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4种常用植被指数的地形效应评估教程

1007-4619 (2013) 01-0210-25 Journal of Remote Sensing 遥感学报

Received: 2012-01-05; Accepted: 2012-05-17

Foundation: National Basic Research Program of China (973 Program) (No. 2010CB833503, 2010CB950702); National High Technology Research and Development Program of China (863 Program) (No. 2009AA122103); Priority Academic Program Development of Jiangsu Higher Education Institutions

First author biography: ZHU Gaolong (1974— ), male, associate professor, Ph.D. His research interests are retrieving biophysical parameters of vege-tation covers using multi-angle remote sensing data. E-mail: zhugaolong@https://www.wendangku.net/doc/8a1787913.html,

Corresponding author biography: JU Weimin (1963— ), male, professor, His research interests are ecology environmental remote sensing and global change. E-mail: juweimin@https://www.wendangku.net/doc/8a1787913.html,

Evaluation of topographic effects on four commonly used

vegetation indices

ZHU Gaolong 1, 2, LIU Yibo 1, JU Weimin 1, CHEN Jingming 1, 3

1. International Institute for Earth System Science , Nanjing University , Nanjing 210093, China ;

2. Department of Geography, Minjiang University , Fuzhou 350108, China ;

3. Department of Geography , University of Toronto , Toronto , Ontario , Canada M5S 3G3

Abstract: Vegetation Indices (VIs) derived from remotely sensed data have been developed to monitor the Earth’s vegetation

cover. However, the topographic influence on VIs is an inevitable issue and is usually neglected in their large scale applications. In this study, the topographic effects on four commonly used vegetation indices, including Simple Ratio (SR), Normalized Difference Vegetation Index (NDVI), Reduced Simple Ratio (RSR), and Modified Normalized Difference Vegetation Index (MNDVI), derived from Landsat TM data over a mountainous forest area are evaluated. Two simple methods, the cosine correction and C-correction models, with different treatments of the influence of the diffused irradiance on reflectance, are used to remove the topographic effects on selected VIs. The results indicate that the reflectance in the Near Infrared (NIR) and Short Wave Infrared (SWIR) bands are more sensitive to topographical variations than that in the red band. Diffused radiance from the sky in the red band can moderate the variations of red band reflectance with topography, while this moderation is weak in the NIR and SWIR bands. The topography affects strongly vegetation indices which are not expressed as band ratios, such as RSR and MNDVI, resulting in negative biases on Sun-facing slopes and positive biases on Sun-backing slopes. As the slope increases, these biases increase rapidly. Therefore, the topographic effects should be carefully removed before using these non-band-ratio vegetation indices for vegetation parameter retrieval. Vegetation indices which are expressed as band ratios, such as SR, NDVI, can greatly reduce the noise caused by topographical variations. However, these indices still include significant topographic ef-fects on steep slopes. SR is more sensitive to topographical variations on steep slopes than NDVI. The C-correction model is much better than the cosine correction model in removing topographic effects on VIs, especially on steep slopes. Key words: vegetation index, topographic effect, topographic correction, band ratio CLC number: TP702 Document code: A

1 INTRODUCTION

Vegetation Indices (VIs) derived from remotely sensed data have been widely used for monitoring the Earth’s vegetation at local, regional, continental, and global scales. The VIs have been proved to be better than a single spectral band for estimating the biophysical parameters of vegetation, including leaf area index (LAI), fractional vegetation cover, biomass, and photosynthetic activity (Clevers, 1989; Myneni & Williams, 1994; Chen, et al., 2006). In addition to vegetation changes, there are a number of factors that also influence VIs, including soil background, atmospheric conditions, topography, illumination and viewing geometry, and sensor calibration (LePrieur, et al., 1994; Chen, 1996). These factors very often cause unknown noises in VIs and impact the effectiveness of their applications. A perfect VI should enhance its sensitivity to vegetation change and minimize the noises caused by other factors. Several Soil Adjusted Vegetation Index (SAVI) family indices have been proposed to reduce the influence of soil background (Huete, 1988; Baret & Guyot, 1991; Qi, et al., 1994; Gilabert, et al., 2002). Modified Normalized Difference Vegetation Index (MNDVI) and Reduced Simple Ratio (RSR) which combine the reflectances in the Red, Near Infrared (NIR), and Short Wave Infrared (SWIR) bands are able to reduce the background effects (Nemani, et al., 1993; Brown, et al., 2000). Global Environment Monitoring Index(GEMI) is designed to minimize atmospheric noise (Pinty & Verstrate, 1992). Enhanced Vegetation Index (EVI) can reduce both the effects of atmospheric condition and soil background (Liu &

Citation format: Zhu G L, Liu Y B, Ju W M, Chen J M. 2013. Evaluation of topographic effects on four commonly used vegetation indices. Journal of Remote Sensing, 17(1): 210–234

ZHU Gaolong, et al.: Evaluation of topographic effects on four commonly used vegetation indices 211

Huete, 1995). Although these indices might have some advan-tages for specific purposes, they are not based on the band ratio form and much of noise may be retained or even enhanced (Chen, 1996). It has been recognized that taking ratios among different spectral bands has the advantage of reducing unwanted noise caused by non-vegetation factors because these factors often make the reflectances in the different bands change in the same direction. Normalized Difference Vegetation Index (NDVI) (Rouse, et al., 1974), simple ratio (SR) (Jordan, 1969), and modified simple ratio (MSR) (Chen, 1996) are expressed as the ratio of NIR and red bands and can remove much of measurement noise in individual bands (Holben & Justice, 1981; Lee & Kauf-man, 1986; Brugess, et al., 1995; Matsushita, et al., 2007).

The topographic effect on radiation may be defined as the difference in reflected radiance observed by a sensor between inclined and horizontal surfaces. This difference is a function of the orientation of the surface relative to the light source and the sensor position (Holben & Justice, 1980). Topographic effects on a pixel are mainly due to terrain shadows, reflection from adja-cent terrains, sky occlusion, and alteration to the Bidirectional Reflectance Distribution Function (BRDF) of the cover type (Schaaf, et al., 1994). The noise induced to VIs by topography is quite complex, and it is usually neglected in their large area applications. However, the topographic effects cannot necessarily be assumed to be insignificant, even when slopes are small (Combal & Isaka, 2002). Kusaka and Sakane (1997) also found that NDVI derived from NOAA/AVHRR data over the rugged surface includes significant topographic effects. Burgess, et al. (1995) showed that topography caused an error of 13.5% in NDVI irrespective of the illumination angle for 50 m resolution pixels. A variety of methods have been developed to remove topographic effects. The most often used models include the Minnaert correction (Smith, et al., 1980), Lambert cosine correc-tion (Teillet, et al., 1982), C-correction (Teillet, et al., 1982), and Sun-Canopy-Sensor (SCS) models (Gu & Gillespie, 1998). Several improved models have been proposed to reduce topo-graphic effects based on different assumptions (Dymond & Shepherd, 1999; Vincini, et al., 2002; Kane, et al., 2008; Huang, et al., 2008; Wen, et al., 2009). Some topographical correction models have been applied to images over forests with some degree of success using high resolution digital elevation model (DEM) data (Meyer, et al., 1993).

The objective of this study is to evaluate the topographic effects on ratio-based VIs including SR, NDVI, and non-ratio based VIs including RSR and MNDVI commonly used for forest LAI retrieval based on remotely sensed data. The ability of two topographical correction models, the Lambert cosine correction

and c-correction, to correct topographic effects are also investi-gated.

2 MATERIALS AND METHODS 2.1 Experiment area

This study is performed in Maoershan Mountain, which is lo-cated in Heilongjiang Province of northern China (45.2659o- 45.3232oN, 127.4957o-127.6047oE). It covers an area of 26620 hm 2. The elevation in this hilly highland varies from 250 m to 817 m with a mean slope of 14.2°. The mean annual temperature and precipitation in this area are 2.8 oC and 723.8 mm, respectively. It is covered by a regenerated forest with various vegetation types. According to the forest inventory dataset generated by Northeast Forestry University in Heilongjiang Province, broadleaf, needleleaf, and mixed forests cover 80%, 15%, and 5% of this study area, respectively. The forests are approximately 50 years old.

2.2 TM data processing

A Landsat-5 TM image covering the study area was down-loaded from United States Geological Survey (USGS). The TM image was acquired on 24 June, 2009, with a solar elevation angle of 61.3° and a solar azimuth angle of 134.7° from north. The TM image was registered to within half a pixel with 17 ground control points. Radiometric correction was made using the gain and offset parameters of each band included in the Landsat-5 TM header file. Surface reflectance was obtained after atmospheric correction using the 6S code with inputs of a conti-nental air-mass, mid-latitude summer climate, a uniform target, and 40 km atmospheric visibility (Vermot, et al., 1997). The non-forest (i.e., croplands, resident areas) and cloud covering areas were excluded by supervised classification and ground reference data. The resultant surface reflectance image was projected in the UTM/WGS84 coordinate at a resolution of 30 m. The total number of the forest pixels is 242131.

2.3 Selection of vegetation indices

Four vegetation indices were selected and calculated from the surface reflectance images to investigate their sensitivities to topographic effects (Table 1). SR and NDVI are the most widely used vegetation indices based on the ratios of red and NIR bands. RSR and MNDVI modify NDVI and SR in the same way by incorporating the SWIR reflectance, resulting in improved relationships with LAI (Nemani, et al., 1993; Brown, et al., 2000; Chen, et al., 2002), but they are not expressed as band ratios.

Table 1 Formulas of several vegetation indices used

Vegetation index

Formula

Reference Normalized Difference Vegetation Index (NDVI) NDVI=(NIR -R )/(NIR +R ) Rouse, et al., 1974 Simple Ratio (SR)

SR=NIR /R

Jordan, 1969 Modified Normalized Difference Vegetation Index (MNDVI) MNDVI=NDVI×(SWIR max ?SWIR )/(SWIR max ?SWIR min ) Nemani, et al., 1993 Reduced Simple Ratio (RSR)

RSR=SR×(SWIR max ?SWIR )/(SWIR max ?SWIR min )

Brown, et al., 2000

Note: R , NIR , and SWIR are the surface reflectances in the red, near infrared, and shortwave infrared bands, respectively. SWIR max and SWIR min are the maximum and minimum surface reflectance in the SWIR band, respectively. They are defined as the 1% minimum and maximum cutoff points in the histogram of the SWIR band reflectance here

2.4 Radiometric topographic effects

A 30 m resolution DEM map derived from the 1:50000 topo-graphic map of Maoershan mountain was used to represent the

topographic variations (Fig. 1). Based on this DEM, the shadows including self-shadows (part of the target slope is not illuminated by the direct radiation) and cast-shadows (the direct radiation is intercepted by the adjacent terrains) at any illumination angle can be generated. Because the slope of Maoershan mountain is not very steep, there are scarcely shadows at the illumination angle when the Landsat TM image was acquired. Even though the solar eleva-tion is about 30°, the total shadow area is less than 2% in the study area. The diffused irradiance from the sky and adjacent hills may be negligible for directly illuminated pixels at high solar elevation angles (Proy, et al., 1989). The amount of irradiance reaching a directly illuminated pixel is proportional to the cosine of the inci-dence angle i , which is defined as the angle between the direction of the Sun and the local surface normal (Meyer, et al., 1993). The incidence angle i represents one of the most important perturba-tions in remote sensing over mountainous terrain (Proy, et al., 1989), and is calculated as

cos i = cos θs cos θ + sin θs sin θcos(φs – A ) (1) where θs and φs are the solar zenith angle and the solar azimuth

angle, respectively; θ and A are the slope and aspect of an inclined

pixel, respectively, which are derived from the 30 m DEM data. In

this case, the topographic effects on the different wavelengths and

VIs can be expressed as

ρ= a ×cos i + b (2)

VI = m ×cos i + n (3) where ρ is the reflectance in the red, NIR, and SWIR bands, re-spectively; VI is a vegetation index; a (m ) and b (n ) are the slope and intercept of the linear regression line between ρ (VI) and cos i . The determination coefficient (R 2

) of the regression represents the sensitivity of the reflectance or VI to topographic variations. The R 2

value increases as the topographic effect increases.

Fig. 1 30 m resolution DEM map of Maoershan mountain

2.5 Assessment methods

In order to analyze the overall topographical effects on VIs, the pixels with slopes from 3° to 27° were binned into 5° slope inter-vals. The five slope classes are tagged by the median value of the

slope range of each class hereafter (i.e., 5°, 10°, 15°, 20°, 25°). The

pixels with slopes more than 27° were excluded since they are too few in the study area. In each class, the mean values at every aspect angle of the surface reflectances in the red, NIR, and SWIR bands, each selected VI, forest age, and altitude were calculated. Polar plots were used to represent these mean values changing with aspect in each class.

Fig. 2 shows the variations of forest age and altitude with aspect

in 5° slope intervals. It can be seen that forest age and altitude gener-ally increase as the slope increases, but these increasing trends become indistinctive when the slopes are larger than 15°. This may be mainly due to relatively frequent deforestation at flat locations.

Within each slope class, the variations of the forest age with aspect are small except a small reduction over the east slopes at 5° and 10

The study area is covered by high density forests with almost closed

Fig. 2 Variations of forest age and altitude with aspect in 5o slope intervals in the study area

(The polar angle represents aspect, and the radius represents the mean value of the forest age or altitude at a given aspect angle on different slopes)

ZHU Gaolong, et al.: Evaluation of topographic effects on four commonly used vegetation indices

213

canopies, so the effects of soil background on VIs are negligible. Because the study area is relatively small, the atmospheric condi-tions of various pixels can be considered to be identical. Since each slope class is composed of relatively homogeneous vegetation species, the variations of a VI within each slope class are mainly caused by topography. As the second criterion, the coefficient of variation (CV ) is used to evaluate the variations of topographic effects on the reflectance and VI with slopes. It is defined as: CV = STDV/Mean×100%

(4)

where STDV and Mean are the standard deviations and the mean values of the reflectance and VI corresponding to a given slope class, respectively. The CV value represents the noise caused by topographic variations. A smaller CV value indicates a smaller topographic effect.

