# Evaluation of Sampling Methods for Validation of Remotely Sensed Fractional Vegetation Cover

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## Abstract

**:**

## 1. Introduction

## 2. Generation of Reference Data

#### 2.1. Framework of Reference Data Generation

**Figure 1.**Flowchart of generating reference fractional vegetation cover (FVC) at a coarse scale and a comparison with the estimated FVC.

#### 2.2. Study Site and in Situitalic> Data Measurements

^{2}kernel area of the experiment (see the area surrounded by the dashed lines in the right frame of Figure 2) is centered on the middle stream of the Heihe River Basin. Various land cover types form the strata. Corn is the dominant vegetation type in the study region, which consisted of approximately 72% agricultural land, 24% impervious surface, and 4% woodland and fruit orchard. Planted in April, the corn was still short on 30 May, thereby corresponding to low NDVI values in Figure 2. Although the croplands cover large areas of the study region, more than 30 villages are dispersed in this area and are the main influences of the spatial variability. FVCs of the impervious surfaces are nearly zero, whereas other land cover types have highly variable FVC values in terms of the vegetation seasonality. In addition, the intrinsic pattern of the cornfields varies with the irrigation schedules and other field crop managements. Therefore, the intra-pixel spatial variability of the coarse-resolution pixels in this area is considerable.

**Figure 2.**Normalized difference vegetation index (NDVI) map of experimental area on 30 May 2012. This map was generated from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data over the area at a resolution of 15 m. The experimental area is surrounded by the black dashed lines in the right frame.

**Figure 3.**In situ sample plots of FVC measurements, implemented in the Heihe River Basin in 2012. Among these samples, 18 plots were located in cornfields, and the other five plots were located in a soybean field, woodland, orchard, wheat field (quite a small area, not shown in the legend) and vegetable field.

#### 2.3. Generation of Reference FVC

^{2}) and the root mean square error (RMSE) of the NDVI and FVC over five time phases. We can see that the RMSE is generally less than 0.031 when data acquired over a single time phase are used in the regression. However, if all the data obtained over five time phases are used to fit one transfer function, the RMSE will be 0.072.

**Table 1.**The statistical parameters related to the regression of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) fractional vegetation cover (FVC). R

^{2}is the coefficient of determination of ASTER Normalized Difference Vegetation Index (NDVI) and field-measured FVC; k is the degree of non-linearity in Equation (1); RMSE refers to the root mean square error between ASTER NDVI and the field-measured FVC; and FVC

_{avg}and FVC

_{dev}are the averages and standard deviations of the field–measured FVC, respectively.

Date | 30 May 2012 | 24 June 2012 | 10 July 2012 | 11 August 2012 | 12 September 2012 | ALL ^{*} |
---|---|---|---|---|---|---|

R^{2} | 0.983 | 0.850 | 0.928 | 0.911 | 0.947 | 0.914 |

k | 1.232 | 1.136 | 0.328 | 0.459 | 1.299 | 0.523 |

RMSE | 0.020 | 0.020 | 0.016 | 0.031 | 0.010 | 0.072 |

FVC_{avg} | 0.181 | 0.623 | 0.690 | 0.720 | 0.133 | 0.469 |

FVC_{dev} | 0.168 | 0.053 | 0.090 | 0.087 | 0.040 | 0.276 |

## 3. Methodology

#### 3.1. Sampling Methods

_{j}is the jth sample’s weight, C

_{i}

_{0}is the covariance between the ith sample and the unknown point, C

_{ij}is the covariance between the ith sample and the jth sample, μ is the Lagrange multiplier, ${\tilde{\sigma}}^{2}$ is the variance, and $\overline{y}$ and ${\tilde{\sigma}}_{R}^{2}$ are the estimated mean and error variance, respectively. The covariance C can be calculated from a semi-variogram function fitted from samples or historical data. The objective of the kriging method is to minimize the error variance. For a given sample number, the locations of samples can be determined using optimization algorithms [23,24].

_{i}

_{0}in Equation (2) is the average covariance between the ith sample and all unknown points in the region. Due to the high correlation between NDVI and FVC, we use NDVI product as a proxy to fit the semi-variogram and sample optimization. When the semi-variogram function is fixed, the estimated error variance of the unknown point or region is only determined by the spatial configurations (distance and direction) of collected samples. A Monte-Carlo-based simulation method is adopted to select a group of samples with minimum theoretical estimated error variance. An iteration process is repeated until the error variance does not decrease or the maximum number of iterations is reached. The maximum number of iterations is 30,000.

