User Commands kuusk_invert(1) NAME kuusk_invert - inversion of Markov Chain canopy reflectance model (see kuusk (1)). [-d data_file] [-p param_file] [-min min_file] [-max max_file] [-powell | -amoeba | -anneal powell/amoeba/anneal file] [-schedule annealing_schedule_function] [-skyl] [-vary nVary vary1 vary2 .....] [-b BoundaryAdd/BoundaryConstrain] [-v][-o output_parameters_file] < in_file > forward_modelled_reflectance DESCRIPTION kuusk_invert performs numerical inversion of input reflec- tance data using the analytical canopy reflectance model devised by Nilson & Kuusk ( Nilson, T. and Kuusk, A. (1989) A Reflectance Model for the Homogenous Plant Canopy and Its Inversion, RSE 27:157-167). The main characteristics of the model are: the consideration of both single and multiple scattering interactions with canopy and soil; formulations for both specular leaf reflectance, and a canopy hot-spot function. OPTIONS -p parameter file containing values of parameters in model to be kept fixed, as well as initial values of parameters to be inverted. These parameters (15 canopy parameters plus the angstrom turbidity fac- tor) are read in from the specified parameter file - the file must start with the line 'kuusk{', and end with another brace ('}') -min parameter file containing minimum values of parame- ters in model that are to be inverted. Same format as parameter file, but without the angstrom turbi- dity factor. -max parameter file containing maximum values of parame- ters in model that are to be inverted. Same format as parameter file, but without the angstrom turbi- dity factor -skyl If specified, inversion is calculated including sky radiance. Default is to calculate without. -powell - the minimisation will be done using the conjugate direction set method of Powell (Numerical Recipes in C, Press et. al. 1994, Chapter 10). If a file is specified following the -powell option, it should contain the following parameters which control the optimisation procedure (and should not be altered without a full understanding of the optimisation SunOS 5.8 Last change: May 1997 1 User Commands kuusk_invert(1) process): kuusk{ 80000 10 500 500 : nfmax,itmax,itbr,nbrak 1e-9 1e-7 1e-13 1e-8 : zeps,tolbr,tiny,ftolp 1.0 0.5 2.0 0.1 : alpha,beta,gamma,dxopt 10. : at } -amoeba - minimisation is carried out in this case using the downhill simplex method of Nelder and Mead (ibid). The parameter file in this case is identi- cal to that required for Powell. -anneal - minimisation is carried out using the method of simulated annealing which incorporates a variant of the downhill simplex algorithm (ibid). The simu- lated annealing process follows an annealing schedule which starts at a temperature T which is then decremented by some factor depending on which annealing schedule is specified. -schedule - the annealing schedule can be specified as one of four functions on the command line (this function is then dynamically linked into the executable): AnnealAlpha - a total of K moves are budgeted for, and T_new=T_initial*(1-k/K)exp(A), where k is the current no. of moves. K=100, A=2. AnnealBeta - after every m moves (m=5) t is set to (f1 - fb)*Beta where Beta = 0.8, f1 = smallest function value currently in simplex, and fb is the best ever point. AnnealEpsilon - T is reduced to (1-E)*T after every m moves (m=5). The defaults for E and T are 0.1 and 300 respectively, but they can be set by adding them (in this order) to a new line in the annealing parameter file (see above). The default is Anneal- Default which simply reduces T by 1 degree each move. NOTE - if no parameter file is specified for any of the minimisation algorithms, appropriate default values will be used (see above). SunOS 5.8 Last change: May 1997 2 User Commands kuusk_invert(1) -vary nVary p0 p1 p2 ..... The number of parameters which the model is minim- ised with respect to is specified following the -vary switch. Following this, the 'numbers' of the parameters to vary are specified e.g. -vary 3 0 1 2 specifies 3 parameters to vary - the first, second and third parameters respectively (*NOTE* the parameters are zero referenced, so 0 is the first one). The order is defined by the order in which they appear in the parameter file. It's probably worth keeping this the same, so as not to get con- fused when trying to work out which is which! invert.kuusk.model(1) will produce a default param- eter file for use with kuusk_invert, and will allow any of the parameters to be varied from the command line. -d n specifies data file containing information on leaf reflectance/transmittance (PROSPECT output - see man page for PROSPECT), water absorption, leaf chlorophyll and lignin concentrations as well as soil reflectance information (Price, J. (1990) On the Information Content of Soil Reflectance Spec- tra. RSE 33:113-121) with respect to wavelength. This data is "#included" by default to make things a lot faster, but a file *could* be specified if the data needed changing. -v verbose option. Outputs rmse and all 15 current parameter values at each stage of minimisation. Very useful for monitoring how the inversion is progressing. -forward Only perform forward modelling i.e. take starting parameters, and just calculate forward modelled reflectance. -inverse Explicitly do inversion - this is the default. PARAMETER LIST An example of the default parameter file for use with kuusk_invert is given below. These values are the default parameter values as generated by invert.kuusk.model(1): kuusk{ 3. : 1 - LAI - LAI 90. : 2 - thm - modal leaf inclinartion SunOS 5.8 Last change: May 1997 3 User Commands kuusk_invert(1) 0.6236 : 3 - eln - -ln(1 - eps) 0.2046 : 4 - sl - leaf size 74.24 : 5 - cAB - chlorophyll, ug/cm2 0.03 : 6 - cW - water, cm 0.001 : 7 - cP - protein, g/cm2 0.001 : 8 - cC - cellul+lignin, g/cm2 1.351 : 9 - N (PROSPECT) 0.6971 : 10 - n_ratio 0.1909 : 11 - s1 - soil parameters -0.0557 : 12 - s2 0.0 : 13 - s3 0.0 : 14 - s4 0.45 : 15 - sz - the Markov clumping parameter 0.68 : b_Angs - angstrom turbidity factor } LAI - leaf area index, range >0 - 10 or more; thm - the modal leaf inclination, range 0 - 90 deg; lnm = ln(1-eps) - range 0 - 10 - eps is the eccentricity of the elliptical distribution i.e. 0 = spherical, 0 - 0.6 = almost spherical, 0.6 - 4 - reaonable variation, >4 narrow LAD with modal inclination thm, >6 - almost fixed inclina- tion (a delta-distribution); sl - the relative size of leaves s_leaf/H, where H is the canopy height, sl between 0.02 and 0.5; C_AB = the chlorophyll content of leaves, ug/cm**2 - range 10 .. 100 (See Jacquemoud & Baret, RSE, 1990, 34:75-91); c_W = leaf water equivalent thickness - range 0.005 .. 0.05; C_Pr = protein content of leaves, g/cm**2 - range 0.0005 .. 0.002 (Jacquemoud et al., RSE, 1996, 56:194-202); C_Cc = the cellulose and lignin content of leaves, g/cm**2 - range 0.0003 .. 0.01; N_L = the effective number of elementary layers inside a leaf - range 1 .. 2.5 (See Jacquemoud & Baret, RSE, 1990, 34:75-91) - N_L significantly influences the transmittance/reflectance ratio of a leaf: the smaller N_L, the lower the transmittance; n_ratio = the ratio of refractive indices of the leaf sur- face wax and internal material - range 0.8 .. 1.2, higher values result in more intensive specular component of bidirectional reflectance; s1 to s4 are the first 4 weights (moments) of Price's func- tion for soil reflectance: 0