# Creating Multi-Temporal Composites of Airborne Imaging Spectroscopy Data in Support of Digital Soil Mapping

^{*}

## Abstract

**:**

^{2}and gain and offset close to one and zero). Finally, the multi-temporal composite image contained more than double the amount of bare soil pixels as compared to a singular acquisition. Summary statistics show that reflectance values of the multi-temporal composite approximate the single image data of 2014 (mean and standard deviation of 2014: 24.2 ± 8.9 vs. 24.0 ± 9.5 for the multi-temporal composite of 2013, 2014 and 2015). This indicates that global differences in soil moisture and land management have been corrected for. As a result, an improved spatial representation of soil parameters can be retrieved from the composite data. Spatial distribution of the correction factors and analysis of the spatial variability of all images, however, indicate that non-linear, short-term differences like variation in soil moisture and land management largely influence the result of the multi-temporal composite. Quantification and attribution of those factors will be required in the future to allow correcting for them.

## 1. Introduction

## 2. Study Area and Soil Types

## 3. Materials and Methods

#### 3.1. Preprocessing of Imaging Spectroscopy Data

^{2}. Subsequently, the following spectral bands were removed because of (I) interpolated bands: 691.0–735.9 nm; 752.9–770.8 nm; 794.9–838.0 nm; 900.4–992.1 nm; 1072.4–1166.5 nm; 1283.0–1495.7 nm; 1738.7–2028.7 nm; and (II) low signal to noise (SNR) bands: below 450 nm and above 2200 nm. This means that, e.g., clay cannot be determined by typical absorption features at 2200 nm, however there is no scientific purpose to apply noisy data to such an analysis.

#### 3.2. Selecting Bare Soil Area

#### 3.3. Multi-Temporal Calibration

_{cor}) of the calibration year:

^{2}, RMSE, gain and offset values, etc.). Cook’s distance (D

_{i}) is based on the relation between the studentized residuals (e

_{i}) and the measure of leverage (h

_{i}) of a data point, which results in Equation (2).

#### 3.4. Analysis of the Multi-temporal Calibration

#### 3.4.1. Difference Analysis

_{i}of the spectra of year x and year y, and n is the number of spectral intervals. Price [65] calculates Equation (6) with integrals instead of summations. We approximate integration using summation, which is a valid approach when using rectangular response functions. The imaging spectroscopy data are processed in such a way that it supports to use summation as an approximation for integration.

^{2}) was calculated.

#### 3.4.2. Spatial Analysis

#### 3.5. Multi-Temporal Compositing

#### 3.6. Analysis of the Multi-Temporal Composites

_{i},y

_{i})) was calculated based on Equation (9):

_{i}and y

_{i}are the spatial locations. The spatial dependency can be plotted as a variogram with γ(x

_{i},y

_{i}) against y

_{i}− x

_{i}. Since we expect anisotropy, y

_{i}− x

_{i}is in this case not equal to h (a vector in distance and angular class y

_{i}− x

_{i}). The characteristics of the variogram are described as: (I) the sill, which is the variance at which there is no spatial dependence between the data (or random field); (II) the range, which is the distance at which there is no spatial dependence between the data; and (III) the nugget, which is the measurement error or micro-scale variation of the data (value of γ(x

_{i},y

_{i}) at y

_{i}− x

_{i}= 0).

#### 3.7. Case Study

^{2}plot. Soil moisture was measured for the topsoil and the upper topsoil by weighing the sample directly in the field and after drying the sample at 45 °C for 24 h. After drying, the topsoil samples were grounded and sieved to 2 mm for laboratory analysis. The data were analyzed in an external laboratory for organic matter, sand, silt and clay percentages.

^{2}was used to select the number of PCs with the best validation results. This number of PCs was then used to predict the soil property for the full bare soil area. Predictions above 100% or below 0% were considered as outliers and excluded from further analysis.

## 4. Results and Discussion

#### 4.1. Selecting Bare Soil Area

#### 4.2. Multi-Temporal Calibration

#### 4.3. Analysis of the Multi-Temporal Calibration

#### 4.3.1. Difference Analysis

^{2}of 0.97 ± 0.03 and 0.98 ± 0.04, respectively. The offset and gain values show that the point cloud of ‘13’14 lies above the one-to-one-line and for ‘15’14 the point cloud lies below the one-to-one-line, this follows the meteorological differences as described before. Furthermore, also these values show that ‘15’14 are closer together than ‘13’14.

