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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This study applies variogram analyses of normalized difference vegetation index (NDVI) images derived from SPOT HRV images obtained before and after the ChiChi earthquake in the Chenyulan watershed, Taiwan, as well as images after four large typhoons, to delineate the spatial patterns, spatial structures and spatial variability of landscapes caused by these large disturbances. The conditional Latin hypercube sampling approach was applied to select samples from multiple NDVI images. Kriging and sequential Gaussian simulation with sufficient samples were then used to generate maps of NDVI images. The variography of NDVI image results demonstrate that spatial patterns of disturbed landscapes were successfully delineated by variogram analysis in study areas. The high-magnitude Chi-Chi earthquake created spatial landscape variations in the study area. After the earthquake, the cumulative impacts of typhoons on landscape patterns depended on the magnitudes and paths of typhoons, but were not always evident in the spatiotemporal variability of landscapes in the study area. The statistics and spatial structures of multiple NDVI images were captured by 3,000 samples from 62,500 grids in the NDVI images. Kriging and sequential Gaussian simulation with the 3,000 samples effectively reproduced spatial patterns of NDVI images. However, the proposed approach, which integrates the conditional Latin hypercube sampling approach, variogram, kriging and sequential Gaussian simulation in remotely sensed images, efficiently monitors, samples and maps the effects of large chronological disturbances on spatial characteristics of landscape changes including spatial variability and heterogeneity.

The influences of large physical disturbances on ecosystem structure and function have garnered considerable attention [

Remotely sensed data can describe surface processes, including landscape dynamics, as such data provide frequent spatial estimates of key earth surface variables [

Spatial patterns in ecological systems are the result of an interaction among dynamic processes operating across abroad range of spatial and temporal scales [

Reliable data analysis of spatially distributed data requires the use of appropriate statistical tools and a sound data sampling strategy [

This study applied variogram analysis to delineate spatial variations of NDVI images before and after large physical disturbances in central Taiwan. The NDVI data derived from SPOT images before and after the ChiChi earthquake (ML=7.3 on the Richter scale) in the Chenyulan basin, Taiwan, as well as images before and after four large typhoons (Xangsane, Toraji, Dujuan and Mindulle) were analyzed to identify the spatial patterns of landscapes caused by these major disturbances. Landscape spatial patterns of different disturbance regimes were discussed. Moreover, conditional LHS (cLHS) schemes with NDVI images were used to select spatial samples from actual NDVI images to detect landscape changes induced by a series of large disturbances. The best cLHS samples selected with the NDVI values were used to estimate and simulate NDVI distributions using kriging and SGS. The simulated NDVI images were compared with actual NDVI images induced by the disturbances.

The Chenyulan watershed, located in central Taiwan, is a classical intermountain watershed, and has an average altitude of 1,540 m and an area of 449 km^{2} (^{2}. Moreover, the main course of the Chenyulan stream had a gradient of 6.1%, and more than 60% of its tributaries had gradients exceeding 20%. The special geological and geographical characteristics of the watershed result in frequent landsides and debris flows [^{2} (250×250 pixels) was selected from the upstream of the large debris flood announced in the watershed, as shown in

Seven cloud-free SPOT images (1996/11/08, 1999/03/06, 1999/10/31, 2000/11/27, 2001/11/20, 2003/12/17 and 2004/11/19) of the Chenyulan watershed were purchased from the Space and Remote-sensing Research Center, Taiwan. The NDVI images of the study area were generated from SPOT HRV images with a resolution of 20 m according to the following equation:

In geostatistical methods, variograms can be used to quantify the observed relationship between the values of samples and the proximity of samples [

Kriging is estimated using weighted sums of adjacent sampled concentrations. The weights depend on the correlation structure exhibited. The weights are determined by minimizing estimated variance. In this context, kriging estimates (Best Linear Unbiased Estimator) are the most accurate of all linear estimators. Accordingly, kriging estimates the value of the random variable at unsampled location X0based on measured values in a linear form:
_{0}) is the estimated value at location _{0}, _{i0} is the estimation weight of _{i}_{i}

