1、植被及多角度遥感植被遥感意义及内容植被遥感意义及内容意义：意义： 人类生存及发展 地气能量及物质交换 环境保护（防止土壤侵蚀，吸收CO2）内容：内容： 植被覆盖区域，划分植被类型 反演植被参数 估算与光合作用有关物理量(蒸腾，光合作用强度，叶面温度)模型冠层内不同高度的光通量植被遥感模型分类植被遥感模型分类 统计统计/经验模型经验模型将反射率特征与冠层参数建立统计关系（植被指数）简单，适用性强，随着地面先验知识积累和观测波段、角度增多，优势减弱。 物理模型物理模型基于辐射传输或几何光学原理 Homogeneous turbid （均匀、绿色气体） Heterogeneous solid（不均匀
2、实体组合，经典的GO模型） Homogeneous discrete （均匀、叶片） Heterogeneous turbid （不均匀、绿色气体） Heterogeneous discrete （不均匀、叶片）RAMI(Radiation transfer Model Intercomparison)植被遥感模型分类植被遥感模型分类Homogeneous discrete在RAMI中的几种典型场景植被遥感模型分类植被遥感模型分类Heterogeneous turbid植被遥感模型分类植被遥感模型分类Heterogeneous discrete植被遥感模型分类植被遥感模型分类考虑地形，圆锥实体
3、（树冠）+圆柱（树干）植被遥感模型分类植被遥感模型分类球形+圆柱形 模拟混合林植被遥感模型分类植被遥感模型分类植被遥感模型分类植被遥感模型分类尺度问题植被遥感模型参数植被遥感模型参数结构参数：结构参数： 总的长、宽、高 LAI(leaf area index)地表单位面积上方所有叶子单面面积或总面积的一半之总和。无量纲。LAI影响与太阳辐射作用及遥感信号强弱。也决定了碳吸收和与大气间的能量交换。 FAVD(Foliage area volume density)某一高度上单位体积内叶面积的总和，单位1/m。 LAD(Leaf Angle Distribution )叶面的法线方向的概率分布，通
4、常只考虑倾角。植被遥感模型参数植被遥感模型参数LAD通常分为五类(deWit, 1965)或六类(Geol and Strebel, 1984)： 12sinLLg1Lg124cossinLLLLg4sinLLLg124sin2sinLLLLg124cos2sinLLLLg统一型 球面型（叶面法线完全随机） 平面型 竖直型 倾斜型 极端型 l代表叶片法线方向植被遥感模型参数植被遥感模型参数LAD具有特征：所有叶片向一个给定的方向W的投影多少与FAVD的乘积决定了该方向植被所占的面积比。为此，引入G函数：WWWW2010),(21),(llllldzgdzGG函数函数 21),(211020Wp
5、ppzGdl = cos l1),(212WWllldzgG函数具有特征： p = cos pp代表观测方向G(z, W)*FAVD(z)表示光从W方向射向植被，在高度z处，与植被发生碰撞的概率植被遥感模型参数植被遥感模型参数光学参数：光学参数： 叶子反射率、透过率 土壤表面反射率植被遥感原理植被遥感原理 模型模型建模基本步骤：建模基本步骤： 建立概念模型（ Specification ） 将概念模型转换为数学模型(formulation) 生成计算机代码，在计算机中运行 (Implementation ) 通过数据显示、敏感性分析、误差分析等对模型进行评价(Evaluation )The m
6、odel is gradually extended so that its output conforms more closely to empirical observations of real vegetation canopies. It is also follows the principal of simplicity sometimes referred to as Occams Razor or, less formally, as Keep It Simple Stupid (KISS)!植被遥感原理植被遥感原理 模型模型植被建模基础概念植被建模基础概念 太阳发射电磁辐
7、射 忽略大气效应，到达地表的太阳辐射可能被吸收或反射回空中。 反射及吸收的平衡是一个控制地球气候的重要因子 吸收部分被作为热辐射再次发射，使地球大气的底层变暖。植被遥感原理植被遥感原理 模型模型植被建模基础概念植被建模基础概念 地球表面由不同的物质覆盖 (比如植被，土壤，水，雪，冰), 每种物质反射不同的太阳辐射。 一个给定的表面所反射的太阳辐射(reflectivity or reflectance)与其物理、化学及生物特性紧密联系。 地球气候系统部分地决定于地球表面物质的分布，而反过来又控制着这些分布。 如果将来气候变冷，地球大部份被冰雪覆盖，大量的入射辐射将被反射回太空，导致地表进一步变
8、冷，大气层降低(positive feedback)。 实际上，大部份地表是不同物质的混合。 因此，被反射或吸收的太阳辐射是这些地表覆盖的相对面积比的函数。植被遥感原理植被遥感原理 模型模型模型建立模型建立 Assumptions of the conceptual model: 不同的表面(比如植被，土壤，水，雪，冰) 反射不同的太阳辐射(反射率是地表类型的函数)。 地表覆盖为不同物质的混合体。 被反射的太阳辐射是研究区域不同地表类型相对面积比的函数。 Note that all the assumptions are testable For the moment, however, we
9、 will simply accept them植被遥感原理植被遥感原理 模型模型Why state the assumptions? Stating the assumptions explicitly achieves a number of things, including:1 We clarify in our own minds the fundamental conceptual basis of our model(让自己清楚)2 We provide sufficient information for potential users of the model to（让别人清
10、楚）i) understand its scope and limitations,ii) challenge its underlying assumptions, and perhapsiii) derive derive an improved model in the future植被遥感原理植被遥感原理 模型模型Formulating the model Imagine an area entirely covered by bare soil The fraction of incident solar radiation that is reflected from this a