2.6 Correction methods

For pixels exposing to the direct radiation, the reflected radiance in a given view direction mostly depends on the direct radiation incident on the slope. Diffuse radiance from the sky and adjacent hills generally varies weakly with direction and contri-butes only a small amount to the total reflected radiance from the surface. In this study, two simple methods are used for slope cor-rection. In the first method, diffused radiation is assumed to make no contribution to the reflectance. Since there are very few shadowed pixels in the study area, this simple method may be

applicable to the image used in this study. If the surface targets are

isotropic reflectors, the simple cosine function is reasonable to

correct the topographic effects (Fig. 3). It can be expressed as

ρH =ρT × cos θs / cos i (5) where ρH is the reflectance observed over a horizontal surface; ρT is

the reflectance observed over an inclined surface. This simple

cosine correction model may cause over correction in faintly

illuminated pixels (Meyer, et al., 1993) because the reflected

diffuse radiation can contributed considerably to the total reflected

irradiance and it is much less dependent on the incident angle of the direct radiation.

Fig. 3 Representation of the incidence angle i and the solar zenith angle θs

In the second method, we adopt the C-correction model proposed by Teillet, et al. (1982), which includes an adjustment

factor c in the cosine correction model:

ρH =ρT × (cos θs + c ) / (cos i + c ) (6) c =b /a (7)

where c is assumed to be constant for a given wavelength and equals the quotient of intercept b and inclination a of the observed empirical linear correlation between ρT and cos i (i.e., Eq.(2)). Although c is added with the intent to reduce the incident angle correction on the diffused component of the reflected radiation, the radiation physics are still not completely described in this simple equation (Gu & Gillespie, 1998).

These two correction models were employed to correct the surface reflectances in the red, NIR, and SWIR bands in each slope class as mentioned above. The selected VIs were recomputed from the topographically corrected reflectance image to access the efficiency of the two topographic correction models.

3 RESULTS

3.1 Topographic effects on surface reflectance

Fig. 4 shows that the surface reflectances in the red, NIR, and

SWIR bands vary with different slopes. The surface reflectance varies strongly with the azimuth angle relative to the Sun. The great-est topographic effects occur on the Sun-facing slopes and the slopes facing away from the Sun. The less topographic effects appear on

other slopes. These results are in agreement with the previous find-ings of Holben and Justice (1981). But this is not the case for the red reflectance on the 5° slope. It shows much larger variations on the west slopes than on the east slopes. This may be due to the red band being relatively sensitive to the vegetation variations which are

relatively larger when the slopes are small. As the slope increases, on

average, the red reflectance decreases slightly, while the NIR and

SWIR reflectances increase rapidly on Sun-facing slopes and

decrease relatively slowly on Sun-backing slopes.

Fig. 5 shows the topographic effects resulting from slope varia-tions on the surface reflectances in the red, NIR, and SWIR bands. Overall, the R 2 values of the linear correlations between the reflec-tance and the cosine of the incidence angle (cos i ) increase as the slope increases for the three bands. Similarly, the CV values of reflectances in the NIR and SWIR bands increase as the slope increases. The change of the CV values of reflectance in the red

band exhibits a parabolic shape, with the minimum CV value on 15° slope. When slopes are larger than 15°, the R 2 and CV values of reflectances in the NIR and SWIR bands are generally much larger than those of reflectance in the red band, particularly on large slopes. The topographic effects on the NIR and SWIR bands are more severe than those on the red band mainly owing to more diffuse illumination from sky in the red band which moderates the topographic effects on this band. Field measurements show that the skylight may represent up to 10% of total irradiance in NIR and up to about 20% in visible bands (Deering, et al., 1994; Shoshany, 1993). This implies the ratio of NIR to SWIR reflectance is supe-rior to the ratio of NIR to red reflectance in reducing the topo-graphic effects.

3.2

Topographic effects on VIs Fig. 6 shows how the values of SR, NDVI, RSR, and MNDVI

vary with aspect at different slopes. The effects of aspect variations

on VIs are quite different. When the slope is 5°, each VI greatly

changes with aspect due to relatively large vegetation variations.

When the slope is above 10o, the changes of the band-ratio vegeta-tion index such as SR and NDVI at a given slope are much

Fig. 4 Changes of mean reflectances in the red, NIR, and SWIR

bands with aspect at 5o slope intervals in the study area (The polar angle represents aspect, and the radius represents the mean reflectance)

smaller than those of the non-band-ratio VIs such as RSR and

MNDVI. The values of SR and NDVI increase as the slope increases, which is similar to the changes of forest age with slope. However, the values of RSR and MNDVI decrease as the slope increases on Sun-facing slopes, while their values increase as the slope increases on Sun-backing slopes. Moreover, at a given slope, the values of RSR and MNDVI of Sun-facing slopes are much smaller than those of Sun-backing slopes. The larger the slope is, the larger the difference is between Sun-facing and Sun-backing slopes. According to the ground reference data as mentioned above, VI over a given slope should be independent of the aspect relative to the Sun, if the topographic effects do not exist. Therefore, it can be inferred that VIs that are expressed as ratios between bands is able to remove a large proportion of noise caused by topographical variations. Topography affects strongly RSR and MNDVI, result-ing in negative biases on Sun-facing slopes and positive biases on Sun-backing slopes.

The topographic effects on the selected VIs are significantly different (Fig. 7). MNDVI presents the largest noise of topography

among all VIs, indicated by the largest

CV values in the range of

Fig. 5 Effects of slope variations on the surface reflectances in the red,

NIR, and SWIR bands

ZHU Gaolong, et al.: Evaluation of topographic effects on four commonly used vegetation indices 215

Fig. 6 Changes of mean values of SR, NDVI, RSR, and MNDVI with aspect in 5o slope intervals in the study area (The polar angle represents aspect, and the radius represents the mean values of each VIs)

Fig. 7 Effects of slope variations on SR, NDVI, RSR, and MNDVI

5.32% to 13.02% corresponding to the slope from 5o to 25o. RSR has the second largest CV values, in the range of 7.09% to 9.81%. SR generally shows a medium CV values in the range of 3.14% to 5.37%. NDVI has the smallest CV values in the range of 0.64% to 1.92%, implying that NDVI can reduce the topographic effects to a large extent. On the whole, the R2 values of linear correlations between each VI and the cosine of the incidence angle (cos i) increase as the slope increases. When the slope is larger than 10o, the R2 values of RSR and MNDVI are in the range of 0.84 to 0.96, indicating that VIs that are not based on band ratios are influenced strongly by topographic variations. Similar conclusion was also reported by Matsushita, et al. (2007), who indicated that EVI (not

based on band ratio) is more sensitive to topographic conditions

than NDVI. However, even VIs based on band-ratio still include

significant topographic effects on steep slopes in the study area,

which is in agreement with the findings of Burgess, et al. (1995) and Kusaka and Sakane (1997) who indicate that shadowed pixels have greater NDVI errors than directly illuminated ones. The R2

value of SR and NDVI are 0.64 and 0.41 on slope equal to 25o, respectively. SR is more sensitive to topographic variations on steep slopes than NDVI. This is mainly due to the relatively dif-ferent topographic effects on the red and NIR bands. Therefore, the topographic effects should be removed before the applications of VIs that are not based on band ratios, even if the slope is small. The topographic effects on VIs based on band-ratio can usually be ignored in mountainous areas, which are not very steep. However, careful topographic correction is also necessary for such VIs on steep slopes.

3.3 Topographic corrections of VIs

Table 2 gives a summary on the usefulness of the cosine correc-tion and C-correction models in correcting topographic effects. The c value in the C-correction model is determined by the slope and intercept of the linear correlations between the corresponding band reflectance and the cosine of the incidence angle (cos i) of each slope class, as described in Section 2.6. It can be seen that the c value decreases as the wavelength increases when the slope is larger than 10o. In general, the two models can effectively reduce the topographic effects on the reflectance in each band and calcu-lated VIs, indicated by the decreasing amplitudes of the CV and R2 values compared to the corresponding values of the uncorrected originals. However, the CV and R2 values remarkably increase as the slope increases for the cosine correction model, indicating the efficiency of the cosine model decreases as the slope increases. Furthermore, the cosine model has no effects on the band-ratio vegetation indices, since the numerator and denominator in these indices are multiplied by the same correction factor. On the contrary, the C-correction model is able to further reduce the topographic effects on VIs based on band-ratio. The CV values of the C-corrected reflectance or VI are commonly much smaller than

Table 2 Comparison of the usefulness of the cosine correction and C-correction models in removing topographic effects

Slope

Uncorrected Cosine correction C-correction

VI STDV Mean CV/% R2 c STDV Mean CV/%R2 STDV Mean CV/% R2

Red 0.0026 0.0330 7.87 0.38 ?0.24810.00210.0331 6.32 0.050.0021 0.0332 6.17 0 NIR 0.0107 0.3639 2.93 0.26 1.1616 0.01170.3658 3.20 0.390.0091 0.3646 2.50 0 SWIR 0.0064 0.1638 3.93 0.67 0.0653 0.00360.1645 2.19 0.010.0036 0.1645 2.18 0 SR 0.6077

11.9716

5.08

0.11 0.607711.9716 5.08

0.110.8799

11.0281 7.98 0 NDVI 0.0159 0.8279 1.92 0.17 0.01590.8279 1.92 0.170.0123 0.8328 1.48 0 RSR 0.4939 6.9684 7.09 0.46 0.3641 6.9246 5.26 0.020.6070 6.3042 9.63 0 MNDVI 0.0255 0.4794 5.32 0.64 0.01540.4766 3.23 0 0.0174 0.4757 3.65 0

10o

Red 0.0019 0.0309 6.29 0.71 0.2628 0.00120.0314 3.74 0.190.0011 0.0313 3.37 0 NIR 0.0170 0.3786 4.49 0.70 0.7195 0.01530.3856 3.96 0.640.0092 0.3819 2.42 0 SWIR 0.0089 0.1652 2.64 0.89 0.3039 0.00420.1681 2.50 0.530.0029 0.1672 1.73 0 SR 0.4446 12.8605 3.46 0.04 0.444612.8605 3.46 0.040.6264 12.2368 5.12 0 NDVI 0.0092 0.8453 1.09 0.14 0.00920.8453 1.09 0.140.0072 0.8486 0.85 0 RSR 0.5316 7.3038 7.28 0.84 0.24937.1397 3.49 0.290.3619 6.8471 5.29 0 MNDVI 0.0328 0.4812 6.82 0.91 0.01360.4706 2.88 0.500.0106 0.4749 2.22 0

15o

Red 0.0016 0.0297 5.45 0.84 0.9000 0.00180.0309 5.77 0.860.0007 0.0302 2.17 0 NIR 0.0259 0.3868 6.70 0.88 0.5404 0.01870.4020 4.64 0.770.0090 0.3951 2.27 0 SWIR 0.0116 0.1663 6.96 0.95 0.4419 0.00670.1728 3.90 0.840.0027 0.1701 1.57 0 SR 0.4203 13.3866 3.14 0.27 0.420313.3866 3.14 0.270.4672 13.1016 3.57 0 NDVI 0.0055 0.8550 0.64 0.04 0.00550.8550 0.64 0.040.0047 0.8580 0.55 0 RSR 0.5315 7.4823 7.10 0.93 0.48607.1321 6.81 0.920.2200 7.1682 3.07 0 MNDVI 0.0405 0.4811 8.42 0.96 0.02440.4579 5.32 0.890.0086 0.4696 1.83 0

20o

Red 0.0017 0.0293 5.80 0.86 1.2971 0.00280.0315 8.92 0.920.0007 0.0300 2.23 0 NIR 0.0344 0.3893 8.84 0.93 0.5113 0.02430.4164 5.85 0.840.0097 0.4041 2.39 0 SWIR 0.0149 0.1669 8.93 0.95 0.4808 0.00980.1784 5.51 0.880.0034 0.1733 1.94 0 SR 0.5156 13.5088 3.84 0.60 0.515613.5088 3.84 0.600.4200 13.4590 3.12 0 NDVI 0.0063 0.8577 0.73 0.41 0.00630.8577 0.73 0.410.0040 0.8616 0.47 0 RSR 0.6258 7.4951 8.35 0.93 0.7436 6.8769 10.810.950.2077 7.1802 2.89 0 MNDVI 0.0511 0.4800 10.65 0.96 0.03690.4388 8.41 0.910.0113 0.4598 2.45 0

25o

Red 0.0021 0.0294 7.20 0.73 1.4806 0.00410.0330 12.430.880.0012 0.0304 3.84 0 NIR 0.0424 0.3855 11.01 0.94 0.5126 0.03260.4286 7.60 0.860.0114 0.4085 2.78 0 SWIR 0.0186 0.1658 11.22 0.94 0.4899 0.01380.1843 7.51 0.840.0052 0.1758 2.94 0 SR 0.7163 13.3412 5.37 0.64 0.716313.3412 5.37 0.640.6188 13.4568 4.60 0 NDVI 0.0101 0.8558 1.18 0.38 0.01010.8558 1.18 0.380.0063 0.8614 0.73 0 RSR 0.7288 7.4261 9.81 0.88 1.0211 6.4561 15.820.950.3235 7.0354 4.60 0 MNDVI 0.0628 0.4823 13.02 0.95 0.05160.4165 12.390.890.0174 0.4507 3.87 0

ZHU Gaolong, et al.: Evaluation of topographic effects on four commonly used vegetation indices 217

Fig. 8 Reflectances corrected by the cosine correction model (the polar angle Fig. 9 Reflectances corrected by the C-correction model (the polar angle represents aspect, and the radius represents the mean reflectance) represents aspect, and the radius represents the mean reflectance)

the corresponding CV values of the cosine corrected reflectance or VI. The R2 values of the regression between the C-corrected reflectance or VI and the cosine of the incidence angle (cos i) are zero for all slopes. This proves that the C-correction model is much better than the cosine correction model in removing the topograph-ic effects, especially on steep slopes.