Based on non-biased constraints and minimizing estimation variance, estimated kriging variance can be presented as:

The cLHS, which is based on the empirical distribution of original data, provides a full coverage of range each variable by maximally stratifying the marginal distribution and ensuring a good spread of sampling points [

Divide the quantile distribution of X into n strata, and calculate the quantile distribution for each variable,

Pick n random samples from

Calculate the objective function. The overall objective function is _{1}_{1} + _{2}_{2} + _{3}_{3}, , where w is the weight given to each component of the objective function. For general applications, w is set to 1 for all components of the objective function.

For continuous variables,
_{i}

For categorical data, the objective function is to match the probability distribution for each class of:
_{i}_{i}

C. To ensure that the correlation of the sampled variables will replicate the original data, another objective function is added:

Perform an annealing schedule [

Generate a uniform random number between 0 and 1. If

Try to perform changes: Generate a uniform random number rand. If

Go to step 3

Repeat steps 3–7 until the objective function value falls beyond a given stop criterion or a specified number of iterations.

In sequential simulation algorithm, modeling of the N-point cumulative density function (ccdf) is a sequence of N univariate ccdfs at each node (grid cell) along a random path [

Establish a random path that is visited once and only once, all nodes {_{i}, i

At the first visited N nodes _{1}:

Model, using either a parametric or nonparametric approach, the local ccdf of _{1}) conditional on n original data {_{α}_{Z}_{1}; _{1}|(_{1}) ≤ _{1}|(

Generate, via the Monte Carlo drawing relation, a simulated value ^{(}^{l}^{)}(_{1}) from this ccdf _{Z}_{1}: _{1}|(

At the i_{th} node _{i}

Model the local ccdf of _{i}^{(}^{l}^{)}(_{i}

Generate a simulated value ^{(}^{l}^{)}(_{i}

Repeat step 3 until all N nodes along the random path are visited.

The SGS assumes a Gaussian random field, such that the mean value and covariance completely characterize the ccdf [

Statistics of remotely sensed images can be used as a basic tool to characterize landscape changes [

Previous studies that quantified the impact of large disturbances did not evaluate the spatial structures of NDVI images in the study areas. To demonstrate the ability of the variogram to depict landscape heterogeneity, spatial variability and patterns, experimental variograms and their variogram models were first analyzed and fit to seven images of areas A and B (

The three main features of a typical variogram model are (1) the range, (2) the sill, and (3) the nugget effect. The sill is the upper limit that a variogram approaches at a large distance, and is a measure of the variability of the investigated variable: a higher sill corresponds to greater variability in the variable. The range of a variogram model is the distance lag at which the variogram approaches the sill, and can reveal the distance above which the variables become spatially independent. The nugget effect is exhibited by the apparent non-zero value of the variogram at the origin, which may be due to the small-scale variability of the investigated process and/or measured errors. In this study, the variogram models of the seven NDVI images for areas A and B areas are exponential models. The spatial variations (Sill; _{0} + _{0} +

High-spatial-resolution observations (e.g., SPOT-HRV, pixel size of 20 m) capture most landscape spatial heterogeneity and are thus can be used to quantify the spatial heterogeneity within moderate spatial resolution pixels [

Sampling strategies are typically based on an assumed theoretical framework (Edwards and Fortin, 2001). Sampling under such a framework involves attempting to locate samples to capture the possible variations and fluctuations in a gradient field [

The LHS approach can also be used in SGS [

The SGS results verify that the limits of spatial analysis and interpolations of landscape variables are based on semivariograms (or autocorrelation functions) solely, stressing the need to account for spatial discontinuities [