11、rea is dependent only on the reflectance of the soil (0r(l)soil 1) r(l)soil has the meaning the reflectance (r) of soil varies as a function of wavelength (l)植被遥感原理植被遥感原理 模型模型Formulating the model Imagine another area entirely covered by vegetation (leaves) through which none of the soil substrate i
12、s visible The fraction of incident solar radiation that is reflected from this area is dependent only on the reflectance of the leaves (0r(l)leaf 1)植被遥感原理植被遥感原理 模型模型Formulating the model Now imagine the case where we have a mixture of vegetation (leaves) and soil Assume some fraction (0 A 1) of the
13、total area is covered by leaves and the remainder (i.e. 1 A) is exposed soil If incoming solar radiation is distributed equally across the area, the total spectral reflectance is given by: r(l)total = Ar(l)leaf + (1 A)r(l)soil植被遥感原理植被遥感原理 模型模型Plotting the results植被遥感原理植被遥感原理 模型模型Enhancing the model
14、Simple model portrays the surface as a single layer (slab) in which the vegetation and soil lie side-by-side Unrealistic representation of most vegetation canopies Leaves are usually located above the soil substrate Implies that we really need a two-layer model Assumptions, scope and limitations of
15、our model are otherwise as before植被遥感原理植被遥感原理 模型模型植被遥感原理植被遥感原理 模型模型Possible pathways(i) reflect directly from leaf layer(ii) pass down through gap in leaf layer, reflect from soil substrate and escape up through gap in leaf layer(iii) pass down through leaf layer, reflect from soil substrate and esc
16、ape up through gap in leaf layer(iv) pass down through gap in leaf layer, reflect from soil substrate and pass up through leaf layer(v) pass down through leaf layer, reflect from soil substrate and pass back up through leaf layer植被遥感原理植被遥感原理 模型模型Transmittance and absorptance Introduced two new pheno
17、mena into conceptual model of Earth surface reflectance one explicitly (transmission or transmittance) and one implicitly (absorption or absorptance): transmission is the process by which radiation passes through an object, such as a leaf transmittance is the fraction of solar radiation incident upo
18、n an object that is transmitted through it absorption is the process by which radiation is absorbed by an object (i.e. radiation that is neither reflected nor transmitted)absorptance is the proportion of incident radiation that is absorbed by the object.植被遥感原理植被遥感原理 模型模型Formulating the model Use the
19、 symbols A, r(l)leaf and r(l)soil as before Define t(l)leaf spectral transmittance of the leaves, a(l)leaf spectral absorptance of the leaves and a(l)soil spectral absorptance of the soil Noting that 1 = r(l)leaf + t(l)leaf + a(l)leaf and 1 = r(l)soil + a(l)soil assuming that the soil is completely
20、opaque植被遥感原理植被遥感原理 模型模型植被遥感原理植被遥感原理 模型模型Components of 2-layer model Components of the two-layer model:(i) A r(l)leaf (ii) (1 A) r(l)soil(1 A)(iii) At(l)leaf r(l)soil(1 A)(iv) (1 A) r(l)soil At(l)leaf(v) At(l)leaf r(l)soil At(l)leaf Even if we ignore the 3rd, 4th and 5th terms, above, our 2-layer mod