#### 4.3.2. Spatial Analysis

^{−2}over these 14 days) and warm (on average 16.7 °C); 2014 was dry (total of 31.2 l·m

^{−2}over these 14 days) but colder (on average 10.8 °C); and 2015 was very wet (total of 99.4 l·m

^{−2}over these 14 days) and even colder (on average 6.6 °C). However, the precipitation data show that only three days before the flight of 2014 a big rain event (24 l·m

^{−2}) took place, in 2015 this was 6, 8 and 11 days before the flight (respectively 26, 23.3 and 35 l·m

^{−2}) and in 2013 this was even more than 14 days before the flight. The three days after the rain event of 2014 were probably not enough to dry the topsoil. The very wet spring of 2015 resulted in wet soils, especially in the lower areas; however, the topsoil had six days to dry. This resulted in large positive differences between ‘15’14 for the lower areas. In the higher areas, the six dry days of 2015 result in topsoils that are comparable or even drier than in 2014, meaning small or even negative SMPE values for the higher areas. Even though 2013 had very dry weather conditions, smaller rain events took place 6, 7 and 10 days before the flight. This resulted in moist soils for both 2013 and 2014 in the lower areas, resulting in small SMPE values for the lower areas. The higher elevated areas were dry for 2013, but still wet for 2014, which results in bigger negative differences.

#### 4.4. Multi-Temporal Composite

#### 4.5. Analysis of the Multi-Temporal Composite

#### 4.5.1. Small Scale Spatial Variability

#### 4.5.2. Large Scale Spatial Variability

#### 4.6. Case Study

^{2}. The optimal number of PCs was between 6 and 7 for all predictions. The prediction R

^{2}ranged between 0.55 ± 0.16 for ’13 and 0.63 ± 0.02 for ’15. This was anticipated because most field samples were taken in 2015, and, in 2013, the number of intersecting samples is very low. For ‘13’14’15 the predicted R

^{2}was 0.58 ± 0.02.

^{2}of 0.40 ± 0.04, 0.41 ± 0.04 and 0.39 ± 0.04 respectively. Soriano-Disla et al. [15] give an overview of the accuracies of the several predicted soil properties with spectroscopy data. The median of the R

^{2}is 0.78, 0.78, 0.67 and 0.86 for, respectively, clay, sand, silt and organic matter percentages. Most of these studies make use of soil samples analysed spectrally in the laboratory, therefore the accuracy values are higher than the accuracy we reach. Nevertheless, it gives a good indication of how well spectroscopy data can predict certain soil properties.

## 5. Conclusions and Outlook

^{2}and gain and offset close to one and zero). Creating a multi-temporal composite of the calibrated imaging spectroscopy data has resulted in more than double the area (106.4%) of bare soils available in a single image. This composite image did not only show similar summary statistics compared to the reference image (mean and standard deviation of 2014: 24.2 ± 8.9 vs. 24.0 ± 9.5 for the multi-temporal composite ‘13’14’15), but also revealed the general long-term spatial pattern that is necessary for deriving soil properties at larger scales. Although global linear variability in short-term processes, such as variation in soil moisture and soil surface roughness, were accounted for, local non-linear variability in short-term processes could not be accounted for.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

APEX | Airborne Prism EXperiment |

DEM | digital elevation model |

nCAI | normalized cellulose absorption index |

NDRBI | normalized difference red blue index |

NDVI | normalized difference vegetation index |

NIR | near-infrared |

PC | principal component |

PCA | principal component analysis |

PLSR | partial least squares regression |

SM(A)PE | symmetric mean (absolute) percentage error |

SNR | signal to noise ratio |

SWIR | short-wave infrared |

VIS | visible |

VNIR | visible and near-infrared |

## Appendix A

Year | n ^{1} | ALL ^{2} | VIS ^{3} | NIR ^{4} | SWIR ^{5} |
---|---|---|---|---|---|

‘13’14 | 54,981 | 11.7 ± 14.1 | 10.6 ± 14.1 | 13.8 ± 12.5 | 11.2 ± 15.1 |

‘15’14 | 154,270 | −8.2 ± 14.0 | −8.7 ± 13.2 | −7.7 ± 14.7 | −8.0 ± 14.3 |

^{1}The number of overlapping pixels (excluding outliers according to Equations (3) and (4));

^{2}Full spectrum 450–2200 nm;

^{3}Visible spectrum 450–700 nm;

^{4}Near-infrared spectrum 700–1400 nm;

^{5}Short-wave infrared 1400–2200 nm.

