# Integrating Remote Sensing Data with Directional Two- Dimensional Wavelet Analysis and Open Geospatial Techniques for Efficient Disaster Monitoring and Management

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials

#### 2.1. Directional 2D Morlet wavelet analysis

_{λ}(r⃑, θ)), and image, Im(φ

_{λ}(r⃑, θ)), parts of φ

_{λ}(r⃑, θ) are illustrated in Figure 1(a).

_{x}× N

_{y}grid nodes. The Morlet wavelet transform of Z(r⃑) is defined by the convolution of Z(r⃑) and the conjugate of the wavelet function, φ

_{λ}(r⃑), as

^{−1}represent the Fourier transform and the reverse Fourier transform, respectively; f⃑ = (f

_{x}, f

_{y})is a frequency.

_{x}N

_{y}times the expectation value of ∣FZ(f⃑)∣

^{2}, and is equal to the square mean of the original data as $\text{\u2211}_{{N}_{x}}\text{\u2211}_{{N}_{y}}{Z}^{2}/\left({N}_{x}{N}_{y}\right)$ [3]. The mean spectrum of the wavelet analysis of any data set can be normalized by the square mean of the original data to show how original data deviates from randomness, while the expectation value of the normalized mean spectrum for a spatial randomness is equal to one.

^{−1}(Im(φ(r⃑, θ))/Re(φ(r⃑, θ))), and the iso-phase lines are perpendicular to the directional vector $\stackrel{\rightharpoonup}{{w}_{0}}\left(\theta \right)$. The wavelet transform decomposes the variation of Z by the filtering bank into elements with periodically changing phases along the directional vector [8].The detecting direction in wavelet analysis is defined by the choice of the directional vector, $\stackrel{\rightharpoonup}{{w}_{0}}\left(\theta \right)$, that varies with the directional angle, θ. Figure 1(b) shows the Fourier transforms of the conjugate of the Morlet wavelet function with different scale factors and directional angles.

_{m}

_{in}, is chosen so that the maximum shift of the center in the Fourier transform of ${\phi}_{\lambda}^{*}\left(\stackrel{\rightharpoonup}{u},\theta \right),\left|\stackrel{\rightharpoonup}{{w}_{0}}\left(\theta \right)\right|/{\lambda}_{min}$, does not excess the Nyquist frequency, 2π∣f⃑∣

_{max}/2. Because ∣φ

_{λ}(u⃑, θ)∣ decays to 0.01∣φ

_{λ}(0,θ)∣ at ∣u⃑∣ = 3λ, the maximum value of the scale factor, λ

_{max}, is chosen by 3λ

_{max}≤ min (N

_{x}, N

_{y})/2 so that that all values of ∣φ

_{λ}(u⃑, θ)∣ being greater than 0.01∣φ

_{λ}(0, θ)∣ should be contained in the study area [14]. By setting N

_{x}=N

_{y}= 256, maximum 1integral value of λ

_{max}is 42 (3λ

_{max}≤ 256/2), while the minimum integral value of λ

_{m}

_{in}is four (6/λ

_{m}

_{in}≤ 2π × 0.5/2). According to Equation (7), determination of ${\text{\u2211}_{{f}_{x}}\text{\u2211}_{{f}_{y}}\left|F{\phi}_{\lambda}^{*}\left(\stackrel{\rightharpoonup}{f},\theta \right)\right|}^{2}$ is N

_{x}N

_{y}× (1±0.1%) in the scale range determined, as shown in Figure 1(c).

#### 2.2. System architecture for rapid information sharing

#### 2.3. Artificial data

#### 2.4. Field data

^{2}. The Chenyulan stream which follows the Chenyulan fault flows from south to north and elongates the watershed in the same direction. Different uplifting along the fault has generated abundant fractures throughout the watershed, resulting in an average slope of 62.5% and relief of 585 m/km