This study presents a novel and effective approach that integrates cLHS, variograms, kriging and SGS in remotely sensed images for efficient monitoring, sampling and mapping of the impacts of chronologically ordered large disturbances on spatial characteristics of landscape changes to spatial structure, variability and heterogeneity. The NDVI images, which can be generated almost immediately after the remotely sensed data are acquired, were used as the inferential index because landscape changes induced by a large disturbance are easily recognized by changes in NDVI images. Variography of multiple NDVI images before and after a large disturbance is an essential method for characterizing and quantifying the spatial variability, structure and heterogeneity of landscapes induced by a disturbance. The variography results illustrated that cumulative impacts of disturbances on spatial variability existed and depended on disturbance magnitudes and paths, but were not always evident in spatiotemporal variability of landscapes in the study areas. Moreover, the cLHS approach is an effective sampling approach for multiple true NDVI images from their multivariate distributions to replicate the statistical distribution and spatial structures of the NDVI images. The sufficient number of NDVI samples using cLHS can be used to monitor and sample changes in landscapes induced by large physical disturbances. Kriging and SGS combined with the sufficient number of cLHS samples can be used to estimate and simulate NDVI images to generate maps that capture the spatial pattern and variability of actual NDVI images of disturbed landscapes. Kriging with sufficient number of NDVI cLHS samples produces NDVI maps with the best local estimates to identify patterns of NDVI images of disturbed landscapes. SGS with sufficient cLHS samples generate multiple realizations and an average of the realizations of NDVI and captures the spatial variability and heterogeneity of disturbed landscapes.

The authors thank the Soil and Water Conservation Bureau of Taiwan for providing field data and financially supporting this research under Contract No. SWCB-92-026-08. The authors also would like to thanks Mr. Deng for treatments of remote sensing data.

Location of the study areas.

NDVI images of area A on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

NDVI images of area B on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

Experimental variograms of NDVI images before and after disturbances in areas (a) A and (b) B.

Experimental variograms of NDVI samples for area A on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20 (f) 2003/12/17, and (g) 2004/11/19.

Experimental variograms of NDVI samples for area B on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

Locations of the 3,000 samples in areas (a) A and (b) B.

Kriging estimated NDVI images based on 3,000 samples in area A on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

Conditional simulated NDVI images based on 3,000 samples in area A on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31 (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

NDVI images estimated by kriging based on 3,000 samples in area B on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

Conditional simulated NDVI images based on 3,000 samples for area B on (a) 1996/11/08, (b) 1999/03/06, (c) 1999/10/31, (d) 2000/11/27, (e) 2001/11/20, (f) 2003/12/17, and (g) 2004/11/19.

Conditional simulated NDVI images for area A based on (a) 100, (b) 500, and (c) 1,000 cLHS samples on 1999/10/31

Conditional simulated NDVI images for area B based on (a) 100, (b) 500, and (c) 1,000 cLHS samples on 1999/10/31.

Statistics of NDVI images.

1996/11/08 | 0.36 | 0.04 | 0.11 | 0.48 | |

1999/03/06 | 0.32 | 0.04 | 0.13 | 0.43 | |

1999/10/31 | 0.14 | 0.07 | -0.22 | 0.33 | |

2000/11/27 | 0.15 | 0.07 | -0.14 | 0.35 | |

2001/11/20 | 0.37 | 0.05 | 0.03 | 0.50 | |

2003/12/17 | 0.15 | 0.06 | -0.12 | 0.33 | |

2004/11/19 | 0.35 | 0.06 | 0.05 | 0.54 | |

| |||||

1996/11/08 | 0.36 | 0.03 | 0.13 | 0.47 | |

1999/03/06 | 0.36 | 0.04 | 0.14 | 0.48 | |

1999/10/31 | 0.16 | 0.05 | -0.20 | 0.38 | |

2000/11/27 | 0.17 | 0.05 | -0.09 | 0.33 | |

2001/11/20 | 0.37 | 0.04 | 0.14 | 0.48 | |

2003/12/17 | 0.20 | 0.06 | -0.08 | 0.44 | |

2004/11/19 | 0.39 | 0.05 | 0.10 | 0.57 |

Variogram models of NDVI images.