## Appendix B

**Figure B1.**Distribution of the predicted sand percentages for all single images (2013, 2014, and 2015) and the multi-temporal composites (‘13’14, ‘14’15, ‘13’15, and ‘13’14’15) next to the distribution of the sand percentages of the field samples of ’14 and ’15.

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**Figure 1.**Study area and the distribution of the bare soil pixels, the colors show in which year(s) the considering bare soil pixel was present. The black rectangles show the locations of the focus area (used in most of the following figures) and the locations of the individual fields in Figure 7, Figure 8, Figure 9 and Figure 10.

**Figure 2.**Precipitation (l·m

^{−2}) and temperature data (°C) in the 28 days before the flight dates (3 September 2013, 11 April 2014 and 10 April 2015).

**Figure 3.**(

**a**–

**c**) RGB-image of the focus area of the spectroscopy data for all flight dates (3 September 2013, 11 April 2014 and 10 April 2015); and (

**d**–

**f**) the corresponding selected bare soils for all three years.

**Figure 4.**Mean reflectance values for all three years (2013, 2014, and 2015): before (

**a**); and after (

**b**) calibration.

**Figure 5.**Distribution of the SMPE values for: (

**a**) ‘13’14; and (

**b**) ‘15’14. Distribution is given for the full spectra (ALL: 450–2200 nm), and for the specific ranges of the spectra (VIS: visible spectrum 450–700 nm, NIR: near-infrared spectrum 700–1400 nm, and SWIR: short-wave infrared 1400–2200 nm).

**Figure 6.**Spatial distribution in the focus area of the SMPE values for: (

**a**) ‘13’14; and (

**b**) ‘15’14.

**Figure 7.**SMPE values for: ‘13’14 (

**a**); and ‘15’14 (

**b**); and DEM (overlaid with a hillshade: 315° azimuth and 45° altitude) for an individual agricultural field (

**c**).

**Figure 9.**Close-up of an individual agricultural field showing the year(s) each bare soil pixel was present (

**a**); and the first PC of the multi-temporal composite (

**b**).

**Figure 10.**The first PC values (

**d**–

**f**,

**k**–

**m**); the corresponding 45° and 315° variograms (

**a**–

**c**,

**h**–

**j**); and the DEM (overlaid with a hillshade: 315° azimuth and 45° altitude) of two individual agricultural fields (Field I and Field II) for all three years (2013, 2014, and 2015) (

**g**,

**n**). The axes of the variograms have the distance (m) on the x-axis and the semi-variance on the y-axis.

**Figure 11.**In-field variability shown by the first PC values: (

**a**–

**c**) for an individual agricultural field for all three years (2013, 2014, and 2015); and the corresponding DEM (overlaid with a hillshade: 315° azimuth and 45° altitude) (

**d**).

**Figure 12.**The 45° and 315° variograms at long distances for the first PC values (

**a**–

**g**) for all single (2013, 2014, and 2015) and multi-temporal composites (‘13’14, ‘14’15, ‘13’15, and ‘13’14’15). On the x-axis the distance (m) and on the y-axis the semi-variance.

**Figure 13.**The 45° and 315° variograms at short distances for the first PC values (

**a**–

**g**) for all single (2013, 2014, and 2015) and multi-temporal composites (‘13’14, ‘14’15, ‘13’15, and ‘13’14’15). On the x-axis the distance [m] and on the y-axis the semi-variance.