^{2}in the watershed. Moreover, the main course of the Chenyulan stream has a gradient of 6.1%, and over 60% of its tributaries have gradients exceeding 20%. The special geological and geographical characteristics of the watershed result in frequent landsides and debris flows [18]. At 01:47′12.6″ on Sep. 21, 1999, the ChiChi earthquake (7.3 on the Richter scale), caused by motion of the Chelungpu thrust fault, struck central Taiwan. The earthquake epicenter was located at 23.87°N and 120.75°E, around 30 km north-northwest of the Chenyulan watershed [19]. One year the earthquake, typhoon Xangsane brushed the eastern side of the watershed as it moved from south to north and dropped 127-270 mm of total rainfall in the watershed between Oct. 31, and Nov. 1, 2000 [20]. Another typhoon, Toraji, which brought intense rainfall over a short duration exceeding 300 years return period, hit the watershed as it moved east to west on July 28-31, 2001. After crossing Taiwan, typhoon Toraji degraded into a tropical storm; however, the typhoon dropped 339-757 mm of rainfall in the watershed [21]. Sediments already loosened by the ChiChi earthquake bore the torrential rainfall brought by the two typhoons. Consequently, a large quantity of loose sediment promoted massive debris flows during subsequent typhoons. The Taiwan Water and Soil Conservation Bureau announced debris flood warnings for several tributaries of the Chenyulan stream after typhoon Toraji. Location of landslides was shifted from mid-hills to hilltops in central Taiwan by the ChiChi earthquake, and hilltop landslides triggered serious debris flows [22]. The study area 3.2×3.2 km

^{2}(256×256 pixels) was selected upstream of the largest debris flood in the watershed (Figure 3).

**X**

_{i}is a matrix composed of NDVI values of 50 control points at stage i;

**X**

_{d}is a matrix composed of NDVI values of 50 control points at the datum image; a and b are coefficients.

## 3. Results and Discussion

#### 3.1. Artificial data

#### 3.2. Field data

#### 3.3. Open GIS

#### 3.4. Discussion

^{2}, determines the local variation around a grid. For an end-user who concerns the exact boundary of the landslides, the modulus of wavelet transform can be substituted into the existing algorithm for edge detecting like Canny algorithm that calculates the maximum wavelet modulus at an edge [28]. The wavelet function have to be directional like Gabor or spline dyadic wavelets [28, 29]. The dominant scale factors are dimensions that illustrate how clustered landslides expand, whereas the dominant directional angles identify the direction in which those landslides were aligned. Landslide initiation is determined by static and dynamic factors. Static factors describing bearing capacity include geomorphology and land-cover, whereas dynamic factors describing triggers of mass movement include hydrological and perturbation conditions [30]. A strong trigger generates a large determinant scale factor for clustered landslides and an intensive NDVI variation (Figure 8(c)). As the anisotropic characteristics of landslides vary with different disturbances, the dominant directional angles identified by directional wavelet analysis vary with different disturbances. Typhoons always generate more recurrent changes along an exposure aspect aligned with the typhoon path, and abrupt changes perpendicular to the aspect. Therefore, the spatial distribution of significant differences in NDVI variations should be located on a terrain with aspects exposed to a typhoon, and along side banks of gullies that are prone to accumulate rainfall (Figure 8(d)).

## 4. Conclusions

## Acknowledgments

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**Figure 1.**Characteristics of the directional 2D Morlet wavelet function. (a) Vertical and lateral views of real and image parts of the Morlet wavelet function, while the directional angle is π/4 and the scale factor is one. (b) Fourier transforms of the conjugate of wavelet function with different scale factors and directional angles, where A's scale factor is three and directional angle is π/4 while B's scale factor is 18 and directional angle is −π/4. (c) For a scale factor between four and 42, determination of Equation (7) is 65536 × (1 ± 0.1%)for a study area composed of 256 × 256 (65536) grid nodes.

**Figure 4.**Two spatially random point patterns were generated with point densities of (a) 0.025 (1639/65536) and (b) 0.1 (6554/65536). Normalized mean spectrums randomly fluctuate around a value of one in the envelope with a maximum of 2.96 and a minimum of 0.23. The expectation value of normalized mean spectrum for a spatial randomness is one. And the envelope is generated from 100 duplicates of spatially random point patterns.