21、el differs from the 1-layer case: A r(l)leaf + (1 A) r(l)soil (1-layer model) A r(l)leaf + (1 A) r(l)soil(1 A) (2-layer model)(植被不透明)植被遥感原理植被遥感原理 模型模型Total canopy reflectance Total canopy reflectance sum of the five component terms:r(l)total = A r(l)leaf + (1 A) r(l)soil(1 A) + At(l)leaf r(l)soil(1
22、A) + (1 A) r(l)soil At(l)leaf + At(l)leaf r(l)soil At(l)leaf Looks daunting, so lets substitute CR for r(l)total (total canopy reflectance), LR for A r(l)leaf (radiation reflected from leaf layer), LT for At(l)leaf (radiation transmitted through leaf layer), SR for r(l)soil (radiation reflected from
23、 soil substrate), and gap for (1 A) (radiation passing through a gap in leaf layer) 植被遥感原理植被遥感原理 模型模型Total canopy reflectance Two-layer model now reads: CR = LR + (gap SR gap) + (LT SR gap) +(gap SR LT) + (LT SR LT) Note 3rd and 4th terms above are equivalent (i.e. LT SR gap = gap SR LT), so we can
24、simplify as follows: CR = LR + (gap SR gap) + 2 (LT SR gap) + (LT SR LT) 植被遥感原理植被遥感原理 模型模型Evaluating the output植被遥感原理植被遥感原理 模型模型Actual vs. expected output植被遥感原理植被遥感原理 模型模型Actual vs. expected output Expect spectral reflectance to have non-linear relationship with respect to fractional vegetation cove
25、r in both the red and the near-infrared parts of the spectrum Red wavelengths relationship is indirect (negative) Near-infrared (NIR) relationship is direct (positive) Both red and NIR exhibit an asymptotic trend, with the red appearing to reach its asymptote sooner than the NIR Discrepancy suggests
26、 that the 2-layer model is still too simplistic Go back once more and improve the conceptual model, updating the associated mathematical and computational models accordingly植被遥感原理植被遥感原理 模型模型Multiple Scattering Current version of the two-layer model is:CR = LR + (gap SR gap) + 2 (LT SR gap) + (LT SR
27、LT) Instructive to note that 1st and 2nd terms, above, describe radiation that has interacted once with the vegetation canopy either the leaf layer (LR) or the soil substrate (gap SR gap), but not both The 3rd term (LT SR gap) describes radiation that has interacted twice with the canopy (in this ca
28、se, the leaf layer and the soil substrate) The 4th term (LT SR LT) describes radiation that has interacted three times with the canopy (the leaf layer, the soil substrate and the leaf layer again)植被遥感原理植被遥感原理 模型模型Multiple Scattering Radiation that interacts more than once with the vegetation canopy
29、is said to be multiply scattered (c.f. singly scattered) Common to refer to the scattering order: 2nd-order scattering radiation scattered (i.e. reflected or transmitted) twice within the canopy, 3rd-order scattering radiation scattered three times, etc. Improve the 2-layer model by incorporating hi
30、gher-order (4th, 5th, . . . ) interaction effects? 4th-order scattering: LT SR LR SR gap植被遥感原理植被遥感原理 模型模型Evaluating the output植被遥感原理植被遥感原理 模型模型Diminishing multiple scattering Taking 4th-order scattering events into account has had very little impact on the output from the two-layer model. Reason? 4t
