# Multiscaling NDVI Series Analysis of Rainfed Cereal in Central Spain

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Description and Zones Selection

#### 2.2. Soil and Weather

#### 2.3. Earth Observation Data

#### 2.4. Plots and Pixels Selection Criteria

#### 2.5. Soils Reflectance Characteristics

#### 2.6. NDVI Series and Statistics

#### 2.7. Generalised Structure Function (GSF)

_{i}), (i = 1, 2, 3,…, N) in which the fluctuations are assessed. These fluctuations can follow a random behavior (Brownian motion) in which the variance is proportional to time intervals of t

_{i}and can be computed through the Hurst exponent H$:\sqrt{\u2206{f}^{2}}\propto {\left(\u2206t\right)}^{H}$ where H is the power exponent in the range of 0.00 < H < 1.00 [55]. A Hurst equal to 0.50 indicates Brownian motion and characterizes non-memory signals. For Values from 0.50 < H < 1.00, the signal is persistent, showing a trending behavior in which the past signal influences the following data sequence and for H. Values ranging 0.00 < H < 0.50 are referred to as the most common signal in nature and show anti-persistent behavior. When the series is anti-persistent, this suggests that the series shows sensitivity to external forces with short-term variations. Thus, an increase will most likely be followed by a decrease or vice-versa (i.e., values will tend to revert to a mean). This means that future values tend to return to a long-term mean.

_{q}parameter is scalar depending on q at any power of ∆i, suggesting in this case that q has a variable relationship with H and $\zeta \left(q\right)$ is the exponent of the structure function (Equation (2)). Thus, the exponent H can be defined for a hierarchy using the $\zeta \left(q\right)$ as:

## 3. Results

#### 3.1. Soils Reflectance Statistics

#### 3.2. NDVI Statistics

^{2}higher than 0.95 in both sites. However, the slope of each one presents different values.

#### 3.3. Scaling Characteristics of NDVI Original Series

#### 3.4. Scaling Characteristics of NDVI Residual and Anomaly Series

## 4. Discussion

#### 4.1. Agroclimatic Zone and NDVI Patterns

#### 4.2. Scaling Characteristics of NDVI Original Series

#### 4.3. Scaling Characteristics of NDVI Residual and Anomalies Series

## 5. Conclusions

- Data from Earth observation, in this case the MODIS satellite, through the soil reflectance differences validated the soil units from a digital soil mapping approach with the self-organizing map (SOM) algorithm.
- NDVI descriptive statistics show a significant difference between the two agroclimatic zones that mainly differ in soil physical properties and the precipitation regime.
- NDVI series exhibits a persistent structure and a clear multiscaling nature.
- When NDVI residual and anomalies series are analyzed, the pattern changes to an anti-persistent structure and a weaker multiscaling nature.
- Generalized Hurst exponents got from NDVI anomaly series can complement agroclimatic zone characterization.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Location of the two agroclimatic zones as case study in the midlands of Eresma-Adaja (EA) watershed. Selected areas with similar edaphoclimatic conditions, denoted as SOM5 and SOM15 that overlies the subbasins 50 and 24 respectively, adapted from [30].

**Figure 2.**Workflow of the sampling method and information extraction from Earth observations and soils map.

**Figure 3.**Intervals of confidence plots from the Least Significant Difference test (LSD) for SOM5 and SOM15 at DOY 49. (

**a**) NIR, (

**b**) Red, (

**c**) Blue, (

**d**) MIR mean band values.

**Figure 4.**Soil lines for SOM5 and SOM15 soil units. NIR and Red values for DOY 49 in the period 2000 to 2019. Slope of linear regression indicates bare soil line (BSL) value which identifies the lowest NIR values for each level of red.

**Figure 5.**Average of NDVI for each DOY and for monoculture cereals crop cycle of SOM5 and SOM15 in comparison with precipitation (bars) for the period 2000 to 2019. The x-axis indicates Day of the Year (DOY) and the cycle starts in October as the same as hydrological cycle in Spain.

**Figure 6.**Linear correlation between accumulated values of precipitation and NDVI patterns from January (DOY 01) to May (DOY 145).

**Figure 7.**NDVI time series from SOM5 (left column) and SOM15 (right column): (

**a**) NDVI original, (

**b**) NDVI residual, (

**c**) NDVI anomaly. In x-axis is represented the year which includes 23 data points from day of the year (DOY) 1 to DOY 353.