Compared with the original reflectances in the red, NIR, and SWIR bands (Fig. 4), the cosine correction model significantly overestimates the reflectances of Sun-backing slopes (Fig. 8). The larger slope, the stronger this overcorrection is. This phenomenon may be due to the fact that the cosine correction method only

models the direct radiation. However, the diffuse irradiance

accounts for a large proportion of total irradiance on Sun-backing

slopes, where topographic shadows are strong (Gu & Gillespie,

1998). The C-correction model which might include path radiance effect can avoid overcorrection on weakly illuminated slopes (Fig. 9). Fig. 10 and Fig. 11 show comparisons between the usefulness of the cosine correction and C-correction models to remove topographic effects on RSR and MNDVI on different slopes. Both the cosine correction and C-correction models can effectively reduce the

Fig. 10 Comparison of the usefulness of the cosine correction and C-correction models in removing topographic effects on RSR on the different slopes Fig. 11 Comparison of the usefulness of the cosine correction and C-correction models in removing topographic effects on MNDVI on the different slopes

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topographic effects on these VIs when the slope is less than 10o, and the difference between the corrected indices using these two models is very small. However, when the slope is above 15o, the cosine correction model usually overestimates indices not based on band ratios on Sun-facing slopes and underestimates them on Sun-backing slopes. These results are in agreement with the state-ments of Gu and Gillespie (1998) and Meyer, et al., (1993). The C-correction model performs rather effectively in removing the effects of slopes on VIs, and its performance is particularly effec-tive at high incident solar elevation angles. This is mainly due to the ability of this model to capture the variations of both direct and diffused radiation with slopes and aspects (Teillet, et al., 1982). However, in the case of low solar elevation angles or large view zenith angles relative to the Sun, at which shadows and occlusions of light by adjacent terrains can occur in many pixels, the perfor-mance of the C-correction model in reducing topographic effects on VIs needs further validation.

3.4 Topographic effects on estimated LAI

The ground LAI measurements of 23 plots in Maoershan mountain (Zhu, et al., 2010) were used here to investigate the topographic effects on LAI retrieved from VIs. Fig. 12 shows the relationships between the measured LAI and RSR calculated from reflectances without and with topographic corrections using the cosine correction and C-correction models. Without topographic correction, RSR can explain 75.5% of the variations of LAI. With the correction using the C-correction model, RSR shows the strongest correlation with the measured LAI, indicating by the highest R 2 of 0.757 and the smallest RMSE of 0.665. This proves the ability of the C-correction model to remove the topographic effects on of LAI retrieved using remote sensing data. However, the cosine correction model performs poorly in correcting topo-graphic effect on LAI retrieval.

Based on above three RSR-LAI relationships, the forest LAI maps of the study area were generated. Fig. 13 shows the changes of mean LAI values with aspect angles. For LAI retrieved using uncorrected reflectances, the mean values are about 4.3 on the southeast slopes and reach 5.0 on the northwest slopes. This spatial pattern of retrieved LAI is in contrast to the reference data which indicate that forest density changes marginally with aspects. Based on the reflectances corrected using the cosine correction model, the LAI values on southeast slopes are much larger than those on northwest slopes, due to its overcorrection over these slopes. The C-correction model produces a relatively rational LAI distribution changing with aspect angles, indicating that this model is better than the cosine correction model in removing the topographic effects on LAI retrieval. The effectiveness of these two topographic models on LAI retrieval using MNDVI is also similar.

4 CONCLUSIONS AND DISCUSSION

In this study, the topographic effects on four commonly used indices (SR, NDVI, RSR, and MNDVI) derived from Landsat TM data over Maoershan mountain were evaluated. Two simple models, the cosine correction and C-correction models, with different treatments of diffused irradiance on slopes, were used to remove the topographic effects on reflectance and VIs. The following

conclusions can be drawn from this study:

(1) Topography strongly affects vegetation indices that are not based on band ratios, such as RSR and MNDVI, resulting in nega-tive biases of their values on Sun-facing slopes and positive biases on slopes facing away from the Sun. As the slope increases, topo-graphic effects increase rapidly.

(2) Vegetation indices based on band ratios, such as SR and NDVI, are able to reduce a large proportion of noise caused by topographical variations. However, they are still significantly influenced by topography in steep terrains where topographic shadows are strong. SR is more sensitive to the topographic varia-tions on steep slopes than NDVI, because the topographic effects on the NIR and SWIR bands are more pronounced than those on

the red band, mainly owing to diffused radiation from the sky in

Fig. 12 Relationships of LAI measured at 23 plots in the study area with RSR based on reflectances without and with topographic correc-tions using the cosine correction and C-correction models

Fig. 13 Changes of mean LAI with aspect in the study area

(The polar angle represents aspect, and the radius represents the mean values of LAI at every aspect angle retrieved by the RSR-LAI relationships in Fig. 11)

the red band which moderates the topographic effects.

(3) The C-correction model is much better than the cosine correction model in removing the topographic effects on VIs, especially on steep slopes, improving LAI retrieval. However, it needs further validation under the conditions of low solar elevation angles and large view-Sun azimuth angles.

It should be kept in mind that vegetation index derived from remotely sensed data is not only sensitive to vegetation changes, but also perturbed by a number of external factors such as topo-graphic effects, soil background, atmospheric effects, leaf inclina-tion, geometry of illumination and viewing, and sensor degradation. In order to assess topographic effects on different vegetation indices in this study area, the variations of each selected vegetation index within a 5° slope interval are assumed to depend on topo-graphic effects only. The influences of other perturbing factors are ignored. Although this simplification is able to facilitate the analy-sis on the sensitivity of these vegetation indices to topographic effects, it might result in some uncertainties in the sensitivity of VIs to topography. The generalization of above conclusions needs further thorough investigations.

Moreover, topographic correction is very challengeable for forests because trees grow geotropically regardless of the under-lying terrain and changes of the canopy structure also vary the topographic effects (Kane, et al., 2008). The art topographic correction methodologies for forest scenes would be the SCS (Gu & Gillespie, 1998) and SCS+C (Soenen, et al., 2005) algorithms, and might also include BRDF-corrections in some cases. Many topographic correction methods perform much better over lower slopes, but most of them eventually fail on steep slopes, so it may require including a complete intercomparison to current topo-graphic correction methods in a study area with steeper slopes. These issues need to be addressed in the future further research. Some three-band vegetation (such as EVI, RSR, MNDVI) indices were developed for constraining atmospheric and background noises by information from SWIR or blue bands. They are normally not in band-ratio form and very sensitive to topographic effects. Efforts should be made to develop three-band indices in band-ratio form.

Topographic effects are also related to the resolutions of remote sensing images used (Deng, et al., 2007). In coarser resolution images, the topographic effects might be moderated due to large samples of slopes and illumination conditions within pixels and less illumination from adjacent pixels. In contrast, the topographic effects might be significant in high resolution remote sensing images. Currently, the MODIS vegetation index (including NDVI and EVI) products are generated at 250m, 500m, 1km, and 5.6km resolutions, respectively. They are valuable for monitoring terrestrial vegetations. The EVI product can improve vegetation monitoring capability through de-coupling

of the canopy background signal and a reduction of atmospheric influences. However, EVI is not expressed as the band-ratio form, which may include more topographic noise than NDVI. The topographic effects might be more significant in vegetation index products derived from Landsat TM, SPOT HRV, HJ CCD, CBERS CCD, and other high resolution remote sensing data. Therefore, we strongly recommend that the topographic effects should be carefully corrected over rugged terrains in high spatial resolution images, especially for non-band-ratio vegetation indices.

REFERENCES

Baret F and Guyot G. 1991. Potentials and limits of vegetation indices for LAI and APAR assessment. Remote Sensing of Environment,

35(2/3): 161?173 [DOI: 10.1016/0034-4257(91)90009-U]

Brown L J, Chen J M, Leblanc S G and Cihlar J. 2000. A short wave infrared modification to the simple ratio for lai retrieval in boreal

forests an image and model analysis. Remote Sensing of

Environment, 71(1): 16?25 [DOI: 10.1016/S0034-4257(99)00035-8] Burgess D W, Lewis P and Muller J P A L. 1995. Topographic effects in A VHRR NDVI data. Remote Sensing of Environment, 54(3):

223?232 [DOI: 10.1016/0034-4257(95)00155-7]

Chen J M. 1996. Evaluation of vegetation indices and a modified simple ratio for boreal applications. Canadian Journal of Remote

Sensing, 22(3): 229?242

Chen J M, Govind A, Sonnentag O, Zhang Y Q, Barr A and Amiro B.

2006. Leaf area index measurements at Fluxnet-Canada forest

sites. Agricultural and Forest Meteorology, 140(1/4): 257?268

[DOI: 10.1016/j.agrformet.2006.08.005]

Chen J M, Pavlic G, Brown L, Cihlar J, Leblanc S G, White H P, Hall R J, Peddle D, King D J, Trofymow J A, Swift E, Van der Sanden

J and Pellikka P. 2002. Derivation and validation of canada-wide

coarse-resolution leaf area index maps using high-resolution

satellite imagery and ground measurements. Remote Sensing of

Environment, 80(1): 165?184 [DOI: 10.1016/S0034-4257(01)

00300-5]

Clevers J G P W. 1989. Application of a weighted infrared-red

vegetation index for estimating leaf area index by correcting for

soil moisture. Remote Sensing of Environment, 29(1): 25?37

[DOI: 10.1016/0034-4257(89)90076-X]

Combal B and Isaka H. 2002. The effect of small topographic variations

on reflectance. IEEE Transactions on Geoscience and Remote

Sensing, 40(3): 663?670 [DOI: 10.1109/TGRS.2002. 1000325]

ZHU Gaolong, et al.: Evaluation of topographic effects on four commonly used vegetation indices 221

Deering D W, Middleton E M and Eck T F. 1994. Reflectance anisotropy

for a spruce-hemlock forest canopy. Remote Sensing of Environment, 47(2): 242?260 [DOI: 10.1016/0034-4257(94) 90159-7]

Deng Y X, Chen X F, Chuvieco E, Warner T and Wilson J P . 2007.

Multi-scale linkages between topographic attributes and vegetation indices in a mountainous landscape. Remote Sensing of Environment, 111(1): 122?134 [DOI: 10.1016/j.rse.2007.03. 016] Dymond J R and Shepherd J D. 1999. Correction of the topographic

effect in remote sensing. IEEE Transactions on Geoscience and Remote Sensing, 37(5): 2618?2620 [DOI: 10.1109/36.789656] Gilabert M A, González-Piqueras J, García-Haro F J and Meliá J. 2002.

A generalized soil-adjusted vegetation index. Remote Sensing of Environment, 82(2/3): 303?310 [DOI: 10.1016/S0034-4257(02) 00048-2]

Gu D H and Gillespie A. 1998. Topographic normalization of Landsat

TM images of forest based on subpixel sun-canopy-sensor geometry. Remote Sensing of Environment, 64(2): 166?175 [DOI: 10.1016/S0034-4257(97)00177-6]

Holben B N and Justice C O. 1980. The topographic effect on spectral

response from nadir-pointing sensors. Photogrammetry and Remote Sensing, 46: 1191?1200

Holben B N and Justice C O. 1981. An examination of spectral band

ratioing to reduce the topographic effect on remotely sensed data. International Journal of Remote Sensing, 2(2): 115?133 [DOI: 10.1080/01431168108948349]

Huang H, Gong P, Clinton N and Hui F. 2008. Reduction of

atmospheric and topographic effect on Landsat TM data for forest classification. International Journal of Remote Sensing, 29(19): 5623?5642 [DOI: 10.1080/01431160802082148]

Huete A R. 1988. A soil adjusted vegetation index (SA VI). Remote

Sensing of Environment, 25(3): 295?309 [DOI: 10.1016/0034- 4257(88)90106-X]

Jordan C F. 1969. Derivation of leaf-area index from quality of light on

the forest floor. Ecology, 50(4): 663?666 [DOI: stable/1936256] Kane V R, Gillespie A R, McGaughey R, Lutz J A, Ceder K and Franklin

J F. 2008. Interpretation and topographic compensation of conifer canopy self-shadowing. Remote Sensing of Environment, 112(10): 3820?3832 [DOI: 10.1016/j.rse.2008.06. 001]

Kusaka T and Sakane M. 1997. Estimation of topographic effects in

NVl data obtained from satellite images. IEEE Proc. IGARSS’97: 972?974

Lee T Y and Kaufman Y J. 1986. Non-lambertian effects on remote

sensing of surface reflectance and vegetation index. IEEE Transactions on Geoscience and Remote Sensing, 24(5): 699?707 [DOI: 10.1109/TGRS.1986.289617]

LePrieur C, Verstraete M M and Pinty B. 1994. Evaluation of the

performance of various vegetation indices to retrieve vegetation cover from A VHRR data. Remote Sensing Reviews, 10(4): 265?284 [DOI: 10.1080/02757259409532250]

Liu H Q and Huete A R. 1995. A feedback based modification of the

NDVI to minimize canopy background and atmospheric noise. IEEE Transactions on Geoscience and Remote Sensing, 33(2): 457?465 [DOI: 10.1109/36.377946]

Matsushita B, Yang W, Chen J, Onda Y C and Qiu G Y . 2007.

Sensitivity of the enhanced vegetation index (EVI) and normalized difference vegetation index (NDVI) to topographic effects: a case study in high-density cypress forest. Sensors, 7(11): 2636?2651 [DOI: 10.3390/s7112636]

Meyer P, Itten K I, Kellenberger T, Sandmeier S and Sandmeier R.

1993. Radiometric corrections of topographically induced effects on Landsat TM data in an alpine environment. ISPRS Journal of Photogrammetry and Remote Sensing, 48(4): 17?28 [DOI: 10.1016/0924-2716(93)90028-L]

Myneni R B and Williams D L. 1994. On the relationship between

fAPAR and NDVI. Remote Sensing of Environment, 49(3): 200?211 [DOI: 10.1016/0034-4257(94)90016-7]

Nemani R, Pierce L, Running S and Band L. 1993. Forest ecosystem

processes at the watershed scale: sensitivity to remotely sensed leaf area index estimates. International J Remote Sens, 14(13): 2519?2534 [DOI: 10.1080/01431169308904290]

Pinty B and Verstrate M M. 1992. GEMI: a non-linear index to monitor

global vegetation from satellites. Vegetatio, 101(1): 15?20 [DOI: 10.1007/BF00031911]

Proy C, Tanré D and Deschamps P Y . 1989. Evaluation of topographic

effects in remotely sensed data. Remote Sensing of Environment, 30(1): 21?32 [DOI: 10.1016/0034-4257(89)90044-8]

Qi J, Chehbouni A, Huete A R, Kerr Y H and Sorooshian S. 1994. A

modified soil adjusted vegetation index. Remote Sensing of Environment, 48(2): 119?126 [DOI: 10.1016/0034-4257(94)90134-1] Rouse J W Jr, Haas R H, Schell J A and Deering D W. 1974.