31、h-order scattering component is the product of five fractional values (i.e. LT SR LR SR gap) So, if A = 0.5, r(l)leaf = 0.475, t(l)leaf = 0.475 and r(l)soil = 0.125 Such that LR = 0.2375, LT = 0.2375, SR = 0.125 and gap = 0.5 4th-order = 0.23750.1250.23750.1250.50.00044 Contribution due to single sc
32、attering from the leaf layer is LR = 0.4750.5 = 0.2375 ( 550 times greater than that due to fourth-order scattering) 植被遥感原理植被遥感原理 模型模型Evaluating multiple scattering植被遥感原理植被遥感原理 模型模型Evaluating multiple scattering(考虑多次反弹考虑多次反弹)间隙率(gap)与开放度(openness)的区别： 开放度可以认为是间隙率在半球空间的积分。 对于简单的两层模型，可以认为二者相等。多次反弹的概念：
33、(multiple bouncing) 光在两种媒质之间的来回反射，属于多次散射植被遥感原理植被遥感原理 模型模型Evaluating multiple scattering(考虑多次反弹考虑多次反弹)多次反弹的表达式： 参加多次反弹的总能量(第一次到达地表)： gap + LT 第一次散射出冠层能量 (gap + LT)SR(gap + LT) 第二次到达地表的能量： (gap + LT)SRAr(l)leaf 公比 SRAr(l)leaf = SRLR 多次反弹(包括与地表一次散射)的总贡献： (gap + LT)SR(gap + LT)1/(1 SRLR)最终的两层模型： CR = LR
34、 + (gap + LT)SR(gap + LT)1/(1 SRLR)植被遥感原理植被遥感原理 模型模型Multiple leaf-layer models Alternative is to increase the number of leaf layers Improved representation of 3D structure of real vegetation canopies植被遥感原理植被遥感原理 模型模型Leaf Area Index（叶面积指数）（叶面积指数） 定义单位地表面积上的总叶片面积（双面或多面）的一半。影响反射、透射的强度，与光合作用、碳吸收等有关，与农业、
35、林业、全球变化等应用直接挂钩。 多层模型中叶面积指数的应用: Leaves in each leaf-layer completely covers the ground below, LAI = n 1, where n is the number of leaf layers (e.g. 2 1 = 2) Leaves in each layer cover half of the ground below, LAI = n 0.5 (e.g. 2 0.5 = 1)植被遥感原理植被遥感原理 模型模型Evaluating multi-layer models（红（红光）光）植被遥感原理植被遥
36、感原理 模型模型Evaluating multi-layer models（近（近红外）红外）植被遥感原理植被遥感原理 模型模型模型的迭代解模型的迭代解 Developed a number of multiple-layer models of reflection from a vegetation canopy Sophistication of the models increased by including More leaf layers Higher-orders of multiple scattering Corollary code became longer and m
37、ore complex植被遥感原理植被遥感原理 模型模型Rethinking the problem Problem of determining all possible pathways through the canopy gets harder as more leaf-layers and higher-orders of multiple scattering are incorporated into the model Over 100 different pathways that solar radiation can trace through the model can
38、opy given three leaf-layers and considering upto 7th-order multiple scattering! Chances of us omitting or double counting certain pathways is quite high under such circumstances Clearly, need to rethink the mathematical and computational solution to the problem植被遥感原理植被遥感原理 模型模型Two-Stream Approximati
39、on Two streams of radiation, travelling in opposite directions, passing through the canopy Upward travelling flux:植被遥感原理植被遥感原理 模型模型Two-Stream Approximation Downward travelling flux:植被遥感原理植被遥感原理 模型模型Iterative ApproachTwo-stream model of radiation transport through a multiple leaf-layer vegetation can
40、opy植被遥感原理植被遥感原理 模型模型Two-Stream Approximation Code preamble and set-up boundary conditions植被遥感原理植被遥感原理 模型模型Two-Stream Approximation Main for loop varies fractional ground cover of leaves per layer (N.B. same for all leaf layers) Next loop calculates the gap fraction and likelihood of reflection or tr