**Table 1.**Sowing and harvest periods for the dominant crops (winter cereals, maize, and rapeseed) in the study area.

Jan. | Feb. | Mar. | Apr. ^{1} | May | Jun. | Jul. | Aug. | Sep. ^{1} | Oct. | Nov. | Dec. | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Barley winter | ||||||||||||||

Triticale winter | ||||||||||||||

Wheat winter | ||||||||||||||

Rye winter | ||||||||||||||

Spelt | ||||||||||||||

Maize corn | ||||||||||||||

Maize silage ^{2} | ||||||||||||||

Rapeseed | ||||||||||||||

^{1}The black vertical lines indicate approximately the date of the flights (3 September 2013, 11 April 2014, 10 April 2015);

^{2}The light green for Maize silage indicates late sowing to grow green silage maize.

**Table 2.**Total number of bare soil pixels and the amount of overlapping pixels for the years 2013, 2014, and 2015.

Year | No. Pixels | No. Overlapping Pixels |
---|---|---|

2013 | 536,213 ^{1} (1.4% ^{2}|2.9% ^{3}) | 63,066 ^{1} |

2014 | 814,240 ^{1} (2.1% ^{2}|4.4% ^{3}) | |

178,075 ^{1} | ||

2015 | 634,013 ^{1} (1.6% ^{2}|3.4% ^{3}) |

^{1}The total area in m

^{2}can be calculated by multiplying the number of pixels with the area of 4 m

^{2}per pixel (2 × 2 m);

^{2}Percentages show the coverage of the total study area (39,564,161 pixels) by bare soil;

^{3}Percentages show the coverage of the total agricultural area (18,647,218 pixels) by bare soil. The agricultural area was calculated based on the agricultural field block map [58].

Year | n ^{1} | ALL ^{2} | VIS ^{3} | NIR ^{4} | SWIR ^{5} |
---|---|---|---|---|---|

‘13’14 | 54,981 | 2.57 ± 3.42 | 1.32 ± 1.94 | 3.64 ± 3.14 | 3.09 ± 4.31 |

‘15’14 | 154,270 | −2.23 ± 3.77 | −1.34 ± 1.95 | −2.48 ± 4.27 | −2.97 ± 4.56 |

^{1}The number of overlapping pixels (excluding outliers according to Equations (3) and (4));

^{2}Full spectrum 450–2200 nm;

^{3}Visible spectrum 450–700 nm;

^{4}Near-infrared spectrum 700–1400 nm;

^{5}Short-wave infrared 1400–2200 nm.

Year | n ^{1} | D ^{2} | θ ^{3} | R^{2} ^{4} | Offset ^{4} | Gain ^{4} |
---|---|---|---|---|---|---|

‘13’14 | 54,981 | 0.33 ± 0.17 | 0.05 ± 0.03 | 0.97 ± 0.03 | −0.29 ± 2.25 | 1.13 ± 0.16 |

‘15’14 | 154,270 | 0.34 ± 0.18 | 0.05 ± 0.03 | 0.98 ± 0.04 | 0.07 ± 2.01 | 0.92 ± 0.17 |

^{1}The number of overlapping pixels (excluding outliers according to Equations (3) and (4));

^{2}The square difference as defined in Equation (5);

^{3}The difference angle as defined in Equation (6);

^{4}R

^{2}, gain and offset calculated according to the linear correlation between the calibration year and the reference year (2014), following Equation (7).

Year | n ^{1} | ALL ^{2} | VIS ^{3} | NIR ^{4} | SWIR ^{5} |
---|---|---|---|---|---|

‘13’14 | 54,981 | 0.02 ± 3.04 | 0.02 ± 1.81 | 0.07 ± 2.95 | −0.03 ± 3.98 |

‘15’14 | 154,270 | −0.04 ± 3.34 | −0.01 ± 1.77 | −0.02 ± 3.72 | −0.09 ± 4.19 |

^{1}The number of overlapping pixels (excluding outliers according to Equations (3) and (4));

^{2}Full spectrum 450–2200 nm;

^{3}Visible spectrum 450–700 nm;

^{4}Near-infrared spectrum 700–1400 nm;

^{5}Short-wave infrared 1400–2200 nm.

