Quantifying the Spatial Heterogeneity of the Land Surface Parameters at the Two Contrasting KoFlux Sites by Semivariogram

Quantifying the Spatial Heterogeneity of the Land Surface Parameters at the Two Contrasting KoFlux Sites by Semivariogram

Sang-Ki Moon

, Youngryel Ryu

, Dongho Lee

, Joon Kim

and Jong-Hwan Lim

1

Dept. of Atmospheric Sciences, Yonsei Univ., Seoul 120-749, Korea

2

Biometeorology Lab., Ecosystem Science Division, Dept. of Environmental Science, Policy, and Management (ESPM), Univ. of California, Berkeley, CA 94720

3

Korea Forest Research Institute, Seoul 130-712, Korea

(Received March 16, 2007; Accepted June 11, 2007)

세미베리오그램을 이용한 KoFlux 광릉(산림) 및 해남(농경지) 관측지 지면모수의 공간 비균질성 정량화

문상기¹·류영렬²·이동호¹·김 준¹*·임종환³

1

연세대학교 대기과학과,

미국 캘리포니아 주립대학교 버클리 캠퍼스 환경과학 정책관리학과

3

국립산림과학원, 산림생태과

(2007년 3월 16일 접수; 2007년 6월 11일 수락)

ABSTRACT

The remote sensing observations of land surface properties are inevitably influenced by the landscape heterogeneity. In this paper, we introduce a geostatistical technique to provide a quantitative interpretation of landscape heterogeneity in terms of key land surface parameters. The study areas consist of the two KoFlux sites: (1) the Gwangneung site, covered with temperate mixed forests on a complex terrain, and (2) the Haenam site with mixed croplands on a relatively flat terrain. The semivariogram and fractal analyses were performed for both sites to characterize the spatial heterogeneity of two radiation parameters, i.e., land surface temperature ( LST ) and albedo.

These parameters are the main factors affecting the reflected longwave and shortwave radiation components from the two study sites. We derived them from the high-resolution Landsat ETM+

satellite images collected on 23 Sep. 2001 and 14 Feb. 2002. The results of our analysis show that the characteristic scales of albedo was >1 km at the Gwangneung site and approximately 0.3 km at the Haenam site. For LST , the scale of heterogeneity was also >1 km at the Gwangneung site and

>0.6 to 1.0 km at the Haenam site. At both sites, there was little change in the characteristic scales of the two parameters between the two different seasons.

Key words : Spatial heterogeneity, LST , Albedo, Semivariogram, Characteristic scale I. INTRODUCTION

Spatial heterogeneity, which causes scaling problems, complicates our understanding of energy and mass exchanges at the land-atmosphere interface. The land- scape heterogeneity obviously brings on questions regarding the spatial (and likely temporal) representa-

tiveness of the sampled area in the measurement and

modeling. In the absence of spatial heterogeneity at a

study site, scaling of measurements between different

scales would be possible without significant errors. The

quantitative analysis of spatial heterogeneity can be

facilitated through processing the digital remote sens-

ing data in a geographic information system (GIS)

Corresponding Author: Joon Kim([email protected])

environment (Quattrochi and Goodchild, 1997).

In such a process, the spatial heterogeneity can be partitioned into two components: (1) the spatial vari- ability of the surface property over the scene under observation and (2) the spatial structure that is also called as objects or patches (Garrigues

2006).

The former is the total amount of variation whereas the latter is an expression of spatial heterogeneity causing spatial pattern and its related process or mechanism (Levin, 1992). Both components can be quantified by the semivariogram analysis which cal- culates the dispersion between two random compo- nents, while statistical variance represents the dispersion from the mean. Based on the relationship between the length scale and measured variation, semivariogram can provide a characteristic length scale of patches, which indicates the size of spatial structure and the approximate scale of related pro- cesses (e.g., Garrigues

2006).

