#include "sd.h" /********************************************************************* Tallgrass State Dynamics Function for ASDP Clint Moore, USGS August 2011 Revised 9/6/12 to reconcile ordering of models Revised 11/14/12 to update model weights Contains the single-stage dynamics model for tallrass units based on two system states, vegetative cover class and defoliation class. Partial controllability is accounted for as a submodel. Can be run with full or partial controllability; as single-model, averaged, or adaptive; and with or without management choice constraints, with these selections controlled in the scenario file. Although this program has been used by the U.S. Geological Survey (USGS), no warranty, expressed or implied, is made by the USGS or the U.S. Government as to the accuracy and functioning of the program and related program material nor shall the fact of distribution constitute any such warranty, and no responsibility is assumed by the USGS in connection therewith. *********************************************************************/ { INT i,j,k,l,d,dd,s_np,s_dx,modsel,pc_index,c,nt, /** Mapping of defoliation states (7) into model-specific defoliation level indices **/ /** Row 1: Last defoliation 5+ years ago -- applies only to model 1 **/ /** Rows 2-4: Last defoliation 2-4 years ago **/ /** Rows 5-7: Last defoliation 1 year ago **/ defmap[7][6] = { { 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0 }, { 1, 0, 1, 1, 1, 1 }, { 1, 0, 2, 2, 2, 2 }, { 1, 0, 0, 0, 0, 0 }, { 1, 0, 1, 1, 1, 1 }, { 1, 0, 2, 2, 2, 2 } }, /** Mapping of defoliation states (7) into preceding-year defoliation states (no, yes) **/ pcmap[7] = { 0, 0, 0, 0, 1, 1, 1 }, /** Mapping of management constraints (3) into treatment options **/ /** Row 1: No constraint -- all 4 treatments available **/ /** Row 2: Rest, GrazeW, and Defoliate are only treatments available (columns 1-3) **/ /** Row 3: Rest, BurnW, and Defoliate are only treatments available (columns 1-3) **/ mcmap[3][4] = { { 0, 1, 2, 3 }, { 0, 1, 3, -1 }, { 0, 2, 3, -1 } } ; DECIMAL /** Model weights for weighted-average single model run **/ /** (See model description in comments below) **/ /* w[6] = { 0.16666666, 0.16666667, 0.16666667, 0.16666666, 0.16666667, 0.16666667 }, */ w[6] = { 0.18721840, 0.12266700, 0.16467031, 0.18931096, 0.16474452, 0.17138881 }, /** Decision selection cumulative probabilities for tall grass units **/ /** 1st level: 3 cases of management constraint: None, No Burn, No Graze /** 2nd level: 2 cases of preceding-year defoliation (No, Yes) /** 3rd & 4th levels: 4x4 treatments [Rest, GrazeW, BurnW, Defoliate] /***** Prior-year defoliation (GrazeW, BurnW, Defol) reduces BurnW by 25% **/ a[3][2][4][4] = { { { { 0.962173816, 0.980942812, 0.981090862, 1.01 }, { 0.11492317 , 0.719755887, 0.745782022, 1.01 }, { 0.112221145, 0.229194956, 0.709699321, 1.01 }, { 0.146816479, 0.270561798, 0.351210986, 1.01 } }, { { 0.962209434, 0.980979125, 0.981090162, 1.01 }, { 0.115690902, 0.724564144, 0.744083745, 1.01 }, { 0.138170713, 0.282193081, 0.642571354, 1.01 }, { 0.150036314, 0.276495493, 0.336982384, 1.01 } } }, { { { 0.962316287, 0.981088062, 1.01 , 1.01 }, { 0.1179941 , 0.738988913, 1.01 , 1.01 }, { 0.159695817, 0.294296578, 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } }, { { 0.962316287, 0.981088062, 1.01 , 1.01 }, { 0.1179941 , 0.738988913, 1.01 , 1.01 }, { 0.159695817, 0.294296578, 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } } }, { { { 0.980578286, 0.980729168, 1.01 , 1.01 }, { 0.127086995, 0.671243409, 1.01 , 1.01 }, { 0.167550009, 0.259588534, 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } }, { { 0.98061528 , 0.980728441, 1.01 , 1.01 }, { 0.165014041, 0.573131352, 1.01 , 1.01 }, { 0.171796074, 0.240824968, 1.01 , 1.01 }, { 1.01 , 1.01 , 1.01 , 1.01 } } } }, /** Transition model for expanded defoliation index **/ /** (7x7 [5L, 2-4L, 2-4M, 2-4H, 1L, 2-4M, 1H] matrix for each of 2 treatments -- no defoliate vs defoliate) **/ x[2][7][7] = { { { 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.388888889, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.03125, 0.4375, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.0, 0.0, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.0, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.0, 0.142857143, 1.000000001, 1.000000001, 1.000000001, 1.000000001, 1.000000001 }, { 0.0, 0.0, 0.454545455, 1.000000001, 1.000000001, 1.000000001, 1.000000001 } }, { { 0.0, 0.0, 0.0, 0.0, 0.75, 1.000000001, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.333333333, 1.000000001, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.0, 0.8125, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.285714286, 1.000000001, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.0, 0.714285714, 1.000000001 }, { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.000000001 } } }, /** Model transition *cumulative* probabilities for tall grass /** (6 models x 4 treatments x 3 defoliation states x 16 input states x 16 outcome states) **/ /** In 2012, model was reorganized as follows: **/ /** Model 1 -- Not state based **/ /** Model 2 -- Invader type **/ /** Model 3 -- Invader type + Defoliation level **/ /** Model 4 -- Invader type + Defoliation level + Invasion level **/ /** Model 5 -- Model 3 + (Graze=Burn if SB dominant) **/ /** Model 6 -- Model 3 + (Defoliate=Rest) **/ p[6][4][3][16][16] = { { { { { 0.751, 0.842, 0.887, 0.933, 0.987, 0.993, 0.997, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.233, 0.466, 0.699, 0.932, 0.949, 0.966, 0.983, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.045, 0.136, 0.887, 0.932, 0.935, 0.942, 0.997, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.045, 0.136, 0.181, 0.933, 0.936, 0.942, 0.946, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.066, 0.074, 0.078, 0.082, 0.648, 0.716, 0.750, 0.785, 0.958, 0.979, 0.989, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.020, 0.041, 0.061, 0.081, 0.257, 0.433, 0.610, 0.785, 0.839, 0.893, 0.946, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.004, 0.012, 0.077, 0.081, 0.115, 0.184, 0.750, 0.784, 0.794, 0.815, 0.989, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.004, 0.012, 0.016, 0.081, 0.116, 0.184, 0.218, 0.787, 0.797, 0.818, 0.828, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.051, 0.057, 0.060, 0.064, 0.651, 0.722, 0.757, 0.792, 0.960, 0.980, 0.990, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.016, 0.032, 0.047, 0.063, 0.245, 0.427, 0.609, 0.791, 0.843, 0.895, 0.948, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.003, 0.009, 0.062, 0.065, 0.100, 0.171, 0.757, 0.793, 0.803, 0.823, 0.990, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.003, 0.009, 0.012, 0.063, 0.098, 0.169, 0.204, 0.791, 0.801, 0.822, 0.832, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.028, 0.031, 0.033, 0.034, 0.812, 0.906, 0.953, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.008, 0.017, 0.025, 0.034, 0.275, 0.517, 0.759, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.002, 0.005, 0.033, 0.034, 0.081, 0.175, 0.953, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.002, 0.005, 0.007, 0.034, 0.081, 0.175, 0.222, 1.100 } }, { { 0.578, 0.767, 0.861, 0.955, 0.982, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.190, 0.574, 0.764, 0.954, 0.963, 0.982, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.862, 0.956, 0.961, 0.969, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.283, 0.378, 0.955, 0.960, 0.969, 0.973, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.079, 0.104, 0.117, 0.130, 0.568, 0.712, 0.783, 0.854, 0.942, 0.971, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.026, 0.078, 0.103, 0.129, 0.274, 0.566, 0.710, 0.855, 0.884, 0.942, 0.971, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.039, 0.118, 0.131, 0.202, 0.345, 0.782, 0.853, 0.867, 0.896, 0.985, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.039, 0.052, 0.131, 0.202, 0.346, 0.417, 0.855, 0.870, 0.898, 0.912, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.065, 0.086, 0.097, 0.107, 0.563, 0.712, 0.786, 0.860, 0.945, 0.972, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.021, 0.064, 0.086, 0.107, 0.257, 0.560, 0.710, 0.860, 0.888, 0.944, 0.972, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.032, 0.096, 0.107, 0.181, 0.331, 0.788, 0.863, 0.876, 0.903, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.032, 0.042, 0.107, 0.181, 0.331, 0.405, 0.862, 0.875, 0.903, 0.916, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.034, 0.045, 0.051, 0.056, 0.627, 0.814, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.012, 0.035, 0.046, 0.058, 0.245, 0.624, 0.812, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.052, 0.057, 0.150, 0.337, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.022, 0.057, 0.150, 0.337, 0.429, 1.100 } }, { { 0.578, 0.767, 0.861, 0.955, 0.982, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.190, 0.574, 0.764, 0.954, 0.963, 0.982, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.284, 0.862, 0.956, 0.961, 0.969, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.283, 0.378, 0.955, 0.960, 0.969, 0.973, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.079, 0.104, 0.117, 0.130, 0.568, 0.712, 0.783, 0.854, 0.942, 0.971, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.026, 0.078, 0.103, 0.129, 0.274, 0.566, 0.710, 0.855, 0.884, 0.942, 0.971, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.039, 0.118, 0.131, 0.202, 0.345, 0.782, 0.853, 0.867, 0.896, 0.985, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.013, 0.039, 0.052, 0.131, 0.202, 0.346, 0.417, 0.855, 0.870, 0.898, 0.912, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.065, 0.086, 0.097, 0.107, 