**Figure 8.**Generalized Structure Function plots for NDVI original series of SOM5 (left column in blue) and SOM15 (right column in red) for: (

**a**) ζ(q) curve and (

**b**) Generalized Hurst exponent H(q), continuous line correspond to non-correlated noise with Hurst value of 0.5.

**Figure 9.**Generalized Structure Function plots for NDVI residual series of SOM5 (left column in blue) and SOM15 (right column in red) for: (

**a**) ζ(q) curve and (

**b**) Generalized Hurst exponent H(q), continuous line correspond to non-correlated noise with Hurst value of 0.5.

**Figure 10.**Generalized Structure Function plots for NDVI anomaly series of SOM5 (left column in blue) and SOM15 (right column in red) for: (

**a**) ζ(q) curve and (

**b**) Generalized Hurst exponent H(q), continuous line correspond to non-correlated noise with Hurst value of 0.5.

**Table 1.**Soil and topographic characteristics of Self-Organizing soil units SOM5 and SOM15 in the midlands of Eresma-Adaja basin. The deviation is showed in round brackets.

SOM Unit | SOM_05 | SOM15 |
---|---|---|

Slope [%] | 1–16 | 1–17 |

Altitude [MASL] | 925–1050 | 888–912 |

Clay [%] | 29 (5.2) | 4 (3) |

Sand [%] | 56 (4.6) | 84 (3.9) |

Silt [%] | 14 (4.4) | 12 (3.5) |

Organic Matter [%] | 0.9 (0.10) | 1.7 (0.15) |

Bulk density [g/cm^{3}] | 1420 (145) | 1839 (129) |

Carbon content [%] | 0.5 (0.08) | 1.0 (0.09) |

Available water content [mm H_{2}O] | 10.1 (0.7) | 5.8 (0.7) |

Hydraulic Conductivity [mm/hr] | 150 (88) | 2890 (981) |

Soil moist albedo [ratio] | 0.08 (0.010) | 0.03 (0.005) |

Effective Soil depth [mm] | 1100 | 825 |

**Table 2.**Monthly average values of precipitation (Pcp), maximum temperature (Tmax), average temperature (Tavg), minimum temperature (Tmin). Study period from 2000–2019.

OCT | NOV | DIC | JAN | FEB | MAR | APR | MAY | JUN | JUL | AUG | SEPT | Annual Values | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Sub-basin 50 (SOM5) | |||||||||||||

Pcp [mm] | 67.1 | 59.7 | 40.1 | 52.3 | 39.0 | 40.7 | 56.1 | 57.0 | 31.7 | 14.5 | 13.8 | 27.1 | 499.1 |

Tmax [°C] | 18.2 | 11.0 | 8.3 | 8.0 | 9.4 | 13.0 | 15.6 | 20.2 | 26.9 | 30.2 | 30.1 | 25.6 | 18.0 |

Tavg [°C] | 12.8 | 6.9 | 4.4 | 4.0 | 4.6 | 7.4 | 9.4 | 13.0 | 18.8 | 21.3 | 21.7 | 18.1 | 11.9 |

Tmin [°C] | 7.3 | 2.8 | 0.4 | 0.0 | −0.1 | 1.8 | 3.2 | 5.8 | 10.6 | 12.5 | 13.3 | 10.6 | 5.7 |

Sub-basin 24 (SOM15) | |||||||||||||

Pcp [mm] | 61.2 | 45.5 | 34.2 | 36.5 | 30.7 | 36.0 | 50.3 | 50.5 | 31.2 | 12.6 | 16.4 | 25.3 | 430.4 |

Tmax [°C] | 17.9 | 11.0 | 8.3 | 8.1 | 9.4 | 12.8 | 15.4 | 20.0 | 26.8 | 30.0 | 29.9 | 25.4 | 17.9 |

Tavg [°C] | 12.6 | 6.9 | 4.4 | 3.9 | 4.6 | 7.2 | 9.2 | 12.8 | 18.5 | 21.0 | 21.4 | 17.9 | 11.7 |

Tmin [°C] | 7.2 | 2.8 | 0.4 | −0.2 | −0.2 | 1.6 | 3.0 | 5.7 | 10.2 | 12.1 | 12.8 | 10.4 | 5.5 |

**Table 3.**Statistics of MOD13Q spectral bands series for SOM5 and SOM15 for DOY 49 associated to bare soil as predominant condition for the period 2000 to 2019.

