. In our results, MSAVI showed lower dispersion than NDVI, pointing out a better potential for characterisation of semiarid pasture grasslands.
Several studies [
62,
63,
70] emphasise that precipitation and temperature combine in a dynamic and complex system; thus, their networks must be considered. As was reported by Suzuki et al. [
71], NDVI could be affected by other complementary variables, such as evapotranspiration, that depends on the combination of local wetness and warmth. The lack of these variables might explain the unusual behaviours in the VIs time series that are not directly related to temperature or precipitation.
We believe that ZMA VIs were higher than ZAV because of the higher amount of precipitation in ZMA during P2 and at the beginning of the P5 phase. Precipitation events increased soil moisture leading to an increment in vegetation growth that VIs detected. We speculate that the interaction between soil moisture and soil texture with the vegetation in P2 and P5 might explain the differences between zones [
72]. At the end of the rainy season (P2), both soils’ water storage is likely to be highest after the winter water recharge. However, water holding capacity was lower for the sandy than for the clayey soil (
Table 1), and so less water was available in the ZMA than in the ZVA soil. During P3, the temperature raised, then the pasture in the ZMA depleted the soil water more quickly than in the ZAV. Therefore, ZMA vegetation decreased faster than ZAV (
Figure 5). A similar effect took place at the beginning of the P5. Water storage in both soils was expected to be the lowest due to the previous dry season (P4). During P5, precipitation increased in both zones. ZMA sandy soil permeability was higher than ZAV clayey soil allowing a faster increment in ZMA vegetation than ZAV.
We detected an increase in the VIs dispersion during P3 and P5. This variability increase was expected due to the precipitation variability increase that occurred during spring and autumn. As reported by Grant et al. [
73], precipitation variability leads to increased soil moisture variability. Therefore, grassland productivity is altered due to water availability fluctuations, leading to higher variability in VIs results.
Fu and Burgher [
74] pointed out the temperature as the most potential driving factor in NDVI dynamics. They also revealed that temperature harms NDVI as we detected the same result in P3. This effect is explained by the limitation in vegetation growth produced by higher temperatures and fewer precipitations during the dry season. These climate conditions enhance the intensity of transpiration and reduce the available soil water [
17]; thus, vegetation growth is expected to be limited in these unfavourable conditions.
Precipitation was the only variable that maintained the same positive trend in all the phases, pointing out that precipitation is regularly favourable in semiarid grassland growth. The same conclusion was achieved by Sala et al. [
75], which presented a positive relationship between precipitation and pasture grasslands growth because of the soil moisture’s positive role in biomass production.
Multiple works have demonstrated transparent relationships between climate and VIs response [
8,
76]. Our results agree with [
9], who showed a negative relationship between temperature and NDVI. In line with Liu et al. [
68], we also found a positive correlation between precipitation and VIs in the semiarid area pasture grasslands.
Cross-correlation results allowed to expose the seasonal behaviour of the VIs over time. Simultaneously, we also observed that there was a lagged response between VIs and climate variables. In line with this idea, most studies indicate an (up to) 3 months lagged relationship between VIs response and climate variable effect [
67]. The range of the period appears to be related to the studied area’s specific characteristics, such as climate, topography, and soil type, affecting VI lagged response [
77,
78].
The VIs seasonal behaviour also plays a crucial role in the VIs dynamics [
79]; therefore, we obtained different strengths in the relationship between VIs and climate over the year. As Helman et al. [
80] reported, NDVI showed a better response to grassland vegetation during wet seasons due to the herbaceous vegetation’s growth in the Mediterranean climate. This effect might explain the higher correlation found in P3 and P5 phases, coincident with the Mediterranean weather’s wet seasons. The same idea might be suggested to the differences between ZMA and ZAV, being ZMA wetter than ZAV.
We achieved better precipitation correlations when the year was divided into phases, although they were not as high as the temperature. This fact is consistent with [
81] work suggesting that Mediterranean precipitation is characterised by a complex seasonal variability pattern, with large and unpredictable rainfall fluctuations from one year to the other, hindering the relationship between precipitation and VIs.
Once the year is divided into phases, our results highlight a variable lag’s usefulness depending on the year’s season to characterise the vegetation–climate system. This result agrees with Zhang et al., study [
33] that supports the idea of a variable
ℓ along the time. In their case,
ℓ varied from 0 to 90 days depending on the season and the climate variable.
In line with this idea, [
62] suggested that the season of the year and the type of vegetation cover are critical in the
ℓ estimation. Even more, other authors indicate that local conditions are crucial in the estimation of
ℓ. Suzuki et al. [
71] revealed that the NDVI lagged response changed inside the same study area. In the northern, NDVI varied because of the warmth variations. On the other hand, in the southern, NDVI varied due to the inter-annual wetness fluctuations instead of warmth changes.