Satellite images of the Moderate Resolution Imag- ing Spectroradiometer (MODIS), ecohydrological modeling and tower flux measurements are being inte- grated to better understand water and carbon cycles in typical landscapes of Korea under the research frame- work of KoFlux (Kim

., 2006; Lee

., this issue). The two contrasting KoFlux sites are the Gwangneung and the Haenam sites, which are charac- terized by mixed temperate forests on a complex terrain and mixed croplands on a simple terrain, respectively.

At both sites, the monitoring, processing and interpre- tation of carbon and water fluxes have been hampered by the difficulties arising from complex topography and/or the heterogeneity of the site.

In this paper, we quantified the spatial heterogeneity of the satellite-driven land surface temperature (

) and albedo at the above two KoFlux sites. The

and albedo are the main factors affecting the upwelling components of net radiation. To investigate whether the quantified scales of heterogeneity at each site vary with seasonal changes in vegetation cover, we selected the Landsat ETM+ satellite images from the growing sea- son (23 Sep. 2001) and the dormant season (14 Feb.

2002). The semivariogram and fractal analyses were then performed to identify the characteristic length scale of patches associated with the two radiation parameters at each site. Finally, the implication of the results was discussed in relation to the evaluation of the reliability of MODIS-based radiation products and scaling algorithms.

II. MATERIALS AND METHODS

2.1. Study sites

The Gwangneung forest (DK) site is located at a deciduous forest catchment (22 ha) with a topographic mean slope of 20

, the soil depth of 0.4-0.8 m on weathered gneiss basement (Moon

, 2005). A detailed description of the Gwangneung supersite can be found in Lee

(this issue). The Haenam agricul- tural site (FK) is located near the southwestern coast of the Korean Peninsula with land cover types consisting of scattered rice paddies and various croplands. The major vegetation near the tower (within ~300 m) is sea- sonally cultivated crops such as beans, sweet potatoes, Indian millet, and sesame. Beyond this area, rice pad- dies prevail in the south, the east and the west. Also found around the tower are the roads, small hills, resi- dential areas, and scattered small forests (Fig. 1).

Topography in the FK site is relatively flat at a regional scale, except Wolch’ul Mountain (809 m a.s.l.) and Duryun Mountain (703 m a.s.l.) which are located about 30 km north and 20 km south from the flux tower, respectively (Lee

2003).

2.2. Semivariogram and fractal analyses Semivariance is a measure to estimate the variability of data at a certain interval (time or space). This vari- ability is defined as the arithmetic mean of the squared differences between two experimental measures [

(

),

z

(

+

)] at any two points separated by the vector

; i.e.,

(1) where

(h) is the number of experimental pairs [

(

),

z

(

+

)] of data separated by the vector

(Journel and Huijbregts, 1978). The semivariogram is the plot of semivariance at each separation distance. When the semivariance no longer increases, the constant semivari- ance is called the

, and the distance at which the semi- variance approaches the variance is called the

of the regionalized variable. This range is a neighborhood within which all locations are related to one another (Davis, 1986). The spatial structures can be quantified by this range. In some circumstances, semivariogram will appear not to pass the origin but rather will have an inter- cept. This phenomenon is called the ‘

’, which is caused by the sampling error or the variability at finer scales than the measurement scale.

γ^*( )h

1 2

---

–

+

i 1= N h( )

= ∑

The semivariogram may increase continually as

increases. In such a case, the semivariogram cannot have range and sill parameters but the fractal property within the image domain. In double log plots of the semivariogram, the fractal shows a linear relationship between

and semivariance. The fractal property can be characterized by the fractal dimension and fractal scale. The fractal dimension can be calculated by the slope (

) of the regression line as followed: Fractal dimension (

) = 3-(

/2) in three dimensions. The frac- tal scale is the scale where there is fractal property, i.e.,

h

where linear relationship appears in a double log plot.

In this study, the range and fractal scale from the semi- variogram are used to quantify spatial heterogeneity of the parameters. The semivariogram and fractal analyses were conducted on two different dates (23 Sep. 2001 and 14 Feb. 2002).