Monitoring vegetation systems in the great plains with ERTS. Proceeding of Third Earth Resources Technology Satellite Symposium 1. Greenbelt, USA, NASA SP-351: 309?317

Schaaf C B, Li X W and Strahler A H. 1994. Topographic effects on

bidirectional and hemispherical reflectances calculated with a geometric-optical canopy model. IEEE Transactions on Geoscience and Remote Sensing, 32(6): 1186?1193 [DOI: 10.1109/36.338367] Shoshany M. 1993. Roughness-reflectance relationship of bare desert

terrain: an empirical study. Remote Sensing of Environment, 45(1): 15?27 [DOI: 10.1016/0034-4257(93)90078-C]

Smith J A, Lin T L and Ranson K J. 1980. The lambertian assumption

and landsat data. Photogrammetric Engineering and Remote Sensing, 46(9): 1183?1189

Soenen S A, Peddle D R and Coburn C A. 2005. SCS+C: a modified

sun-canopy-sensor topographic correction in forested terrain. IEEE Transactions on Geoscience and Remote Sensing, 43(9): 2148?2159 [DOI: 10.1109/TGRS.2005.852480]

Teillet P M, Guindon B and Goodenough D G. 1982. On the

slope-aspect correction of multispectral scanner data. Canadian Journal of Remote Sensing, 8(2): 1537?1540

Vermote E, Tanré D, Deuzé J L, Herman M and Morcette J J. 1997.

Second simulation of the satellite signal in the solar spectrum, 6s: an overview. IEEE Transactions on Geoscience and Remote Sensing, 35(3): 675?686 [DOI: 10.1109/36.581987]

Vincini M, Reeder D and Frazzi E. 2002. An empirical topographic

normalization method for forest TM data. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium IGARSS. Toronto Ont, Canada: IEEE, 4: 2091?2093 [DOI: 10.1109/IGARSS.2002.1026454]

Wen J G, Liu Q H, Liu Q, Xiao Q and Li X W. 2009. Parametrized BRDF

for atmospheric and topographic correction and albedo estimation in Jiangxi rugged terrain, China. International Journal of Remote Sensing, 30(11): 2875?2896 [DOI:10.1080/ 01431160802558618] Zhu G L, Ju W M, Chen J M, Zhou Y L, Li X F and Xu X C. 2010.

Comparison of forest leaf area index retrieval based on simple ratio and reduced simple ratio. Proceeding of 18th International Conference on Geoinformatics. Beijing, China: IEEE GRSS: 18?20 [DOI: 10.1109/GEOINFORMATICS.2010.5568204]

收稿日期：2012-01-05；修订日期：2012-05-17

基金项目：国家重点基础研究发展计划(973计划) (编号：2010CB833503，2010CB950702)；国家高技术研究发展计划项目(863计划)(编号：2009AA122103)；

江苏省高校优势学科建设工程

第一作者简介：朱高龙(1974— )，男，副教授，主要从事多角度光学植被遥感研究。E-mail ：zhugaolong@https://www.wendangku.net/doc/8a1787913.html,

通信作者简介：居为民(1963— )，男，教授，博士生导师，主要从事生态环境遥感和全球变化研究。E-mail ：juweimin@https://www.wendangku.net/doc/8a1787913.html,

4种常用植被指数的地形效应评估

朱高龙1, 2，柳艺博1，居为民1，陈镜明1, 3

1. 南京大学国际地球系统科学研究所，江苏南京 210093；

2. 闽江学院地理科学系，福建福州 350108；

3. Department of Geography, University of Toronto, Toronto, Ontario, Canada, M5S 3G3

摘要：植被指数已经广泛应用于地表植被覆盖监测，但是地形对植被指数的影响难以避免，却经常在大尺度遥感应用时被忽略。本文利用山区森林的Landsat TM 数据计算SR 、NDVI 、RSR 、MNDVI 4种常用植被指数，评估了地形对这些植被指数的影响，并利用余弦校正和C 校正模型分别对它们进行地形校正。结果表明，近红外和短波红外比红光波段的地形影响更为敏感，原因是更强的红光天空漫反射削弱了红光的地形影响。地形强烈影响非波段比值型植被指数(如RSR 和MNDVI 等)，导致阳坡的植被指数相对偏小，阴坡的植被指数相对偏大，这种地形效应随坡度增大而显著增大。因此，利用非波段比值型植被指数反演山区植被参数时必须做严格的地形校正。与之相反，波段比值型植被指数(如SR 和NDVI 等)可以很大程度上消除地形影响，但是在大坡度情况下，地形影响仍然不能被忽略，而且此时SR 比NDVI 的地形效应更大。C 地形校正效果好于余弦校正效果，特别是大坡度情况下更为明显。关键词：植被指数，地形效应，地形校正，波段比值中图分类号：TP702 文献标志码：A

1 引言

从遥感数据中获取的植被指数VIs (Vegetation Indices)已经广泛应用于监测各种尺度的地表植被覆盖。在估算植被生物物理参数如叶面积指数(LAI)、植被覆盖度、生物量、光合活性等应用方面，植被指数被证明具有比单波段遥感数据更可靠的反演精度(Clevers ，1989；Myneni 和Williams ，1994；Chen 等，2006)。除了植被自身变化会引起植被指数变化外，还有很多外界因素如土壤背景、大气条件、地形、光照与观测角度、传感器定标等也会影响植被指数(LePrieur 等，1994；Chen ，1996)。这些因素经常会带来不确定的噪声，从而影响植被指数的应用效果。理想的植被指数应该能够增强对植被信息的敏感性，而且能够抑制外界噪声的影响。几种基于土壤线的植被

指数可以减小土壤背景的影响(Huete ，1988；Baret 和Guyot ，1991；Qi 等，1994；Gilabert 等，2002)；由红光、近红外、短波红外3波段组合而成的修正归一化差值植被指数MNDVI (Modified Normalized Difference Vegetation Index)和减化简单比植被指数RSR (Reduced Simple Ratio)能够抑制地表背景的影响(Nemani 等，1993；Brown 等，2000)；全球环境监测指数GEMI (Global Environment Monitoring Index)被设计用于降低大气噪声(Pinty 和Verstrate ，1992)；增强植被指数EVI (Enhanced Vegetation Index)可以同时减少土壤背景和大气的影响(Liu 和Huete ，1995)。虽然这些植被指数在某些特定应用具有某种优势，但是它们的波段组合都不是基于比值形式，因此仍然可能保留甚至增强各种噪声影响(Chen ，1996)。由于这些非植被噪声对各波段反射率通常具有同向的影响，因

引用格式：朱高龙，柳艺博，居为民，陈镜明．2013．4种常用植被指数的地形效应评估．遥感学报，17(1): 210-234

Zhu G L, Liu Y B, Ju W M, Chen J M. 2013. Evaluation of topographic effects on four commonly used vegetation indices. Journal of Remote Sensing, 17(1): 210–234

朱高龙等：4种常用植被指数的地形效应评估 223

此通过波段比值可以减少这些不期望的噪声，例如基于近红外和红光波段各种比值组合的归一化差值植被指数

NDVI (Normalized Difference Vegetation

Index)(Rouse 等，1974)、简单比植被指数SR (Simple Ratio)(Jordan ，1969)和修正简单比植被指数MSR (Modified Simple Ratio) (Chen ，1996)被证明能够消除大量隐含在各波段中的观测噪声(Holben 和Justice ，1981；Lee 和Kaufman ，1986；Burgess 等，1995；Matsushita 等，2007)。

地形对辐射的影响可以定义为传感器接收到的斜坡反射辐射与平地反射辐射的差值，它是相对于光源和传感器位置的坡面方向的函数(Holben 和Justice ，1980)。地形效应的主要原因是地形阴影、临近地表反射、天空遮挡以及由其引起的地物双向反射分布函数(BRDF)的变化(Schaaf 等，1994)。植被指数中的地形噪声是相当复杂的，因此在大范围遥感应用时地形影响常被忽略。但是，即使是在坡度较小的情况，地形影响也不能简单地被认为是无关紧要(Combal 和Isaka ，2002)。Kusaka 和Sakane(1997)发现崎岖地表的NOAA/AVHRR 计算的NDVI 包含相当大的地形影响。Burgess 等人(1995)发现在忽略光照角度变化的情况下，50 m 分辨率像元NDVI 的地形误差为13.5%。目前已经发展了很多种用于去除地形影响的方法。最常用的地形校正方法包括Minnaert 校正(Smith 等，1980)、朗伯余弦校正(Teillet 等，1982)、C 校正(Teillet 等，1982)、SCS(Sun-Canopy-Sensor)模型(Gu 和Gillespie ，1998)等。随后各种基于不同假设的改进型地形校正方法也相继提出(Dymond 和Shepherd ，1999；Vincini 等，2002；Kane 等，2008；Huang 等，2008；Wen 等，2009)。其中一些地形校正方法利用高精度的数字高程模型(DEM)在森林地区的应用取得成功(Meyer 等，1993)。

本文评估了常用于森林LAI 反演的比值型植被指数SR 和NDVI 与非比值型植被RSR 和MNDVI

的地形效应，同时还比较了朗伯余弦校正与C 校正的地形校正效果。

2 数据与方法

2.1 研究区概况

研究区选择在黑龙江省帽儿山，覆盖范围为45.2659°?45.3232°N ，127.4957°?127.6047°E ，面积约26620 hm 2。

研究区属低山丘陵区，海拔为250—817 m ，平均坡度为14.2°。年均温为 2.8 oC ，年降雨量为 723.8 mm 。地表覆盖为多种植被类型的天然次生林区。根据东北林业大学森林调查数据显示，研究区阔叶林、针叶林、混交林所占面积分别为80%、15%和5%，平均林龄为50年。 2.2 TM 数据处理

本研究使用的Landsat-5 TM 图像来自美国地质调查局(USGS)网站，成像日期为2009年6月24日，获取时太阳高度角为61.3°，太阳方位角为134.7°。利用17个地面控制点进行TM 图像几何精校正，误差控制在0.5个像元以内，并利用TM 头文件中参数进行辐射定标。采用6S 模型(Vermote 等，1997)对图像进行大气校正，输入参数：大陆型气溶胶、中纬度夏季模式、均一地表、40 km 大气能见度，最后得到地表反射率图像，投影方式为UTM/WGS84，空间分辨率为30 m 。森林像元总数为242131个。 2.3 植被指数选择

本文选择由地表反射率计算的4种植被指数并评估其地形效应(表1)。SR 和NDVI 是最常用的基于近红外与红光波段比值形式的植被指数。RSR 和MNDVI 都以相同的方式利用短波红外反射率分别修正SR 和NDVI ，从而改善它们与LAI 的相关性(Nemani 等，1993；Brown 等，2000；Chen 等，2002)，但是它们都不是基于波段比值形式。

表1 植被指数计算公式

植被指数

计算公式

参考文献归一化差值植被指数 (NDVI) NDVI=(NIR ?R )/(NIR +R ) Rouse 等, 1974 简单比植被指数 (SR)

SR=NIR /R

Jordan, 1969 修正归一化差值植被指数 (MNDVI) MNDVI=NDVI×(SWIR max ?SWIR )/(SWIR max ?SWIR min ) Nemani 等, 1993 减化简单比植被指数 (RSR)

RSR=SR×(SWIR max ?SWIR )/(SWIR max ?SWIR min )

Brown 等, 2000

注：表中R 、NIR 、SWIR 分别是TM3、TM4、TM5波段地表反射率；SWIR max 、SWIR min 分别为完全郁闭冠层和开放冠层的TM5波段反射率，分别取TM5地表反射率直方图两端1%处的反射率值。

2.4 辐射地形效应

利用1:5万的帽儿山地形图导出30 m 分辨率的DEM(图1)。基于该DEM 可以生成任何光照角度下的地形阴影，包括本影(坡地自身未被直射光照射的部分)和落影(直射光被临近地物遮挡)两部分。由于帽儿山坡度较缓和，该TM 图像获取时刻的地形阴影几乎没有；即使太阳高度角为30°时，研究区阴影面积也不超过总面积的2%。当太阳高度角很大时，可以忽略直射像元中的来自天空和临近山体的散射辐射(Proy 等，1989)，直射像元接受的辐射量正比于入射角i 的余弦值，入射角i 定义为太阳光与坡面法线的夹角(Meyer 等，1993)。入射角i 是一个最重要的山区遥感干扰因子(Proy 等，1989)，它由下式给出：

cos i = cos θs cos θ+sin θs sin θcos(φs –A ) (1) 式中，θs 与φs 分别为太阳天顶角与太阳方位角，θ与 A 分别为由DEM 导出的坡度与坡向。各波段或植被指数的地形效应可以表达为：

ρ= a ×cos i + b

(2) VI = m ×cos i + n

(3)

式中，ρ为红光或近红外或短波红外的反射率，VI 为某种植被指数，a (m )和b (n )是ρ(VI)与cos i 线性回归线的斜率与截距。回归方程的确定系数(R 2)表征了反射率或植被指数对地形变化的敏感性。R 2越大，地形效应越强烈。

图1 30 m 分辨率的帽儿山地区DEM 图

2.5 评估方法

为了方便评估地形对植被指数的影响，所有坡度在3°到27°之间的像元被分成5°坡度间隔的5个等级。下文中每个等级用坡度中值(即5°、10°、15°、20°和25°)表示。由于研究区坡度大于27°的像元极少，该部分像元被排除。然后分别统计每个坡度等级内的各个坡向的林龄、海拔高度、各波段反射率、植被指数的平均值，分析每个坡度等级内这些平均值随坡向的变化。

图2显示研究区各个坡度等级的林龄和海拔高度随坡向的变化。可以看出林龄和海拔高度总体上随坡度的增加而增加，但是当坡度大于15°时，这种趋势变得不明显了，其原因可能是海拔越低地势越平坦的区域，森林砍伐越严重。除了5°和10°两个坡度等级东坡的林龄比其他坡向相对有些偏小外，其他坡度等级内的林龄随坡向的变化非常小。由于研究区为浓密的森林覆盖区，土壤背景对植被指数的影响基本可以忽略。研究区面积相对较小，可以假定每个像元的大