Reflectance Bands | ||||||||
---|---|---|---|---|---|---|---|---|

NIR | RED | Blue | MIR | |||||

SOM soil unit | 5 | 15 | 5 | 15 | 5 | 15 | 5 | 15 |

Mean | 0.294 | 0.343 | 0.133 | 0.161 | 0.063 | 0.076 | 0.177 | 0.232 |

Typical error | 0.009 | 0.011 | 0.004 | 0.006 | 0.002 | 0.003 | 0.011 | 0.016 |

Median | 0.290 | 0.332 | 0.136 | 0.161 | 0.064 | 0.076 | 0.185 | 0.222 |

Standard deviation | 0.038 | 0.051 | 0.018 | 0.028 | 0.010 | 0.012 | 0.049 | 0.071 |

Kurtosis | −0.553 | −0.707 | −0.122 | −0.906 | −0.548 | −0.636 | −1.184 | −0.421 |

Skewness | 0.005 | 0.412 | −0.607 | 0.006 | −0.229 | −0.217 | −0.331 | 0.583 |

Count | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |

Normality test | ||||||||

Shapiro–Wilk | ||||||||

Statistic | 0.932 | 0.922 | 0.955 | 0.965 | 0.971 | 0.973 | 0.964 | 0.959 |

P-value | 0.170 | 0.108 | 0.442 | 0.644 | 0.971 | 0.808 | 0.624 | 0.523 |

Kolmogorov–Smirnov | ||||||||

P-value | 0.776 | 0.749 | 0.932 | 0.898 | 0.934 | 0.912 | 0.969 | 0.987 |

**Table 4.**Analysis of variance (ANOVA) showing significant statistical differences (p-value < 0.01) for single bands (NIR, Red, Blue and MIR) for the two soil units SOM5 and SOM15.

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Ratio | p-Value |
---|---|---|---|---|---|

NIR | |||||

Between SOMs | 0.024 | 1 | 0.024 | 11.93 | 0.001 |

Within SOMs | 0.078 | 38 | 0.002 | ||

Total (corrected) | 0.103 | 39 | |||

Red | |||||

Between SOMs | 0.008 | 1 | 0.008 | 14.67 | 0.001 |

Within SOMs | 0.021 | 38 | 0.001 | ||

Total (corrected) | 0.029 | 39 | |||

Blue | |||||

Between SOMs | 0.002 | 1 | 0.002 | 13.51 | 0.001 |

Within SOMs | 0.005 | 38 | 0.000 | ||

Total (corrected) | 0.006 | 39 | |||

MIR | |||||

Between SOMs | 0.030 | 1 | 0.030 | 8.03 | 0.007 |

Within SOMs | 0.142 | 38 | 0.004 | ||

Total (corrected) | 0.172 | 39 |

Source | Sum of Squares | Df | Mean Square | F-Ratio | p-Value |
---|---|---|---|---|---|

Intercepts | 0.0016 | 1 | 0.0016 | 79.53 | 0.0000 |

Slopes | 0.0001 | 1 | 0.0001 | 4.46 | 0.0383 |

**Table 6.**Analysis of variance (ANOVA) of NDVI for the two sampling sites SOM5 and SOM15 using the average index value of the plots for each sensing date range between March and June from 2000 to 2019.

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Ratio | p-Value |
---|---|---|---|---|---|

NDVI | |||||

Between SOMs | 0.112 | 1 | 0.112 | 10.15 | 0.002 |

Whitin SOMs | 2.635 | 238 | 0.011 | ||

Total (corrected) | 2.747 | 239 |

**Table 7.**Multifractal parameters for each zone and each NDVI series. H(q = 1) generalized Hurst index for q = 1; H(q = 2), generalizes Hurst index for q = 2; ΔH(q) = H(q = 0.25) − H(q = 4).

Zone | NDVI Series | H(q = 1) | H(q = 2) | ΔH(q) |
---|---|---|---|---|

SOM5 | Original | 0.78 | 0.70 | 0.40 |

Residual | 0.41 | 0.37 | 0.12 | |

anomaly | 0.40 | 0.37 | 0.09 | |

SOM15 | Original | 0.80 | 0.70 | 0.40 |

Residual | 0.46 | 0.43 | 0.14 | |

anomaly | 0.37 | 0.34 | 0.09 |

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## Share and Cite

**MDPI and ACS Style**

Rivas-Tabares, D.A.; Saa-Requejo, A.; Martín-Sotoca, J.J.; Tarquis, A.M.
Multiscaling NDVI Series Analysis of Rainfed Cereal in Central Spain. *Remote Sens.* **2021**, *13*, 568.
https://doi.org/10.3390/rs13040568

**AMA Style**

Rivas-Tabares DA, Saa-Requejo A, Martín-Sotoca JJ, Tarquis AM.
Multiscaling NDVI Series Analysis of Rainfed Cereal in Central Spain. *Remote Sensing*. 2021; 13(4):568.
https://doi.org/10.3390/rs13040568

**Chicago/Turabian Style**

Rivas-Tabares, David Andrés, Antonio Saa-Requejo, Juan José Martín-Sotoca, and Ana María Tarquis.
2021. "Multiscaling NDVI Series Analysis of Rainfed Cereal in Central Spain" *Remote Sensing* 13, no. 4: 568.
https://doi.org/10.3390/rs13040568