2.3. Landsat ETM+ processing

For this analysis, two high resolution satellite imag- eries (visual and near infrared band: 30 m, thermal band: 60 m) of Landsat ETM+(23 Sep. 2001 and 14 Feb. 2002) were used after the geometric correction using a digital map (1:5,000), and the atmospheric cor- rection using a COST model (Chavez, 1996). The

was calculated from thermal band digital numbers using the conversion equations following the Landsat Project Science Office (http://ltpwww.gsfc.nasa.gov/

IAS/handbook/handbook_htmls/chapter11/

chapter11.html):

(2) where

is spectral radiance (Wm

ster

m

), and

DN

is digital number.

is transformed into at-satellite brightness temperature:

Lλ

= 0.037

+ 3.200

Fig. 1. The IKONOS images of the Gwangneung (upper) and Haenam (lower) sites including flux towers in winter.

(3)

where

B is effective at-satellite temperature (K),

= 666.09 mWcm

ster

m

,

=1282.71 K. Equation (3) is just black body temperature of which the emis- sivity is assumed to be 1. The correction needs to be applied to actual land cover using spectral emissivity (

). One method of estimating emissivity is using frac- tional cover mixture model. The model assumes that the emissivities of background soil and vegetation are already known and these values are mixed according to the fractional cover (Sobrino

2001). The frac- tional vegetation cover is estimated from the normal- ized difference vegetation index (

). Choudhury

(1994) suggested that the relationship between

NDVI

and fractional cover:

(4) where

max is the case of complete vegetation cover, and

min is the case of bare soil. In this study, the maximum and minimum of

in imag- eries were used. The coefficient

is the function of leaf orientation distribution. The erectophile canopy has

of 0.60 while that of the planophile canopy is 1.25. Here, we used the averaged value of 0.92. The emissivity esti- mated from the vegetation cover is calculated as fol- lows:

(5) where

indicates composite emissivity,

v vegetation emissivity, and

s soil emissivity. The mean

s and

v of Landsat ETM+thermal band can be estimated to be

TB K2

ln

--- 1

+

⎝ ⎠

⎛ ⎞

---

=

1

–

NDVI_max

–

---

⎝ ⎠

⎛ ⎞^a

–

=

ε_λ^≈ε_vfv

+

1 –

Fig. 2. The ^LST images (1 km

1 km) at the DK and FK sites on 23 Sep. 2001 and 14 Feb. 2002. (The white circle indicates

the eddy covariance tower.)

0.978 (Li

, 2004) and 0.985 (Sobrino

, 2001), respectively. The emissivity corrected

(

) is calcu- lated as follows (Artis and Carnahan, 1982):

(6) where

is the wavelength of emitted radiance (for which the peak response and the average of the lim- iting wavelengths (=11.5

m) was used; Markham and Barker, 1986) and

is a constant (=

c

/

=1.438

10

m K, where

is the Boltzmann’s constant (= 1.380

10

J K

),

is the Planck’s constant (= 6.626

10

J s), and c is the speed of light (= 2.998

10

m s

)).

Then, the broadband albedo was calculated from a linear formula using three bands (Liang, 2004):

(7) where

is the 2

band (0.52 to 0.60

m) reflectance,

α4

is the 4

band (0.72 to 0.90

m) reflectance, and

is the 7

band (2.09 to 2.35

m) reflectance.

III. RESULTS AND DISCUSSION

3.1. Scales of heterogeneity of LST and albedo

Fig. 2 shows the

images in the DK and FK sites on 23 Sep. 2001 (growing season) and on 14 Feb. 2002 (dormant season). At the DK, the semivariograms of

LST

show a linear relationship, i.e., a fractal property throughout the image domain on both days (Fig. 3). At the FK, the semivariogram of

also shows a fractal property on 14 Feb. 2002, but produced a characteristic scale of > 600 m on 23 Sep. 2001 (Fig. 3).