Year | n ^{1} | D ^{2} | θ ^{3} | R^{2} ^{4} | Offset ^{4} | Gain ^{4} |
---|---|---|---|---|---|---|

‘13’14 | 54,981 | 0.22 ± 0.14 | 0.04 ± 0.02 | 0.98 ± 0.03 | 0.07 ± 2.06 | 1.01 ± 0.15 |

‘15’14 | 154,270 | 0.25 ± 0.15 | 0.04 ± 0.03 | 0.98 ± 0.03 | 0.19 ± 2.00 | 1.01 ± 0.17 |

^{1}The number of overlapping pixels (excluding outliers according to Equations (3) and (4));

^{2}The square difference as defined in Equation (5);

^{3}The difference angle as defined in Equation (6);

^{4}R

^{2}, gain and offset calculated according to the linear correlation between the calibration year and the reference year (2014), following Equation (7).

**Table 7.**Total number of bare soil pixels and the corresponding increase compared to 2014 (814,240 pixels is equal to 100%) for the multi-temporal composites ‘13’14, ‘14’15, ‘13’15, and ‘13’14’15.

Year | No. Pixels | Increase (2014 = 100%) |
---|---|---|

‘13’14 | 1,287,387 ^{1} (3.3% ^{2}|6.9% ^{3}) | 158.1% |

‘14’15 | 1,270,178 ^{1} (3.2% ^{2}|6.8% ^{3}) | 156.0% |

‘13’15 | 1,082,639 ^{1} (2.7% ^{2}|5.8% ^{3}) | 132.9% |

‘13’14’15 | 1,680,799 ^{1} (4.2% ^{2}|9.0% ^{3}) | 206.4% |

^{1}The total area in m

^{2}can be calculated by multiplying the number of pixels with the area of 4 m

^{2}per pixel (2 × 2 m);

^{2}Percentages show the coverage of the total study area (39,564,161 pixels) by bare soil;

^{3}Percentages show the coverage of the total agricultural area (18,647,218 pixels) by bare soil. The agricultural area was calculated based on the agricultural field block map [58].

**Table 8.**Mean and standard deviation of the reflectance values for the individual and multi-temporal images.

Year | ALL ^{1} | VIS ^{2} | NIR ^{3} | SWIR ^{4} |
---|---|---|---|---|

2013 | 26.0 ± 9.9 | 14.9 ± 5.3 | 31.0 ± 7.6 | 34.1 ± 6.1 |

2014 | 24.2 ± 8.9 | 13.9 ± 3.7 | 28.4 ± 6.7 | 32.0 ± 6.3 |

2015 | 21.7 ± 8.9 | 12.6 ± 3.7 | 25.4 ± 6.5 | 28.5 ± 5.7 |

‘13’14 | 24.0 ± 9.6 | 13.8 ± 3.8 | 28.1 ± 6.5 | 31.8 ± 5.5 |

‘14’15 | 24.1 ± 9.6 | 13.9 ± 3.5 | 28.3 ± 6.2 | 31.9 ± 5.5 |

‘13’15 | 24.0 ± 9.1 | 14.0 ± 3.5 | 28.2 ± 5.5 | 31.7 ± 3.7 |

‘13’14’15 | 24.0 ± 9.5 | 13.9 ± 3.7 | 28.1 ± 6.2 | 31.8 ± 5.1 |

^{1}Full spectrum (450–2200 nm);

^{2}Visible spectrum ranging from 450–700 nm;

^{3}Near-infrared spectrum ranging from 700–1400 nm;

^{4}Short-wave infrared ranging from 1400–2200 nm.

**Table 9.**Sill and range values for the small-scale variogram for the agricultural field I and II (Figure 9).

Year | Field I | Field II | ||
---|---|---|---|---|

Sill | Range | Sill | Range | |

2013 | 8.3 | 69.5 | 31.3 | 685.6 |

2014 | 11.7 | 63.8 | 8.2 | 49.3 |

2015 | 2.8 | 54.9 | 13.6 | 128.9 |

Year | Long Distance | Short Distance | ||
---|---|---|---|---|

Sill | Range | Sill | Range | |

2013 | 87.5 | 312.9 | 64.2 | 95.1 |

2014 | 108.5 | 317.8 | 100.7 | 222.5 |

2015 | 113.2 | 358.1 | 95.2 | 194.4 |

‘13’14 | 100.6 | 266.5 | 98.0 | 195.6 |

‘14’15 | 112.5 | 275.3 | 106.6 | 189.4 |

‘13’15 | 86.9 | 291.9 | 72.7 | 134.0 |

‘13’14’15 | 101.6 | 234.5 | 99.2 | 170.2 |

Sand (%) | Silt (%) | Clay (%) | OM ^{1} (%) | SM ^{2} (%) | SM_{upper} ^{3} (%) |
---|---|---|---|---|---|