气条件基本一致。因此可以认为植被覆盖相对均匀的各个坡度等级内的植被指数变化主要是地形造成的。因此，变异系数(CV )可以用于评价地形对反射率和植被指数的影响，CV 定义为：

CV = STDV/Mean×100%

(4)

式中，STDV 与Mean 分别为某个坡度等级内的反射率或植被指数的标准差和平均值。CV 代表了地形变化引起的噪声。CV 越小，地形效应越小。 2.6 地形校正方法

对于被直射光照射的像元而言，某个方向上的反射辐射主要取决于坡面的直射入射辐射，来自天空和临近山体的散射辐射随方向变化很小并且对于总反射辐射的贡献量很小。由于研究区阴影像元极少，可以忽略散射辐射的影响。如果假定地物为朗伯体，则可以用简单余弦函数进行地形校正(图3)：

ρH =ρT × cos θs / cos i

(5)

式中，ρH 是水平地面反射率，ρT 是倾斜坡面反射率。简单余弦校正模型可能导致较暗像元的过度校正(Meyer

等，

1993)，这是因为这些像元的散射辐射在总反射量中的贡献相当大，而且它与直射辐射入射角i 基本无关。

朱高龙等：4种常用植被指数的地形效应评估 225

图2 研究区各个5o坡度间隔内的林龄和海拔高度随坡向的变化

(圆周代表坡向，半径代表某个坡度等级内该坡向的林龄或海拔高度的平均值)

图3 坡面太阳入射角i 与太阳天顶角θs 示意图

另外一种地形校正方法是采用Teillet 等(1982)提出的C 校正模型，它是在余弦校正模型中添加了一个调节参数c : ρH =ρT × (cos θs + c ) / (cos i + c ) (6)

c =b /a

(7)

对于某一特定波段，c 被假定是一个常数，c 等于ρT 和cos i 线性回归关系(式(2))的截距b 与斜率a 的比值。虽然添加参数c 的目的是减小散射光成分的过

度校正，但其物理机理并不明确(Gu 和Gillespie ，1998)。

本文采用这两种模型分别校正红光、近红外、短波红外反射率，再利用地形校正后的反射率图像重新计算植被指数，从而评估这两种模型的地形校正效果。

3 结果与分析

3.1 地表反射率的地形效应

图4显示不同坡度的红光、近红外、短波红外的地表反射率随坡向的变化。可以看出各波段反射率的变化与坡面相对太阳的位置密切相关，最大地形效应发生在阳坡和阴坡，其他坡向的地形效应相对较小，这与Holben

和Justice(1981)

的结论基本一致。

但是5

°坡度等级的红光反射率情况有所不同，其西坡的反射

率变化比东坡更大，这可能是因为坡度较小的植被覆盖变化相对较大，而红光对这种变化相对敏感。平均而言，随着坡度的增加，红光反射率轻微减小，而近红外和短波红外反射率在阳坡快速增加，在阴坡缓慢减小。

图4 研究区各个5o坡度间隔内的红光、近红外、短波红外

平均地表反射率随坡向的变化

(圆周代表坡向，半径代表平均反射率)

图5显示坡度变化对红光、近红外、短波红外地表反射率的影响。总体而言，这3个波段反射率与cos i 线性关系的R 2随坡度的增加而增加。与之类似，近红外与短波红外反射率的CV 值也随着坡度的增加而增加。红光反射率的CV 值呈现抛物线形状，最小值出现在15°坡度左右。当坡度大于15°时，近红外与短波红外反射率的R 2和CV 值大于红光反射率的相应值，特别在大坡度时这种情况更为明显。由此可见近红外与短波红外的地形影响比红光更为严重，这主要是因为更强天空红光漫反射削弱了红光的地形影响。野外观测也表明天空光对近红外亮度的贡献可达10%，对可见光亮度的贡献甚至达到20%(Deering 等，1994；Shoshany ，1993)。这也表明对于减小地形影响而言，近红外与短波红外的比值优于近红外与红光的比值。 3.2 植被指数的地形效应

图6显示SR 、NDVI 、RSR 、MNDVI 随坡向的变化。可以看出坡向对不同植被指数的影响差别很大。当坡度为5°时，各种植被指数随坡向的变化都很大，这可能是该坡度植被自身变化相对较大的缘故。当坡度大于10°时，比值型植被指数(SR 和NDVI)随坡向的变化远小于非比值型植被指数(RSR 和MNDVI)随坡向的变化。SR 和NDVI 随坡度的增加而增加，这种情况类似于林龄随坡度的变化。但是，RSR 和MNDVI 在阳坡随坡度的增加而减少，在阴坡随坡度的增加而增加；而且，在同一个坡度等级内，阳坡值小于阴坡值，坡度越大，两者差值也越大。根据前述地面调查资料，如果不考虑地形影响，每个坡度等级内的植被指数不会随坡向发生大的变化。由此可见，比值型植被指数可以消除大量的地形影响，非比值型植被指数受地形影响严重，导致阳坡出现负偏差，阴坡出现正偏差。

图7可以看出地形对这4种植被指数的影响差别很大。MNDVI 的CV 值最大，当坡度从5°—25°时，相应的CV 值从5.32%上升到13.02%，这表明MNDVI 中的地形噪声最为严重。RSR 的CV 值在7.09%—9.81%变化，略小于MNDVI 。SR 的CV 值居中，变化范围为 3.14%—5.37%。NDVI 具有最小的CV 值，在

0.64%—1.92%变化，这表明NDVI 能在很大程度上减小地形影响。总体上说，各个植被指数与cos i 线性关系的R 2随坡度的增加而增加。

当坡度大于10°时，RSR 和MNDVI

的R

2在0.84—0.96变化，意味着这些非比值型

朱高龙等：4种常用植被指数的地形效应评估 227

图5 坡度变化对红光、近红外、短波红外地表反射率的影响

图6 研究区各个5o

坡度间隔内的SR

、

NDVI 、

RSR 、MNDVI 随坡向的变化

(圆周代表坡向，半径代表平均植被指数)

图7 坡度变化对SR、NDVI、RSR、MNDVI的影响

植被指数地形影响非常强烈。Matsushita等人(2007)也指出非比值型EVI比NDVI的地形影响更为敏感。但是，即使是比值型植被指数在研究区陡坡仍存在大量的地形噪声，这与Burgess等人(1995)和Kusaka 和 Sakane(1997)的结论基本一致，他们指出阴影像元比直射像元包含更大的NDVI地形误差。当坡度为25°时，SR和NDVI的R2分别为0.64和0.41，表明SR对地形变化比NDVI更为敏感，这主要是因为红光与近红外的地形效应差异造成的。因此，即使在坡度较小的情况下，非比值型植被指数的应用也必须做地形校正；比值型植被指数的地形效应通常可以忽略，但在陡坡地区也需要做严格的地形校正。

3.3 植被指数的地形校正

表2总结了余弦校正模型与C校正模型的地形校正效果。C校正模型中的参数c取决于每个坡度等级内的各波段反射率与cos i回归关系的截距与斜率。大于10°坡度的参数c随波长的增加而减小。总体上说，这两种模型校正后的各波段反射率的CV和R2都有所减小，表明它们可以有效地减小地形对反射率的影响。但是，余弦模型校正后的CV和R2随坡度增大显著增加，表明余弦模型校正能力随坡度增大而减小。另外，余弦模型对比值型植被指数不起作用，这是因为这些植被指数的分子和分母都乘以相同的校正系数。相反地，C校正模型可以进一步减小比值型植被指数的地形影响。C校正模型校正后的CV总体上比余弦模型的CV小很多。对于各个坡度等级，C 校正模型校正后的R2都为零。这证明了C校正模型地形校正效果优于余弦模型，特别是在大坡度情况下优势更明显。

与原来反射率(图4)相比较，余弦模型对阴坡反射率校正过度(图8)，坡度越大，这种过度校正越明显，这是因为余弦模型仅考虑了直射光，而阴坡散射光占总辐射的比重相当大(Gu和Gillespie，1998)。C校正模型考虑了辐射影响，能够避免较暗像元的过度校正(图9)。图10和图11比较了余弦模型与C校正模型对RSR和MNDVI的地形校正效果。当坡度小于10°时，这两个模型都能有效减小RSR和MNDVI的地形效应，两者差别较小。但是当坡度大于15°时，余弦模型通常高估了阳坡的植被指数，低估了阴坡的植被指数，这与Gu和Gillespie(1998)以及Meyer等人(1993)的结论基本一致。C校正模型能够更有效地减小植被指数的地形效应，特别是在大坡度的情况下更为明显，这是因为C校正模型同时考虑了地形引起的直射光与散射光的变化(Teillet等，

1982)。低太阳高度角或

大观测天顶角会产生大量的阴影或邻近地表的光

线遮挡现象，此时的C校正模型地形校正能力需要

进一步验证。

朱高龙等：4种常用植被指数的地形效应评估 229

表2余弦校正模型与C校正模型的地形校正效果比较

坡度

未校正余弦校正C校正VI STDV Mean CV/% R2 c STDV Mean CV/%R2STDV Mean CV/%R2

5°

Red 0.0026 0.0330 7.87 0.38 ?0.24810.00210.0331 6.320.050.0021 0.0332 6.17 0 NIR 0.0107 0.3639 2.93 0.26 1.16160.01170.3658 3.200.390.0091 0.3646 2.50 0 SWIR 0.0064 0.1638 3.93 0.67 0.06530.00360.1645 2.190.010.0036 0.1645 2.18 0 SR 0.6077

11.9716 5.08 0.11 0.607711.9716 5.080.110.8799 11.0281 7.98 0

NDVI 0.0159 0.8279 1.92 0.17 0.01590.8279 1.920.170.0123 0.8328 1.48 0 RSR 0.4939 6.9684 7.09 0.46 0.3641 6.9246 5.260.020.6070 6.3042 9.63 0 MNDVI 0.0255 0.4794 5.32 0.64 0.01540.4766 3.230 0.0174 0.4757 3.65 0

10°

12.8605 3.46 0.04 0.444612.8605 3.460.040.6264 12.2368 5.12 0

NDVI 0.0092 0.8453 1.09 0.14 0.00920.8453 1.090.140.0072 0.8486 0.85 0 RSR 0.5316 7.3038 7.28 0.84 0.24937.1397 3.490.290.3619 6.8471 5.29 0 MNDVI 0.0328 0.4812 6.82 0.91 0.01360.4706 2.880.500.0106 0.4749 2.22 0

15°

13.3866 3.14 0.27 0.420313.3866 3.140.270.4672 13.1016 3.57 0

NDVI 0.0055 0.8550 0.64 0.04 0.00550.85500.640.040.0047 0.8580 0.55 0 RSR 0.5315 7.4823 7.10 0.93 0.48607.1321 6.810.920.2200 7.1682 3.07 0 MNDVI 0.0405 0.4811 8.42 0.96 0.02440.4579 5.320.890.0086 0.4696 1.83 0

20°

13.5088 3.84 0.60 0.515613.5088 3.840.600.4200 13.4590 3.12 0

NDVI 0.0063 0.8577 0.73 0.41 0.00630.85770.730.410.0040 0.8616 0.47 0 RSR 0.6258 7.4951 8.35 0.93 0.7436 6.876910.810.950.2077 7.1802 2.89 0 MNDVI 0.0511 0.4800 10.65 0.96 0.03690.43888.410.910.0113 0.4598 2.45 0

25°

13.3412 5.37 0.64 0.716313.3412 5.370.640.6188 13.4568 4.60 0

NDVI 0.0101 0.8558 1.18 0.38 0.01010.8558 1.180.380.0063 0.8614 0.73 0 RSR 0.7288 7.4261 9.81 0.88 1.0211 6.456115.820.950.3235 7.0354 4.60 0 MNDVI 0.0628 0.4823 13.02 0.95 0.05160.416512.390.890.0174 0.4507 3.87 0

植被光谱分析与植被指数计算

植被光谱分析与植被指数计算在遥感中，常常结合不同波长范围的反射率来增强植被特征，如植被指数（vegetation i ndices ——VI）的计算，植被指数（VI）是两个或多个波长范围内的地物反射率组合运算，以增强植被某一特性或者细节。目前，在科学文献中发布了超过150种植被指数模型，这些植被指数中只有极少数是经过系统的实践检验。本文总结现有植被指数，根据对植被波谱特征产生重要影响的主要化学成份：色素（Pigments）、水分（Water）、碳（Carbon）、氮（Nitrogen），总结了7大类实用性较强的植被指数，即：宽带绿度、窄带绿度、光利用率、冠层氮、干旱或碳衰减、叶色素、冠层水分含量。这些植被指数可以简单度量绿色植被的数量和生长状况、叶绿素含量、叶子表面冠层、叶聚丛、冠层结构、植被在光合作用中对入射光的利用效率、测量植被冠层中氮的相对含量、估算纤维素和木质素干燥状态的碳含量、度量植被中与胁迫性相关的色素、植被冠层中水分含量等。包括以下内容： ? ?●植被光谱特征 ? ?●植被指数 ? ?●HJ-1-HSI植被指数计算 1.植被光谱特征植被跟太阳辐射的相互关系有别于其他物质，如裸土、水体等，比如植被的“红边”现象，即在<700nm附近强吸收，>700nm高反射。很多因素影响植被对太阳辐射的吸收和反射，包括波长、水分含量、色素、养分、碳等。研究植被的波长范围一般为400 nm t o 2500 nm，这也是传感器设计选择的波长范围。这个波长范围可范围以下四个部分： ??●可见光（Visible）：400 nm to 700 nm ??●近红外（Near-infrared——NIR）：700 nm to 1300 nm ??●短波红外1（Shortwave infrared 1—— SWIR-1）：1300 nm to 1900 nm ??●短波红外2（Shortwave infrared 2——SWIR-2）：1900 nm to 2500 nm 其中NIR和SWIR-1的过渡区（1400nm附近）是大气水的强吸收范围，卫星或者航空传感器一般不获取这范围的反射值。 SWIR-1 和SWIR-2的过渡区（1900nm附近）也是大气水的强吸收范围。植被可分为三个部分组成： ??●植物叶片（Plant Foliage） ??●植被冠层（Plant Canopies） ??●非光合作用植被(Non-Photosynthetic Vegetation) 这三个部分是植被分析的基础，下面对他们详细介绍。 1.1植物叶片（Plant Foliage）植物叶片包括叶、叶柄以及其他绿色物质，不同种类的叶片具有不同的形状和化学成份。对波谱特征产生重要影响