The existence of a fractal property can be explained by the existence of large patches comparable to the scale of the image (i.e., 1 km

1 km) (Fig. 2). Based on a careful examination of the IKONOS images of the two sites (in Fig. 1), for example, such large patches can be related to the aspect of hillslopes (facing south or north) in the catchment at the DK. The characteristic scale of 0.6 to 1 km at the FK site may correspond to

St TB

1 +

---

ln

---

=

α

= 0.5260

+ 0.3139

+ 0.1120

Fig. 3. The fractals and semivariograms of LST at the DK and FK sites on 23 Sep. 2001 and 14 Feb. 2002. (Exp(a, b ) in the

semivariogram implies an exponential model with the range of b and the partial sill (sill-nugget) of a . AiC stands for Arkaike

Information Criteria .)

the size of residential area including the weather station where the eddy covariance flux tower is located (Figs.

1 and 2). Overall,

images at the DK and FK sites on both days have a consistent spatial structure (i.e., a fractal structure) and a large scale of heterogeneity (i.e.,

> 600 m), suggesting a relatively homogeneous struc- ture of

within the 1 km

1 km image.

Fig. 4 shows the broadband albedo images of the DK and FK sites on those two selected days. It is immedi- ately noted in Fig. 4 that the structure of albedo at the DK site is hierarchical, such that small patch mosaics (consisting of smaller steep hillslopes with a slope of

>20

) are embedded in larger hillslopes. Such a hierar- chical structure is clearly demonstrated in both images that represent the growing and non-growing seasons.

Fig. 5 shows evidently that the broadband albedo at the DK site has a fractal property, which corresponds to the

large patches of the southward and northward hills- lopes of the catchment studied here.

At the FK site, the spatial structure of the broadband albedo was quite different and characterized by smaller patches (Fig. 4). The patches of a similar size (of a few hundred meters) with different values of albedo are scattered throughout the whole image domain. The results of the semivariogram analysis in Fig. 5 also sup- port this observation from the images. The two semi- variograms demonstrate no fractal property but an exponential form with the characteristic length scale of approximately 300 m (Fig. 5). Further examinations of the IKONOS (Fig. 1) and other available images sug- gest that the dominant patch size of ~300 m is likely associated with bare soils scattered in the field and/or rice paddies during the non-growing season whereas in residential areas during the growing season.

Fig. 4. Broadband albedo images (1 km ^× 1 km) at the DK and FK sites on 23 Sep. 2001 and 14 Feb. 2002. (The white circle

indicates the eddy covariance tower.)

The spatial structures of the broadband albedo at the DK and FK sites are clearly different. In short, the DK site was more homogeneous than the FK site in terms of albedo because the former has larger patches char- acterized by fractal property while the latter has smaller patches characterized by the characteristic scales of approximately 300 m.

The fractal property found in the DK site did not change with season for both

and albedo (Figs. 3 and 5). Similarly, at the FK site, the forms of exponen- tial semivariogram (or spatial structures) of albedo did not change. For the albedo of the FK site, the spatial structure varied a little between ~250 m (in fall) and

~350 m (in winter), demonstrating a consistent charac- teristic length scale that is much smaller than that of the DK site by a factor of 3 to 4. We may conclude that there was little seasonal change in terms of both

and albedo at each site. Further examination, however, is needed with more satellite images which represent a wide range of vegetation cover and wetting/drying con- ditions.

3.2. Implication and application of the quan- tified heterogeneity

Various plot scale measurements have been con- ducted in the DK and FK sites to monitor temporal and spatial changes of ecohydrological and biogeochemical variables such as soil moisture content, soil tempera- ture, hydraulic conductivity, soil CO

efflux, leaf area index, leaf/water isotope, litter fall, heat and water vapor fluxes, radiation, etc. However, due to the inher- ent spatial heterogeneity of each site, the outcomes of these variables may vary depending significantly on the representativeness of individual plot locations. It would be desirable to identify the characteristics and the dis- tribution of relatively homogeneous patch mosaics in the site so that the field measurements may be coordi- nated by taking such information into account (Lee

., this issue). As demonstrated in the previous sec- tions, these patch mosaics can be identified based on satellite observations and cartographically expressed using the size derived from semivariogram and fractal analyses.