41、ansmission from each leaf layer植被遥感原理植被遥感原理 模型模型Two-Stream Approximation Next iterate to a solution for each leaf layer植被遥感原理植被遥感原理 模型模型Kubelka-Munk Equations Equations that underpin the previous code commonly known as the Kubelka-Munk equationsdIh = (S + K)Ihdx + IiSdx (1)dIi = (S + K)Iidx + IhSdx
42、(2) where x is distance into the turbid medium, K is an absorption coefficient, S is a scattering coefficient, Ih is the upward travelling flux and Ii is the downward travelling flux.植被遥感原理植被遥感原理 模型模型Plotting the results (Red)植被遥感原理植被遥感原理 模型模型Plotting the results (Nir) 植被遥感原理植被遥感原理 模型模型Taking things
43、 further Can use the model to determine how much light penetrates to different depths into the canopy植被遥感原理植被遥感原理 模型模型辐射传输模型辐射传输模型辐射传输理论(Radiative transfer theory)辐射传输理论最初是从研究光辐射在大气（包括行星大气）中传输的规律和粒子（包括电子，质子，中子等基本粒子）在介质中的输出规律时总结出来的规律性知识。基本表现：“碗边”效应，随着观测角增大，反射亮度增大可以解释为视线穿过的路径变长，包含了较多的散射植被遥感原理植被遥感原理 模型
44、模型植被遥感原理植被遥感原理 模型模型植被辐射传输模型的理论基础是辐射传输方程，但是辐射传输方程是一个微分积分方程，只有数值解，目前通用的解法KM理论（四通量近似或二流近似）土壤z = - hz = 0冠层顶层1层2层3观察方向太阳直射光通量(F )F+向下漫散射通量(E )向上漫散射通量(E+ )植被遥感原理植被遥感原理 模型模型FSFSEEddE21)(atFSFSEEddE21)(atFSSKddF)(21tFSSKddF)(21t(1)(2)(3)(4)KM方程a 为吸收系数， 为散射系数，S1与S2分别为平行辐射的散射系数，即由准直辐射向漫辐射的转换系数，脚标“1”与“2”分别表示前
45、向与后向，K为平行辐射的吸收系数。植被遥感原理植被遥感原理 模型模型tdLdEsin),;(2020tdLdEsin),;(2020 dzzFAVDdt植被遥感原理植被遥感原理 模型模型KM方程各项的物理意义：以方程（1）为例， E的减少由下列因素决定： 通过dt时因吸收和散射而减少的量； 由E+的后向散射而增加的量； 由直射辐射向散射辐射的转化而增加的量（包括前向与后向）； 方程（3）（4）表明准直辐射自身在传输过程中永远是“减少项”，即直射向漫射的转变是不可逆的。植被遥感原理植被遥感原理 模型模型几何光学模型几何光学模型 （Geometric optical model）主要用来描述宏观物
46、体的方向性反射现象基本表现是“热点”效应，即沿着太阳方向看去非常的亮。主要是由于阴影减少，直到看不到阴影植被遥感原理植被遥感原理 模型模型基本思想是景合成模型，即光照面与阴影面的加权和。可以解释热点现象。关键：光照面与阴影面的所占比例的计算 光照面与阴影面的亮度？代表：Li-Strahler 几何光学模型 最早用圆锥来表示针叶林，后吸取了Jupp等的改进，用椭球来模拟。zzttccggsLKLKLKLKL植被遥感原理植被遥感原理 模型模型irRbhirRRh椭球在垂直方向拉伸变换为球zxzxZ = (R/b)Zh = (R/b)hi = tan-1(b/R)tanir = tan-1(b/R)
47、tanr植被遥感原理植被遥感原理 模型模型irGrGiO(i, r , i r)Gi = R2 /cosi = R2seci Gr = R2 /cosr = R2secr 把三维空间的计算投影到二维把三维空间的计算投影到二维i rrcriGG,121在r方向看到的树冠承照面部分植被遥感原理植被遥感原理 模型模型引入概率几何学中的基本原理引入概率几何学中的基本原理 Boolean 原理原理假设在区域A内随机投掷N个炸弹，每个炸弹的平均破坏面积为a，则没有遭到炸弹破坏的面积A：aAaNAeAeAl)(aeAAKl单位面积有l个植被遥感原理植被遥感原理 模型模型riririOgeKlGG,可见光照地
48、面Li Strahler 几何光学模型中四分量的面积比ceKcGl1可见光照树冠rceeKtGGll阴影树冠tcgzKKKK1阴影地面对于稀疏林地、灌丛当森林茂密，观测方向远离天顶时，需考虑树冠间的相互遮蔽GOMS模型植被遥感原理植被遥感原理 模型模型GO-RT模型：几何光学向辐射传输的逼近 联系两者的关键是间隙率模型间隙率：间隙率： 概率间隙率，当光线穿越树冠距离为S时，而不被拦载的概率。 几何间隙率，设树冠的投影面积为A，而其中光斑的总面积为S，则 S / A被称为几何间隙率。 物理间隙率，设在树冠的阴影面内有一点（x,y），其辐照度为E（x,y），如果投射到树冠上的辐照度为E0，则E(x
49、,y)/E0，便称之为物理间隙率。植被遥感原理植被遥感原理 模型模型dxdyyxgAGgAyxgapgapyxgap),(1,10）（为光照点）（否则dxdyyxeAEEoyxEyxegapAyxgapgap),(1.),(),(),(dxdyyxpAPAyxgap),(1),(* 几何孔隙率* 物理空隙率* 概率空隙率注意不同的（x,y）对应着不同的S值，显然P(x,y)是与S值相联系的，而前两种定义并不关心S的取值大小。植被遥感原理植被遥感原理 模型模型对于均匀连续的植被冠层，Monsi和Sakei首先建议采用下面的负指数衰减的表示式：coskLgapPe其中L为叶面积指数，k是叶面积在方
50、向的投影比例。 对于不连续的植被，李小文和Strahler定义间隙率为路径长度s的函数： KsL DsgapPseet其中，t = KL/D，表示每单位长度的衰减指数，D = V/B, 为一个植被体的平均厚度，K表示单位叶面积指数的衰减指数，与叶倾角分布及叶片的透过率有关。植被遥感原理植被遥感原理 模型模型树冠的间隙率为不同位置间隙率的积分：dxdyeAPyxsAgap),(1)(t将二维问题变为一维： 0sgapPp s edst对于规则的形体，可以计算路径长度及其分布植被遥感原理植被遥感原理 模型模型利用冠层间隙率可以推算利用冠层间隙率可以推算LAIIn Situ Measurements