国民经济统计学

1.国民经济核算体系国民经济核算体系由基本核算表、国民经济账户和附属表三部分构成。基本核算表包括国内生产总值表、投入产出表、资金流量表、国际收支表和资产负债表。生产范围国民经济核算的生产范围包括以下三部分：第一，生产者提供或准备提供给其他单位的货物或服务的生产；第二，生产者用于自身最终消费或固定资本形成的所有货物的自给性生产；第三，自有住房提供的住房服务和付酬家庭雇员提供的家庭服务的自给性生产。（生产范围包括所有货物的生产，不论是对外提供的货物还是自产自用的货物，而服务的生产，则基本上限于对外提供的部分，自给性服务，除了自有住房服务和付酬家庭雇员提供的家庭或个人服务外，则被排除在生产范围之外。被排除在生产范围之外的自给性服务是指住户成员为本住户提供的家庭或个人服务，如清扫、做饭、照顾老人、教育儿童等等。）消费范围生产范围决定消费范围，用于最终消费的货物和服务只能是生产范围内所包括的货物和服务。生产范围包括所有货物的生产和除住户成员为本住户提供的家庭或个人服务之外的所有服务的生产，从而消费范围也限于包括在上述生产范围内的货物和服务。资产范围国民经济核算中的资产是根据所有权的原则界定的经济资产，也就是说，资产必须为某个或某些单位所拥有，其所有者因持有或使用它们而获得经济利益。根据这个定义，金融资产和由生产过程创造出来的固定资产、存货等，以及某些不是经过生产过程创造出来的自然产生的资产（如土地、矿藏、森林、水资源资产等），只要某个或某些单位对这些资产有效地行使所有权，并能够从中获得经济利益，都属于资产范畴。资产范围中不包括诸如大气或公海等无法有效地行使所有权的那些自然资源与环境，以及尚未发现或难以利用的矿藏，即一定时期内，鉴于它们本身的状况和现有的技术不能为其所有者带来任何经济利益的资源与环境。国民经济核算体系核算原则 1、权责发生制原则在国民经济核算中，各种交易的记录时间是按照权责发生制原则来确定的，即交易在债权债务发生、转移或取消的时间记录。这一原则适用于各种交易，包括同一机构部门内部的交易。权责发生制原则意味着交易在其实际发生时记录，而不是在相应的收入与支付发生时记录。 2、估价原则在国民经济核算中，各种交易、资产和负债的记录价格，遵循以下规定，凡发生货币支付的交易，都按交易双方认定的成交价格，即市场价格来估价；没有发生货币支付的交易，如同一机构单位内部的交易（如自制设备、自给性消费等），按市场上相同货物和服务的市场价格或按所发生的实际成本来估价。一般来说，货物和服务产出按生产者价格估价；大多数货物和服务的使用（如中间消耗、固定资产形成和最终消费）按购买者价格估价。固定资产存量按编制资产负债表时的现价估价，而不是按原购置价格估价。国民经济核算体系主要作用及影响一、国民经济核算是反映国民经济运行状况的有效工具二、国民经济核算是宏观经济管理的重要依据三、国民经济核算是制定和检验国民经济计划的科学方法

几种常用的经济指数

几种常用的经济指数指数作为一种重要的经济分析指标和方法，在实践中得到了广泛应用。但在不同场合，往往需要运用不同的指数形式。一般而言，选择指数形式的主要标准应该是指数的经济分析意义，除此之外，有时还要考虑实际编制工作的可行性，以及对指数分析性质的某些特殊要求。一、工业生产指数工业生产指数概括反映一个国家或地区各种工业产品产量的综合变动程度，它是衡量经济增长水平的重要指标之一。世界各国都非常重视工业生产指数的编制，但采用的编制方法却不完全相同。在我国，工业生产指数是通过计算各种工业产品的不变价格产值来加以编制的。其基本编制过程是: 1.对各种工业产品分别制定相应的不变价格标准(记为p n )； 2.然后逐项计算各种产品的不变价格产值，加总起来就得到全部工业产品的不变价格总产值； 3.将不同时期的不变价格总产值加以对比，就得到相应时期的工业生产指数。记t 时期的不变价格总产值为∑p q n t (t=0，1，2，3，…)，则该时期的工业生产指数就是固定加权综合指数的形式: ∑∑= p q p q k n n t q 采用不变价格法编制工业生产指数的特点是，只要具备了完整的不变价格产值资料，就能够很容易地计算出有关的生产指数；而且可以在不同层次上(如各地区、各部门、各企业等)进行编制，满足各方面的分析需要。然而，不变价格的制定和不变价格产值的计算本身却是一项非常浩繁的工作，这项工作又必须连续不断地、全面地展开，其难度可想而知。尤其是在市场经济条件下，要在整个工业生产领域内运用不变价格计算完整的产值资料，面临着很多实际的问题。因此，我国工业生产指数编制方法的改革势在必行。与我国的情况不同，在国外，较为普遍地采用平均指数的形式来编制工业生产指数。计算公式为: ∑∑= q p q p k k q q 0 其中，k q 为各种工业品的个体产量指数， p 0则为相应产品的基期增加值。编制这种工业生产指数的目的是为了说明工业增加值中物量因素的综合变动程度，其分析意义与一般的工业总产量指数是有所不同的。在实践中，为了简化指数的编制工作，常常以各种工业品的增加值比重作为权数，并且将这种比重权数相对固定起来，连续地编制各个时期的工业生产指数： ∑∑? = w w k k q q 这里运用了“固定加权算术平均指数”。二、消费者价格指数和零售物价指数消费者价格指数（又称生活费用指数）是综合反映各种消费品和生活服务价格的变动程度的重要经济指数，通常简记为CPI 。该指数可以用于分析市场物价的基本动态，调整货币工资以得到实际工资水平，等等。它是政府制定物价政策和工资政策的重要依据，世界各国都在编制这种指数。我国的消费者价格指数（居民消费价格指数）是采用固定加权算术平均指数方法来编制的。其主要编制过程和特点是： 1.将各种居民消费划分为八大类，包括食品、衣着、家庭设备及用品、医疗保健、交通和通讯工具、文教娱乐用品、居住项目以及服务项目等，下面再划分为若干个中类和小类；

常用指标

常用指标 1、KDJ随机指标通过一个特定的周期（常为9日、9周等）内出现过的最高价、最低价及最后一个计算周期的收盘价及这三者之间的比例关系，来计算最后一个计算周期的未成熟随机值RSV，然后根据平滑移动平均线的方法来计算K值、D值与J值，并绘成曲线图来研判股票走势。 1) K线是快速确认线——数值在90以上为超买，数值在10以下为超卖； D线是慢速主干线——数值在80以上为超买，数值在20以下为超卖； J线为方向敏感线，当J值大于100，特别是连续5天以上，股价至少会形成短期头部，反之J值小于0时，特别是连续数天以上，股价至少会形成短期底部。 2) 当K值由较小逐渐大于D值，在图形上显示K线从下方上穿D线，显示目前趋势是向上的，所以在图形上K线向上突破D 线时，即为买进的讯号。实战时当K，D线在20以下交叉向上，此时的短期买入的信号较为准确；如果K值在50以下，由下往上接连两次上穿D值，形成右底比左底高的“W底”形态时，后市股价可能会有相当的涨幅。

3) 当K值由较大逐渐小于D值，在图形上显示K线从上方下穿D线，显示目前趋势是向下的，所以在图形上K线向下突破D 线时，即为卖出的讯号。实战时当K，D线在80以上交叉向下，此时的短期卖出的信号较为准确；如果K值在50以上，由上往下接连两次下穿D值，形成右头比左头低的“M头”形态时，后市股价可能会有相当的跌幅。 4) 通过KDJ与股价背离的走势，判断股价顶底也是颇为实用的方法： A) 股价创新高，而KD值没有创新高，为顶背离，应卖出； B) 股价创新低，而KD值没有创新低，为底背离，应买入； C) 股价没有创新高，而KD值创新高，为顶背离，应卖出； D) 股价没有创新低，而KD值创新低，为底背离，应买入；需要注意的是KDJ顶底背离判定的方法，只能和前一波高低点时KD值相比，不能跳过去相比较。 2、MACD移动平均线利用短期（常用为12日）移动平均线与长期（常用为26日）移动平均线之间的聚合与分离状况，对买进、卖出时机作出研判的技术指标。 1.当DIF和DEA处于0轴以上时，属于多头市场，DIF线自下而上穿越DEA线时是买入信号。DIF线自上而下穿越DEA线时，如果两线值还处于0轴以上运行，仅仅只能视为一次短暂的回落，

国民经济统计学名词解释

国民经济统计学名词解释 Company number：【WTUT-WT88Y-W8BBGB-BWYTT-19998】

国民经济统计学名词解释 1.国民经济核算是按照一套既定概念方法对一个国民经济总体(通常指一个国家)所进行的系统定量描述。 2.国民经济指一国（或地区）的全部经济活动的总和。 3.经济领土指由该国政府实行有效经济控制的区域在确定的经济领土上，该国公民、货物、资本可以自由流动，不受国界的限制一国经济领土的基础是该国的地理疆域，但是，它并不等同于地理疆域4.常住单位如果一个单位在一国经济领土上拥有一定的活动场所（住宅、厂房或其他建筑物）从事一定规模的经济活动并超过一定的时期（一般以一年为标准） 5.机构单位是指能够独立拥有资产、承担负债从事经济活动并与其他单位进行经济交易的经济实体是进行经济决策的基本单位 6.基层单位

即产业活动单位在一个地点、从事一种或主要从事一种类型生产活动具有相应收支核算资料的生产单位它只是生产决策的单位，难以进行独立的财务决策 7.交易是指两个机构单位之间按照相互协议而进行的活动 8.经济流量反映一段时期内各种经济活动发生规模的总量 9.经济存量反映在特定时点上经济资源的拥有量的总量（经济流量与经济存量的对应关系：就特定时期而言，经济流量是在期初经济存量基础上发生的，然后经济流量改变了经济存量，使之从期初状态变化为期末状态） 10.国内生产总值从价值构成上看，国内生产总值是一国范围内各生产单位当期增加值的总和从实物构成上看，国内生产总值是一时期一国范围内各生产单位所生产的最终产品的价值总和 11.中间产品是指在一个生产过程生产出来然后又在另一个生产过程中被完全消耗掉或形态被改变的产品 12.最终产品是指当期生产的被用于最终消费、积累和出口的产品

几种常用的经济指数

几种常用的经济指数指数作为一种重要的经济分析指标和方法，在实践中获得了广泛应用。但在不同场合，往往需要运用不同的指数形式。一般而言，选择指数形式的主要标准应该是指数的经济分析意义，除此而外，有时还要考虑实际编制工作的可行性，以及对指数分析性质的某些特殊要求。现以国内外常见的主要经济指数为例，对指数方法的具体应用加以介绍。一、消费者价格指数和零售物价指数消费者价格指数（又称生活费用指数）是综合反映各种消费品和生活服务价格的变动程度的重要经济指数，通常简记为CPI 。该指数可以用于分析市场物价的基本动态，调整货币工资以得到实际工资水平，等等。它是政府制定物价政策和工资政策的重要依据，世界各国都在编制这种指数。我国的消费者价格指数（居民消费价格指数）是采用固定加权算术平均指数方法来编制的。其主要编制过程和特点是：首先，将各种居民消费划分为八大类，包括食品、衣着、家庭设备及用品、医疗保健、交通和通讯工具、文教娱乐用品、居住项目以及服务项目等，下面再划分为若干个中类和小类；其次，从以上各类中选定325种有代表性的商品项目（含服务项目）入编指数，利用有关对比时期的价格资料分别计算个体价格指数；再次，依据有关时期内各种商品的销售额构成确定代表品的比重权数，它不仅包括代表品本身的权数（直接权数），而且还要包括该代表品所属的那一类商品中其他项目所具有的权数（附加权数），以此提高入编项目对于所有消费品的一般代表性程度；最后，按从低到高的顺序，采用固定加权算术平均公式，依次编制各小类、中类的消费价格指数和消费价格总指数： 100∑∑∑?=?= w i w w i I q q q 例给出居民消费价格指数计算表（见表）。已知各大类、交通工具和通讯工具中类及其代表商品（代表规格品）的有关资料（有关数据均为假设）。要求据以编制有关的价格指数，并填充表中空缺的数据。解：利用表中资料和公式，依次计算各类别的消费价格指数和消费价格总指数如下：（1）计算交通工具和通讯工具两个中类的价格指数。交通工具类指数为： %37.104100 111.5570.53693.45100 =++=?= ∑w i I p p 通讯工具类指数为：表某市居民消费价格指数计算表

几种常见植被指数精编WORD版

几种常见植被指数精编 W O R D版 IBM system office room 【A0816H-A0912AAAHH-GX8Q8-GNTHHJ8】

植被指数主要反映植被在可见光、近红外波段反射与土壤背景之间差异的指标，各个植被指数在一定条件下能用来定量说明植被的生长状况。在学习和使用植被指数时必须由一些基本的认识： 1、健康的绿色植被在NIR和R的反射差异比较大，原因在于R对于绿色植物来说是强吸收的，NIR则是高反射高透射的； 2、建立植被指数的目的是有效地综合各有关的光谱信号，增强植被信息，减少非植被信息 3、植被指数有明显的地域性和时效性，受植被本身、环境、大气等条件的影响一、RVI——比值植被指数：RVI=NIR/R，或两个波段反射率的比值。 1、绿色健康植被覆盖地区的RVI远大于1，而无植被覆盖的地面（裸土、人工建筑、水体、植被枯死或严重虫害）的RVI在1附近。植被的RVI通常大于2； 2、RVI是绿色植物的灵敏指示参数，与LAI、叶干生物量(DM)、叶绿素含量相关性高，可用于检测和估算植物生物量； 3、植被覆盖度影响RVI，当植被覆盖度较高时，RVI对植被十分敏感；当植被覆盖度<50%时，这种敏感性显着降低； 4、RVI受大气条件影响，大气效应大大降低对植被检测的灵敏度，所以在计算前需要进行大气校正，或用反射率计算RVI。二、NDVI——归一化植被指数：NDVI=(NIR-R)/(NIR+R)，或两个波段反射率的计算。 1、NDVI的应用：检测植被生长状态、植被覆盖度和消除部分辐射误差等；