1996/11/08 | Exponential model | _{0}=0.000453, _{0}+ |
(SS=7.774E-08; ^{2}=0.832, _{0}/_{0}+ |
^{2} =0.722 | |

1999/03/06 | Exponential model | _{0}=0.000147, _{0}+ |
(SS=3.490E-08; ^{2}=0.978, _{0}/_{0}+ |
^{2}=0.893 | |

1999/10/31 | Exponential model | _{0}=0.000878, _{0}+ |
(SS=1.573E-07; ^{2}=0.873,_{0}/_{0}+ |
^{2}=0.839 | |

2000/11/27 | Exponential model | _{0}=0.000761, _{0}+ |
(SS=18.597E-08; ^{2}=0.961, _{0}/_{0}+C=0.310) |
^{2}=0.894 | |

2001/11/20 | Exponential model | _{0}=0.000518, _{0}+ |
(SS=5.124E-08; ^{2}=0.878, _{0}/_{0}+ |
^{2}=0.723 | |

2003/12/17 | Exponential model | _{0}=0.000700, _{0}+ |
(SS=3.420E-07; ^{2}=0.893, _{0}/_{0}+ |
^{2}=0.737 | |

2004/11/19 | Exponential model | _{0}=0.000229, _{0}+ |
(SS=1.918E-07; ^{2}=0.930, _{0}/_{0}+ |
^{2}=0.862 | |

1996/11/08 | Exponential model | _{0}=0.000138, _{0}+ |
(SS=1.610E-08; ^{2}=0.953, _{0}/_{0}+C=0.104) |
^{2}=0.781 | |

1999/03/06 | Exponential model | _{0}=0.000712, _{0}+ |
(SS=6.070E-08; ^{2}=0.945, _{0}/_{0}+ |
^{2}=0.901 | |

1999/10/31 | Exponential model | _{0}=0.000590, _{0}+ |
(SS=1.678E-07; ^{2}=0.939, _{0}/_{0}+ |
^{2}=0.849 | |

2000/11/27 | Exponential model | _{0}=0.0001863, _{0}+ |
(SS=2.474E-07; ^{2}=0.952, _{0}/_{0}+ |
^{2}=0.908 | |

2001/11/20 | Exponential model | _{0}=0.0001205, _{0}+ |
(SS=5.621E-08; ^{2}=0.933, _{0}/_{0}+ |
^{2}=0.728 | |

2003/12/17 | Exponential model | _{0}=0.0001258, _{0}+ |
(SS=1.567E-07; ^{2}=0.949, _{0}/_{0}+ |
^{2}=0.820 | |

2004/11/19 | Exponential model | _{0}=0.0001161, _{0}+ |
(SS=1.186E-07; ^{2}=0.977, _{0}/_{0}+ |
^{2}=0.902 |

_{0}=Nugget; _{0}+

Statistics of 100, 500, 1,000 and 3,000 samples from NDVI images.

1996/11/08 | 0.36 | 0.04 | 0.22 | 0.44 | 1996/11/08 | 0.36 | 0.03 | 0.17 | 0.45 | ||||

1999/03/06 | 0.36 | 0.05 | 0.22 | 0.45 | 1999/03/06 | 0.36 | 0.04 | 0.17 | 0.47 | ||||

1999/10/31 | 0.16 | 0.05 | 0.00 | 0.24 | 1999/10/31 | 0.16 | 0.05 | -0.10 | 0.33 | ||||

2000/11/27 | 0.17 | 0.05 | 0.00 | 0.28 | 2000/11/27 | 0.17 | 0.05 | 0.00 | 0.33 | ||||

2001/11/20 | 0.37 | 0.04 | 0.19 | 0.44 | 2001/11/20 | 0.37 | 0.04 | 0.20 | 0.46 | ||||