0.563, 0.712, 0.786, 0.860, 0.945, 0.972, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.021, 0.064, 0.086, 0.107, 0.257, 0.560, 0.710, 0.860, 0.888, 0.944, 0.972, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.032, 0.096, 0.107, 0.181, 0.331, 0.788, 0.863, 0.876, 0.903, 0.986, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.011, 0.032, 0.042, 0.107, 0.181, 0.331, 0.405, 0.862, 0.875, 0.903, 0.916, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.034, 0.045, 0.051, 0.056, 0.627, 0.814, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.012, 0.035, 0.046, 0.058, 0.245, 0.624, 0.812, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.052, 0.057, 0.150, 0.337, 0.907, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.017, 0.022, 0.057, 0.150, 0.337, 0.429, 1.100 } } }, { { { 0.492, 0.884, 0.932, 0.980, 0.990, 0.998, 0.999, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.145, 0.689, 0.835, 0.980, 0.983, 0.994, 0.997, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.048, 0.440, 0.933, 0.982, 0.983, 0.990, 0.999, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.048, 0.441, 0.489, 0.981, 0.982, 0.990, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.122, 0.218, 0.230, 0.242, 0.588, 0.862, 0.896, 0.930, 0.965, 0.993, 0.997, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.036, 0.170, 0.206, 0.242, 0.344, 0.727, 0.829, 0.931, 0.942, 0.980, 0.990, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.012, 0.108, 0.229, 0.241, 0.275, 0.550, 0.896, 0.930, 0.933, 0.961, 0.997, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.012, 0.109, 0.121, 0.243, 0.276, 0.551, 0.585, 0.930, 0.934, 0.962, 0.965, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.000, 0.000, 0.001, 0.001, 0.100, 0.180, 0.189, 0.199, 0.565, 0.856, 0.892, 0.928, 0.964, 0.993, 0.996, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.030, 0.140, 0.170, 0.199, 0.307, 0.712, 0.820, 0.928, 0.939, 0.979, 0.989, 1.100 }, { 0.000, 0.000, 0.000, 0.001, 0.010, 0.090, 0.189, 0.199, 0.235, 0.527, 0.894, 0.930, 0.933, 0.961, 0.997, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.010, 0.089, 0.099, 0.198, 0.234, 0.526, 0.562, 0.928, 0.932, 0.960, 0.964, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.050, 0.090, 0.095, 0.100, 0.552, 0.911, 0.956, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.015, 0.070, 0.085, 0.100, 0.233, 0.733, 0.866, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.045, 0.094, 0.099, 0.143, 0.503, 0.955, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.045, 0.050, 0.100, 0.144, 0.504, 0.549, 1.100 } }, { { 0.578, 0.767, 0.861, 0.955, 0.982, 0.991, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.191, 0.575, 0.765, 0.955, 0.964, 0.982, 0.991, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.283, 0.861, 0.955, 0.959, 0.968, 0.996, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.094, 0.283, 0.377, 0.955, 0.960, 0.969, 0.973, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.081, 0.107, 0.120, 0.133, 0.572, 0.715, 0.786, 0.857, 0.944, 0.972, 0.986, 1.000, 1.000, 1.000, 1.000, 1.100 }, { 0.026, 0.079, 0.105, 0.132, 0.276, 0.567, 0.711, 0.855, 0.884, 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0.049, 0.052, 0.058, 0.158, 0.857, 0.909, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.039, 0.054, 0.060, 0.060, 0.664, 0.909, 1.100 }, { 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.006, 0.035, 0.038, 0.059, 0.158, 0.624, 0.675, 1.100 } } } }, }, z_np, z_d, z1, q[4][7][16][16]; /** Management constraint type (0, 1, 2) -- indexes row of mcmap matrix **/ c = (int)outcome[4]; /** Number of treatments available **/ nt = 4*(c==0) + 3*(c>0); /** Decision values -- actual treatment types are inferred from d according values of mcmap matrix **/ /** (first row of mcmap: 0 = Rest, 1 = GrazeW, 2 = BurnW, 3 = Defol) **/ d = (int)dec[0]; /** Stochastic defoliation index transition outcome **/ z_d = outcome[0]; /** Stochastic NP transition outcome **/ z_np = outcome[1]; /** Determine whether single model, weighted-average model, or adaptive run from scenario file **/ /** Index j loops over the 7-state defoliation index, but it pulls model values from appropriate /** levels of 3-state defoliation index through the defmap matrix **/ modsel = (int)outcome[3]; /** Single-model run **/ for (i=0; i a[c][pc_index][d][j]) j++; } /** Using NP state matrix, find index of cumulative probability value exceeded by z_np **/ i = 0; while (z_np > q[j][s_dx][s_np][i]) i++; /** Store this index as next prairie state **/ nxt_state[1] = i; /** Determine if action taken this period is a defoliation treatment **/ dd = (j>0); /** Using defoliation index state matrix, find index of cumulative probability value exceeded by z_d **/ i = 0; while (z_d > x[dd][s_dx][i]) i++; /** Store this index as next defoliation index state **/ nxt_state[0] = i; return; }