**Figure 5.**(a) Point clumps with different densities were generated in 4 ′A′ regions each with area of 20 × 25 on a random background ′B′ with area of 256 × 256. The background randomness has a point density of 0.025 (1639/65536). Spectrum maps of clumps with (b) 2-fold, (c) 4-fold, (d) 6-fold, (e) 8-fold, and (f) 24-fold point densities relative to the background were used to verify the performance of directional 2D Morlet wavelet analysis in separating true patterns from random fluctuations. The dashed polygons represent shapes and scales of point clumps. For a recognizable pattern, the thick solid line, that represents a normalized mean spectrum of one, is expected to be totally contained in the dashed polygon.

**Figure 6.**Belt patterns with different declinations and widths for directional 2D Morlet wavelet analysis in finding dominant scales and angles. (a) The largest normalized mean spectrum is marked in a directional angle perpendicular to the belt declination. (b) Distinguishing belt ′B′ from belt ′A′ by their normalized mean spectrum values can be done only with a scale factor of filtering banks in wavelet analysis larger than clump sizes, e.g. a scale factor of 40.

**Figure 7.**Significant differences at a pre-defined location in (a) two patterns denominated as pre- and post-disturbances were assessed by their (b) normalized mean spectrums, where dashed polygons represent shapes and scales of point clumps. (c) Increments of normalized mean spectrums for post-disturbances relative to pre-disturbance patterns were identified by scale factors and directional angles. (d) Localized spectrums determined by setting the filtering bank according to identified scale factors and directional angles were calculated for every node of the post-disturbance pattern. Location of high spectrums (shaded area) in the post-disturbance pattern coincided with the pre-defined location (empty polygon).

**Figure 8.**(a) NDVI images at four Stages were assessed by (b) normalized mean spectrums. (c) Significant differences of NDVI variations between stages were identified by scale factors and directional angles. (d) Locations of significant differences between stages were drawn in post-disturbance images. Hill aspects within ±π/4 aligned with typhoon paths were also depicted to verify the orographic effects in typhoons.

**Figure 9.**Implements for quick transformations of interoperable and exchangeable disaster information by open geospatial technologies with GML compliant documents that can be (a) transformed into SVG and browsed by a web browser, (b) retrieved by a WFS request, and (c) down-loaded and operated in a user-end application.

**Table 1.**Comparisons between WMS/WFS and GML standards. *

Standards | Web Map Service (WMS)/Web Feature Service (WFS) | Geography Markup Language (GML) |

Briefs | Specifications standardize the way in which maps are requested by clients and the way that servers describe their data holdings. | A specification for the transport and storage of geographic information, including both the spatial and non-spatial properties of geographic features. |

Properties | Maps are generally rendered in common formats like Graphics Interchange Format (GIF), Portable Network Graphics (PNG), etc. Data products are in the form of static maps. | GML specification is more suitable for vector data exchange between WebGISes. However, Adaptation of GML in WebGIS environment comes with a computational overhead. |

^{*}Compilation from [35].

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**MDPI and ACS Style**

Lin, Y.-B.; Lin, Y.-P.; Deng, D.-P.; Chen, K.-W.
Integrating Remote Sensing Data with Directional Two- Dimensional Wavelet Analysis and Open Geospatial Techniques for Efficient Disaster Monitoring and Management. *Sensors* **2008**, *8*, 1070-1089.
https://doi.org/10.3390/s8021070

**AMA Style**

Lin Y-B, Lin Y-P, Deng D-P, Chen K-W.
Integrating Remote Sensing Data with Directional Two- Dimensional Wavelet Analysis and Open Geospatial Techniques for Efficient Disaster Monitoring and Management. *Sensors*. 2008; 8(2):1070-1089.
https://doi.org/10.3390/s8021070

**Chicago/Turabian Style**

Lin, Yun-Bin, Yu-Pin Lin, Dong-Po Deng, and Kuan-Wei Chen.
2008. "Integrating Remote Sensing Data with Directional Two- Dimensional Wavelet Analysis and Open Geospatial Techniques for Efficient Disaster Monitoring and Management" *Sensors* 8, no. 2: 1070-1089.
https://doi.org/10.3390/s8021070