2003/12/17 | 0.19 | 0.06 | 0.01 | 0.33 | 2003/12/17 | 0.20 | 0.06 | 0.00 | 0.38 | ||||

2004/11/19 | 0.39 | 0.05 | 0.19 | 0.05 | 2004/11/19 | 0.40 | 0.05 | 0.17 | 0.54 | ||||

1996/11/08 | 0.36 | 0.04 | 0.24 | 0.44 | 1996/11/08 | 0.16 | 0.07 | 0.00 | 0.30 | ||||

1999/03/06 | 0.31 | 0.05 | 0.20 | 0.38 | 1999/03/06 | 0.36 | 0.05 | 0.15 | 0.47 | ||||

1999/10/31 | 0.13 | 0.08 | -0.08 | 0.28 | 1999/10/31 | 0.15 | 0.06 | -0.04 | 0.29 | ||||

2000/11/27 | 0.15 | 0.07 | 0.00 | 0.28 | 2000/11/27 | 0.36 | 0.06 | 0.12 | 0.50 | ||||

2001/11/20 | 0.35 | 0.06 | 0.20 | 0.46 | 2001/11/20 | 0.36 | 0.04 | 0.17 | 0.44 | ||||

2003/12/17 | 0.15 | 0.07 | -0.05 | 0.29 | 2003/12/17 | 0.32 | 0.04 | 0.16 | 0.41 | ||||

2004/11/19 | 0.35 | 0.08 | 0.16 | 0.49 | 2004/11/19 | 0.14 | 0.07 | -0.12 | 0.29 | ||||

1996/11/08 | 0.37 | 0.04 | 0.17 | 0.44 | 1996/11/08 | 0.36 | 0.04 | 0.15 | 0.46 | ||||

1999/03/06 | 0.36 | 0.04 | 0.19 | 0.46 | 1999/03/06 | 0.36 | 0.04 | 0.16 | 0.48 | ||||

1999/10/31 | 0.16 | 0.05 | -0.20 | 0.26 | 1999/10/31 | 0.16 | 0.05 | -0.10 | 0.30 | ||||

2000/11/27 | 0.17 | 0.05 | 0.00 | 0.31 | 2000/11/27 | 0.17 | 0.05 | 0.00 | 0.33 | ||||

2001/11/20 | 0.37 | 0.04 | 0.19 | 0.45 | 2001/11/20 | 0.37 | 0.04 | 0.15 | 0.48 | ||||

2003/12/17 | 0.20 | 0.06 | 0.00 | 0.36 | 2003/12/17 | 0.20 | 0.06 | 0.00 | 0.44 | ||||

2004/11/19 | 0.40 | 0.06 | 0.17 | 0.53 | 2004/11/19 | 0.39 | 0.06 | 0.13 | 0.57 | ||||

1996/11/08 | 0.35 | 0.04 | 0.17 | 0.44 | 1996/11/08 | 0.36 | 0.04 | 0.20 | 0.46 | ||||

1999/03/06 | 0.32 | 0.04 | 0.18 | 0.40 | 1999/03/06 | 0.32 | 0.04 | 0.16 | 0.41 | ||||

1999/10/31 | 0.13 | 0.07 | -0.15 | 0.25 | 1999/10/31 | 0.14 | 0.07 | -0.19 | 0.33 | ||||

2000/11/27 | 0.15 | 0.06 | 0.00 | 0.30 | 2000/11/27 | 0.15 | 0.07 | 0.00 | 0.32 | ||||

2001/11/20 | 0.36 | 0.05 | 0.17 | 0.46 | 2001/11/20 | 0.36 | 0.05 | 0.07 | 0.47 | ||||

2003/12/17 | 0.14 | 0.06 | -0.05 | 0.31 | 2003/12/17 | 0.15 | 0.06 | -0.11 | 0.31 | ||||

2004/11/19 | 0.35 | 0.06 | 0.15 | 0.49 | 2004/11/19 | 0.35 | 0.06 | 0.12 | 0.52 |