Fig. 5. The fractals and semivariograms of broadband albedo at the DK and FK sites on 23 Sep. 2001 and 14 Feb. 2002.

The effect of land surface heterogeneity on the MODIS driven

and albedo has been pointed out recently by Ryu

(2007). In their study, the MODIS atmospheric (5 and 10 km scale) and land (1 km scale) products were used as inputs to estimate radiation components (1 km scale) over the DK and FK sites. It is worth noting that our results of the dif- ferent scales of heterogeneity between the DK and FK sites are clearly and uniquely reflected in the errors associated with the retrievals of outgoing shortwave (i.e., albedo) and longwave radiation (

) in Ryu

. (2007). They reported a large discrep- ancy between the measured and the MODIS-driven albedo at the FK site but a better agreement at the DK site. This is consistent with our results that the FK site is more heterogeneous (with a smaller patch scale of the order of 300 m) than the DK site (Figs. 2 and 4). As expected, they found a very good agree- ment in

for both FK and DK sites where the

LST

, a major determinant of

, has a larger scale of spatial heterogeneity (> 0.6 to 1 km).

To minimize the uncertainties related to the scale dependency of measurements and modeling mentioned above, the primary task is to quantitatively describe the spatial heterogeneity of important land surface param- eters (Garrigues

, 2006). In this regard, the spatial characteristics of albedo and

derived in this study can be implemented to improve the reliability of satel- lite and model algorithms that are currently involved in KoFlux researches.

IV. CONCLUSIONS

Spatial heterogeneity is a common rule in nearly all landscapes of Korea. It is a demanding task to infer the scale of ecohydrological processes from geo- graphically distributed phenomena, which are mea- sured by remote sensing. In this paper, we have demonstrated a relatively simple way to do this by using the semivariogram and fractal analysis. The quantitative interpretation of complexity and hetero- geneity of the study sites need to be incorporated not only in the experimental design of ground truth mea- surements, but also in the algorithms of models and satellite remote sensing. This study presents an important step forward to make effective use of the remote sensing resource with a wide range of spatial, spectral, and temporal resolutions in integrating and interpreting data from different scales.

적 요

경관의 비균질성은 원격 탐사에 의한 지면 특성 관 측에 필연적으로 영향을 준다 . 본 연구에서는 주요 지 면 모수의 경관 비균질성을 정량적으로 해석할 수 있 는 지구통계기법을 소개한다 . 연구지역은 두 곳의

KoFlux 연구지로서 (1) 복잡지형의 온대 혼합림으로 구성된 광릉 연구지와 (2) 비교적 평탄한 농경지인 해 남 연구지이다 . ^{복사 모수인 지면온도} ( ^LST ) ^{와 알베도의}

공간적 비균질성을 특성화하기 위하여 세미베리오그램 과 프랙털 분석을 수행하였다 . 이 두 모수는 두 연구 지의 상향 장파 및 단파 복사를 결정하는 중요한 인 자들이다 . 이 모수들은 2001 년 9 월 23 일과 2002 년 2

월 14 ^{일의 두 지역의 고해상도} Landsat ETM+ ^영상에

서 추출하였다 . 분석 결과 , 광릉과 해남 연구지는 알베 도의 특성 규모가 각각 1 km 이상 그리고 약 0.3 km 이었다 . 지면온도의 경우 , 특성 규모는 광릉이 1 km ^{이상 그리고 해남이} 0.6-1.0 km ^{이상이었다} . ^두

지면 모수의 특성 규모는 두 지역에서 모두 계절 변 화를 보이지 않았다 .

ACKNOWLEDGEMENTS

This work was supported by the Sustainable Water Resources Research Center of 21st Century Frontier Research Program (Grant code: 1-8-2); the Eco-Tech- nopia 21 Project of the Ministry of Environment; and the BK21 program, Ministry of Education and Human Resource Management of Korea. The authors would also like to thank two anonymous reviewers for helpful comments that improved this paper.

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