From another point of view, several authors reported that
ℓ depends on the observed time scale. Cui and Shi [
7] found a 30-day NDVI lagged response to precipitation. Meanwhile, Wang et al. [
6] suggested that the bi-weekly lag was the most correlated. As we stated before, it is essential to note that these relationships were found in these local conditions and the proposed phases. If the analysis is applied to a broader area, the relationships might not be statistically significant as the conditions could differ in space and time [
82].
We already emphasised the incredible complexity of the vegetation–climate system in the previous analysis. Ecological systems present nonlinear dynamics, combining chaotic and periodic cycles, whose equations controlling the systems are unknown [
83,
84]. Thus, the nonlinear analysis provides complementary information about the system. In our work, we detected a dimensionality increase in MSAVI RPs. More detailed soil information was introduced through L in the MSAVI series; thus, a higher embedding dimension was expected. This result agrees with previous literature findings [
85,
86], which relate dimensionality increases to complexity increases. In this line, Marwan et al. [
87] demonstrated the usefulness of RPs to describe nonlinear behaviours in high-dimensional systems, such as VI time-series.
In MSAVI RPs, we found white stripes in the RPs pattern. These structures are related to atypical values and an interruption in the vegetation pattern [
42]. We believe that this behaviour is due to an extreme climatic event that increased soil moisture; consequently, VI series values atypically increased, being detected in the MSAVI RPs.
Diagonal-wise profiles of the CRPs revealed the maximum lag in each zone, and it is expected to vary between zones, seasons, and vegetation cover. Several lags have been reported in the literature. Cao et al. [
77] reported a twenty-day lag in precipitation and temperature in Xinjiang’s arid area (China). In contrast, Richard and Poccard [
88] reported a maximum lag of three months in South Africa.
Other authors refer to seasons as the most crucial factor in the variation of maximum lag. As reported by Zhao et al. [
89], precipitation showed a 1–2 month lag in spring, whereas maximum lag is reduced to 1 month in the Autumn season. They also revealed that temperature showed the same lag as precipitation in the spring; however, maximum lag might be increased up to 3 months in autumn. This result is in concordance with the recurrence profile results, where the temperature did not show an evident maximum lag in the first 50 days.
The CRQA analysis allowed us to quantify the different dynamics of the VIs and climate variables. The DET value has been utilised to indicate climate stability [
45] or detecting bioclimatic transitions [
40]. The MSAVI time-series showed a higher value of DET in comparison to NDVI. Our results suggest that MSAVI allowed us to characterise the semiarid grasslands better. We speculate that soil moisture is being detected by the MSAVI index, allowing us to improve the NDVI results in ZMA. The same phenomena happened in the VI-PCP CRPs, where MSAVI achieved a higher DET value than NDVI in ZMA. Our results agree with Marwan et al. [
87] that found a higher DET in a humid grassland area than a dry grassland.
Regarding LT, both VIs obtained low values compared to the periodic series [
40]. This fact might indicate that vegetation may be predicted in the short term due to the incredible complexity of ecological systems, as reported by Beckage et al. [
90].
Now, let us discuss the values of ENTR, which refer to the disorder of the system. Standard values obtained by Zhao et al. [
40] noted that stochastic systems tend to obtain lower ENTR values (0.2) in comparison with those of periodic systems (2.20). We speculate that the high value of ENTR in the MSAVI case (see
Table 8) is the consequence of the high number of precipitations in ZMA. Marwan et al. [
87] sustained this fact, suggesting that wet grassland areas tend to obtain higher ENTR values than dry grassland areas.
The LAM and TT are related to the vertical structures created in the RPs and CRPs. LAM refers to the chaos transitions and represents the number of laminar states [
91]. MSAVI presents a higher value than NDVI, indicating that values are trapped during specific periods, decreasing time-series dispersion, and supporting the idea of higher predictability and determinism of the MSAVI index. TT represents the average length of vertical structures and indicates how long the state will be trapped, while MSAVI showed a higher TT value than NDVI. We believe that this fact is the consequence of the behaviour of each time series. MSAVI is less dispersed, and then it is expected to be trapped in similar states much longer than NDVI. The same principle might be applied to temperature and precipitation. Temperature is seasonal and did not dramatically change between two consecutive measures. In contrast, precipitation is erratic, and it is not equally distributed over time [
81], especially in the Mediterranean climate.
Overall, our results highlight the incredible complexity of the grassland system. We observed that the time scale is a critical component in the analysis of the VIs series. At the same time, we prove that RPs, CRPs and CRQA are a promising analysis that could provide complementary information about the system dynamics that the linear methods could not describe.