_{h}is the sample number in the hth stratum; y

_{hi}is the ith sample in the hth stratum, with w

_{hi}being its weight, which is solved from the MSN model; $\Re $ and ${\Re}_{h}$ are the areas of the pixel and the hth stratum; ${a}_{h}={\Re}_{h}/\Re $; μ

_{h}is the Lagrange multiplier; $y\left(s\right)$ denotes the sample at location s; and $C\left(y\left(s\right),y\left({s}^{\prime}\right)\right)$ is the covariance between the sample $y\left(s\right)$ and the sample $y\left({s}^{\prime}\right)$. Similar to kriging, we also used the MSN model to optimize the sampling by minimizing the error variance ${\tilde{\sigma}}^{2}$ with an annealing simulation [24]. This method attempts to determine the most appropriate sample number and spatial locations to minimize the variance via a Monte Carlo simulation similar to that in the above kriging sampling method.

#### 3.2. Design of Experiments

#### 3.2.1. Sparse Sampling (Scene 1)

#### 3.2.2. Dense Sampling (Scene 2)

**Figure 4.**Distributions of fixed and optimized samples in the sparsely distributed scene using the mean of surface with non-homogeneity (MSN) method (

**a**) and the ordinary kriging method (

**b**). Coarse pixels in (a,b) marked as Nos. 1–15, have a resolution of 1 km.

**Figure 5.**Distributions of the fixed and optimized samples in the dense sampling scene calculated using the MSN method (

**a**) and the ordinary kriging method (

**b**) (in the red rectangular region).

#### 3.3. Scaling Bias of FVC Estimates

## 4. Results and Analysis

#### 4.1. Spatial and Temporal Pattern of ASTER FVC

**Figure 6.**(

**a**–

**e**) Spatial distributions of ASTER FVC in different growth stages (15-m resolution). In each growth stage, the FVC profile along the transect line (red line) is demonstrated.

Date | 30 May 2012 | 24 June 2012 | 10 July 2012 | 11 August 2012 | 12 September 2012 |
---|---|---|---|---|---|

Scene 1 | 0.068 | 0.102 | 0.104 | 0.130 | 0.053 |

Scene 2 | 0.197 | 0.107 | 0.106 | 0.141 | 0.057 |

#### 4.2. Sparsely Distributed Samples

**Figure 7.**Scattering plots of reference FVC and estimated FVC using the MSN method (

**a**) and the original kriging method (

**b**) at a scale of 1 km (Scene 1).

#### 4.3. Densely Distributed Samples

**Figure 8.**Scattering plots of reference FVC and estimated FVC using the MSN (

**a**); simple random sampling (

**b**); stratified sampling (

**c**); and ordinary kriging (

**d**) methods over an area of 3 km

^{2}(Scene 2). The simple random sampling and stratified sampling methods were applied 100 times.

#### 4.4. Evaluation of Sampling Methods with Changing Number of Samples

**Figure 9.**Averages of absolute errors of FVC generated by applying different sampling methods in Scene 2 with increasing sample numbers: (

**a**) 30 May; (

**b**) 24 June; (

**c**) 10 July; (

**d**) 11 August; (

**e**) 12 September; and (

**f**) average errors of FVC over all the time phases.

## 5. Discussions

**Table 3.**Predicted scaling biases (Bias_Pred) and the real biases (Bias_Real) of the estimated FVC using the MSN method.

Date | 30 May 2012 | 24 June 2012 | 10 July 2012 | 11 August 2012 | 12 September 2012 |
---|---|---|---|---|---|

Scene 1 | |||||

Bias_Pred | −0.004 | 0.000 | 0.006 | 0.011 | −0.005 |

Bias_Real | 0.009 | 0.008 | 0.030 | 0.023 | 0.007 |

Scene 2 | |||||

Bias_Pred | 0.037 | 0.010 | 0.010 | 0.013 | 0.015 |

Bias_Real | 0.000 | 0.034 | 0.027 | 0.007 | 0.008 |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Mu, X.; Hu, M.; Song, W.; Ruan, G.; Ge, Y.; Wang, J.; Huang, S.; Yan, G. Evaluation of Sampling Methods for Validation of Remotely Sensed Fractional Vegetation Cover. *Remote Sens.* **2015**, *7*, 16164-16182.
https://doi.org/10.3390/rs71215817

**AMA Style**

Mu X, Hu M, Song W, Ruan G, Ge Y, Wang J, Huang S, Yan G. Evaluation of Sampling Methods for Validation of Remotely Sensed Fractional Vegetation Cover. *Remote Sensing*. 2015; 7(12):16164-16182.
https://doi.org/10.3390/rs71215817

**Chicago/Turabian Style**

Mu, Xihan, Maogui Hu, Wanjuan Song, Gaiyan Ruan, Yong Ge, Jinfeng Wang, Shuai Huang, and Guangjian Yan. 2015. "Evaluation of Sampling Methods for Validation of Remotely Sensed Fractional Vegetation Cover" *Remote Sensing* 7, no. 12: 16164-16182.
https://doi.org/10.3390/rs71215817