32.3 ± 10.0 | 38.2 ± 7.7 | 29.5 ± 11.4 | 10.3 ± 4.5 | 24.3 ± 7.6 | 2.6 ± 2.4 |

^{1}Organic matter;

^{2}Soil Moisture in the topsoil (upper 5 cm);

^{3}Soil Moisture upper topsoil (upper 1 cm).

Year | No. of Samples ^{1} | No. of PCs ^{2} | R ^{3} ± sd |
---|---|---|---|

‘13 | 12 | 6 | 0.55 ± 0.16 |

‘14 | 41 | 6 | 0.63 ± 0.03 |

‘15 | 73 | 6 | 0.63 ± 0.02 |

‘13’14 | 51 | 7 | 0.61 ± 0.03 |

‘14’15 | 80 | 7 | 0.57 ± 0.02 |

‘13’15 | 75 | 6 | 0.63 ± 0.02 |

‘13’14’15 | 81 | 7 | 0.58 ± 0.02 |

^{1}The results of the intersection between the field samples and the spectral bare soil information;

^{2}The amount of PCs selected to make the soil property prediction;

^{3}The corresponding prediction R

^{2}and its standard deviation calculated based on the bootstrapping results.

**Table 13.**Summary statistics of the results of predicted sand percentages of the overlapping bare soil pixels in all three years and of the sand percentages of the field samples (last row).

Year | n ^{1} | NAs ^{2} | Mean ± sd (%) ^{3} | Median (%) | IQR (%) ^{4} | Min–Max (%) |
---|---|---|---|---|---|---|

‘13 | 25061 | 62 | 35.7 ± 11.6 | 36.6 | 28.5–44.0 | 0.4–99.5 |

‘14 | 25061 | 101 | 35.7 ± 11.5 | 36.4 | 29.1–43.9 | 0.0–93.7 |

‘15 | 25061 | 109 | 35.0 ± 11.9 | 34.0 | 26.2–44.4 | 0.0–83.7 |

‘13’14 | 25061 | 352 | 39.3 ± 12.7 | 37.7 | 31.5–44.6 | 0.0–100.0 |

‘14’15 | 25061 | 59 | 35.7 ± 11.6 | 36.6 | 28.6–44.0 | 0.1–90.0 |

‘13’15 | 25061 | 7 | 36.3 ± 11.5 | 36.4 | 29.6–43.8 | 0.4–98.3 |

‘13’14’15 | 25061 | 152 | 34.6 ± 12.4 | 34.2 | 25.9–43.3 | 0.0–82.3 |

FW’14’15 | 89 | 0 | 32.3 ± 10.0 | 29.1 | 25.4–36.9 | 17.8–64.9 |

^{1}The number of overlapping pixels;

^{2}The number of pixels excluded because the predicted values were below 0 or above 100;

^{3}The mean and its corresponding standard deviation;

^{4}The interquartile range.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Diek, S.; Schaepman, M.E.; De Jong, R. Creating Multi-Temporal Composites of Airborne Imaging Spectroscopy Data in Support of Digital Soil Mapping. *Remote Sens.* **2016**, *8*, 906.
https://doi.org/10.3390/rs8110906

**AMA Style**

Diek S, Schaepman ME, De Jong R. Creating Multi-Temporal Composites of Airborne Imaging Spectroscopy Data in Support of Digital Soil Mapping. *Remote Sensing*. 2016; 8(11):906.
https://doi.org/10.3390/rs8110906

**Chicago/Turabian Style**

Diek, Sanne, Michael E. Schaepman, and Rogier De Jong. 2016. "Creating Multi-Temporal Composites of Airborne Imaging Spectroscopy Data in Support of Digital Soil Mapping" *Remote Sensing* 8, no. 11: 906.
https://doi.org/10.3390/rs8110906