2、-1<=NDVI<=1，负值表示地面覆盖为云、水、雪等，对可见光高反射；0表示有岩石或裸土等，NIR和R近似相等；正值，表示有植被覆盖，且随覆盖度增大而增大； 3、NDVI的局限性表现在，用非线性拉伸的方式增强了NIR和R的反射率的对比度。对于同一幅图象，分别求RVI和NDVI时会发现，RVI值增加的速度高于NDVI增加速度，即NDVI对高植被区具有较低的灵敏度； 4、NDVI能反映出植物冠层的背景影响，如土壤、潮湿地面、学、枯叶、粗超度等，且与植被覆盖有关；三、DVI\EVI——差值\环境植被指数：DVI=NIR-R，或两个波段反射率的计算。 1、对土壤背景的变化极为敏感；? 四、SAVI\TSAVI\MSAVI——调整土壤亮度的植被指数：SAVI=((NIR- R)/(NIR+R+L))(1+L)，或两个波段反射率的计算。 1、目的是解释背景的光学特征变化并修正NDVI对土壤背景的敏感。与NDVI相比，增加了根据实际情况确定的土壤调节系数L，取值范围0~1。 L=0 时，表示植被覆盖度为零；L=1时，表示土壤背景的影响为零，即植被覆盖度非常高，土壤背景的影响为零，这种情况只有在被树冠浓密的高大树木覆盖的地方才会出现。 2、SAVI仅在土壤线参数a=1,b=0（即非常理想的状态下）时才适用。因此有了TSAVI、ATSAVI、MSAVI、SAVI2、SAVI 3、SAVI4等改进模型。五、GVI——绿度植被指数，k-t变换后表示绿度的分量。

资料分析常用指标及计算公式(2)

资料分析常用指标及计算公式（2）了解 GDP 随着经济日渐成为人们生活的焦点，经济领域的一个重要指标 ----------------- GDP （国内生产总值）越来越受到社会的关注。尽管大多数人都听说过 GDP ，但真正能明白的人恐怕并不多。日前有报道说我国的 GDP 中有约 10％— 20％是无效成本，这具体是怎么回事呢？记者采访了国家统计局国民经济核算司司长许宪春博士。内在含义是什么许宪春介绍说， GDP 是宏观经济中最受关注的经济统计数字，因为它被认为是衡量国民经济发展情况最重要的一个指标。 GDP 是按市场价格计算的国内生产总值的简称，是指一个国家（或地区）所有常住单位在一定时期内生产活动的最终成果。它涉及的是经济活动，是实实在在的。一般来说，国内生产总值有三种形态，即价值形态、收入形态和产品形态。从价值形态看，它是所有常驻单位在一定时期内生产的全部货物和服务价值与同期投入的全部非固定资产货物和服务价值的差额，即所有常驻单位的增加值之和；从收入形态看，它是所有常驻单位在一定时期内直接创造的收入之和；从产品形态看，它是货物和服务最终使用减去货物和服务进口。不应混淆概念针对日前有关报道说，我国市场交易中的无效成本占 GDP 的比重至少为 10％— 20％的问题，许司长说，国家统计局作为 GDP 发布的权威机构至今从未公布过这一数据，无效成本是经济学名词，国家统计局在统计 GDP 时从未使用过这个术语。漏和重复在所难免，但使用无效成本来衡量是不恰当的，至少有关都不涉及无效成本的概念。有关报道中还提到，我国每年因为逃废债务造成的直接损失约局统计，由于合同欺诈造成的直接损失约 55 亿元，还有产品质量低劣和制假售假造成的各种损失至少有 2000 亿元，由于三角债和现款交易增加的财务费用约为 2000 亿元，由于不合理的税外收费和不必要的审批造成的各种费用约 3000 亿元，另外还有逃骗税款损失以及发现的腐败损失等，正是这些因素造成无效成本占了国内生产总值的比重至少为 10％— 20％。对此，许宪春说，上述报道中提到的概念很混乱，它们和 GDP 不是一个口径，比如三角债、逃废债务造成的损失、欺诈造成的损失等，这些概念和 GDP 都不是同一类概念。通常我们在计算 GDP 时使用的数据是来自统计部门、财政部门和各有关部门，如金融保险系统、铁路系统、民航系统、邮电系统等，这些部门的数据均不会讨论无效成本的概念。当然， GDP 也不是万能的，并非什么数值都能往 GDP 上靠，否则容易造成混乱。 GDP 值是如何确定的国家统计局每年公布 GDP 数据是怎么得到的呢？许宪春说， GDP 计算需要经过以下几个过程：初步估计过程、初步核实过程和最终核实过程。初步估计过程一般在每年年终和次年年初进行。它得到的年度 GDP 数据只是一个初步数，这个数据有待于获得较充分的资料后进行核实。初步核实过程一般在次年的第二季度进行。初步核实所获得的 GDP 数据更准确些，但因仍缺少 GDP 核算所需要的许多重要资料，因此相应的数据尚需要进一步核实。最终核实过程一般在次年的第四季度进行。这时， GDP 核算所需要的和所能搜集到的各种统计资料、会计决算资料和行政管理资料基本齐备。与前一个步骤相比，它运用了更全面、更细致的资料，所以这个 GDP 数据显得就更准确些。虽然在核算 GDP 时，疏 GDP 三种形态的计算中 1800 亿元；国家工商总

国民经济统计计算公式

国民经济统计计算公式 The latest revision on November 22, 2020

国民经济核算一、中国国民经济核算体系由基本核算表、国民经济账户和附属表三部分构成。基本核算表包括国内生产总值表、投入产出表、资金流量表、国际收支表和资产负债表；国民经济账户包括经济总账户、国内机构部门账户和国外部门账户；附属表包括自然资源实物量核算表和人口资源与人力资本实物量核算表。二、核算价格主要有基本价格、生产者价格和购买者价格三种价格。基本价格=是生产者生产的单位货物和服务向购买者出售时获得的价值—其应付产品税+加上其应收补贴。基本价格是一种理想的核算价格，而不是现实存在的价格。生产者价格=是生产者生产的单位货物和服务向购买者出售时获得的价值—开给购买者发票上的增值税或类似可抵扣税。购买者价格=是购买者购买单位货物和服务所支付的价值+包括购买者按指定的时间和地点取得货物所发生的运输和商业费用+购买者缴纳的不可扣除的增值税和其他税。三、国内生产总值计算方式（GDP）： 1、生产法：将国民经济各产业部门生产法增加值相加，得到生产法国内生产总值。增加值＝总产出（按生产者价格计算）－中间投入（按购买者价格计算） 2、收入法：收入法也称分配法，从生产过程形成收入的角度，对常住单位的生产活动成果进行核算。增加值＝劳动者报酬+生产税净额+固定资产折旧+营业盈余 3、支出法：支出法国内生产总值是从最终使用的角度反映一个国家一定时期内生产活动最终成果的一种方法。支出法国内生产总值＝最终消费（按购买价计算的实际消费+虚拟消费）+资本形成总额（有形无形资产购入+存货购入-有形无形资产和存货处置支出）+净出口（货物、服务的出口——进口后的离岸价格）四、国民生产总值计算方式（GNP）=国民总收入（GNI）计算公式：国民生产总值（GNP）=国内生产总值(GDP)+（来自国外的要素收入－支付国外的要素收入）＝GDP+国际收支平衡表中经常项目下收益贷方减借方的差额国际收支平衡表中经常项目下收益包括投资收益和职工报酬。其中，投资收益包括直接投资的利润、利息收支和再投资收益、证券投资收益（股息、利息等）和其他投资收益（利息）。职工报酬指我国个人在国外工作（一年以下）而得到并汇回的收入以及我国支付在华外籍员工（一年以下）的工资福利。

关于经济学中常用的指数

关于经济学中常用的指数 1、SPCI 标准普尔商品指数它的成分商品均为美国国内市场交易的品种，目前包含17种商品，权重的设计是按照期货市场中的持仓量大小来确定的。标准普尔商品指数最大的特点是，采取几何算法来对指数进行计算，在这种算法下，指数的波动性下降，稳定性提高。 2、恒生指数香港股市价格的重要指标，指数由若干只成份股（即蓝筹股）市值计算出来的，代表了香港交易所所有上市公司的12个月平均市值涵盖率的70%，恒生指数由恒生银行属下恒生指数有限公司负责计算及按季检讨，公布成份股调整。 3、日经指数全名叫“日经道·琼斯平均股价指数”，它的采样股票分别来自制造业、建筑业、运输业、电力和煤气业、仓储业、水产业、矿业、不动产业、金融业及服务业等行业，覆盖面极广；而各行业中又是选择最有代表性的公司发行的股票作为样本股票。同时不仅样本股票的代表公司和组成成份随着情况的变化而变化，而且样本股票的总量也在不断增加，目前已从225种扩增为500种。因此，该指数被看作日本最有影响和代表性的股价指数，通过它可以了解日本的股市行情变化和经济景气变动状况。 4、纳斯达克指数它是反映纳斯达克证券市场行情变化的股票价格平均指数，基本指数为100。纳斯达克的上市公司涵盖所有新技术行业，包括软件和计算机、电信、生物技术、零售和批发贸易等。主要由美国的数百家发展最快的先进技术、电信和生物公司组成，包括微软、英特尔、美国在线、雅虎这些家喻户晓的高科技公司，因而成为美国“新经济”的代名词。纳斯达克综合指数是代表各工业门类的市场价值变化的晴雨表。因此，纳斯达克综合指数相比标准普尔500指数、道·琼斯工业指数（它仅包括30个大公司）更具有综合性。目前，纳斯达克综合指数包括5000多家公司，超过其他任何单一证券市场。因为它有如此广泛的基础，已成为最有影响力的证券市场指数之一。 5、CRB指数

几种常见植被指数

常用的植被指数，土壤指数，水体指数有哪些？植被指数与土壤指数一、RVI——比值植被指数：RVI=NIR/R，或两个波段反射率的比值。 1、绿色健康植被覆盖地区的RVI远大于1，而无植被覆盖的地面（裸土、人工建筑、水体、植被枯死或严重虫害）的RVI在1附近。植被的RVI通常大于2； 2、RVI是绿色植物的灵敏指示参数，与LAI、叶干生物量(DM)、叶绿素含量相关性高，可用于检测和估算植物生物量； 3、植被覆盖度影响RVI，当植被覆盖度较高时，RVI对植被十分敏感；当植被覆盖度<50%时，这种敏感性显著降低； 4、RVI受大气条件影响，大气效应大大降低对植被检测的灵敏度，所以在计算前需要进行大气校正，或用反射率计算RVI。二、NDVI——归一化植被指数：NDVI=(NIR-R)/(NIR+R)，或两个波段反射率的计算。 1、NDVI的应用：检测植被生长状态、植被覆盖度和消除部分辐射误差等； 2、-1<=NDVI<=1，负值表示地面覆盖为云、水、雪等，对可见光高反射；0表示有岩石或裸土等，NIR和R近似相等；正值，表示有植被覆盖，且随覆盖度增大而增大；

3、NDVI的局限性表现在，用非线性拉伸的方式增强了NIR和R的反射率的对比度。对于同一幅图象，分别求RVI和NDVI时会发现，RVI值增加的速度高于NDVI增加速度，即NDVI对高植被区具有较低的灵敏度； 4、NDVI能反映出植物冠层的背景影响，如土壤、潮湿地面、学、枯叶、粗超度等，且与植被覆盖有关；三、DVI\EVI——差值\环境植被指数：DVI=NIR-R，或两个波段反射率的计算。 1、对土壤背景的变化极为敏感；四、SAVI\TSAVI\MSAVI——调整土壤亮度的植被指数： SAVI=((NIR-R)/(NIR+R+L))(1+L)，或两个波段反射率的计算。 1、目的是解释背景的光学特征变化并修正NDVI对土壤背景的敏感。与NDVI相比，增加了根据实际情况确定的土壤调节系数L，取值范围0~1。L=0 时，表示植被覆盖度为零；L=1时，表示土壤背景的影响为零，即植被覆盖度非常高，土壤背景的影响为零，这种情况只有在被树冠浓密的高大树木覆盖的地方才会出现。 2、SAVI仅在土壤线参数a=1,b=0（即非常理想的状态下）时才适用。因此有了TSAVI、ATSAVI、MSAVI、SAVI2、SAVI 3、SAVI4等改进模型。五、GVI——绿度植被指数，k-t变换后表示绿度的分量。

国民经济统计计算公式

1. 现有人口＝常住人口－常住人口中临时外出的人口＋外来临时寄居的人口 2. 常住人口＝现有人口＋常住人口中临时外出的人口－外来临时寄居的人口 3. 期末人口总数＝期初人口总数＋期内增加人口数－期内减少人口数其中：期内增加人口数＝期内出生人口数＋期内迁入人口数 4. 期内减少人口数＝期内死亡人口数＋期内迁出人口数 5. 平均人口数是指某一时期内的各个时点人口的平均数。 6已知年初和年末人口数时 . 7. 已知年初和各季末人口数时 8. 城乡人口百分比的计算公式 9. 10. 11. 12． 13． 14． 15. 16. 2 年末人口数年初人口数年平均人口数+=()()时点间隔不等时点间隔相等∑?+++?++?+=++++=-f f a a f a a f a a a n a a a a a n n n o n 22222 122111210 )()(平方公里该地区土地面积人某地区人口数人口密度= %100)(?=全部人口数或女性人数男性人数性别构成%100?=总人口城市(乡村)人口人口百分比城市(乡村)人口占总%100?=乡村人口城市人口城乡人口比例100?=女性人数男性人数性别比例总人口数岁以下人口数少儿人口系数14=总人口数岁以上人口数老年人口系数65=岁人口数岁以上人口数岁以下人口数总负担系数64156514- +=岁人口数岁以上人口数负担老年人口系数岁人口数岁以下人口数负担少年人口系数641565641514-=-=∑?=?==-=-=受该学制教育人数受该学制教育人数某种学制年限人均受教育程度总人口数大学在学人数大学教育普及程度指标岁及以上的人口数很少的人数岁及以上不识字与识字文盲率岁人口数中学在学人数中等教育就学率岁人口数小学在学人数初等教育就学率10000015151914136

常用的经济指标

常用的经济指标 GNP是什么? ( Gross National Product , 简称GNP ) 国民生产总值指一个国家全体居民在国内与国外一年内生产或服务所赚取之报酬总和，不包括外国人所拥有之国内生产因素所赚取之所得报酬。用途︰是经常用评来评估全国所有国民经济活动的专有名词。意义︰ 1 、它表示整个国家于某一时期( 通常以一年为单位)所制成之所有各种货物与劳务之价值的总和。 2 、国民生产总值越多，代表国家生产力的能力越高 GNP = C + I + G + (X - M) C :民间消费支出 I :国内投资总值，或称国内资本形成总值 G :政府消费支出 X :出口M :进口 * ( X - M ) 为正值时，为贸易顺差, 为负值时，为贸易逆差国民生产总值( GNP ) : 世界银行在2000年，公布1999年全球排名平均每人国民生产总值统计数字中，台湾排名第23 名，数字为13,235美元，显示台湾的生产力在全世界的前百分之十五以内。 GDP是什么? ( Gross Domestic Product , 简称GDP ) 国内生产总值 GDP = C + I + G + (X - M) 包括本国境内之所有生产，不论生产要素来自国内或国外。与金融市场关联度: 1. 反映该国经济成长状况。 2.由GDP 成长率可预估该国之经济成长表现。国民生产总值(GNP) 国民生产总值越多，代表国家生产力的能力越高国内生产总值(GDP) 由GDP成长率可预估该国之经济成长的表现。国民生产总值(GNP) V.S. 国内生产总值(GDP) 计算基础的区别? 国民生产总值(Gross National Product) ，简称GNP 指一个国家全体国民在国内与国外一年内生产或服务所赚取之报酬总和，不包括外国人所拥有之国内生产因素所赚取之所得报酬。国内生产总值(Gross Domestic Product) ，简称GDP 指一国于一年内在该国内从事生产或服务后所得报酬之总和。它包括住在国内的外国人所赚取的报酬，但不包含本国国民在国外之所得报酬。

股票常用指标说明

常用指标说明反趋向指标 KDJ ROC W&R威廉指标 RSI BIAS ADTM ATR OSC UDL KDJ 指标说明：KDJ，其综合动量观念、强弱指标及移动平均线的优点，早年应用在期货投资方面，功能颇为显著，目前为股市中最常被使用的指标之一。买卖原则： 1 K线由右边向下交叉D值做卖，K线由右边向上交叉D值做买。 2 高档连续二次向下交叉确认跌势，低挡连续二次向上交叉确认涨势。 3 D值<20%超卖，D值>80%超买，J>100%超买，J<10%超卖。 4 KD值于50%左右徘徊或交叉时，无意义。

5 投机性太强的个股不适用。 6 可观察KD值同股价的背离，以确认高低点。 ROC 当ROC向下跌破零，卖出信号；ROC向上突破零，买入信号。股价创新高，ROC未配合上升，显示上涨动力减弱。股价创新低，ROC未配合下降，显示下跌动力减弱。股价与ROC从低位同时上升，短期反弹有望。股价与ROC从高位同时下降，警惕回落。 W&R威廉指标算法： N日内最低价与当日收盘价的差，除以N日内最高价与最低价的差，结果放大100倍参数： N 统计天数一般取14天用法： 1.低于20，超买，即将见顶，应及时卖出 2.高于80，超卖，即将见底，应伺机买进 3.与RSI、MTM指标配合使用，效果更好 RSI RSIS为1978年美国作者Wells WidlerJR。所提出的交易方法之一。所谓RSI英文全名为Relative Strenth Index，中文名称为相对强弱指标．RSI的基本原理是在一个正常的股市中，多空买卖双方的力道必须得到均衡，股价才能稳定;而RSI是对于固定期间内，股价上涨总幅度平均值占总幅度平均值的比例。 1 .RSI值于0-100之间呈常态分配，当6日RSI值为80‰以上时，股市呈超买现象，若出现M头为卖出时机;当6日RSI 值在20‰以下时，股市呈超卖现象，若出现W头为买进时机。

国民经济统计概论重点内容

第一章绪论第一节统计学的性质及分类一、统计学的性质统计学的概念：以搜集、整理、分析或推断数据，并以此为依据对所研究对象做出判断或决策的方法科学论。二、统计学的分类理论统计学研究如何对客观现象的数量进行计量、观测、概括和表述，是统计学的基础和统计研究工作的第一步，内容包括统计指标及其设计、统计调查、统计整理、统计图表、集中趋势测度、离散程度测试、统计指数和时间序列常规分析等理论方法。推断统计学是现代统计学的核心内容，它以概率论为理论依据，利用部分数据对总体数据的某些性质或数量特征进推断和检验。理论统计学和应用统计学的关系：理论统计学所提出的科学的数量方法为应用统计学研

究提供了理论依据和条件，而应用统计学的发展又可进一步改进、完善和发展理论统计学所提出的数量方法。第二节统计学的基本概念一、总体和个体总体：构成统计活动研究对象的全部事物的整体为总体（有限总体、无限总体）个体：总体中每个个体事物。总体容量：总体中全部个体事物的数量称为总体的容量。统计总体根据统计研究的目的来确定。二、样本样本是指从总体中随机抽取出来，并作为其代表的那一部分个全所组成的子集。样本的特点:每个个体必须取自于总体的内部，从一个总体可以抽取许多个不同的样本，样本是总体的代表，样本的随机性。三、变量变量：客观现象的特征取值或类别在一个以上者均为变量四、指标及其测度

用来测度研究对象某种特征数量的概念称为统计指标，简称指标。第三节统计指标体系及其设计一、统计指标体系的概念反映总体及其所含个体的各个方面特征数量的一系列相互联系、相互补充的统计指标所形成的体系，称为统计指标体系。二、统计指标体系中指标的分类三、统计指标体系设计的内容： 1、设置框架 2、确定内涵和外延 3、确定计量单位 4、确定计算方法四、统计指标体系设计的原则统计指标体系设计的原则：目的性、科学性、可行性、联系性

宏观经济数据有哪些指标

国内生产总值（GDP）：是某一国在一定时期其境内生产的全部最终产品和服务的总值。反映一个国家总体经济形势的好坏，与经济增长密切相关，被大多数西方经济学家视为“最富有综合性的经济动态指标”。主要由消费、私人投资、政府支出、净出口额四部分组成。数据稳定增长，表明经济蓬勃发展，国民收入增加，有利于美圆汇率；反之，则利淡。一般情况下，如果GDP连续两个季度下降，则被视为衰退。此数据每季度由美国商务部进行统计，分为初值、修正值、终值。一般在每季度末的某日北京时间21：30公布前一个季度的终值。工业生产（INDUSTRIAL PRODUCTION）：某国工业生产部门在一定时间内生产的全部工业产品的总价值。在国内生产总值中占有很大比重。由于工业部门雇佣了大量工人，其变动对整个国民经济有着重大影响，与汇率呈正相关。尤其以制造业为代表。此数据由美联储统计并在每月15日左右晚间21：15或22；15发布。失业率（UNEMPLOYMENT RATE）：经济发展的晴雨表，与经济周期密切相关。数据上升说明经济发展受阻，反之则看好。对于大多数西方国家来说，失业率在4%左右为正常水平，但如果超过9%，则说明经济处于衰退。此数据由美国劳工部编制，每月第一个周五21：30公布。贸易赤字（TRADE DIFICIT）：国际间的贸易是构成经济活动的重要环节。当一国出口大于进口时称为贸易顺差；反之，称逆差。美国的贸易数据一直处于逆差状态，重点是在赤字的扩大或缩小。赤字扩大不利于美圆，反之则有利。此数据由美国商务部编制，每月中、下旬某日晚间21：30公布前一个月数字。经常项目收支：经常帐为一国收支表上的主要项目，内容记载一国与外国包括因为商品/劳务进出口、投资所得、其他商品与劳务所得以及片面转移等因素所产生的资金流出与流入的状况。如果为正数，为顺差，有利本国货币；反之，则不利于本国货币。此数据由美国商务部编制，每月中旬某日21：30公布。资本帐收支：主要描述一国的长、短期资本流动情况，包括长期资本、非流动性短期私人资本、特别提款权、误差与遗漏，以及流动性短期私人资本等项目。资本项目在金融日益国际化、自由化的今天，影响不亚于经常帐项目，金融市场对外开放程度越高，影响越大。其对汇率的影响的观察方法与经常帐基本相同。利率（INTRESTRATE）：利率是借出资金的回报或使用资金的代价。一国利率的高低对货币汇率有着直接影响。高利率的货币由于回报率较高，则需求上升，汇率升值；反之，则贬值。美国的联邦基金利率由美联储的会议来决定。

ENVI中常见植被指数介绍

作业9 植被指数植被指数概念：利用卫星不同波段探测数据组合而成的，能反映植物生长状况的指数。植物叶面在可见光红光波段有很强的吸收特性，在近红外波段有很强的反射特性，这是植被遥感监测的物理基础，通过这两个波段测值的不同组合可得到不同的植被指数。不同的植被覆盖类型可以通过其特有的光谱特征进行区分，这是由于叶绿素在红波段内对太阳辐射的吸收以及叶片细胞结构对红外波段内太阳辐射的强反射。 Broadband Greenness(5 indices)（宽带绿色指标(5)）宽带绿度指数可以简单度量绿色植被的数量和生长状况，它对植物的叶绿素含量、叶子表面冠层、冠层结构比较敏感，这些都是植被光合作用的主要物质，与光合有效辐射（fAPAR）也有关系。宽带绿度指数常用于植被物候发育的研究，土地利用和气候影响评估，植被生产力建模等。宽带绿度指数选择的波段范围在可见光和近红外，一般的多光谱都包含这些波段。下面的公式中规定波段的中心波长：ρNIR=800nm，ρRED=680nm，ρBLUE=450nm。 1. Normalized Difference Vegetation Index归一化植被指数增强在近红外波段范围绿叶的散射与红波段范围叶绿素的吸收差异。简称NDVI： NDVI=(NIR-R)/(NIR+R) （1）应用：检测植被生长状态、植被覆盖度和消除部分辐射误差等；（2）-1<=NDVI<=1，负值表示地面覆盖为云、水、雪等，对可见光高反射；0表示有岩石或裸土等，NIR和R近似相等；正值，表示有植被覆盖，且随覆盖度增大而增大；（3）NDVI的局限性表现在，用非线性拉伸的方式增强了NIR和R的反射率的对比度。对于同一幅图象，分别求RVI和NDVI时会发现，RVI值增加的速度高于NDVI增加速度，即NDVI 对高植被区具有较低的灵敏度；（4）NDVI能反映出植物冠层的背景影响，如土壤、潮湿地面、学、枯叶、粗超度等，且与植被覆盖有关； 2.Simple Ratio Index比值植被指数在近红外波段范围绿叶的散射与红波段范围叶绿素吸收的比值。简称SR：SR=ρNIR/ρRED 在LAI 值很高，即植被茂密时其灵敏度会降低.SR值的范围是0~30，一般绿色植被区的范围是2~8 3.Enhanced Vegetation Index 增强植被指数增强NDVI,解决土壤背景和大气气溶胶对茂密植被的影响。简称：EVI

常用指标详解

常用指标详解一：WR威廉指标一．用途：该指标表示的涵义是当天的收盘价在过去一段日子的全部价格围所处的相对位置，是一种兼具超买超卖和强弱分界的指标。它主要的作用在于辅助其他指标确认讯号。二．使用方法： 1、从WR的绝对取值方面考虑。 A、当WR 高于80，即处于超卖状态，行情即将见底，应当考虑买进。 B、当WR 低于20，即处于超买状态，行情即将见顶，应当考虑卖出。 2、从WR的曲线形状考虑。 A、在WR进入高位后，一般要回头，如果这时股价还继续上升，这就产生背离，是卖出的信号。 B、在WR进入低位后，一盘要反弹，如果这时股价还继续下降，这就产生背离，是买进的信号。 C、WR连续几次撞顶（底），局部形成双重或多重顶（底），则是卖出（买进）的信号。三．使用心得： 1．W%R主要可以辅助RSI，确认强转弱或弱转强是否可靠？RSI向上穿越50阴阳分界时，回头看一看W%R 是否也同样向上空越50？如果同步则可靠，如果不同步则应多参考其他指标讯号再作决定。相反的，向下穿越50时，也是同样的道理。注意！比较两者是否同步时，其设定的参数必须是相对的比例，大致上W%R 5日、10日、20日对应RSI6日、12日、24日，但是读者可能可以依照自己的测试结果，自行调整其最佳对应比例。 2．W%R进入超买或超卖区时，应立即寻求MACD讯号的支援。当W%R进入超买区时，我们当成一种预警效果，回头看看MACD是否产生DIF向下交叉MACD的卖出讯号？一律以MACD 的讯号为下手卖出的时机。相反的，W%R进入超卖区时，也适用同样的道理。四．计算公式： n日WMS=[(Hn-Ct)/(Hn-Ln)] ×100 式中：Cn---当天的收盘价； Hn和Ln---最近N日（包括当天）出现的最高价和最低价二：布林线BOLL 一．用途：该指标利用波带显示其安全的高低价位。股价游走在"上限"和"下限"的带状区间，当股价涨跌幅度加大时，带状区会变宽，涨跌幅度缩小时，带状区会变窄。二．使用方法： 1．向上穿越"上限"时，将形成短期回档，为短线的卖出时机。 2．股价向下穿越"下限"时，将形成短期反弹，为短线的买进时机。 3．当布林线的带状区呈水平方向移动时，可以视为处于"常态围"，此时，采用1、2两个使用方法，可靠